The Theory and Practice of Membrane Extractions

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THE THEORY AND PRACTICE OF MEMBRANE EXTRACTIONS

By

M ark A nthony LaPack

A DISSERTATION

S ubm itted to M ichigan State U n ive rs ity

in p a rtia l fu lfillm e n t o f the requirem ents fo r the degree o f

DOCTOR OF PHILOSOPHY

D epartm ent o f C hem istry

1994


TJMI N um ber: 9631302

Copyright 1995 by LaPack, Mark AnthonyAll rights reserved.

UMI Microform 9631302 Copyright 1996, by UMI Company. All rights reserved.

This microform edition is protected against unauthorized copying under Title 17, United States Code.

UMI300 North Zeeb Road Ann Arbor, MI 48103


ABSTRACT

THE THEORY AND PRACTICE OF MEMBRANE EXTRACTIONS

ByM ark A nthony LaPack

The selection o f a m em brane fo r a given separation o f a m ix tu re

is generally based upon the "like-d isso lves-like" ru le , w h ich often

tim es is an inadequate guide. In th is w ork, m em brane extractions

have been studied us ing silicone mem branes and mass spectrom etry.

Aqueous and gas samples were exposed to one side o f the mem brane

w h ile the contents on the other side were analyzed by mass

spectrom etry. P redictive perm eation m odels have been developed.

Good corre la tions are observed between the perm eation data,

chrom atographic data, a so lu b ility param eter m odel, and a model

based on the b o ilin g po in ts o f the analytes. The effects o f

experim enta l param eters on m em brane extractions have also been

exam ined. The effects o f the con figu ra tion o f the m em brane

extracto r, m em brane dim ensions, tem perature, sam ple flow ra te, and

o ther param eters are presented in the context o f op tim iz ing the

separation technique. A mem brane extraction mass spectrom etric

technique has been developed fo r on -line analysis o f organic

com ponents o f m u ltip le liq u id and gas stream s, and applied in an

aerobic b io logica l wastewater trea tm ent process. Mass balance

de term inations were perform ed by q u a n tita tive ly m easuring organic

contam inants in in flu e n t and e ffluen t w ater and a ir stream s.


C opyright by

MARK ANTHONY LAPACK

1995


to my Pat

i


ACKNOWLEDGMENTS

F irs t, I th a n k m y research advisors. I th a n k C hris Enke fo r

sharing w ith me h is w isdom , crea tiv ity , encouragem ent, and h is

patience. I also th a n k J im Tou fo r h is support and encouragem ent and

fo r h is keen a tte n tio n to de ta il. I w ill always rem em ber the pioneering

s p ir it o f these tw o men.

I th a n k V ic k i M cG uffin fo r he r enthusiasm , in sp ira tio n , and

techn ica l guidance.

For th e ir va luable com binations o f c ritiq u e and encouragem ent,

I th a n k D r. Jack W atson, D r. Jam es H arrison, D r. B ill Reusch, and Bob

Bredeweg.

For th e ir com plete support o f th is w ork, I th a n k the

m anagem ent o f the Dow Chem ical Company, especially M el Koch, J im

Havel, Foppe D upuis, M ary lu Gibbs, Wes W estover, Don Calvin, Paul

Dean, Jackie Kelym an, and Irv Snyder.

To m y friends a t MSU and in M id land, fo r th e ir friendsh ip and

encouragem ent, especially Jane Tou, J im Shao, M ike D esJardin, Bruce

Bell, M a rk Cole, Paul O 'Connor, M ark D ittenhafer, Steve H um phrey,

the Enke G roup and the Special A nalysis G roup.

For he lp ing me to keep m y p rio ritie s in check, I th a n k m y

b e a u tifu l ch ild ren , M akenzie and D aniel.

i i


I am very gra te fu l fo r the love o f m y two fam ilies in Ind ianapo lis -

especially m y m other, fa ther, and sib lings, who never m issed a chance

to rem ind me how long I have been in school.

For m y w ife, Patty, fo r standing by me, fo r tak in g on m ore than

he r share o f keeping ou r home together, and fo r p laying the role o f

the single parent.

F ina lly , I th a n k God w ith a ll m y heart fo r b ring ing a ll o f these

w onderfu l people and opportun ities in to m y life .

i i i


TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

CHAPTER

1 INTRODUCTION

Background

Purpose o f th is w ork

2 PERMEATION FUNDAMENTALS

Steady state perm eation

Non-steady state perm eation

O rganic enrichm ent

3 THE CORRELATION OF PERMEABILITY TO HILDEBRAND SOLUBILITY PARAMETERS

The s o lu b ility param eter

Developm ent o f the theory

C orre la tion o f data to theory

4 A MODEL FOR CHARACTERIZING AND PREDICTING MEMBRANE EXTRACTIONS BASED ON CHROMATOGRAPHIC RETENTION

Retention and d is trib u tio n e q u ilib ria

Band spreading and d iffu s iv ity

E ffic iency and enrichm ent

iv


5 PRACTICAL ASPECTS OF MEMBRANE EXTRACTIONS

119

M em brane d im ension considerations

Tem perature considera tions

Sam ple flow ra te considerations

E x tra c to r con figu ra tion considerations

Effects o f distance between the extracto r and the analyzer

6 THE APPLICATION OF MEMBRANE EXTRACTIONMASS SPECTROMETRY TO THE ANALYSIS OF GAS AND LIQ UID PROCESS STREAMS

E xpe rim en ta l

M u ltip le gas and liq u id stream analysis

A p p lica tion to a b io log ica l w astew ater tre a tm e n t process

Conclusions

• APPENDIX

Perm eation m easurem ents

154

186


LIST OF TABLES

Table 1.1. Membrane separation term s and some analogous term s used in ana lytica l chem istry.

Table 2.1. E ffect o f ho llow fib e r m em brane ra d ia l d im ensions on ana ly tica l response. The silicone ho llow fibers were 2 .5-cm long. Tem perature = 23 °C.

Table 2 .2 . Survey o f tem perature effects on detection lim its (S /N = 2) fo r organic com pounds in a ir and w ater. The m em brane is a 2.5-cm long, 0.0305-cm i.d ., 0.0635-cm o.d. s ilicone ho llow fibe r.

Table 2.3. E ffects o f m em brane th ickness on response tim e fo r gas phase organic com pounds. The m em branes are 2.5-cm long silicone ho llow fibers. Tem perature = 23 °C.

Table 2.4. Survey o f tem perature effects on response tim e, tso. fo r organic com pounds in n itrogen. The m em brane is a 2 .5-cm long,0.0305-cm i.d ., 0.0635-cm o.d. silicone ho llow fibe r.

Table 2.5. Survey o f tem perature effects on the en richm ent over the sam ple m a trix fo r organic com pounds in n itrogen and w ater.

Table 3.1. M olar volum es (v4) and H ildebrand s o lu b ility param eters (8j) from References 1, 12, and 28.

Table 3.2. E xperim ental perm eation param eters fo r substances in a silicone elastom er m em brane a t 25 °C.

Table 3.3. E xperim enta l and theore tica l d is trib u tio n ra tios fo r substances in a silicone elastom er membrane, a t 25 °C.

Table 3 .4 . E xperim enta l and theore tica l d is tr ib u tio n se lectiv ities fo r substances re la tive to m ethane and to m ethanol in a silicone elastom er mem brane a t 25 °C.

Table 3.5. P artia l m o la r volum es. v 'it fo r surface-active fu n c tio n a l groups from Reference 31.

v i


Table 3.6. Data fo r determ ining the active volum e ra tio . V 'f/V p, in a silicone elastom er membrane a t 25 °C.

Table 3.7. Experim ental and theore tica l d iffu s iv ities fo r substances in a silicone elastom er membrane a t 25 °C.

Table 3.8. Experim ental and theore tica l (D -k model. E quation 3.42) d ifiu s iv ity selectivities fo r substances re la tive to methane and to m ethanol in a silicone elastom er membrane a t 25 °C.

Table 3.9. E nrichm ent factors fo r com pounds re lative to m ethane and to m ethanol in a silicone elastom er membrane a t 25 °C. Theoretical values were obtained from the p roduct o f d is trib u tio n (Equation 3.16) and d iffu s ion selectivities (D -k model. Equations 3.36 and 3.42).

Table 4.1. M olar volum es, H ildebrand so lu b ility param eters (7, 8, 10), and bo ilin g po in ts (11) fo r the com pounds used in th is study.

Table 4.2. Experim ental d is trib u tio n ra tios, Ki( determ ined b y ME and GO a t 25 °C.

Table 4.3. Values fo r the heats o f so lu tion fo r selected com pounds in the membrane and chrom atographic sta tionary phases.

Table 4.4. D is trib u tio n selectivities fo r com pounds over n itrogen and heptane a t 25 °C. Tb = predicted from the bo ilin g po in ts (Equation 4.7); SP = predicted from so lu b ility param eter theory (Equation 4.3); ME = experim ental from ME data; GC = experim ental from GC data.

Table 4.5. M obile phase d iffus iv ities, D i m, and chrom atographic band spreading com ponents used to calculate d iffu s iv ities in the s ta tiona ry phase a t 25 °C.

Table 4.6. D iffus iv ities a t 25 °C in the sta tionary phase fo r com pounds o f in te re s t determ ined by mem brane extraction experim ents (ME), and gas chrom atographic experim ents (GC).

Table 4.7. Values fo r the activa tion energies fo r d iffus ion fo r selected com pounds in the membrane sta tionary phase.

Table 4.8. D iffus ion selectivities fo r com pounds over n itrogen and over heptane a t 25 °C. Tb = predicted from bo ilin g p o in t m odel (Equation 4.24); SP = predicted from so lu b ility param eter theory (Equation 4.31); M E = experim ental from ME data; GC = experim ental from GC data.

Table 4.9. Values fo r the activa tion energies fo r perm eation fo r selected com pounds in the membrane sta tionary phase.

v ii


Table 4 .10. E nrichm en t factors fo r com pounds over n itrogen and heptane a t 25 °C. T*, = predicted from tiie b o ilin g p o in t m odel (Equation 4.40); SP = predicted from s o lu b ility param eter theory (Equations 4.3 and 4.32); M E = experim ental from ME data (Pt/P j);GC = experim enta l from GC data (Equation 4.35).

Table 5.1. Gas perm eabilities and perm eation ra te s /u n it concentra tion (given per u n it ppm b y volum e) th rough a 2.54-cm -long, 0.0305-cm -i.d ., 0.0635-cm -o.d. s ilicone ho llow fib e r m em brane.

Table 5.2. Perm eabilities and flow rates fo r gases th rough a 2 .5-cm - long, 0 .0305-cm -i.d ., 0.0635-cm -o.d. silicone ho llow fib e r m em brane.

Table 5.3. The effects o f interface tube length on response.

Table 5.4. Com parisons between response tim e (tso-tq) and rise tim e (tgo-tio ) fo r 1-butanol.

Table 5.5. The effects o f analyzer conductance on response tim e.

Table 6.1. Spike sets w ith volum e % in acetone, m onitored ions, and standard response factors. Baseline response was 0.0005.

Table 6.2. Spike concentrations (m g/L) in the in flu e n t wastewater.

Table 6.3. C oncentrations (m g/L) detected in the e ffluen t w ate r and the a ir stream s in the reactive process. Styrene and chlorobenzene are n o t detected (N.D.) above the baseline in the e ffluen t w ater.

Table 6.4. Percent recoveries and standard deviations fo r the spiked organic com pounds.

Table 6.5. Percent recoveries and standard deviations in the e ffluen t w ate r stream s.

Table 6.6. Percent recoveries and standard deviations in the e ffluen t a ir stream s.

Table 6.7. Percent b io -up take and standard deviations. Experim ental values corrected fo r the recoveries in the an a ly tica l tes t reactor (reactor 2) are given in parentheses.

Table A . l. Mass spectrom etric response factors, re la tive to to luene, used to determ ine perm eation param eters.

Table A .2. Relative standard deviation fo r each know n source o f e rro r and fo r each com puted perm eation param eter.

v iii


LIST OF FIGURES

Figure 1.1. The com ponents o f a typ ica l m em brane extractor.

F igure 1.2. A typ ica l mem brane perm eation response curve.

F igure 2.1. A cross-section view o f the general com ponents o f the perm eation process.

Figure 2.2. The mass spectrom etric response and pressure vs. concentration o f to luene in the feed stream . Aqueous standard concentrations are reported on a g ra m s /lite r basis w h ile gas standards are reported on a vo lum e/vo lum e basis. The po rtion o f the to luene in a ir response curve labeled ¥ deviates from lin e a rity due to excessive pressure in the ion source.

Figure 2.3. The effects o f tem perature on perm eability.

Figure 2.4. A p lo t o f so lu tions to non-steady state perm eation (Equation 2.12), calcu lated from tso values, and perm eation response data fo r ch loroform a t 26 °C and 85 °C.

F igure 2.5. Norm alized perm eation response curves fo r 1,2,4- trich lorobenzene as a fu n c tio n o f tem perature.

Figure 3.1. Therm odynam ic in te ra c tio n effects o f a fille r on d iffus ive tra nspo rt.

F igure 3.2. H ollow fib e r m em brane perm eation cell.

F igure 3.3. C orre lation between d is trib u tio n ra tio and so lu b ility param eter fo r substances in a silicone elastom er m em brane a t 25 °C.

Figure 3.4. C orre la tion between d iffu s iv ity , corrected fo r to rtu o s ity , and the m o la r volum e fo r substances in a silicone elastom er m em brane a t 25 °C.

Figure 3.5. C orre la tion between surface free energy, [R T /(N 1/ 3*v i2/ 3)]* [ln (k ’i) - ln (V f/V p)], and cohesive energy density, 8 j2, fo r substances in a silicone elastom er m em brane, a t 25 °C. The lin e is fitte d to the halogenated com pound and alcohol data only.

ix


Figure 3 .6 . C orre la tion between experim enta l and theore tica l se lectiv ities fo r substances re la tive to m ethane in a silicone elastom er a t 25 °C.

F igure 3 .7 . C orre la tion between experim enta l and theore tica l se lectiv ities fo r substances re la tive to m ethanol in a s ilicone elastom er a t 25 °C.

F igure 4.1 . The effect o f tem perature on the s ta tiona ry phase/m ob ile phase d is trib u tio n ra tio , Kit obtained by ME (a) and b y GC fb).

F igure 4.2. The corre la tion o f the d is trib u tio n ra tio , Kit w ith b o ilin g po in t, Tbj, a t 25 °C, obtained b y M E (a) and by GC Cb).

F igure 4.3 . The effect o f tem perature on d iffu s iv ity , Di s, in the M E sta tiona ry phase.

Figure 4.4 . The corre la tion o f d iffu s iv ity , Di s, w ith b o ilin g po in t, Tb i. a t 25 °C, obtained by ME (a) and by GC Cb).

F igure 4 .5 . The effect o f tem perature on perm eability, Pit in the M E sta tiona ry phase.

F igure 4 .6 . The corre la tion o f the enrichm ent fac to r (over n itrogen),

£ i/N 2* w it*1 b o ilin g po in t, Tbj. fo r the data obtained by ME a t 25 °C.

F igure 4.7 . The corre la tion o f GC re ten tion tim es w ith M E perm eation param eters a t 25 °C.

F igure 5.1. Flow-over ho llow fib e r m em brane extractor.

Figure 5.2. F low -through ho llow fibe r m em brane con figura tion .

Figure 5.3. A cross-section view o f the effect o f boundary layers on the perm eation process.

Figure 5.4. Response fo r to luene vs. sample flow rate th rough a 2 .5 - cm -long, 0.0305-cm i.d ., 0.0635-cm o.d. ho llow fibe r.

Figure 5.5. The response curves fo r m /z 92 fo llow ing a step change in the concentra tion o f toluene in a gas sam ple w ith d iffe ren t lengths o f M E-M S in te rface tube lengths.

Figure 5.6. Response tim e vs. ME-MS interface tube leng th fo r various vo la tile com pounds.

F igure 5.7. The response curves fo r 1-bu tano l (m /z 56) w ith d iffe re n t lengths o f ME-M S in terface tube.

x


Figure 5.8. Com parison o f response vs. concentration p lo ts fo r the flow -over and the flow -th rough membrane extracto r con figurations.

F igure 5.9. Relative o rgan ic/w ater response ra tios fo r the flow -over vs. flow -th rough in le ts obtained a t com parable sample lin e a r velocities.

F igure 5.10. Exploded view o f the ho llow fibe r m em brane extracto r valve.

■ F igure 5.11. Exploded view o f the sheet m em brane extracto r valve.

F igure 5.12. A membrane extraction valve coupled to a d ire c t in se rtio n probe.

F igure 5.13. A con figura tion o f ME valve where the low er section o f the valve is expanded so th a t the process is carried o u t in d irect con tact w ith the m em brane.

F igure 6.1. A configura tion fo r the in flu e n t and e ffluen t analysis by M E-M S o f a m u lti-s trea m , m u lti-phase process.

F igure 6.2. A diagram o f the wastewater trea tm ent b ioreactor.

F igure 6 .3 . The syringe and m ix ing ja r con figura tion fo r sp ik ing organic com pounds in to liq u id streams.

F igure 6.4. A process flow diagram illu s tra tin g the sp ik ing and on-line sam pling o f three w astewater trea tm ent bioreactors.

F igure 6.5. Mass flow ra te p lo ts fo r carbon te trach lo ride in A, reactor 3 (reactive, no t spiked), B, reactor 2 (non-reactive, spiked), and C, reactor 1 (reactive, spiked). The spike was begun a t the 8 -h o u r m ark.

F igure 6.6. Mass flow rate p lo ts fo r benzene in A, reactor 3 (reactive, n o t spiked), B, reactor 2 (non-reactive, spiked), and C, reactor 1 (reactive, spiked). The spike was begun a t the 8 -hou r m ark.

F igure A . 1. E xperim ental de term ination o f perm eation param eters.

x i


CHAPTER 1

Introduction

The need fo r rea l-tim e trace analysis o f a ir and w ater stream s

has increased in recent years. M ethods are being sought fo r on -line

analysis o f process stream s fo r process op tim iza tion and contro l. The

challenge o f environm enta l m on ito ring o f a ir and wastewater

em issions grows w ith increasing ly stringen t governm ent regula tions.

In m any cases, the extraction , concentration, desorption, and analysis

o f organic com pounds from a ir o r w ater stream s can be accom plished

in a single step using a membrane extraction device.

BACKGROUND

Membranes have long been used in in d u s try and m edicine fo r

processes re qu irin g p u rifica tio n o r enrichm ent o f a gas o r liq u id

stream (1, 2). These m em brane processes inc lude separation o f

hydrocarbons, separation o f the com ponents o f a ir, p u rifica tio n o f

w ater, and de toxifica tion o f blood. The same m em branes used in

these in d u s tria l and m edical processes also m ay be u tilize d on a

sm alle r scale in ana ly tica l separations. Term s th a t are com m only used

by membrane technologists (3) and the analogous term s th a t m ay be

used by ana lytica l chem ists are sum m arized in Table 1.1. These term s

m ay be used interchangeably in th is work.

l


Table 1.1. Membrane separation term s and som e analogous term s used in analytical chem istry.

m em brane technology termm em branefeedre je c tperm eatep e rm se le c tiv ity

sta tionary phasesample stream , m obile phasewaste stream , vent streamextract streamenrichm ent facto r, concentra tion fac to rd iffu s io n coe ffic ientperm eation coe ffic ien t H enry's law coefficient, d is trib u tio n ra tio

a lte rna te term s

d iffu s iv itype rm e a b ilityso lu b ility

In general, m em brane processes are com prised o f the

m em brane, the feed stream (sample), the re ject stream (waste o r

vent), and the permeate stream (sample extract) as shown in F igure

1.1. The permeate stream is enriched in analytes due to the selective

perm eation properties o f the mem brane. The perm eation o f an

analyte th rough a m em brane is defined by three processes;

1) selective p a rtitio n in g o f the analyte from the sam ple in to the

m em brane polym er m a trix ,

2) selective d iffu s ion o f the analyte th rough the membrane, and

3) desorption o f the analyte from the m em brane in to a vacuum or

sweep gas.

D iffus ion th rough the membrane is assumed to be the ra te

de term in ing process, w h ile p a rtitio n in g a t the sam ple surface and

desorp tion from the permeate surface are considered to be

2


reject(waste)

permeate(extract)membrane

feed(sample)

Figure 1.1. The com ponents o f a typical membrane extractor.


NORM

ALIZ

ED

AM

OU

NT

steady state

non-steady state

t=o TIME

feed concentration permeation rate

Figure 1 .2 . A typ ical m em brane perm eation response curve.

4


instantaneous. A step change in analyte concentration in the sample

resu lts in the typ ica l perm eation response curve shown in Figure 1.2.

The sensitiv ity o f a membrane separation technique is determ ined by

the steady state perm eation response, w hile the non-steady state

perm eation characteristics o f the analyte in the membrane determ ine

the response tim e. These processes w ill be discussed in de ta il in the

fo llow ing chapters.

The development o f membrane extraction (ME) techniques

have given b irth to a fam ily o f powerful hyphenated analytica l

techniques, inc lud ing ME-mass spectrom etry (ME-MS) (4, 5), ME-gas

chrom atography (ME-GC) (6), M E-flow in jection analysis (ME-FIA) (7),

M E -liqu id chrom atography (8), M E-ion chrom atography (9), and

others, inc lud ing GC-ME-MS (10, 11) and FIA-ME-MS (12, 13). The

membrane extractor is m uch more than an in le t o r sam pling system

fo r an analyzer. Membrane extractors have become indispensable fo r

techniques th a t require high specificity, sensitiv ity, and speed,

p a rticu la rly fo r on-line analyses (14-16).

A lthough applicable to any analytica l technique, the membrane

studies and applications described in th is w ork were perform ed w ith

analyses o f the permeate by mass spectrom etry. H istorica lly,

membranes have been used as m olecular separators in gas

chrom atography-m ass spectrom etry (GC-MS) to reduce the am ount o f

he lium carrie r gas flow ing in to the mass spectrometer. Llewellen and

L ittle jo h n (10) have used a fla t silicone membrane th a t is selectively

permeable to organic molecules relative to helium . The GC effluent

5


flows across one surface o f the membrane, th rough w hich the organic

m olecules permeate in to the analyzer w hile the he lium is largely

rejected. Lipsky, H orvath, and M cM urray (11) used a heated Teflon

tube to act as a m olecular separator interface fo r GC-MS. In th is case,

he lium preferentia lly permeates the porous Teflon membrane,

re su ltin g in an enrichm ent o f the organic analytes flow ing in to the

analyzer as the stream rejected by the membrane.

Westover, Tou, and M ark (5) evaluated various ho llow fibe r

mem brane m ateria ls fo r MS analysis o f organic com pounds in a ir and

w ater w ith o u t GC separations. The membrane was the d irect interface

between the sample and the analyzer, w ith the inside o f the hollow

fib e r exposed to the MS vacuum and the ou ter surface exposed to the

sample. Th is p a rticu la r configuration w ill hereafter be term ed the

"flow-over" ho llow fibe r in le t. Cooks and co-workers (17) reversed the

configura tion such th a t sample flows through the inn e r volum e o f the

ho llow fib e r w hile the ou ter surface is exposed to the MS vacuum .

Hence, "flow -through" w ill be the term inology describing th is

configuration . The two configurations are contrasted and discussed in

de ta il in C hapter 5. Except where specifically stated, a ll o f the data

reported in the present w ork were obtained w ith a flow -through

ho llow fibe r membrane extractor. There are advantages to analyzing

the sample d irectly w ith o u t chrom atographic separation. In cases

where interferences between analytes are m in im a l or can be

accounted for, the analysis o r screening o f batch samples can be

shortened (12). In addition, trans ien t processes can be m uch be tter

stud ied by d irect and continuous analysis (18, 19).

6


GOALS OF THIS WORK

M uch o f the lite ra tu re on the subject o f sam pling w ith

m embranes is devoted to usefu l applications. Relatively little em phasis

has been placed on the development o f p ractica l models (a) fo r

p red icting the capacity o f a membrane to separate two com ponents in

a sam ple o r (b) fo r choosing the appropriate m ateria l fo r perform ing a

desired membrane separation. A goal o f the present w o rk was to

provide use fu l models and experim ental guidelines fo r perform ing

m em brane extractions so th a t the ve rsa tility o f the technique m ay be

be tte r exploited.

In C hapter 2, generalized form s o f the perm eation rate

equation fo r ana lytica l applications to bo th a ir and w ater samples are

developed. Results and discussion o f the effects o f various

experim ental param eters on perm eation rates are presented w ith

th e ir theore tica l bases. A mass spectrom etric m ethod fo r determ ining

the perm eation param eters, inc lud ing enrichm ent factors,

perm eabilities, d iffus iv ities, and d is trib u tio n ratios, w ill be presented.

M any o f the resu lts in th is chapter have been published (20, 21).

In C hapter 3, a perm eation model is developed based on

regu la r so lu tion theory. E q u ilib rium p a rtitio n in g o f substances

between the mem brane and feed phases resu lts in two phases th a t

m ay modeled u tilizing H ildebrand so lu b ility param eters. In addition ,

the effect on d iffusive tra nspo rt o f p a rtitio n in g a d iffus ing substance

between a fille r and polym er phase in a composite m em brane also may

7


be correlated to so lu b ility param eters. F ina lly, experim ental and

theore tica l enrichm ent factors fo r a composite membrane are

correlated in the so lu tion-d iffus ion model. The in fo rm ation presented

in th is chapter has been published (22).

C hapter 4 is a p ractica l extension o f the princ ip les developed

in C hapter 3. In Chapter 4, chrom atographic separation princ ip les

and data are applied to m em brane extractions. Since both techniques

are governed by the same therm odynam ic and k ine tic factors, a m odel

is described u tiliz in g w ell know n chrom atographic princip les. Very

good experim ental agreement is observed in corre lations made

between the selectivities obtained by membrane extractions and by gas

chrom atography. Such corre lations become more com plicated fo r

strong hydrogen bonding compounds because the membrane contains

a fin e ly dispersed s ilica fille r to provide it w ith strength and e lastic ity.

T h is s ilica fille r affects both the therm odynam ic and the tra n sp o rt rate

properties o f the m ateria l. Com parisons are made between a sim ple

b o ilin g p o in t m odel and the so lu b ility param eter model described in

C hapter 3. The in fo rm ation presented in th is chapter has been

subm itted fo r pub lica tion (23).

In C hapter 5, guidelines fo r the construction and use o f sim ple

m em brane in le ts are presented. Experim ental param eters are

discussed in the context o f ana lytica l sensitiv ity and response tim e.

These experim ental param eters include analyte concentration, sample

flow rate, tem perature, membrane thickness and surface area,

m em brane extracto r configuration, and distance o f the membrane

8


extracto r from the analyzer and the sample. Portions o f th is chapter

have been previously published (20, 21). M uch o f the additiona l

in fo rm a tion has been subm itted fo r pub lica tion (24).

In C hapter 6, the application o f an ME-MS technique th a t was

developed fo r on-line analysis o f organic components o f m u ltip le liq u id

and gas stream s is presented. The silicone membranes are shown to

a llow fo r extraction o f organic chem icals from complex and d irty

m atrices w ith no sample preparation. M u ltip le streams o f bo th a ir and

w ater were analyzed on-line w ith a single analyzer. This m ethod has

been applied in an aerobic bio logical wastewater treatm ent process.

Mass balance determ inations were performed by quantita tive ly

m easuring the organic contam inants in the in flu e n t wastewater

stream , in the e ffluen t w ater stream, and in the effluent a ir stream .

The in fo rm a tion presented in th is chapter has been published (25).


REFERENCES

(1) B ier, M., Ed. Membrane Processes in Ind ustry and B iom edicine: Plenum Press: New York, NY; 1971.

(2) Hwang, S.-T.; Kammermeyer, K. Membranes in Separations: Robert E. Krieger Publishing: M alabar, FL; 1984.

(3) Gekas, V. D e s tin a tio n 1988, 68, 77.

(4) Hoch, G.; Kok, B. Arch. Biochem Biophys. 1963, 101, 160.

(5) Westover, L.B .; Tou, J . C.; M ark, J . H. AnaL Chem 1974, 46, 568.

(6) Bredeweg, R. A .; Langhorst, M. L.; D ittenhafer, D. R.; S trandjord, A. J .; W illis , R. S. 16th A nnual Meeting o f the Federation o f A na lytica l C hem istry and Spectroscopy Societies, Chicago, IL, 1989.

(7) Melcher, R. G. AnaL Chim. Acta 1988, 214, 299.

(8) Melcher, R. G.; Bouyoucos, S. A. Process Control and Q uality 1990, 1, 63.

(9) Stevens, T. S.; Jew ett, G. L.; Bredeweg, R. A. AnaL Chem 1982, 54, 1206.

(10) Llewellen, P. M.; L ittle john , D. P. U.S. Patent 3,429,105, February, 1969.

(11) Lipsky, S. R.; Horvath, C. G.; M cM urray, W. J . AnaL Chem 1966, 38, 1585.

(12) Langvardt, P. W.; Brzak, K. A .; Kastl, P. E. 34 th ASMS Conference on Mass Spectrom etry and A llied Topics, C incinnati, OH, 1986.

10


(13 ) Hayward, M. J .; Kotiaho, T.; L ister, A. K.; Cooks, R G.; A ustin , G. D.; Narayan, R ; Tsao, G. T. AnaL Chem. 1990, 62, 1798.

(1 4 ) Kallos, G. J .; Tou, J . C. Environ. Set TechnoL 1977 , 11, 1101.

(1 5 ) Heinzle, E.; Reuss, M. Mass Spectrom etry inB iotechnological Process A nalysis and C on tro l: P lenum Press: New York, NY; 1987.

(1 6 ) Savickas, P. J .; LaPack, M. A .; Tou, J . C. AnaL Chem 1989, 61, 2332.

(1 7 ) (a) B ier, M. E.; Cooks, R G.; Tou, J. C.; Westover, L. B. U.S. Patent 4 ,791,292, 1989.(b) B ier, M. E.; Cooks, R G. AnaL Chem 1987, 59, 597.

(1 8 ) Tou, J. C.; Westover, L. B.; Sonnabend, L. F. J. Phys. Chem 1974, 78, 1096.

(19 ) Calvo K. C.; Weisenberger, L. B.; Anderson, L. B.; Klapper, M. H. AnaL Chem 1981, 53, 981.

(20 ) LaPack, M. A .; Tou, J. C.; Enke, C. G. 37 th ASMS Conference on Mass Spectrom etry and A llie d Topics, 1989, M iam i Beach, FL.

(21 ) LaPack, M. A.; Tou, J.C .; Enke, C.G. AnaL Chem 1990, 62, 1265.

(22 ) LaPack, M. A.; Tou, J . C.; M cG uffin, V .L.; Enke, C. G. J. Membrane Set 1994 , 86, 263.

(2 3 ) LaPack, M. A.; Tou, J. C.; M cG uffin, V .L.; Enke, C. G. AnaL Chem subm itted fo r pub lica tion .

(2 4 ) LaPack, M. A.; Tou, J. C.; Cole, M. J .; Enke, C. G. AnaL Chem subm itted fo r pub lica tion .

(2 5 ) LaPack, M.A.; Tou, J.C .; Enke, C. G. AnaL Chem 1991, 63, 1631.

l i


CHAPTER 2

Perm eation Fundam entals

Perm eation is a broad term th a t describes a va rie ty o f processes

invo lv ing tra n sp o rt o f substances across boundaries (1). M any o f these

processes have been given specific phenom enological names. For

exam ple, as opposed to gas perm eation, the term pervapora tion is

often used to describe the penetra tion o f a substance in to a polym er

from the liq u id phase, d iffu s ion o f the substance th rough the polym er,

and desorp tion from the polym er in to the gas phase (2, 3). I t has

been suggested th a t the te rm sorp tion ind ica tes the penetra tion in to

the polym er o f a substance from the gas phase w hile absorption

ind ica tes the penetra tion from the liq u id phase (4). Regarding the

w o rk described in the fo llow ing pages, the m ore b road ly descrip tive

term s, perm eation and sorption , w ill be used in bo th gas and liq u id

app lica tions. The te rm adsorp tion w ill be used in describ ing the

ass im ila tion o f m olecules from a gas o r liq u id phase by an im perm eable

surface. The te rm desorp tion describes the reverse process o f

sorp tion , absorp tion, and adsorption.

As in troduced in C hapter 1, the perm eation o f a com pound

th roug h an am orphous polym er is governed by sorption o f the

com pound in to the polym er, d iffusive tra n sp o rt th rough the polym er

m a trix , and desorption from the downstream side o f the polym er.

12


T h is de scrip tion o f the perm eation process is generally know n as the

so lu tio n -d iffu s io n m odel (5). S orp tion and desorption are e q u ilib riu m

processes th a t m ay be described by classical therm odynam ics (6, 7) as

w ill be discussed fu rth e r in Chapters 3 and 4. Because i t is such a

ra p id process, desorption o f the perm eating com pound in to a vacuum

o r ca rrie r gas is com m only ignored when d iscussing the perm eation o f

gases and vo la tile organic com pounds. The d iffu s ion process is driven

by the concentra tion grad ient across the th ickness o f the m em brane.

Q uan tita tive treatm ents o f d iffu s ion in solids under various conditions

have been presented (8, 9). In th is chapter, so rp tion and d iffu s io n are

discussed in regards to the two regions o f the perm eation ra te curve,

steady state and non-steady state (see Figure 1.2), and to th e ir

im portance to the se lectiv ity o f the perm eation process.

STEADY STATE PERMEATION

Steady state perm eation is described by F ick's f irs t law

Fj = -A»Dis «3Ci<s/3 x (2 .1)

where Fj is the flow rate (perm eation rate) o f substance i in the

perm eate (extract stream), A is the surface area o f the m em brane, Di s

is the d iffu s iv ity o f the substance in the m em brane polym er (sta tionary

phase), and 3ci s/3 x is the concentration grad ient fo r substance i

across the m em brane th ickness. For a sheet m em brane, F ick 's firs t

law gives

13


Fi = A*DitS*(ci sl - ci>s2)/d (2.2)

and fo r a ho llow fib e r membrane.

Fi = 2 * jfL *D i>s* (q s l - q s2)/ln (o .d ./i.d .) (2 .3)

where q sj and q s2 are the concentrations o f substance i in the feed

surface and the permeate surface o f the membrane, respectively, d is

the th ickness o f the sheet membrane, L is the length o f the ho llow

fiber, and o.d. and i.d . are the ou ter and in n e r ra d ii o f the ho llow fiber,

respectively. The general com ponents o f the perm eation process are

shown in Figure 2.1 (for a sheet membrane). I f the permeate side o f

the membrane is exposed to the mass spectrom eter vacuum o r swept

w ith a ca rrie r gas, a concentration gradient is established and cs2i

becomes ve iy sm all re la tive to q s l and can be ignored. This

concentration grad ient is the d riv ing force fo r d iffus ion . The

concentra tion q s l is established by the p a rtitio n in g process and, fo r

gas samples, is d ire c tly p roportiona l to the p a rtia l pressure o f

com ponent i, pit in the sample by the Henry's law o f so lu b ility

coefficient, Sj, such th a t ci s l = S^p*. However, since the desired

m easurem ent fo r m ost ana lytica l methods is concentration and no t

p a rtia l pressure o f a substance in the sample. Equations 2.2 and 2.3

can be rew ritten fo r the sheet as

Fi = A-D^s-Si-pt^Pi/ptl/d (2 .4)

and fo r the hollow fib e r as

14


Permeation through a Membrane

1) Sorption into the membrane2) Diffusion through the membrane3) Desorption from the membrane

membrane(stationary phase

sample or feed stream (mobile phase)

extract or permeate stream

►

Figure 2 .1 . A cross-section view o f the general com ponents o f the perm eation process.

15


Fi = 2*7t*L*Di>s*Si*pt*(pi/p t)/ln(o.d./i.d.) . (2.5)

The substance i p a rtia l p re ssu re /to ta l sam ple pressure ra tio ,

Pi/Pt, gives the m o la r concentra tion o f the substance in the feed

(m obile phase), q m. The p roduct, S |*pt , can be re w ritte n to y ie ld the

ra tio o f the concentra tion in the m em brane, ci>si, to the concentra tion

in the feed, q m, w h ich is defined as the concentra tion d is trib u tio n

ra tio , where K i = ci s l/c i m. The d is trib u tio n ra tio provides a more

generalized fo rm o f the perm eation ra te equation, where fo r the sheet

Th is fo rm o f the perm eation ra te equation is also re ad ily applied

to aqueous sam ples where the m em brane/w ater d is trib u tio n ra tio fo r

the substance and the concentration o f the substance in the aqueous

sam ple are used (10). The p roduct o f d iflu s iv ity and d is trib u tio n ra tio

is the perm eab ility (Pj = Di s«Ki). T yp ica lly , m em brane technologists

u tilize the H enry's Law coefficient (Pj = D i s*Sj) and the u n its

cm 3*cm /[s *cm 2»cm-Hg] fo r gas perm eabilities. S ince the d is trib u tio n

ra tio has no u n its , the u n its fo r pe rm eab ility w ill be given as

cm 2/[s»Ci m] where appropria te in the present w ork.

Fi = A*D iiS*Ki*Ci m/d (2 .6)

and fo r the ho llow fib e r

Fi = 2*Ji*L*Di s*K i*q s/ln (o .d ./i.d .) (2 .7)

16


A t a given tem perature and pressure, the perm eability and the

d im ension facto r (A /d fo r the sheet, 2 tc L /ln (o .d ./i.d .) fo r the ho llow

fiber) are constants. The perm eation ra te and therefore the ana ly tica l

s ignal, Ij, is d ire c tly p ropo rtiona l to the sam ple concentra tion, where

h = 9 i-F i = rfi'C i.m (2 .8)

where Q j is the absolute ins trum e n ta l response facto r and r f j is the

a n a ly tica l response facto r fo r com pound i. Depending upon the

app lica tion , the sam ple concentration may, in fact, be expressed in

any use fu l u n its to obta in an ana lytica l w orking curve. For example,

organic contam inants in aqueous samples are often expressed in u n its

o f m g /L , w h ile organic contam inants in a ir m ay be expressed in u n its

o f L /L o r m ole/m ole.

The lin e a r re la tionsh ip between perm eation ra te and sam ple

concentra tion is exh ib ited over a w ide dynam ic range, as shown in

F igure 2.2, in w h ich the response is d ire c tly p ropo rtiona l to the

perm eation rate. The upper lim it o f th is range is determ ined by the

m axim um am ount o f analyte th a t the analyzer w ill to lerate fo r lin e a r

response a n d /o r the sw elling o f the m em brane due to h igh so rp tion o f

organic analytes. Aqueous samples generally provide a w ider dynam ic

range because the low end o f the range is extended. The detection

lim its fo r aqueous samples are generally low er th a n fo r a ir samples.

17


10000

c 1000 - - toluene in water.

100 - -

toluene in air10 - -

0.1

»(O0)1_

Q.C/>

Io

76543210

toluene in air

toluene in water

1 100 10000 1000000

Concentration, ppb

Figure 2 .2 . The m ass spectrom etric response and pressure vs. concentration o f toluene in the feed stream . Aqueous standard concentrations are reported on a gram s/liter basis w hile gas standards are reported on a volum e/volum e basis. The portion o f the toluene in air response curve labeled ¥ deviates from linearity due to excessive pressure in th e ion source.

18


E ffects o f membrane dim ensions

I t is apparent from Equations 2.6 and 2.7 th a t increasing the

surface area o f the sheet and the length o f the ho llow fibe r

p ro p o rtio n a lly increases the perm eation ra te. Membrane th ickness

has an inverse effect on perm eation. For a sheet membrane, the

perm eation ra te is s im p ly p ropo rtiona l to 1 /d . For a given length o f

ho llow fibe r, the effect o f ho llow fib e r ra d ia l dim ensions on

perm eation is given by l/ ln ( r 0/r i) . A com parison o f signals obtained

from the analysis o f organic com pounds in a ir w ith two ho llow fibers o f

approxim ate ly equal lengths, b u t d iffe ren t ra d ia l dim ensions, is shown

in Table 2.1. E xperim ental and theore tica l response ra tios show

reasonably good agreement fo r in d iv id u a l com ponents as w e ll as fo r

the to ta l gas th roug hp u t ind icated by the analyzer pressure.

Table 2 .1 . E ffect o f hollow fiber membrane radial dim ensions on analytical response. The silicone hollow fibers were 2.5-cm long. Tem perature = 23 °C.

response, (a rb itra ry un its)

com pound d ich lo rom ethane1,1 -d ich lo ro e th ene chlorobenzene acetone

m em brane 1 m em brane 2 responsei.d .=0.0305 cm i.d .=0.147 cm ra tio , 11/ I 2

o.d.=0.0635 cm o.d.=0.196 cm exp. theor.2.8 5.5 2.0 2.50.6 1.3 2.2 2.51.2 2.4 2.0 2.50.8 2.0 2.5 2.5

analyzer pressure 6 .2 x l0 "8 1 .4 x l0 '7 2.3 2.5(to rr)analyzer base pressure = 2.0x10-9 to rr.

19


E ffects o f tem perature

Perm eation is a tem perature-dependent phenom enon obeying

the A rrh en iu s re la tion :

Pi = Pi>0*exp [-E Pi. ( l/R T - l/R T 0)] (2 .9)

where the in itia l perm eability o f substance i, Pi 0, is given a t some

in it ia l tem perature, T0, the activa tion energy fo r perm eation, EPi, is

the sum o f the activa tion energy fo r d iffus ion , EDi, and the difference

in heats o f so lu tion between the m em brane and the sam ple m a trix ,

AHgi = H gi(m em brane)-H si(m atrix) fo r substance i. S u b s titu tin g

D i s*K i = Pi in to E quation 2.9 gives

Di>s*K i = D j s0«Ki 0*exp[-(EDi + AHSi) * ( l/R T - l/R T 0)] (2 .10)

The activa tion energy, EDi, is greater th a n zero, w h ile in

general, AHSi is less tha n zero. The d irection fo r the change in

pe rm eab ility w ith changing tem perature is dependent upon w he ther

the change in d iffu s iv ity o r d is trib u tio n ra tio dom inates, as determ ined

by the re la tive m agnitudes o f EDi and AHgi-

The re la tive trends fo r the perm eabilities o f a ir, w ater, and

organic com pounds w ith increasing tem perature are shown in F igure

2.3. A t h igher tem peratures, perm eabilities o f a ir and w ate r increase

because increasing d iffu s iv itie s dom inate th e ir pe rm eab ility-

tem perature re la tionsh ip . O rganic perm eabilities from w ate r sam ples

also increase largely due to increasing d iffus iv ities . In con trast to

20


Rel

ativ

e R

espo

nse

(arb

itrar

y un

its)

14 - -

water12 - -

10 - -

8 - - bromoform in water

6 - -

4 - -nitrogen

(oxygen follows)2 - -

bromo iorm in air

20 40 60 80Temperature, °C

Figure 2 .3 . The effects o f tem perature on perm eability.


Table 2 .2 . Survey o f tem perature effects on detection lim its (S/N = 2) for organic com pounds in air and water. The membrane is a 2 .5- cm long, 0 .0305-cm i.d ., 0 .0635-cm o.d. silicone hollow fiber.

de tection lim it (ppb)

in a ir in w ate r

com pound m /z

O0CO<N 45 °C 26 °C 45i °C

ch lo rom ethane 50 325 368 - -

d ich lo rom ethane 84 669 742 6 5

ch lo ro fo rm 83 182 233 7 5

carbon te trach lo ride 117 130 163 18 13

ch lo roe thene 62 269 301 - -

1.1 -d ich lo ro e th ene 61 101 125 6 5

trich lo ro e th e n e 128 30 39 29 25

te trach lo roe the ne 166 29 3 4 32 25

dibrom om ethane 172 28 36 106 93

brom o fo rm 171 14 21 62 34

benzene 78 42 54 3 2

to luene 91 31 38 2 2

ethylbenzene 106 45 57 6 5

chlorobenzene 112 12 14 8 7

1,3-d ich lo robenzene 146 3 3 23 16

1,2 ,4 -trich lo ro ben zene 180 3 5 51 29

22


aqueous samples, a ir samples show a decrease in perm eabilities fo r

organic com pounds due to th e ir reduced p a rtitio n in g in to the

m em brane a t h igher tem peratures. Th is effect w ill be discussed

fu rth e r in the fo llow ing chapters. Since, as shown in Table 2.2,

organic perm eabilities decrease fo r a ir samples w ith increasing

tem peratures, th e ir detection lim its increase. Because o f the greater

perm eabilities o f organic com pounds from w ater a t h igher

tem peratures, th e ir detection lim its im prove. However, organic

enrichm ents decay a t h igher tem peratures, as discussed below.

F u rth e r observations on these tem perature-related phenom ena are

presented below in the discussion on organic enrichm ent and th e ir

im p lica tions in chem ical analyses are discussed in C hapter 5.

NON-STEADY STATE PERMEATION

Non-steady state perm eation is governed by F ick 's second law:

The m athem atical so lu tion fo r d iffus ion through a m em brane o f

th ickness d fo llow ing a step change in sample concentra tion is (11)

where F ^) and Fi(ss) ind ica te the perm eation ra te o f substance i a t tim e

t and a t steady state conditions, respectively. The perm eation process

exh ib its an asym ptotic approach to steady state, th u s the tim e

3ci s/8 t = -D i s»(32Ci s/3 x 2). (2 . 11)

Fi(t) = Fi(ss)*{l + I2 *S (-l)n»exp(-(n*7c/d)2 Di s*t)]}. (2 . 12)

23


requ ired to achieve steady state, o r even 95% steady state, tgs, m ay be

d iffic u lt to determ ine. I t is convenient, therefore, to re la te response

tim e to the tim e required to achieve 50% steady state perm eation, tso,

w h ich is m ore easily determ ined. The firs t order approxim ation a t

tso, neglecting a ll b u t the firs t exponential term (n = l), can be used to

determ ine the d iffu s io n coeffic ient (12), where

F u rth e r evaluation yie lds a tgs /tso theoretical ra tio o f 2.7. Good

agreem ent is obtained fo r tim es greater than tso when the firs t

approxim ation is applied to experim ental response curves, as shown

in F igure 2.4. Thus, the response tim e approxim ation tgs = 2.7«t5o is

va lid . For tim es less tha n tso, add itiona l term s in the po lynom ia l are

required fo r a good fit. Response tim es are reported in th is w o rk in

term s o f tso m easurem ents.

E ffects o f membrane dim ensions

Since d iffu s iv ity is a constant fo r a given substance in a given

po lym er and a t a given tem perature, the response tim e-th ickness

re la tionsh ip can be expressed as follows:

The increase in response tim es fo r organic gases perm eating a

ho llow fib e r m em brane w ith a 0.0216-cm w a ll th ickness compared

w ith th a t fo r a 0.0165-cm w a ll th ickness is shown in Table 2.3. As

24

Dis = 0 .1 4 *(d 2 /t50) (2 .13)

^ 5 0 )2 /^ 5 0 )1 = (d 2 /d i ) 2 . (2 .14)


0.9

0.885 °C

0.7

26 °C= 0.6

| 0.5 a>Q.

0.4■aa>N __= 0.3

0.2

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Time, minutes

Key;C ircles and squares = experim enta l dataT h in lines = so lu tions using on ly the firs t te rm (n = l) o f the po lynom ia l Heavy lines = so lu tions using the firs t five term s (n = l-5 )

Figure 2 .4 . A p lot o f solutions to non-steady state perm eation (Equation 2.12), calculated from t ^ values, and perm eationresponse data for chloroform at 2 6 °C and 8 5 °C.


described in the Appendix, the experim enta l m easurem ent o f tso is

dependent upon errors in de fin ing the steady state perm eation

response and in estab lish ing the tim e when the sample m akes in itia l

con tact w ith the mem brane, to- T h inn in g o f the m em brane caused by

the pressure difference between the inside and the outside o f the

ho llow fib e r also m ay re su lt in the deviations between the

experim enta l and theore tica l response tim e ra tios in Table 2.3.

Table 2 .3 . E ffects o f membrane th ickness on response tim e for gas phase organic com pounds. The m em branes are 2.5-cm long silicon e hollow fibers. Temperature = 23 °C.

response tim e (m inutes) ^(50)2/ f (50)1

com pound d i= 0 .0 165 cm do=0.0245 cm exp. theor.d ich lo rom ethane 0.38 0.60 1.6 2.21,1 -d ich lo ro e th ene 0.28 0.48 1.7 2.2chlorobenzene 0.72 1.60 2.2 2.2acetone 1.88 3.02 1.6 2.2


D iffu s iv ity obeys the A rrhen ius re la tion given by

^ i.s = ^i,so*exP l“^D i* (1 /R T -l/R T o )]. (2 .15)

H igher tem peratures re su lt in increased d iffu s iv itie s and therefore

sho rte r response tim es. The perm eation ra te response curves fo r a

step change in sam ple concentration a t various tem peratures are

shown fo r 1,2,4-trichlorobenzene in Figure 2.5. The tso values fo r

26


Nor

mal

ized

Pe

rmea

tion

Rat

e

$

10 15 20 25

Time, minutes

30 35 40

Figure 2 .5 . Normalized perm eation response curves for 1,2,4- trichlorobenzene as a function o f temperature.

27


Table 2 .4 . Survey o f tem perature effects on response tim e, t 50, for organic com pounds in nitrogen. The membrane is a 2.5-cm long, 0.0305-cm i.d ., 0 .0635-cm o.d. silicone hollow fiber.

response tim e, tso, (m inutes)

com pound 26 °C 45 °C 65 °C 00 01 o O

ch lo rom ethane 0.23 0.19 0.18 0.17

d ich lo rom ethane 0.34 0.30 0.24 0.20

ch lo ro fo rm 0.42 0.36 0.30 0.24

carbon te trach lo ride 0.52 0.38 0.32 0.27

ch lo roe thene 0.25 0.20 0.18 0.16

1,1 -d ich lo ro e th ene 0.36 0.30 0.25 0.23

trich lo ro e th e n e 0.41 0.35 0.28 0.21

te trach lo roe the ne 0.78 0.55 0.41 0.33

dib rom om ethane 0.57 0.40 0.33 0.25

brom o fo rm 1.30 0.88 0.62 0.50

benzene 0.43 0.32 0.26 0.24

to luene 0.59 0.46 0.35 0.24

ethylbenzene 0.86 0.60 0.42 0.30

chlorobenzene 0.93 0.63 0.45 0.37

1,3-d ich lo robenzene 4.40 1.70 1.00 0.95

1,2 ,4 -trich lo robenzene 8.70 4.60 3.00 2.00

28


several gas phase organic com pounds a t d iffe ren t tem peratures are

given in Table 2.4. Aqueous sample response tim es m im ic gas sam ples

w hen the tra nspo rt-ra te th rough the sam ple is neglig ible, as discussed

in de ta il in C hapter 5.

ORGANIC ENRICHMENT

The re la tive perm eab ility th rough the m em brane fo r one

com pound over another determ ines m em brane se lectiv ity . The

en richm ent factor, £ i/ j, o f one com ponent, i, over another, j , (e.g., an

organic com pound over the sample m atrix) is defined by the ra tio o f

th e ir pe rm eab ilities;

S i/j = (Dj s#K i)/(D j s*Kj) = (Fi/c i>m)/(F j /c j>m) (2.15)

Effects o f membrane dim ensions

The enrichm ent fac to r is independent o f m em brane

dim ensions, as seen in Equation 2.15. Increasing the length or

num ber o f the ho llow fib e r w ill increase perm eation ra tes o f a ll

com ponents p ropo rtion a lly , w ith no effect on observed organic

enrichm ent, i f cmi does no t change over the length o f the ho llow fibe r.

Typ ica lly, increasing the membrane surface area w ill be more

e ffic ie n tly accom plished by increasing the num ber, ra th e r than the

length, o f ho llow fibers exposed to the sam ple.

29



W ith increasing tem perature, the enrichm ent factors fo r organic

com ponents are reduced because the perm eabilities fo r a ir and w ater

increase m ore th a n the perm eabilities fo r m ost organic com pounds

stud ied, as shown in Figure 2.3. For trace level organic sam ples, the

analyzer pressure follow s the perm eabilities o f the a ir o r w ater.

Based on steady state response data used to determ ine the

detection lim its in Table 2.2, perm eabilities from aqueous sam ples

increased an average 35% (range = 14-83%) when the tem perature

was increased from 26 °C to 45 °C fo r the com pounds analyzed in

w ater. D iffu s iv itie s th rough the m em brane fo r these same organic

com pounds increased an average 46% (range = 13-159%) based upon

the response tim e data in Table 2.4, where [Ds(45 °)-Ds(26 °)]/D s(26 °)

= [ l / t 50(45 ° ) - l / t 50(26 ° ) ] / [ l / t 50(26 °)J. A lthough the organic

pe rm eab ilities increased, w ater pe rm eab ility increased 130% fo r the

same tem perature change.

For a ir sam ples, organic responses decreased an average 20%

(range = 10-33%) when the tem perature was increased from 26 °C to

45 °C, even though d iffu s iv ities increased an average 43% (range = 13-

159%). Therefore, the decrease in the m em bra ne /a ir d is trib u tio n

ra tio dom inates the perm eabilities fo r these com pounds. W hile the

organ ic pe rm eab ilities decreased, the n itrogen pe rm eab ility increased

29%. E nrichm en t factors re la tive to n itrogen and w ater fo r several

organic com pounds are given in Table 2.5.

30


Table 2 .5 . Survey o f tem perature effects on the enrichm ent over th e sam ple m atrix for organic com pounds in nitrogen and water.

enrichm ent fac to r

re la tive to n itrogen re la tive to w ater

com pound 26°C 45°C 26°C 45°C

ch lo rom ethane 40 27 - -

d ich lo rom ethane 48 33 1900 1100

ch lo ro fo rm 91 58 2100 1100

carbon te trach lo ride 110 74 1800 1100

ch lo roe thene 37 26 - -

1,1 -d ich lo ro e th ene 57 35 3300 1800

trich lo ro e th e n e 140 81 970 530

te trach lo roe the ne 310 180 600 360

dib rom om ethane 84 50 190 100

brom o fo rm 320 170 570 330

benzene 170 110 2600 1400

to luene 380 230 2300 1300

ethylbenzene 450 280 2200 1200

chlorobenzene 550 330 1300 730

1,3-d ich lo robenzene 520 350 470 300

1,2 ,4 -trich lo ro ben zene 780 400 450 390

31


M ost o f the perm eation param eters (perm eability, d iffu s iv ity ,

so lu b ility , and enrichm ent factors) reported in the lite ra tu re are fo r

sim ple gases such as hydrogen, nitrogen, oxygen, argon, and lig h t

hydrocarbons and alcohols (15-20). Very few studies have been

perform ed to determ ine these param eters fo r the m ore com plex

organic com pounds th a t are o f in te res t to ana ly tica l chem ists (21, 22).

A mass spectrom etric technique developed fo r ob ta in ing the

perm eation param eters reported in th is w ork is described in the

A ppendix.

32


REFERENCES

(1 ) Hwang, S.-T.; Kammermeyer, K. Membranes in Separations. Robert E. Krieger P ublish ing Co., Inc.; M alabar, FL; 1984.

(2 ) Frennesson, I.; Tragardh, G.; Hahn-Hagerdal, B. Chem. Eng. Commun. 1986 , 45, 277.

(3 ) M ulder, M. H. V.; Smolders, C. A. J. Membrane Set 1984 , 17, 289.

(4 ) Conway, B. E. In The Solid-Gas Interface. Vol. 2, Flood, E. A ., ed.; M arcel Dekker, Inc.: New York, NY; 1967.

(5 ) Mears, P. In Membrane Separation Processes; Mears, P., Ed.; E lsevier: Am sterdam , N etherlands; 1976.

(6 ) Ben-Naim , A. S olvation Therm odynam ics: Plenum Press: New York, NY; 1987.

(7 ) Karger, B. L.; Snyder, L. R ; H orvath, C. An In trod uctionto S eparation Science: W iley-Interscience: New York, NY; 1973.

(8 ) B arrer, R M. D iffusion in and Through Solids: Cambridge U n ive rs ity Press: New York, NY; 1951.

(9 ) C rank, J . The M athem atics o f D iffus ion . 2nd Ed.; Oxford U n ive rs ity Press: New York, NY; 1975.

(1 0 ) Lee, C. H. J. App. Polym. Set 1975, 19, 83.

(1 1 ) Pasternak, R A.; Schim scheim er, J . F.; Heller, J . J. Polym. Set 1970 , 8, 467.

(1 2 ) Ziegel, K. D .; Frensdorff, H. K.; B la ir, D. E. J. Polym. Set 1969, 7, 809.

33


(1 3 ) B ier, M. E.; Kotiaho, T.; Cooks, R G. AnaL Chem. A cta 1990, 231, 175.

(1 4 ) Lauritsen , F. R In t J. Mass Spectrom. Ion Proc. 1 9 90 , 95, 259.

(1 5 ) S tem , S. A .; Shah, V. M .; Hardy, B. J . J. Polymer S et: P art B : Polym er Physics 1 9 8 7 , 25, 1263.

(1 6 ) Kam m erm eyer, K. Ind . Eng. Chem. 1 9 57 , 49, 1685.

(1 7 ) Hodgson, M. E. F iltr. and Separ. 1973, Ju ly /A u g u s t, 418.

(1 8 ) K im , T. H .; Koros, W. J .; O 'Brien, K. C. J. Membrane Set 1988 , 37, 45.

(1 9 ) Friedlander, H . Z.; L itz , L. M. In Mem brane Processes inIn d u s try and B iom edicine. B ier, M ., Ed.; P lenum Press: New York, NY; 1971.

(2 0 ) B ell, C .-M .; Gem er, F. J .; S trathm an, H. J. Membrane Set 1988 , 36, 315.

(2 1 ) Ho, J . S.-Y.; Schlecht, P. C. Am. Ind. Hyg. Assoc. J. 1981, 42, 70.

(2 2 ) Tou, J . C.; R ulf, D. C.; DeLassus, P. T. AnaL Chem. 1990, 62, 592.


CHAPTER 3

The Correlation of Permeability w ith Hildebrand Solubility Parameters

In a d d itio n to gu id ing the selection o f liq u id extraction solvents,

the "like -d isso lves-like " ru le is com m only used to guide the selection

o f m em brane m ateria ls. For example, the extraction o f non po la r

organic com pounds from an aqueous m a trix can be accom plished w ith

a s ilicone m em brane because o f the trem endous se lectiv ity th is

po lym er exh ib its fo r the perm eation o f the non po la r m ateria ls (Table

2.5). However, th is sim ple ru le does no t p red ic t no r exp la in the fact

th a t, in the gas phase, 1-propanol permeates th is same silicone

m em brane nearly tw o tim es be tte r tha n pentane and m ethanol

perm eates over fo rty tim es be tte r tha n m ethane. In add ition ,

m em brane extractions are k in e tic , as w ell as therm odynam ic,

processes such th a t the effects o f selective d iffu s iv ities in the

m em brane become im po rta n t, no t on ly fo r the separation efficiency,

b u t also fo r the ana lytica l response tim e.

A fundam enta l understand ing o f the m em brane extraction

process, fa c ilita te d by a sim ple m odel, can help to generate m ore

versa tile separation techniques and perhaps a w ider selection o f

m em brane m ateria ls. In th is chapter, a perm eation m odel is

developed based upon H ildebrand so lu b ility param eters. A corre la tion

35


o f th is model is made to the p a rtitio n selectivity, to the d iffus ion

se lectiv ity, and to the perm selectivity o r enrichm ent factor.

THE SOLUBILITY PARAMETER

As discussed in Chapter 2, the so lu tion -d iffus ion perm eation

m odel assumes th a t a perm eating substance is in eq u ilib riu m a t the

in terface between the feed and membrane phases. Th is equ ilib rium ,

in com bination w ith a vacuum or sweep flu id a t the permeate side o f

the membrane, establishes a concentration grad ient across the

mem brane th a t resu lts in d iffusive flow. For com ponent i, the

perm eation coefficient, Pj, is given by the product o f the d iffu s iv ity ,

D j s, and the H enry’s law so lu b ility coefficient, Sj,

The perm selectiv ity or enrichm ent factor, S j/j, o f a mem brane fo r one

substance, i, re lative to another, j , is defined as

By assum ing th a t the sorption o f a gas in to a polym er phase may

be modeled as a so lu tion process, a corre lation o f s o lu b ility param eters

to the so lu tion -d iffus ion perm eation model arises n a tu ra lly .

H ildebrand so lu b ility param eters have been used in estim ating the

co m p a tib ility o f polym ers w ith solvents, additives, and coatings (1-6).

(3 .1)

£ i/j = ff>i.s/D j,sM Si/S j) (3 .2)

36


The s o lu b ility param eter, 6i? (7, 8) fo r substance i is the square roo t o f

the cohesive energy density fo r the pure liq u id substance, defined as

8j = [A E v i/v J l/2 = [(AHv r R T )/v i] l/2 (3 .3)

where AEyi is the m o la r energy o f vaporization, Vj is the m o la r volum e,

AHVi is the m o la r heat o f vaporization, R is the gas constant and T is

the absolute tem perature. The re la tionsh ip between the s o lu b ility

param eter and the a c tiv ity coefficient, s, fo r some substance i in

some phase m is given by the F lory-H uggins re la tionsh ip (5)

where vs and Os are the m olar volum e and the volum e fra c tio n o f the

phase m , respectively, and the b in a ry in te ractio n param eter, %i s, is

A pp lica tion o f the s o lu b ility param eter to separation processes

has been m ost successful fo r so lu tions o f s im ila r m ateria ls where

d ispersion in te ra c tio n forces predom inate. The s o lu b ility param eter

theory has been expanded (1, 9) to inc lude other in te ra c tio n forces

such as dipole in d u c tio n and o rien ta tion forces as w e ll as hydrogen-

bond ing forces. In the present study, the single param eter trea tm en t

was found to give reasonably good corre lations w ith experim enta l

re su lts fo r a m em brane composed o f poly(dim ethylsiloxane) w ith a

fum ed-s ilica fille r.

ln [yi<s] = ln [V i/v s] + (1 - [v i/v s])*4>s + Xi.s#<I>s2 (3.4)

Xi.s = Ivi /(R T )].[8 i - 5S]2 (3.5)

37


DEVELOPMENT OF THE MODEL

For the m odel described below, the fo llow ing assum ptions are

made:

1) The feed o r m obile phase is an ideal gas.

2 ) The perm eating substance is a t in fin ite d ilu tio n in bo th m obile

(feed) and s ta tio n a iy (membrane) phases.

3 ) The d is trib u tio n process can be described us ing the regu la r

so lu tion m odel as m odified by F lory-H uggins [51, w ith a ll assum ptions

in h e re n t the re in . S pecifica lly, no changes in phase volum es occur due

to sorp tion .

4 ) The d iffu s ion process obeys F ick's laws, w ith a ll assum ptions

in h e re n t the re in .

D is tribu tion equ ilib rium

In the so lu tion -d iffus io n m odel, an e q u ilib riu m is established a t

the feed-m em brane in terface fo r a perm eating substance as described

by H en iy 's law:

Xi.s = P i/[p i0#Yi,s] (3 .6 )

where X i s is the m ole fra c tio n and yi s is the a c tiv ity coefficient o f

substance i in the m em brane sta tiona ry phase, s, and p* and Pi° are

the e q u ilib riu m and standard-sta te p a rtia l pressures, respectively, fo r

the substance in the m obile phase. E quation 3.6 m ay be expressed in

the n a tu ra l logarithm ic fo rm and com bined w ith E quation 3.4 and

E quation 3.5 to y ie ld

38


ln [X is ] = In fo /p i0] - lnlVi/Vg] - (1 - [Vi/vs])*<E>s

- [V i/tRDM Si - 8s]2.<Ds2 ( 3 .7 )

In the case o f a membrane consisting o f tw o d is tin c t phases, such as a

polym er w ith a u n ifo rm ly d is trib u te d fille r, the m o la r volum e is

defined by

where vp and Vf are the m o lar volum es and where Xp s and X fs are the

m ole frac tions o f the polym er and the fille r, respectively, in the

sta tiona ry phase. These param eters need n o t be quan tita tive ly

specified in the trea tm ent described below. T ransport p roperties fo r

a substance in a polym eric membrane conta in ing a fille r have also been

modeled using the additive properties o f the two phases in the

m em brane (10, 11). S im ila rly , the so lu b ility param eter fo r the

s ta tiona ry phase based on regular so lu tion theory is given by

where 8p and 8 f are the s o lu b ility param eters fo r the polym er and fille r

phases, respectively, and Op and d>f are the volum e fractions o f the

po lym er and the fille r, respectively, in the m em brane. E quation 3.7 is

rearranged to give

vs = vp, x p,s + vfX f,s (3 .8)

8S = 5p*Op + 8 fO f (3 .9)

ln [X i,s.(V i/v s)] = In lp i/p i0] - (1 - [V i/vs])*Os

- [Vi/tRDMSi - 8S]2.0S2 (3 .10)

39


A t in fin ite d ilu tio n , X j s = n i s/n s, where the ra tio n i>s/n s is the num ber

o f moles o f sorbed substance i per mole o f s ta tiona ry phase. Therefore,

the vo lum etric concentration o f the substance in the sta tionary phase,

Cis , is given by

X i,s*[V i/vs] = Vi>s/V s = Ci>s (3 .11)

where V i s/V s is the volum e o f the sorbed substance per u n it volum e o f

s ta tio na ry phase. S im ila rly , the vo lum etric concentration o f the

substance in the gaseous m obile phase, Cj m, is given by the ra tio o f the

p a rtia l pressure to to ta l feed pressure:

P i/P t ~ Vi.m /Vm = Cj m (3.12)

E quation 3.10 can now be represented in term s o f the concentration

d is trib u tio n ra tio , Cj S/C j m = Kj, where

ln [K j] = ln [p t /p j° ] - (1 - [V j/vs])*Os

- [V j/(R r)]*[8 j - 8s]2.<Ds2 (3.13)

Because substance i is assumed to be a t in fin ite d ilu tio n , Os = 1.

In add ition , the m olar volum e o f the sta tionary phase, vs, is m uch

greater th a n th a t o f the sorbed substance, Vj. Therefore, Equation

3.13 reduces to

ln [K j] = ln [p t / Pi°] - 1 - [V j/(RT)M Sj - 8S]2 (3 .14)

40


Th is re la tionsh ip is consistent w ith gas chrom atographic stud ies o f

d ilu te so lu tions o f organic m olecules in polym ers (5). H ildebrand,

P rausnitz, and Scott proposed a m odel fo r the so lu b ility o f a gas in a

solvent in w h ich the gas firs t condenses to a hypothetica l pure liq u id

and then dissolves in the solvent (8 ). In the case o f non po la r gases a t

tem peratures above th e ir c ritic a l tem perature, they have calcu la ted

fugacities o f these hypothetica l liq u id s to estim ate so lu b ilitie s .

S o lu b ility param eters have been calculated fo r such gases by P rausnitz

and S ha ir (12). G iddings, et. a l (13) have described an expression fo r

de term in ing the so lu b ility param eters o f compressed gases us ing th e ir

c ritic a l properties. In the present w ork, an a ttem pt is made to

develop a general m odel th a t provides pred ictions fo r the s o lu b ility o f

gases o f vary ing po la rities and c ritic a l tem peratures, us ing a m in im um

o f read ily available param eters. Th is m odel u tilizes the hypothe tica l

and experim enta l so lu b ility param eter values provided in the

lite ra tu re . In th is model, the vapor pressure term in E quation 3.14 is

re la ted to the H ildebrand so lu b ility param eter by E quation 3.3 and the

C lausius-C lapeyron equation in the fo llow ing m anner:

ln [Pt/ Pi°] = [V i/tR D H S j - a )2 (3 .15)

The experim enta lly determ ined constant, a, corresponds to the

s o lu b ility param eter fo r the hypothetica l liq u id feed m a trix and

corrects fo r deviations from H enry’s law , F lo iy-H uggins, and regu la r

so lu tion theory. A corre la tion between the d is trib u tio n ra tio and

s o lu b ility param eter is then given by the fo llow ing equation:

41


lnlK j] = [vj/tRDW Gi - «)2 - &i - 8S)2] - 1 (3 .16)

The d is trib u tio n se lectiv ity fo r substance i re la tive to substance j

is calcu la ted from

K i/K j = exp^tfs-aM SiVi-SjVj) + (a2-8s2)*(vr Vj)]/(RT)} (3 .17)

D iffusion

According to the free volum e theory o f B rand t (14), the

activa tion energy fo r d iffusion , EDi, in elastom ers is dom inated by

in te rm o le cu la r forces and m ay be re lated to the cohesive energy

density o f the polym er, 8p2, as w e ll as dim ensions o f the polym er

chains and d iffu s ing substance. The re la tionsh ip is given by (10):

EDi = 0.5*Sp«ap«Oi«5p2«N (3 .18)

where sp is the polym er segment length associated w ith the free

volum e, ap is the average diam eter o f the polym er m olecule, Cj is the

diam eter o f the d iffus ing substance, and N is Avogodro's num ber.

E quation 3.18 m ay be expressed in term s o f the m o la r volum e o f the

d iffus ing substance:

EDi = 0.62»N2/3*sp*Cp*8p2*vi 1 / 3 (3 .19)

A lthough the free volum e o f some liq u id s m ay be s ign ifican t, fo r m any

substances the liq u id m olar volum e is consistent w ith the m olecu lar

volum e (7). For the purpose o f the present model, the liq u id m o la r

42


volum e o f the d iffu s ing substance is used ra th e r than the m olecular

volum e so th a t consistency w ith the so lu tion m odel is m a in ta ined and

so th a t the num ber o f variable term s are m inim ized.

The constan ts and po lym er-related term s in E quation 3.19 m ay

be com bined in to a single constant param eter, ft, so th a t the activa tion

energy m ay be w ritte n to be p ropo rtiona l to the m o la r volum e o f the

d iffu s in g substance. The dependence o f the d iffu s iv ity on the m o la r

volum e m ay then be described by

ln [D itp] = ln [D 0 p] - [ft/(R T )l-v ^ /S (3 .20)

where ft, the polym er-re lated constant, and ln [D 0 p], the n a tu ra l

lo g a rith m o f the d iffu s iv ity o f some hypothetica l substance w ith v=0 ,

are determ ined from the slope and the y-in te rcep t, respectively, o f a

p lo t o f ln [D i p] vs. v ^ /3.

E qua tion 3 .20 does n o t account fo r the effects o f a fille r on

d iffus ive tra n sp o rt in a polym er. Therm odynam ic p a rtitio n in g o r

adsorp tion o f some substances m ay become s ign ifican t in cases where

the tw o phases o f the fille d m em brane are qu ite d iffe ren t in p o la rity or

hydrogen-bonding character. T h is in h ib itio n o f d iffusive flow th rough

a fille d m em brane is m anifested as an apparent d iffu s iv ity th a t is lower

th a n pred icted from the m olar volum e o f the substance. I f i t is

assum ed th a t m ig ra tion o f a substance th rough the membrane occurs

on ly in the po lym er phase, any delay in th is m ig ra tion tim e is due to

p a rtitio n in to o r adsorption onto the fille r. The in d iv id u a l re ten tio n

43


processes o f th is tra n sp o rt m echanism is illu s tra te d in F igure 3.1.

The degree o f re ten tio n by the fille r in a com posite m em brane is

determ ined by the m o la r p a rtitio n o r adsorp tion coefficient, k 'i,

k i — n i ,f /n i,p — fti.s " ti,p)/ti,p (3 .21)

where n itf and n ip are the num ber o f moles o f substance i in the fille r

and the polym er phases, respectively, a t eq u ilib riu m , t ip is the tim e

fo r d iffu s io n o f substance i th rough the polym er, and t i>s is the tim e fo r

d iffu s io n o f i th rough the fille d mem brane. E quation 3.21 m ay be

rearranged to give

It is c lear from E quation 3.22 th a t no re ten tion is observed when the

d iffu s in g substance has no a ffin ity fo r the fille r (i.e., k 'i = 0). The

d iffu s iv ity o f substance i in the mem brane m ay be determ ined

experim enta lly from the so rp tion ra te curves (15) using the fo llow ing

equation:

where d is the m em brane th ickness and t(5Q) is the tim e required to

a tta in one-ha lf steady-state perm eation fo llow ing a step-change in the

concentra tion o f the substance in the m obile phase. By com bining

E quations 3.22 and 3.23, a re la tionsh ip is obtained between the

d iffu s iv itie s w ith and w ith o u t re tention by the fille r:

ti.s = ti.p’ U + k 'i) (3 .22)

D i = 0 .1 4 .d 2 /t(50) (3 .23)

44


FEED MEMBRANE PERMEATE

Polymer Phase

Distribution ratio, K, established at

membrane/feed interface

\ partition or aasorption s j coefficient, k', established ' 5 at filler/polymer interface £ \ in membrane \

Figure 3 .1 . Thermodynamic interaction effects o f a filler on diffusive transport.

diffusive flow


D i.s = Di>p/(1 + k'i) (3 .24)

where Di>s is the d iffu s iv ity o f substance i in the fille d polym er

s ta tio na ry phase and Di>p is the d iffu s iv ity in the u n fille d polym er. Th is

re la tion sh ip is consistent w ith th a t reported by B arrer and coworkers

(16, 17). In add ition , a reduction in mass tra nspo rt rates is observed

in a po lym er con ta in ing im perm eable partic les or c rys ta llite s due to

the to rtu o u s pa th the d iffus ing substance m ust travel (18). These

effects have been sum m arized by van Amerongen (19), where the

d iffu s iv ity in a m em brane con ta in ing a non-retentive spherica l fille r is

re la ted to th a t in the u n fille d polym er by the volum e fra c tio n o f the

fille r in the membrane, Of, such tha t:

The re ten tio n and to rtu o s ity term s are com bined to y ie ld the

d iffu s io n -p a rtitio n (D-k) m odel given by the fo llow ing equation:

To estim ate the d iffu s iv ity o f a substance in a membrane th a t contains

a fille r. Equations 3.20 and 3.26 are com bined to give

Di.s = Di,p/[1 + (Of/2 )] (3 .25)

D i.s = Di,p/{[1 + (Of/2 ) ]* [ l + k^]} (3 .26)

Di,s = D0,p*exp{-[d/(RT)]*Vil/3}

/ { [ l + (Of/2 ) ] - [ l + k 'i]} (3 .27)

46


Whereas retention processes may play a large role, the tortuosity

factor is independent of the nature of the permeating substance and

is, therefore, not im portant for estimating selectivity.

W here re ten tio n arises from a therm odynam ic p a rtitio n process,

the d is trib u tio n coeffic ient m ay be estim ated using s o lu b ility

param eter theory. A t e q u ilib riu m , i f substance i is p a rtitio n e d between

the polym er and fille r phases, then

Xi.f/Xi,p = YiiP/ Yi.f (3.28)

where the subscrip ts f and p designate the fille r and polym er,

respectively. Rearranging and com bin ing E quation 3.28 w ith

E quations 3.4 and 3.5 y ie lds the fo llow ing re la tion :

ln[Xi f/X j p] = ln[Vi/vp] - ln[Vj/v^ + (1 - [Vj/VpD-Op

- (1 - [Vj/vf])*<I>f + [Vi/fRTlMSi - 8p]2.<I>p2

- [Vi/fRDMSi - 8{]2.<l>f2 (3 .2 9 )

Assum ing in fin ite d ilu tio n fo r substance i in a ll phases and assum ing

the m o la r volum e o f substance i to be sm all re la tive to the m o la r

volum es o f the fille r and polym er phases, E quation 3.29 is s im p lified

to the fo llow ing:

In lX j f /X i p] = ln [(Vi/ Vp) /(Vi/ V{)] + [v j/tR D M tS i - Sp)2]

- [vi/(RT)].[(8i - 8f)2] (3.30)

47


Follow ing the su b s titu tio n o f Equation 3.11 in to E quation 3.30, the

d is trib u tio n ra tio fo r substance i pa rtitioned between the fille r and

polym er is given by

Since the d is trib u tio n ra tio is the p roduct o f the m o la r p a rtitio n

coeffic ient and the volum e phase ra tio , K 'j = k '^ fV p /V f), then E quation

3.31 can be re w ritten as follows:

I f re ten tion arises from an adsorption process, the en tire

m olecule m ay n o t pa rtic ipa te in the in te rac tio n w ith the solid

adsorbent surface. The energy o f adsorption a t the surface is typ ica lly

described by the surface free energy, E ^ / (N1 / 3 «Vi2 / 3), and involves

on ly the m olar area, N 1/ 3^ 2/ 3, o f the adsorbed m olecules (7, 20, 21).

Karger, Snyder, and Eon (9) have proposed a model o f liq u id -so lid

chrom atography in w h ich the adsorp tion energy is p ropo rtiona l to the

p rodu ct o f the area o f the adsorbed m olecule and the cohesive energy

density. Th is re la tionsh ip is given in the present m odel as

ln [C iff/C ifP] = ln lK 'J = [v j/fR U M G i - 8p)2]

- [Vi/(R T)M (5i - 5f)2] (3 .31)

ln lk ’J = ln [V f/V p] + (V tR D M tfi - 8p)2]

- [V i/IR D M fS i - 8f)2] (3 .32)

E ^ = (R D lnlK 'i) = v^ /S -lA -S i2 + B] (3 .33)

48


where the p ropo rtion a lity constants, A and B, are determ ined

experim enta lly. The m o la r adsorp tion coefficient is correlated to the

H ildebrand so lu b ility param eter and m olar volum e by the fo llow ing

equation:

This theoretica l model may be compared w ith a model using a

m odifica tion o f Equation 3.32 to describe adsorption o f substances on

the fille r phase. Since the entire m olecule does n o t partic ipa te in the

adsorption process, the p a rtia l m o lar volum e, v’i, o f the surface-active

func tion a l group may be substitu ted fo r the to ta l m olar volum e, Vj, in

E quation 3.32. In such cases, the m olar adsorption coefficient m ay be

estim ated as follows:

where V 'f is the in te rfac ia l layer volum e and V f/V p is the active volum e

ra tio , w h ich is determ ined experim enta lly.

From Equation 3.27, the d iffus ion se lectiv ity between substance i

and j is given by

talk'd = ln[Vf/Vp] + [vi2 /3 /(RT)].[A.5i2 + B] (3 .34)

talk'd = ln[V'f/V p] + [VCRUM tSi - 8p)2]

- [vyO R D H G i - 8 f)2] (3 .35)

Di.s/Dj.s = ([1 + k'j]/[l + k'i)}

• expHiV(RT)]«[Vil/3 - y /3 ] } (3 .36)

49


where the molar adsorption coefficients, k'j and k'j, are obtained from

the experimental solutions for Equation 3.34 or Equation 3.35.

The d is trib u tio n and d iffus ion -re ten tion models have been

evaluated fo r a silicone elastom er membrane th a t contains a fum ed-

s ilica fille r. The experim ental mem brane separation param eters and

th e ir corre la tions w ith the models are presented below.

CORRELATION OF DATA TO THE MODEL

E xperim enta l conditions

The m em brane used to investigate the corre la tion o f s o lu b ility

param eters w ith perm eability was a silicone elastom er, composed by

w eight o f 69% poly(dim ethylsiloxane) and 31% fum ed s ilica (0.011-

jim diam eter particles). The membrane was a S ilas tic™ silicone

elastom er ho llow fib e r (2.5-cm length, 0.0305-cm i.d ., 0.0635-cm o.d.)

from Dow C om ing C orporation. The ho llow fib e r was m ounted in a

sta in less-steel tee as shown in Figure 3.2.

Gas-phase samples were prepared by in jec tin g know n am ounts

o f the substances o f in te rest in to a n itrogen-filled 5-L Saran™ gas

sam pling bag (22, 23). The concentration o f organic substances was

su ffic ie n tly low to prevent sw elling o f the mem brane (less tha n 0 . 1%

by volum e gas phase). The samples were analyzed im m ediate ly a fte r

p repara tion to m inim ize sorption in to the bag. The gas-phase samples

were pu lled th rough the ho llow fib e r membrane a t a ra te o f 1 0 0 -

cm 3/m in u te w ith a gas pum p from M etal Bellows C orporation.

50


Hollow Fiber Membrane

Sealant to Mass Spectrometer

Permeate

Figure 3 .2 . Hollow fiber membrane perm eation cell.

51


Perm eation m easurem ents were obtained by mass spectrom etry w ith a

H ew lett-P ackard 5971-A Mass Selective D etector m odified fo r process

analysis app lica tions (24). A ll experim ents were perform ed a t 25 °C.

The m em brane separation param eters in c lu d in g enrichm ent

factor, 8 , perm eability, P, d iffu s iv ity , D, and d is trib u tio n ra tio , K, were

determ ined fo r the substances o f in te rest from mass spectra l data in

com bina tion w ith data from lite ra tu re sources. The m ethod fo r the

de te rm ina tion o f these param eters is described in C hapter 2 and in

the A ppend ix o f th is w ork. The enrichm ent facto r (£ i/N 2 = P i/P ^ )

values were determ ined from mass spectrom etric response ra tios and

m o la r response factors (25), as described previously (26). The

pe rm eab ilities were estim ated from these experim enta lly determ ined

en richm ent factors and a lite ra tu re value fo r Pn2 (26), where Pj =

£ i/N 2 (exP)#PN2 (lit)- The d iffu s iv itie s were determ ined us ing E quation

3.23 and the perm eation ra te curves generated from the mass

spectrom etric experim ents (26). The d is trib u tio n ra tio , Kit in th is

s tudy replaces the H enry's law so lu b ility coefficient (S* = Pi/D i s)

tra d itio n a lly used in gas perm eation studies. The d is trib u tio n ra tio o f

the substance between the gaseous m obile phase and membrane

s ta tiona ry phase is s im p ly the product o f S* and the to ta l feed pressure

(26), where K, = Ci>s/C i>m = Sj*76 cm Hg.

In order to provide a com prehensive tes t o f the theore tica l

m odels, a w ide varie ty o f substances w ith d iffe ring size and chem ical

fu n c tio n a lity was examined in th is study. These substances include

perm anent gases, alkanes, ch lorinated and brom inated hydrocarbons,

52


Table 3 .1 . Molar volum es (vj) and Hildebrand solubility param eters (6}) from R eferences 1, 12, and 28.

m olar volum e s o lu b ility param eter com pound cm3/m o le fJ /c m 3 ) 1/ 2gasesn itro g e n 32 .4 5.3oxygen 33 .0 8.2argon 57.1 10.9carbon d ioxide 55.0 12.3alkanesm ethane 52.0 11.6ethane 70.0 13.5propane 85.0 13.6butane 101.4 13.9pentane 116.2 14.3hexane 131.6 14.9heptane 147.4 15.1arom atic hydrocarbonsbenzene 89 .4 18.8to luene 106.8 18.2ethylbenzene 123.1 18.0cblorom ethanesch lo rom ethane 55.4 19.8d ich lo rom ethane 63.9 19.8ch lo ro fo rm 80.7 19.0carbon te trach lo ride 97.1 17.6cbloroethenesch lo roe thene 6 8 . 1 16.01 ,1 -d ich lo ro e the ne 79.0 18.6tric h lo ro e th e n e 90.2 18.8te tra ch lo ro e th e n e 101.1 19.0brom om ethanesbrom om ethane 56.1 19.6d ib rom om ethane 68.9 22.3brom o fo rm 87.5 21.8alcoholsm ethano l 40 .7 29.7e thano l 58.5 26.01-p ropano l 75.2 24.31-butanol 91.5 23.3

53


Table 3 .2 . E xperim ental perm eation param eters fo r sub stan ces in asilicone e lastom er m em brane a t 25 °C.

com pound PfX103)a D cfX 1 0 3)b Scgasesn itro g e n 0.028 2 1 0.0013oxygen 0.053 2 1 0.0025argon 0.053 2 1 0.0025carbon dioxide 0.33 13 0.026alkanesm ethane 0.13 16 0.0079ethane 0.33 1 1 0.030propane 0.80 6.4 0.13butane 1 .0 6.3 0.16pentane 6.9 4.5 1.5hexane 8 . 8 3.5 2.5heptane 2 2 3.2 7.0aromatic hydrocarbonsbenzene 13 4.9 2 . 8to luene 27 3.5 7.6ethylbenzene 42 1.7 25chlorom ethaneschlorom ethane 1.9 1 1 0.17d ich lo rom ethane 9.7 9.1 1 .2ch lo ro fo rm 1 2 4.9 2.4carbon te trach lo ride 1 2 2.9 4.2chloroethenesch lo roe thene 1 .6 9.1 0 . 2 11 , 1 -d i ch lo roe thene 8 . 0 5.8 1.4trich lo ro e th e n e 18 3.7 4.8te tra ch lo ro ethene 45 2.4 19brom om ethanesbrom om ethane 1.9 9.1 0 . 2 1dibrom om ethane 16 4.2 3.8brom oform 67 1.3 52alcoholsm ethanol 5.3 0.42 13ethanol 1 1 0.40 281 -p ropano l 13 0.47 281-butanol 14 0.50 29

a U n its fo r perm eability are cm3 (STP) • cm / [ s • cm 2 • cmHg] b U n its fo r d iffu s iv ity are cm2/sc U n its fo r s o lu b ility are cm3 (STP)/[cm 3 polym er*cm Hg].

54


alcohols, and arom atic hydrocarbons. As shown in Table 3.1, the

m o la r volum es o f these substances vary from 32.4 to 147.4 cm3/m o le

and the s o lu b ility param eters vary from 5.3 to 29.7 (J /cm 3 ) 1/ 2 (2, 10,

28). The values fo r the membrane separation param eters, Pj, D i s, and

Sj m easured fo r these substances are sum m arized in Table 3.2. These

data illu s tra te th a t perm selectivity fo r these substances in the silicone

elastom er m em brane is determ ined predom inantly by the re la tive

so lub ilities . The so lub ilities vary by as m uch as fo u r orders o f

m agnitude whereas the d iffus iv ities fo r m ost o f the substances vary by

less th a n a facto r o f ten. However, a com parison between the

d iffu s iv itie s o f the alcohols and those o f the alkanes illu s tra te s the

in fluence o f the s ilica fille r on the ra te o f mass transport. The

d iffu s iv itie s fo r the alcohols are very low and e xh ib it no apparent

dependence upon m olar volum e. I t is clear th a t re ten tion by the

h ig h ly po la r s ilica fille r m ust be considered to enhance the predictive

value o f the model.

D istribu tion selectivity

The constan t a and the so lu b ility param eter fo r the membrane

s ta tiona ry phase, Ss, from Equation 3.16 were calculated

sim ultaneously. Rearrangement o f Equation 3.16 yie lds the fo llow ing

re la tion :

IRT/V iH lnfK i) + 1] = 2*[8S - cc]-^ + [a2 - 8S2] (3 .37)

The p lo t o f [R T/vjK lnfK j) + 1] vs. Sj in Figure 3.3 y ie lds a s tra ig h t line

w ith a slope o f 2»[8S - a] = 21.8 and y-in te rcep t o f [a2 - 8S2] = -223.

55


>I-cc

600.0

500.0

400.0

300.0

200.0

100.0

0.0

- 100.0

- 200.0

10 15 20

Solubility Prameter

25 30

Key:X = gasesd a rk c irc les = alkanes c irc les = arom atics d a rk diam onds = chlorom ethanes diam onds = chloroethenes tria ng le s = brom om ethanes d a rk squares = alcohols.

Figure 3 .3 . Correlation betw een distribution ratio and solubility param eter for substances in a silicone elastom er membrane a t 25 °C.

56


By sim ultaneous so lu tion o f these equations, experim ental values are

obtained fo r a = 4 .8 (J /cm 3 ) 1/ 2 and 5S = 15.7 (J /cm 3)1/ 2. The

s o lu b ility param eter reported in the lite ra tu re fo r

po ly(d im ethylsiloxane) is 14.9 (J /cm 3 ) 1/ 2 (29). The value fo r the fille d

s ilicone m em brane is expected to be h igher due to the po la r na tu re o f

the s ilica fille r, whose estim ated so lu b ility param eter is 32.2

(J /c m 3 ) 1/ 2 (30). The so lu b ility param eter fo r a m ix tu re is estim ated

from the co n trib u tio n s o f the in d iv id u a l com ponents according to

E quation 3.9 (8 ). W hen the s o lu b ility param eter values and the volum e

fra c tio n s (4>p = 0.75, O f = 0.25) fo r the polym er and fille r are

su b stitu te d in to E quation 3.9, the calcu lated s o lu b ility param eter fo r

the s ta tio na ry phase is 19.2 (J /cm 3)1/ 2. The discrepancy between th is

ca lcu la ted value and the experim ental value o f 15.7 (J /cm 3 ) 1/ 2

suggests th a t the fille d m em brane does n o t e xh ib it the mass tra nspo rt

p roperties th a t w ou ld be expected fo r a homogeneous m ix tu re o f the

in d iv id u a l phases. In add ition , the fille r is im perm eable so th a t

so rp tion occurs on ly in the volum e associated w ith the p o ly m e r/fille r

in te rfa c ia l layer. Since the volum e o f th is in te rfa c ia l layer is d iffic u lt to

define, the experim enta lly determ ined value fo r 5S w ill be used in the

presen t m odel.

The experim ental values fo r the d is trib u tio n ra tios and the

theore tica l values calcu lated from E quation 3.16 are given in Table 3.3.

The d is tr ib u tio n selectiv ities, K i/K j, w ith respect to m ethane and to

m ethanol were determ ined experim enta lly and were calcu la ted using

the m odel described by E quation 3.17. These values are presented in

Table 3.4.

57


Table 3 .3 . E xperim ental and th eo re tica l d istrib u tio n ra tio s forsubstances in a silicone elastom er m em brane, a t 25 °C.

d is trib u tio n ra tiocom pound exp. theor.gasesn itro g e n 0 . 1 0 0.090oxygen 0.19 0 . 2 0argon 0.19 0.51carbon dioxide 1.9 0.99alkanesm ethane 0.60 0 . 6 8ethane 2.3 2.7propane 9.7 3.1butane 1 2 9.5pentane 1 2 0 23hexane 190 80heptane 530 2 0 0aromatic hydrocarbonsbenzene 2 1 0 310to luene 580 650ethylbenzene 1900 1600chlorom ethaneschlorom ethane 13 39dich lo rom ethane 93 79ch lo ro fo rm 180 180carbon te trach lo ride 320 2 0 0chloroethenesch lo roe thene 13 1 21 ,1 -d ich lo roe thene 1 0 0 1 2 0trich lo ro e th e n e 370 330te trach lo roe thene 1400 880brom om ethanesbrom om ethane 16 37dibrom om ethane 290 550brom oform 3900 2700alcoholsm ethanol 950 390ethanol 2 1 0 0 1 2 0 01 -p ropano l 2 1 0 0 40001 -butanol 2 2 0 0 13000

58


T able 3 .4 . E xperim ental and th eo re tica l d istrib u tio n se lec tiv itie sfo r su b stances rela tive to m ethane an d to m ethano l in a siliconeelasto m er m em brane a t 25 °C.

d is trib u tio n se lectiv ityre la tive to m ethane re la tive to m ethanol exp. theor. exp. theor.com pound

gases n itro g e n oxygen argoncarbon dioxide alkanes m ethane ethane propane butane pentane hexane heptane arom atic hydrocarbonsbenzene 350to luene 950ethylbenzene 3100chlorom ethanes ch lo rom ethane 2 1d ich lo rom ethane 150ch lo ro fo rm 310carbon te trach lo ride 530 chloro eth en es ch lo roe thene 2 21 ,1 -d ich lo ro e th ene 170tric h lo ro e th e n e 610te tra ch lo ro e th e n e 2400brom om ethanes brom om ethane 26d ib rom om ethane 480b rom o fo rm 6500alcoholsm ethano l 1600ethano l 35001 -p ropano l 35001-butanol 3600

0.13 1.1X10-4 2.3X10-40.30 2.0X10 ' 4 5.2X10-40.75 2.0X10-4 1.3X10-31.5 2.0X10 -3 2.5X10-3

1 .0 6.3X10-4 1.8X10-34.0 2.4X10-3 7.0X10-34.5 0 . 0 1 0 8.0X10-314 0.013 0.02534 0 . 1 2 0.0591 2 0 0 . 2 0 0 . 2 1290 0.56 0.51

450 0 . 2 2 0.79950 0.60 1.72400 2 . 0 4.2

57 0.014 0.0991 2 0 0 . 1 0 0 . 2 0270 0.19 0.47290 0.33 0.50

17 0.014 0.030180 0 . 1 1 0.31480 0.38 0.831300 1.5 2.3

54 0.017 0.095800 0.30 1.43900 4.1 6.9

570 1 .0 1 .01800 2 . 2 3.15900 2 . 2 1 02 0 0 0 0 2.3 34

0.170.310.313.2

1.03.81620190320880

59


The corre la tion between the experim enta l and theore tica l values

appears qu ite reasonable fo r m ost o f the substances. W hereas the

d is trib u tio n ra tios vary over a range greater tha n fo u r orders o f

m agnitude, the difference between the experim enta l and theore tica l

values is typ ica lly w ith in a facto r o f two or three. W ith few exceptions,

the se lectiv ity data show s im ila rly good corre lations. The m ost

s ig n ifica n t discrepancy is seen fo r 1 -bu tano l, where the theore tica l

d is trib u tio n se lectiv ity is a facto r o f s ix greater tha n the experim enta l

value. The experim enta l se lectiv ities fo r the alcohols are qu ite s im ila r,

as are the so lu b ility param eters (Table 3.1). Conversely, the

theore tica l se lectiv ities fo r the alcohols more closely fo llow the m o la r

volum e th a n they do the s o lu b ility param eter. The theore tica l

se lectiv ities are consisten t w ith the experim enta l se lectiv ities fo r the

o ther classes o f substances studied. These data suggest th a t the -OH

group dom inates the sorp tion process fo r the alcohols.

D iffus ion selectivity

I f no adsorption on the fille r occurs, the d ififus iv ity o f a m olecule

in a given m em brane is dependent upon the size o f the m olecule and

is independent o f chem ical properties (Equation 3.20). W ith

correction fo r to rtu o s ity (Equation 3.25), a p lo t o f ln [( l + <$»f/2)»(Di s)]

vs. Vj1/ 3 is shown in F igure 3.4 fo r substances in the fille d mem brane.

A lthough a ll substances w ith in a given class exh ib it a lin e a r

re la tionsh ip , a single line is no t observed fo r a ll classes as predicted

th e o re tica lly .

60


The presence o f two d is tin c t phases in the m em brane, a non

po la r polym er phase and a po lar s ilica phase, resu lts in a m arked

decrease in d iffusive flow fo r the substances w ith greater hydrogen-

bonding character. As the fun ction a l groups e xh ib it greater hydrogen

bonding (i.e. -OH > -B r > -C l > -CH3 ), the behavior deviates fu rth e r

fro m a sim ple co rre la tion w ith m o lar volum e. These deviations are

pred icted by E quation 3.27. In the m ost extreme case, the

d iffu s iv itie s o f the alcohols show no corre la tion w ith m o la r volum e,

w h ich suggests th a t on ly the p a rtia l m o la r volum e o f the -OH group is

involved in re ten tion on the s ilica fille r. For c la rity , the arom atic

hydrocarbons and chloroethenes are n o t shown in th is p lo t. The

d iffu s iv ity behavior o f the arom atic hydrocarbons closely fo llow s th a t o f

the alkanes and the chloroethenes e xh ib it tra n sp o rt p roperties ve iy

s im ila r to the chlorom ethanes.

I f the alkanes are assumed to d iffuse th rough the m em brane

w ith o u t re te n tio n by the s ilica (k 'i = 0 ), then the slope o f the

regression lin e in F igure 3.4 gives the value fo r the polym er-

dependent term , ft, in Equation 3.27, w hile the pre-exponentia l te rm ,

D 0 p, is found from the in te rcep t (not shown). T h is p lo t suggests th a t

d iffu s io n in the polym er is described by:

D ip = 8.25X10-4*e x p [-l.0 6 ^ / 3 ] (3 .38)

In the d iffu s ion -re te n tion (D-k) m odel o f E quation 3 .27 fo r

d iffu s iv ity in the fille d elastomer, bo th the physica l and chem ical

p roperties o f the system are considered. To p red ic t d iffu s iv itie s in

61


>(03•*-

Qc

-1 0 .0

- 11.0

- 12.0

-13.0

-14.0

-15.0

3.00 3.50 4.00 4.50 5.00 5.50

(Molar Volume)

Key:X = gasesda rk circles = alkanes da rk diam onds = chlorom ethanes triang les = brom om ethanes d a rk squares = alcohols.

Figure 3 .4 . Correlation between diffusivity, corrected for tortuosity, and th e molar volum e for substances in a silicone elastom er membrane at 25 °C.

62


the fille d elastom er, i t is necessary to estim ate k 'j by means o f e ithe r

E quation 3.34 o r 3.35. In the model described by Equation 3.34, the

p ro p o rtion a lity constants A and B were determ ined from a p lo t o f the

surface free energy, [R T /(N 1/ 3 *vi2 / 3 )]*[ln (k 'i) - ln(V f/V p)] vs. the

cohesive energy density, Sj2, where the actua l fille r to polym er volum e

ra tio , V f/V p = 0.33, was used. From th is p lo t, shown in Figure 3.5, i t

was determ ined th a t A = 1.84 and B = -569 when the Avogadro's

num ber term , N 1/ 3, is incorporated in to these param eters. The

so lu tion fo r the m olar adsorption coefficient now becomes

The m odel described by E quation 3.35 requires knowledge o f

the p a rtia l m o la r volum es o f the surface-active fun c tion a l groups, v 'j.

These p a rtia l m o la r volum es have been defined by Fedors (31) and are

given in Table 3.5.

Table 3 .5 . Partial molar volum es, v’if for surface-active functional groups from R eference 31 .

func tion a l group m olar volum e, cm3/m o le

ln (k ’i) = -1.10 + [vi2/ 3/(R T )]*[1 .84*5 i2 - 569] (3 .39)

Cl 24.026.027.330.031.032.410.0

C l(d isubstitu ted)C l(trisu b s titu te d )B rB r(d isu bstitu ted )B r(trisu b s titu te d )OH

63


>*O)0)cUJ

0)0)

©ow3

C /3

16.00

14.00

12.00

10.00

8.00

6.00

4.00

2.00 CD

0.00 - X x

- 2.00

-4.00

- 6.00

0 100 200 300 400 500 600 700 800 900

Cohesive Energy Density

Key;X = gasesd a rk circles = alkanes c irc les = arom atics d a rk diam onds = chlorom ethanes diam onds = chloroethenes triang les = brom om ethanes d a rk squares = alcohols.

Figure 3 .5 . Correlation betw een surface free energy,[RT/(N1/ 3«V£^/®)l»Pntk,|) - lnCVf/Vp)l, and cohesive energy density, 5i2, for substances in a silicone elastom er membrane, a t 25 °C. The lin e is fitted to the halogenated compound and alcohol data only.

64


P artia l m o la r volum es were n o t used fo r the gases, alkanes, and

a rom atic com pounds, since no s ig n ifica n t o rie n ta tion effects are

predicted fo r these substances. For these substances, i t was assumed

th a t v 'j = Vj. As noted previously, a value fo r the active volum e ra tio ,

V f/V p , was n o t know n. B y com paring the experim ental values fo r

ln (k 'j) and the theo re tica l values fo r ln(K 'i) fo r the series o f alcohols,

the active volum e ra tio was estim ated. Values fo r ln fk 'j) were

determ ined from E quation 3.24 us ing experim enta l d iffu s iv itie s and

E qua tion 3 .36 where

ln (k’i) = ln[{(8.25X10-4/ D i>s)*exp(-1.06*vl/3)} - l] (3.40)

Theore tica l va lues fo r ln (K 'i) were determ ined from E qua tion 3.35

w here

ln (k 'i) - ln tV f/V p ) = ln tK ’j) = [v j/fR n M S j - 14.9]2

- Iv’i/(RTr)]-[5i-32-2]2 (3 .4 1 )

These re su lts are sum m arized in Table 3.6.

Table 3 .6 . Data for determ ining th e active volum e ratio, V f/V p , in a silicon e elastom er membrane at 2 5 °C.

ln (k 'i) ln (K 'j) in (vy v p:com pound Eqn. 3.39 Eon. 3.41 In fk 'i/K .v

m ethano l 3.92 3.57 0.35ethano l 3.49 2.75 0.741-p ropano l 2.94 2.43 0.511-butano l 2.56 2.29 0.27

65


The mean value fo r the active volum e ra tio is 1.6, w h ich is

approxim ate ly five tim es greater tha n the to ta l volum e ra tio , V f/V p =

0.33. T h is re su lt is consistent w ith the expectation th a t the active

fille r surface area o r in te rfa c ia l volum e is expected to be greater tha n

the actua l volum e o f the fille r.

For the s ilica -fille d elastom er, the so lu tion to the D -k m odel

us ing the surface areas o f sorbed substances is given by

D i>s = S ^S X lO '^ e x p I-l.O e -V ii/S l/U

+ 0.33*exp{[vi2 /3 /(R T)]*[1 .84«8i2 - 569]} (3 .42)

The so lu tio n using the p a rtia l m olar volum es o f the surface-active

fu n c tio n a l groups is given by

Di>s = 8.25X10'4«exp[-1.06*Vil/3]/[l

+ 1.6*exp{[V j/ (RT)]• [Si - 14.9]2

- lv 'i /(R T)]*[S i -32.2]2}] (3 .43)

B oth o f these so lu tions were applied to the substances stud ied. The

re su lts are given in Table 3.7 along w ith experim ental d iffu s iv itie s and

theore tica l values calcu lated from Equation 3.38 fo r non-reta ined

tra nspo rt. The D -k models (Equation 3.42 and Equation 3.43)

generally e xh ib it a be tte r corre la tion w ith the experim ental values

th a n does the non-reta ined tra nspo rt model. B oth D -k models

successfu lly p red ic t litt le re ten tion on the fille r by the alkanes b u t

w ide ly va ry ing degrees o f re ten tion fo r the other organic com pounds.

66


Table 3 .7 . E xperim ental and th eo re tica l d iffusivities fo r substancesin a silicone elastom er m em brane a t 25 °C.

diffusivity. X10~6 cm^/stheor.

Eqn. 3.38 Eqn. 3.42compound exp. No Retention D-k Modelgasesnitrogen 21 28 27oxygen 21 28 26argon 21 14 13carbon dioxide 13 15 14alkanesmethane 16 16 15ethane 11 10 9.8propane 6.4 7.8 7.5butane 6.3 5.9 5.6pentane 4.5 4.7 4.4hexane 3.5 3.8 3.5heptane 3.2 3.1 2.9aromatic hydrocarbonsbenzene 4.9 7.2 4.4toluene 3.5 5.4 3.6ethylbenzene 1.7 4.2 2.9chloromethaneschloromethane 11 15 8.0dichloromethane 7.9 12 6.3chloroform 4.9 8.5 5.0carbon tetrachloride 2.9 6.3 4.7chloroetheneschloroethene 9.1 11 9.31,1-dichloroethene 5.8 8.8 5.6trichloroethene 3.7 7.1 4.3tetrachloroethene 2.4 5.9 3.3bromomethanesbromomethane 9.1 14 8.1dibromomethane 4.2 11 2.4bromoform 1.3 7.5 1.6alcoholsmethanol 0.42 22 0.41ethanol 0.40 13 0.641-propanol 0.47 9.4 0.641-butanol 0.50 7.0 0.57

Eqn. 3.43 D-k Model

28271415

16 107.85.94.73.83.1

7.25.44.2

9.07.56.05.3

9.66.4 5.03.9

103.42.4

0.370.520.490.42

67


Table 3 .8 . E xperim en tal and th eo re tic a l (D-k m odel, E q uation 3.42)diffusivity se lec tiv ities for substances relative to m eth an e and tom eth an o l in a silicone elastom er m em brane a t 25 °C.

d iffu s ion se lectiv ityre la tive to methane re la tive to m ethanol

com pound exp. theor. exp. theor.gasesn itro g e n 1.3 1 .8 50 6 6oxygen 1.3 1 .8 50 63argon 1.3 0.90 50 32carbon dioxide 0.81 0.92 31 33alkanesm ethane 1 .0 1 .0 38 36ethane 0.69 0.65 26 23propane 0.40 0.50 15 18butane 0.39 0.38 15 13pentane 0.28 0.30 1 1 1 1hexane 0 . 2 2 0.24 8.4 8.5heptane 0 . 2 0 0.19 7.6 6.9arom atic hydrocarbonsbenzene 0.31 0.24 1 2 8 . 6to luene 0 . 2 2 0 . 2 2 8.4 7.7ethylbenzene 0 . 1 1 0.18 4.1 6.5chlorom ethanesch lo rom ethane 0.69 0.38 26 13d ich lo rom ethane 0.49 0.30 19 1 1ch lo ro fo rm 0.31 0.26 1 2 9.5carbon te trach lo ride 0.18 0.29 6.9 1 0chloroethenesch lo roe thene 0.57 0.58 2 2 2 11 ,1 -d ich lo ro e th ene 0.36 0.31 14 1 1trich lo ro e th e n e 0.23 0.24 8 . 8 8.4te trach lo roe the ne 0.15 0.18 5.7 6 . 6brom om ethanesbrom om ethane 0.57 0.39 2 2 14dib rom om ethane 0.26 0 . 1 0 1 0 3.6b rom o fo rm 0.081 0.071 3.1 2.5alcoholsm ethano l 0 .026 0.028 1 .0 1 .0ethanol 0.025 0.032 0.95 1 .11 -p ropano l 0.029 0.030 1 .1 1 .11-bu tano l 0.031 0.027 1 .2 0.97

68


The so lu tion to the D -k m odel given in E quation 3.42 was used

to determ ine the d iffu s io n selectiv ities (E quation 3.36) re la tive to

m ethane and to m ethanol. The experim enta l and D -k m odel d iffu s ion

se lectiv ities are given in Table 3.8. The re su lts from the D -k m odel

show reasonable corre la tion to experim enta l se lectiv ities re la tive to a

non-re ta ined reference (methane) as w e ll as a h ig h ly re ta ined

reference (m ethanol).

E n ric h m e n t

The co rre la tions between the experim enta lly determ ined

en richm ent factors, E i/j, and the p rodu ct o f the theore tica l d iffu s io n

and d is tr ib u tio n selectivities, (D j/D jM K i/K j), are given re la tive to

m ethane and re la tive to m ethanol in Table 3.9. The theore tica l

d is trib u tio n se lectiv ities were determ ined based on E quation 3 .17 and

the d iffu s io n se lectiv ities were based on the D -k m odel given by the

com bina tion o f Equations 3.36 and 3.42. W ith the notable exceptions

o f 1 -propanol and 1 -butano l, reasonable corre la tion is observed

between the experim enta l and theore tica l en richm ent factors.

For m ost o f the substances stud ied, the devia tion between the

experim enta l and theore tica l values fo r the d is trib u tio n selectiv ities

are opposite in d ire c tio n from the d iffu s io n selectiv ities.

Consequently, these errors compensate fo r one another, such th a t the

enrichm ent factors are accurately predicted. For some substances,

however, these deviations are in the same d irec tion so th a t poorer

co rre la tio n between the experim enta l and the o re tica l enrichm ent

factors is observed.

69


Table 3 .9 . Enrichm ent factors for com pounds relative to m ethane and to m ethanol in a silicone elastom er membrane at 25 °C. Theoretical values were obtained from the product o f distribution (Equation 3.16) and diffusion selectiv ities (D-k m odel. Equations 3 .3 6 and 3.42).

____________enrichm ent facto rs___________re la tive to m ethane re la tive to m ethanolexp. theor. exp. theor.com pound

gasesn itro g e n oxygen argoncarbon dioxide alkanesm ethane ethane propane butane pentane hexane heptanearom atic hydrocarbonsbenzene to luene ethylbenzene chlorom ethanes ch lo rom ethane d ich lo rom ethane ch lo ro fo rm carbon te trach lo ride chloroethenes ch lo roe thene1 ,1 -d ich lo ro e th ene trich lo ro e th e n e te trach lo roe the ne brom om ethanes brom om ethane d ibrom om ethane b rom o fo rm alcohols m ethano l 41ethano l 871-p rop ano l 1 0 01-butano l 1 1 0

0.24 5.2X10 ' 3 0 .0150.52 0 . 0 1 0 0 .0330.67 0 . 0 1 0 0 .0421.3 0 .063 0.085

1 .0 0.024 0 .0632 . 6 0.063 0.172.3 0.15 0.145.2 0.19 0.331 0 1.3 0 .6428 1.7 1 . 856 4.2 3.5

130 2 . 6 8.4230 5.0 15470 7.9 3 0

30 0.35 1.949 1 .8 3.190 2.3 5.791 2.3 5.8

1 0 0.30 0 . 6 667 1.5 4.3140 3.4 8.7290 8 . 6 18

30 0.36 1.9130 3.0 8 . 1410 13 2 6

16 1 .0 1 . 076 2 .1 4.8250 2.5 16740 2.7 4 7

0.220.410.412.6

1.02.66.47.95470180

110210330

15769495

1263140360

15130530

70


E rro r analysis (see Appendix) ind icates th a t the estim ated

re la tive standard deviations fo r the d iffu s iv ity and d is trib u tio n

se lectiv ity m easurem ents are 60 % and the re la tive standard deviation

fo r the enrichm ent facto r m easurem ents are 14 %. In add ition ,

experim ental e rro r m ay re su lt from absorption o f a substance in to the

w a lls o f the sam pling bag used to prepare the m obile phase gas

m ixtu res.

G raphica lly, the corre la tion fo r experim enta l and theore tica l

values fo r the d is trib u tio n , d iffusion , and perm eation selectivities

re la tive to m ethane are shown in Figure 3.6. The same corre la tion fo r

selectiv ities re la tive to m ethanol are shown in Figure 3.7. These p lo ts

dem onstrate the predictive capab ilities o f the model.

A lthough the predictive a b ility o f the model was qu ite good, i t

could be im proved by an expanded s o lu b ility param eter treatm ent th a t

takes in to account specific chem ical in te ractions between the sorbed

substances, the polym er, and the fille r. The consistency o f the model

possib ly suffers from the use o f m olar volum es and so lu b ility

param eters th a t were no t a ll generated by a single researcher.

However, the reasonable application o f a predictive perm eation m odel

us ing read ily available param eters has been dem onstrated fo r a w ide

varie ty o f substances.

71


10.00

8.00

6.00

§ 4.00Ek.0>g- 2.00LU

0.00

- 2.00

- 4.00

- 2.00- 4.00 0.00 2.00 4.00 6.00 8.00 10.00

Theory

Key:circ les = perm eation diam onds = d is trib u tio n ra tio squares = d iffu s iv ity .

Figure 3 .6 . Correlation betw een experim ental and theoretical selectiv ities for substances relative to m ethane in a silicone elastom er at 25 °C.


6.00

4.00

O O2.00

0.00

OD- 2.00

- 4.00

- 6.00

- 8.00

- 10.00

- 10.00 - 8.00 - 6.00 - 4.00 - 2.00 0.00 2.00 4.00 6.00

Theory

Key:circles = perm eation diam onds = d istribution ratio squares = diffusivity.

Figure 3 .7 . Correlation between experim ental and theoretical selectiv ities for substances relative to m ethanol in a silicone elastom er at 25 °C.


REFERENCES

(1 ) C. Hansen and A. Beerbower, S o lu b ility param eters, in : A. S tanden (Ed.), K irk -O th m er Encyclopedia o f Chem ical Technology. Suppl. Vol. 2nd. Ed.: 1971.

(2 ) A. F. M. Barton, S o lu b ility param eters, Chem. Rev. 1975, 75, 731

(3 ) H. B u rre ll, S o lu tion Properties: S o lu b ility Param eter Values, in : J B randrup and E. H. Im m ergut (Eds.), Polymer H andbook. 2nd ed.; W iley-Interscience: New York, NY; 1975.

(4 ) B. Schneier, J . A ppl. Polym. Set 1 972 , 16, 2343.

(5 ) A. F. M. Barton, Handbook o f Polvm er-Liquid In te raction Param eters: CRC Press: Boca Raton, FL; 1990.

(6 ) H. W. S tarkw eather, J r., Macromolecules 1977 , 10, 1161.

(7 ) J . H. H ildebrand and R. L. Scott, The S o lu b ility o fN one lectro lvtes. 3 rd ed.; Reinhold: New York, NY; 1950.

(8 ) J . H. H ildebrand, J . M. Prausnitz, and R. L. Scott, Regular andRelated S o lu tions: Van N ostrand-R einhold: P rinceton, NJ; 1970.

(9 ) B. L. Karger, L. R. Snyder, and C. Eon, AnaL Chem. 1978, 50, 2126.

(1 0 ) V. S tannett, S im ple gases, in : J . C rank and G. S. Park (Eds.), D iffu s io n in Polym ers: Academic Press: New York, NY; 1968.

(1 1 ) H. F. M ark, N. M. B ikales, C. G. Overberger, G. Menges, and J . I. K roschw itz (Eds.), Encyclopedia o f Polym er Science and E ng ineering . Vol. 3; W iley-Interscience: New York, NY; 1985.

(1 2 ) J . M. P rausnitz and F. H. Shair, A.I.CH.E. J. 1961, 7, 682.

74


(13 ) J . C. G iddings, M. N. Myers, L. McLaren, and R A. Keller, Science 1 9 68 , 162, 67.

(14 ) W. W. B randt, J. Phys. Chem., Wash. 1959, 63, 1080.

(1 5 ) K. D. Ziegel, H. K. Frensdorff, and D. E. B la ir, J. Polym. ScL 1969, A-2, 809.

(1 6 ) R M. Barrer, J . A. Barrie, and N. K. Raman, Polymer 1962, 3, 605.

(1 7 ) R M. Barrer, J . A. Barrie , and M. G. Rogers, J. Polym. ScL 1963, A - l, 2565.

(1 8 ) A. S. M ichaels and H. J . B ix le r, J. Polym. ScL 1961, 50, 413.

(1 9 ) G. J . van Amerongen, Rubber Chemistry and Technology 1964, 37, 1065.

(20) S. W u, J. Phys. Chem. 1968, 72, 3332.

(21 ) A. Beerbower, Surface free energy: A new re la tionsh ip to b u lk energies, J. Colloid Interface ScL 1 9 7 1 , 35, 126.

(22 ) L. B. Westover, J . C. Tou, and J . H. M ark, AnaL Chem. 1974, 46, 568.

(2 3 ) S tandard test m ethod fo r C l th rough C5 hydrocarbons in the atm osphere by gas chrom atography, in : 1990 A nnual Book o f ASTM S tandards: Volum e 11.03, ASTM, 1916 Race Street, P h iladelphia , PA, 19103-1187.

(2 4 ) J . C. Fjeldsted, presented a t the Instrum en t Society o f Am erica In te rn a tio n a l Conference and E xh ib itio n , New Orleans, LA, 1990.

75


(25 ) A na lytica l Sciences Mass Spectral Data Base, The Dow Chem ical Co., M idland, M I, in te rn a l com m unication, based on m ethod by V. Caldecourt, AnaL Chem. 1955, 27, 1670.

(26) M. A. LaPack, J . C. Tou, and C. G. Enke, AnaL Chem. 1990, 62, 1265.

(27) M. E. Hodgson, Filtr. and Separ. 1973, Ju ly , 418.

(28) A. F. M. Barton, Handbook o f S o lub ility Parameters and O ther Cohesion Parameters: CRC Press: Boca Raton, FL; 1983.

(2 9 ) G. L. Lee, S. A. S tem , J . E. M ark, and E. Hoffm an, Investigation o f S tructu re -S erm eab ilitv Selationships o f S ilicone Solvm er Sem branes: F ina l Report October 1982 - September 1986, Gas Research In s titu te , Chicago, IL.

(30) P. J . Shoenmakers, H. A. H. B illie t, and L. de Galan, Chromatographia 1982, 15, 205.

(31) R. F. Fedors, Polym. Eng. ScL 1974, 14, 147.


CHAPTER 4

A Model for Characterizing and Predicting Membrane Extractions based on

Chromatographic R etention

As dem onstrated in C hapter 3, the capacity to separate

com ponents in a m ix tu re can be predicted u tiliz in g fundam enta l

separation p rinc ip les. Chrom atography is governed by these same

fundam enta l p rinc ip les and can therefore be a use fu l too l fo r

characte riz ing the so rp tion and tra n sp o rt properties o f polym eric

m ateria ls (1 ,2 ). A m em brane extraction model based upon

chrom atographic p rin c ip les is developed in th is chapter. The effect o f

chem ical properties and experim enta l cond itions on pe rm eab ility

param eters are discussed in the context o f th is model. F ina lly , the

m odel provides a quan tita tive ly use fu l ru le o f thum b w ith sim ple

corre la tions between m em brane extraction efficiencies and such

read ily available data as bo iling po in ts and so lu b ility param eters.

EXPERIMENTAL METHODS

Gas chromatography

The chrom atography colum n was a 15 m eter-long, 250 (im -i.d .,

1 (im -film th ickness DB-1 (poly(dim ethylsiloxane) bonded phase)

ca p illa ry from J& W S cientific , Folsom, CA. The he lium or n itrogen

77


m obile phase lin e a r velocity was 50 cm /s . The colum n tem perature

was 25 °C isotherm al. Mass analysis o f the chrom atographic e ffluen t

was perform ed w ith the firs t quadrupole o f a F inn igan TSQ-70 G C/M S.

The scan ra te was 0.2 seconds/scan fo r a 10-300 da lton range. The

secondary e lectron m u ltip lie r voltage was -1000 V. The dynode

voltage was -2000 V.

M em brane extraction

A flow -th ro ugh silicone ho llow fib e r m em brane separator w ith

m ass spectrom etric detection was used fo r the m easurem ent o f the

perm eation data. The m em brane was a 2.5 cm length o f Dow C om ing

S ilastic™ M edical Grade T ub ing (0.0635 cm o.d., 0.0305-cm i.d ., 69 %

po ly(d im ethylsiloxane), 31 % s ilica by weight) m ounted in a sta in less

steel tee (3). The n itrogen m obile phase flow th roug h the ho llow fib e r

m em brane was 100 cm 3 /m in u te . The m em brane tem perature was 25

°C iso therm al. The perm eation m easurem ents were made w ith the

ME device in te rfaced d ire c tly w ith a H ew lett-Packard 5971-A MSD

quadrupole mass spectrom eter m odified fo r process analysis

app lica tions (4). The scan ra te was 0.3 s /scan fo r a 10-180 da lton

range. The e lectron m u ltip lie r voltage was -1500 V.

Review ing the so lu tio n -d iffu s io n m odel (5), perm eation th roug h

a m em brane m ay be described by three processes: 1) selective

p a rtitio n in g o f a substance between the m em brane s ta tiona ry phase

and the m obile phase, 2 ) selective d iffu s io n o f the substance th rough

the m em brane phase, and 3) desorption o f the substance from the

78


m em brane phase in to a sweep flu id o r vacuum . The perm eation rate,

F j, fo r a com ponent, i, is described by F ick 's firs t law :

Fj = A#Dis «Kj*cim /d (4.1)

where A is the m em brane surface area, Dsi is the d iffu s iv ity o f

com ponent i in the sta tiona ry (membrane) phase, K j is the d is trib u tio n

ra tio fo r com ponent i in e q u ilib riu m between the m em brane s ta tiona ry

phase and the m obile phase, ci>m is the concentra tion o f com ponent i

in the m obile phase, and d is the m em brane th ickness. The product

D j sK i is the perm eab ility constant, Pj, fo r com ponent i in the

m em brane. J u s t as w ith chrom atography, the a b ility o f a m em brane

phase to separate tw o com ponents from a m obile phase is dependent

upon bo th therm odynam ic (d is trib u tio n ra tio ) and k in e tic (d iffus iv ity)

param eters. The ana ly tica l power o f membranes lies in th e ir a b ility to

provide an enriched analyte stream to the analyzer. The perm eation

en richm ent factor, S j/ j, fo r com ponent i over com ponent j is given by

the re la tive perm eation rates o f the two com ponents norm alized w ith

respect to th e ir concentrations in the sam ple

The m ethod fo r de term in ing m em brane perm eation param eters

such as d is trib u tio n ra tios and d iffu s iv ities is described in de ta il in the

A ppendix o f th is w ork. In th is chapter, the two selective processes

(d is trib u tio n and d iffusion) are discussed separately and then th e ir

im p lica tio n s to the extraction process are presented.

£ i/ j = [Fi/Fj]/[ci<m/cj,m] = [Di,s/D j>s]*[K i /K j ] = P j/P , (4.2)

79


RETENTION AND DISTRIBUTION

The difference in the a b ility o f two d iffe ren t phases to solvate a

substance is a m ajor d riv ing force fo r m any membrane and

chrom atographic separation processes. These solvation processes

have been shown to exh ib it a fundam ental re la tionsh ip th a t m ay be

described by regu la r so lu tion theory, as m odified by F lo iy-H uggins (6 -

8 ). H ildebrand et. a l. (9) have proposed th a t the so lu b ility o f a gas in a

liq u id solvent can be described as a two-step process invo lv ing firs t

the com pression o f the gas in to some hypothetica l liq u id state

followed by sorp tion o f th is hypothetica l liq u id in to the solvent. The

extension o f th is model to gases dissolving in a polym er, w ith F lo iy -

Huggins correction, has been given in C hapter 3 as follows:

ln lK J = [vi /R T ]*[(5 i - cx)2 - (6 j - 8S)2] - 1 (4 .3)

W here Kj is the concentration d is trib u tio n ra tio (ci>s/C i m), v4 is the

m olar volum e o f the p a rtition in g substance i, R is the ideal gas

constant, T is the absolute tem perature, 8 j and 8S are the so lu b ility

param eters fo r the p a rtitio n in g com pound i and the s ta tiona ry phase,

respectively, and a is an experim enta lly determ ined constan t th a t

corrects fo r non-ideal behavior and approxim ates the so lu b ility

param eter o f the hypothetica l compressed m obile phase. Values fo r

m o la r volum es, so lu b ility param eters (7, 8 , 10), and bo ilin g p o in t

tem peratures (11) used in these stud ies are presented in Table 4.1.

80


Table 4 .1 . Molar volum es, Hildebrand solubility param eters (7, 8, 10), and boiling points (11) for th e com pounds used in th is study.

com pound v}, cm3/m o le 8 ^ (MPaU/2 Tb, Kn itro g e n 32.4 5.3 77.4oxygen 33.0 8 . 2 90.2argon 57.1 10.9 87.5carbon dioxide 55.0 12.3 194.7m ethane 52.0 1 1 . 6 109.2ethene 65.0 13.5 169.5ethane 70.0 13.5 184.6propane 89.4 13.4 231.1butane 101.4 13.9 272.7pentane 116.2 14.3 309.3hexane 131.6 14.9 342.2heptane 147.4 15.1 371.6benzene 89.4 18.8 353.3to luene 106.8 18.2 383.8ethylbenzene 123.1 18.0 409.4chlorobenzene 1 0 2 . 1 19.4 405.2ch lo rom ethane 55.4 19.8 249.0d ich lo rom ethane 63.9 19.8 313.3ch lo ro fo rm 80.7 19.0 334.9carbon te trach lo ride 97.1 17.6 349.7ch lo roe thene 6 8 . 1 16.0 259.81 ,1 -d ich lo ro e th ene 79.0 18.6 310.2tr ic h lo ro ethene 90.2 18.8 360.2te trach lo roe the ne 1 0 1 . 1 19.0 394.2brom om ethane 56.1 19.6 276.8d ibrom om ethane 68.9 22.3 370.2brom ofo rm 87.5 2 1 . 8 422.7w a te r 18.0 47.9 373.2m ethanol 40.7 29.7 338.1ethanol 58.5 26.0 351.71 -p ropano l 75.2 24.3 370.62 -p ropano l 76.8 23.3 355.61-butanol 91.5 23.3 390.4acetone 74.0 20.3 329.42 -butanone 90.1 19.0 352.8

81


For ide n tica l m obile and sta tiona ry phases, the

chrom atograph ica lly determ ined d is trib u tio n ra tio fo r an analyte w ill

be the same as th a t determ ined from perm eation m easurem ents. The

e q u ilib riu m d is trib u tio n o f a substance between the s ta tiona ry and

m obile phases m ay be determ ined from chrom atographic re ten tion

tim es and the phase ra tio us ing the fo llow ing re la tion :

K i = k j.p = [(tr i- t0) / t 0 ]*[V m/V s] (4 .4)

where lq is the m o la r p a rtitio n coefficient, t r i is the e lu tion tim e fo r a

re ta ined com ponent i, to is the e lu tio n tim e fo r a non-re ta ined

com ponent, and p is the vo lum etric phase ra tio .

The d is trib u tio n ra tios fo r several substances obtained from GC

and ME m easurem ents are given in Table 4 .2 . The d is trib u tio n ra tio

fo r the perm anent gases is so low th a t th e ir re ten tion in the

chrom atographic s ta tiona ry phase is essentia lly zero. The tim e

observed fo r the e lu tion o f the a ir peak (N2, 0 2, A r, and C 02 are no t

separated) is taken to be to. In practice, n itrogen ca rrie r gas is more

representative o f the a ir sam ple m a trix th a t is reported in m ost ME

applications, w h ile he lium is a m ore com m on ca rrie r gas since its

low er density allows fo r h ighe r lin e a r velocities (12). As dem onstrated

in Table 4.2 , no s ign ifica n t differences are observed in the GC

re ten tion tim e data when the tw o d iffe ren t ca rrie r gases are used.

The ME data described below were obtained w ith n itrogen

ca rrie r gas w h ile the GC data were obtained w ith he lium ca rrie r gas.

82


T able 4 .2 . E xperim en tal d istrib u tio n ra tio s, K{, d eterm in ed by MEand GC a t 25 °C.

ME w ith N2 GC w ith He GC w ith N2com pound m obile phase m obile phase m obile phasen itro g e n 0 . 1 0 0 . 0 0 . 0oxygen 0.19 0 . 0 0 . 0argon 0.19 0 . 0 0 . 0carbon dioxide 1.9 0 . 0 0 . 0m ethane 0.60 0 . 0 _

ethene 2 . 2 3.1 _

ethane 2.3 3.1 -

propane 9.7 6 . 2 -

butane 1 2 2 1 -

pentane 1 2 0 67 64hexane 190 190 180heptane 530 530 490benzene 2 1 0 310 290to luene 580 870 820ethylbenzene 1900 2 2 0 0 2 0 0 0chlorobenzene 1600 1800 1700chlo rom ethane 13 1 2 -

d ich lo rom ethane 93 81 77ch lo ro fo rm 180 190 180carbon te trach lo ride 320 330 300ch lo roe thene 13 19 -

1 ,1 -d ich lo ro e th e n e 1 0 0 76 73trich lo ro e th e n e 370 45 0 420te trach lo roe the ne 1400 1300 1 2 0 0brom om ethane 16 28 -

dib rom om ethane 290 410 380brom o fo rm 3900 2 2 0 0 2 1 0 0w ate r 340 9.3 -

m ethanol 950 15 23ethanol 2 1 0 0 37 411-p rop ano l 2 1 0 0 1 1 0 1 2 02 -p rop ano l 834 56 591-butano l 2 2 0 0 310 330acetone 1 0 0 0 49 502 -butanone 1500 140 150

83


W ith in experim enta l error, m ost o f the com pounds th a t e xh ib it weak

o r no hydrogen bonding show good agreement fo r the two techniques.

The effect o f the s ilica partic les dispersed in the m em brane is

apparent when com paring the d is trib u tio n ra tios obtained by the two

techniques fo r the strong hydrogen bonding substances. The s ilica

provides a hydrogen-bonding com ponent to the membrane, re su ltin g

in a m uch h igher a ffin ity fo r com pounds th a t e xh ib it hydrogen bonding

th a n does the otherw ise non po la r silicone phase.

J u s t as w ith chrom atographic systems, the capacity o f the

m em brane to perform therm odynam ic separations decreases as the

tem perature o f the system increases. Th is effect is shown in Figure

4.1 in the p lo t o f K* vs. T fo r various components. Due to the presence

o f the s ilica in the membrane, a dram atic difference in the position o f

the curves fo r 1-butano l is seen when com paring the ME data (Figure

4.1a) w ith the GC data (Figure 4.1b). Since they exh ib it little a ffin ity

fo r the s ilica , the non po lar com pounds in these p lo ts dem onstrate

nearly ide n tica l behavior between the two systems. The tem perature

dependence o f the d is trib u tio n ra tio illu s tra te d in these p lo ts is given

b y the fo llow ing re la tion :

a d n lK iD M l/T ) = -AHSi/R (4.5)

where AHgi is the difference in entha lpy o f so lu tion fo r the substance

in the s ta tiona ry phase and the m obile phase (AHSi = H g ifs ta tionary

phase) - Hsi(m obile phase)). Values fo r AHgj were obtained from the

slope o f a p lo t o f ln lK j] vs. 1 /T fo r selected com pounds and are

84


(a)

2500

2000 - •

1500

jo 1000 - ■

500

0 20 8040 60 100

Temperature, °C

(b)

2500

2000 - ■o

11 1500 - ■co1000 - ■

3■O

£a 500 - ■

0 20 40 60 80 100

Temperature, °C

Key;X = carbon te trach lo ride square = 1-butano l diam ond = chlorobenzene tria ng le = toluene.

Figure 4 .1 . The effect o f temperature on th e stationary phase/m obile phase distribution ratio, Kj, obtained by ME (a) and byGC(b).

85


presented in Table 4.3. Generally, AHsi values fo r gas-phase organic

com pounds are negative, and the m agnitude o f AHsi ind ica tes the

a b ility o f the silicone sta tiona ry phase to extract the com pound from

the m obile phase. Deviations in these AHsi determ inations m ay re su lt

from in te ractions between the com pounds and the s ilica fille r as w ell

as im precis ion in chrom atographic e lu tio n tim e and perm eation

m easurem ents.

Table 4 .3 . Values for th e heats o f solution for selected com pounds in th e membrane and chromatographic stationary phases.

H gi (kJ/m o le)

com pound M E GCn itro g e n - 8

heptane -27 -33to luene -34 -3 4chlorobenzene -48 -36carbon te trach lo ride -31 -291-butano l -46 -31

By the H ildebrand ru le (6 ), a strong corre la tion exists between

the so lu b ility param eter and the bo ilin g po in t, Tbi. fo r a substance.

Thus, a corre la tion also exists between ln lK J and Tbi where, fo r a

hom ologous series o f com pounds, the corre la tion m ay be given by (13)

ln lK i) = m *Tbi + b (4 .6)

86


(a)

9.00 -r

7.00 Oo

5.00

= 3.00o cc □> 1.00

-1 .0 0

- 3.00

50 150 250 350 450

Boiling Point Temperature, °C

(b)

9.00

7.00

5.00

- = 3.00COo cco 1.00

- 1.00

- 3.00

50 150 250 350 450


Key;square = weak or non-hydrogen bonding com pound circle = strong hydrogen bonding com pound.

Figure 4 .2 . The correlation o f th e distribution ratio, K*, w ith boiling point, Tbi, a t 25 °C, obtained by MB (a) and by GC (b).

87


where M is the slope and B is the y-ax is in te rcep t fo r the p lo t o f ln [K j]

vs. Tbi* A p lo t o f ln [K |] vs. Tbi is given fo r the ME and GC data in

F igure 4.2. The com pounds th a t e xh ib it strong hydrogen bonding are

seen to deviate s ign ifica n tly from the s tra ig h t lin e p lo t re su ltin g from

lin e a r regression o f data fo r the com pounds th a t e xh ib it weak o r no

hydrogen bonding. For the silicone m em brane a t 25 °C, th is line a r

regression yie lds values fo r the slope, where m = 2 .85X 10 '2, and fo r

the y-in te rcep t, where b = -4 .38. For the low est b o ilin g p o in t

com pounds, d is trib u tio n ra tios could n o t be determ ined by gas

chrom atography because no re ten tion was observed. However, even

w ith fewer data po in ts, the chrom atographic experim ents yie lded a

nearly ide n tica l lin e w ith a slope m = 2 .87X 10 '2 and the in te rcep t b =

-4 .37. M ost o f the strong hydrogen bond ing com pounds e xh ib it ln [K j]

values th a t are h igher than predicted by the s tra ig h t line p lo t fo r the

ME experim ents (Figure 4.2a). Th is re s u lt is consistent w ith the

a ffin ity o f these com pounds fo r the s ilica in the m embrane. In the

case o f the GC data, a p lo t o f ln lK J vs. Tbi yie lds a negative deviation

from a s tra ig h t lin e p lo t fo r the hydrogen bonding com pounds (Figure

4.2b) because hydrogen bonding in te ractions re s u lt in b o ilin g po in t

tem peratures th a t are h igher tha n predicted from d ispersion

in te ra c tio n s alone (14).

The se lectiv ity o f the m em brane to perform a given

therm odynam ic separation on the basis o f know n b o ilin g po in ts can be

pred icted from w ith a general form o f E quation 4.6 .

K i/K j = exp{2.85X10-2.(Tbi-Tbj)} (4.7)

88


Table 4 .4 . D istribu tion se lec tiv ities for com pounds over n itrog enand h ep tan e a t 25 °C. Tj, = p red ic ted from boiling p o in ts (E quation4.7); SP = predicted from solubility param eter theory (Equation4.3); ME = experim ental from ME data; GC = experim ental fromGC data.

relative to nitrogencomDOund l b SP MEnitrogen 1.0 1.0 1.0oxygen 1.4 2.3 1.9argon 1.3 5.7 1.9carbon dioxide 28 11 19methane 2.5 7.6 6.0ethene 14 26 22ethane 21 30 23propane 80 49 97butane 260 106 120pentane 740 260 1200hexane 1900 890 1900heptane 4400 2200 5300benzene 2600 3400 2100toluene 6200 7200 5800ethylbenzene 13000 18000 19000chlorobenzene 11000 15000 16000chloromethane 130 430 130dichloromethane 830 880 930chloroform 1500 2000 1800carbontetrachloride 2300 2200 3200chloroethene 180 130 1301,1 -dichloroethene 760 1300 1000trichloroethene 3200 3600 3700tetrachloroethene 8300 9800 14000bromomethane 160 400 150dibromomethane 4200 6100 2900bromoform 19000 30000 39000water 4600 1600 3400m ethanol 1700 4300 9500ethanol 2500 14000 210001 -propanol 4300 44000 210002-propanol 2800 28000 83001-butanol 7500 150000 22000acetone 1300 2800 100002-butanone 2600 4200 15000

relative to heptanel b SP ME GC2.2X10-4 4.5X10-4 1.9X10-4 03.3X10-4 1.0X10-3 3.6X10-4 03.0X10-4 2.6X10-3 3.6X10-4 06.5X10"3 5.0X10-3 3.6X10-3 05.7X10-4 3.4X10-3 1.1X10-3 03.2X10'3 1.2X10-2 4.1X10-3 5.8X10-34.8X10-3 1.4X10-2 4.3X10-3 5.8X10-31.8X10"2 2.2X10-2 1.8X10-2 1.2X10-26.0X10-2 4.8X10-2 2.2X10-2 3.9X10-20.17 0.12 0.22 0.120.43 0.40 0.36 0.361.0 1.0 1.0 1.00.59 1.5 0.40 0.581.4 3.3 1.1 1.62.9 8.2 3.5 4.12.6 6.9 3.1 3.33.0X10-2 0.20 2.4X10-2 2.3X10-20.19 0.40 0.17 0.150.35 0.93 0.35 0.36

0.54 0.99 0.60 0.614.1X10-2 5.8X10-2 2.4X10-2 3.5X10-20.17 0.62 0.20 0.140.72 1.6 0.69 0.841.9 4.5 2.7 2.56.7X10-2 0.19 3.0X10-2 5.2X10-20.96 2.8 0.55 0.764.3 13 7.4 4.21.0 0.72 0.64 1.7X10-20.39 2.0 1.8 2.9X10-20.57 6.2 3.9 6.9X10-20.97 20 4.0 0.200.63 13 1.6 0.101.7 68 4.1 0.580.30 1.3 2.0 9.2X10-20.59 1.9 2.8 0.27

89


Exam ples o f d is trib u tio n se lectivities are given in Table 4.4 along

w ith those predicted by m odified regu la r so lu tion theory (Equation

4.3) and by bo ilin g p o in t corre la tions (Equation 4.7). Since n itrogen is

assumed to be non retained by the GC sta tionary phase, the

se lectiv ities com pared w ith n itrogen cannot be presented fo r the

chrom atographic data. Instead, d is trib u tio n se lectivities w ith respect

to heptane are presented fo r bo th ME and GC as w ell as the

se lectiv ities predicted from E quation 4.7. A lthough the hydrogen

bonding substances deviate from the values predicted by E quation 4.7,

s ig n ifica n t se lectiv ities fo r these com pounds (i) w ith respect to

n itrogen (j) are s till p redicted fo r the membrane.

The predictive m odels and the data dem onstrate th a t the

d is trib u tio n ra tio se lectivities increase as the m o lar volum e (or

m o lecu lar weight) o f the com pounds increase w ith in a series. For a

se lectiv ity m odel, a facto r o f tw o o r three difference between the

predicted values and the experim enta l values m ay be considered qu ite

good considering th a t one o f the m ost w idely used ME app lica tions o f

separating organic analytes from a ir is a process th a t favors the

analytes by one to fo u r orders o f m agnitude. W ith a few exceptions,

m ost o f the se lectiv ity data re la tive to n itrogen meet th is c rite rio n . As

expected, the pred ictions based upon the bo ilin g po in ts show the

greatest deviation from the experim ental data fo r the com pounds th a t

e xh ib it strong hydrogen bonding. Using the s o lu b ility param eter

m odel, the predicted se lectiv ity fo r 1-bu tano l is a fac to r o f seven

h ighe r tha n observed by the M E m ethod. An expanded m odel (7, 15)

th a t conta ins specific s o lu b ility param eters fo r dipole in te ractions and

90


hydrogen bond ing m ay provide b e tte r corre la tions. However, even the

sim ple m odels in the present w ork provide a reasonably qu an tita tive

approxim ation .

Except fo r the strong hydrogen bond ing com pounds, the

se lectiv ity values re la tive to heptane obtained b y M E are in excellent

agreement w ith the values obtained b y GC. The values predicted by

the s o lu b ility param eter m odel show less agreem ent fo r the m ost p a rt

because heptane exh ib its a fac to r o f m ore th a n tw o h ighe r d is trib u tio n

ra tio th a n is predicted by the model, as discussed in C hapter 3. In any

case, the therm odynam ic re la tion sh ip between the M E and the GC

processes is evident and the ru les th a t guide the use o f one technique

read ily app ly to the other.

BAND SPREADING AND DIFFUSION

The band w id th s o f chrom atographic peaks are h ig h ly d iffu s io n -

dependent as described b y the Van Deem ter equation (16) fo r packed

colum ns and the Golay equation (17) fo r open tubes. The Golay

equation states th a t fo r open tu b u la r colum ns, effective theore tica l

p la te he ight, h it fo r a com ponent is the sum o f p la te he igh t

co n trib u tio n s from the sta tiona ry phase, h i>s, and from the m obile

phase, h i m, where

h j = h j s + h i m (4 .8)

The p la te he igh t co n trib u tio n s in b o th phases are due to tra n sp o rt in

bo th the ra d ia l, r, and lo n g itu d in a l, 1, d irections in the colum n, where

91


î.s — î.sr + î,sl (4 .9)

and

h i.m — ^ i.m r + ^ i.m l (4 .10)

Therefore, band spreading is due to lo n g itu d in a l d iffu s ion and ra d ia l

d iffu s ion in bo th phases. Bandspreading in the s ta tiona ry phase is

dependent upon the d iffu s iv ity , Di s o f com ponent i, in the sta tiona ry

phase o f th ickness d, the p a rtitio n coefficient, k i, and the lin e a r

ve locity o f the m obile phase, u, where

Bandspreading in the m obile phase is dependent upon the in n e r

rad ius, r, o f the open tu b u la r colum n, the p a rtitio n coefficient, the

lin e a r ve locity o f the m obile phase, and the d iffu s iv ity , D j m, o f

com ponent i in the m obile phase gas, where

h i.sr = [2 /3 M k i / ( l+ k i)2 ][d2 /D itS]u (4 .11)

and

h ilSi = 2*D iiS.k i/u (4 .12)

h i.m r = [(l+ 6 *k i+ l l * k i2 )/(2 4 .( l+ k i)2)][r 2 /D i,m]u (4 .13)

and

92


him i = 2*D i<m/u (4 .14)

Values fo r Di m are read ily estim ated from the m ethod developed

b y F u lle r, Shettler, and G iddings (18) where, in a he lium m obile

phase,

D im = 1.75X10-3.T*[(Mi+MHe)/(M i.M He)]1/2

where T is the absolute tem perature, M j and MHe are the m olecular

w eights fo r the com ponent i and he lium , respectively, and p is the gas

pressure. In the present model, the em pirica l m o lecular d iffus ion

volum e fo r substance i, (Xv)j, given by the sum o f the em pirica l

d iffu s ion volum es fo r the atoms com prising substance i and the atom ic

d iffu s ion volum e o f he lium , VHe, are replaced by m o lar volum e term s,

Vj, given in Table 4.1, factored by Avogadro’s num ber, NA, where

By com bining and rearranging Equations 4.8, 9, 11, and 12, the

fo llow ing quadratic equation is obtained fo r de term in ing d iffu s iv ities in

the sta tionary phase:

/{p .[(E v)i l / 3 + V Hei/3 ]2 } (4 .15)

(Ev)i = V j /N A (4 .16)

0 = [2*Vu]*Di>s2 - [hr h iim]*Di>s + [2/3M ki/( l+ k i)2].d2.u (4.17)

The so lu tion fo r Di s is given by

93


DiiS = [hr h im ]»u /[4 *k i]

- Klhi-h i.m]»u /I4«k i])2 - ll/3 ]* [d*u /(l+ k i)]2}i/2 (4 . i 8)

E xperim enta lly, the p la te he ight, h j, is determ ined from the

co lum n length, L, the experim enta l re ten tion tim e, t r i, and the band

w id th a t h a lf m axim um , W j, (19) where

^ = L*Wi2 /(5 .5 4 *tri2) (4 .19)

C alculated gas-phase d iffus iv ities, long itud ina l and ra d ia l

com ponents o f band spreading, and experim ental p la te he ights are

sum m arized in Table 4.5 fo r the com ponents o f in te rest. The

m easurem ents o f W j are made w ith m uch less ce rta in ty fo r poorly

re ta ined com pounds. In fact. W j was im possible to determ ine fo r some

o f these com pounds under the present experim ental cond itions,

because on ly two or three data po in ts could be obtained fo r an e lu ting

band, w hich was an in su ffic ie n t num ber to obta in a m easurable peak

p ro file . T h is common problem is d iffic u lt to resolve w ith a scanning

in s tru m e n t (20). A th icke r chrom atographic s ta tiona ry phase m ig h t

help a lleviate th is problem , b u t w ou ld re su lt in extrem ely long

re ten tion tim es and broad bands fo r the com pounds w ith h igher

b o ilin g po in ts. Recording the analog signal from , fo r example, a flam e

ion iza tion detector m igh t provide more accurate pro files. However,

band overlap a t h igher tem peratures w ould pose an even m ore serious

problem . The mass spectrom eter provides an add itiona l degree o f

separation in such cases.

94


Table 4 .5 . Mobile phase diffusivities, Dt ni, and chromatographic band spreading com ponents used to calculate diffusivities in the stationary phase at 25 °C.

com poundn itro g e noxygenargoncarbon dioxidem ethaneetheneethanepropanebutanepentanehexaneheptanebenzeneto lueneethylbenzenechlorobenzenechlo rom ethaned ich lo rom ethanech lo ro fo rmcarbon te trach lo ridech lo roe thene1 ,1 -d ich lo ro e th enetrich lo ro e th e n ete trach lo roe the nebrom om ethanedibrom om ethanebrom ofo rmw ate rm ethano lethanol1 -p ropano l2 -p ropano l1-butanol acetone2 -butanone

Di.m ^i,m rfEqn. 4.151 fEan. 4.131

0.32 1.2X1 O'30.31 1.2X1 O'30.25 1.5X10'30.26 1.4X10'30.28 1.3X1 O'30.24 2.4X1 O'30.24 2.4X1 O'30.21 3.2X1 O'30.20 7.4X1 O'30.19 9.3X1 O'30.18 1.6X10'20.17 2.1X10-20.21 1.5X10*20.19 1.9X10*20.18 2.2X10-20.19 2.0X10-20.25 3.5X1 O'30.24 8 .1X1 O'30.21 1.3X10*20.20 1.6X10-20.23 4.6X10-30.22 8.6X1 O'30.20 1.7X10-20.19 2.0X10-20.25 5.5X10-30.23 1.5X10-20.20 1.9X10-20.40 1.9X10'30.29 3.4X1 O'30.25 6.5X10-30.22 1.3X10-20.22 9.2X10-30.20 2.0X10-20.22 8.5X10-30.21 1.6X10-2

^ i.m l h ifEqn. 4.141 fEan. 4.191

1.1X10-2 -1.1X10-2 -

8.8X10*3 -

8.8X1 O'3 -

9.7X10"3 -

6.5X10"3 -

6 .3X10*3 -

5.6X10"3 -6.9X10-3 -

6.4X1 O’3 5.1X10-26.1X10'3 4.6X10-25.8X1 O’3 3.8X10-27.2X10"3 4.0X10-26 .6X1 O'3 3.3X10-26.2X10'3 4.3X10-26.7X10’3 3.4X10-26.8X1 O'3 4.2X10*28.2X1 O'3 3.6X10-27.4X10"3 4.0X10-26.8X10*3 4.6X10-26.2X1 O'3 8.8X10-27.5X10-3 4.3X10-27.1X10*3 3.6X10-26.7X10'3 3.6X10-26.6X1 O'3 7.4X10-27.8X10*3 3.1X10-27.1X10’3 3.4X10*21.1X10-2 3.7X10-27.7X10"3 3.9X10-26 .6XIO-3 5.1X10-26.0X1 O'3 0.115.9X10*3 4.0X10-25.5X10"3 9.4X10-26.0X10*3 3.9X10-25.5X10*3 4.7X10-2

95


For organic substances in po ly(dim ethylsiloxane), d iffu s iv itie s are

typ ica lly less th a n 1X1 O' 5 cm2/s and m o la r p a rtitio n coefficients, k j,

are typ ica lly less tha n 100. Consequently, lo n g itu d in a l band-

broadening in the sta tiona ry phase (Equation 4.12) m ay be neglected

to y ie ld the fo llow ing so lu tion fo r Di s:

In some app lica tions where very narrow bore colum ns and h igh

lin e a r ve locity m obile phases are used, the m obile phase com ponents

o f band spreading, h* m, m ay also be neglected (2). U nder these

conditions, the d iffu s iv ity o f a substance in the sta tiona ry phase can be

estim ated e n tire ly from experim enta l data com bin ing E quations 4.19

and 2 0 , a fte r su b s titu tin g u = L /to and k j = (tri-t0) / t 0 to yie ld the

fo llo w in g sim ple re la tion :

From Table 4.5, i t is apparent th a t fo r the experim ental

cond itions in the present study, band spreading in the m obile phase is

n o t neglig ib le. Therefore, Equations 4.18 o r 4.20 are applicable to the

cu rre n t w ork. W ith in three s ign ifica n t figures, id e n tica l resu lts are

obtained fo r ca lcu la tions using Equations 4.18 and 4.20, ind ica ting

th a t h j si is neglig ible. Values fo r Di s determ ined fo r the m em brane

and the chrom atographic phase, us ing E quation 4.20, are provided in

Table 4 .6 . The d iffu s iv itie s in the m em brane fo r com pounds th a t

e xh ib it hydrogen bonding are low er when com pared w ith the da ta fo r

DitS = [2 /3 M k i/ ( l+ k i)2 ].[d 2 .u ]/[h i-h i>m] (4 .20)

Di>s = 3 .69*d2 .(tr i- t0)/W i2 (4 .21)

96


Table 4 .6 . D iffusivities at 25 °C in the stationary phase for com pounds o f in terest determ ined by membrane extraction experim ents (ME), and gas chrom atographic experim ents (GC).

com pound M Epentane 4.4X10-6hexane 3.6X10-6heptane 3.2X10-6benzene 4.8X10-6to luene 3.6X10-6ethylbenzene 1.7X10-6chlorobenzene 1.8X10-6ch lo rom ethane 1.1X10-5d ich lo rom eth ane 8.0X10-6ch lo ro fo rm 4.8X10-6carbon te trach lo ride 2.9X10-6ch lo roe thene 9.0X10-61 ,1 -d ich lo ro e th e n e 5.9X10-6tric h lo ro e th e n e 3.8X10-6te tra ch lo ro e th e n e 2.3X10-6brom om ethane 9.0X10-6dib rom om ethane 4.2X10-6b rom o fo rm 1.3X10-6w a te r 2.5X10-6m ethano l 4.2X10 -7

ethano l 4.0X10 -7

1 -p rop ano l 4.6X10-72 -p rop ano l 3.2X10-71-bu tano l 4.8X10*7acetone 5.0X10-72 -butanone 8.6X10-7

GC fEan. 4.201 2.7X10 ' 6

2.9X10-6 3.1X10-6 2.9X10-6 3.6X10-6 6.9X10 ' 7

1.7X10-6 2.2X10-6 4.8X10-6 3.6X10-6 2.3X10-6 1.1X10-6 3.6X10-6 3.3X10-6 1.7X10-6 1.7X10-6 5.3X10-6 1.3X10-6 2.3X10-6 2.9X10-6 3.1X10-6 1.2X10-6 5.1X10*6 1.0X10-6 5.1X10-6 4.1X10-6

97


the GC sta tionary phase. Th is effect is due to adsorption o f these

com pounds on the s ilica in the membrane. Th is adsorp tion re su lts in

decreased d iffusive transport, as described below. W hile the

trea tm ent resu lting in Equation 4.21 w ill be discussed again,

ca lcu la tions from the m ore rigorous Equation 4.20 w ill be used in the

corre la tions w ith membrane extraction data.

D iffu s iv itie s increase w ith increasing tem peratures, as illu s tra te d

in Figure 4.3 fo r d iffu s iv itie s fo r selected com pounds in the m em brane

vs. tem perature. Th is effect resu lts in narrow er chrom atographic

bands fo r GC analyses and faster response to steady state in membrane

extraction analyses. The effect o f tem perature on d iffu s iv ity is

described by the A rrhen ius re la tion

3(ln [D iiS]) /a ( l/T ) = -EDi/R (4 .22)

where EDi is the energy o f activa tion fo r d iffus ion . The activa tion

energies fo r d iffu s ion fo r selected com pounds were obtained and are

presented in Table 4.7. The activa tion energies fo r d iffu s io n are

always positive so th a t d iffus ion increases w ith increasing tem perature.

As stated above, because the d iffu s iv ities increase w ith increasing

tem peratures, the m easurem ents o f and W j by GC were made w ith

less re lia b ility a t tem peratures h igher tha n 25 °C. The d iffu s iv ity in

the m em brane fo r 1-bu tano l and other strong hydrogen-bonding

substances are decreased re la tive to the other com pounds when

com pared w ith the data fo r the GC sta tionary phase (Table 4.7). Th is

98


o©WOJE0CO1oX

’ >

CO3

12

10

6

4

0

0 20 40 60 80 1 0 0

Temperature, °C

Bey:X = carbon te trach lo ride square = 1-butano l d iam ond = chlorobenzenetria ng le = toluene

Figure 4 .3 . The effect o f tem perature on diffusivity, Di s, in th e ME stationary phase.

99


is a re su lt o f the adsorp tion o f the hydrogen-bonding substances on

th e s ilica in the m em brane.

Table 4 .7 . Values for th e activation energies for diffusion for selected com pounds in th e membrane stationary phase.

E pi (kJ /m o le l

com poundn itro g e nheptaneto luenechlorobenzenecarbon te tra ch lo rid e1 -bu tano l

M E161517231430

In the free-volum e theory o f d iffu s io n (21), d iffus ive tra n sp o rt o f

a substance in an u n fille d , ru b b e iy polym er is re lated to the m o la r

volum e o f the substance as described in C hapter 3. T h is re la tionsh ip

can be expressed as follows:

w here D* p is the d iffu s iv ity o f com ponent i in the polym eric

m em brane, the pre-exponentia l term , D0 p, is the d iffu s iv ity o f some

hypothe tica l substance w ith zero m o la r volum e, and 0 is a constant

th a t is re la ted to the free-volum e and the cohesive energy density o f

the polym er. In add ition , the b o ilin g po in ts o f a hom ologous series o f

w eak o r non hydrogen bonding com pounds d isp lay a d ire c t

Di,p = Do>p*exp{[-0/(RT)].vi l/3} (4 .23)

100


relationship w ith molecular diameter and, therefore, w ith Vj1/ 3.

Consequently, a use fu l corre la tion may be obtained from a p lo t o f

ln f l /D j s) vs. Tb i, as shown in Figure 4.4. The so lu tion to the curve in

F igure 4.4a fo r the com pounds th a t e xh ib it weak o r non hydrogen

bonding shows a slope o f 6 .96X 10 '3 and an in te rcep t o f 10.1. Because

o f the in a b ility to determ ine the d iffu s iv itie s o f the com pounds w ith

low b o ilin g po in ts (i.e., the poorly re ta ined com pounds) by the

chrom atographic m ethod, the line p lo tted in Figure 4.4b was obtained

from the ME data. The d iffu s ion se lectiv ity w ith the silicone

m em brane m ay be estim ated from

D i>s/D j,s = exp{6.96X lO -3*(Tbj-Tbi)} (4 .24)

Again, the effect o f s ilica on the tra n sp o rt o f the strong hydrogen

bond ing substances is observed in the ME m easurem ents. The s ilica

in h ib its the d iffusive tra n sp o rt o f these substances in a process a k in to

fro n ta l o r in te g ra l chrom atography (22). T h is re ten tion process is

described in C hapter 3 by the fo llow ing re la tion :

D i,p /D i.s = 1+k’i (4.25)

w h ich is derived from the d e fin itio n o f chrom atographic re ten tio n

(2 3 ),

t r / t D = 1+k'i (4 .26)

and the so lu tion fo r de term in ing d iffu s ion in a m em brane (24),

101


(a)

16.0

o 15.0©>C >. 14.0

13.0

12.0CO303z

11.0

10.050 250150 350 450


(b)

16.0

15.0

14.0>%.c >- « 13.0 o =O) —

3 Q 12.0

11.0

10.050 250150 350 450


Key:square = weak o r non-hydrogen bonding com pound c irc le = strong hydrogen bonding com pound

Figure 4 .4 . The correlation o f diSusivity, Di s, w ith boiling point, Th , a t 25 °C, obtained by MB (a) and by GC (b).

102


Di>s = 0 .1 4 .d 2 /t50 (4 .27)

where Di s is the d iffusive transpo rt th a t is observed w ith re ten tion by

the s ilica phase, D ip is the d iffu s iv ity th rough the polym er phase in

the absence o f a re tentive phase, k 'j is the m o la r p a rtitio n coefficient

fo r com pound i a t e q u ilib riu m between the s ilica and polym er phases,

and t 5 Q is the tim e required to achieve 50 % steady state perm eation

fo llow ing a step change in concentration in the m obile phase. The

d iffu s iv ity o f substance in polym ers con ta in ing fille rs have also been

shown to be effected by the to rtuous path the substances m ust trave l

(25) so th a t the re la tion describ ing the effect o f a fille r on d iffus ive

tra n sp o rt is given by

where Of is the volum e fraction o f the fille r in the s ta tiona ry phase. In

the case o f the silicone elastom er, Of = 0.25. I t is easily seen th a t fo r

the chrom atographic s ta tiona ry phase (or fo r an u n fille d membrane),

the values fo r k 'j and O f are zero so th a t Di s = Di p. By com bining

Equations 4.23 and 4.28, the fo llow ing general so lu tion to the

re ten tion-m od ified d iffu s ion process is obtained:

D i>s = Di>p/ [ 1 + k 'iM 1+ (O f/2)] (4 .28)

D i,s = Do p *exp {[-0 /(R T )]*v i 1/3 } /{ [ l+ k ,i]* [l+ (O f/2 )]} (4 .29)

The constant values D0 p, 0 , and O f have been determ ined

experim enta lly (Chapter 3) to y ie ld the fo llow ing so lu tion fo r

d iffu s iv itie s in the silicone elastom er a t 25 °C:

103


T>i s = 8.25X10-4*expi-1 .06*V ii/3}/[i + k «j ( 4 .3 0 )

I t is believed th a t the forces th a t govern separations by liq u id -

so lid chrom atography (26, 27) also govern th is re ten tion and w ou ld

therefore depend upon the na tu re o f bo th the po lym er phase and the

fille r phase. For describ ing the process o f a substance p a rtitio n in g

between a perm eable m obile phase and an im perm eable s ta tio na ry

phase, i.e ., adsorption, the m o la r area, ra th e r th a n the m o la r volum e o f

the p a rtitio n in g substance is typ ica lly used (6-9, 15). In liq u id -so lid

chrom atography, the therm odynam ic descrip tion has been presented

as a lin e a r re la tionsh ip between energy o f adsorp tion and the square o f

the s o lu b ility param eter (15). S im ila rly , the fo llow ing re la tion sh ip has

been shown in C hapter 3 to describe the process o f adsorp tion o f a

substance onto a s ilica fille r from a poly(dim ethylsiloxane) phase:

ln (k 'i) = ln (V f/V p) + [vi2 /3 /(RT)][A .8 i2 + B] (4 .31 )

where the fille r/p o ly m e r volum e phase ra tio , V f/V p, is know n to be

0.33, and the constants A and B have been experim enta lly determ ined

in C hapter 3. W ith these values, and com bin ing Equations 4.29 and

4.30, the fo llow ing so lu tion to the d iffu s io n -p a rtitio n process is given:

D is = S ^S X lO ^-e xp l-l.O e -V i1/ 3}

/ [ l + 0.33*exp{[V i2/3/(R T)]*[ 1 .84*8^ - 569]}] (4 .32 )

Presented in Table 4 .8 are the d iffu s ion selectivity, D i s/D j/s, values

predicted from th is equation and from the b o ilin g p o in t m odel

104


Table 4 .8 . D iffusion se lec tiv ities fo r com pounds over n itro g en andov er h e p ta n e a t 25 °C. Tj, = p red ic ted from boiling p o in t m odel(Equation 4.24); SP = predicted from solubility param eter theory (Equation 4.31); ME = experim ental from ME data; GC = experim ental from GC data.

relative to n itrogen relative to heptan ecompound l b SP ME Tb SP ME GCnitrogen 1.0 1.0 1.0 6.7 9.1 6.6 -

oxygen 0.91 1.0 1.0 6.2 8.8 6.6 -

argon 0.93 0.50 1.0 6.3 4.5 6.6 -

carbon dioxide 0.44 0.51 0.62 3.1 4.7 4.1 -

m ethane 0.80 0.55 0.76 5.4 5.0 5.0 -

ethene 0.52 0.40 0.52 3.7 3.7 3.4 -

ethane 0.47 0.36 0.52 3.3 3.3 3.4 -

propane 0.34 0.25 0.30 2.5 2.3 2.0 -

butane 0.26 0.21 0.30 1.9 1.9 2.0 -

pentane 0.20 0.16 0.21 1.5 1.5 1.4 0.88hexane 0.16 0.13 0.17 1.2 1.2 1.1 0.93heptane 0.13 0.11 0.15 1.0 1.0 1.0 1.0benzene 0.15 0.16 0.23 1.1 1.5 1.5 1.0toluene 0.12 0.14 0.17 0.92 1.2 1.1 1.1ethylbenzene 9.9X10'2 0.11 8.1X10-2 0.78 1.0 0.53 0.22chlorobenzene 0.10 0.11 8.6X10-2 0.80 1.0 0.56 0.56chlorom ethane 0.30 0.30 0.52 2.1 2.7 3.4 0.70dichlorom ethane 0.19 0.23 0.38 1.5 2.1 2.5 1.6chloroform 0.17 0.19 0.23 1.1 1.7 1.5 1.2carbontetrachloride 0.15 0.18 0.14 0.91 1.6 0.83 0.73chloroethene 0.28 0.34 0.43 2.1 3.1 2.8 0.371,1 -dichloroethene 0.20 0.21 0.28 1.5 1.9 1.8 1.2trichloroethene 0.14 0.16 0.18 1.1 1.5 1.2 1.1tetrachloroethene 0.11 0.12 0.11 0.72 1.1 0.75 0.54bromomethane 0.25 0.30 0.43 1.8 2.8 2.8 0.56dibromomethane 0.13 8.9X10-2 0.20 1.0 0.81 1.3 1.7bromoform 9.0X10-2 5.8X10-2 6.2X10-2 0.72 0.53 0.41 0.40water 0.13 2.3X10-4 0.12 0.99 2. lXlO'3 0.78 0.74m ethanol 0.16 1.5X10-2 2.0X10-2 1.2 0.14 0.13 0.93ethanol 0.15 2.4X10-2 1.9X10-2 1.1 0.22 0.13 0.991 -propanol 0.13 2.4X10-2 2.2X10-2 1.0 0.22 0.15 0.392-propanol 0.14 3.9X10-2 1.5X10-2 1.1 0.36 0.10 1.61-butanol 0.11 2.1X10-2 2.3X10-2 0.89 0.19 0.16 0.32acetone 0.17 0.16 2.4X10-2 1.3 1.4 0.16 1.72-butanone 0.15 0.15 4.1X10-2 1.1 1.4 0.27 1.3

105


(E quation 4.24) fo r selective d iffu s ion over n itrogen and heptane fo r

the com pounds studied. Again, the bo iling p o in t model exh ib its the

poorest co rre la tion w ith the ME data fo r the strong hydrogen bonding

com pounds. The bo ilin g p o in t model typ ica lly pred icts re la tive

d iffu s iv itie s th a t are five to ten tim es h igher th a n observed by ME fo r

these com pounds. On the other hand, th is model yie lds good

co rre la tion w ith the GC data. The so lu b ility param eter model fo r the

m em brane considers the effect o f the s ilica on the d iffusive tra n sp o rt

and y ie lds a very good corre la tion fo r m ost o f the com pounds. The

com pounds th a t yie ld low d is trib u tio n ra tios fo r the GC sta tionary

phase y ie ld the poorest corre la tion between the GC and ME data

because o f the in a b ility to accurately measure the w id ths o f these GC

bands as discussed above.

J u s t as w ith the d is trib u tio n ra tio selectivities, the d iffus ion

se lectiv ities m ay be modeled by the chrom atographic process. For the

best corre la tion , bo th the GC and the ME phases should be iden tica l,

since the presence o f polym er additives and fille rs m ay s ig n ifica n tly

a ffect the therm odynam ic and k in e tic tra nspo rt properties. As

dem onstrated, the presence o f such additives and fille rs m ay be taken

in to account us ing know n chrom atographic princ ip les.

EFFICIENCY AND ENRICHMENT

Since the perm eation enrichm ent factor, Sj/j = (Di>s/D jtS)(Kj/Kj),

is com prised o f param eters th a t have been characterized by so lu b ility

param eter theory, then the enrichm ent facto r m ay be modeled by

106


com bining Equation 4.3 fo r the d is trib u tio n ra tio w ith E quation 4.32

fo r the d iffu s iv ity .

From chrom atography, the d is trib u tio n se lectiv ity m ay be

w ritte n as

K i/K j = k i/k j = (tj-j—10)/( tj- j—10) (4 .33)

and from Equation 4.20, a fte r su b s titu tin g u = L /to and k j = (t^ -to )/tQ

the d iffu s ion se lectiv ity m ay be w ritte n as

D i,s /D j>s = U tri-toJ/C trj-to ll-ttrj/tj-il^^^lC hj-h j m) /(h i-h i>iri)] (4 .34)

Therefore, the re la tion sh ip between the perm eation enrichm ent

factor, S j/j = (Di s /D j sKK j/K j), and chrom atographic m easurem ents

m ay be w ritte n as follows:

£ i/ j = [(tr i- to ) /( tI j- t0) l2 .[tI j / t r i]2 .[(h j -h jiin ) /(h r h i ,m)] (4 .35)

I f ideal conditions prevail, where the band spreading in the m obile

phase is negligible, then Equation 4.21 is used to determ ine

d iffu s iv itie s so th a t the re la tionsh ip between the perm eation

enrichm ent facto r and chrom atographic m easurem ents is given by:

8 i / j = rWj / W j] 2 • [ (t r l-10) / (t^ -10) ] 2 (4 .36)

107


Since the chrom atographic effective theore tica l p la te num ber

fo r com ponent i is defined as (19)

N j = S ^ -K tr t- to J /W ja (4 .3 7 )

The re su ltin g re la tion sh ip between S and N can be expressed as

E i/j = (N j/N j) (4 .38)

The effect o f tem perature on the enrichm ent fac to r is given by

a o n E i/ jj/a d /n = -a e p/ r (4 .3 9 )

where AEp is the difference in activa tion energy fo r perm eation

between com pounds i and j, given by AEp = Epr Epj. Values o f EPi fo r

selected com pounds in the silicone elastom er are given in Table 4.9.

Table 4 .9 . Values for th e activation energies for perm eation for selected com pounds in the membrane stationary phase.

E Pi fkJ /m o le l

com pound M En itro g e n 8heptane -12to luene -17chlorobenzene -25carbon te trach lo ride -171-butanol -16

108


The activa tion energy fo r perm eation is in fact the sum o f the

heat o f so lu tion and the activa tion energy fo r d iffus ion . In the case o f

the s ilicone s ta tio n a iy phases, the heats o f so lu tion fo r m ost organic

com pounds are greater in m agnitude th a n th e ir activa tion energies fo r

d iffu s io n , therefore an increase in tem perature re su lts in a reduced

pe rm eab ility . The p lo ts o f lnfPj) vs. tem perature in F igure 4.5

dem onstrate th e dom inance o f the d is trib u tio n ra tio in the effect th a t

tem perature has on the perm eation o f organic com pounds in the

silicone m ateria ls. For gases such as n itrogen and oxygen, the

ac tiva tion energies fo r d iffu s ion dom inate so th a t th e ir perm eabilities

increase w ith increasing tem perature. The re su lt is th a t as the

tem peratu re increases, the enrichm ent fac to r fo r the organic

com pounds over n itrogen (and a ir) decreases. Since m easurem ents o f

the chrom atographic band w id th s a t tem peratures above 25 °C were

n o t re liab le , these data are no t shown.

The p lo t o f ln [£ (i/N 2 )l vs. Tbi shown in Figure 4 .6 illu s tra te s the

dom inance th a t the d is trib u tio n ra tio exh ib its fo r the perm eation

process. The co rre la tion between enrichm ent fac to r and b o ilin g p o in t

fo r the non- and w eakly hydrogen bonding com pounds is given by

S i/j = exp{2.15X10-2.(Tb i-Tbj)} (4 .40)

w h ich is the p rodu ct o f Equations 4.7 and 4.24. The hydrogen

bond ing com pounds show a reasonable corre la tion w ith the lin e

p lo tted fo r the com pounds th a t e xh ib it weak or no hydrogen bonding.

109


3500

g 3000CO

cviE 2500 oCOo 2000 X^ 1500

« 1000 ©E® 500

80 1000 20 40 60

Temperature, °C

Key:X = carbon te trach lo ride square = 1-bu tano l d iam ond = chlorobenzene tria n g le = toluene.

Figure 4 .5 . The effect o f tem perature on perm eability, Pj, in the MB stationary phase.

110


CD>ocCDE.c'k.cU J

05o

23CO

8.50

7.50

6.50

5.50

cCDO)O

4.50

.•= 3.50Z

2.50

1.50

0.50

-0.50

50 150 250 350 450


Key;square = weak o r non-hydrogen bonding com pound c irc le = strong hydrogen bonding com pound

Figure 4 .6 . The correlation o f enrichm ent factor (over nitrogen),

&1/N2’ TOth boiling point, Tw , for data obtained by ME at 25 °C.

i l l


T h is im proved corre la tion m ay be due to the in h ib ite d d iffu s ion from

the s ilica being offset by enhanced p a rtitio n in g .

The enrichm ent factors over n itrogen and over heptane are

presented in Table 4.10 fo r the b o ilin g p o in t and so lu b ility param eter

m odels as w e ll as the ME and N j/N j data. The so lu b ility param eter

m odel showed good corre la tion w ith the ME data fo r the enrichm ent

o f the com pounds over nitrogen. O nly fo r pentane, hexane, heptane,

2 -propanol, and 1-bu tano l do the values predicted from th is m odel

deviate s ig n ifica n tly from the experim ental data. M any o f the values

fo r the se lectiv ity over heptane again showed deviation from the

experim enta l values using th is so lu b ility param eter model. In general,

the co rre la tion between the ME and GC enrichm ent factors was qu ite

good.

FURTHER CONSIDERATIONS

The resu lts described in th is chapter suggest th a t

chrom atographic data m ay be the basis fo r a sim ple and p ractica l

m ethod fo r selecting a membrane fo r a specific separation app lica tion .

In general, i f two com ponents are read ily separated by

chrom atography, then they w ill be read ily separated by a m em brane

composed o f the chrom atographic sta tionary phase. The d is trib u tio n

ra tios fo r com pounds between the sta tionary and m obile phases w ill be

lin e a r w ith the chrom atographic re ten tion tim es, w h ile the

d iffu s iv itie s w ill rough ly be inversely p roportiona l to the re ten tion

tim es. The im p lica tion o f th is "ru le-o f-thum b" to an analysis is th a t the

112


Table 4 .1 0 . E n rich m en t fac to rs fo r com pounds over n itro g en andh ep tan e a t 25 °C. Tj, = p red ic ted from th e boiling p o in t m odel(Equation 4.40); SP = predicted from solubility param eter theory (Equations 4 .3 and 4.32); ME = experim ental from ME data (Pi/Pj);GC = experim ental from GC data (Equation 4.35).

relative to n itrogen relative to h ep tan ecompound l b SP ME l b SP ME GCnitrogen 1.0 1.0 1.0 I.8 XIO- 3 4.1X10-3 1.2X10-3 -oxygen 1.3 2.2 1.9 2.4X10'3 9.0X10-3 2.3X10-3 -argon 1.2 2.8 1.9 2.2X10-3 1.2X10-2 2.3X10-3 -

carbon dioxide 12 5.6 12 2.2X10-2 2.3X10-2 1.5X10-2 -

methane 2.0 4.2 4.6 3.5X10-2 1.7X10-2 5.6X10-3 -

ethene 7.2 11 12 1.3X10-2 4.4X10-2 1.4X10-2 -ethane 10 11 12 1.8X10-2 4.5X10-2 1.5X10-2 -propane 27 12 29 4.9X10-2 5.1X10-2 3.6X10*2 -butane 67 22 36 0.12 9.1X10-2 4.4X10-2 -

pentane 150 42 250 0.26 0.17 0.31 0.11hexane 300 120 320 0.53 0.48 0.39 0.34heptane 560 240 810 1.0 1.0 1.0 1.0benzene 380 560 490 0.67 2.3 0.61 0.55toluene 730 970 960 1.3 4.0 1.2 1.9ethylbenzene 1300 1974 1500 2.3 8.2 1.9 0.91chlorobenzene 1200 1600 1400 2.1 6.8 1.7 1.8chloromethane 40 130 67 7.2X10*2 0.53 8.4X10-2 1.6X10-2dichlorom ethane 160 210 350 0.29 0.85 0.43 0.24chloroform 250 380 430 0.45 1.6 0.53 0.42carbontetrachloride 350 380 440 2.0 1.6 0.54 0.44chloroethene 50 44 57 9.0X10-2 0.18 6.9X10-2 1.3X10-21,1 -dichloroethene 150 280 290 0.27 1.2 0.35 0.16trichloroethene 440 580 650 0.78 2.4 0.80 0.90tetrachloroethene 910 1200 1600 1.6 5.0 2.0 1.4bromomethane 73 120 69 0.13 0.52 8.6X10-2 2.9X10-2dibromomethane 540 540 580 0.97 2.2 0.72 1.3bromoform 1700 1700 2400 3.0 7.1 3.0 1.7water 580 0.37 390 1.0 1.5X10-3 0.48 1.3X10-2m ethanol 270 67 190 0.49 0.28 0.24 2.7X10-2ethanol 360 320 400 0.65 1.3 0.49 6.9X10-21-propanol 550 1100 490 0.98 4.4 0.59 7.9X10-22-propanol 400 1100 130 0.71 4.5 0.16 0.171-butanol 840 3200 520 1.5 13 0.64 0.19acetone 230 450 260 0.40 1.8 0.31 0.152-butanone 370 650 600 0.67 2.7 0.75 0.35


m ore perm eable a com pound is, the longer is its response tim e.

These p rinc ip les are illu s tra te d in the gas chrom atogram and the

perm eation param eters given in F igure 4.7.

In add ition to gas analysis, ana lytica l ME techniques are also

com m only used fo r the analysis o f aqueous samples. The same

p rinc ip les described above m ay be applied to these separations. In the

case o f com pounds th a t e xh ib it weak o r no hydrogen bonding, the

com pounds w ith the lower b o ilin g po in ts e xh ib it h igher enrichm ent

factors over w ater because o f th e ir low so lu b ility in the w ate r as shown

in C hapter 2. The strong hydrogen bonding com pounds p a rtitio n

poorly in to the m em brane from an aqueous m a trix , w hich resu lts in

low perm eabilities.

114


GC ME100D E/N

, 2 s/cm

,39001900

,7700.5900

,2400.1500

bromoform — ethylbenzene

.1600 .5600 .1400chlorobenzene

_© .1400 4200 .1600tetrachloroethene

.580 .2900 .960toluene

.530

.370*290320

*210.180

.31002700.24003400*2000.2000

.810650580440430

_430

heptane

trichloroethene dibromomethane -

carbon tetrachloride - —benzenechloroform

,1000.34

,1700480

^90dichloroethene - pentane

nitrogen

Figure 4 .7 . The correlation o f GC reten tion times w ith MB perm eation param eters at 25 °C.


REFERENCES

(1) B raun, J .-M .; G uille t, J . E. Adv. Polym. Set 1976, 21, 107.

(2) Lloyd, D. R ; W ard, T. C.; Schreiber, H. P., eds. Inverse Gas Chrom atography. ACS Symposium Series; Am erican Chem ical Society: W ashington D.C., 1989.

(3) LaPack, M. A .; Tou, J . C.; Enke, C. G. AnaL Chem. 1990, 62, 1265.

(4) Fjeldsted, J . C. Instrum ent Society o f Am erica In te rna tiona l Conference and E xh ib ition , New Orleans, LA, 1990.

(5) Mears, P. In : Membrane Separation Processes: Mears. P., Ed.; Elsevier: Am sterdam , Netherlands, 1976.

(6 ) H ildebrand, J . H .; Scott, R L. The S o lub ility o f Nonelectrolvtes. 3 rd Ed.; Reinhold: New York, NY, 1950.

(7) Hansen, C.; Beerbower, A. S o lub ility Parameters, In K irk -Q thm er Encyclopedia o f Chem ical Technology. Supp l. Vol., 2nd. Ed.; 1971.

(8 ) Barton, A. F. M. Handbook o f S o lub ility Parameters and O ther Cohesion Parameters: CRC Press, Inc.: Baco Raton, FL, 1983

(9) H ildebrand, J. H .; P rausnitz, J . M .; Scott, R L. Regular andRelated Solutions: VanNostrand-Rheinhold: Princeton, NJ, 1970.

(10) Prausnitz, J . M.; Shair, F. H. A.LCH.E. J. 1961, 7, 682.

(11) Weast, R C., ed. Handbook o f Chem istry and Phvsics.64 th Ed.; CRC Press, Inc.: Baco Raton, 1983.

(12) Jennings, W. Gas Chrom atography w ith Glass C apilla ry C olum ns. 2nd Ed.; Academic Press: New York, NY, 1980.

116


(13) Bermejo, J.; Guillen, M .D. Chromatographia 1983, 17, 664.

(14) Karger, B. L.; Snyder, L. R.; H orvath, C. An In trod uction to Separation Science: W ilev-Interscience: New York, NY, 1973.

(15) Karger, B. L.; Snyder, L. R.; Eon, C. AnaL Chem. 1978, 50, 2126.

(16) Van Deempter, J . J .; Zuiderweg, F. J .; K likenberg, A. Chem. Eng. Sri. 1956, 5, 271.

(17) Golay, M. J. E. In : Gas Chrom atography 1957: East Lansing Symposium, Coates, V. J .; Noebels, H. J .; Fagerson, I. S., Eds.; Academic Press: New York, NY, 1958.

(18) Fu lle r, E. N.; Schettler, P. D .; G iddings, J . C. Ind. Eng. Chem. 1966, 58, 19.

(19) Desty, D. H.; Goldup, A.; Swanton, W. T. In : Gas Chrom atography. Brenner, N; Callen, J . E.; Weiss, M. D ., Eds.; Academic Press:New York, NY, 1962.

(20) H olland, J . F.; Enke, C. G.; A llison, J .; S tu lts , J . T.; P inkston, J . D .; Newcome, B .; W atson, J . T. AnaL Chem. 1983, 55, 997A.

(21) B randt, W. W. J . Phys. Chem., W ash.., 1959, 63, 1080.

(22) Grob, R. L. Modem Practices o f Gas Chrom atography: W ilev- Interscience: New York, NY; 1977.

(23) G iddings, J . C. Dynam ics o f Chrom atography. Vol. 1; M arcel Dekker: New York, NY; 1965.

(24) Ziegel, K. D.; Frensdorff, H. K.; B la ir, D. E. J. Polym. S ri. 1969, 7, 809.

(25) van Amerongen, G. J . Robber Chem. Technol 1964, 37, 1065.

117


(26) Snyder, L. R. P rincip les o f A dsorption C hrom atographyJVIarcel D ekker: New York, NY; 1968.

(27) K irk land , J . J ., fEd.) M odem Practice o f L iqu idChrom atography; W ilev-Interscience: New York, NY; 1971.

118


CHAPTER 5

Practical Aspects of Membrane Extractions

In th is chapter, p ractica l aspects fo r op tim izing experim ental

and in s tru m e n ta l param eters are discussed fo r membrane extraction

mass spectrom etry. Some experim ental conditions th a t affect

m em brane extraction efficiencies include tem perature and sample

flow ra te. The experim ental conditions under w hich an analysis o f a

chem ical process is perform ed are often d ictated by the process itse lf.

The in s tru m e n ta l param eters th a t m ay be more easily controlled

inc lude the m em brane dim ensions, the ME device configuration, and

the distance between the membrane extracto r and the analyzer.

A nother concern fo r the analyst is the po ten tia l fo r a th in -w a lled

m em branes to ru p tu re , a llow ing the sample o r process stream to vent

the m ass spectrom eter. Th is is o f p a rticu la r concern in process

app lica tions where m any process stream s are com plex and the

m em brane m ay degrade by physical, chem ical, o r therm al means.

A varie ty o f devices fo r ME have been developed to separate

com pounds o f in te rest from a sample m a trix and in troduce these

com pounds in to a mass spectrom eter. Hollow fibe r o r tube

m em branes have seen a great deal o f use in ME-MS applications (1-7).

Several groups have also devised systems fo r m aking sheet ME-MS

interfaces (7-10). More recently, ho llow fibe r and sheet membrane

119


extractors have been incorporated d irectly in to the vacuum cham ber

and even the ion source o f the mass spectrom eter w ith the goal o f

im proving the sensitivities and response tim es (11-13).

Two hollow fibe r membrane extractor configurations have been

reported and contrasted. The flow -through device fo r ME is

configured such th a t sample flows through the in te rio r o f the hollow

fibe r membrane w hile the analytes permeate ra d ia lly to the outside,

where they are analyzed. Conversely, the flow-over device fo r ME is

configured such th a t the outside o f the hollow fibe r membrane is

exposed to the sample w hile the inside is exposed to the MS vacuum .

Basic designs fo r flow-over and the flow -through ho llow fibe r

membrane extractors are illu s tra te d in Figures 5.1 and 5.2.

The follow ing po ints are im portan t experim ental considerations

fo r on-line ME-MS techniques:

1) Experim ental contro l is desired over param eters th a t affect

perm eability or th a t may damage the membrane, such as the

membrane tem perature and linea r velocity o f the sample.

2) The membrane should be protected from being to m due to

p inch ing o r abrasion.

3) In the event o f a rup tu red membrane, the analyzer should

im m ediately be isolated from the ME device so th a t the mass

spectrom eter is no t vented by the sample.

4) The surface area and void volume o f the ME-MS interface should

be m inim ized. Interface tub ing, fittings, vacuum -protection valves,

120


sealant

tosample pump

hollow fiber membrane

i sample

iii

permeate to mass spectrometer

Figure 5 .1 . Flow-over hollow fiber membrane extractor.

121


sealant

tosample pump


iii

to mass spectrometer

sample

Figure 5 .2 . Flow-through hollow fiber membrane configuration.

122


and the ME device con tribu te to the surface area and void volum e in

the M E-M S in terface.

5) In processes where h ig h ly reactive analytes o r reaction k ine tics

are to be m easured, the shortest distance possible between the sam ple

and the m em brane extracto r is desired to m in im ize loss o f the analyte

o r skew ing o f the reaction p ro file .

6 ) In some applications, i t is desirable to m o n ito r m u ltip le stream s

o f gas and liq u id process stream s, as discussed in C hapter 6 , thu s

m ore th a n one ME device m ay be required.

Several experim enta l param eters are discussed below in the

con text o f op tim iz ing the ana ly tica l speed, sens itiv ity , and se lectiv ity.

MEMBRANE DIMENSION CONSIDERATIONS

The perm eation equations discussed in C hapter 2 show th a t the

perm eation ra te increases, and therefore the detection lim it

decreases, as a fu n c tio n o f sheet m em brane area o r ho llow fib e r

m em brane length. In the case o f the ho llow fibe r m em brane, the

perm eation ra te fo r the analyte increases w ith increasing length on ly

to the lim it where the concentration o f the analyte in the sam ple does

n o t change along the ho llow fib e r due to e ffic ien t extraction in to the

m em brane (14, 15). In such cases, i t is preferred th a t the m em brane

extrac to r be constructed w ith several sh o rt ho llow fib e r m em branes,

ra th e r tha n w ith a single long one to ensure un ifo rm sample

concentra tion along the m em brane surface.

123


The am ount o f analyte removed by the perm eation process per

u n it length o f membrane is actua lly qu ite sm all as illu s tra te d by the

perm eation rates per u n it concentration th rough a silicone ho llow

fib e r mem brane given in Table 5.1 fo r several gas phase com pounds.

B y pum ping a w ater sample from a 48-cc vo la tile organic analysis

(VOA) v ia l th rough the membrane and back in to the v ia l, sm all samples

have been analyzed w ith o u t appreciable consum ption o f the sample

and w ith o u t fo rm ation o f headspace in the v ia l. A w ater sample spiked

w ith toluene and dichlorom ethane was pum ped a t various rates

th roug h three flow -through ho llow fib e r mem brane extractors in

series and th e ir permeate stream s were analyzed. No s ig n ifica n t drop

in perm eation ra te between the firs t and the th ird mem brane in the

series was observed.

The detection lim it fo r an analyte is p roportiona l to the

th ickness o f a sheet membrane. In the case o f ho llow fibe r

m em branes, the fo llow ing treatm ent m ay be use fu l in understanding

the perm eation ra te-ho llow fib e r w a ll th ickness re la tionsh ip . In

C hapter 2, i t was shown th a t the perm eation rate th rough a hollow

fib e r mem brane is given by

Since o .d ./i.d . = ou ter rad ius (o .r.)/in n e r rad ius (i.r.), and since d = o.r.

- i.r., then Equation 5.1 can be w ritte n as

F i = 2 *7t*L*Pi*cmi/ln (o .d ./i.d .) (5.1)

F* = 2 *7i»L*Pi*cmi/ ln ( l + d /i.r .) (5.2)

124


Table 5 .1 . Gas perm eabilities and perm eation rates/u n it concentration (given per un it ppm by volum e) through a 2.54-cm - long, 0 .0305-cm -i.d ., 0.0635-cm -o.d. silicone hollow fiber membrane.

com poundpe rm e ab ility

flO '6cm 2 /rs*C jl)perm eation ra te

(1 O' 10cm 3 / fs*ppm l)n itro g e n 2 .1 0.46oxygen 4.0 0.87argon 4.0 0.87carbon dioxide 25 5.5ethene 24 5.2m ethane 9.7 2 .1ethane 25 5.5propane 61 13butane 76 16pentane 530 1 1 0hexane 670 150heptane 1700 370benzene 1 0 0 0 2 2 0to luene 2 0 0 0 440ethylbenzene 3200 690chlorobenzene 3000 640ch lo rom ethane 140 31d ich lo rom ethane 740 160ch lo ro fo rm 900 2 0 0carbon te trach lo ride 920 2 0 0ch lo roe thene 1 2 0 261 ,1 -d ich lo ro e th ene 600 130trich lo ro e th e n e 1400 290te trach lo roe the ne 3500 750brom om ethane 140 31dib rom om ethane 1 2 0 0 260b rom o fo rm 5100 1 1 0 0m ethano l 40 0 87ethanol 840 1801 -p ropano l 1 0 0 0 2 2 02 -p ropano l 270 581-butano l 1 1 0 0 240acetone 540 1 2 02 -butanone 1300 280w a te r 87 19


Therefore, a reduction o f the th ickn e ss /in n e r rad ius ra tio fo r a ho llow

fib e r m em brane resu lts in an increase in perm eation rates and th u s an

im provem ent in the detection lim its .

In ad d ition to im proved detection lim its , fas te r response tim es

are achieved w ith th in n e r membranes. The m em brane th ickness-

response tim e re la tionsh ip given by E quation 2.13 shows the response

tim e to be d ire c tly p ropo rtiona l to the square o f the th ickness fo r bo th

the sheet and the ho llow fib e r membranes. As stated above, a concern

fo r m ass spectrom etrists is the po ten tia l fo r the th in -w a lled

m em branes to ru p tu re , a llow ing the sam ple o r process stream to vent

the mass spectrom eter. In m any cases, the polym er m em brane is

su ffic ie n tly strong th a t leaks are more lik e ly to occur a t the sealant

used to a ttach the mem brane to the ME device.

Because the enrichm ent facto r is given by the ra tio o f the

perm eabilities fo r two com ponents in a sam ple, i t is n o t affected by

the dim ensions o f the m em brane. Therefore, u tiliz in g m em branes

th a t have th in n e r w alls o r larger surface areas w ill im prove the speed

and sens itiv ity , b u t no t the selectivity.

TEMPERATURE CONSIDERATIONS

As described in the previous chapters, the perm eation rates fo r

organic com pounds from gas phase samples are dom inated by the

m em brane/gas d is trib u tio n ra tio . Because th e ir perm eabilities

decrease w ith increasing tem peratures, th e ir detection lim its increase

126


(see Table 2.2). The effect o f tem perature on the perm eabilities fo r

organic com pounds from w ater appears to be d iffusion-dom inated,

there fore a t h ig he r tem peratures, th e ir detection lim its im prove.

H igher tem peratures re su lt in increased d iffu s iv itie s and therefore

sh o rte r response tim es. However, enrichm ent factors degrade a t

h ig he r tem peratures. In add ition , fo r trace level organic sam ples, the

analyzer pressure follows the perm eabilities o f the a ir o r w ate r m a trix .

Therefore, low er tem peratures are desired fo r low er analyzer

pressures and to m inim ize oxygen and w ater in the mass

spectrom ete r.

For the m ost e ffic ien t m em brane extractions, a lte rin g the

m em brane dim ensions ra th e r tha n increasing the tem perature is

genera lly b e tte r fo r ob ta in ing im proved detection lim its and response

tim es. B u t the choice o f m em brane th ickness is lim ite d to

com m ercia l a va ila b ility o r the capab ility to cast th in , supported

m em branes th a t w ill w ithstand the pressure d iffe re n tia l im posed by

the sam ple and mass spectrom eter. W ith a given m em brane, the

desire fo r increased sen s itiv ity and reduced response tim e m u s t be

balanced w ith the need fo r e ffic ien t separations. H igher tem peratures

m ay be w arranted fo r k in e tic stud ies re qu irin g fast response.

Processes have been stud ied a t tem peratures exceeding 100 °C (16)

and perform ance evaluations have been carried ou t a t tem peratures

greater tha n 200 °C (17). The membrane m ateria l is ra ted fo r a

w orkable tem perature range o f -54 °C to 249 °C (18). However, the

life tim e o f the m em brane is expected to be reduced a t elevated

tem peratures. A t room tem peratures, the S ilastic m a te ria l has a

127


reported she lf-life (for m edical uses) o f 5 years. The operating

life tim e w ill depend upon the conditions o f the app lica tion .

SAMPLE FLOW RATE CONSIDERATIONS

Poor m ix ing a t the sam ple/m em brane in terface can cause the

fo rm ation o f a layer o f analyte depletion, re su ltin g in low response.

T h is phenom enon is com m only reported by the users o f fla t

m em branes (19, 20). The effect o f the boundary layer is depicted in

F igure 5.3 where the perm eation ra te is now given by

Fi = A .P i.c mi7 d (5 .3)

The reduced concentra tion o f analyte i, cm i*, a t the in terface o f

the boundary layer and the membrane now establishes the

concentra tion grad ient in the m em brane. T u rb u le n t flow is preferred,

p a rtic u la rly fo r w ate r samples where the ra te o f d iffu s ion th rough the

m em brane m ay be greater tha n th rough w ater fo r m any com pounds.

The tra n s itio n from lam in a r flow to tu rb u le n t flow occurs a t Reynolds

num ber values o f 2000-3000 (21),

NRe = i.d .*v*p /p (5 .4)

where v is the sam ple lin e a r velocity, p is the density o f the flu id , and

|i is the flu id viscosity. To achieve these values however, volum e flows

o f over 25 cm3/m in u te fo r w ater (25 °C) are required in a 0.0305-cm

i.d . ho llow fibe r membrane.

128


membrane (stationary phase)

sample or feed stream

(mobile phase)extract or

permeate stream

m

F = A«D*K>cm* /d ►

Figure 5.3 . A cross-section view o f the effect o f boundary layers on th e perm eation process.

129


1 0 0

90C0

80c3

70>»(0 60!o 50COW 40 0)« 30oa - 20(0a>CC 10

0.0 2.0 4.0 6.0 8.0 10.0Flow Rate, cc/min.

+ +200 400 600

Reynolds Number800

Figure 5 .4 . Response for toluene vs. sam ple flow rate through a 2.5- cm -long, 0 .0305-cm i.d ., 0 .0635-cm o.d. hollow fiber.

130


The effect o f lin e a r ve locity on response fo r to luene in w ate r is

shown in F igure 5.4. Flow rates approaching 10 cm 3/m in u te appear to

reduce the boundary laye r to dim ensions where the change in

perm eation ra te w ith change in sam ple flow ra te becomes sm a ll fo r

m ost vo la tile organic analytes stud ied. W hen draw ing the sam ple

th rough the 0.0305-cm i.d . ho llow fib e r by pum ping a t the ou tle t, flow

ra tes h igher th a n 1 0 cm 3/m in u te often re s u lt in the fo rm ation o f

bubbles in the sam ple stream . To avoid undue pressuriza tion o f the

m em brane, sam ples are generally n o t pushed th rough the m em brane

b y the sam ple pum p. Increased tu rbu lence (and th u s perm eation

rates) fo r a given flow ra te have been achieved by segm enting the flow

stream (2 2 ) and packing the in te rio r o f the ho llow fib e r m em brane

w ith in e rt beads (23). These techniques have no t been em ployed in

th is w ork.

The observed increases in organic perm eation rates fro m w ater

w ith increasing tem perature m ay in p a rt be due to the fact th a t the

Reynolds num ber increases w ith tem perature according to the

re la tio n N r6 = d*v«(0.00538*T2 + 2.38*T + 48.7) so th a t boundary

layers are reduced a t h igher tem peratures. Th is re la tion was

determ ined from cu rve -fittin g a p lo t o f w ate r de ns ity /v isco s ity ra tios

(24) vs. tem perature.

In a d d ition to reduced steady state response, poor m ix ing also

re su lts in longer response tim es due to the add ition a l boundary layer

th rough w h ich the analyte m ust d iffuse. Increasing the w ater flow ra te

th rough the ho llow fib e r from 1.3 cm3/m in u te to 3.5 cm3/m in u te

131


re su lts in an approxim ate ly 50% decrease in tso m easurem ents fo r

bo th to luene and dichlorom ethane. Th is effect on response tim e is

dependent upon the d iffu s iv ity o f the substance in the sam ple m a trix

and upon the th ickness o f the boundary layer. E lim ina tio n o f th is

boundary layer reduces the response tim e to the lim it im posed by the

m em brane. For to luene and dichlorom ethane, response tim e appear

to become constan t a t flow rates greater tha n about 8 cm 3 /m in u te .

W hen an analyte-depleted boundary layer is established, the

observed enrichm ent fac to r is reduced due to the depressed

a n a ly te /m a trix ra tio a t the sam ple-m em brane interface. A p lo t o f the

a n a ly te /m a trix response ra tio vs. flow ra te follows the same tre nd as

th a t fo r the analyte response shown in F igure 5.4. The m a trix is in

such large excess th a t changes in its response are re la tive ly sm all.

W hen the perm eation rates becomes independent o f sam ple flow rate,

so do the organic enrichm ents.

THE EFFECTS OF DISTANCE BETWEEN THE MEMBRANE EXTRACTOR AND THE MASS SPECTROMETER

A t least tw o phenom ena associated w ith the ME-MS in terface

tube m ay re su lt in extended response tim es and decreased

sensitiv ities; poor conductance and adsorption. The m em brane no t

on ly serves to separate the com ponents o f in te res t from the sam ple

m a trix , b u t because the flow rate th rough the m em brane is so sm all, as

shown in Table 5.1, the membrane also provides the necessary

pressure drop from the am bient pressure sam ple to the h igh vacuum

132


in the mass spectrom eter. For example, the perm eabilities and flow

rates th rough the membrane are given in Table 5.2 fo r nitrogen,

dichlorom ethane, toluene, acetone, and 1-butanol. The n itrogen is the

sam ple m a trix and approaches 100% concentration. The organic

com pounds are 1 0 0 ppm by volum e in the sample.

Table 5 .2 . Gas perm eabilities and flow rates through a 2.5-cm -long, 0.0305-cm -i.d ., 0.0635-cm -o.d . silicone hollow fiber membrane.

concentra tion pe rm eab ility flow ra tecom pound % bv volum e cm 2 /fs«cj] cm3 /sn itro g e n 1 0 0 2. lX lO -6 4.6X10 ' 5

dich lo rom ethane 0 .0 1 7.4X10"4 1.6X1 O' 7

to luene 0 .0 1 2.0X10 ' 3 4.4X10-7acetone 0 .0 1 5.4X10 ' 4 1.2X10-71-butanol 0 .0 1 1.1X10-3 2.4X10-7

The permeate side o f the membrane is under h igh vacuum ,

therefore m olecular flow conditions prevail in the interface tube. In

the two-step process o f d iffus ion through an am orphous polym er

followed by m olecular flow through a tube, the d iffus ion step w ill be

ra te lim itin g . Since the ana lytica l response fo r a com ponent is

dependent upon the conductance o f the com ponent in to the ion

source, then any effect th a t the interface tub ing m igh t have on

conductance w ould be observed in bo th the response and the response

tim e. The data in Table 5.3 fo r steady state response m easurem ents

fo r dichlorom ethane, toluene, acetone, and 1-propanol showed no

s ig n ifica n t change w ith the ho llow fib e r ME device a t distances o f 40

133


cm, 70 cm, and 100 cm from the ion source. In add ition , no change

in the analyzer pressure was observed fo r the d iffe ren t lengths o f

in te rface tub ing .

Table 5 .3 . The effects o f interface tube length on response.

response fac to r (in te n s ity /p p m )com pound m /z L=40 cm L=70 cm L=100 cmd ich lo rom ethane 84 1600 1600 1600to luene 91 26000 24 000 2 4 000acetone 58 550 550 5501-bu tano l 56 5100 5000 5000

The effect o f in terface tube length on response tim es were

exam ined by m aking step changes in the sample concentration and

m easuring the tim e required to reach steady state perm eation. The

effect o f in terface tube length on response tim e fo r to luene is

illu s tra te d in F igure 5.5. No s ign ifican t changes in these response

curves are observed. A p lo t o f response tim e vs. interface tube length

fo r dich lorom ethane, toluene, acetone, and 1 -bu tano l are shown in

F igure 5.6. O nly 1-bu tano l showed a dependency on the tube leng th as

shown in Figures 5.6 and 5.7. Th is pronounced dependency on the

in te rface tube leng th or, m ore precisely, on the in terface tube surface

area fo r alcohols has also been reported by Lauritsen (13). In the

present study, th is adsorption phenom enon is shown to be m in im ized

by sim ply heating the interface tube as dem onstrated by the large

square data p o in t in Figure 5.6 and the p lo t designated d in F igure 5.7.

134


% 188-

88 -

68 -

20 -

8 18 28 38 48 68SBTIME (sec)

— -------- --- 40 cm--------------------70 cm-------------------- 100 cm

Figure 5 .5 . The response curves for m /z 92 following a step change in th e concentration o f toluene in a gas sam ple w ith different lengths o f ME-MS interface tube lengths.

135


350 -r

300

© 250CO

fl>£ 200 H

150 -■<B COc oco 100Q>DC

50

0 $30 40 50 60 70 80 90

Interface Tube Length, cm

100 110

Key;square = 1-bu tano l c irc le = acetone diam ond = toluene tria n g le = d ich lorom ethanelarge square = 1-bu tano l w ith the in terface tube heated to 150 °C

Figure 5 .6 . R esponse tim e vs. ME-MS interface tube length for various volatile compounds.

136


% TOO-

50-

* 100-

50-

% 100-

50 -

50 -

■ ‘ 2 6 0 ■ • ‘2 fe0 ‘ ‘ ‘s id • ‘ '340' ‘ ' ‘4 6 0 ’ ’ ‘ Aio '

Time, sec.

Key;a) 1 = 4 0 cm , 2 3 °Cb) 1 = 7 0 cm , 23 °Cc) 1 = 100 cm , 2 3 °Cd) 1 = 100 cm , 150 °C

Figure 5 .7 . The response curves for 1-butanol (m /z 56) w ith different lengths o f ME-MS interface tube.


As discussed in C hapter 2, the response tim e fo r a com ponent is

defined as the tim e required to reach 50% o f the steady state signal,

t 5Q, fo llow ing a step change in sample concentration a t to- I t m ay also

be use fu l to use an experim ental rise tim e from t^o to tQ0 to describe

the response tim e o f the mem brane extraction technique. For F ick ian

behavior, the corre la tion o f tso to th is rise tim e is approxim ated by

[t9 0 'tio ] = 0*6#[t50'to] (5 .5)

I f F ick ian behavior is no t observed (e.g., i f adso rp tion /deso rp tion o f

the analyte on the m em brane o r analyzer surfaces is the ra te lim itin g

step to a tta in steady state), then th is rise tim e w ill y ie ld a m isleading

system response tim e. The rise tim e m easurem ent is determ ined

on ly from the permeate response curve w ith no reference made to the

sample. Values fo r the rise tim e and t^Q are given in Table 5.4 fo r 1-

bu tano l. These data illu s tra te th a t the rise tim e gives no in d ica tio n o f

the system response tim e and therefore gives no in d ica tio n w hen a

change occurs in the sample o r process.

Table 5 .4 . Comparisons betw een response time (t50-to) and rise tim e (tgo-tio) for 1-butanol.

in te rface tso-to tgo -tiotube length seconds seconds40 cm 75 9570 cm 180 1 0 0

1 0 0 cm 340 1 0 0

100 cm, 150 °C 80 1 1 0

138


O ther causes fo r non-F ickian behavior are common (25-27).

M any rubbery membranes conta in fille rs such as s ilica o r carbon b lack

to provide m echanical strength (28). As described in C hapters 3 and

4, the s ilica has a dram atic effect on the response tim e fo r m olecules

th a t e xh ib it strong hydrogen bonding due to adso rp tion /deso rp tion

processes occu rring w ith in the membrane. I f th is

adso rp tion /deso rp tion process is reversible, as i t appears to be fo r low

m olecu lar w eight com pounds, then F ick ian behavior is observed.

However, i f a very strong in te raction occurs between the fille r and the

perm eating com pound, non-F ickian tra n sp o rt w ou ld re su lt,

resem bling the characteristics o f adsorp tion /deso rp tion a t surfaces

observed in th is study.

W hen tra n sp o rt th rough the mem brane is the ra te -lim itin g step

fo r the response tim e (i.e., the membrane is near the ion source o r no

in te ra c tio n o f the analyte w ith the interface surfaces is observed), then

the rise tim e m ay yie ld erroneous values fo r the system response tim e.

I t w ou ld appear th a t the m ost useful characterization o f response tim e

should provide a reference to the sample, e.g., t 50-to o r tgp-to ( if tgo

can be accurate ly measured), in add ition to the rise tim e (17).

A nother m a jo r factor th a t may affect response tim e th a t has no t

been addressed in the previous discussion is the effect o f the mass

spectrom eter. The geometry o f the ion source and the vacuum

cham ber m ay have a s ign ifican t effect upon the response tim e th a t is

independent o f the mem brane extracto r and in terface tube. The

response tim e fo r dichlorom ethane and toluene are given fo r three

139


d iffe re n t m ass spectrom eters in Table 5.5. W hereas the response

tim e da ta collected w ith the MSD and the TSQ are com parable, the

response tim es m easured w ith the Balzers in s tru m e n t are s ig n ifica n tly

longer. T h is phenom enon is presum ably due to poor sam ple gas

conductance th rough the 0.08-cm orifice in the Balzers gas-tigh t ion

source to w h ich the 1/ 8 -inch ME-M S in te rface tube is connected.

Table 5 .5 . The effects o f analyzer conductance on response tim e.

response tim e (sec.)analyzer d ich lo rom ethane to lueneF inn igan TSQ-70 11 14HP 5971-A MSD 10 11Balzers Q M G -511 2 0 35

MEMBRANE EXTRACTOR CONFIGURATION CONSIDERATIONS

In general, ho llow fib e r m em branes provide greater extraction

efficiencies th a n do sheet m em branes because o f the greater sam ple

volum e-to-m em brane surface ra tio and the h igher sample lin e a r

ve locities obtainable. In add ition , a flow -over ho llow fib e r m em brane

probe can be inserted d ire c tly in to sam ples, such as blood vessels in

the in vivo analysis o f b lood gases (29), th a t are beyond the reach o f

sheet m em branes. However, m ateria ls fo r sheet m em branes are

com m ercia lly available in a w ider va rie ty o f m ateria ls and dim ensions.

In ad d ition , w ith o u t special equipm ent, custom -m ade m em branes are

m ore easily prepared in sheet fo rm tha n ho llow fibers. A lthough the

140


m a jo rity o f ME-MS w ork reported in the lite ra tu re u tilize s

po ly(d im ethylsiloxane) m em branes, the developm ent o f p ra c tica l

sam ple-m em brane in te rac tio n m odels such as described in Chapters 3

and 4 w ill undoubtedly re su lt in the use o f a varie ty o f m ateria ls.

E valuation o fjlo w -o ve r and Jlow-through membrane extractors

The com parisons o f absolute s igna l from the analysis o f a sam ple

us ing a flow -over and a flow -th rough ME device shows a s ign ifica n t

advantage fo r the flow -th rough con figura tion . A pproxim ate ly 50-fo ld

greater response was observed fo r the flow -th rough in le t as illu s tra te d

in F igure 5.8. Collapsing o f the soft m em brane in the flow -over

con figu ra tion resu lted in a s ign ifica n t reduction in effective m em brane

area. Conversely, the inverted pressure drop in the flow -th rough

con figu ra tion takes m axim um advantage o f the m em brane in n e r

ra d iu s /th ickn e ss ra tio . For ide n tica l volum e flows, h igher Reynolds

num bers are m ore easily achieved w ith the flow -th rough con figura tion .

However, there m ay be cases where the flow -over con figu ra tion is

preferred, as i t can be made in to a probe convenient fo r on-line

m o n ito rin g o f hazardous o r reactive chem icals (1 0 , 16).

N either the flow -th rough n o r the flow -over in le t d isp lays an

advantage in response tim e when s im ila r sam ple flow cond itions are

established. U nder s im ila r sam ple lin e a r ve locity cond itions, the

enrichm ent fac to r is also independent o f the con figura tion . The p lo t

in F igure 5.9 shows o rgan ic /w a te r s igna l ra tios fo r the flow -over in le t

vs. th a t fo r the flow -th rough in le t w ith com parable feed lin e a r flows.

141


10000.00

1000.00

flow-throughO)c©-I

100.00c2a>01coQ .(0ffl

DC

flow-over10.00

1.00

0.01 0.1 1 10010

Concentration Dichloromethane in Water, ppm

Figure 5 .8 . Comparison of response vs. concentration plots for the flow-over and the flow-through membrane extractor configurations.

142


(0 oc

oCDcoa.CDa>CC

atCO|c>cCOO)

a>>o•o

6.0

5.0

4.0

3.0□ h

2.0

en1.0

0.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Flow>through Organic/Water Response Ratio

Key:a = d ich lorom ethane c = brom odichlorom ethane e = brom oform g = trich lo roe thene i = 1 , 1 -d ich loroethane k = toluene m = chlorobenzene

b = chloroform d = dibrom ochlorom ethane f = 1 , 1 -d ich loroethene h = tetrachloroethene j = 1 , 1 , 1 -trich lo roe thane I = ethylbenzene n = 1 ,2 -dichlorobenzene.

Figure 5 .9 . Relative organic/water response ratios for flow-over vs. flow-through in lets obtained at comparable sam ple linear velocities.

143


As expected, no enrichm ent advantage is observed fo r e ith e r

con figu ra tion since the perm eation ra te fo r w ater also is affected by

the effective m em brane area. Again, the flow -th rough con figu ra tion is

generally preferred because o f the cap ab ility to m ore easily achieve

h ighe r lin e a r velocities a t re la tive ly low sam ple volum e flow s and the

effective m em brane surface area is m axim ized.

Design o f the ME Valve

A n exploded view o f the ho llow fib e r ME valve is shown in Figure

5.10. Th is ME device consists o f tw o sections - upper and low er - o f

the valve body, a valve plunger, a ho llow fib e r mem brane, and some

sealant fo r a ttach ing the m em brane to the valve body. The low er

section o f the valve body was fabrica ted to f i t the upper section and

p lunger from com m ercia lly available solenoid valves (1X259 24VDC

norm ally-c losed solenoid valve from K ip Incorporated). The low er

section o f the valve body is provided w ith two po rts th rough w h ich

sam ples are pum ped in to the valve body, th rough the ho llow fib e r

m em brane, and ou t o f the valve body. The m em brane is a 2.5-cm

leng th o f 0 .0305-cm -i.d ., 0.0635-cm .-o.d. S ilastic m edical grade tu b in g

from Dow C om ing Corp. The ho llow fib e r m em brane is sealed in to the

tw o sam ple p o rt openings in the valve w ith Dow C om ing RTV 734

S ilas tic sealant. The analytes selectively permeate th rough the

m em brane and in to the valve cavity. The permeate stream flow s in to

the mass spectrom eter fo r analysis.

The sheet ME valve design in Figure 5.11 shows th a t the two

sam ple ports are connected in te rn a lly by a groove. The m em brane

144


valve body: upper section

valve plunger

plunger seal

o-ring


sealant

valve body: lower section

sample ports


Figure 5 .10 . Exploded view o f th e hollow fiber membrane extractor valve.

145


valve body: upper section

valve plunger

plunger seal

o-ring

sheet membrane support disc

sheet membrane

valve body: lower section

sample groove

sample ports


Figure 5 .11 . Exploded view o f the sh eet membrane extractor valve.

146


lays across th is groove, separating the sample from the valve cavity.

The preferred m ethod fo r sealing the sheet m em brane in the valve is

to 'sandw ich' the mem brane between the valve body and a d o nu t-like

disc, as shown in Figure 5.11. A groove th rough the disc corresponds

to the sam ple channel in the valve body and provides a passage fo r

perm eating m ateria ls to enter the valve cavity.

The ME valves were m ounted to a probe and the ME-MS

in terface was made w ith a 1 /8 -in ch (0.32-cm) o.d., 0 .22-cm -i.d .

sta in less steel tube v ia the d irec t inse rtion probe in le t o f the mass

spectrom eter, as shown in F igure 5.12. In add ition to the d ire c t

in se rtio n probe interface, the ME valve m ay be m ounted d ire c tly to

the mass spectrom eter in a m anner s im ila r to solenoid valves

com m only used fo r in trodu c ing ca lib ra tion gases. The void volum e in

the ME valves (~1 cm 3) does no t cause an excessive pressure surge in

the mass spectrom eter when the valve was opened. Both the ho llow

fib e r and the sheet ME valves have been successfully evaluated.

No know n ME device fu lfills a ll o f the requirem ents stated a t the

beginn ing o f th is chapter fo r the ideal ex trac tion /sam p ling device.

The advantages o f the ME valve over some cu rre n tly existing

technology include a com bination o f the fo llow ing a ttribu tes:

1) The tem perature o f the membrane and flow ra te o f the sam ple

m ay be w e ll contro lled w ith the ME valve.

2 ) The valve body provides pro tection to the m em brane from

physical shock th a t m ay cause tearing o r rup tu re .

147


sampleflow ME valve

permeateflOW /m

o o o o ol

S SSsjo o o o oME-MS >

interface tubedirect insertion probe to mass spectrometer

power supplymass spectrometer vacuum gage

controller

Figure 5 .12 . A membrane extraction valve coupled to a direct insertion probe.

148


3) The solenoid m ay be powered th rough the vacuum -pro tection

c irc u it o f the m ass spectrom eter so th a t in the event o f a pressure

surge due to a m em brane ru p tu re or seal fa ilu re , the mass

spectrom eter can be in s ta n tly isolated from the sample.

4 ) The device is constructed w ith a sm a ll vo id volum e and surface

area. Response tim es and carry-over are m in im ized re la tive to those

o f m em brane extracto r and valve in series. A lthough i t m ay be

desirable to m in im ize the d istance between the m em brane extracto r

and the m ass spectrom eter, th is distance is n o t generally a tra nspo rt-

ra te lim itin g param eter. The in te rface tube can be made ve iy short

and is typ ica lly heated independently o f the ME valve.

5) The ME valve m ay be placed as close as possible to e ithe r the

process o r the analyzer, depending upon the requirem ents o f the

analysis. A va ria tio n o f the ME valve described above m ay be used in

cases where i t is desirable to contact the m em brane d ire c tly w ith a

reactive o r k in e tic process. As shown in F igure 5.13, th is va ria tion

involves expanding the low er section o f the valve body so th a t the

process ac tu a lly occurs w ith in the ME devices.

6 ) The ME valve m ay be use fu l in m u ltip le stream sam pling where

each sam ple stream requires a separate M E device. I f the m embranes

are housed ins ide o f 3-way valves, then when one ME valve is no t

activated, the valve cavity m ay be evacuated th rough the d ive rt p o rt to

an a u x ilia iy vacuum pum p to prevent accum ulation o f permeate.

149


to MS

valve

membrane

Figure 5 .13 . A configuration o f ME valve where th e lower section o f th e valve is expanded so th at the process is carried out in direct contact w ith th e membrane.

150


REFERENCES

(1 } Westover, L. B .; Tou, J. C.; M ark, J . H. AnaL Chem. 1974, 46, 568.

(2 ) LaPack, M. A.; Tou, J . C.; Enke, C. G. AnaL Chem. 1990, 62, 1265.

(3 ) Lipsky, S. R ; Horvath, C. G.; M cM urray, W. J . AnaL Chem. 1966, 38, 1585.

(4 ) Kallos, G. J .; Tou, J . C. Environ. Set TechnoL 1977, 11, 1101.

(5 ) Heinzle, E .; Reuss, M ., eds. Mass Spectrom etry inB iotechnological Process Analysis and C on tro l: P lenum Press: New York, 1987.

(6 ) Langvardt, P. W.; Brzak, K. A.; Kastl, P. E. 34 th ASMS Conference on Mass Spectrom etry and A llied Topics, 1986, C inc inna ti, OH.

(7 ) Pungor J r., E.; Pecs, M .; Szigeti, L.; Nyeste, L. AnaL Chim. A cta 1984, 163, 185.

(8 ) Llewellen, P. M .; L ittle john , D. P. U.S. Patent 3,429,105, February, 1969.

(9 ) Harland, B. J .; N icholson, P. J. D .; G illings, E. W at Res. 1987, 21, 107.

(10 ) Calvo, K. C.; Weisenberger, C. R ; Anderson, L. B.; K lapper, M. H. AnaL Chem. 1981, 53, 981.

(11 ) a) B ier, M. E.; Cooks, R G.; Tou, J . C.; Westover, L. B. U.S. Patent 4,791,292, 1989.

b) B ier, M. E.; Cooks, R G. AnaL Chem. 1987, 59, 597.

151


(1 2 ) B ier, M . E .; Cooks, R G.; Kotiaho, T. 3 7 th ASMS Conference on Mass Spectrom etry and A llied Topics, 1989, M iam i Beach, FL.

(1 3 ) Lauritsen , F. R In t J. Mass Spectrom. Ion Proc. 1990, 95, 259.

(1 4 ) Bredeweg, R A .; Langhorst, M. L.; D ittenhafer, D. R ; S trandjord, A. J .; W illis , R. S. 16th A nnua l M eeting o f the Federation o f A n a ly tica l C hem istry and Spectroscopy Societies, Chicago, IL, 1989.

(1 5 ) Hwang, S.-T.; Kammermeyer, K. Mem branes in Separations. Robert E. Krieger Publish ing Co., Inc.; M alabar, FL, 1984.

(1 6 ) Savickas, P. J .; LaPack, M. A.; Tou, J . C. AnaL Chem. 1989, 61, 2332.

(1 7 ) B ier, M. E .; Kotiaho, T.; Cooks, R G. AnaL Chim. A cta 1990, 231, 175.

(1 8 ) M edical M ateria ls Business Product Form No. 51-772B-89; Dow C om ing Corp., M idland, M I.

(1 9 ) Tojo, K.; Ghannam, M.; S im , Y.; Chien, Y. W. J. C ont Release 1985 , 1, 197.

(2 0 ) Petropoulos, J . H .; Tsim boukis, D. G. J. Membrane Set 1986, 27, 359.

(2 1 ) Perry, R. H .; Green, D. Perry's Chem ical Engineer's Handbook. 6 th Ed.; M cgraw -H ill Book Company: New York, NY; 1984.

(2 2 ) Peters, T. L.; Stevens, T. S. U. S. Patent 4,684,470, 1987.

(2 3 ) Stevens, T. S.; Jewett, G. L.; Bredeweg, R. A. A na l Chem. 1982, 54, 1206.

152


(2 4 ) W east, R C.; Astle, M. J .; Beyer, W. H .; eds. Handbook o fC hem istry and Phvsics.64 th Ed.; CRC Press, Inc.: Baco Raton, FL; 1983; curve fitte d from density data, p. F-5 and viscosity data, p. F-38.

(2 5 ) C rank. J . The M athem atics o f D iffus io n . 2nd Ed.; O xford U n ive rs ity Press: New York, NY; 1971.

(2 6 ) Korsm eyer, R W .; Lustig, S. R ; Peppas, N. A. J. Polym. Set Polym. Phys. Ed. 1986, 24, 395.

(2 7 ) E verett, D. H . In The Solid-G as In te rface . V ol. 2, Flood, E. A ., ed.; M arcel D ekker, Inc.: New York, NY; 1967.

(2 8 ) Lee, G. L.; S tem , S. A .; M ark, J . E.; Hoffm an, E. Investiga tion o f S tructu re -P erm e ab ilitv R elationships o f S ilicone Polym er M em branes: F in a l Report O ctober 1982 - Septem ber 1986; Gas Research In s titu te : Chicago, IL.

(2 9 ) B rodbelt, J . S.; Cooks, R G.; Tou, J . C.; Kallos, G. J .; D iyzga, M. D. AnaL Chem. 1987, 59, 454.


CHAPTER 6

The Application of Membrane Extraction Mass Spectrometry to the Analysis of

Gas and Liquid Process Streams

The efficiency o f chem ical processes is becom ing an increasing ly

im p o rta n t issue w ith the grow ing push tow ard waste reduction and

m in im iz in g organic em issions in a ir and water. A na ly tica l chem istry

can p lay a v ita l ro le in achieving and m a in ta in ing op tim um process

opera ting conditions. As opposed to o ff-line analysis, on -line analysis

can provide more e ffic ien t use o f in fo rm a tion about a process in term s

o f the am ount o f data, the qu a lity o f data, and the a b ility to respond to

changes in the process as exh ib ited by the data (1). As a sim ple

example, the continuos tem perature m easurem ents obtained w ith a

therm ocouple device can provide a m ore s ta tis tica lly use fu l data set

and m ore precise ind ica tions o f changes in the process tem perature

th a n in te rm itte n t m anual m easurem ents w ith a therm om eter. The

same is tru e fo r o ther tra d itio n a lly m easured process param eters such

as pressure and pH, as w ell as the m ore sophisticated m easurem ents

o f the process com position. C urren tly , on -line process com position

m easurem ents are often obtained from chrom atographic (2 ),

spectroscopic (3, 4), or so lid state chem ical sensor (5) techniques, as

d icta ted by the na tu re o f the analyte and the process m a trix . A lthough

the speed, sens itiv ity , and se lectiv ity o f mass spectrom etry m ake the

154


technique attractive , on-line analysis by mass spectrom etry has u n til

recently been lim ite d to clean, w ell-defined gas phase stream s.

Sam pling is generally the m ost d iffic u lt problem associated w ith

the on-line analysis o f process stream s, regardless o f the ana lytica l

technique (6 ). M any gas and liq u id process stream s are chem ically

and physica lly complex and require pretreatm ent p rio r to analysis.

Th is has been especially tru e fo r mass spectrom etry, w hich has

generally u tilize d a cap illa ry or orifice sample in tro d u ctio n system th a t

is lim ite d to filte red gases. M any sam pling problem s can be

circum vented u tiliz in g membrane extraction techniques. Advantages

o f sam pling w ith the silicone ho llow fibe r membranes include the

s im p lic ity o f the membrane extracto r device, the h igh sample surface

area-to-volum e ra tio in the hollow fiber, the capab ility to obtain high

lin e a r flows a t re la tive ly low volum e flows, and the a b ility o f the

m em brane to provide e ffic ien t extractions o f organic com pounds from

bo th a ir and water. In addition , the inertness o f the silicone

mem brane m ateria l makes it suitable fo r use in m any bio logical and

chem ically reactive systems. The headspace gases in reactors have

been successfully m onitored by ME-MS (7-10) as have liq u id stream s

(11-14). However, the sim ultaneous on-line analysis o f the in flu e n t

and e ffluen t gas and liq u id streams o f a reactor have no t been

previously reported.

W hile previous w ork focused on the m easurem ent o f com pounds

in e ithe r the e ffluen t gas o r the e ffluen t liq u id , a ll stream s m ust be

considered fo r complete process characterization. Assum ptions made

155


about the q u a n tity o f a com pound in the in flu e n t stream can yie ld

s ig n ifica n t errors in the mass balance determ inations. As w ill be

dem onstrated in th is chapter, the m easurem ent o f the in flu e n t as w ell

as the e ffluen t stream s m inim izes these errors. A generic process th a t

has liq u id in flu e n t and e ffluen t stream s and gas in flu e n t and e ffluen t

stream s is illu s tra te d in Figure 6.1. T h is chapter describes the

developm ent o f an on-line m u lti-g a s /liq u id -s tre a m m on ito ring

technique and its application to the sim ultaneous trace analysis o f

com plex and d irty stream s in three wastewater trea tm ent reactors.

EXPERIMENTAL SECTION

Chem icals

The com pounds used in th is study were obtained from F isher

S c ien tific (Fair Lawn, New Jersey) and A ld rich Chem ical Company

(M ilwaukee, W isconsin). These com pounds were generally non po la r

and re la tive ly inso lub le in w ater, so they were prepared in acetone to

fa c ilita te d isso lu tion when spiked in to the in flu e n t wastewater stream .

W ater standards were prepared in a 1-L glass ja r o f deionized

w ater w ith the same so lu tions used to spike the in flu e n t w ater stream .

A ir standards were prepared in a 100-L Saran™ (The Dow Chem ical

Company, M id land, M ichigan) bag fille d w ith a ir by in jec tin g know n

volum es o f 1:1 m ixtu res o f the two com pounds being studied. The

standards were analyzed fo llow ing each reaction analysis.

156


membrane extractors

effluentgas

effluentliquid to MSSPROCESS N

influentliquid

influentgas

Figure 6 .1 . A configuration for th e influent and effluent analysis by ME-MS o f a m ulti-stream , m ulti-phase process.

157


A nalyzer

A Balzers QMG 511 quadrupole mass spectrom eter was used in

th is study. The mass spectrom eter, sam pling valve, and data

a cq u is ition were contro lled by in-house w ritte n software on a PDP 11-

73 com puter from D ig ita l E quipm ent C orpora tion (M aynard,

M assachusetts). The ins trum e n ta l conditions were as follows:

Mass range: 60-200 daltons

Scan rate: 30 m sec/da lton, 10 scans averaged

Secondary electron m u ltip lie r voltage: 1900 V fo r w ate r stream s, 2000

V fo r a ir stream s.

A nalyzer pressure: 1 X 10-5 to rr fo r w ater stream s, 3 X 10"6 to rr fo r

a ir stream s.

The com bina tion o f 10 averaged re la tive ly slow scans was selected

because these in s tru m e n ta l conditions provided very good se n s itiv ity

fo r fu ll scans in less than one m inu te . To the lim it where ion

transm issions decay a t h igh scan rates, the use o f slow scan rates w ith

a quadrupole mass analyzer w ill provide signal-to-noise ra tios

com parable to those obtained from averaging several fas t scans over

the same du ra tio n o f tim e.

M em brane and sam pling system

The process stream s were pum ped from the reactors th rough

the m em brane extractors v ia 6 -m eter long, 1/ 8 -in ch (0.32-cm ) o.d.

sta in less steel tubes. The silicone ho llow fib e r m em branes used in

th is s tudy were constructed by sealing 2.5-cm lengths o f Dow C om ing

(M id land, M ichigan) S ila s tic™ m edical grade tu b in g in to 1/ 8 -in ch

sta in less steel tu b in g tees, as shown in Figure 5.2. The two ends o f

158


the ho llow fib e r mem brane are sealed in to stain less steel fe rru les w ith

Dow C om ing S ilastic silicone sealant. For sam pling the e ffluen t a ir

stream s, 0.0305-cm i.d ., 0.0635-cm o.d. ho llow fib e r mem branes were

used. The e ffluen t a ir was pum ped th rough the membrane extractors

a t the ra te o f 60 cm3/m in u te w ith an a ir pum p from M etal Bellows

Corp. (Sharon, Massachusetts). Aqueous samples were draw n th rough

0.147-cm i.d ., 0.196-cm o.d. ho llow fibe r m embranes a t the ra te o f 10

cm 3/m in u te w ith flu id pum ps from F lu id M etering Corp. (Oyster Bay,

New York).

A 1 /8 inch SC-12-HT hastelloy-C ro ta ry sw itch ing valve from

Valeo Instrum ents Co., Inc. (Houston, Texas) was used to in terface the

m em branes to the mass spectrom eter. Th is valve was com puter-

actuated so th a t a d iffe ren t stream was sampled every 5 m inutes. The

analyzer side o f a ll in le ts, when no t selected fo r sam pling to the mass

spectrom eter, was con tinuously evacuated by a vacuum pum p to

prevent accum ula tion o f perm eating species. The m embranes and

valve assem bly were m ounted in an oven and m ainta ined a t 30 °C. The

perm eation process is tem perature dependent, as discussed in

C hapter 2, therefore the in le t was m ainta ined s lig h tly above the

process and m axim um am bient tem peratures. The analyzer vacuum

cham ber and transfe r line between the valve and the mass

spectrom eter were heated to 100 °C.

W astew ater treatm ent apparatus

To dem onstra te the u t il ity o f M E-M S fo r o n -lin e re a c tio n

m o n ito rin g o f m u ltip le stream s, th is s tu d y was perform ed w ith

159


PrimaryStream

TREATMENTBASIN

Air-stripStream

Air Stream

SecondaryStream

CLARIFIER

¥Figure 6 .2 . A diagram o f the wastewater treatm ent bioreactor.

160


bioreactors in a wastewater treatm ent p ilo t p la n t a t the Dow Chem ical

Com pany in M idland, M ichigan. The p ilo t p la n t consists o f three 75-L

reactors, depicted in Figure 6.2, th a t were designed to s im ula te a

large scale trea tm ent process and were stocked w ith biom ass from a

general w astew ater trea tm ent p lan t. The flow -th rough reactors were

composed o f s tirre d trea tm ent basins and c la rifie rs fo r recycling the

biom ass back in to the basins. The tem perature o f the reactors was

m ainta ined a t about 27 °C.

The in flu e n t wastewater was firs t filte red by 100-pm and 50-pm

can is te r filte rs and then m ixed w ith the spike so lu tion in s tirre d 1-L

glass m ix ing ja rs . A 10-cm3 syringe w ith a syringe pum p from Sage

Instrum en ts (Cambridge, M assachusetts) was used to in je c t the spike

so lu tion a t a ra te o f 5 p l/m in u te in to the in flu e n t wastewater, w h ich

was flow ing in to the m ixing ja r a t a ra te o f 110 cm 3/m in u te (Figure

6.3). The caps o f the m ix ing ja rs were fitte d w ith Te flon™ -(E .I. du

Pont de Nemours and Company, W ilm ington Delaware) coated silicone

ru bbe r seals to prevent losses due to evaporation. The b ioreactor

in flu e n t stream s, flow ing a t a ra te o f 35 cm 3 /m in u te , were draw n from

the wastewater stream flow ing from the m ix ing ja r. A second m ix ing

ja r provided an unspiked wastewater stream to a b ioreactor used to

generate baseline data. The wastewater flows were driven by

M aste rflex™ p e ris ta ltic pum ps from Cole Parm er In s tru m e n t

Company (Chicago, Illino is). The in flu e n t a ir con tinuously flowed a t a

ra te o f 900 cm3/m in u te in to the bottom o f each basin. The tops o f the

reactors were covered w ith polyethylene sheeting tig h t enough to

reduce the d ilu tio n o f the e ffluen t a ir stream due to a ir cu rren ts in the

161


Primary Stream 110 cc/min.

■ £ J -f l

Overflow to Drain 25 cc/min.

SPIKED PRIMARY STREAM MIXING VESSEL IIi i_

U

to Sample Inlet10 cc/min.

rlto Basin 1 35 cc/min.

to Basin 2 35 cc/min.

Overflow to Drain 70cc/min.

Primary Stream 110 cc/min.

to Basin 3 35 cc/min.

to Sample Inlet10 cc/min.

PRIMARY STREAM MIXING VESSEL

Figure 6 .3 . The syringe and m ixing jar configuration for spiking organic com pounds in to liquid stream s.

162


room , b u t no t so tig h t as to cause a positive pressure in the reactor

headspace.

RESULTS AND DISCUSSION

The system developed has been tested and evaluated in the

context o f process analysis. In m any processes, bo th in flu e n t and

e ffluen t stream s need to be analyzed fo r com plete characte riza tion o f

the process and to m in im ize errors due to im p u ritie s o r inaccura te

assum ptions about the in flu e n t com position. Results o f the technology

developm ent, perform ance tests, and an app lica tion o f the technique

to rea l processes are described below.

M u lti-gas/liqu id -s tream ana lys is

By analyzing the stream s in flu e n t and e ffluen t to a process, as

illu s tra te d in F igure 6.1, mass balance determ inations can be

perform ed and a m ore com plete p ic tu re o f a process can be obtained.

For a given com ponent entering the process under non-reactive

conditions, the steady state mass balance equation is

m il + m ig = m el + rrigg (6 . 1 )

and un de r reactive conditions is

m il + m ig = m el + m eg + m p (6 .2 )

163


where m is the mass flow rate fo r the com ponent in the stream

designated by the subscrip t, and where the subscrip ts i, e, 1, and g

designate the in flu e n t, e ffluent, liq u id , and gas stream s, respectively.

The mass flow rate due to uptake o f the com pound by the process is

designated m p. The values fo r m ^, n^g, m ei, and m eg are determ ined

from the on-line extraction and analysis o f the stream s and m p is

calcu lated from Equation 6.2.

The mass flow rates fo r a com ponent in the d iffe ren t process

stream s are calcu lated by m u ltip ly in g the process stream

concentration (m g/L) by the process stream flow ra te (L /m inu te ). For

example, the mass flow rate fo r a com ponent in the in flu e n t liq u id

stream is determ ined mass spectrom etrica lly from the fo llow ing

equation:

m il = Fil*C ii = FU*r -f-std,l*Iil (6.3)

where is the concentration o f the com ponent in the process

stream , Kgtd is the ana lytica l response factor fo r the com pound

obtained from analyzing the liq u id standards, and Id is the response

fo r the com pound in the process stream. This equation applies in the

determ ination o f bo th liq u id and gas phase mass flow rates a fte r

su b s titu tin g in the appropriate param eters.

I t is use fu l to present the mass balance determ inations in

Equations 6 .1 and 6.2 as percent recovery or percent conversion,

defined as follows:

164


%Rec = 100% *(mel + m eg )/(m ii + m ig) (6 .4)

%Con = 100%*mp/(m ii + m ig) = 100% - %Rec. (6 .5)

Furtherm ore, the fate o f unreacted m ateria ls in the process is

determ ined by ca lcu la ting the percent recovery fo r the com pound in

each e fflu en t stream . For example, the unreacted percent recovery fo r

the com pound in the liq u id e ffluen t stream is calculated as follows:

The capacity to m o n ito r m u ltip le stream s and even m u ltip le

processes provides the a b ility to no t on ly make mass balance

de term inations, b u t also to analyze reference baseline stream s (no

added reactants) to make these determ inations more accurate. The

percent recovery fo r process A is obtained from E quation 6.7, where

the an a ly tica l resu lts from process A are background corrected w ith

the re su lts from the baseline process B.

%RecA = 100% *[(meiA - m ^B ) + (megA - m ^B )]

M ore accurate resu lts are obtained from de term in ing percent

recoveries fo r each sam pling cycle ra th e r tha n ca lcu la ting the

recoveries from tim e-w eighted averages o f each stream , since the

background levels and the baseline signals may no t be constan t over

tim e .

% Recei = 100%»mei/ ( n iii + m ig) (6.6)

/[(m ^A - m aB) + (migA - m igB)] (6 .7)

165


To dem onstrate the u tility o f the ME-M S technique and the

im portance o f analyzing process in flu e n t stream s, two aqueous stream s

- one o f w h ich was con tinuously spiked w ith non po la r organic

com pounds - were analyzed. The stream s were a com plex m a trix o f

chem ical w astew ater con ta in ing so lids and trace level organic

contam inants. The diagram in F igure 6.3 shows the syringe and

m ix ing ja r con figu ra tion fo r sp ik ing the aqueous stream w ith the

organic com pounds. These com pounds, th e ir concentra tion in the

acetone dispersant, the m ass/charge ra tios (m /z) o f the ions used fo r

q u a n tita tio n , and th e ir m g/L-based response factors are lis ted in Table

6.1. Each spike set contained tw o o f the com pounds o f in te rest. The

second w astew ater stream , w h ich was n o t spiked, was analyzed in the

same m anner to ob ta in a baseline fo r ca lcu la ting the spike

co n trib u tio n . A n advantage o f us ing ho llow fib e r membranes fo r the

d irec t analysis o f such com plex sam ples is th a t fo u ling of the

m em brane by so lids is in h ib ite d by the h igh lin e a r sam ple flow s w hich

con tinuous ly sweep the m em brane surface.

D iffic u lty was encountered in sp ik ing the aqueous stream - a

problem th a t underscores the im portance o f analyzing the process

in flu e n t stream s. The m easurem ents o f some o f the spiked

com pounds in the stream exiting the m ix ing ja r were in itia lly as low as

5% o f the ca lcu la ted levels. The arom atic com pounds in p a rtic u la r

showed very poor d isso lu tion in to the aqueous stream . A pparently, as

the spike so lu tio n approached the ex it tip o f the 1 /16-inch sta in less

steel syringe tu b in g , the acetone dissolved in the w ate r stream , and

the m ore inso lu b le organic com pounds e ith e r p recip ita ted in the

166


Table 6 .1 . Spike se ts w ith volum e % in acetone, m onitored ions, and standard response factors. Baseline response was 0 .0005 .

% inspike sets acetone

1 to luene 7.6

d ich lo rom eth ane 5.0

2 benzene 7.5

carbon te trach lo ride 4.2

3 ethylbenzene 7.6

ch lo ro fo rm 4.4

4 styrene 12.0

1,1 ,2 -trich lo ro e th a n e 7.6

5 chlorobenzene 6.0

te tra ch lo ro e th e n e 4.0

6 b rom o fo rm 3.8

1 , 1 , 1 -trich lo ro e th a n e 8 .2

response /m g /L m /z in a ir in w ater

91 8 . 8 0.088

84 0.6 0.016

78 9.0 0 .10

117 2.5 0.034

106 7.6 0.055

83 2.1 0.060

104 10.3 0.092

97 2.5 0.030

112 1.4 0.018

129 0.9 0.006

173 0.8 0.007

97 0.3 0.015

167


bo ttom o f the m ix ing ja r o r dissolved back in to the acetone so lu tion in

the syringe. Th is problem was no t observed when preparing

standards by q u ick ly in jec tin g 2 0 p i a liquots o f the spike so lu tions in to

a 1-L ja r o f w ater. These resu lts suggest th a t i f the lin e a r ve locity o f

the sp ike so lu tion was increased su ffic ien tly , more complete m ix ing o f

the spiked organic liq u id s in to the aqueous phase w ould occur. The

syringe was m odified such th a t a 4-cm length o f 50-pm i.d . fused s ilica

tu b in g was sealed w ith epoxy in to the tip o f the syringe needle,

th roug h w hich the spike so lu tion flowed in to the in flu e n t stream . The

m odified syringe provided a calculated 400-fo ld increase in lin e a r

ve locity fo r the spiked so lu tion and the sp ik ing efficiency, fo r the m ost

pa rt, im proved dram atica lly.

The calcu lated concentrations based upon the am ount o f

com pound spiked and the actua l measured concentrations o f the

com pounds in the wastewater are lis ted in Table 6.2. In spite o f the

im provem ents in the sp ik ing technique, ethylbenzene continued to

e xh ib it poor sp ik ing efficiencies, possibly due to a com bination o f the

low s o lu b ility fo r ethylbenzene in w ater (lowest among the com pounds

studied) and the h igh a ffin ity o f ethylbenzene fo r solids as noted by

H anna and co-workers (15). D uring the study o f the wastewater

tre a tm e n t process discussed below, the w ater exiting the m ix ing ja rs

was used as the liq u id in flu e n t stream s fo r the bioreactors. The

m easured in flu e n t values - n o t the calculated values - were used in the

b io reacto r mass balance determ inations, th u s m in im iz ing the errors

th a t m ay re su lt from the false assum ption th a t the spikes were 1 0 0 %

e ffic ie n t.

168


Table 6 .2 . Spike co n cen tra tio n s (m g/L) in th e in flu en t w astew ater.

com pound calcu lated m easuredto luene 3.57 2.35d ich lo rom ethane 3.57 3.40ethylbenzene 3.47 0.49ch lo ro fo rm 3.47 2.66benzene 3.54 3.71carbon te trach lo ride 3.61 3.61styrene 5.78 5.391,1,2 trich lo roe tha ne 5.81 5.81chlorobenzene 3.43 4.69te trach lo roe the ne 3.36 3.75b rom o fo rm 5.95 2.981,1,1 trich lo roe tha ne 5.95 3.78

A pplica tion to a biological w astew ater treatm ent process

The analyses o f vo la tile organic com pounds in wastewater and a ir

are m ost com m only perform ed o ff-line a fte r firs t extracting and

concentra ting the organic com pounds from the m a trix (16, 17).

These procedures are often laborious, tim e-consum ing, and require

sam ple m an ipu la tion . W ith ME-MS, the on-line extraction ,

concentration, and analysis o f the in flu e n t liq u id and the e ffluen t

liq u id and gas stream s from the process shown in F igure 6.2 were

perform ed nearly sim ultaneously. The in flu e n t a ir stream s were

analyzed fo r p u rity by ME-MS p rio r to the on-line analyses, b u t were

no t con tinuously m onitored.

The process fo r the rem oval o f vo la tile organic com pounds from

the wastewater m a in ly occurs v ia two m echanism s in a bioreactor:

169


biodegradation and a ir-s trip p in g . In m any cases, these appear to be

ra te-com petitive processes such th a t biodegradation o f m any

com pounds is im proved when th e ir residence tim e in the "biom ass" is

increased, i.e ., w hen a ir-s trip p in g is reduced. However, fo r aerobic

b iodegradation, aeration o f the biom ass is required, im p ly in g th a t

some a ir-s trip p in g is inevitable. The process shown in F igure 6.2 was

stud ied by perform ing mass balance determ inations fo r the organic

p rio rity p o llu tan ts lis ted in Table 6.1. W ith the m u lti-g a s /liq u id -

stream analysis capability , process mass flow rates were determ ined

fo r three d iffe ren t reactors. As shown in F igure 6.4, each reactor was

prepared d iffe ren tly : In reactors 1 and 2, the in flu e n t w astew ater was

con tinuously spiked to 3-6 m g /L w ith the target com pounds. Reactor

3, serving as the ana ly tica l b la n k o r reference, was no t spiked.

Reactor 2, the ana lytica l test sample, was spiked, b u t its biom ass was

rendered non-reactive by m a in ta in ing the contents a t pH less th a n 2.

The aqueous stream s were analyzed w ith the flow -th rough

silicone ho llow fib e r m em brane extracto r w ith a 0.147-cm i.d ., 0 .196-

cm o.d. ho llow fib e r membrane. A Reynolds num ber value o f

approxim ate ly 160 was achieved fo r the 1 0 cm3/m in u te sam ple flow s

from the wastewater in flu e n t and e ffluen t stream s. By m in im iz ing the

effects o f bounda iy layers, Reynolds num bers approaching 800 have

been shown to im prove the m em brane extraction efficiency fo r m any

com pounds as discussed in C hapter 5. Reynolds num ber values o f 800

were achieved w ith a 1 0 cm3/m in u te wastewater flow by u tiliz in g a

0.0305 cm i.d . ho llow fib e r membrane, b u t p lugging w ith solids and

sludge resulted. A sample flow o f 50 cm3/m in u te in the larger ho llow

170


to vacuum pump MS

drain

ea;eaeaewew ew

notspiked

spikedspiked

activebiomass

inactivebiomass

activebiomass

IW,

IW,IW

Key:

nt

iw = in flu e n t w astew ater stream iws = spiked in flu e n t w astewater stream ia = in flu e n t a ir stream ew = e ffluen t w ater stream ea = e ffluen t a ir stream .

Figure 6 .4 . A process flow diagram illustrating th e spiking and onlin e sam pling o f three wastewater treatm ent bioreactors.

171


fib e r w ou ld be required to a tta in these Reynolds num bers, b u t due to

lim its on sam ple consum ption, 1 0 cm3/m in u te was chosen as the

m axim um flow rate. Zero sample consum ption could have been

achieved by recycling the sam ple stream s back in to the process,

however, th is was n o t done in th is study. In any case, the sensitiv ities

were su ffic ie n t w ith the larger diam eter mem brane. The e fflu en t a ir

sam ples were pum ped th rough the 0.0305-cm i.d . ho llow fib e r a t a

ra te o f 60 cm 3 /m in u te . Convective m ixing o f the a ir stream s is n o t as

im p o rta n t because the d iffu s ion o f organic vapors in a ir is m uch more

ra p id th a n perm eation th rough the membrane.

Mass flow ra tes were determ ined from the mass spectrom etric

steady state process data and Equation 6.4. Pure a ir was used fo r the

in flu e n t gas, therefore m ig = 0 fo r the organic com pounds. Table 6.3

lis ts the steady state concentrations in m g /L fo r the com pounds in the

e fflu en t w ate r and a ir stream s in the reactive process (w ith the

background signal from reactor 3 subtracted). These data

dem onstrate the cap ab ility o f the technique to provide sensitive on

lin e analyses o f the physica lly and chem ically com plex m u lti-phase

process. Mass flow ra te vs. tim e p lo ts are displayed in Figures 6.5 and

6 . 6 fo r carbon te trach lo ride and benzene, respectively, from the three

reactors. Carbon te trach lo ride was observed to be m uch m ore in e rt to

the action o f the biodegradation process than was benzene, as

discussed in m ore de ta il below. As dem onstrated by these p lo ts, mass

flow ra te de term inations can be more m eaningfu l tha n concentra tion

values w hen de fin ing a chem ical process.

172


Table 6 .3 . Concentrations (mg/L) detected in th e effluent water and th e air stream s in th e reactive process. Styrene and chlorobenzene are not detected (N.D.) above the baseline in th e effluent water.

com pound effluen t w ater e ffluen t a ird ich lo rom ethane 0.41 0.003ch lo ro fo rm 0.32 0.044carbon te trach lo ride 0.07 0.0461 , 1 ,1 trich lo roe thane 0.30 0.0731 , 1 ,2 trich lo roe thane 2.09 0.076te trach lo roe thene 0.15 0.065brom oform 1.58 0.026benzene 0.07 0.005toluene 0.31 0 .0 1 2

ethylbenzene 0 .0 1 0.005styrene N.D. 0.003chlorobenzene N.D. 0.003

The percent recoveries fo r reactor 1 were calcu la ted from

E quation 6.7 w ith reactor 3 provid ing the background values. The

percent recoveries from reactor 2 were calcu lated from the steady

state mass flow rates using Equation 6.4. A fo u rth reactor, no t spiked

and conta in ing non-reactive biomass, w ould provide baseline data fo r

reactor 2, b u t was no t available fo r th is study. For these calcu la tions, i t

was assumed th a t the signal was due en tire ly to the com pound o f

in te rest. The percent recoveries fo r each com pound in reactors 1 and

2 are sum m arized in Table 6.4. Had the am ount o f spiked com pound

added to the reactor in flu e n t been assumed to be correct and no t

measured, serious errors in the mass balance determ inations w ould

have resulted. The data in Table 6.4 dem onstrate the capacity o f the

173


0.04

0.02

0

.iw ea-ew

0.12iw

0.10

c 0.08I"3> 0.06 E- 0.04 o>

(80 .0 2

5o

ew

COCOcs 0.12

iw0.10

0.08

0.06

ea0.04

0.02

ew0

0.0 10.0 20.0 30.0 40.0

Time, hours

Key;iw = in flu e n t wastewater stream ew = the e ffluen t w ater stream , ea = e ffluen t a ir stream

Figure 6 .5 . Mass flow rate p lots for carbon tetrachloride in A, reactor 3 (reactive, n ot spiked), B, reactor 2 (non-reactive, spiked), and C, reactor 1 (reactive, spiked). The spike was begun at th e 8-hour mark.

174


0.04

0.02 +

0/ lw ew

[ * ea ,

0.12iw

g 0.10o>E 0.08

ea0.06

0.04

ew“ • 0.02

0

0.12iw

0.10

0.08

0.06

0.04

0.02ea

— ew0

0.0 10.0 20.0 30.0 40.0

Time, hours

Key:iw = in flu e n t wastewater stream ew = the e ffluen t w ater stream , ea = e ffluen t a ir stream

Figure 6 .6 . Mass flow rate p lots for benzene in A, reactor 3 (reactive, n o t spiked), B, reactor 2 (non-reactive, spiked), and C, reactor 1 (reactive, spiked). The spike was begun at the 8-hour mark.

175


on -line an a ly tica l system to determ ine the re la tive inertness o f

d iffe ren t organic m ateria ls to a reactive process, where the substances

e xh ib itin g h ighe r percent recoveries are m ore in e rt to the process.

Table 6 .4 . Percent recoveries and standard deviations for th e spiked organic com pounds.

com pound reactive process non-reactive processd ich lo rom ethane 15; 1 100; 4ch lo ro fo rm 64; 3 92; 5carbon te trach lo ride 42; 1 72; 31 , 1 ,1 trich lo ro e th a n e 69; 4 85; 6

1 , 1 ,2 trich lo roe tha ne 77; 7 87; 8

te tra ch lo roe th e n e 59; 7 103; 4b rom o fo rm 80; 14 105; 12benzene 6 ; 4 8 8 ; 4to luene 29; 2 1 0 0 ; 6

ethylbenzene 34; 33 113; 20

styrene 2 ; 1 75; 6

chlorobenzene 2 ; 1 96; 3

The capacity to determ ine the re la tive a ir-s trip p in g process

efficiencies fo r the d iffe ren t com pounds is also dem onstrated. The

frac tions o f the organic com pounds rem ain ing in the e ffluen t w ater

and removed from the w ater by the a ir-s trip p in g process were

calcu lated using Equation 6 .6 and are given in Tables 6.5 and 6 .6 ,

respectively. Again, the resu lts fo r reactor 1 are baseline-corrected.

176


Table 6 .5 . Percent recoveries and standard deviations in the effluent water stream s.

com pound reactive process non-reactive processd ich lo rom ethane 1 2 ; 1 30; 2ch lo ro fo rm 1 2 ; 2 18; 1

carbon te trach lo ride 2 ; 1 1 1 ; 1

1 , 1 ,1 trich lo roe thane 8 ; 2 1 0 ; 1

1 , 1 ,2 trich lo roe thane 36; 4 41; 4te trach lo roe the ne 4; 1 9; 1b rom oform 53; 11 74; 11benzene 2 ; 1 24; 1to luene 13; 1 2 1 ; 2ethylbenzene 1 ; 1 19; 1styrene 0 ; 1 18; 1

chlorobenzene 0 ; 1 17; 1

Table 6 .6 . Percent recoveries and standard deviations in the effluent air stream s.

com pound reactive process non-reactive processd ich lo rom ethane 3; 1 70; 2ch lo ro fo rm 52; 3 75; 4carbon te trach lo ride 40; 1 61; 31 ,1 ,1 trich lo roe thane 61; 4 75; 51 , 1 ,2 trich lo roe thane 41; 3 46; 4te trach lo roe the ne 55; 7 94; 4b rom oform 27; 3 31; 3benzene 4; 3 64; 2to luene 16; 1 79; 5ethylbenzene 33; 33 94; 20styrene 2 ; 1 58; 5chlorobenzene 2 ; 1 79; 3

177


The background-corrected fra c tio n o f organic m a te ria l removed

due to uptake by the biom ass in reactor 1 was calculated from

E quation 6.5. T h is b io -up take term represents the unrecovered

fra c tion o f m ateria l and m ay be a com bination o f b io logical

fe rm enta tion and absorption. The actua l percent rem oval due to the

biom ass m ay be affected by o ther factors. D eviations from 100%

recoveries in the non-reactive process in reactor 2 are presum ed to be

due to experim enta l e rro r as w e ll as the presence o f solids. These

deviations are assumed to be consistent fo r the three reactors.

Therefore, given the capacity to m o n ito r a ll o f the reactors, the

recoveries from reactor 2 cou ld be used as correction factors in

ca lcu la ting corrected b io-uptake values:

% B io -u p ta ke 1 (corrected) = 100%*[1 - (% R eci/% R ec2 )l (6 .8 )

B oth the uncorrected and corrected (given in parentheses)

values fo r the b io-uptake are lis ted in Table 6.7, along w ith values

reported in the lite ra tu re from o ff-line analyses (18-23). The

ca p a b ility to dem onstrate the re la tive re ac tiv ity o f the d iffe ren t

com pounds in b io logical w astew ater trea tm ent processes is provided

by these analyses.

In m ost cases, the percent b io -up take resu lts from th is s tud y are

consistent w ith the percent biodegradation values reported in the

lite ra tu re . The greatest d isp a rity is observed fo r 1,1,1-trich lo roe thane

and tetrachloroethene, where essentia lly no biodegradation was

reported in one lite ra tu re reference (18), a lthough b io -up take o f 19%

178


Table 6 .7 . Percent bio-uptake and standard deviations. Experim ental values corrected for the recoveries in th e analytical te s t reactor (reactor 2) are given in parentheses.

com pound experim enta l lite ra tu re

d ich lo rom ethane 85; 1 (85; 1) 50-95b, 100d, 96e

ch lo ro fo rm 37; 3 (31; 4) 50-95b, 0a

carbon te trach lo ride 58; 1 (41; 4) 50-95b

1 , 1 ,1 trich lo roe tha ne 31; 4 (19; 4) 5b, 0a

1 , 1 ,2 trich lo roe tha ne 23; 7 ( 1 2 ; 2 )

te trach lo roe the ne 41; 7 (42; 7) 0 a

brom ofo rm 20; 14 (24; 7)

benzene 94; 4 (94; 4) 50 -95b, 85-88f

to luene 71; 2 (71; 1) 50-95b, 84-88f, 40

ethylbenzene 6 6 ; 33 (70; 28) 50 -95b, 85-97f,

styrene 98; 1 (97; 1)

chlorobenzene 98; 1 (98; 1) 91a, 79-93c

Bey:a = Reference 18 b = Reference 19 c = Reference 20 d = Reference 21 e = Reference 22 f = Reference 23.

179


and 42% , respectively, were observed in th is study. As w ith any

process, b iodegradation is h ig h ly dependent upon the reaction

cond itions. The age and species o f biomass, organic in flu e n t

concen tra tion , m in e ra l n u trie n t content, process flow ra te (re ten tion

tim e), oxygen concentra tion, tem perature, pH, and o ther factors

in fluence the biodegradation process. As is apparent from the

com parison o f lite ra tu re values, the resu lts can vary w idely depending

upon these process conditions. For example, one study (18) showed

no b iodegradation o f ch loroform (as w e ll as 1 , 1 , 1 -trich lo roe thene and

te trach lo roe thene), w h ile ano ther (19) reported the b iodegradation o f

ch lo ro fo rm to be in a range o f 50-95% . A corrected value o f 31% b io

up take fo r ch loroform was observed in th is study.

In sp ite o f the use o f filte rs , the flow o f sludges and sm all

p a rticu la te s was constan tly observed in the in flu e n t wastewater. The

concentra tion o f solids was n o t constant and could no t be predicted.

The in flu e n t w ater was sometimes clear one day and tu rb id w ith solids

the next day. These solids apparently were road d ir t (earth m oving

vehicles were w o rk in g in the area), ta rs , and sludge from aggregated

biom ass. E x trac tin g the organic com pounds from th is physica lly

com plex w astew ater m a trix was a c ru c ia l step in these experim ents,

because sam ple m a trix effects can lead to large errors in trace analyses

(24). Even sm all errors in a stream analysis m ay re su lt in large errors

in the m ass balance determ inations.

Frequently, the presence o f so lids affected the process w hen the

so lid levels became p a rtic u la rly h igh in the in flu e n t wastewater,

180


causing the recoveries to become s ig n ifica n tly depressed. For

exam ple, when h igh tu rb id ity was observed du ring one process

analysis, mass balance determ inations fo r dichlorom ethane and

to luene around the non-reactive process (reactor 2 ) showed

recoveries o f on ly 39% and 32%, respectively. Large differences were

s t ill observed between the reactive and non-reactive processes fo r th is

experim ent, where mass balance determ inations around the reactive

process (reactor 1) showed recoveries o f on ly 1 .6 % fo r

d ich lorom ethane and 1 .0 % fo r toluene.

These re su lts dem onstrate the capacity o f the ana ly tica l system

to m o n ito r the effects o f so lids on the em issions o f organic vapors

from wastewater. However, the absorption o f the organic com pounds

in to the solids represented another process, th u s in tro d u c in g another

up take variab le in to the mass balance equation. Th is second uptake

variab le was d iffic u lt to separate from the b io-uptake variable and it

was n o t w ith in the scope o f th is study to do so. Therefore, when poor

recoveries were observed from reactor 2 , the experim ent was

repeated a fte r the in flu e n t w ater became less tu rb id . As a re su lt, the

recoveries were su ffic ie n t fo r reactor 2 (mean percent recovery = 93,

a = 1 2 ) considering the com plexity and the concentra tion levels o f the

process stream s. Relatively large standard deviations in the recoveries

exh ib ited fo r ethylbenzene are like ly due to its low in flu e n t

concentra tion (0.49 m g/L) w h ich enhances the effects o f random

e rro r and process baseline changes. Again, these resu lts dem onstrate

the im portance o f analyzing the in flu e n t stream ra th e r tha n re ly ing on

the calcu la ted spike values.

181


W hen the process flows were in te rru p ted fo r some reason (e.g.,

pum p fa ilu re o r plugging o f the stain less steel sam pling tubes) and

solids dried on the membranes, the perm eation characte ristics

changed. Th is happened occasionally and sim ply required

replacem ent o f the membranes. Follow ing each study (every 3-4

days), the sample tubes and m embranes fo r sam pling the wastewater

stream s were flushed w ith clean tap w ater and allowed to s it fo r

several hours to prevent the grow th o f anaerobic bacteria on the inside

o f the tub ing. The membranes th a t were used to sample the gas

stream s showed no observable change in properties th roug ho u t these

experim ents.

CONCLUSIONS

I t has been dem onstrated th a t, w ith little o r no sample

preparation, membranes can be used as an effective interface between

com plex and d irty m atrices (gas and liqu id ) and a mass spectrom eter.

The use o f a single technique and a single analyzer fo r a m u lti-phase

and m u lti-s trea m process m inim izes experim ental errors and

s im plifies ca lib ra tion . The ana lytica l system can be used to study,

optim ize, and po ten tia lly to help con tro l and autom ate processes. In

ad d ition to the determ ination o f the fate o f organic com pounds in

waste trea tm ent processes, o ther app lica tions include the on -line

s tudy o f ferm entation, d is tilla tio n , absorption, devolatilization,

s trip p ing , degassing, and membrane separation processes. The

re lia b ility o f the continuous analysis o f such processes depends upon a)

the general re lia b ility o f the analyzer, b) the re lia b ility o f the sam pling

182


system , and c) the re lia b ility o f the process itse lf. Mass spectrom eters

fo r process m on ito ring are com m ercia lly available and have

dem onstrated re lia b ility fo r specific applications. However, as stated

a t the beginn ing o f th is chapter, sam pling the process is generally the

lim itin g facto r such th a t the analyzer is on ly as good as the sam ple

in tro d u c tio n system . U ltim ate ly, the analysis depends upon ro u tine

m aintenance and the continuous operation o f the process a t the range

o f cond itions fo r w hich i t - and the sam pling system - was designed.

183


REFERENCES

(1 ) C allis, J . B .; Mm an, D. L.; Kowalski, B. R AnaL Chem 1987, 59, 624A.

(2 ) M anka, D .P. Autom ated Stream A nalysis fo r Process C on tro l. V ol. 1; Academ ic Press: New York, NY; 1982.

(3 ) Eckstein, R J .; Owens, G. D.; Bairn, M. A .; Hudson, D. A. AnaL Chem. 1986 , 58, 2316.

(4 ) Seitz, W. R AnaL Chem. 1984, 56, 16A.

(5 ) Schuetzle, D .; Hamm erle, R Fundam entals and A pp lica tions o f C hem ical Sensors. ACS Sym posium Series 309; A m erican C hem ical Society: W ashington, DC; 1986.

(6 ) Blaser, W. W .; R uhl, H. D.; Bredeweg, R A. Amer. Lab. January 1989, 69.

(7 ) Tou, J . C.; W estover, L. B. J. Phys. Chem. 1974, 78, 1096.

(8 ) Kallos, G. J .; Tou, J . C. Environ. Set Technol 1977, 11, 1101.

(9 ) Savickas, P. J .; LaPack, M. A .; Tou, J. C. AnaL Chem 1989, 61, 2332.

(10) Van Nugteren-Osinga, I. C.; Bos, M .; Van Der Linden, W. E. AnaL C him A cta 1989, 226, 171.

(11) Pungor J r.. E.; Pecs, M .; Szigeti, L.; Nyeste, L. AnaL C h im A cta 1984 , 163, 185.

(12) Heinzle, E .; Reuss, M. Mass Spectrom etry inB io techno log ica l Process Analysis and C on tro l: P lenum Press: New York, NY; 1987.

184


(13) B ier, M. E.; Kotiaho, T.; Cooks, R G. AnaL Chim. A cta 1990, 231, 175.

(14) Hayward, M . J .; Kotiaho, T.; L ister, A. K.; Cooks, R G.; A ustin , G. D .; Narayan, R ; Tsao, G. T. AnaL Chem. 1990, 62, 1798.

(15) Hanna, S. A .; A ustem , B. M .; E ralp, A. E.; W ise, R H. J. W ater PolluL Control Fed. 1986, 58, 27.

(16) EPA Test M ethods fo r E va luating Solid W aste, Volum e IB ; M ethods 8240 and 8270; U.S. EPA O ffice o f Solid Waste and Em ergency Response; W ashington, D.C.; 1986.

(17) NIOSH M annual o f A na ly tica l M ethods, 3 rd Ed.; M ethods 1003 and 1501; P. M. E lle r, ed.; U.S. DHHS (NIOSH) P ub lica tion No. 84-100; U.S. Governm ent P rin tin g O ffice: W ashington D.C.

(18) Bouwer, E. J .; M cCarty, P. L. Environ. Set TechnoL 1982, 16, 836.

(19) Eckenfelder J r., W. W .; Patoczka, J .; W atkin , A. T. Chem. Eng. 1985, 60.

(20) K irsch, E. J .; W ukasch, R F. Report to M un ic ipa l E nvironm enta l Research Laboratory; Office o f Research and Development, U.S. E nvironm enta l P rotection Agency: C inc inn a ti, Ohio, 45268.

(21) K lecka, G. M . App. and Environ. M icrobiology 1 9 8 2 , 44, 701.

(22) R ittm ann, B. E.; M cCarty, P. L. App. and Environ. M icrobiology 1980 , 39, 1225.

(23) K incannon, D. F.; Fazel, A. 41st A nnua l Purdue In d u s tria l W aste Conference, Purdue U niversity, W est Lafayette, Ind iana , 1986.

(24) U.S. EPA M ethod 1624 and 1625; Federal Registry, 49(209); 1984.

185


APPENDIX

Permeation M easurements

The d ire c t m easurem ent o f perm eation param eters is com m only

made by exposing the feed side o f the membrane to a pure substance

a t a know n pressure w hile m easuring e ithe r the increasing pressure a t

the permeate side o f the mem brane w ith a pressure gauge (1) or the

permeate flow w ith a flow m eter (2, 3) o r a sim ple detector such as a

the rm a l conductiv ity detector (4, 5). O ther m ethods inc lude

m easuring the w eight gain o f the polym er in the presence o f the gas o f

in te rest (6 , 7). These techniques only a llow fo r the analysis o f a single

com ponent a t any tim e and m ay suffer from interferences i f the

substance being tested is n o t pure or i f the cham ber leaks on e ither

side o f the membrane. In addition , contacting silicone w ith m ost pure

organic solvents resu lts in sw elling o f the polym er, y ie ld ing non-

F ick ian behavior. The sensitiv ity and specific ity o f a mass

spectrom eter provides fo r perm eation ra te m easurem ents a t low

concentra tions and independent o f o ther com ponents (8 - 1 0 ).

The response o f the mass spectrom eter to a gaseous substance

flow ing in to the ion source, e ithe r by perm eation th rough a membrane

o r by effusion through an orifice, is ideally given by E quation 2.8. The

mass spectral response factor, Qj, is no t easily m easured w ith a

membrane, b u t m ay be obtained by analyzing gas standards from a

186


large reservoir th rough an orifice in a th in m etal fo il (11). A t

su ffic ie n tly low pressures o r sm all orifice size (i.e., o rifice rad ius

sm alle r tha n the mean free pa th fo r gases), the flow ra te o f a

com ponent th rough an orifice o f area Aq in to a vacuum is given by (1 2 )

F j = 0.225*Ao*pi /(M i*RT) 1/2 (A. 1)

where p j is the p a rtia l pressure o f com ponent i in the reservoir, M i is

the m olecu lar w eight o f the com ponent, R is the ideal gas constant,

and T is the absolute tem perature. Therefore,

Q i = Ij (Mi.R T )l/2 /(0 .2 2 5 » A o*p i) (A.2)

where I i is the ana ly tica l response fo r the com ponent. W ith the

de term ination o f Qj, the perm eability m ay be determ ined by

su b s titu tin g Equation 2.8 in to Equation 2.6 o r Equation 2.7. For the

sheet m em brane.

Pi = D i s»Ki = (rfi*d)/(Q i«A ) (A.3)

The value fo r Dsi is determ ined from the perm eation response curve

and E quation 2.13, and is calculated from the ra tio

K i = P i/D i s (A.4)

The com ponents o f the perm eation response curve used to determ ine

Pi and D i,s are shown in Figure A. 1.

187


ANAL

YTIC

AL

RE

SP

ON

SE

P = rf*d/(QA) = DS*K

t(50) TIME

Figure A .1. Experim ental determ ination o f perm eation param eters.

188


I t is generally tru e th a t any quantita tive analysis (i.e., the

perm eation ra te measurem ent) should be perform ed soon before or

a fte r standard iza tion o f the analyzer (i.e., by the orifice technique).

The num ber o f com pounds th a t can be stud ied in a reasonable tim e

period is lim ite d by the operations such as sw itch ing back and fo rth

between the o rifice and the mem brane extractor. In add ition , the

perm eation m easurem ents m ay be tim e-consum ing fo r larger organic

m olecules since they require no t on ly the tim e to reach steady state

perm eation fo llow ing a step change in the sam ple concentration, b u t

tim e is also required to achieve a baseline fo llow ing rem oval o f the

sam ple and p rio r to the next sample in tro d u c tio n . A more e ffic ien t

approach to these m easurem ents is to determ ine values fo r Qj fo r the

com pounds to be stud ied and norm alize a ll o f them to one o f the

com pounds. These response factors, m any o f them re la tive to toluene,

have been previously determ ined by a m ethod developed by C aldecourt

(11) fo r a large num ber o f com pounds and tabula ted in a Dow Chem ical

A na ly tica l Sciences mass spectral data base (13). A s im ila r data base,

w ith response factors re la tive to butane, has been generated by the

S hell O il Com pany (14). The re la tive response facto r is defined here

as follows:

qt = (It/wtl/Ui/Wi) (A. 5)

where w is the w eight o f the substance in jected in to the reservo ir and

the sub scrip t t ind ica tes toluene, w h ich is chosen to be the com pound

to w h ich a ll others are norm alized. Values fo r fo r several

com pounds exam ined in th is w ork are lis ted in Table A. 1. For a given

189


Table A .1. Mass spectrom etxic response factors, relative to toluene, used to determ ine perm eation param eters.

com poundn itro g e noxygenargoncarbon dioxidem ethaneetheneethanepropanebutanepentanehexaneheptanebenzeneto lueneethylbenzenechlorobenzenech lo rom ethaned ich lo rom ethanecarbon te trach lo ridech lo roe thene1 ,1 -d ich lo ro e th enetrich lo ro e th e n ete tra ch lo roe th e n ebrom om ethaned ib rom om ethaneb rom o fo rmw a te rm ethano le thano l1 -p ropano l2 -p ropano l1 -bu tano l acetone2 -butanone

re la tive response fac to r 0.39 0.51 0.33 0.49 0.27 0.71 1.21 1.964.03 1.75 1.701.09 0.651.00 1.93 1.07 0.82 1.41 3.901.10 1.87 2.8111.3 2.18 3.15 20.8 0.961.03 1.29 0.67 0.74 1.53 0.93 0.73

m /z2832404416273044584343437892

1061125049

117626195949493911831313145564343

190


m ass spectrom eter under proper operating conditions, the re la tive

response facto r is a constant. D ay-to-day ins tru m e n t d r ift re su ltin g in

va ria tions in the response fo r one substance w ill re su lt in p ropo rtiona l

va ria tions in response fo r the second substance. W hen a d iffe ren t

m ass spectrom eter is used, add itiona l errors are in troduced.

However, w ith proper tu n in g o f the analyzer, these errors are

m in im ized and the perm eation param eters m ay be adequately

estim ated fo r several com pounds in a re la tive ly sho rt period o f tim e.

The w eight o f the standard added to the reservo ir is re la ted to

the p a rtia l pressure by the ideal gas equation, where Wj =

P i^M ^V /lR ^T), w hich when substitu ted in to E quation A. 5 y ie lds the

fo llow ing :

The re la tionsh ip between th is re la tive response fac to r and the

absolute response facto r in Equation A.2 is given by

A pplying E quation A. 3 to th is re la tionsh ip yie lds the enrichm ent facto r

fo r com pound i re la tive to toluene

(A. 6 )

(A. 7)

8 i/t = P i/Pt = qi*(rfi/ r f t)*(Mt/M i)3/2 (A. 8 )

191


I f Pt is m easured by the technique described above, then the

perm eabilities fo r a ll o f the com ponents where values are available

can be easily estim ated.

As stated previously, m ost o f the perm eation param eters fo r

gases such as nitrogen are known fo r m any membranes. I t can easily

be shown th a t the enrichm ent factors re la tive to n itrogen fo r the

com ponents where qj is know n can be determ ined by the fo llow ing

equation:

^ i/N 2 = P i/^N 2 = (r fi/r fN 2 ), (£l i / <lN2 )*(MN2 /M i)3 / 2 (A.9)

The advantages to using th is so lu tion are 1) as stated above, the

pe rm eab ility param eters fo r n itrogen are w e ll established fo r m ost

m em brane m ateria ls and 2 ) the n itrogen m a trix , in w h ich m ost

standards are prepared, is m uch more representative o f the a ir m a trix

m ost com m only encountered in tru e ana lytica l applications. A s im ila r

equation is used to determ ine the enrichm ent factors re la tive to

w ater.

ERROR ANALYSIS

Assum ing th a t errors in the calcu lated perm eation param eters

are random , and th a t the sources o f these errors can be id e n tified and

th e ir m agnitudes estim ated, then the re la tive standard devia tion fo r

each param eter can be estim ated. The re la tive variance fo r a

m easurem ent is given by the square o f the re la tive standard deviation.

192


The re la tive standard devia tion fo r the calcu la ted perm eation

param eters is given by the square roo t o f the sum o f the variances fo r

a ll o f the sources o f e rro r (15). The equations used to ca lcu la te the

perm eation param eters and th e ir corresponding re la tive standard

devia tion expressions are sum m arized as follows:

E nrichm ent fa c to r (re la tive to nitrogen)

^ i/N 2 = (Ii/lN 2^*^cN2 / ci^*^(l i / (lN2 )*(MN2 /M i)3 / 2 (A. 10)

^£i/N2/£i/N2 = {0Ii/Ii)2 + 0 In2/^N2^2 + 0 ci / ci)2

+ Ocj/Ci)2 + O qi/qi)2 + 0 q j/q j)2}1/2 (A. 11)

The re la tive response factors, q j and q ^2 » 3X6 assumed to be

consisten t from one m ass spectrom eter to another, as stated above.

The m olecu lar w eights, and MN2, used in E quation A. 10 are

assum ed to be accurate.

P erm eab ility

P i = PN 2*£i/N 2 (A - 1 2 )

3Pi/Pi = [PN2/Pil*^ i/N 2 = ^ /N 2 /^ i /N 2 (A. 13)

The value fo r the perm eability o f n itrogen, PN2 ’ used in E quation A. 12

is assum ed to be accurate.

193


Difrfusivity

D us = 0 .14«d2/ ( t50-to) (A. 14)

3DiiS/D i>s = {(2*ad/d)2 + aatso-atoi/itso-toi)2}1/ 2 (A. 15)

The e rro r in the response tim e m easurem ent is dependent upon

the e rro r in determ in ing the tim e o f in itia l contact o f sam ple w ith the

m em brane, to, and in determ in ing the tim e where one-ha lf steady

sta te perm eation is achieved, t 5 0, as described in C hapter 2. The

e rro r in the tim e o f in itia l contact is estim ated to be approxim ate ly

;0 .5 seconds. The e rro r in the m easurem ent o f the tim e requ ired fo r

on e -h a lf steady state perm eation is the difference in tim es between

da ta po in ts (;0.25 seconds) in the ion in te n s ity vs. tim e perm eation

p ro file p lo t.

D is trib u tio n ra tio

The to ta l sam ple pressure, p t = 76 cmHg, used in E quation A. 16

is assumed to be accurate.

Ki = 76 cm Hg.Pi /D i ,s (A. 16)

aKi/K i = {©Pj/Pija + 0D i.s/D itS)2}l/2

= {08i/N2/£ i/N 2)2 + 0D i.s /D i.s)2}1/2 (A. 17)

194


Values estim ated fo r the re lative standard deviation fo r each

know n source o f e rro r are given, along w ith the re la tive standard

deviations fo r the com puted resu lts fo r enrichm ent factors,

perm eabilities, d iffus iv ities, and d is trib u tio n ra tios, in Table A.2. The

re la tive standard deviations estim ated fo r the ana lytica l signals, Ij, and

the response tim es, (tso-to), are com pound-dependent. Com pounds

th a t dem onstrate poor ana lytica l sensitiv ities and sho rt response tim es

e xh ib it the greatest re lative variances. However, these sources o f

e rro r are typ ica lly negligible when compared w ith the errors

estim ated fo r the re la tive response factors, qj, and the m em brane

th ickness, d. The range o f the re lative standard deviations fo r the

an a ly tica l responses does no t affect the erro r analysis fo r the

enrichm ent factors o r the perm eabilities. The range o f the re la tive

standard deviations fo r the response tim es on ly s lig h tly affect the

e rro r analysis fo r the d iffus iv ities and the d is trib u tio n ra tios. The

tolerance reported fo r the membrane w a ll th ickness (16), 3 d /d =

31%, is m uch larger than observed experim entally. In the cu rre n t

studies, re la tive standard deviation fo r the membrane th ickness is

m ore reasonably estim ated to be less than 1 0 %, in w h ich case the

range fo r the re lative standard deviation fo r d iffu s iv ities is 20-24% and

fo r the d is trib u tio n ra tios is 24-28%.


Table A .2. Relative standard deviation for each known source of error and for each com puted perm eation param eter.

know n source o f e rro r

a i i / i i

^ 2 / ^ 2

acj/ci

3cN2 /c N2

9 q i/q i

9qN2/qN2

3d /d

(3t5Q-3to) / (t5o_to)

result

^^ i/N 2 /^ i/N 2

3Pi/Pi

SKj/K i

range o f estim ated re la tive standard deviation

2.9X10-2-1.7 %

6.0X10-3 0/0

1.0 %

1.0 %

1 0 %

1 0 %

31 %

0.21-14 %

14 %

14 %

62-64 %

64-66 %


REFERENCES

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The Theory and Practice of Membrane Extractions

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