Development of Continuous Two-Dimensional Thermal Field ...

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University of Helsinki Faculty of Science Department of Chemistry Laboratory of Analytical Chemistry Finland Development of Continuous Two-Dimensional Thermal Field-Flow Fractionation for Polymers Pertti Vastamäki ACADEMIC DISSERTATION To be presented, with the permission of the Faculty of Science of the University of Helsinki, for public criticism in Chemicum Auditorium A129, (A.I. Virtasen Aukio 1, Helsinki), on May 9 th 2014, at 12 o’clock. Helsinki 2014

Transcript of Development of Continuous Two-Dimensional Thermal Field ...

University of Helsinki

Faculty of Science

Department of Chemistry

Laboratory of Analytical Chemistry

Finland

Development of Continuous Two-Dimensional

Thermal Field-Flow Fractionation for Polymers

Pertti Vastamäki

ACADEMIC DISSERTATION

To be presented, with the permission of the Faculty of Science of the University of

Helsinki, for public criticism in Chemicum Auditorium A129, (A.I. Virtasen Aukio 1,

Helsinki), on May 9th

2014, at 12 o’clock.

Helsinki 2014

Supervisor Professor Marja-Liisa Riekkola

Laboratory of Analytical Chemistry

Department of Chemistry

University of Helsinki

Finland

Reviewers Professor Jukka Lukkari

Department of Chemistry

University of Turku

Finland

Dr. Karel Klepárnik

Institute of Analytical Chemistry

Academy of Sciences of the Czech Republic

Czech Republic

Opponent As. Professor Catia Contado

Department of Chemical and Pharmaceutical

Sciences

University of Ferrara

Italy

Custos Professor Marja-Liisa Riekkola

Laboratory of Analytical Chemistry

Department of Chemistry

University of Helsinki

Finland

ISBN ISBN 978-952-10-9892-5 (pbk.)

ISBN ISBN 978-952-10-9893-2 (PDF)

http://ethesis.helsinki.fi

Unigrafia Oy, Helsinki 2014

Preface

This thesis is based on research carried out in the Laboratory of Analytical Chemistry of

the Department of Chemistry, University of Helsinki. Financial support for the research

was provided by the Oskar Öflunds Foundation, the Association of Finnish Chemical

Societies, and the Department of Chemistry, University of Helsinki. Thesis leave for

writing was provided by VTT Technical Research Centre of Finland.

I am most grateful to my supervisor, the Chair of Analytical Chemistry, Professor

Marja-Liisa Riekkola, for the opportunity to carry out this research project on a part-time

basis over the course of several years. I would like also to thank Professor Jukka Lukkari

and Dr. Karel Klepárnik for their careful reading of the thesis and the comments they

supplied.

Sincere thanks are expressed to my co-authors Matti Jussila, Dr. Steve Williams, and

Professor Michel Martin for their support and professional criticism during the course of

the research.

In addition, I would like to thank co-authors and colleagues involved this and related

projects: Professor Heli Sirén, Professor Francisca Sundholm, Docent Kari Hartonen,

Docent Susanne Wiedmer, Dr. Juhani Kronholm, Dr. Stella Rovio, Dr. Gebrenegus

Yohannes, Dr. Ritva Dammert, Pentti Jyske, and many other former and present

colleagues of the Laboratory of Analytical Chemistry, the Department of Chemistry, and

VTT Technical Research Centre of Finland. Special thanks go to Pekka Tarkiainen, Merit

Hortling, Erja Pyykkö, Liisa Heino, and Karina Moslova for their help in all technical and

practical matters.

Further thanks are due to Dr. Kathleen Ahonen for revising the language of the thesis

and the manuscripts.

Above all, loving thanks to Liisa, to my family members, to my relatives, and to my

friends, for their support and understanding during the progress of my work.

Munsaari, March 2014

Pertti Vastamäki

Abstract

This research work was focused on the development of instrumentation, operations,

and approximate theory of a new continuous two-dimensional thermal field-flow

fractionation (2D-ThFFF) technique for the separation and collection of macromolecules

and particles. The separation occur in a thin disk-shaped channel, where a carrier liquid

flows radially from the center towards the perimeter of the channel, and a steady stream of

the sample solution is introduced continuously at a second inlet close to the center of the

channel. Under influence of the thermal field, the sample components are separated in

radial direction according to the analytical ThFFF principle. Simultaneously, the lower

channel wall is rotating with respect to the stationary upper wall, while a shear-driven

flow profile deflects the separated sample components into continuous trajectories that

strike off at different angles over the 2D surface. Finally, the sample components are

collected at the outer rim of the channel, and the sample concentrations in each fraction

are determined with the analytical ThFFF. The samples were polystyrene polymer

standards and the carrier solvents cyclohexane and cyclohexane‒ethylbenzene mixture in

continuous 2D-ThFFF and tetrahydrofuran in analytical ThFFF.

The thermal field had a positive effect on the sample deflection, although broadening

of the sample zone was observed. Decreasing the channel thickness and the radial and

angular flow rates of the carrier caused significant narrowing of the zone broadening.

Systematic variation of the experimental parameters allowed determination of the

conditions required for the continuous fractionation of polystyrene polymers according to

their molar mass. As an example, almost baseline separation was achieved with two

polystyrene samples of different molar masses.

Meanwhile, an approximate theoretical model was developed for prediction of the

trajectory of the sample component zone and its angular displacement under various

operating conditions. The trends in the deflection angles without and with a thermal

gradient were qualitatively in agreement with predictions of the model, but significant

quantitative differences were found between the theoretical predictions and experimental

results. The reasons for discrepancies between theory and experiment could be the

following: relaxation of the sample already at the sample inlet, effect of solvent partition

when binary solvent is used as the carrier, dispersion of the sample, limitations of the

instrument, and geometrical imperfections. Despite its incompleteness, the theoretical

model will provide guidelines for future interpretation and optimization of separations by

continuous 2D-ThFFF method.

Contents

Preface 3

Abstract 4

List of original publications 7

Abbreviations 8

Symbols 9

Introduction 10

2 Aims of the Study 11

3 Field-Flow Fractionation 12

3.1 Thermal field-flow fractionation 14

3.1.1 Principle and theory of ThFFF 14

3.1.2 Applications 17

3.1.3 ThFFF instrumentation 18

4. Continuous Two-Dimensional ThFFF 21

4.1 Continuous two-dimensional separations 21

4.2 Principle and Theory of Continuous Two-Dimensional ThFFF 23

4.3. Experimental 26

4.3.1 Continuous 2D-ThFFF Instrumentation 26

4.3.2 Reagents 28

4.3.3 Continuous fractionation procedure 29

5. Results and Discussion 31

5.1 Exploration of continuous fractionation of polymers 31

5.2 Effect of run conditions on continuous fractionation 36

5.2.1 Effect of molar mass and thermal gradient 38

5.2.2 Effect of rotation rate of the lower wall and thermal fields 41

5.2.3 Effect of radial flow rate with and without the field 42

5.3 Additional effects not counted for in the modeling 44

6. CONCLUSIONS AND FUTURE PERSPECTIVES 47

References 50

7

List of original publications

This thesis is based on the following publications referred to in the text by their roman

numerals:

I Vastamäki, P., Jussila, M., Riekkola, M.-L., 2005. Continuous Two-

Dimensional Field-Flow Fractionation: A Novel Technique for Continuous

Separation and Collection of Macromolecules and Particles. Analyst 130,

427-432. DOI: 10.1039/B410046H Copyright The Royal Society of

Chemistry 2005.

II Vastamäki, P., Jussila, M., Riekkola, M.-L., 2001. Development of

Continuously Operating Two-Dimensional Thermal Field-Flow

Fractionation Equipment. Sep. Sci. Technol. 36, 2535-2545.

DOI:10.1081/SS-100106108 Copyright Taylor & Francis 2001.

III Vastamäki, P., Jussila, M., Riekkola, M.-L., 2003. Study of Continuous

Two-Dimensional Thermal Field-Flow Fractionation of Polymers, Analyst

128, 1243-1248. DOI: 10.1039/B307292B Copyright The Royal Society of

Chemistry 2003.

IV Vastamäki, P., Williams, P. S., Jussila, M., Martin, M., Riekkola, M.-L.,

2014. Retention in Continuous Two-Dimensional Thermal Field-Flow

Fractionation: Comparison of Experimental Results with Theory, Analyst

139, 116-127. DOI: 10.1039/C3AN01047C Copyright The Royal Society of

Chemistry 2014.

Authors contributions:

Paper I The author invented the original idea, carried out the method development,

and presented an overview of related continuous methods and the sample

applications within field-flow fractionation. The author wrote the paper

together with the co-authors.

Paper II The author invented the original idea, carried out the instrument construction

and method development, and wrote the paper together with the co-authors.

Paper III The author carried out the continuous thermal field-flow fractionation

instrument and method developments and wrote the paper together with the

co-authors.

Paper IV The author carried out the continuous thermal field-flow fractionation

method development and participated in the theory development. The author

wrote the paper together with the co-authors.

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Abbreviations

FFF field-flow fractionation

ThFFF thermal field-flow fractionation

FlFFF flow field-flow fractionation

SedFFF sedimentation field-flow fractionation

ElFFF electrical field-flow fractionation

MgFFF magnetic field-flow fractionation

GrFFF gravitational field-flow fractionation

SEC size exclusion chromatography

GPC gel permeation chromatography

LC liquid chromatography

HDC hydrodynamic chromatography

CE capillary electrophoresis

LS light scattering

GC-MS gas chromatography – mass spectrometry

MALDI TOF MS matrix-assisted laser desorption/ionization time-of-flight mass

spectrometry

NMR nuclear magnetic resonance

SPLITT splitt flow thin fractionation

QMS quadrupole magnetic flow separator

DMF dipole magnetic fractionator

2D-FFF two-dimensional field-flow fractionation

2D-ThFFF two-dimensional thermal field-flow fractionation

UV/VIS ultraviolet/visible detector

RI refractic index detector

FTIR Fourier Transform infrared spectroscopy

THF tetrahydrofurane

PS polystyrene

PET polyethylene terephthalate

PMMA polymethylmethacrylate

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Symbols

αT thermal diffusion factor

c concentration (g mol-1

)

c0 concentration at accumulation wall (g mol-1

)

D diffusion coefficient (cm2 s

-1)

DT thermal diffusion factor (cm2 s

-1 K

-1)

l mean layer thickness (nm, μm)

M molar mass (g mol-1

)

Mw weight average molar mass (g mol-1

)

Mn number average molar mass

Mw/Mn polydispersity

r radial distance (mm, cm)

ri radial distance of the sample inlet (cm)

ro outlet radius (cm)

reff effective channel radius (cm)

R retention ratio

Rr retention ratio in the radial direction

Rθ angular retention ratio

S Soret coefficient (K-1

)

t time (s, min)

tr retention time of retained sample (s, min)

t0 void time ( VV /0 ) (s, min)

T absolute temperature (K)

Tc cold wall temperature (K, oC)

dT/dx thermal gradient inside channel (K cm-1

, oC cm

-1)

ΔT temperature difference (K, oC)

V0 effective void volume of the channel (ml)

Vr retention volume (ml)

V carrier fluid flow rate (ml min-1

)

<vr> mean radial fluid velocity (ml min-1

)

w channel thickness (μm)

x distance from the accumulation wall (μm)

λ retention parameter

ξ reduced distance from accumulation wall (= x/w)

θ angular displacement (deg)

θr final elution angle (deg)

θ0 non-retained elution angle (deg)

φi fractional recovery of the polymer collected at

port i (%)

relaxation time (s, min)

Ω angular fluid velocity (rounds min-1

, rpm)

<Ω> mean angular fluid velocity (rpm)

Ω0 angular velocity of rotating wall (rpm)

π geometrical constant

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Introduction

The two-dimensional (2D) separation principle has been applied in many analytical

separation techniques, mostly for the separation of small molecules. However, only a

handful of 2D-techniques and methods are available for the separation of large sample

species‒among them electrophoretic, chromatographic and field-flow fractionation (FFF)

techniques. Electrophoresis is suited only for the separation of charged sample species,

and chromatography is limited by upper molar mass exclusion limits, sample adsorption

on the stationary phase, and shear degradation. Meanwhile, field-flow fractionation

represents a family of analytical techniques developed for the separation and

characterizion of different kinds of macromolecules, supramolecular assemblies, colloids,

and particles. FFF is a chromatography-like method, but the fractionation is carried out in

a single eluent phase and in an empty ribbon-like channel under the influence of an

external field perpendicular to the direction of the sample flow.

The elution in 2D continuos separation is realized along a single axis to give a

continuous collection of separated sample streams. This feature of 2D continuous

separation distinguishes it from combined 2D-separation methods, where two separation

mechanisms with different selectivities are employed simultaneously or in sequence. If all

known separation mechanisms are taken as building blocks, the possibilities of 2D-

separtions are almost endless.

In this work, the selective thermal field-flow fractionation mechanism was established

along one axis and flow displacement with a relatively small selectivity along the

orthogonal axis. The combination of these simultaneously acting mechanisms underlies

the 2D-dimensional continuous fractionation in a single fractionation channel.

The doctoral thesis includes an introduction to continuous two-dimensional field-flow

fractionation, which is a completely new approach among the continuous separation

systems for macromolecular and particular materials (paper I). A prototype instrument

constructed and verified in the laboratory with use of soluble polystyrene standards as

samples is reported in paper II, and the applicability of the instrument to the separation of

polymers of different molar masses is described in paper III. An approximate theory was

developed and experimental results were compared with theoretical predictions in paper

IV.

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2 Aims of the Study

The primary aims of the present study were to construct a new continuous two-

dimensional thermal field-flow fractionation instrument to elaborate its working principle

and approximate theory on the basis of analytical thermal field-flow fractionation, two-

dimensional separation mechanism, and fluid dynamics: and to compare the experimental

and theoretical results. In the experimental studies, polymer standards of known molar

mass and polydispersity and known carrier solvents were exploited to exclude all sample-

based uncertainties during the verification of the new method. The running conditions,

such as sample introduction rate, radial flow rate, and rotation rate of the accumulation

wall (angular flow rate), were optimised, along with the thermal field gradient, and study

was made of their effects on the deflection of samples with different molar masses.

Concentrations of the continuously collected sample components were then determined by

an analytical ThFFF method. An approximate model was developed for prediction of the

continuous fractionation of polystyrene samples under various operating conditions.

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3 Field-Flow Fractionation

Field-flow fractionation (FFF) is a method for the fractionation of macromolecules, colloids,

and particulate materials in a thin ribbon-like channel, where an external force field effects

the fractionation of sample components, dissolved or suspended in a flowing carrier liquid

(Fig. 1). In the years since 1966, when FFF was pioneered by Calvin Giddings [1], the

method has evolved into different FFF techniques, reflecting the variety of applicable force

fields needed for the fractionation of a large spectrum of samples. The most commonly

applied FFF techniques are flow FFF (FlFFF), sedimentation FFF (SedFFF), and thermal

FFF (ThFFF), all of which are commercially available [2]. Other fields, such as electrical

(ElFFF), force of gravity (GrFFF), magnetic (MgFFF), and a few less common fields, have

also been applied in FFF [3]. Depending on the FFF methods, they can be used for the

characterization of molar mass, particle size, and polydispersity of different samples [4]. In

addition, FFF methods are feasible for preparative purposes, quality control of different kinds

of industrial processes, and for fraction collection of certain sample components for further

analysis.

Figure 1 Principle of field-flow fractionation (paper I).

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The term one-phase chromatography technique has sometimes been suggested for FFF

because of its resemblance to chromatography, in which the separation of distinct sample

zones is achieved by differential migration along an axial tube. However, in FFF the

separation takes place in a single moving fluid flow without adsorbing surfaces and,

requires an external field [5]. In addition, the FFF channel does not contain a packed

stationary phase and it is constructed of inert materials. The main advantages of the FFF

method are the minimized shear degradation of high molar mass macromolecules,

flexibility due to adjustable and programmable fields, versatility of the possible force

fields, capability for rapid analysis, and the small amount of sample required [6-8]. FFF is

applicable for materials with molar masses ranging from 103 g/mol to ca. 10

18 g/mol and

for particulate samples with particle sizes from 1 nm up to ca. 100 m [9]. Typical sample

types analyzed by FFF are collected in Table I.

Table I. Sample types and their properties characterized by field-flow fractionation. (paper I)

Sample Determined properties Source

Synthetic polymers

(polystyrene, poly-

methylmethacrylate,

polyethylene oxide)

molar mass

molar mass distribution

compositional distribution

Polymer synthesis, industrial

processes and products

Biological and

environmental

macromolecules

(proteins, lipoproteins,

humic substances)

molecular mass

molecular mass distribution

compositional distribution

biological activity

Biological and environmental

samples and processes

Synthetic particles

(polystyrene latex

beads, glass-beads,

metal particles)

particle size

particle size distribution

surface properties

Particle synthesis, industrial

samples, products and processes

Environmental

particles (coal fly ash,

clay, mineral particles)

particle size

particle size distribution

surface properties

biological activity

Biological, environmental and

industrial samples, products and

processes

Cells and organelles

(bacteria, viruses,

liposomes, algae)

particle size

particle size distribution

multipolydispersity (size, density,

shape, and rigidity)

surface properties

bioadherence

biological activity

biomass distribution

cell growth

Biological and environmental

samples and processes

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3.1 Thermal field-flow fractionation

Thermal field-flow fractionation (ThFFF) was the first technique in which the principle of the

FFF was demonstrated for polymer samples [10]. Following the discovery of the separation

of polymer standards of different molar masses in different organic solvents, studies of

retention and column parameters were carried out to formulate a basic theoretical background

for the new technique [11-13]. Instrument development, operational practice, and theoretical

development have since then been continued by a number of research groups.

3.1.1 Principle and theory of ThFFF

The general principle of the FFF method is illustrated in Figure 1. A steady stream of a

carrier flow is pumped through an injector to the inlet of the channel, where the carrier liquid

flows laminarly through a thin channel. Because of friction between a viscous solvent and the

channel walls, the flow velocity is highest in the center of the channel and slows down close

to the surface of the walls. The resulting velocity profile is parabolic. After a narrow sample

band is injected at the head of the channel, the field applied perpendicular to the flow across

the channel causes the sample components to migrate to the lower channel wall, which is

often termed the accumulation wall. In ThFFF the movement of the solutes in the transverse

direction depends on the thermal diffusion of the solute species and their back diffusion away

from regions of higher concentration (Fig. 2). Each solute reaches a steady state distribution

close to the accumulation wall and the components, which are compressed closed to the

fastest moving flow region, are eluted first while the components closest to the wall are

eluted last. Soluble polymers usually elute obeying this normal mode FFF mechanism,

although so-called steric effects have been observed with ultrahigh-molar-mass polymers

[14]. Because the separation relies mainly on the interaction of the sample molecules with the

field and within the open channel geometry, exposure of the sample components to surfaces

is minimized. These features enable a gentle separation of large molecules with minimal

disruption [15, 16].

Figure 2 Schematic illustration of normal mode ThFFF with solutes A and B

undergoing differential flow transport under the influence of a thermal field.

DT is thermal diffusion, D ordinary diffusion, T thermal difference, w

channel thickness, and l mean layer thickness of the solute layer.

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In FFF, the retention of a sample component is specified by its retention ratio R, which

is calculated as

Eq. 1 R = t0/tr = V

o/Vr

where t0

is the void time, tr the retention time of the retained sample component, Vo the

geometrical void volume of the fractionation channel, and Vr the retention volume of the

retained sample component.

Assuming a constant field and a parabolic velocity profile, R is related to the

fundamental FFF retention factor as follows [12, 17]:

Eq. 2

where is defined as = l/w, with w the thickness of the channel and l the mean layer

thickness of the solute layer compressed against the accumulation wall of the channel. For

low l values or high levels of retention (i.e., λ<<1), Eq. 1 can be approximated by

Eq. 3

The dependence of on physicochemical parameters varies with the nature of the applied

field and, for ThFFF, we have

Eq. 4

where S is the Soret coefficient, D the diffusion coefficient, DT the thermal diffusion

coefficient. The derivative dT/dx is the thermal gradient inside the channel, which is well

approximated by T/w, where T is the thermal difference between the channel walls and

w the channel thickness. Thus, retention in ThFFF is governed by the Soret coefficient (S

= DT/D) and T [17-20].

In ThFFF, must be expressed in terms of a dimensionless thermal diffusion factor

and related transport constants, in order to relate experimental retention to the

underlying driving force of thermal diffusion. The equation is expressed as [12]

2

2

1coth6R

TD

D

dxdTwS T

)/(

1

6R

16

Eq. 5

This equation can be used to obtain values from the calculated s. Since

= DTT/D, an alternate expression for is [11, 13]

Eq. 6

where DT and D are for the given polymer/solvent system.Values of DT cannot be

calculated from the thermal FFF retention data unless D is know.

In ThFFF, the carrier flow is usually stopped, when the sample enters the channel, in

order to allow the relaxation to the steady-state concentration profile at the accumulation

wall under the influence of the applied field. Stopping the carrier flow during the sample

relaxation diminish band broadening. The relaxation time can be estimated by

Eq. 7

A 30-s stop-flow time is adequate for the relaxation of most polymers when a

conventional channel thickness is used [21].

The theoretical basis of thermal diffusion in the liquid phase is not very well known. It

has been shown that DT is almost independent of molar mass, chain length and branching

configuration of a polymer, but strongly dependent on the chemical composition of the

polymer and solvent [22-24]. Only limited data on thermal diffusion coefficients is

available, which means that calibration is often necessary in ThFFF work [17]. Usually,

narrow molar mass standards are used for calibration, but excellent calibration curves have

also been obtained by using a set of well-characterized broad standards [25]. Universal

calibration is possible only if the thermal diffusion coefficients of samples and standards

are known, other wise the standards should be of the same polymer as the samples. This is

often impossible, unfortunately, because of the limited availability of polymer standards

TD

w

T

2

17

[26, 27]. Polymers that differ chemically can be separated by ThFFF even when their

molar masses are identical [28], because the thermal diffusion coefficient DT varies with

the composition of both polymer and solvent [22]. These differences in DT can also be

used to separate copolymers according to chemical composition [29, 30].

The polymer‒solvent interactions can also be exploited by applying a binary solvent

system instead of a pure solvent to enhance the retention in ThFFF. Thus, solvent

segregation has been observed for some solvent mixtures, which provides an extra driving

force that can be used to enhance the retention of polymers in ThFFF. When the local

solvent composition is changed under the influence of the thermal gradient, the polymer is

partitioning according to the resulting solvent gradient. This creates an additional driving

force, the solvent-induced partitioning, which can enhance or diminish the retention

depending on the type of solvent enriched on the cold wall. However, enhanced retention

has been observed only when a better solvent is enriched on the cold wall. An additional

factor is the influence of the ordinary diffusion coefficient D, which may change nonlinearly

with solvent composition [31-35].

In addition to the use of binary solvent systems, very high thermal gradients with high

pressure enhance the ThFFF retention [36], and the operation using a programmed force

field, i.e. varying the thermal gradient during the fractionation process, has been shown to

lead to satisfactory separations at high flow rates with reduced analysis times [37-40].

3.1.2 Applications

ThFFF has been applied for the fractionation and characterization of a number of

lipophilic polymers, gels, and particles in organic and aqueous solvents [41-47]. From the

beginning the most commonly used synthetic polymer has been polystyrene (PS), and its

narrow molar mass standards have been also used for the calibration and study of the

physicochemical parameters and instrumental performance of the ThFFF method [11, 12,

48, 49]. Typically ThFFF can be applied for polymers with masses ranging from 20,000 g

mol-1

up to ultra-high molar masses (>106 g mol

-1) [15, 16]. Channels are usually

calibrated empirically, because the retention is dependent not only on molar mass but also

on the polymer‒solvent interactions. Many other soluble polymers, such as

polytetrahydrofuran, polyolefins, polybutadiene, poly(methylmethacrylate), polyisoprene,

polysulfone, polycarbonate, and copolymers, have been characterized [22, 50-60]. Water-

soluble polymers polyvinylpyrrolidone, polyvinylpyridine, polysaccharides, starch,

cellulose, pullulan, etc., have been studied, too. [42, 61, 62] During the past decades

ThFFF has been shown to be applicable for fractionation of sub- and sup-micron size

particles in both aqueous and non-aqueous solvents. [42-47, 63-70] Although thermal

diffusion is weak in polar solvents, such as water and alcohols, enhanced retention has

18

been obtained with the addition of organic solvents, salts, and surfactants. [43-45] A

relatively new micro-ThFFF system is suitable for fractionation of polymers and particles

[72-74], even for the fractionation of living cells. [75]

FFF techniques have been used for the characterizatithe on of physicochemical

properties of polymer samples. ThFFF is particularly well suited for the characterization

of industrial polymers and their deformation processes. It has been applied in the

determination of molar mass of polyethylene terephthalate (PET) after different plasma

treatment procedures [76] and in investigation of the degradation of high molar mass

polymethylmethacrylate (PMMA) and natural rubber adhesives exposed to an electron

beam at different dosages [77, 78]. In addition, ThFFF has been used to determine the

shear degradation of macromolecules in diluted solutions during the fractionation

experiments [79, 80]. It has been found to be beneficial in the quality control of industrial

polymers involving the analysis of microgels and elastomers [57, 60, 77, 78, 81-87] and in

the characterization of complex industrial copolymers and blends, as well as asphaltenes

and other heavy oil fractions [55-61, 88-91].

3.1.3 ThFFF instrumentation

The ThFFF system consists of a fractionation channel, which is typically cut out of a thin

polymer foil and clamped between two metal blocks, a pump, an injector for sample

introduction, a pressure control unit for the carrier, valves for switching the flow off during

relaxation, and a detector. The channel dimensions are 25‒90 cm in length and 1‒2 cm in

width, and the thickness is maintained by clamping a 50–250 m thick channel spacer

between the metal blocks [7]. Recently, some smaller ThFFF channels have been constructed

for rapid particle separation [74, 75] since, by reducing the channel dimensions, operational

advantages such as reduced material consumption, improved separation efficiency, and

higher analysis rate can be achieved [92]. In ThFFF, the maximal thermal gradient across the

channel is limited at a fixed channel thickness because of the heat transfer rate of the solvent

[93, 94].

Depending on the sample under investigation, typical detectors for ThFFF are a

spectrophotometer (UV/VIS), a refractive index detector (RI), a viscometer, FTIR, or a light

scattering detector [8, 81, 95]. Also, matrix-assisted laser desorption/ionization time-of flight

mass spectrometry (MALDI-TOFMS) has been shown to be capable of off-line analyses of

polymer fractions from ThFFF [96]. Recently, copolymers have been characterized using

ThFFF coupled with NMR [97, 98]. The pump, the injector, and the detector are identical

with those used in liquid and size exclusion chromatography. The thermal gradient T across

the channel is obtained by measurement of the temperatures of both walls and is maintained

by computer-control of the heating power. Computer programs are also used for data

acquisition and handling.

19

The surface finish of the channel walls has been shown to have a critical role in determining

the instrumental performance of FFF systems [99]. Therefore, the metal blocks of the ThFFF

channel are most often made of copper with even and highly polished surfaces and are coated

electrochemically with chromium and/or nickel to increase the mechanical and corrosion

resistance. Spacer materials such as MylarTM

(polyester terephthalate) and KaptonTM

(polyimide) are feasible owing to their low thermal conductivity, inert properties with

organic solvents, and stability at high operation temperatures. Teflon™ and multilayer

spacers have been applied in the FFF instruments, too. The upper wall is heated using liquid

circulation or electric cartridges and the lower wall is cooled by circulating the thermostated

liquid through the drilled holes. Very high thermal gradients exceeding 10,000 K cm-1

, can be

achieved [35]. The tubings for solvent inlet and outlet are fitted or soldered into drilled holes

of the metal block. The exploded view in Figure 3 illustrates schematically the ThFFF

construction.

Figure 3 Exploded schematic view of analytical ThFFF channel.

In this work the inlet and outlet capillaries into the channel were made of stainless steel (OD

1/16", ID 0.5 mm) and they were tightly sealed to copper bars with stainless steel fittings

(Swagelok Co., OH, USA). The thermal gradient across the channel was measured using

thermocouples at three positions along the channel: at the inlet and outlet and in the middle of

the channel. The average temperature difference was obtained with a computer program

(programmed by Matti Jussila, University of Helsinki). The channel was pressurized by

nitrogen gas delivered from an external pressurized bottle via the outlet of the channel. (Fig.

4). The pressure was kept constant during both relaxation and fractionation periods.

20

Figure 4 Scheme of pressurized ThFFF system.

The ThFFF system of this work has been described in paper II, and it was used to

determine sample concentrations in each of the collected 2D-ThFFF fractions. In addition,

the retention parameter λ for each polystyrene sample was determined as presented in

papers III and IV. The parameter λ was applied for the theoretical prediction of the elution

angle in the continuous 2D-ThFFF method (paper IV).

The analytical ThFFF system consisted of an in-house constructed fractionation

channel (45 cm x 2 cm x 125 μm), a HPLC pump (PU-2080; Jasco Corp., Tokyo, Japan),

two valves for injection and bypass (C6W: Valco Instrument Co, Inc, Houston, USA), a

UV detector (SP8450; Spectra Physics Inc., San Jose, CA, USA) operating at 254 nm for

the runs with HPLC-grade tetrahydrofuran, and at 280 nm with the binary mixture of

cyclohexane and ethylbenzene, The injection volume was 10 μL and the flow rate of the

carrier 150 µl/min. Various temperature differences ΔT across the channel were used. For

the determination of the concentrations of the polystyrene fractions collected from the

continuous 2D-ThFFF runs, the ΔT value was 100 K for the samples PS 19.8k and PS 98k,

80 K for PS 51k, 25 K for PS 520k, and 15 K for PS 1000k. For the measurement of the λ

vs. 1/ΔT plots for polymers PS 51k, 520k, and 1000k, ΔT values were varied between 16

K and 70 K, depending on the sample. The binary solvent used in the continuous method

was applied for determination of λ values. Sample properties and concentrations of the

stock solutions are presented in paper III.

21

4. Continuous Two-Dimensional ThFFF

4.1 Continuous two-dimensional separations

A number of examples of continuous, two-dimensional separations have been described in

the literature. Wankat [100, 101] described the relationship between one-dimensional,

time-dependent separations and two-dimensional, steady state (continuous) separations.

The continuous two-dimensional separations usually involve a selective displacement of

sample components along one direction and a non-selective displacement along an

orthogonal direction. According to Giddings [102, 103], the second displacement need not

be non-selective, but it is necessary that the second, selective displacement must not be

strongly correlated with the first. In fact, it is necessary only for two selective

displacements to have sufficiently different selectivity.

Different kinds of continuous separation methods have been developed. Examples of

continuous electrophoresis methods are continuous two-dimensional electrophoresis [104]

and continuous free-flow electrophoresis [105]. Continuous separation is achieved in the

dipole magnetic fractionator (DMF) [106-108] using a field-flow configuration identical

with that of continuous free-flow electrophoresis. Turina et al. [109] described a

continuous two-dimensional gas‒liquid chromatographic apparatus, but only preliminary

experiments were carried out. Giddings [110] described the theory of a continuous annular

gas chromatograph. Sussman and co-workers [111-113] have developed an approach to

continuous two-dimensional gas chromatography using radial flow between two closely

spaced glass plates. The method was referred to as continuous disk chromatography or

continuous surface chromatography. Continuous two-dimensional liquid chromatographic

separations have been carried out in annular packed columns [114-116]. Another

important implementation of continuous two-dimensional separation is that of split-flow

thin channel (SPLITT) fractionation, invented by Giddings [117], and developed further

with several design features [118-120]. FFF methods have been combined with a field-

induced displacement perpendicular to the FFF displacement, as in the case of the

continuous steric FFF [121, 122], where the selectivities of the longitudinal migration

(steric FFF) and the lateral migration (sedimentation) are different. In addition, Ivory et al.

have assembled a two-dimensional sedimentation FFF device, where field-flow

fractionation with transverse sedimentation has been implemented using a sedimentation

FFF channel tilted with respect to the axis of rotation [123]. Giddings has suggested that

continuous FFF could be carried out using radial flow between rotating disks, as in

rotating disk chromatography [124]. Continuous separation methods based on different

mechanisms and principles are collected with references in Table II.

22

Table II. Continuous separation methods based on different analytical mechanisms.

Method/Principle References

Two-dimensional separation principle 100-103, 124

Continuous two-dimensional electrophoresis 125-132

Continuous free-flow electrophoresis 133-135

Continuous free-flow electrophoresis in annular channel 136, 137

Continuous free-flow isoelectric focusing in a pH gradient 138-140

Continuous free-flow isotachophoresis 139-141

Continuous dipole magnetic fractionator (DMF) 106-108

Continuous two-dimensional gas-liquid and gas chromatography 109,111-113

Continuous annular gas chromatography 142-144

Continuous in paper and thin layer chromatography 145

Continuous two-dimensional liquid chromatography 114, 115, 146-165

Rotational chromatography 115, 159-161, 166

Continuous two-dimensional split-flow thin channel (SPLITT) fractionation 117-120, 167, 168

Annular SPLITT separation channel, quadrupole magnetic flow separator

(QMS). 106-108, 169-172

Continuous steric field-flow fractionation 121, 122

Continuous two-dimensional field-flow fractionation separations 123, 124, I-IV

Figure 5 illustrates the principle of continuous 2D separation, where selective

displacement occurs in the direction of the y-axis and non-selective flow in the direction

of the x-axis.

Figure 5 Sample paths for continuous 2D separation.

23

4.2 Principle and Theory of Continuous Two-Dimensional ThFFF

Continuous two-dimensional thermal field-flow fractionation (2D-ThFFF) is a relatively

new field-flow fractionation technique for the continuous fractionation of macromolecules

and particles. The general concept and construction of the instrument, method

development, and preliminary results were presented in papers II and III. In addition, a

theoretical model, together with a comparison of the calculated and experimental results,

was presented in paper IV.

The channel system is in some respect similar to the systems of continuous disk

chromatography [114-116] and rotating disc gravitational FFF [124]. Here, the carrier

stream flows from an inlet at the center of the heated upper wall to 23 outlets spaced

evenly around the circumference of the disk-shaped channel. The first outlet is aligned

with the injection port. Collection syringes are installed at the channel outlets and the flow

is maintained by suction at the syringes. In addition to the parabolic flow profile

established in the radial direction, a shear-driven flow component is generated in the

angular direction by slowly rotating the cooled lower channel wall. A steady stream of the

sample mixture is introduced continuously at a certain distance from the carrier inlet and

the sample components are subjected to two orthogonal displacement mechanisms:

selective field-flow fractionation along the radial direction and a flow displacement along

the angular direction that has a relatively small selectivity. It is the combination of these

simultaneously acting mechanisms that underlies the two-dimensional continuous

fractionation [102, 124, paper I]. The sample stream is broken into continuous component

filaments that strike off at different angles over the two-dimensional surface, and the

separated components are then collected at different locations around the perimeter of the

channel (Fig. 6).

24

Figure 6 Schematic drawings of the flow between two parallel disc-shaped walls and

the separation of two-component samples: a) sample zones separated in a

parabolic radial flow by the influence of a force field; b) two sample zones

separated in tangential flow established by the rotation of the lower channel

wall; and c) hypothetical sample trajectories (A) viewed from the top of the

instrument; (B) is the channel axis, (C) is the sample-introduction port, and

(D) represents the outlet ports (paper II).

An approximate theoretical model for predicting the trajectory of a sample component

zone, and the angular displacement of its elution point from the initial point of

introduction was derived in paper IV. The model is based on the following assumptions:

1. The radial fluid velocity profile is assumed to be parabolic. The small departure from

parabolic profile, caused by the variation of viscosity with temperature across the

channel thickness, can easily be taken into account by using the corrected equation for

retention ratio presented in the literature [173].

2. It is assumed that there is a simple shear flow in the angular direction. (variation in

viscosity will also influence the flow profile in the angular direction).

3. The concentration profile for each sample component is assumed to be exponential

across the channel thickness.

4. The sample flow rate is assumed to be negligible in comparison with the radial carrier

flow rate.

25

A schematic view of the 2D-ThFFF system with the flow components and geometrical

parameters is shown in Figure 7.

Figure 7 Schematic illustration of the disk-shaped 2D-ThFFF channel. Flow and

geometrical parameters, and symbols shown are: V , the eluent volumetric

flow rate; iV , the volumetric flow rate of a continuous sample feed; Ω0,

rotation rate of the lower wall; w, channel thickness; ri, radial distance of

sample inlet from the axis; ro, radius of the 2D channel disks; <vr>, mean

radial flow velocity; <Ω>, mean angular flow velocity; θ, rotation angle; A,

eluent exit and sample collection; B, section of upper channel wall; C, section

of lower (accumulation) wall; and D, field across the channel. For clarity only

one of the 23 channel exits is shown (paper IV).

Assuming a parabolic fluid velocity profile, the radial retention ratio Rr is given by Eq.

2 on page 15 with definition of the retention factor . If accumulation occurs at the

rotating wall, the angular retention ratio Rθ is given by

Eq. 8

1

2 2 11 exp 1/

R

The final angle θr for the trajectory at the time of elution tr is given by

Eq. 9 2 2 0

2r o i

r

Rr r w

R V

where ro is the outer radius of the system, ri the initial radial distance, w the channel

thickness, Ω0 angular velocity, and V the total carrier flow rate. Replacing π(ro2 – ri

2)w by

the effective void volume of the channel V0, we can write Eq. 9 in the form

26

Eq. 10 00

0 0

2 2r

r r

R R tV

R V R

where t0 is the void time, given by

0 /V V . The non-retained elution angle, θ0, is

obtained by setting Rr = Rθ = 1 in Eq. 10

Eq. 11 00

0 0 0

2 2

tV

V

Hence, the θr/θ0 ratio is equal to Rθ/Rr, and using the high retention limits for these

retention ratios we obtain for a rotating accumulation wall:

Eq. 12

0

1

3 1 2

r

The derived theoretical model was applied for the prediction of elution angles of known

polystyrene samples in continuous 2D-ThFFF method, and the results were compared with

experimental results in paper IV.

4.3. Experimental

4.3.1 Continuous 2D-ThFFF Instrumentation

The continuous 2D-ThFFF instrument consisted of an in-house constructed

fractionation channel, a microflow pump (Micro Feeder Model MF-2, Azumadenki

Kogyo, Tokyo, Japan) with an HPLC syringe of 500 μL for sample introduction, an

electrically-driven fraction collection unit above the channel, an electric motor for rotating

the water-cooled lower channel wall, and an electric resistance heater (max 700 W)

installed into the stationary upper wall to generate the thermal gradient across the channel.

The disk-shaped channel was cut into a 125 m or 250 m thick Mylar® sheet, which also

acts as a spacer between the wall elements. The diameter of the disk-shaped fractionation

space was 135 mm. The channel circumference edge was sealed with two fluoroelastomer

(VitonTM

) O-rings located between the stationary upper wall and the O-ring housing fitted

onto the surface of the lower block. The carrier was introduced at the center of the channel

and the sample at a port located 17 mm from the center. The symmetric radial flow was

established by suction of the pressurized carrier into fraction collection syringes (Discardit II,

Becton Dickinson, S.A., Fraga, Spain), which also collected the fractions at 23 collection

27

ports equally spaced around the circumference of the channel. A schematic cross-section of

the detailed apparatus is presented in Figure 8.

Figure 8 Construction of the continuous 2D-ThFFF channel. (A), rotating

accumulation wall; (B), stationary upper wall with collection ports; (C), disk-

shaped channel; (D), cooling water conduct with a guide plate; (E), water

inlet; (F), water outlet; (G), sample introduction port; (H), carrier inlet port;

(I), electrical heater surrounded by ceramic material; (J), one of the 23 sample

collection syringes (paper I).

Experimental conditions in each continuous fractionation study are collected in Table

III. A ΔT value of 21 K or 37 K represents the highest practical temperature difference in

the prototype instrument, with a channel thickness of 125 μm or 250 μm, respectively

(corresponding to thermal gradients of 1680 or 1480 K cm-1

, respectively). The cold wall

temperature Tc was dependent on the flow rate and the temperature of the circulating tap

28

water used for cooling. For a ΔT value of 0 K (i.e., no thermal gradient), the instrument

was operated at room temperature without the cooling water circulating through the lower

wall.

Table III. Experimental conditions in continuous 2D-ThFFF studies.

Paper II Paper III Paper IV

Channel thicknesses 250 μm 125 μm

250 μm

125 μm

Carrier solvents cyclohexane cyclohexane

cyclohexane-

ethylbenzene (75:25 v/v)

cyclohexane-

ethylbenzene (75:25 v/v)

Carrier (radial) flow

rates

1541 μl/min

1909 μl/min

2300 μl/min

221 μl/min

276 μl/min

221 μl/min

276 μl/min

Rotation rates

(angular flow rate)

0.96 rpm

1.92 rpm

2.88 rpm

4.80 rpm

0.016 rpm

0.024 rpm

0.032 rpm

0.016 rpm

0.024 rpm

0.032 rpm

0.040 rpm

Sample flow rates

5.0 μl/min 0.417 μl/min

0.625 μl/min

1.250 μl/min

2.500 μl/min

1.250 μl/min

2.500 μl/min

Samples PS 19.8k

PS 96k

PS 19.8k

PS 51K

PS 96k

PS 520k

PS 1000k

PS 51k

PS 520k

PS 1000k

Temperature

difference

block

temperatures:

T=13oC (cold

wall)

T=55oC (hot wall)

ΔT = 10-37 K ΔT = 10-21 K

4.3.2 Reagents

Five standard polystyrene polymers were used as samples in studies of the sample elution

in the continuous 2D-ThFFF method. Their molar masses, polydispersities, stock

solutions, and manufacturers are reported in Table IV.

29

Table IV. Polystyrene (PS) samples used in the study and the concentrations of prepared

stock polymer solutions (w/w) (paper III). Polymer

(PS)

Manufacturer Molar Mass

Mw (g/mol)

Polydispersity

Mw/Mn

Concentration

% (w/w)

19.8k Waters Associates, MA, U.S.A 19,850 1.01 0.35

51k Waters Associates, MA, U.S.A 51,000 1.03 0.38

96k Polymer Laboratories Ltd, UK 96,000 1.04 0.51

520k Polymer Laboratories Ltd, UK 520,000 1.05 0.40

1000k Polymer Laboratories Ltd, UK 1000,000 1.03 0.41

The solvents in the continuous 2D-ThFFF studies were analytical grade cyclohexane (Merck

KGaS, Darmstadt, Germany) and a binary solvent consisting of 75% analytical-grade

cyclohexane (Merck KGaS, Darmstadt, Germany) and 25% reagent-grade ethyl benzene

(Sigma-Aldrich GmbH, Steinheim, Germany). The polymer standards of higher molar

masses dissolved better in the binary solvent than in cyclohexane, because of their poor

solubility in cyclohexane below the -temperature (37.5 oC). The fractions collected from the

continuous runs were evaporated to dryness and dissolved in 100 L of HPLC-grade

tetrahydrofuran (Labscan Ltd, Dublin, Ireland), which was used routinely as the carrier in

the analytical ThFFF channel. However, to obtain the λ values in the analytical ThFFF for

the polystyrene samples with higher molar masses, the same cyclohexane‒ethylbenzene

binary carrier was used as in the continuous method.

4.3.3 Continuous fractionation procedure

Before the continuous fractionation was initiated, the run conditions, such as carrier flow,

rotation of the accumulation wall, and thermal gradient across the channel, were properly

adjusted and stabilized. The thermal gradient was measured regularly with two thermistors

installed into the vicinity of the two wall surfaces. Because one wall was rotating, the

relative positions of the two thermistors changed during the fractionation. For runs where

a thermal gradient was applied, the temperature of each of the walls was measured,

whereas when no gradient was applied, the room temperature was assumed to apply inside

the channel. The temperatures were measured every 10 minutes to determine the mean

thermal gradient for each run. The sample introduction was initiated only when steady-

state conditions were achieved.

30

After the continuous 2D-ThFFF run, the collected samples from the syringes, containing

equal amounts of the binary carrier solutions, were transferred to test tubes and evaporated

to dryness. A small amount of tetrahydrofuran (100 μl) was added to each test tube to

dissolve the polymer fractions. The same solvent was used as a carrier in the analytical

ThFFF instrument. Relative concentrations of the polymer in each fraction were calculated

from the peak areas of the fractograms.

31

5. Results and Discussion

Continuous runs were carried out using different temperature differences and flow

conditions. The first series of runs were performed without an applied thermal gradient for

the determination of the deflection angle (θ0) for a non-retained sample. Next, the thermal

gradient was applied and the polymers with different molar masses were used as samples.

The elution angles for retained (θr) and non-retained samples were determined both

experimentally and theoretically, and the results were compared.

5.1 Exploration of continuous fractionation of polymers

In the first study, two polystyrene samples with molar masses of 19,800 g mol-1

and

96,000 g mol-1

, were used for preliminary testing of the performance and experimental

conditions of the continuous ThFFF equipment (paper II). Cyclohexane was used as a

carrier for continuous fractionation runs and tetrahydrofuran for analytical ThFFF to

determine the relative concentrations of the samples in each of the collected fractions. The

continuous fractionation runs were performed without and with the thermal gradient (Fig.

9a and 9b). In both cases, using radial flow rate of 2300 μl/min and rotation rate of 0.96

rpm, no polymers were found in the first and second collection syringes, but both were

present in syringe 3. In the absence of the thermal field, no polymers were found beyond

syringe 4. With the thermal field on, the samples were spread up to the collection port 8,

indicating the sample deflection by influence of the thermal gradient. A slight continuous

fractionation of two samples was observed, too. The experiment was repeated using

rotation rates of 1.92, 2.88, and 4.80 rpm and, radial flow rates of 1541 and 1909 μl/min,

respectively. These preliminary results were promising and supported further studies.

32

Figure 9 Fractograms and peak areas obtained with the conventional ThFFF (ΔT =

100oC) for the sample fractions collected from the continuous fractionation.

The continuous runs were performed without (a) and with (b) the thermal

gradient. The rotation rate was 0.96 rph and the radial flow rate 100 μl/min.

(paper II).

In further studies with the samples PS 19.8k and PS 96k, both the radial flow rate and

rotation rate were decreased ca. tenfold from that in the preliminary studies. With a

constant radial flow rate of 276 μl/min, enhanced retention was found with rotation rates

of 0.016 and 0.032 rpm, and by applying a thermal difference ΔT between 13-37 K (paper

III). Figure 10 shows that the retention of the polymer components was enhanced by

increasing the field strength. Higher rotation rate resulted in broader deflected sample

zones, but they increased the angular separation of the peak maxima.

33

Figure 10 Effect of the thermal gradient in 2D-ThFFF on the retention of two-

component polystyrene sample components: □, PS 19.8k; ■, PS 96k. Column

I: rotation speed, 0.016 rpm; radial flow rate, 12.0 μl min-1

at each sample

collection port, channel thickness, 250 μm. Column II: rotation speed, 0.032

rpm; radial flow rate, 12.0 μl min-1

; channel thickness, 250 μm. The carrier

was cyclohexane and the collection time 75 min in each run. Sample

introduction rate was 1.250 μl min-1

. Percentages of sample recovery were

calculated from the peak areas obtained in a conventional ThFFF run of the

fractions. Channel thickness, 250 μm, and radial flow rate, 12.0 μl min-1

, are

constant in all runs. (paper III).

34

In addition to the flow conditions, the channel thickness was found to contribute to the

zone broadening. When the channel thickness was decreased, the samples were collected

into fewer outlet syringes, representing a narrower sample zone along the channel

periphery. With a constant field strength and radial flow rate of 276 μl/min, and with the

channel thickness varying from 250 μm to 125 μm, the zone broadening was clearly

decreased with decreasing rotation rate in the fractionation of the samples PS 19.8k and

PS 96k (Fig. 11).

Figure 11 Effect of 2D-ThFFF channel thickness on sample trajectory broadening for

two polystyrene samples: , PS 19.8k; ■, PS 96k. A: Channel thickness, 250

m; radial flow rate, 12.0 l/min at each port; rotation speed, 0.016 rpm. B:

Channel thickness, 125 m; radial flow rate, 12.0 l/min; rotation speed,

0.016 rpm. C: Channel thickness, 250 m; radial flow rate, 12.0 l/min,

rotation speed, 0.032 rpm. D: Channel thickness, 125 m; radial flow rate,

12.0 l/min; rotation speed, 0.032 rpm. The carrier was cyclohexane. Sample

introduction rate was 1.250 l/min. Radial flow rate, 12.0 μl min-1

, is constant

in all runs. (paper III).

The relaxation effects in the thin channel were expected to be negligible. In addition to

the channel thickness, the sample load affects the retained sample zone in analytical FFF

methods [174]. However, in continuous 2D-ThFFF, the effect of the sample feed rate on

the zone broadening was found to be negligible (Fig. 12).

35

Figure 12 Effect of the sample introduction rate on the 2D-ThFFF collection without

thermal gradient and with cyclohexane as a carrier. The sample was PS 19.8k.

The run conditions were rotation speed, 0.016 rpm; radial flow rate at each

collection port, 12.0 μl min21; channel thickness, 250 m (paper III).

Considering the applied polystyrene samples, their complete separation by analytical

ThFFF method required a thermal gradient of 90‒100oC with the channel thickness of 125

m. Such a high field was not possible with the continuous method because of material

limitations and the rather low maximum heating efficiency (700 W) of the upper channel

wall. Therefore, it was not possible to enhance retention by increasing the field strength.

Meanwhile, additional polystyrene samples of higher molar masses were chosen for the

further studies (papers III-IV). The molar masses of the PS samples were now 51,000 g

mol-1

, 520,000 g mol-1

, and 1000,000 g mol-1

(Table IV). In addition, cyclohexane was

replaced with a mixture of cyclohexane and ethylbenzene, because the samples of higher

molar masses were poorly soluble in cyclohexane alone, whereas the binary carrier is a

good solvent for polystyrene, tending to enhance retention in ThFFF [32, 33]. The

fractionation results from the conventional ThFFF experiments for the samples PS 51k, PS

520k, and PS1000k are presented in Figure 13 as plots of λ vs. 1/ΔT, together with the

linear regression fits to the data for each polymer standard (paper IV). These plots

describe the effect of molar mass on the parameter λ in the cyclohexane‒ethylbenzene

carrier.

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8

2.500 ul/min

1.250 ul/min

0.625 ul/min

0.417 ul/min

Collection Port

36

Figure 13. Linear trendlines for plots of λ vs 1/ΔT, determined for polystyrene samples

PS 51k, PS 520k, and PS 1000k in cyclohexane‒ethylbenzene (75:25 v/v)

eluent using different thermal gradients. Other run conditions: flow rate, 100

µl/min; and UV detection at 280 nm (paper IV).

5.2 Effect of run conditions on continuous fractionation

It was shown that 2D-ThFFF is a promising method for continuous fractionation of the

samples PS 19.6k and PS 98k under the influence of a thermal gradient (papers III and

IV) Continuing the study, the new results with samples of higher molar masses were

compared with predictions of the theoretical retention model described in the previous

chapter. The method is rather complex because of the number of relevant parameters. The

influence of the molar mass of the sample, the angular rotation rate, and the radial flow

rate of the carrier on the deflection of the sample zone were examined. The parameters

affecting deviations from the theory, such as angular broadening of the deflected sample

zone, the effect of the temperature of the lower wall, and the lack of relaxation time, were

discussed, too.

Theoretical non-retained elution angles were calculated using Eq. 11 and the retained

angles using Eq. 10, and the results were compared with the experimental results. The

retention parameters λ used in calculations were predicted from the retention data (Fig. 13)

obtained using the analytical ThFFF instrument (Papers III and IV). Figure 14 shows the

theoretically predicted (by Eqs. 2, 8, and 10) dependence of the elution angle (θr) on the

dimensionless retention parameter λ, for different rotation rates Ω0 of the accumulation

wall at fixed radial flow rate (Fig. 14 A), and for different radial flow rates at fixed

y = 1,6514x - 0,014

y = 3,475x - 0,0164

y = 6,8155x - 0,0006

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0,18

0,01 0,02 0,03 0,04 0,05 0,06 0,07

PS 1 M

PS 520k

PS 51k

Re

ten

tio

n p

ara

me

ter

1/T

37

rotation rate (Fig. 14 B). From these curves it is clear that the elution angle is predicted to

increase with decreasing λ or radial flow rate, or with increasing angular velocity of the

cold wall. These findings are, in fact, in good agreement with the following experimental

results.

Figure 14 Calculated effect of the retention parameter λ on the retention angle θr for (A)

different rotation speeds at fixed V of 276 µl/min, and (B) different radial

flow rates at fixed rotation rate of 0.016 rpm (paper IV).

In the experiments the polymer samples were eluted over several collection ports at the

channel periphery. The results were thus reported by plotting the fractional recovery of the

0

50

100

150

200

250

300

350

0 0.05 0.1 0.15 0.2 0.25 0.3

Retention parameter

Rete

nti

on

r/d

eg

.

0

2

4

6

8

10

12

14

16

18

20

22

Fra

cti

on

nu

mb

er

276.0 l/min

220.8 l/min

165.6 l/min

B

38

polymers collected at each port. Those were plotted as functions of the different outlet port

numbers. For each run, the mean elution angle is computed according to (360°/23)(Σ (i-

1) φi), where φi is the fractional recovery of the polymer collected at port i, port number 1

being aligned with the sample introduction port. These mean angles are expressed as

elution angles θr if a temperature gradient is applied and as θ0 if no gradient is applied.

Results obtained for a set of experiments performed using three polystyrene samples

and five temperature differences (0, 10, 14, 17, and 21 K) are shown in Fig. 15A-C in

section 5.2.1. A fixed carrier flow rate V of 221 µl/min, and a fixed angular velocity of the

accumulation wall Ω0 of 0.024 rpm were used in these experiments. The theoretically

predicted and the experimentally observed mean elution angles together with their

percentage errors are listed in Table V.

Experimental results obtained with the sample PS 1000k at four rotation rates (0.016,

0.024, 0.032, and 0.040 rpm) and three temperature differences (ΔT = 0, 12, and 20 K), at

a fixed carrier flow rate (276 µl/min) are shown in Fig. 16A-D in section 5.2.2 . The

results for the mean elution angles are reported in Table VI, again compared with

theoretically predicted values.

Similarly, elution profiles for PS 1000k obtained at a fixed rotation rate (0.016 rpm),

but at two carrier flow rates (276 and 221 µl/min) and two temperature differences (ΔT =

0 and 20 K) are shown in Fig. 17A-B in section 5.2.3. Experimentally observed mean

elution angles are compared with theoretical predictions in Table VII.

5.2.1 Effect of molar mass and thermal gradient

According to Table V and Figure 15, the experimental mean elution angle θ0(exp) for each

polymer sample, obtained without an applied thermal field, for a constant radial flow rate

and rotation rate, corresponds rather well with the predicted non-retained elution angle

θ0(theory), calculated from Eq. 11. When the thermal gradient is applied, the experimental

deflection angles θr(exp) for PS 51k correspond very well with the predicted values of

θr(theory). The experimental peak elution angles for the moderately retained sample PS

520k also agree very well with the predicted values at ΔT of 10 to 17 K. For the more

retained sample PS 1000k, the experimental elution angles are significantly smaller than

the predicted mean values when the field is applied. However, the results show clearly that

the deflection angles increase with the molar mass and thermal gradient, as predicted by

the theory.

39

Table V. Experimental and calculated mean elution angles for three polystyrene samples

with percentage errors. The collection port 0 at angle 0o is aligned with the sample

introduction port and one revolution corresponds to 23 ports and 360°/23 ≈ 15.7°. Rotation

rate of the accumulation wall was 0.024 rpm and radial flow rate at each collection port

9.6 µl/min (total flow rate 221 µl/min) (paper IV).

Sample PS 51k PS 520k PS 1000k

ΔT = 0 K θ0 (exp) 38° 36° 33°

θ0 (theory) 32.8° 32.8° 32.8°

% error

15% 11% -0.3%

ΔT = 10 K θr (exp) 44° 57° 69°

θr (theory) 42.0° 54.1° 87.9°

% error 5.6 % 5.3% -22%

θr/θ0 (exp) 1.2 1.6 2.1

θr/θ0 (theory) 1.3 1.6 2.7

ΔT = 14 K θr (exp) 43° 67° 90°

θr (theory) 46.3° 65.5° 119°

% error -7.5% 2.5% -25%

θr/θ0 (exp) 1.1 1.8 2.7

θr/θ0 (theory) 1.4 2.0 3.6

ΔT = 17 K θr (exp) 47° 81° 100°

θr (theory) 49.8° 75.0° 145°

% error -4.9% 8.1% -30%

θr/θ0 (exp) 1.3 2.2 3.1

θr/θ0 (theory) 1.5 2.3 4.4

ΔT = 21 K θr (exp) 57° _______ 129°

θr (theory) 54.6° 88.8° 182°

% error 4.0% _______ -29%

θr/θ0 (exp) 1.5 _______ 3.9

θr/θ0 (theory) 1.7 2.7 5.5

40

Figure 15 Experimental sample distributions in channel outlets for different

temperature differences. Samples: (A) PS 51k, (B) PS 520k, and (C) PS

1000k. In each run the rotation rate Ω0 of the lower channel wall was 0.024

rpm, and the total radial flow rate 221 µl/min. Temperature differences

varied between 0 K and 21 K, as indicated (paper IV).

41

5.2.2 Effect of rotation rate of the lower wall and thermal fields

According to Table VI and Figure 16, the experimental mean elution angle θ0(exp) for the

sample PS 1000k is consistently larger than the theoretically predicted angle θ0(theory)

without the field, but the difference decreases with increasing rotation rate. However, the

calculated elution angle θ0 increases gradually, too, with increasing rotation speed.

According to the theory presented in paper IV, the θ0/Ω0 ratio should not depend on the

rotation rate and should, according to Eq. 11, be equal to t0/2, i.e., to 3.0 min under the

flow conditions of Figure 16 and Table VI. In fact, it is seen that, experimentally, θ0/Ω0 is,

in all cases, larger than its theoretical value, but it decreases with increasing rotation rate.

Figure 16 Experimental sample distribution for the solute PS 1000k with different

rotation rates of the lower channel wall, with and without an applied

temperature gradient. Rotation rates Ω0 were (A) 0.016 rpm; (B) 0.024

rpm; (C) 0.032 rpm; and (D) 0.040 rpm. Temperature differences ΔT of 0

K, 12 K, and 20 K were used. The total radial flow rate in each run was 276

µl/min, and the sample feed rate was 1.25 or 2.50 µl/min (paper IV).

42

Table VI. Experimental and calculated mean elution angles with percentage errors for the

sample PS 1000k using four different rotation rates of the lower channel wall. Port number

0 at angle 0° is aligned with the sample introduction port, one revolution corresponding to

23 ports and 360°/23 ≈ 15.7°. Radial flow rate at each collection port was 12.0 µl/min

(total flow rate 276 µl/min) (paper IV).

Ω0 (rpm) 0.016 0.024 0.032 0.040

ΔT = 0 K θ0 (exp) 29

o 38

o 42

o 46

o

θ0 (theory) 17.5

o 26.3

o 35.1

o 43.8

o

% error 67% 46% 19% 4.4%

θ0/ Ω0 (exp) 5.1 4.4 3.6 3.2

ΔT = 12 K θr (exp) 58° 66° 78° 97°

θr (theory) 55.0° 82.5° 110° 138°

% error 6% -20% -29% -29%

θr/θ0 (exp) 2.0 1.7 1.9 2.1

θr/θ0 (theory) 3.1 3.1 3.1 3.1

ΔT = 21 K θr (exp) 55° 90° 144° ____

θr (theory) 92.0° 138° 184° 230°

% error -41% -35% -22% ____

θr/θ0 (exp) 1.9 2.3 3.4 ____

θr/θ0 (theory) 5.2 5.2 5.2 5.2

When the thermal field is applied, the experimental mean elution angles, θr(exp), are seen

to be smaller than the theoretical values θr (theory) in almost all cases, the exception being

for ΔT = 12 K and Ω0 = 0.016 rpm. As the temperature drop is increased from 0 K to 12 K

and 20 K, then, whatever the rotation rate, the distribution of the polymer along the exit

ports becomes wider and is shifted toward larger port numbers, as expected for samples

accumulating at the rotating wall. For ΔT = 12 K, the relative error between the

experimental and theoretical values of θr tends to increase with the rotation rate. For

ΔT = 20 K, the relative error decreases with increasing rotation rate. The experimental

θr/θ0 ratios are all smaller than the theoretical values.

5.2.3 Effect of radial flow rate with and without the field

The influence of the carrier flow rate on the elution behavior of the polymer in unretained

and retained conditions is shown in Figure 17 and Table VII for ΔT= 0 K and 20 K, at the

lowest rotation rate of 0.016 rpm. As the carrier flow rate is lowered, both θ0 and θr

increase. This is expected from Eqs. 10 and 11 since a reduction in V leads to an increase

in the time spent in the channel and thus to an increased deflection induced by the rotation

of one plate. Whatever the carrier flow rate, the experimental value of θ0(exp) is larger

43

than expected, the more so for the lower flow rate. However, while the experimental

elution angle θr(exp) is lower than the theoretical angle when V = 276 µl/min, it is

observed to be slightly larger than theoretically expected when V = 221 µl/min. Still, for

both flow rates, the experimental θr/θ0 ratio is smaller than theoretically expected.

Figure 17 Experimental sample distribution for the solute PS 1000k for the rotation

rate Ω0 = 0.016 rpm and two different total radial flow rates: (A) 276

µl/min, (B) 221 µl/min. Temperature differences ΔT of 0 K and 20 K were

used as indicated (paper IV).

Table VII. Experimental and calculated mean elution angles with percentage errors for the

sample PS 1000k with two different radial flow rates. Port number 0 at angle 0° is aligned

with the sample introduction port, and one revolution corresponds to 23 collection ports

and 360°/23 ≈ 15.7°. Rotation rate of the accumulation wall was 0.016 rpm (paper IV).

V (µl/min) 276 221

ΔT = 0 K θ0 (exp) 29° 59°

θ0 (theory) 17.5° 21.9°

% error 67% 170%

ΔT = 20 K θr (exp) 55

o 124°

θ0 (theory) 92.0° 115°

% error -41% 8.0%

θr/θ0 (exp) 1.9 2.1

θr/θ0 (theory) 5.2 5.2

44

5.3 Additional effects not accounted for in the modeling

When the operational parameters were changed one by one, the observed effects were,

in general, qualitatively in accordance with the theoretical predictions. However,

significant quantitative differences were observed between the experimental and

theoretical values. In order to unravel the origins of these differences, several effects that

could affect the operation of the 2D-ThFFF system but were not accounted for in the

modeling, are discussed below.

Solvent partitioning effect. In order to meet some practical constraints, a mixture of

cyclohexane and ethylbenzene was selected as carrier liquid. Ethylbenzene was added to

increase the solubility of the polymers with high molar masses and to increase the

retention with the limited temperature gradient achievable in the 2D system. Under a

thermal gradient, this binary mixture is subject to the Soret effect [34, 175], which causes

a weak gradient in the composition of the binary mixture to form across the channel.

Under this composition gradient, the polystyrene molecules tend to concentrate in the

better solvent, which is ethylbenzene. It has been shown that the cold regions become

slightly enriched in cyclohexane and the hot regions in ethylbenzene, [32] and this solvent

partitioning effect thus leads to enhanced accumulation of polystyrene molecules closer to

the cold wall. As a result, the steady-state concentration profile of the polymer in the

channel thickness is no longer exponential and the value of determined from Figure 13

is an apparent value. This should not affect the correctness of the determination of Rr from

Eq. 2 using this apparent value because the values reported in Figure 13 are obtained

via Eq. 2 from experimental measurements of Rr in a conventional thermal FFF system

employing the same binary solvent mixture. However, this will lead to erroneous

calculations of R from Eq. 8 because Eq. 8 assumes an exponential distribution profile in

the channel thickness. This also does not explain why the elution angles of the PS 1000k

sample are lower than expected, since the solvent partitioning effect increases with the

molar mass of the polymer [32]. A more detailed study is required to clarify the impact of

the solvent partition effect on the mean elution angle.

Flow velocity profile. In thermal FFF, the carrier flow velocity profile is not parabolic

because of the temperature dependences of the carrier viscosity and thermal conductivity.

Furthermore, these physico-chemical parameters might be affected by the partitioning

effect of the binary solvent mixture discussed above. As a consequence, the relationships

between Rr and and between R and are not given exactly by Eqs. 2 and 8,

respectively. Still, for the reason noted above, this imprecision does not affect the Rr

values used in the computations since these were deduced from the calibration curves

shown in Figure 13, but it should affect the value of R. Because of the relatively low T

45

applied in the experiments, the corresponding deviations are nevertheless likely to be

small and have only a minor effect.

Effective channel outlet radius. The theoretical model assumes that the sample

trajectory can intersect the channel periphery at any location. In practice, this is not the

case, because the number of outlet collection ports is finite (and equal to 23 in the present

system). If there was no rotation, the flow streamlines, which would be radially distributed

near the central injection port, would not follow a radial line as they approach the edge of

the channel but would be bent to focus onto the closest outlet port. When the lower plate is

rotating, the flow streamlines follow curved lines which are similarly modified as they

approach the edge and converge to an outlet port. There is, therefore, a perturbation region

near the channel periphery, where fractionation does not occur because all nearby flow

streamlines converge to the same outlet port. This may be thought of in terms of an

effective channel radius, reff, which is smaller than the true channel radius and within

which the fractionation is supposed to take place. For every sample collected at any

collection port, the deflection angle is set to the value of that port, which may introduce a

systematic bias for the determination of the mean deflection angle. This limits the

accuracy of the determination of the mean elution angles 0 and r.

Sample flow rate. The model assumes that the sample flow rate is negligible compared

with the carrier flow rate. In the present system, the ratio of the sample to carrier flow

rates ranged between 0.0045 and 0.0113, which is indeed small. However, the flow of

sample into the channel might slightly reduce the void time and, consequently, the elution

angle according to Eq. 10, although the sample flow rate has been shown to have a

negligible influence on θ0

(paper III). Computational fluid dynamics could help in

understanding the effect and possibly estimating its magnitude.

Sample relaxation. The theory assumes that the samples migrate from a point of entry

according to Eqs. 2 and 8. This is not the case, however. After the sample injection, the

sample components must approach their equilibrium distributions across the channel

thickness by the mechanisms of thermophoresis and molecular diffusion under flowing

conditions. The thermal diffusion coefficient and, therefore, the rate of the field-induced

transport across the channel are independent, or nearly independent, of molar mass. It is

therefore expected that the relaxation toward equilibrium distribution should result in

reduced retention times and reduced θr. This was not observed in the experiments (see

Table V). The experimental values for θr, are in most cases lower than the predicted

values, and while relaxation effects could contribute to these discrepancies they do not

fully account for them.

46

Non uniformity of ΔT. It is assumed that the temperature of each disk is constant

across its surfaces and that the temperature difference ΔT between the surfaces is constant

throughout the 2D channel. However, any local variation in thermal gradient would

influence the values of the observed deflection angles θr.

Geometrical imperfections. Finally, geometrical imperfections of the 2D channel

should be considered. The theory assumes that the disks are perfectly flat and the spacing

between them is uniform throughout, from the axis to the circumference. The slightest

variation in disk spacing across the faces would have a strong effect on the radial flow

velocity as a function of angle and also result in angular components to flow that vary

with radius and angle. In addition, this pattern could rotate relative to either disk, or to

both, as they rotate relative to one another. Small channel imperfections associated, for

example, with surface roughness and evenness might account for the remaining

discrepancies between theory and experiment.

47

6. CONCLUSIONS AND FUTURE PERSPECTIVES

In this work a prototype of a continuous 2D-ThFFF instrument was constructed, a

preliminary theoretical model of its operation was developed, and the experimental and

theoretical results were compared. An analytical ThFFF method was used for the

determination of polymer concentrations in each continuously collected fraction and

determination of the retention factor . The samples were polystyrene polymer standards

with different molar masses and narrow polydispersity. In the continuous 2D-ThFFF,

cyclohexane and a binary solvent consisting of cyclohexane and ethylbenzene were used

as carriers. Both are suitable for ThFFF experiments, and the instrument was inert to their

physico-chemical properties. In the analytical ThFFF, however, tetrahydrofuran was used

as the carrier, after first evaporating the collected fractions to dryness and then adding the

THF solvent to dissolve the samples. This was done for practical reasons and to decrease

the consumption of other carrier solvents.

In the first experiments two polystyrene samples of different molar masses were used

for preliminary testing of the performance and experimental conditions of the continuous

2D-ThFFF method. A positive effect of the thermal gradient on the sample deflection was

observed, although increased rotation rate resulted in broader deflected sample zones. In

further study, a 50% decrease in the channel thickness led to significant reduction in the

zone broadening with and without the thermal field. In addition, with decrease of both the

radial and angular flow rates the deflection of the sample trajectories increased. In addition

to the flow components and channel geometry, the use of a cyclohexane‒ethylbenzene

binary carrier and samples of higher molar mass showed enhanced performance in the

continuous fractionation. The systematic variation of the experimental parameters allowed

determination of the conditions required for the continuous fractionation of polystyrene

polymers according to their molar mass. As an example, almost baseline separation was

achieved with two polystyrene samples of molar mass 51.000 and 1000.000 g/mol (Fig.

18).

48

Figure 18 Continuous fractionation of a mixture of two polystyrene samples: , PS

51k; ■, PS 1000k. The carrier was a binary solvent of cyclohexane and

ethylbenzene and the run conditions were rotation speed 0.024 rpm, radial

flow rate 9.6 l/min, channel thickness 125 m, collection time 90 min.

Sample introduction rate was 1.250 l/min (paper III).

A theoretical model was developed and applied for prediction of the sample trajectory

and its angular displacement under various experimental conditions. The trends in the

deflection angles without and with a thermal gradient (θ0 and θr, respectively) were

qualitatively in agreement with predictions of the model, but significant quantitative

differences between the experimental results and theoretical predictions were also found.

Some possible reasons for the discrepancies between theory and experiment were

discussed. The stop-flow procedure used for sample relaxation in conventional FFF is not

possible with the continuous separation system, and the sample is assumed to be relaxed

already at the sample inlet point. The instrumental limitations, such as a rather low

maximum thermal gradient, a limited number of collection ports, and the noncontinuous

fraction collection, restrict the full-scale operation. However, none of the considered

complications could provide an unambiguous explanation for the observed discrepancies.

The theoretical model will, however, provide guidelines for future interpretation and

optimization of separations by the continuous 2D-ThFFF method. The theoretical model

constitutes a first step in the modeling of the system, and there are structural design and

construction issues that can be addressed in future instruments.

Since ThFFF separates samples according to their chemical composition, molar mass,

and particle size, the applications of continuous 2D-ThFFF in science and industry can be

extended from polymers to other macroscopic objects, such as particles and microgels.

Through use of some other fields than thermal force field, the continuous 2D method can

be extended to biotechnology and the characterization of new materials. However, in the

present form, the preparative separation of the continuous 2D-ThFFF is not very good in

practice, because the separation resolution in FFF techniques is generally not very high,

49

and the much narrower molar mass distributions needed in analytical and industrial

chemistry cannot easily be achieved by any elution-based separation methods. Therefore,

much additional experimental and theoretical work will be needed to discover the benefits

and drawbacks associated with the continuous 2D-FFF channel variants.

50

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