Molecular Weights, Polymers, & Polymer Solutions (Part...

Chemistry 5861 - Polymer Chemistry 1

Molecular Weights, Polymers, & Polymer Solutions (Part I - Chapter 2 in Stevens)1

I Number and Weight Average Molecular Weight - An Introduction

Importance of MW and MW Distribution A)

1)

a)

2)

a)

b)

3)

a)

b)

Optimum MW, MW Distribution, etc.

depends upon application via processing and performance tradeoffs

Typical MW values for commercial polymers

Vinyl polymers in the 105 and 106 range

Strongly H-bonding polymers in the 104 range

i)

i)

ii)

iii)

iv)

v)

vi)

e.g., 15,000 - 20,000 for Nylon

MW Determinations (many more details later in chapter)

We wish to determine both average values of MW and information about MW

distribution

Some Important Methods

Gel Permeation Chromatography, GPC

Light Scattering

Viscometry

Mass Spectroscopy

End Group Analysis (Chemical & Spectroscopic)

Colligative Properties (P-Chem Methods)

Boiling Point Elevation

Freezing Depression (Cryoscopy)

1 The graphics in these notes indicated by “Figure/Table/Equation/Etc., x.x in Stevens” are taken from our lecture text: “Polymer Chemistry: An Introduction - 3rd Edition” Malcolm P. Stevens (Oxford University Press, New York,

©2002, Dr. Allen D. Hunter, Youngstown State University Department of Chemistry


B)

Osmometry, etc.

Number Average Molecular Weight, Mn bar

1)

a)

2)

3)

a)

C)

This term is very sensitive to the total number of molecules in solution and hence is

especially sensitive to the low molecular weight monomers and oligomers

Determined by End Group Analysis and Colligative Properties

Mn bar = ΣNiMi / ΣNi

Example

9 moles of MW = 30,000 and 5 moles of MW = 50,000 ⇒ Mn bar ≈ 37,000

Weight Average Molecular Weight, Mw bar

1)

a)

2)

3)

a)

4)

This term is sensitive to the mass of the molecules in solution and hence is especially

sensitive to the very highest MW species present in the system

Determined by Light Scattering and Ultracentrifugation

Mw bar = ΣWiMi / ΣWi = ΣNiMi2 / Σ NiMi

Example

9 moles of MW = 30,000 and 5 moles of MW = 50,000 ⇒ Mw bar ≈ 40,000

Note:

a)

b)

c)

Mw bar ≥ Mn bar (Draw MW distribution chart)

Mw bar/Mn bar = Polydispersity Index

Mw bar/Mn bar = 1, Mw bar = Mn bar for a sample having a single MW

(Monodisperse)

1999).



d)

D)

Mw bar/Mn bar ≥ 1 is Polydisperse

General Molecular Weight Expression & Mz bar and Mv bar

1)

2)

a)

3)

a)

b)

II

M bar = ΣNiMi(a+1) / Σ NiMi

a

A Higher Order MW, called the Z average, is closely related to processing

characteristics ⇒ a = 2

Mz bar = ΣNiMi(2+1) / Σ NiMi

2 = ΣNiMi3) / Σ NiMi

2

A viscosity based MW, Mv bar, has 0 ≤ a ≤ 1 and closer to 1 (i.e., to Mw bar)

MV bar = ΣNiMi(1.x) / Σ NiMi

0.x

i)

ii)

i)

ii)

iii)

Where x is typically close to 1 and ∴ 1.x is typically close to 2

∴ MV bar = ΣNiMi(1.9) / Σ NiMi

0.9 in a typical case

Mz bar ≥ Mw bar ≥ Mv bar ≥ Mn bar

Polymer Solutions

Steps Dissolving a Discrete Molecule and a Polymer A)

1)

a)

2)

a)

Discrete Molecule Dissolution Steps for a Crystalline Sample

Polymer Dissolution Steps

solvent diffusion

solvation & swelling

⇒ Gel formation

network polymers stop at this stage, degree of swelling correlated with

crosslink density



b)

B)

True dissolution

i)

ii)

untangling of chains

very slow process and may not occur on timescale of real world

Thermodynamics of Polymer Dissolution

1)

a)

b)

2)

a)

b)

c)

3)

a)

b)

c)

4)

5)

C)

Choosing a Solvent for Polymers

Polymer Handbook!!!!! lists solvents and nonsolvents for common polymers

Rule of Thumb: Like dissolves Like

∆G = ∆H - T∆S

∆G must be negative for spontaneous (but not necessarily fast) dissolution

∆S will be positive because of greater mobility in solution

∴ need ∆H to be negative or at least not too positive

∆Hmix ∝ (δ1 - δ2)2

∆Hmix is the Enthalpy of mixing (dissolution)

δ1 is the Solubility Parameter of one component

δ2 is the Solubility Parameter of the other component

In practice, ∆H is seldom negative and we simply try to keep it from getting too

positive

∴ we see that we want the polymer and the solvent to have as similar of Solubility

Parameters as possible

Solubility Parameters, δ

1) The δ Parameters is related to the heat of vaporization of the sample



2)

3)

a)

4)

a)

For small molecules these can be measured experimentally

∴ the δ Parameters of solvents are tabulated

multiple parameter expressions can also be used for more precision

For conventional polymers these can be estimated using tables

Group Molar Attraction Constants

b)

c)

D)

Table 2.1 in Stevens

δ = d ΣG / M

i)

ii)

iii)

G = the individual Group Molar Attraction Constants of each structural

fragment

d = density

M = molecular weight

Hydrodynamic Volume in Solution

1)

2)

The apparent size of the polymer in solution

Reflects both the polymer chain itself and the solvating molecules in inner and outer

spheres

3)

4)

a)

b)

Figure 2.1 in Stevens

Hydrodynamic Volume is related to an

Expansion Factor, α

α = 1 is the value for the “non-expanded” polymer in the “ideal” statistical coil

having the smallest possible size

as α increases, so does the Hydrodynamic Volume of the sample



E) The Theta State (θ)

1)

2)

3)

4)

F)

Solubility varies with temperature and the nature of the solvent

∴ there will be a minimal dissolution temperature call the Theta Temperature and at

that point the solvent is said to be the Theta Solvent

The Theta State at this point is the one in which the last of the polymer is about to

precipitate

Compilations of Theta Temperatures & Solvents are available in the literature

Intrinsic Viscosity & Molecular Weight

1)

2)

a)

b)

c)

III

[η] = Intrinsic Viscosity (i.e., the viscosity in an “Ideal Solution”)

Mark- Houwink-Sakurada Equation

[η] = K (Mv bar)a

K and a are characteristic of the particular solvent/polymer combination (more

later)

Mv bar = the Viscosity Average Molecular Weight

Measurement of Number Average Molecular Weight

A) General Considerations

1)

a)

Ideal Instrument

Gives full information on the molecular weight distributions for sample

i)

ii)

Reliable for all species in sample from monomers to crosslinked polymers

From this MW distribution can be extracted mathematically for the

various types of MW averages (Mw bar, Mn bar, Mv bar, etc.)



iii)

iv)

i)

i)

ii)

iii)

i)

i)

Highly sensitive so can use small & very dilute samples

Data quality

b)

c)

2)

a)

b)

c)

d)

e)

f)

B)

highly accurate

highly precise

Requires no calibration

Neither at the start of each run nor for different types of samples

Cost and convenience

low cost to buy and maintain

highly reliable/robust

easy to operate

Real Instruments

Most methods give only averages

exceptions are: GPC, Light Scattering, & MS

Most methods’ results vary depending on the structure of the sample

∴ need to calibrate each sample and/or know some structural information

such as branching

Most methods have limited sensitivities and/or linear ranges

Most methods require expensive instrumentation

There can be substantial disagreements between the results of different techniques

However, many methods are improving in these areas rapidly

End-Group Analysis

1) Basic principles



a)

b)

c)

2)

a)

b)

c)

3)

a)

b)

c)

The structures of the end groups must be different from that of the bulk repeating

units (e.g., CH3 vs. CH2 in an ideal polyethylene)

∴ If you detect the concentration of the end group and know the total amount of

sample present you can calculate the average MW, Mn bar

i)

ii)

i)

ii)

iii)

i)

i)

ii)

need to have either a perfectly linear polymer (i.e., two end groups per

chain) or need to know information about the amount of branching

∴ the Mn bar values that come out for “linear” polymers must typically be

considered an upper bound since there may be some branching

Detection of concentrations of end groups

Spectroscopy - IR, NMR, UV-Vis

Elemental Analysis

Radioactive or Isotopic labels

Strengths

The requisite instruments are in any department

can be quite quick

Sometimes this information comes out “free” during polymer structural studies

Weaknesses

does not give MW distribution information

need to know information about the structure

identity and number of end groups in each polymer molecule

limited to relatively low MW for sensitivity reasons

5,000 - 10,000 is typical MW range

Can be high with some detections types



C)

radioactive labeling of end groups

fluorescent labeling of end groups

Colligative Properties - Membrane Osmometry

1) Figures 2.2, 2.3, & 2.4 in Stevens

2)

a)

b)

c)

3)

a)

4)

a)

b)

Basic principles

molecules dissolved in solvents change the structure of the solution

solvent molecules want to diffuse into the solution with the highest solute

concentration (in terms of moles)


Strengths

quick

Weaknesses


range of 50,000 to 2,000,000 limited by low molecular weight species present and

sensitivity, respectively



D) Colligative Properties - Vapor Pressure Osmometry

1)

a)

b)

2)

a)

b)

c)

3)

a)

b)

E)

Basic principles

Diagram

Same physical chemistry principles as membrane osmometry except that the

solvent molecules move through gas phase instead of membrane

Strengths

quick

not hurt by low MW species as is membrane Osmometry

home-made systems can be very inexpensive

Weaknesses


while can be used up to MW of 40,000 is more typically used for MW below

25,000

Colligative Properties - Cryoscopy & Ebulliometry

1)

a)

2)

a)

3)

a)

b)

Basic principles

changes in solution structures upon dissolution decrease mp and increase bp

Strengths

can be quick and inexpensive

Weaknesses


mostly limited to MW below 20,000



IV Measurement of Weight Average Molecular Weight

A) Light Scattering

1)

a)

Basic Principles - Static and Dynamic

Instrumentation

i)

ii)

iii)

i)

ii)

iii)

iv)

Figures 2.7 in Stevens

Moving detector

Multiple Solid State Detectors

b)

c)

each polymer molecule in solution (and its associated solvent molecules) has a

different refractive index than neat solvent

∴ they behave as tiny lenses and scatter light

scan detector over a range of angles or use multiple detectors

measure scattered intensity as a function of angle and concentration

Use “Zimm” plot to extrapolate to infinite dilution and to zero degrees


d)

2)

a)

b)

c)

3)

a)

Brownian motion effects and dynamic

light scattering

Strengths

an absolute method that does not need

calibration

can give shape information as well as MW information

quite sensitive and easy to couple to an LC

Weaknesses

cost!



B) Ultracentrifugation

1)

a)

b)

c)

2)

a)

3)

a)

b)

c)

d)

V

Basic Principles

each polymer molecule in solution (and its associated solvent molecules) has a

different density than neat solvent

∴ if one has a density gradient in the solution (ultracentrifuge generates this from

the salt solution) the polymers will settle to their optimum levels

measure sedimentation height/velocity

Strengths

excellent for polymers having a variety of specific MWs, e.g., proteins

Weaknesses


costly if don’t have an ultracentrifuge for other reasons

time consuming

not as useful with true “bell curve” MW distributions

Viscometry

A) Viscosity Measurement

1)

2)

a)


Basic Principles

Math & Mark-Houwink-Sakurada Equation

[α] = K (Mv bar)a i)



ii)

iii)

i)

ii)

iii)

i)

i)

ii)

i)

K and a are characteristic of the particular solvent/polymer combination

(more later)

Mv bar = the Viscosity Average Molecular Weight

b)

c)

d)

Measurement of [η]

Make up 5-6 solutions at different

concentrations of the same sample and

of pure solvent

measure the time it takes each of

them to flow through the viscometer

extrapolate to viscosity at zero concentration which gives the intrinsic

viscosity

Measurement of [η] K and a

Plot the [η] values against the MW values from another technique and get

K and a from the intercept and slope

MW determination for a polymer of known structure

Look up K and a in the Polymer

Handbook

e)


Use the [η] values to calculate Mv bar

directly

Bootstrapping for a new polymer

make 3 or more samples of your polymer having different average MWs

measure the viscosities of each of these



ii)

iii)

iv)

v)

vi)

vii)

viii)

go to Polymer Handbook or your own research and find K and a values for

the most closely related polymer

3)

a)

b)

4)

a)

b)

these are a 1st guess/estimate of those for your polymer

use these K and a values and the experimental [η] values to give a 1st

estimate of the MW values for your polymer

use these 1st estimate MW values and the experimental [η] values to

calculate new K and a values

use these new K and a values and the experimental [η] values to get a

better estimate of the MW values

use these 2nd estimate MW values and the experimental [η] values to

calculate new K and a values

use these new K and a values and the experimental [η] values to get a

better estimate of the MW values

continue until these results converge

Strengths

very quick and reliable

no expensive equipment required

Weaknesses


need good values for K and a



VI Molecular Weight Distribution

A) Gel Permeation Chromatography, GPC

1) Basic Principles

a)

b)

c)


this is a type of liquid chromatography

(also called size exclusion

chromatography)

one uses a different type of column for separation

i)

ii)

iii)

iv)

v)

i)

ii)

NOT affinity but rather via the residence time in different sized pores of

the packing material

the beads are made from styrene and divinyl benzene copolymer where the

exact conditions and the nature of the template molecules allows the vendors

to make packing beads of controllable diameters

High MW samples come through

first (they don’t fit in the pores)

Low MW samples come through

last


d)

e)

The Chromatogram is a graph of intensity vs. time

Calibration curve


this needs to be calibrated wrt.



standards to put MW on bottom axis

f)

typically monodisperse polystyrene or poly(vinyl alcohol)

iii)

iv)

v)

i)

ii)

iii)

iv)

want a perfectly linear calibration chart for MW from 0 to 100,000,000

however, it curves up at high MW because all of the large polymers are

excluded from the pores and ∴ come strait through

also, it curves down at low MW because to all of the small molecules the

pores are equally oversized

need to do a calibration curve for each polymer/solvent combination

Gives Polystyrene (or Poly(vinyl alcohol)) Equivalent MWs

Universal calibration


log([η]M) is plotted with time on the x

axis

All or almost all polymers then fit on

the same curve as the intrinsic viscosity

acts as a “fudge factor”

Gives Polystyrene (or Poly(vinyl

alcohol)) Equivalent MWs

2)

a)

3)

a)

b)

Strengths

gives a full molecular weight distribution

Weaknesses

costs

need to calibrate



c)

B)

∴ use an online absolute detector such as a light scattering detector

Mass Spectrometry

1)

a)

b)

c)

Basic Principles

sample volatilization

i)

ii)

iii)

iv)

v)

i)

ii)

iii)

i)

Field Desorption, FD

Fast Atom Bombardment, FAB

Laser Desorption, LD

Matrix Assisted Laser Desorption, MALDI

Electrospray, ESI

ion separation by mass

Ion Traps / Ion Cyclotron Resonance, IT/ICR

Quadrupole, Q

Time of Flight, TOF

Combinations of different components,

e.g., MALDI-TOF


d)

2)

a)

b)

c)

3)

Rapidly improving due to proteomics/genomics research

Strengths

One often has the equipment for other purposes

Can give MW distributions, especially when coupled to an LC

Can give structural information

Weaknesses




a)

b)

C)

cost

time to optimize conditions

Fractional Solution & Fractional Precipitation

1)

2)

3)

Basic Principles

Strengths

Weaknesses

Molecular Weights, Polymers, & Polymer Solutions (Part...

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