THE MOLECULAR MASS OF POLYMERS

1.1 Methods for measuring molecular mass........................................21.2 Special considerations....................................................................31.3 Importance of molecular mass.......................................................31.4 Molecular Mass Averages...............................................................6

1.4.1 Polydispersity..............................................................................61.4.2 Effect of Mn and Mw on properties...............................................71.4.3 Classes of molecular mass determination techniques................7

1.5 Colligative Properties.....................................................................81.5.1 Osmometry..................................................................................81.5.2 Vapour Pressure Osmometry.....................................................10

1.6 Viscometry....................................................................................101.6.1 Theory of molecular mass determination by viscometry...........101.6.2 Mark–Houwink equation...........................................................121.6.3 Viscosity-concentration relationships........................................121.6.4 Evaluation of []........................................................................14

1.7 End Group Analysis......................................................................141.8 Melt Flow Index............................................................................141.9 K values and ISO viscosity number..............................................151.10 Light scattering............................................................................15

1.10.1 Dynamic light scattering........................................................171.11 Size exclusion chromatography (SEC) or gel permeation chromatography (GPC)...........................................................................18

1.11.1 Introduction............................................................................181.11.2 Equipment..............................................................................19

1.11.2.1.............................................................................................Pumps19

1.11.2.2...........................................................................Sample Injection19

1.11.2.3...........................................................................................Column20

1.11.2.4........................................................................................Detectors22

1.11.2.5..........................................................................................Solvents24

1.11.3 Quantitative aspects of GPC...................................................241.11.3.1.................................Calibration - Polymer solvent interaction.

241.11.3.2............................Molecular mass elution volume relationship

251.11.3.3....................................................................Universal calibration

261.11.4 Data interpretation.................................................................26

1.11.4.1...............................................................Semi—quantitative data26

1.11.4.2.........................................................Quantitative interpretation26

1.11.4.3...............................................More about universal calibration27

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1.1 Methods for measuring molecular mass

The common feature of each of these methods is that they measure the number of polymer molecules in a given mass of polymer. The methods involve the measurement of colligative properties of dilute polymer solutions.

1. Membrane Osmometry

2. Vapour Pressure Osmometry

3. Ebulliometry and Cryoscopy

In some cases it is also possible to determine the number of moles of end-groups of a particular type in a given mass of polymer.

4. End Group Analysis

Scattering Methods

The interaction of electromagnetic radiation with a molecule results in either absorption or scattering of the radiation. Scattering results from the interaction of the molecules with the oscillating field of the radiation, creating a dipole which is a source of electromagnetic radiation — the scattered light.

5.Static Light Scattering

6. Dynamic Light Scattering

7. Small-angle X-ray and Neutron Scattering

Frictional Properties

The viscosity of a dilute polymer solution is considerably higher than that of the pure solvent, and the magnitude of the viscosity increase is related to the dimensions of the polymer molecules in solution.

8. Dilute Solution Viscometry

Measurements of the sedimentation behaviour of polymer molecules in solution can provide information on hydrodynamic volume, average molecular masses and molecular mass distribution.

9. Ultracentrifugation

Molecular Mass Distribution

The polymer can be separated into a number of fractions, each of which has a narrow distribution of molar mass or size exclusion chromatography can be used.

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10.Fractionation -

11.Gel Permeation Chromatography (GPC)

4

1.2 Special considerations

The determination of molecular masses of polymers presents two problems not generally encountered with low molecular mass substances. Firstly, a polymer sample usually contains molecules with a wide diversity of molecular masses, so that molecular mass determinations merely yield some average value for the various molecules present. Low molecular mass materials are monodisperse, all molecules having the same size. Secondly, most molecular mass determinations are carried out in solution, and whenever the physical properties of polymer solutions are studied, these properties are generally much more concentration dependent than in the case of low molecular mass substances, with the result that well established methods require modification. The spatial configuration of polymer molecules in solution will be considered in detail later (phase equilibria section) and here it is sufficient to note that the average polymer molecule may be equated to a spherically symmetrical statistical distribution of the chain elements about the centre of gravity, and that the actual volume encompassed is many times the actual volume of the molecule. This is a most important feature which distinguishes polymers from other substances. Thus the volume over which a molecule exerts its influence is several hundred times its own molecular volume, depending on molecular size, chain flexibility, solvent/polymer interaction etc. All of the physical methods used for the determination of molecular masses require that the molecules contribute individually to the property; clusters of molecules will lead to erroneous results. Only if the solution is sufficiently dilute to permit molecules to occupy separate portions of the solution will satisfactory results be obtained. Concentrations of below 1% are generally required, and even when low concentrations are used it is necessary to extrapolate results to zero concentration.

1.3 Importance of molecular mass

It is necessary at this point to stop briefly and remind ourselves why molecular mass measurements are so crucial in polymer science. Some polymer properties, such as density, refractive index and hardness are fairly independent of molecular mass for high polymers (not for low polymers e.g. waxes).

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However, properties such as melt viscosity (processing), softening point (useful max. temp.), tensile and impact strength, heat resistance etc. can be strongly dependent on chain length. In the figure above the tensile and impact strength increase rapidly as the molecular mass increases and then level off, while melt viscosity continues to increase. Since polymers with a very high melt viscosity are difficult to process a compromise must be reached between maximum physical properties and processability.

The most extreme example of the dependence of properties on molecular mass can be demonstrated by reference to ethylene and its polymeric forms:

Ethane DP = 1 gas bpt — 89°CButane DP = 2 gas bpt — 0.5°C DP > 3 paraffin oilsDP > 30 greaseDP > 50 waxDP > 400 hard resinDP > 1000 polymer

Degree of polymerization is the number of monomer repeating units in the polymer chain. The molecular mass of a particular chain can be found by multiplying the DP by the molar mass of

the repeat unit.

Furthermore, within a specific polymeric sample a wide variation in molecular masses occurs; it is impossible for all chains to commence

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melt viscosity commercial range tensile strength

property

impact strength

average molecular mass

growing and to terminate at the same time. Hence, with polymers, we refer to an average molecular mass.

Molecular mass distribution is important since it affects many of the characteristic physical properties of a polymer. As an example polystyrene with a degree of polymerization of 1000 (Mm  105) is stiff and brittle at room temperature; one of degree of polymerization of 10 (Mm 1000) is soft and tacky at room temperature.

Subtle batch to batch differences in molecular mass distribution (remember the average morecular mass can still remain the same) can cause significant differences in the end-use properties of a polymer. Molecular mass is an extremely important variable because it relates directly to a polymer’s physical properties. In general, the higher the molecular mass the stronger the polymer. However, too high a molecular mass can lead to processing difficulties. What defines an optimum molecular mass depends on the intended application and processing technique, i.e. the technological process whereby the polymeric article is to be manufactured.

Examples of such properties which depend on molecular mass include,

Tensile strength Elastomer relaxation timeBrittleness Flex lifeImpact strength ToughnessDrawability Adhesive tackAdhesive strength Coefficient of frictionElastic modulus Melt viscosityHardness Melting temperatureTear strength Film hazeEnvironmental stress crack resistance (ESCR)

Some properties such as specific heat capacity are unaffected by molecular mass while other such as elongation at break (or yield) may show complicated behavious (first increasing and then decreasing).

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63 342 104

106 Molecular mas

No of molecules

Cu Sucrose Polymer

Note that with two samples with different molecular distributions, one could find that the tensile strengths and melt viscosities could be identical and yet one of the other properties, could result in their having quite different abilities to be fabricated into usable durable products.

The figure below shows how the properties of a typical thermoplastic polymer vary with temperature. Melting temperature increases with increasing molecular mass but tends to an asymptotic maximum. The glass transition temperature reaches this asymptote far sooner. At the same time thermal degradation becomes more pronounced as molecular mass rises. The properties in the table above show an asymptotic increase with molecular mass. Solubility, by contrast, shows a decrease with increasing molecular mass.

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Thermal degradation

ViscousTemperature liquid Tm

Viscoelastic solid

Tg

Elastic solid

Molecular mass

1.4 Molecular Mass Averages

With the exception of some naturally occurring polymers, most polymers have a molecular mass distribution like the one below

In such a situation, defining an exact molecular mass is dififficult. One approach is to quote the most probable molecular mass (i.e. the position of the peak), but this becomes problematic where the distribution is bimodal. A number of other molecular masses are more commonly used.

Where a range of molecular masses exist, different experimental methods of determining molecular mass will yield different results, since these methods are based on different averaging procedures. Two groupings of average values are generally measured. Properties that are determined solely by the number of molecules present will yield number average molecular masses Mn. eg. measurement of colligative properties of a solution, like vapour pressure depression, freezing point depression, bpt elevation, osmotic pressure and end group analyses. In light scattering experiments the molecular mass values obtained are influenced by the number of molecules present as well as their sizes, shapes and flexibility. These measurements yield mass average molecular masses Mw.

The number average molecular mass is defined as:

where

The mass average molecular mass (also called the weight average molecular weight) is defined as:

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Number ofmolecules

Molecular mass/chain length

1.4.1 Polydispersity

The ratio is called the polydispersity.

In monodisperse systems in which all the molecules have the same molecular mass, the two expressions will yield the same result.

More typically for polydisperse systems. Its value is a measure of

the non—uniformity of the sample. In many instances the polydispersity lies in the range 1.5-2.0.

It is usually true that for polymers with the same molecular mass, the polymer with the smaller polydispersity in general has greater tensile and impact strengths. Similarly abrasion resistance and chemical resistance increases with lower polydispersity

At the same time they is usually has higher viscosities making processing more difficult. This is because small molecules in the broader distribution tend to lubricate the system. Broader distributions also cause longer cycle time in injection moulding because of slower crystallization and thermal conductivity. In extrusion processes higher polydispersities reduce the likelihood of melt fracture because of short lubricant molecules. Broader distributions though have greater extrudate swell (the result of the large molecule tail). The high molecular weight tail may also be degraded where shear forces are significant.

Some applications such as melt-spinning of fibres require very narrow molecular mass distributions.

1.4.2 Effect of Mn and Mw on properties

The figure below is a graphical representation of the relationship between Mn and Mw on a variety of properties. The arrows indicate an increase in the property in that direction.

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Impact strength

Mn

Resistance tomelt Melt elasticityfracture

SpeedFlowability of crystallization

Mw

1.4.3 Classes of molecular mass determination techniques

There are a number of techniques available to determine the molecular mass of a polymer in solution. These can be divided into two main categories:

Relative: Require calibration with samples of known molecular mass. Eg. viscosity, vapour pressure osmometry and GPC

Absolute: Require no calibration as the molecular mass is directly related to the property being measured. Eg. Light scattering and colligative properties

1.5 Colligative Properties

The physical properties of a solution are in general quite different from those of the pure solvent, the:difference being a function of the solute concentration. The escaping tendency of the solute is proportional to the number of solute particles present in solution, if the solution is sufficiently dilute. This holds true for both polymeric and monomeric materials although the statement “sufficiently dilute” is more stringent for polymeric solutes. The activity of the solute is proportional to its mole fraction in very dilute solutions, and it follows that the depression of the activity of the solvent by a solute is equal to the mole fraction of the solute.

Colligative property methods make use of these differences in properties of the solvent and solution and measurements are based on vapour pressure lowering, freezing point depression (cryoscopy), boiling point elevation (ebulliometry), and osmotic pressure (osmometry). The data below represent some typical values

Q Mn = 10,000c = 2x10-2g cm-3

Mn = 1,000,000c = 2x10-2g cm-3

Lowering of vapour pressure at 25°C

2.4 Pa 0.024 Pa

Depression of freezing point at 1

atm0.0116°K 0.000116°K

Elevation of boiling point at 1 atm

0.0062°K 0.000062°K

Osmotic pressure at 25°C

4960 Pa 49.6 Pa

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1.5.1 Osmometry

Osmosis requires the prescence of a semi—permeable membrane. If a pure solvent is separated from a solution by a semi-permeable membrane, initially the the free energy of the solvent in the solution will be lower than the solvent in the pure solvent compartment. Solvent will spontaneously move from the high to low free energy side and the hydrostatic pressure of the solution will increase. The diffusion process will cease when the hydrostatic pressure difference balances the free energy difference. Alternatively diffusion may be counteracted by the application of an external pressure to the solution side.

This pressure is the osmotic pressure. For dilute polymer solutions:

This can he related to the ratio of the amounts of each component in the limits of infinite dilution.

since n1V1. is the volume of the solvent, and ln(n2/n1) = (n2/n1) then

V = n2RT

We subsititute and

Then

pure solvent solution pure solvent solution

initially at equilibrium

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Only under special conditions, when the polymer is dissolved in a theta () solvent will (/c) be independent of concentration. We hence take measurements of a few different concentrations and extrapolate to zero concentration. Due to polymer solvent interactions the expression is expanded with virial coefficients – due to polymer-solvent interactions.

The second virial coefficient depends on a large number of factors:

1) the particular polymer solvent system

2) the MM and MM distribution of the polymer

3) the temperature

4) the tacticity of the chain

It is thus often advantageous to select a poor solvent for the polymer as the slope of /c vs c will be small resulting in a smaller percentage error. This method requires no calibration and gives the mass average molecular mass Mn. The membrane permeability imposes a lower limit of about Mn = 15000 g/mol.

1.5.2 Vapour Pressure Osmometry

Direct measurement of vapour pressure is not done. The vapour pressure osmometer measures the difference in temperature between a solvent and solution drop placed on two thermistors. Due to the vapour pressure difference between the two drops their evaporation rates differ when placed in an atmosphere saturated with the solvent vapour. A steady state temperature difference develops and this is sent as a voltage signal to a recorder.

For dilute solutions

T = d m

d = constant

m = molality

The method requires calibration with low molecular mass standards to obtain d. The conditions during calibration have to be carefully controlled and reproduced during the sample measurement.

The method is rapid and commonly used for molecular masses Mn < 20 000. One still has to use dilute solutions and ones differing in composition

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so as to extrapolate to infinite dilution. (zero concentration).

1.6 Viscometry

1.6.1 Theory of molecular mass determination by viscometry

When two low molecular mass liquids with reasonably similar liquid lattices are mixed there is generally little change in the mobility of the constituent molecules. The amorphous solid polymer can be considered to have a liquid-like structure and on solution the small solvent molecule will penetrate the solid structure, separating the long polymer molecules, and increasing their mobility markedly. The dissolved polymer molecule will change its dimensions in accordance with the extent of polymer—solvent interaction. The molecule will interact with thousands of solvent molecules situated along the length of the coiled but expanded polymer chain. This interaction between polymer and solvent results in a marked increase in viscosity of the pure solvent and can be used to determine the average molecular mass of the polymer. The usefulness of the technique has been recognised since the early work on macromolecules by Staudinger in 1930.

Factors governing the viscosity of a solution are

1. Solvent

2. Polymer

3. Temperature

4. Concentration

5. Molecular mass

However, it has not been found possible to relate the observed viscosity change of a solution to the molecular mass of the polymer without introducing parameters that are experimentally inaccessible and, as a result, the viscosity method constitutes a secondary technique involving empirical constants. The method is nevertheless most useful as it can be carried out rapidly using relatively simple equipment.

An Ostwald or an Ubbelohde viscometer is usually used in which the time taken for the level of solution to pass between two reference marks is determined, and is related to the viscosity according to the Poiseuille equation for Newtonian flow

where P = pressure difference maintaining flowr = capillary radius = length of capillary

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= viscosity

The Ostwald (A) and Ubbelohde suspended level (B) Viscometers

A given volume of liquid or solution is put in the viscorneter and the liquid level is sucked or blown to above the upper mark above the small bulb. The liquid is allowed to flow back into the larger bulb and the time is taken for the liquid level to pass between the mark just above and the mark just below the small bulb. The flow time for a solution of given concentration is usually denoted as t and that for the pure solvent as to. As we have seen viscosity is dependent on temperature so the whole experiment will normally be done in a thermostat bath.

Before we can go any further we must define some terms commonly used in viscometric experiments.

t and to refer to the flow times for the solution and solvent respectively while c is the solute (i.e. the polymer) concentration in the solution.

viscosity of solution (eta)viscosity of solvent 0

viscosity ratio

specific viscosity

viscosity number

limiting viscosity number

1.6.2 Mark–Houwink equation

It was mentioned above that the relationship between solution viscosity

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and molecular mass is an empirical one. The relationship most commonly used is that of Mark and Houwink

where M is the molecular mass and K and are constants specific to a polymer-solvent system. A plot of log [] vs log M should be a straight

For some polymers K and are concentration dependent. In these case plot of log [] vs log M may be represented by two intersecting lines (associated with 2 pairs of K and )

1.6.3 Viscosity-concentration relationships

We have seen that the Poiseuille equation relates the viscosity of the liquid to the volume rate of flow.

Suppose a volume V of liquid is contained between the two reference marks and the flow times for the solvent and solution are to and t respectively, then the viscosity ratio becomes

The pressure differences maintaining the flow are dependent on the average liquid height h and the liquid density p. Hence we can rewrite the equation as

For dilute solutions

0

Therefore

When we deal with the theory of polymer solutions we will encounter various equations relating solution viscosity to concentration. For the moment we will simply write down tw o of these and see how they can be used in this instance.

Huggins equation:

Kraemer equation:

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Usually

Using either of the relationship Kraemer or Huggins can be found by extrapolation from data obtained for a number of dilute solutions. The figure below demonstrates this.

1.6.4 Evaluation of []

Substitution of [] into the Mark-Houwink equation gives M if K and alpha are known. The average molecular mass calculated will be either a mass average Mw or a number average Mn depending on the method used in evaluating constants K and alpha.

It should be noted that the Mark-Houwink constants refer to Mn or Mw. The constants are valid only provided the polymer has the same molecular mass distribution as that used in determining the constants, i.e. Mn or Mw. Tables of Mark-Houwink constants often refer to the molecular mass ranges to which the constants are applicable.

Care needs to be taken when using this equation to use the correct units. [] is normally expressed in mL g-1. c is normally expressed in g mL-1. K and are i.t.o. these units.

1.7 End Group Analysis

This method counts the number of polymer molecules in a known mass of polymer sample. It is only applicable when the molecules posses a known number of detectable end groups. These end groups are estimated using standard physical or chemical methods and the number of molecules calculated directly. Typically polymer molecules that have –OH, -COOH,

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or NH2 groups at their ends are accessible by this technique. This can be done either by titration or via a spectroscopic technique such as IR or NMR. Above a molecular mass of 25000 g mol-1, the number of end groups per unit mass becomes very low and the technique becomes insensitive.

1.8 Melt Flow Index

The flow characteristics of plastics materials are of great importance to the processing industries. The apparatus used to determine MFI is shown below. The polymer is heated for a given time after which a constant load is applied and the mass of polymer extruded through the capillary in 30s (or 60s) is weighed. The mass in grams is referred to as the MFI. A high MFI relates to a low molecular mass. It can be related to molecular mass empirically.

It must be noted that there is no general correlation between MFI and Mm

but this correlation needs to be performed for each polymer composition and in fact for different polydispersities. MFI is more often used as a quality control variable.

1.9 K values and ISO viscosity number

Plastics like PVC will degrade if subjected to MFI measurements. Commercially molecular mass differences are characterized by K values calculated from relative viscosities. The K value can be calculated from:

K = 1000 k

K values increase with increasing molecular mass but depend on the

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solvent used and it is becoming more common to quote the ISO viscosity numbers which is usually the limiting viscosity.

1.10 Light scattering

Light scattering is one of the most popular methods for determining the weight average molecular mass Mw.

Light is an electromagnetic wave, and when it strikes atoms or molecules the electrons are perturbed and oscillate with the same frequency as the exciting beam. These transient dipoles re-emit the absorbed energy in all directions, ie. scattering takes place.

The apparatus used consists of a light source (laser or Hg lamp) and a detector that can measure the scattered light intensity at various angles.

*

If we consider scattering from a polymer solution where the dimensions of the polymer molecules are less than /20. The intensity I at angle is given by the equation

We can express this as a reduced intensity

After some simplification this becomes

where K is given by:

In order to obtain Mw from the experimental measureinents of R we rearrange the: above equations to give

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coherence determining

field stop photomultiplier

Where NA is Avogadro’s number and is the change in refractive

index with concentration.

R is determined for a series of polymer solutions of different concentration. The scattered intensity is usually measured at 900 to the

incident beam. We plot vs c for each sample and extrapolate

to zero concentration to eliminate the effects of polymer solvent interaction. The intercept gives 1/Mw directly. It must be remembered that

R’ = R,solution - R,solvent

If the molecule is larger than /20 it can no longer be regarded as a point source for scattering. Light will be scattered from different points of the molecule resulting in interference effects. No interference occurs at zero angle, but the scattered beam is obscured by the incident beam.

We can express a particle scattering factor, P() as:

where is the mean square of the radius of gyration, a measure of the polymer dimensions in solution.

We can now write our basic equation as

A plot of against sin2 (/2) at constant c gives a straight line

which can be extrapolated to zero angle. The intercepts from a number of different cones can then be plotted against cone and extrapolated to yield 1/Mw.

It can thus be seen that the results are both angle and concentration dependant. These two extrapolations can be performed in one step using

a Zimm plot. The quantity is plotted against sin2(/2) + k c,

where k is an arbitrary constant chosen to separate the lines corresponding to various concentrations. We plot two sets of lines, one

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corresponds to constant c and various values of , and the other to constant and various c.

From this plot we can obtain the following information

1) The y-intercept yields 1/Mw

2) The second virial coefficient can be obtained from the slope of the = 0 line

3) The root mean square end to end distance of the polymer chain is found from the slope of the c = 0 line

This approach is called static light scattering and gives an average value of all the molecules in solution.

The more modern approach to light scattering uses the phenomena of brownian motion. This technique is called dynamic light scattering, quasielastic light scattering or photon correlation spectroseopy. Instead of looking at the average intensity at a particular angle, the change in intensity with time is examined. Due to brownian motion the molecules change position in the solution. This results in a change in the scattered intensity with time. By applying some complicated mathematical techniques it is possible to determine the diffusion coefficient for the molecules or particles and hence their hydrodynamic radii. This technique can produce a particle size distribution of a polydisperse system, and not just the average size.

1.10.1 Dynamic light scattering

Also called photon correlation spectroscopy (PCS).

In a typical experimental arrangement we use a laser as a light source. This is important, because we require the light to be in phase. The light source is usually focussed down to a narrow beam that travels through the sample. The sample is maintained at a constant temperature, this

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assures that the viscosity of the solution does not change.

Light scattered from the solution is observed by a photodetector which can move over a range of angles. The scattered light can be detected at any angle to the incident light.

Experimental set-up for dynamic light scattering techniques

When a particle is illuminated, photons will be scattered at all angles, if several stationary particles are illuminated, light will be scattered at all angles and the photodetector will see a sum of all light scattered. However, this sum is not just a simple addition, but depends on the phase of all the scattered photons. The phase difference will depend on the positions of the particles such that the light scattered from particles a wavelenght apart will constructively interfere and particles a half a wavelenght apart, destructively.

The next step is to remember these particles are not stationary, but will be moving under brownian motion, thus the relative positions of the particles are continuously changing so the intensity at the detector changes with time. The rate of fluctuation of the scattered light will depend on the speed of diffusion of the particles. Small particles diffuse faster than large particles. The particle size distribution is calculated from the speed at which the particles are diffusing.

1.11 Size exclusion chromatography (SEC) or gel permeation chromatography (GPC)

1.11.1 Introduction

In size exclusion chromatography, also called molecular-exclusion or gel permeation chromatography, separation is based on the solute’s ability to enter into pores of the column packing. Smaller solutes spend more time in the pores and hence take longer to elute from the column.

SEC/GPC gives a molecular mass distribution in the form of an elution

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trace of detector response vs time. The larger molecular mass components elute first and the smaller molecular mass components elute later with the solvent generally eluting last (smallest molecular mass).

The elution information can be converted into absolute molecular mass data yielding number average, mass average, viscosity average molecular masses. The most fundamental characteristic of a polymer viz., its molecular mass distribution, is commercially the most important information obtained using SEC/GPC.

1.11.2 Equipment

Schematic of a typical gel permeation chromatograph

Generalized SEC/GPC system

1.11.2.1 Pumps

Constant reproducible flow rate is essential. This includes reproducibility for changes of viscosity with different polymer solutions.

Since changes of solvent necessitate system flushing, the pumps must have low internal volumes to keep time and solvent usage to a minimum. Solvent reservoir on the other hand should be of large volume for continuous operation, yet readily replaceable to facilitate solvent change over.

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1.11.2.2 Sample Injection

The sample injector must be capable of small volume injection for molecular mass determination and large sample injection for fraction collection.

Two systems are used.

A simple injection port allowing insertion of micro syringes of volumes varying between 10 and 100 inicrolitres. Reproducibility of injection volume is not good but little solution is wasted and so it is useful where only a small volume of sample is available.

A rheodyne, is a more accurate and reproducible system consisting essentially of a loop of steel micro tubing connected across a valve assembly. The loop can easily-be replaced with other loops of different volume and even cut to give desired volumes. Reproducibility of volume and time of injection are the major advantages of such a system.

The major disadvantage is that a loss of a fairly large volume of sample occurs where a minimum of five loop volumes is required to flush the valve-loop assembly, generally 1-2 mL of solution would be used.

1.11.2.3 Column

Various columns are available with differing ranges of separating ability. A linear column allows for all sizes of molecules to be analyzed, but is not good for detecting small differences in molecular mass. In this column there is a gel of varying exclusion limits, say 103 at the top and 105 at the bottom. the resolution is poorer since the column length is less. A single column functioning over a limited range of molecular masses can be used for a narrow molecular mass range sample or a series of columns covering narrower ranges of molecular masses can be used, to cover a wider range of molecular masses, but is expensive to use in that a

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number of columns is required.

Column Material

Columns consist generally of polymers of varying degree of cross-linking which swell in the solvents for which they are made. In aqueous applications (gel filtration) a hydrophilic stationary phase is used. Hydrophobic stationary phases are employed in gel permeation chromatography where the mobile phase is a non-polar organic solvent.

Two important gels are available commercially. Sephadex, a poly dextran for aqueous solutions. Styragel, consisting of crosslinked polystyrene, is generally used for polymers dissolved in tetrahydrafuran solutions.

Gel particles consist of networks of crosslinked polymer chains which are aggregated into strands with random joins. Electron microscopic studies reveal pores’ (not tubular structures) which are interconnecting apertures of void spaces between clusters of chains.

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In a lightly crosslinked gel the pore size therefore varies greatly if different solvents are used, depending on the compatibility of the solvent. The network is flexible and collapses if the column dries out or is filled with a non solvent, where the internal volume is squeezed out.

Heavily crosslinked gels swell a lot less and are rather insensitive to the solvent properties generally speaking. Being more rigid these columns withstand pressure better than less crosslinked gels and don’t clog as easily.

The different gels are said to have differing exclusion limits, quoted in angstrom units, this being the minimum size particles unable to pass through the pores of the column.

Size selectivity

The size selectivity of a particular packing is not infinite, but is limited to a moderate range. All solutes significantly smaller than the pores of the packing move through the column’s entire volume and elute with a retention volume Vr of,

Vr = Vi + Vo

where Vi is the volume of the mobile phase occupying the packing materials pore space, and Vo is the volume of the mobile phase in the remainder of the column. The maximum solute size for which the above equation holds is known as the packing materials inclusion limit and below this maximum size no separation is possible. All solutes too large to enter the pores elute simultaneously with a retention volume of

Vr = Vo

which defines the packing materials exclusion limit and above this maximum size no separation may occur.

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Elution volume

Log

(mole

cula

r m

ass

)

Exclusion limit

Inclusion limit

1.11.2.4 Detectors

The detector monitors the separation and responds to the components as they elute from the column. Detectors should be non destructive so that the fractions may be collected for further studies. A wide sensitivity range is necessary.

GPC has one major advantage since only one solvent of constant composition at constant temperature is used. This makes it feasible to use continuous detectors to record the concentration of polymer in the eluant.

Differential refractometer.

The differential refractometer is known as the universal detector, so naxne.d because all compounds refract light and can be monitored by such a detector. The refractive index of polymers is almost constant for molecular masses above 1000 and so the detector response is directly proportional to polymer concentration. The detectors used in a continuous system are sensitive to concentrations down to ppm and use minute cell volumes in the order of microlitres. Refractive index detectors are useful as they allow quantitative analysis of solutes that may be difficult to detect by other methods of detection. The detector, however, has a relatively high limit of detection due to its low signal to noise ratio.

Infrared detector

Modern day instruments use diode array detectors and are extremely useful being able to record a full infrared spectrum (4000 —300 cm-1 ) in 20 microseconds every 50 microseconds. These are not only useful for qualitative identification of components but can be used for their quantitative analysis as well (functional group concentration determination). Needless to say these detectors are expensive and not commonly used.

Ultraviolet detector

Widely used in GPC analyses and very useful when used in conjunction with differential refractometers. It can only be used for uv active compounds and this is a limitation in some synthetic polymers. Aromatic

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containing compounds are naturally suited to analysis by UV detectors.

Modern detectors employ taper cells to improve sensitivity. These cells allow for refraction resulting in a greater proportion of light reaching the photodiode detector.

Careful combination of this detector with a universal detector, e.g. RI may allow analysis of polymer blends, e.g. PS and PMMA. The RI detector responds to both but th UV response can be limited to just the PS.

Evaporative light scattering detector

In ELSD detection the effluent from the column is passed through a nebulizer to produce a fine mist, which is passed through a heated evaporation tube where the solvent is completely vaporized. Light from a laser beam is then passed through the sample and scattered by the presence of solute particles. The absolute weight and size of the solute may be calculated from the scattered light as a function of the angle. The detection system is relatively universal but is restricted to solutes that are not volatile (not a problem with polymers). In addition the mobile phase must be volatile in order for it to vaporize in the evaporation tube.

More sophisticated detectors make measurements at multiple angles [multi angle light scattering (MALLS) detectors]. Such detectors are useful because they can provide information about radii of gyration and branching as well as molecular mass data.

Viscometric detectors

When the sample is introduced to the detector, it is split, following two different paths, flowing through capillaries. Along one path the sample is diluted using pure solvent. This causes an imbalance which is measured as a pressure difference. A second pressure transducer measures the absolute solvent pressure drop across a resistance. The specific viscosity of the sample is then calculated from the two measured pressure signals. Viscometric detectors are universal in nature.

1.11.2.5 Solvents

The solvent should dissolve the polymer sample, not attack the gel, not interfere with the detector system possibly allow either solvent or polymer to be recovered at the end. Expensive solvents are usually recycled. Higher temperature operation requires finer control of operating conditions and so it is for this reason one tries to keep the operating temperature low (not possible if the polymer is insoluble in a wide range of solvents). Viscosity is lower, and diffusion rates are higher at higher temperatures and it would be desirable for these reasons to do high. temperature studies. Yet most GPC work is still done at room temperature.

The nature of the gels used necessitate that the solvent change over

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should be gradual if it is to be done. This allows the gel to reawell and at the same time prevents “shocking the gel thereby causing permanent disfunction of the column through structurally damaging the gel. Typical change over is best carried out over a 24hr period.

Tetrahydrofuran is most commonly used as a solvent since it dissolves a large number of polymers (excluding poly(olefins)). Toluene at elevated temperatures is suitable for poly(olefins). Remember that low concentrations of polymer are used and that very limited solubility is required.

Where extremely high temperatures are required (e.g. for PE and PP), dedicated SEC instruments are often used in which the entire system is maintained at elevated temperature so that the polymer does not precipitate out of solution and clog the system. With eleveated temperature SEC/GPC care must be taken that the elevated temperatures don’t cause further polymerization (thereby increasing Mm) or degradation (decreasing Mm). This can be an especial problem with step-growth (condensation) polymers.

PET is another polymer which requires special solvents (often toxic cresols with or without high temperature) although more recently a method has been develop using hexafluoroisopropanol at room temperature to dissolve the PET, followed by conventional low temperature GPC.

1.11.3 Quantitative aspects of GPC

1.11.3.1 Calibration - Polymer solvent interaction.

Separation in GPC occurs as a result of the fact that dissolved polymer molecules of different sizes penetrate into gel pores to a greater or lesser extent. One can consider the dissolved polymer to be a spherical molecule unit (although later in your course you will look at the configuration of dissolved polymers in detail).

As shown in the figure the size of the ball is related to the molecular mass of the polymer. But we see from the next figure that the polymer — solvent interaction is important since for a given molecular mass polymer

Mn = 105 Mn = 103

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the better the solvent — polymer interaction the more solvent the polymer ‘ball imbibes and the larger is its size in solution.

This means that you cannot calibrate a column in terms of the “molecular mass of a polymer~ generally but that a calibration will be specific for a particular polymer — solvent system. For example PMMA in THF will elute at a different volume from the same molecular mass polystyrene sample dissolved in the same solvent.

1.11.3.2 Molecular mass elution volume relationship

For a wide variety of polymers in different solvents the following equation has been found approximately correct.

Ve = -B log(M) + C

where Ve = elution volume to peak maximum (= time flow rate)

M = molecular mass of narrow fractionB,C = constants

The GPC is calibrated by passing a series of polymer fractions of known molecular masses through the column and noting the elution volumes for the peak maxima. The average molecular masses of the fractions must be determined by independent means. log M vs Ve (above equation) should yield a straight line. Note that the solution concentration must be low enough to ensure that there is no shift in Ve with concentration The calibration curve will be accurate (hold good) for a given flow rate, temperature, polymer, solvent and all measurements must be conducted under these set conditions.

Calibration standards are only commercially available as polystyrene fractions at a cost. This is because the polymerization reaction can be closely controlled to produce polymer of any required molecular mass with a narrow mass distribution.

Mn = 104

Good solvent Poor solvent

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Other standards have to be prepared by fractionation by the experimentalist.

1.11.3.3 Universal calibration

The problems associated with obtaining suitable standards for GPC calibration resulted in the effort to develop a universal calibration technique.

1.11.4 Data interpretation

1.11.4.1 Semi—quantitative data

As said in the introduction a lot of commercial application lies in semi—quantitative analysis in comparing batches of polymers~ This can measure effects certain factors may have on molecular mass distribution. For example heating during processing or light due to outdoor exposure, or aeging by oxidation in air would be some factors which would cause a change in the shape of a GPC trace.

1.11.4.2 Quantitative interpretation

Calibration curve

The first requirement for quantitative interpretation is a suitable calibration graph of molecular mass vs elution volume (or time) for the particular polymer.

Data

The sample of unknown molecular mass is injected into the column and the usual curve of detector response vs eluted volume as shown is obtained.

The deflections observed at the low molecular mass end of the GPC trace are due to impurities or dissolved gases in the polymer or solvent, e.g the concentration of hydroperoxides in THF will slowly build up with time.

When using freshly distilled THF you will notice that the peaks are much smaller.

Remember that the “event marker” indicates the passage of 5 ml (or 2.5 ml) of solution. You can work i.t.o. the number of time or mL.

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Calculation of Mn and. Mw

(i) Draw a base line.

(ii) Measure the height of the curve above the base line at a number of equidistant points. Heights are proportional to the polymer concentration i.e. MiNi.

(iii) Complete the table Column 1 can be in “mL” or “time”. The data in column 3 is obtained from the calibration graph

(iv) Calculate Mn and. Mw according to the formulae:

1 2 3 4 5

Retention time

Height(NiMi)mass

Molar massMi

from calibration

No of molecsNi

col 2/col 3NiMi2

col 2 x col 3

1 0.5 300 000 1.67 x 10-6 1.5 x 105

2 3.6 285 000 1.26 x 10-5 1.03 x 106

| | | | |

| | | | |

| | | | |

| | | | |

NiMi Ni NiMi2

1.11.4.3 More about universal calibration

Each polymer exhibits a different interaction with a specific solvent. This

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interaction determines the degree to which the polymer chain swells in the solvent. GPC detects the size of the swollen polymer sphere in the solvent (hydrodynainic volume) and thus needs to be calibrated for the particular polymer being investigated. The universal calibration allows us to extend a calibration curve to more than one polymer type.

The hydrodynamic volume of a polymer is measured as []M where [] = intrinsic viscosity. This parameter forms the basis for the universal calibration. The hydrodynamic volumes of polymers 1 and 2 are given by:

[1]M1 = K1M11+1

[2]M2 = K1M12+1

By equating the hydrodynamic volumes of polymers 1 and 2, the molecular weight of polymer 2 may be obtained in terms of polymer 1 from the relationship

The constants K and are obtainable from the literature. These days they are oftened included in the databases provided with GPC software. Note that they are solvent and temperature dependent.

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