Foundation GPC Part 2 – Basic Gel Permeation Chromatography

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Introduction

This presentation introduces gel permeation chromatography (GPC)

The mechanism of GPC shall be discussed

The method of analysing data shall be introduced

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Types of Liquid Chromatography

Interactive adsorption, partition, ion exchange, etc

Non-interactive GPC, SEC, GFC

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Nomenclature

Gel Permeation Chromatography GPC

Size Exclusion Chromatography SEC

Gel Filtration Chromatography GFC

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1. Reciprocating piston pump delivers eluent from reservoir at a constant volumetric flow rate. GPC is always an isocratic separation

2. Two position injection valve permits introduction of sample solution without interrupting solvent flow. GPC tends to use larger injection volumes than HPLC (typically up to 200ul)

3. GPC columns perform a separation based on the molecular size of polymer molecules in solution. Resolution and/or resolving range is increased by use of multiple column systems

4. Detector responds to concentration of polymer molecules eluting from the GPC columns

What is a GPC System?

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Additional Components Used in GPC

Concentration detectors

Differential refractometer (RI)

Ultraviolet absorbance (UV)

Evaporative light scattering or mass detector (ELS, EMD)

Infra-red (IR)

Molecular weight sensitive detectors

Viscometry

Light scattering

Additional systems

Online degasser

Autosampler

Column oven

Additional specific detectors

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Polymer Molecules in Solution

GPC is based on the behaviour of polymer molecules in solution

In the solid state polymers can be considered like spaghetti – a confusing mass of intertwined chains

In solution, polymer molecules are discrete entities

Due to entrophic effects all but the most rigid of polymer chains curls up in solution to form a ball like shape

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GPC Column Packings

GPC columns are packing with cross-linked, insoluble beads, typically co-polymers of styrene and divinyl benzene for organic GPC

These beads have a rigid pore structure that remains intact in the presence of solvent

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Synthesis of Porous Beads

High cross-link content gives a rigid, low swelling product with a well-defined pore structure

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Permeation of Polymer Molecules

Polymer coils in solution can permeate the pores on GPC packing materials

Exclusion, partial permeation and total permeation are possible

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GPC Separation Mechanism

Polymer is prepared as a dilute solution in the eluent and injected into the system

The GPC column is packed with porous beads of controlled porosity and particle size

Large molecules are not able to permeate all of the pores and have a shorter residence time in the column

Small molecules permeate deep into the porous matrix and have a long residence time in the column

Polymer molecules are separated according to molecular size, eluting largest first, smallest last

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Elution Profiles

As a result of the GPC separation mechanism, polymer molecules elute from the column in order of size in solution

Largest elute first, smallest elute last

The separation is purely a physical partitioning, there is no interaction or binding

The separation is isocratic

If polymer molecules have the same molecular dimensions, they will co-elute by GPC and may not be separated by this technique

The calibration curve describes how different size molecules elute from the column

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GPC Column Technology

Columns are packed with porous particles, controlled pore size and particle size

Columns are produced by slurry packing technique, packed at pressures in excess of 2000psi

Column dimensions typically 7-8mm i.d., 250-600mm in length

Exclusion volume (Vo) - Upper MW limit (also known as void volume)

Total permeation volume (Vt) – Lower MW limit

Pore volume (Vp) – Working resolving range of MW

Vp = Vt - Vo

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Typical Calibration Curves for PLgel Individual Pore Size Columns

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Determination of Polymer Molecular Weight Distribution by GPC

Produce a GPC calibration curve for the column set relating log M to retention time (RT)

Chromatograph the polymer sample

Normalise and integrate the GPC response versus retention time plot for the polymer sample

Convert retention time to logM via the GPC calibration curve

Present a logM distribution plot and calculate molecular weight averages (Mn, Mw) for the distribution

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Peak Integration in GPC

The sample peak when integrated can be assumed to be a histogram consisting of a number of individual “slices”

For each slice, i, the molecular weight (Mi) can be derived from the RT and the number of molecules (Ni) from the detector response

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Calibration of GPC Columns Using Narrow Standards

Chromatograph a series of well characterised, narrow polydispersity polymer standards

Plot peak retention time (RT) versus peak log molecular weight (logM)

Fit the data using a mathematical function

The calibration curve will be characteristic of the GPC column set used

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Performing Narrow Standard GPC Calibration

Injections of multiple narrow standards reduces the time taken to calibrate the system

Injection 1 Injection 2

Standards peaks in each chromatogram must be fully resolved to obtain repeatable retention times

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EasiCal Pre-prepared Calibrants

EasiCal PS-1 separation on 3 x PLgel 10µm MIXED-B

Spatula A Spatula B

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Narrow Standards Available from PL

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Polymer Calibrants for GPC

Most commonly used polymer calibrants

Polystyrene - THF, toluene, chloroform, TCB

Polymethyl methacrylate - MEK, ethyl acetate, acetone, DMF

Polyethylene oxide/glycol - aqueous eluents, DMF, DMSO

Mn - number average molecular weight

Mw - weight average molecular weight

Mv - viscosity average molecular weight

Mp - peak molecular weight

Mw/Mn - polydispersity by GPC

Must be extremely well characterised

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Individual standard EasiVial

Example Certificates of Analysis

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Calibration Methods for Conventional GPC

Narrow standards

Broad standards

Hamielec

Broad on Narrow

Integral

Aim : to produce a mathematical model for log M versus retention time

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Curve Fitting for Narrow Standards Calibration

Polynomial

All data points fitted with one function of the form

Log M = A + B(t) Linear (1st order)

Log M = A + B(t) + C(t2) Quadratic (2nd order)

Log M = A + B(t) + C(t2) + D(t3) Cubic (3rd order)

Cubic spline

Sets of points fitted with a series of cubic equations

Point to point

Points fitted with a series of linear equations

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Calibration of GPC Columns Using Narrow Standards

Chromatograph a series of well characterised, narrow polydispersity polymer standards

Plot peak retention time (RT) versus peak log molecular weight (logM)

Fit the data using a mathematical function (e.g. polynomial order 1,2,3, etc)

The calibration curve will be characteristic of the GPC column set used

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Errors Due to Limited Calibration Region

The column calibration should cover the full elution time region of the sample to avoid errors due to extrapolation

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Broad Standard Calibration - Hamielec Method

Requires a single polydisperse sample where Mn and Mw are known

Assumes a linear calibration Log M = A + B(t)

Requires only a single injection to calibrate

1. Chromatograph broad standard

2. Input actual Mn and Mw

3. Computer searches for suitable values of A and B that when back calculated give the correct values for Mn and Mw

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Broad Standard Calibration - Broad on Narrow Method

Requires a series of narrow standards plus a broad standard of known Mn and Mw

Valid for non-linear calibration curves

Requires several injections to calibrate

1. Chromatograph the narrow standards and fit the data with a mathematical function log Mns = F(t)

2. Input the Mn and the Mw values for the broad standard

3. Chromatograph the broad standard

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Broad Standard Calibration - Broad on Narrow Method

Universal Calibration theory predicts that

log Mbs = log (Kns/Kbs) + (1+ans) log Mns

(1+abs) (1+abs)

As Kns, Kbs, ans and abs are constants this can be simplified to

log Mbs = A log Mns + B

The computer searches for suitable values of A and B that results in the correct values of Mn and Mw for the broad standards when back calculated.

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Broad Standard Calibration - Integral Method

Requires a broad standard which has been fully characterised to give a cumulative molecular weight table, e.g.

Log M Wt %

2.800 0.000 Accuracy is improved

2.865 0.005 with increased number

2.929 0.020 of data points, usually

….. 50-60 points are used

5.705 99.80

5.789 99.99

5.870 100.00

There are few broad standards available with this level of characterisation

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Broad Standard Calibration - Integral Method

The broad standard is chromatographed and integrated, the log M values are assigned to the distribution based on the wt % values quoted in the table. This results in a calibration table with as many points as there are entries in the table.

The Log M versus retention time data is then fitted with a mathematical function as usual.

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Use of Mark-Houwink Constants in GPC

There are few well characterised polymer standards for GPC calibration. Therefore “unknown” polymer molecular weight can be derived from a GPC calibration curve obtained using polymer standards and applying the following theory:

Molecular size = hydrodynamic volume (HV)

HV = M [n], where M is molecular weight and [n] is intrinsic viscosity

In GPC molecules with the same HV elute at the same retention time

Therefore for different polymer types M1 [n]1=M2 [n]2

For a given polymer system Mark-Houwink equation applies : [n] = K M

Rearranging these relationships

logM2 = log(K1/K2) + (1+ 1) logM1

(1+ 2) (1+ 2)

where K1, 1 for polymer standards and K2, 2 for polymer under investigation are known

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Interpreting Chromatograms

The data obtained in a GPC experiment will be in the form of a chromatogram showing detector response as a function of retention time

There are fundamental parameters that are present on all chromatograms

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Peak Separation

Peak separation in GPC is dependent upon resolution and on molecular size

If two samples have different molecular sizes, then they will be separated to baseline assuming there is sufficient resolution

However, if samples are the same molecular size, then they cannot be separated by GPC as the mechanism of SEC is based upon size

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If two peaks are not baseline resolved in GPC, they cannot be analysed as two separate peaks

Although the calculations will give you results, the numbers will be meaningless as not all of the peak is defined and so the distribution will not be correct

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Excluded Peaks

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Partial Exclusion

The dead space of the separation will be around half of the total elution volume

Peaks eluting close to this volume may be partially excluded

Look for sharp peaks at the front of your chromatograms

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Oligomeric Resolution

In GPC, the relationship between molecular weight and retention time is logarithmic

As a result, peaks equidistant in molecular weight elute closer together with increasing molecular weight

This is a classic way to tell a separation is based on SEC

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With some columns it is possible to calibrate the column using the oligomers

The molecular weights of the initiator fragment and the repeat unit of the polymer must be known

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Interpreting Molecular Weight Distributions

The molecular weight distribution shows the amount of material present as a function of the molecular weight

The MWD looks a bit like a ‘mirror image’ of the chromatogram

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Effect of Baseline Position

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The whole peak should be analysed to get a true reflection of the sample

The peak should go down to the baseline on either side

Leaving out components of the peak will leave an ‘incomplete’ MWD