Advanced GPC Part 2 - Polymer Branching

Introduction

Polymers are versatile materials that can have a variety of chemistries giving different properties

As we have seen the molecular weight of polymers affects many of their physical parameters

However, the structure of polymers, particularly the presence of branches, also has a strong affect on their behaviour

It is possible to investigate the structure of polymers using GPC

This presentation gives an overview of the analysis of polymer branching by GPC

Branching in Polymers

Polymers are said to be branched when the linear chains diverge in some way

Branching can result from the synthesis method of from post-synthesis modification of the polymer

Branching leads to compact, dense polymers compared to their linear analogues, with radically difference melt, flow and resistance properties

There is much interest in polymer branching as a method of controlling the properties of well-known polymers

Branching Structures

Polymers may have a wide variety of branching structures depending on how they have been made or modified

Dendrimers are special cases of polymer that combined the structures of star and hyperbranched polymers

The branching can further be characterised by the length of the branch into long chain or short chain branching

Long chain branching affects the size and density of polymer molecules and is easier to measure by GPC

Short chain branching is not in the remit of this presentation

The effect of branching is to reduce the size and increase the density of a polymer molecule at any given molecular weight in solution

If we can measure the density or size of a branched molecule and compare it to a linear molecule of similar chemistry, we might be able to get information on the nature of the branching

Effect of Branching on Molecular Properties

If we can measure the density or size of a branched molecule and compare it to a linear molecule of similar chemistry, we might be able to get information on the nature of the branching

Luckily, we have some methods that can be used to measure these properties

GPC/Viscometry allows us to measure the intrinsic viscosity of a polymer molecule, a property related to molecular density

GPC/light scattering allows us to measure the size of a polymer molecule

We can therefore use these technique to assess the level of branching on a polymer molecule

To do this we need to see how the intrinsic viscosity or molecular size varies with molecular weight

This is done with the Mark-Houwink and Conformation plots

Measuring Size and Density of Polymer Molecules

The Mark-Houwink Plot

The values of the Mark-Houwink parameters, a and K, depend on the particular polymer-solvent system

For solvents, a value of α = 0.5 is indicative of a theta solvent

A value of α = 0.8 is typical for good solvents

For most flexible polymers, 0.5 < α < 0.8

For semi-flexible polymers, 0.8 < α

For polymers with an absolute rigid rod, such as Tobacco mosaic virus, α = 2.0

The Conformation Plot

The values of the Conformation plot parameters, ν and K, depend on the particular polymer-solvent system

For solvents, a value of ν = 0.3 is indicative of a theta solvent

A value of ν = 0.5 is typical for good solvents

For most polymers, 0.5 < ν < 0.8

For polymers with an absolute rigid rod, such as Tobacco mosaic virus, ν = 1.0

If we consider a linear polymer versus branched polymer

Comparing the two on a conformation plot, the branched polymer will be smaller at any given molecular weight so Rg will be lower

Comparing the two on a Mark-Houwink plot, the branched polymer will be more dense at any given molecular weight so IV will be lower

This is illustrated in the following application

Branching Calculations by Multi Detector GPC

Hyperbranched Polyesters – Effect of Branching on IV

S. Kunamaneni, W. Feast, IRC in Polymer Science and Technology, Department of Chemistry, University of Durham, UK

Polyester AB/AB2 polymers produced by the condensation of A and B end groups

Branching introduced by the addition of AB2 monomers into the reaction

A Hyperbranched polymer structure is formed

Different chain length AB2 monomers can be used to vary the ‘compactness’ of the polymer molecule in solution

Eluent : THF (stabilised with 250 ppm BHT)

Columns : 2 x PLgel 5µm MIXED-B (300x7.5mm)

Flow rate : 1.0 ml/min

Injection volume : 100µl

Sample concentration : 1 mg/ml

Temperature : 40°C

Chromatographic system : PL-GPC 220

Detectors : DRI + PL-BV 400 viscometer

Data handling : Cirrus Multi Detector Software

Analysis of the Polyesters - Chromatography Conditions

Molecular Weight Distributions of Hyperbranched Polyesters

There is no trend in molecular weight distributions

Mark-Houwink Plots of Hyperbranched Polyesters

Clear trend in Mark-Houwink plots

Increased branching/decreased molecular size leads to a decrease in IV

Branching Calculations

For many polymers and applications this is as far and the branching analysis can be taken

This is especially true if the nature of the polymer is not known or if it is complex, or if the nature of the branches is not certain

At this point a qualitative indication of the level of branching is obtained

The analysis can only be advanced to give values if the exact repeat unit structure of the polymer is understood and the nature and rough distribution of the branched is known

Many of the methods that are used when measuring branching numbers only really apply to polyolefins

This is because polyolefins have a very simple structure and also because the presence of branching has proved of great commercial significance

Contraction Factors

The ratio of the intrinsic viscosity or radius of gyration of a branched polymer compared to a linear polymer of the same molecular weight is known as a contraction factor:

At any given molecular weight

The Rg contraction factor measures a contraction in size, the IV contraction factor measures an increase in molecular density and they are not equivalent

The value of g can be obtained from g’ using the following relationship where ε is the structure factor, a value between 0.5 and 1.5

Once the contraction factors are known, different statistical models are used to determine branching from g and g’, based on assumptions about the distribution of branches on the polymer backbone

Changing the branching model will result in radically differing results

Results given as the Branching number Bn

Bn = number of branches per 1000 carbons in the backbone

From Bn, the branching frequency lambda can be calculated

(m)= RBn / m

R is the molecular mass of the repeat unit and m the molecular weight

Calculating Branching Numbers

There are many different statistical models for polymer branching structures

Star branching models are designed for star polymers, either regular (all arms the same length) or random (all arms different lengths)

The random branched models are for branched chain molecules

Number average branching indicates the branching is on average equal across the molecular weight range, whereas weight average indicates there is more branching at high molecular weight

Ternary branching indicates a single branch point off the back bone, whereas quaternary indicates a two-way branch point

Ternary Quaternary

The values calculated are dependent on the model – different models give different values

Different Branching Models

Polyolefins are important high-tonnage engineering polymers

Crystalline materials, only soluble at >120°C

Polymers can contain branching structures depending on the method of synthesis

Long chain branching (over 6 carbons in length) can serious effect viscosity, density and processability

Multi detector GPC is an ideal means of probing the structure of polyolefins

Polyethylene – Calculating Branching Numbers

Eluent : TCB (stabilised with 250 ppm BHT)

Columns : 3 x PLgel 10µm MIXED-B (300x7.5mm)

Flow rate : 1.0 ml/min

Injection volume : 200µl

Sample concentration : Accurately at nominally 2 mg/ml

Temperature : 160°C

Chromatographic system : PL-GPC 220

Detectors : DRI + PL-BV 400 viscometer + Precision Detectors PD 2040 light scattering detector

Data handling : Cirrus Multi Detector Software

Analysis of Polyethylene - Chromatography Conditions

Polyethylene Triple Detection Data

Light scattering clearly shows this is a complex material

Key

Molecular Weight Distribution

The presence of branching can be seen in the MWD

Mark-Houwink Plot

Downward curvature of the plot at high molecular weight indicative of branching

Branching Number and g Plot

Branching number Bn and branching frequency calculated

Values are dependent on the choice of branching model

Star-branched PMMA – Investigative Structural Analysis

Series of polymethyl methacrylate (PMMA) star polymers were synthesised using Atom Transfer Radical Polymerisation (ATRP) techniques

The stars were assembled from a ‘core first’ approach in which a core molecule was modified to contain multiple initiation points and then polymer chains were grown from each point

The ATRP reaction produces polymer chains with narrow polydispersity

The stars were small in size and so light scattering was not employed

Eluent : THF (stabilised with 250 ppm BHT)

Columns : 2 x PLgel 5µm MIXED-D (300x7.5mm)

Flow rate : 1.0 ml/min

Injection volume : 100µl

Sample concentration : 1 mg/ml

Temperature : 40°C

Chromatographic system : PL-GPC 220

Detectors : DRI + PL-BV 400 viscometer

Data handling : Cirrus Multi Detector Software

Analysis of the Stars - Chromatography Conditions

Mark Houwink Plots for the Stars

g’ can be calculated by comparison of the Mark Houwink plots for the stars and a linear analogue (broad PMMA)

g can be calculated from g’ using a value of ε from the literature (0.83)

Two models can then be used to estimate the f, the number of arms:

Cirrus Multi Detector Software was used to calculate g’, g and f for the stars based on the GPC/Viscometry data

Estimating f, the Number of Arms

Comparison f Calculations for the Stars

With number of initiation points < 7, the stars can be fitted to the regular model

With number of initiation points of 14, the stars deviate from the regular model but the random model gives good agreement

With 21 initiation points, both the regular and random arm models deviate from the predicted values

Summary

The presence of a branched structure affects many of the physical properties of polymers

On the molecular scale, size and density are influenced by the presence of branches

GPC/Viscometry and GPC/Light scattering are tools that allow these properties to be measured, and are therefore suitable for the analysis of polymer branching

The methodology involves determining contraction factors for size and density properties in comparison to a linear analogue material, and modeling the results

The values obtained are only as good as the fit of the model to the sample, and in many cases it is not possible to produce anything more than qualitative results