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/AB 2 polymers produced by the condensation of A and B end groups  Branching introduced by the addition of AB 2 monomers into the reaction  A Hyperbranched polymer structure is formed  Different chain length AB 2 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