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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
Effect of Branching on Molecular Properties
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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
Measuring Size and Density
of Polymer Molecules
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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
The Mark-Houwink Plot
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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
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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
Branching Calculations
by Multi Detector GPC
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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 MarkHouwink 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
Hyperbranched Polyesters
– Effect of Branching on IV
 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
structure is formed
polymer
 Different
chain length AB2
monomers can be used to vary
the
‘compactness’
of
the
polymer molecule in solution
S. Kunamaneni, W. Feast, IRC in Polymer Science and
Technology, Department of Chemistry, University of Durham,
UK
Analysis of the Polyesters Chromatography Conditions
 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
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
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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
Calculating Branching Numbers
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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
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From Bn, the branching frequency lambda l can be calculated
l (m)= RBn / m
R is the molecular mass of the repeat unit and m the molecular weight
Different Branching Models
 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
 The
Quaternary
values calculated are dependent on the model – different models give
different values
Polyethylene – Calculating
Branching Numbers
 Polyolefins are important hightonnage engineering polymers
 Crystalline
materials,
soluble at >120°C
only
 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
Analysis of Polyethylene Chromatography Conditions
 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
Polyethylene Triple Detection Data
Key
 Light
scattering
clearly shows this is
a complex material
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
Analysis of the Stars Chromatography Conditions
 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
Mark Houwink Plots for the Stars
Estimating f, the Number of Arms
 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
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