P Lovell and RAYoung - Introduction to Polymers, Chapman and Hall
LH Sperling - Physical Polymer Science Wiley
G Strobl - Polymer Physics Springer (2nd ed)
Man-made polymers frequently contain both crystalline and amorphous regions, although some are completely amorphous.
A good example is polyethylene ('polythene'), which is rarely more than about 75% crystalline – and that value is high for a polymer.
Essentially no polymers are 100% crystalline (with the exception of those produced by epitaxial means).
Polymers are long chain molecules, usually with a carbon backbone (although some are based on silicon in the backbone).
They consist of a string of repeating units called monomers, joined together.
Simplest is polyethylene (polythene)
or (CH2)N
N is known as the degree of polymerisation and may run to thousands.
Other common polymers include perspex and nylon.
Perspex is the (British)
trade mark for poly (methyl
Nylon (so-called because of developments made collaboratively in New York and London), has various forms depending on the number of carbons
E e.g nylon 6-10
➖
Poly dimethyl siloxane (the basis of silicone rubber):
Tacticity and Stereochemistry
In practice the molecule is a 3-dimensional entity, and where the groups attached to each carbon atom are non-identical one can identify 3 ways in which the attachment can occur:
Isotactic
Syndiotactic
Atactic
Atactic polymers are generally easy to synthesise, but these polymers cannot crystallise due to their irregularity.
With suitable polymerisation routes, it is possible to prepare isotactic and syndiotactic polymers (at least in some cases), and these can crystallise.
Building up models of long chain molecules we can begin to see that there are many possible conformations they can adopt.
How can we characterise them?
You might think because polymers are long, complicated objects, they might be equally complicated to deal with.
For many properties this is not true.
Many of their properties depend much more strongly on their length (or equivalently degree of polymerisation N), than on specific chemistry.
Also a single chain tends to interact with many other chains.
This means we can average out the interactions of surrounding chains and use so-called mean field theory and statistical mechanics to understand their behaviour.
This leads to so-called scaling
laws.
It turns out mean field theories are better obeyed by polymers than for many simpler, atomic species.
For
more information see
P-G de Gennes - Scaling Laws in Polymer Physics, Cornell UP.
Random walks will be familiar to you from statistical mechanics in general.
We can use this approach to derive a scaling law for the mean end-to-end distance of a polymer chain.
Simple model – freely jointed chain i.e. each of N segments of length a is independent.
End-to-end distance
r = a1 + a2
+ a3 + a4+….. aN =
Mean ½r½2 is
Since there are no correlations between segments
<r2>
= Na2 scaling law for random walk
In practice this is a very
unphysical model for a chain.
The chemistry of the chain
means that there are fixed angles between segments.
For segments m apart
<ri.ri-m> = a2cosmq
Correlations therefore die
away along the chain.
There will be subunits
(multiple segments) which are uncorrelated, and these can then be used as the
basic building blocks.
g links/subunit, each
described by vector cI;
N/g subunits per chain.
b is known as the statistical step
length
b>a clearly.
How much greater is a measure of how strong the correlations are along the
chain.
This can be described by the characteristic ratio C∞.
Tells you about how
stiff/straight the chain is.
C∞ can be
worked out from the chemical details of the chain (bond angles etc).
This is an example of how we
can find universal behaviour for polymers, even though the chemical specificity
clearly matters too. We can find scaling
laws in terms of the general quantities
e.g.
but what b is depends on the
specific polymer.
Our model is still too simple.
Correlations along a chain may
die out quite fast, but a chain may still loop back on itself.
Two remote segments can interact with one
another.
This interaction may be
energetically favourable or unfavourable, and depending on this the chain
statistics are correspondingly affected.
·
The interaction is unfavourable. Then the segments will tend to keep away
from each other and the chain will swell: a "self-avoiding
walk".
Mean
field theory (due to Flory) says in this case
<r2>1/2 = N na
where
n= 3/5 (ie greater
than 0.5).
Modern
renormalisation group methods give n=0.588. Experimentally
very difficult to distinguish between these two values of n.
These
statistics apply in a so-called 'good solvent'.