Physica Scripta. Vol. T35, 11-16, 1991.
Cavendish Laboratory, Cambridge CB3 OHE, U.K.
Received April 9, 1990: accepted January
Simple models of the behaviour of polymers in networks are shown to be
translatable into equations of motion and hence to equations of viscoelasticity.
These simplest models have notable success, but there are disturbing features
in scattering experiments and in ‘second order’ theoretical analysis which are
discussed but not resolved.
Polymeric networks are a major subdivision of condensed
matter and offer a challenge to physicists of a different nature
to other branches of condensed matter physics in that the
problems are primarily topological i.e., concern the ways
molecules are configured relative to one another. This paper
is mainly concerned with melts i.e., pure polymer above the
glass temperature, so that our material is in high thermal
agitation and therefore can flow as a viscoelastic liquid, or, if
permanently cross linked, is a rubbery material, but occasion-
ally reference will be made to concentrated solutions i.e.,
melts with a swelling solvent added.
A central fact is that it is possible to normalize the behav-
iour of most polymer melts so that transport properties all lie
31. (In a solution the arc
concentration is clearly related to the mass concentration but
even in a melt, different polymers have quite different
bulky polymer like polystyrene having a
much smaller than
our picture is now of a quickly changing local pattern
in Fig. 1 leading to a slowly changing pattern of Fig. 2.
Indeed Fig. 2 can only change by the polymer diffusing to
form a new tube by reptation in a melt and not at all n a cross
linked system. However, a deformation of the bulk material
will deform the primitive path, in the simplest model affinely,
so one can work out what happens again by simple pictures
which are given below in Section
The picture offered above has
but if one uses liquid
crystal polymers hinged together as is now possible, one can
have a situation where
and materials can be thus made
whose viscosity is infinite but which have no cross linkage at
all. There is no time in this paper to consider these further,
but there is no doubt of their future importance.
on master curves. Similarly most rubbers show the same
stress strain behaviour. It appears that the chemical nature of
2. Statistical mechanics of networks
the polymer gives rise to an effective friction in the motion
of the polymer relative to its surroundings and to a Kuhn
length which relates the size of the polymer to its molecular
weight and another Kuhn like length which characterizes the
topological specification of the polymer in the melt; but that
is all [l]. This means that one should be able to explain all
the properties of melts and networks by simple diagrams in