Title:

The modelling of network polymers

This thesis considers the modelling of two and three dimensional molecular networks
with a view to being able to predict how the geometry of a network will affect the
elastic constants and specifically the Poisson's ratios of the network. Materials with
negative Poisson's ratios have much better engineering properties then those with
positive Poisson's ratios. Theory states that a network polymer, with negative
Poisson's ratios at a molecular level, would have much better properties than most
materials with negative Poisson's ratios made to date.
Molecular modelling has been used to examine the elastic constants of those two and
three dimensional network polymers which are most likely to be synthesised in the
near future. Such networks have been predicted to have either large positive or large
negative Poisson's ratios depending on the molecular arrangement of the network.
Poisson's ratios varying between 0.96 and 0.86 for the three dimensional cases and
between 0.9 and 1.26 for the two dimensional cases have been calculated. Young's
moduli in the order of 1 GPa have been observed for the three dimensional networks
as compared to Young's moduli in the order of 20  400 kPa which have been
experimentally measured for foam materials. Comparison with local density
functional calculations for two 2D networks with the molecular modelling have
confirmed the negative Poisson's ratio in these networks and shown that it is not a
function of the molecular modelling packages or force field used. The offaxis
properties for both the two and three dimensional networks have been calculated.
These show that whilst the networks with a positive Poisson's ratio in the principal
axis directions always have a positive Poisson's ratio, those networks with a negative
Poisson's ratio in the principal axis directions have offaxis Poisson's ratios that vary
between large and positive and large and negative. In general the networks with
positive Poisson's ratios are much more isotropic than those with negative Poisson's
ratios.
Analytical models which model the networks using simple beam theory have been
produced for various two and three dimensional networks. These models can be used
to predict the elastic constants of a network without the need to do time consumingmolecular modelling calculations to a first approximation. Comparison of the
molecular models and analytical models has led to the development a library of force
constants for two dimensional networks which can be used to more accurately predict
the elastic constants of a network based on a knowledge of the geometry of the
network and the constituent `subunits' from which it is made
