Statistical models of elasticity in main chain and smectic liquid crystal elastomers
James Michael Adams
Liquid crystal systems typically consist of rod like molecules that
spontaneously align along a chosen direction (the director) below a
certain temperature or above a certain concentration. When these
molecules are connected to polymers, the alignment of the molecules
can alter the conformation of the polymer backbone. This effect can be
seen on a macroscopic level by cross-linking the polymer chains
together to form a liquid crystal elastomer (LCE). In this thesis the
elastic properties of main chain and smectic liquid crystal elastomers
are modelled, and a mechanism of piezoelectricity in LCEs is explored.
These three projects are summarised below.
In the strongly nematic state main chain liquid crystalline polymers
have hairpin defects along their length. When these chains are
cross-linked together they show unusual soft elastic properties
experimentally. The elastic properties of a main chain elastomer are
modelled here by calculating the stiffness of chains with hairpin
defects and of those without. The dramatically different spring
constants motivate a non-affine model for deformation of the resulting
elastomer. The chains with hairpin defects are less stiff than those
without and so take up more of the macroscopic strain. As the
elastomer is stretched the macroscopic strain becomes more
concentrated in the elastically weaker hairpinned chains, and so the
rubber shows a plateau in its stress-strain curve.
A mechanism of developing a polarisation in chiral main chain LCE is
analysed. In this mechanism the dipoles of the chiral monomers can
be aligned by a shear deformation. It is shown that the polarisation
of a pure LCE is zero in equilibrium due to rotation of the director.
The response of the director must be altered in a specific way in
order to realise a non-zero result. Three methods of circumventing
this result are explored: oscillating shear, pinning the director with
smectic layers, and using a mixture of chiral and non-chiral chains.
Each of these methods is shown to produce a polarisation which is much
larger per unit stress than that of quartz crystal.
A fully non-linear model of elasticity in smectic A elastomers is
developed from a phantom network model. The rigid constraints required
by the layered smectic system are analysed from a geometric
perspective. The results of this model are then compared to a wide
range of experimental observations: extreme Poisson ratios, in-plane
modulus, modulus before and after threshold when the elastomer is
stretched along the layer normal. This model is then used to look for
soft modes in biaxial smectic A elastomers and smectic C elastomers. A
general procedure for the calculation of soft modes is developed and
specific examples of soft modes given.