When dealing with liquid crystalline polymers (see the CWRU primer) our primary goal is to establish the fundamental dynamic equations valid on macroscopic time and lengths scales. For side-chain systems the interplay between the viscoelasticity (the transient elasticity) of the backbone and the liquid crystalline degrees of freedom of the side chains is studied. The most interesting part of the dynamics is related to electro-optical and electro-elastic behaviour (including the response to external fields).
Liquid crystalline elastomers (LCEs) are a new class of materials obtained by crosslinking
liquid crystalline polymers. Originally only polydomain sidechain LCEs could be
synthesized, but meanwhile also mainchain and lyotropic systems are available. In addition,
it became possible to generate monodomains of a LCE, a liquid single crystal elastomer (LSCE) by using
two cross-linking steps, where the first one is used to generate a weakly cross-linked network,
which is then stretched to induce a monodomain, which is then fixed by the second cross-linking step.
Depending on whether the cross-linking is done in the isotropic or the nematic phase
a material with different properties results. When the cross-linking is done in the
nematic phase, the orientational information is fixed in the vicinity of the cross-linking points leading to an 'imprinted' order (also often called 'frozen-in' order).
One of the fundamentally interesting issues in the field of liquid crystalline elastomers
is the question of the physical consequences of the coupling between the two sub-systems,
namely the mesogenic parts and the network. For weakly cross-linked liquid crystalline
elastomers and gels, it turns out that relative rotations between the two subsystems play
a crucial role in the understanding of the reaction of liquid crystalline sidechain
elastomers to external electric, magnetic and mechanical fields.
A rather prominent feature of liquid crystalline elastomers is the observation of a plateau region
with small slopes for intermediate values of the strain in the static stress-strain curves for two situations:
i) for the polydomain - monodomain transition and ii) for the director reorientation in monodomains under the influence of an external mechanical force applied perpendicularly to the original director orientation
The latter phenomenon has been interpreted in the neo-classical Gaussian chain model to reflect the property of
'soft' or 'semi-soft' behavior. Here 'soft elasticity' means that one of the elastic shear moduli vanishes.
It is known for some time that such a situation occurs, if isotropic solids undergo a spontaneous change into
an anisotropic state. Then they must have a zero shear modulus due to the Nambu-Goldstone theorem. This symmetry argument, however, is not applicable for the LCE at hand, since at the isotropic to nematic
phase transition real side chain elastomers condense into a multi-domain structure without a shape change, if untreated. Only after stretching by an external force single domain elastomers are obtained. Then, of
course, the shape anisotropy is not spontaneous, in particular for systems that are cross-linked for a second time in the stretched state. Like in ordinary anisotropic solids, there is no symmetry reason for that shear elastic modulus to vanish. And indeed a finite modulus has been measured directly [A].
The notion of 'soft elasticity' has been changed into 'semi-soft elasticity' meaning that the relevant shear elastic modulus is zero only in ideal systems, while in real systems -- due to imperfections -- it is finite, but small. Such a description would be reasonable, if the 'ideal' case would describe the basic features and the 'imperfections' would add some corrections. However, the measurements in [A,B] clearly show that it is neither zero nor small, but of the order of the other elastic moduli, and therefore it is
not appropriate to use it as a small perturbation.
To describe the nonlinear elastic behavior of nematic LSCEs, in particular the plateau-like stress/strain behavior under perpendicular stretching, we employ standard nonlinear elasticity theory amended by nonlinear relative rotations between the network and the nematic director [C] (following the original idea of de Gennes). The occurrence of the plateau is accompanied by a complete reorientation of the director and by shear deformations and is in accordance with experiments [D]. The onset of the plateau at a given prestrain A_{1} is an instability of the forward bifurcation type resembling a second order phase transition. There are critical fluctuations at the transition (and the end of the plateau) due to the vanishing of the effective elastic coefficient as well as of the effective nematic director orientation susceptibility in an external electric field [E]. This soft mode behavior at the transition is not related to any proposed (almost) Nambu-Goldstone mode and can occur even at large values of A_{1} [E].
Theories based on the semi-soft elasticity picture also can describe the phenomenology of the nonlinear plateau, at least for small A_{1} (small semi-soft parameter).
A more detailed exposition of this topic is provided by recent talks Kent 2009 [1 MB pdf-file] and Lisbon 2011 [1.8 MB pdf-file].
Other research topics:
Instabilities in Complex Fluids, Active Soft Matter
Rheology of Complex Fluids
Banana and Dolphin Phases
Membranes, Films and Surface Waves
Banana and Tetrahedral Phases
Magnetic Fluids and Elastomers