Dynamic Theory of Polydomain Liquid Crystal Elastomers

Abstract

When liquid-crystal elastomers are prepared without any alignment, disordered polydomain structures emerge as the materials are cooled into the nematic phase. These polydomain structures have been attributed to quenched disorder in the cross-linked polymer network. As an alternative explanation, we develop a theory for the dynamics of the isotropic-nematic transition in liquid-crystal elastomers, and show that the dynamics can induce a polydomain structure with a characteristic length scale, through a mechanism analogous to the Cahn-Hilliard equation for phase separation.Liquid-crystal elastomers are remarkable materials that combine the elastic properties of cross-linked polymer networks with the anisotropy of liquid crystals [1]. Any distortion of the polymer network affects the orientational order of the liquid crystal, and any change in the magnitude or direction of liquid-crystal order influences the shape of the polymer network. Hence, these elastomers are useful for applications as actuators or shapechanging materials.For many applications, it is necessary to prepare monodomain liquid-crystal elastomers. In practice, this can be done by applying a mechanical load or other aligning field while crosslinking [2]. Surprisingly, elastomers prepared without an aligning field do not form monodomains. Rather, they form polydomain structures with nematic order in local regions, which are macroscopically disordered. These polydomain structures have been seen in many experiments, using a wide range of techniques [3][4][5][6][7]. Indeed, a recent polarized light scattering study shows that liquid-crystal elastomers evolve toward a state of increasing disorder as the isotropicnematic transition proceeds, unless the disorder is suppressed by a gradually increasing load [8].One important issue in the theory of liquid-crystal elastomers is how to understand the polydomain state. Several theoretical studies have attributed this state to quenched disorder in the polymer network, which can be understood by analogy with spin glass theory [9][10][11][12][13][14][15][16][17]. Effects of quenched disorder have further been modeled and visualized through numerical simulations [18][19][20][21]. More macroscopic theories have shown that the resulting polydomain structure has profound consequences for the material's effective elasticity [22,23].The purpose of this paper is to suggest a different mechanism for the origin of the polydomain state, not related to quenched disorder. We develop a theory for the dynamics of the isotropic-nematic transition in liquidcrystal elastomers, in which growing nematic order is coupled to elastic strain. We explore this theory in two dimensions (2D), using two models for dynamic evolution of nematic order and strain. The theory shows that dynamics can itself select a characteristic length scale for a disordered polydomain structure, through a mechanism similar to the Cahn-Hilliard equation for phase separation. In particular, the theory predicts formation of structures with the form shown in Fig. 1...

Microscopy of Diffuse Nematic–Isotropic Transition in Main-Chain Nematic Liquid-Crystal Elastomers

“…Thus, ξ D would be uniquely identified by an inherent heterogeneity imprinted upon polymerization. This is different from the idea suggested by Duzgun et al, in which ξ D is kinetically determined.…”

“…Uchida had first theoretically predicted that a similar pattern with a ±45° director correlation appears as a consequence of the elastic interaction between the neighboring domains, coupled to their nematic order. This is simply because additional strain due to spontaneous elongations upon emergence of the nematic order in domains is locally accommodated in adjacent domains without macroscopic deformation.…”

“…So far, in the pure polydomain LCE material, the experimental method to evaluate the local order parameter Q , which is different from the macroscopic alignment measurement characterized by X-ray or birefringence, has been limited to NMR, where deuterium substitution on the polymer network is usually needed. ,,, Thus, more convenient methods to evaluate Q at least at the length scale of the single nematic domain, ∼1 μm, would help studying the N–I transition in various LCEs recently synthesized. ,− Here, we introduce two alternative techniques leveraging the conventional polarized optical microscopy (POM) and the polarized fluorescence microscopy (PFOM). − The former and latter give local material birefringence and the local dichroism of fluorescent probes, respectively, both of which are closely related to the value of Q averaged in polydomain LCEs. Moreover, since PFOM also provides real-space information on the local nematic director orientation, it is possible to monitor the T -dependent domain properties, e.g., the characteristic polydomain textures ,− and the correlation length, changing upon N–I transition. Although the inherent quenched random disorder, disturbing the long-range nematic order, is assumed to be the origin of the correlation length (equilibrium domain size), the related experiment has been limited, e.g., to that in the reciprocal space by the depolarized light scattering (DPLS). , In the recently developed main-chain LCE based on the thiol-ene reaction, ,− no polydomain texture has been studied yet.…”

Collision-enhanced friction of a bouncing ball on a rough vibrating surface

“…Density enhancements near walls have been studied for a variety of active matter systems. Non-interacting Active Brownian Particles were shown to give rise to an exponential density enhancement at the wall 16 . Similar effects have also been observed for motile bacteria 17 , though in this latter case the enhancements are a collective phenomenon.…”

“…Grains vibrated on a roughened surface have some features in common with molecular fluids 8 while also exhibiting non-equilibrium effects, including anomalous velocity statistics [9][10][11] and long-range spatial correlations [12][13][14] . Vibrated grains, under certain conditions, also show features in common with some active matter systems, such as an increasing probability density as one approaches boundaries [15][16][17] .…”