Phenomenological Theory of Isotropic-Genesis Nematic Elastomers

We consider the impact of the elastomer network on the nematic structure and fluctuations in isotropic-genesis nematic elastomers, via a phenomenological model that underscores the role of network compliance. The model contains a network-mediated nonlocal interaction as well as a new kind of random field that reflects the memory of the nematic order present at network formation and also encodes local anisotropy due to localized nematogenic polymers. This model enables us to predict regimes of short-ranged oscillatory spatial correlations (thermal and glassy) in the nematic alignment.

Figure 1

(a) Glassy correlator (rescaled) ${\tilde{\mathcal{C}}}^G(r)\equiv (60{\pi }^2\mathcal{L}/T{\mu }_D){\mathcal{C}}^G(r)$, for $t_p\gg T{H}_{\mathbf{0}}/T_p{\mathcal{A}}^0$; $t=0.1\mathcal{L}/\mathcal{A}{\xi }_L^2$, at (i) $H_{\mathbf{0}}/H^{(c)}=0.5$ (weak disorder; dashed line) and (ii) $H_{\mathbf{0}}/H^{(c)}=40$ (strong disorder; solid line). (b) Thermal correlator (rescaled) ${\tilde{\mathcal{C}}}^T(r)\equiv (2{\pi }^2\mathcal{L}/T{\mu }_D){\mathcal{C}}^T(r)$, for the same parameters. On going from weak to strong disorder, both correlators cross over from simple exponential decay to oscillatory decay at wavelength of order ${\xi }_L$.