Theoretical investigation on dynamics of photopolymerization-induced phase separation and morphology development in nematic liquid crystal/polymer mixtures

Abstract

A theoretical investigation of the dynamics of photopolymerization-induced phase separation (PIPS) and morphology development in a nematic liquid crystal (LC) polymer network mixture has been undertaken by incorporating photopolymerization kinetics into the coupled time-dependent Ginzburg-Landau (TDGL–Model C) equations. The simulation on the spatio-temporal evolution of the coupled LC concentration and orientation order parameters reveals that both morphological and scattering patterns for the orientation order parameter initially lag behind those of the concentration order parameter. However, the two fields evolve to the same spatial topologies with the progression of time. The PIPS dynamics is characterized only by the late stage of phase separation. We also observed a subtle change in the curvature of the growth curve associated with the onset of nematic ordering. The growth behavior and the simulated morphology consisting of LC droplets dispersed in a matrix of polymer appears the same for all compositions, except that the size gets somewhat larger with increasing LC concentration. Decreasing the rate of reaction increases the size of droplets due to the dominance of structural growth driven by thermal relaxation. Of particular interest is that our simulation captures the observed domain topologies.

Phase Properties of Interpenetrating Polymer Networks and Liquid Crystals

“…Variation of the Flory-Huggins interaction parameter with various quantities (such as the polymer concentration) has been a subject of a long debate in the literature arousing a particular interest for a long time [22][23][24]31,32] and still continues to be a question of controversial arguments. Koningsveld and co-workers [33,34] reported a systematic study of liquid-liquid-phase separation in multicomponent polymer systems and copolymers.…”

“…The thermodynamic phase behavior of blends of polymer networks and LCs is generally described by combining the different theoretical schemes developed separately for polymers and LC [7,[22][23][24]. In the case when the polymer is made of crosslinked chains, the Flory-Rehner theory [25][26][27] is used to express the rubberlike elasticity of the network and the effects of crosslinks in inhibiting polymer swelling.…”

Spatial Frequency Responses of Anisotropic Refractive Index Gratings Formed in Holographic Polymer Dispersed Liquid Crystals

“…It is generally given by [39,42]:$\begin{array}{cc}trueright\frac{\partial {\varphi }_L}{\partial t}& left=\nabla ·\left(\Lambda ,\nabla ,\left(\frac{\delta G}{\delta {\varphi }_L}\right)\right)+{\eta }_{{\varphi }_L}\end{array}$$\begin{array}{cc}trueright\frac{\partial {\varphi }_m}{\partial t}& left=\nabla ·\left(\Lambda ,\nabla ,\left(\frac{\delta G}{\delta {\varphi }_m}\right)\right)-u+{\eta }_{{\varphi }_m}\end{array}$$\begin{array}{cc}trueright\frac{\partial {\varphi }_p}{\partial t}& left=\nabla ·\left(\Lambda ,\nabla ,\left(\frac{\delta G}{\delta {\varphi }_p}\right)\right)+u+{\eta }_{{\varphi }_p}\end{array}$$\begin{array}{cc}trueright\frac{\partial s}{\partial t}& left=-R_s\left(\frac{\delta G}{\delta s}\right)+{\eta }_s\end{array}$ where Λ is the mutual diffusion coefficient; G is the total free energy of the system; u is the photopolymerization rate; and ${\eta }_i$ is the Langevin noise for the density and orientation fields ($i={\varphi }_L,{\varphi }_m,{\varphi }_p,s$) with the following constraint due to the fluctuation-dissipation theorem [56]:$\begin{array}{cc}trueright<{\eta }_{{\varphi }_i}(\mathit{r},t){\eta }_{{\varphi }_j}({\mathrm{bold-italicr}}^{\prime },t^{\prime })>& left=-2k_{B}T\Lambda {\nabla }^2\delta (\mathit{r}-{\mathrm{bold-italicr}}^{\prime })\delta (t-t^{\prime }){\delta }_{ij}\end{array}$$\begin{array}{c}trueright<{\eta }_s\end{array}$…”

“…Since the sizes of LC and monomer are more or less similar, it may be legitimate to set $r_L$ and $r_m$ to be unity for simplicity [39,40,41,43,56]. In addition, $r_p$ is given by [59]:$\begin{array}{c}trueright{r}_p=\frac{1}{1-f\alpha /2}\end{array}$ where $f(\ge 2)$ is the functionality of multifunctional monomer (necessary to induce the crosslinking network structure for the efficient mutual diffusion of LC and monomer molecules under holographic exposure) and α is the polymer conversion given by [59]:$\begin{array}{c}trueright\alpha =\frac{2(1-{\varphi }_m)}{f}\end{array}$…”

“…It should be noted that $r_p$ is usually taken very large ($r_p\to \infty$) so as to be $D_p=0$ and ${\Lambda }_p=0$ in the past works since the emerging polymer chains are fixed at the chemical junction due to the charactristic of the cross-linking reaction [39,40,41,42,43,56]. It means that the diffusion term of emerging polymers on the right-hand side of Equation (A1c) is neglected.…”