Partially phase-separated liquid-crystal/polymer dispersions display highly fibrillar domain morphologies that are dramatically different from the typical structures found in isotropic mixtures. To explain this, we numerically explore the coupling between phase ordering and phase separation kinetics in model two-dimensional fluid mixtures phase separating into a nematic phase, rich in liquid crystal, coexisting with an isotropic phase, rich in polymer. We find that phase ordering can lead to fibrillar networks of the minority polymer-rich phase.Mixtures of liquid crystals with a small amount of polymer (polymer-stabilized liquid crystals [1][2][3], or PSLC's) show promise for electro-optic devices such as light shutters and displays [4][5][6][7], because the polymer tends to form a network that aligns the liquid crystal [8]. Since polymers and liquid crystals tend to be immiscible, the dispersions are prepared by mixing a small amount of miscible monomer with the liquid crystal and photopolymerizing. As the polymers grow, the system phase separates into an ordered phase rich in liquid crystal and an isotropic phase rich in polymer. Long before the system reaches equilibrium, however, the polymerization "freezes" the mixture into a crosslinked network of polymer-rich domains. Thus, the fabrication of PSLC's involves interplay among three kinetic processes: polymerization, phase separation, and phase ordering. Depending on the time scales that control these processes, a rich variety of morphologies have been observed [9][10][11][12]. Because of the number of nonequilibrium processes involved, however, there is little theoretical understanding of the factors that control the domain morphology. In this Letter, we focus on the interplay between phase separation (PS) and phase ordering (PO) kinetics in mixtures of short, rigid polymers (rods) and long, flexible polymers (coils), as a first step towards rational design and control of the network morphology.It is well known that thermodynamic factors such as the anisotropy of the isotropic/nematic interfacial tension can influence domain morphology, leading to anisotropic domain shapes. However, there are also kinetic factors that control domain morphology, such as the anisotropic diffusion coefficient of a rod. To capture these thermodynamic and kinetic effects, we use a CahnHilliard framework that allows composition and orientational density to evolve in a coupled fashion as functions of position and time following a temperature quench [13]. In contrast to earlier studies that treat orientational density as a scalar order parameter [14,15], this framework includes the orientational density's second-order tensorial nature [16]. Although it is instructive to study the case of two coupled scalar order parameters (Model C [17]), a scalar cannot capture the direction of nematic order. Because a vector does not have head/tail symmetry, it is crucial to retain the tensor order parameter to obtain domain anisotropy [18].To assess the effects of phase ordering, we study two sy...

We examine the pressure and temperature dependences of a nanoscale structural rearrangement in periodic silica/surfactant composites with a goal of understanding how the silica framework modifies the molecular environment of the organic surfactant. Hydrothermal treatment is used to force surfactant-templated silica to undergo a phase transition from a hexagonal phase to a lamellar phase; the experiment is carried out both at 0.001 and at 1 GPa. The transition midpoint shifts to a higher temperature when the composite transforms under elevated pressure. Applying the concepts of surfactant packing and compressibility to this curvature-driven transition leads us to estimate the pressure felt by the composite's organic phase when the composite is subjected to an external pressure of 1 GPa. Our results indicate that this internal pressure is approximately 0.1 GPa, which is significantly smaller than the applied pressure of 1 GPa. The results confirm the idea that the high rigidity of the silica framework provides a protected molecular scale environment within the organic domains of the composite.

In this work, we examine the role of curvature and surfactant packing in controlling the structure of periodic silica/surfactant composites by driving such materials through a transformation from a hexagonal to a lamellar phase. We focus on how the interplay of desired packing and volume constraints dictates the resulting structures. In general, surfactants expand in a complex way upon heating, and this can cause a change in the optimal packing geometry. However, the presence of a rigid silica framework may prevent surfactants from reaching this preferred volume and/or curvature. Real-time in situ X-ray diffraction is used to monitor the structural evolution of these materials heated under hydrothermal treatments. Because the thermal-driven disorder of the surfactant tails drives the phase transition, we examine four types of composites with varying tail density. Ordinarily, composites consist of surfactants with one 20-carbon tail and one positively charged ammonium headgroup. Tail density is varied by replacing a small amount (0-16%) of these single-tail, single-head surfactants with single-tail, double-head 'gemini' surfactants. A greater head--tail ratio indeed produces different results, causing the phase transition to occur at higher temperatures. Using simple geometric models to gain better understanding of our experimental results, we find that, while both unfavorable curvature and limited volume may exist for the surfactants in these composites, the constrained curvature appears to be the dominant effect in driving structural rearrangement.