Destruction of bulk ordering by surface randomness

Disordered boundaries destroy bulk phase separation in scalar active matter

We show that disordered boundaries destroy bulk phase separation in scalar active systems in dimension d<d_{c}=3. This is in strong contrast with the equilibrium case where boundaries have no impact on the bulk of phase-separated systems. The underlying mechanism is revealed by considering a localized deformation of an otherwise flat wall, from which the case of a disordered boundary can be inferred. We find long-ranged correlations of the density field as well as a cascade of eddies which we show prevent bulk phase separation in low enough dimensions. The results are derived for dilute systems as well as in the presence of interactions, under the sole condition that the density field is the unique hydrodynamic mode. Our theoretical calculations are validated by numerical simulations of microscopic active systems.

Smectic order, pinning, and phase transition in a smectic-liquid-crystal cell with a random substrate

We study smectic-liquid-crystal order in a cell with a heterogeneous substrate imposing surface random positional and orientational pinnings. Proposing a minimal random elastic model, we demonstrate that, for a thick cell, the smectic state without a rubbed substrate is always unstable at long scales and, for weak random pinning, is replaced by a smectic glass state. We compute the statistics of the associated substrate-driven distortions and the characteristic smectic domain size on the heterogeneous substrate and in the bulk. We find that for weak disorder, the system exhibits a three-dimensional temperature-controlled phase transition between a weakly and strongly pinned smectic glass states akin to the Cardy-Ostlund phase transition. We explore experimental implications of the predicted phenomenology and suggest that it provides a plausible explanation for the experimental observations on polarized light microscopy and x-ray scattering.

Random-field and random-anisotropy O(N) spin systems with a free surface

We study the surface scaling behavior of a semi-infinite d-dimensional O(N) spin system in the presence of a quenched random field and random anisotropy disorders. It is known that above the lower critical dimension d(LC) = 4 the infinite models undergo a paramagnetic-ferromagnetic transition for N > N(c) (N(c) = 2.835 for the random field and N(c) =9.441 for random anisotropy). For N < N(c) and d < d(LC) there exists a quasi-long-range-order phase with a zero order parameter and a power-law decay of spin correlations. Using a functional renormalization group, we derive the surface scaling laws that describe the ordinary surface transition for d > d(LC) and the long-range behavior of spin correlations near the surface in the quasi-long-range-order phase for d < d(LC). The corresponding surface exponents are calculated to one-loop order. The obtained results can be applied to the surface scaling of periodic elastic systems in disordered media, amorphous magnets, and (3)He-A in aerogel.

Interface-induced anisotropy and the nematic glass/gel state in jammed aqueous Laponite suspensions

Aqueous suspensions of Laponite, a system composed of disklike nanoparticles, are found to develop optical birefringence over several days, well after the suspensions solidified because of jamming. The optical anisotropy is particularly enhanced near the air-Laponite suspension interface over length scales of several millimeters, which is beyond 5 orders of magnitude larger than the particle length scale, suggestive of large-scale ordering influenced by the interface. The orientational order increases with time and is always greater for higher concentration of salt, higher concentration of Laponite, and higher temperatures of the suspension. Although weakly birefringent, Laponite suspensions covered by paraffin oil do not show any enhancement in optical anisotropy near the interface compared to that in the bulk. We suggest that the expedited structure formation near the air interface propagating progressively inside the sample is responsible for the observed behavior. We discuss the observed nematic ordering in the context of glass-like and gel-like microstructure associated with aqueous Laponite suspensions.

Stability and distortions of liquid crystal order in a cell with a heterogeneous substrate

We study stability and distortions of liquid crystal nematic order in a cell with a random heterogeneous substrate. Modeling this system as a bulk xy model with quenched disorder confined to a surface, we find that nematic order is marginally unstable to such surface pinning. We compute the length scale beyond which nematic distortions become large and calculate orientational correlation functions using the functional renormalization-group and matching methods, finding universal logarithmic and double-logarithmic distortions in two and three dimensions, respectively. We extend these results to a finite-thickness liquid crystal cell with a second homogeneous substrate, detailing crossovers as a function of random pinning strength and cell thickness. We conclude with analysis of experimental signatures of these distortions in a conventional crossed-polarizer-analyzer light microscopy.

Liquid crystal cells with "dirty" substrates

We explore liquid crystal order in a cell with a "dirty" substrate imposing a random surface pinning. Modeling such systems by a random-field xy model with surface heterogeneity, we find that orientational order in the three-dimensional system is marginally unstable to such surface pinning. We compute the Larkin length scale, and the corresponding surface and bulk distortions. On longer scales we calculate correlation functions using the functional renormalization group and matching methods, finding a universal logarithmic and double-logarithmic roughness in two and three dimensions, respectively. For a finite thickness cell, we explore the interplay of homogeneous-heterogeneous substrate pair and detail crossovers as a function of disorder strength and cell thickness.

Quenched disorder in a liquid-crystal biosensor: Adsorbed nanoparticles at confining walls

We analyze the response of a nematic liquid-crystal film, confined between parallel walls, to the presence of nanoscopic particles adsorbed at the walls. This is done for a variety of patterns of adsorption (random and periodic) and operational conditions of the system that can be controlled in experimental liquid-crystal-based devices. We compute simulated optical textures and the total optical output of the sensor between crossed polars, as well as the correlation function for the liquid-crystal tensor order parameter; we use these observables to discuss the gradual destruction of the original uniform orientation. For large concentrations of particles adsorbed in random patterns, the liquid crystal at the center of the sensor adopts a multidomain state, characterized by a small correlation length of the tensor order parameter, and also by a loss of optical anisotropy under observation through crossed polars. In contrast, for particles adsorbed in periodic patterns, the nematic at the center of the cell can remain in a monodomain orientation state, provided the patterns in opposite walls are synchronized.

Liquid crystals in random porous media: disorder is stronger in low-density aerosils

The nature of glass phases of liquid crystals in random porous media depends on the effective disorder strength. We study how the disorder strength depends on the density of the porous media and demonstrate that it can increase as the density decreases. We also show that the interaction of the liquid crystal with random porous media can destroy long-range order inside the pores.

Dynamic melting of confined vortex matter

We study dynamic melting of confined vortex matter moving in disordered, mesoscopic channels by mode-locking experiments. The dynamic melting transition, characterized by a collapse of the mode-locking effect, strongly depends on the frequency, i.e., on the average velocity of the vortices. The associated dynamic ordering velocity diverges upon approaching the equilibrium melting line T(m,e)(B) as v(c) approximately (T(m,e)-T)(-1). The data provide the first direct evidence for velocity dependent melting and show that the phenomenon also takes place in a system under disordered confinement.