Dislocation dynamics in an anisotropic stripe pattern

Enhanced Lateral Ordering in Cylinder Forming PS-b-PMMA Block Copolymers Exploiting the Entrapped Solvent

The self-assembly of block copolymer (BCP) thin films produces dense and ordered nanostructures. Their exploitation as templates for nanolithography requires the capability to control the lateral order of the nanodomains. Among a multiplicity of polymers, the widely studied all-organic polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) BCP can easily form nanodomains perpendicularly oriented with respect to the substrate, since the weakly unbalanced surface interactions are effectively neutralized by grafting to the substrate an appropriate poly(styrene-random-methyl methacrylate) P(S-r-MMA) random copolymer (RCP). This benefit along with the selective etching of the PMMA component and the chemical similarity with the standard photoresist materials deserved for PS-b-PMMA the role of BCP of choice for the technological implementation in nanolithography. This work demonstrates that the synergic effect of thermal annealing with the initial solvent naturally trapped in the basic RCP + BCP system after the deposition process can be exploited to enhance the lateral order. The solvent content embedded in the total RCP + BCP system can be tuned by changing the molecular weight and thus the thickness of the grafted RCP brush layer, without introducing external reservoirs or dedicated setup and/or systems. The appropriate supply of solvent supports a grain coarsening kinetics following a power law with a 1/3 growth exponent for standing hexagonally ordered cylinders.

Dislocations and metastable chevrons in the electroconvective inplane normal roll state of a bent core nematic liquid crystal

We report experimental results on the formation, dynamics, and annihilation of edge dislocations of opposite topological charge in the electroconvective inplane vortex state of a bent core nematic liquid crystal. The approach of paired, oppositely charged defects toward each other is a two-step process. Near constant velocity at large separation and accelerated motion close to annihilation are found, as in the case of nematic rolls belonging to standard electroconvection. Periodic arrays of dislocations of alternating polarity form upon a sudden, strong elevation of the control parameter. Chevron structures that appear between undulatory defect chains are metastable, and their decay with time is accompanied by an exponential reduction in the dislocation density. The initial periodicity of defect chains also drops exponentially with increasing field.

Coarsening in potential and nonpotential models of oblique stripe patterns

We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic length scale growing in time as t1/2. Further from onset, the characteristic lengths along the preferred directions x and ŷ grow with different exponents, close to 1/3 and 1/2, respectively. In this regime, one-dimensional dynamical scaling relations hold. We draw an analogy between this problem and model A in a stationary, modulated external field. For deep quenches, nonpotential effects produce a complicated dislocation dynamics that can lead to either arrested or faster-than-power-law growth, depending on the model considered. In the arrested case, small isolated domains shrink down to a finite size and fail to disappear. A comparison with available experimental results for electroconvection in nematics is presented.

Grain boundary dynamics in stripe phases of nonpotential systems

We describe numerical solutions of two nonpotential models of pattern formation in nonequilibrium systems to address the motion and decay of grain boundaries separating domains of stripe configurations of different orientations. We first address wave-number selection because of the boundary, and possible decay modes when the periodicity of the stripe phases is different from the selected wave number for a stationary boundary. We discuss several decay modes including long wavelength undulations of the moving boundary, as well as the formation of localized defects and their subsequent motion. We find three different regimes as a function of the distance to the stripe phase threshold and initial wave number, and then correlate these findings with domain morphology during domain coarsening in a large aspect ratio configuration.

Impact of noise on domain growth in electroconvection

The growth and ordering of striped domains has recently received renewed attention due in part to experimental studies in diblock copolymers and electroconvection. One surprising result has been the relatively slow dynamics associated with the growth of striped domains. One potential source of the slow dynamics is the pinning of defects in the periodic potential of the stripes. Of interest is whether or not external noise will have a significant impact on the domain ordering, perhaps by reducing the pinning and increasing the rate of ordering. In contrast, we present experiments using electroconvection in which we show that a particular type of external noise decreases the rate of domain ordering.

Early time evolution of Freédericksz patterns generated from states of electroconvection

We report on the early time ordering in a nematic liquid crystal subjected to a sudden change in an external ac electric field. We compare time evolution for two different initial states of electroconvection. Electroconvection is a highly driven state of a nematic liquid crystal involving convective motion of the fluid and periodic variations of the molecular alignment. By suddenly changing either the voltage or the frequency of the applied ac field, the system is brought to the same thermodynamic conditions. The time ordering of the system is characterized by the evolution of features of the power spectrum, including the average wave number, total power, and shape of the power spectrum. We observe that ordering of the system occurs faster after a sudden change in frequency than it does after a sudden change in voltage.

Coarsening of topological defects in oscillating systems with quenched disorder

We use large scale simulations to study interacting particles in two dimensions in the presence of both an ac drive and quenched disorder. As a function of ac amplitude, there is a crossover from a low drive regime where the colloid positions are highly disordered to a higher ac drive regime where the system dynamically reorders. We examine the coarsening of topological defects formed when the system is quenched from a disordered low ac amplitude state to a high ac amplitude state. When the quench is performed close to the disorder-order crossover, the defect density decays with time as a power law with alpha = 1/4 to 1/3. For deep quenches, in which the ac drive is increased to high values such that the dynamical shaking temperature is strongly reduced, we observe a logarithmic decay of the defect density into a grain boundary dominated state. We find a similar logarithmic decay of defect density in systems containing no pinning. We specifically demonstrate these effects for vortices in thin film superconductors, and discuss implications for dynamical reordering transition studies in these systems.

Growth of order in an anisotropic Swift-Hohenberg model

We have studied the ordering kinetics of a two-dimensional anisotropic Swift-Hohenberg (SH) model numerically. The defect structure for this model is simpler than for the isotropic SH model. One finds only dislocations in the aligned ordering striped system. The motion of these point defects is strongly influenced by the anisotropic nature of the system. We developed accurate numerical methods for following the trajectories of dislocations. This allows us to carry out a detailed statistical analysis of the dynamics of the dislocations. The average speeds for the motion of the dislocations in the two orthogonal directions obey power laws in time with different amplitudes but the same exponents. The position and velocity distribution functions are only weakly anisotropic.

Amplitude modulation and relaxation-oscillation of counterpropagating rolls within a broken-symmetry laser-induced electroconvection strip

We report a liquid-crystal pattern-formation experiment in which we break the lateral (translational) symmetry of a nematic medium with a laser-induced thermal gradient. The work is motivated by an improved measurement (reported here) of the temperature dependence of the electroconvection threshold voltage in planar-nematic 4-methoxybenzylidene-4-butylaniline. In contrast with other broken-symmetry-pattern studies that report a uniform drift, we observe a strip of counterpropagating rolls that collide at a sink point, and a strong temporally periodic amplitude modulation within a width of 3-4 rolls about the sink point. The time dependence of the amplitude at a fixed position is periodic but displays a nonsinusoidal relaxation-oscillation profile. After reporting experimental results based on spacetime contours and wave number profiles, along with a measurement of the change in the drift frequency with applied voltage at a fixed control parameter, we propose some potential guidelines for a theoretical model based on saddle-point solutions for Eckhaus-unstable states and coupled complex Ginzburg-Landau equations.