Universal features in growth kinetics: Some experimental tests

Phase-ordering kinetics in the Allen-Cahn (Model A) class: Universal aspects elucidated by electrically induced transition in liquid crystals

The two-dimensional (2D) Ising model is the statistical physics textbook example for phase transitions and their kinetics. Quenched through the Curie point with Glauber rates, the late-time description of the ferromagnetic domain coarsening finds its place at the scalar sector of the Allen-Cahn (or Model A) class, which encompasses phase-ordering kinetics endowed with a nonconserved order parameter. Resisting exact results sought for theoreticians since Lifshitz's first account in 1962, the central quantities of 2D Model A-most scaling exponents and correlation functions-remain known up to approximate theories whose disparate outcomes urge experimental assessment. Here we perform such assessment based on a comprehensive study of the coarsening of 2D twisted nematic liquid crystals whose kinetics is induced by a superfast electrical switching from a spatiotemporally chaotic (disordered) state to a two-phase concurrent, equilibrium one. Tracking the dynamics via optical microscopy, we first show the sharp evidence of well-established Model A aspects, such as the dynamic exponent z=2 and the dynamic scaling hypothesis, to then move forward. We confirm the Bray-Humayun theory for Porod's regime describing intradomain length scales of the two-point spatial correlators and show that their nontrivial decay beyond the Porod's scale can be captured in a free-from-parameter fashion by Gaussian theories, namely the Ohta-Jasnow-Kawasaki (OJK) and Mazenko theories. Regarding time-related statistics, we corroborate the aging hypothesis in Model A systems, which includes the collapse of two-time correlators into a master curve whose format is, actually, best accounted for by a solution of the local scaling invariance theory: the same solution that fits the 2D nonconserved Ising model correlator along with the Fisher-Huse conjecture. We also suggest the true value for the local persistence exponent in Model A class, in disfavor of the exact outcome for the diffusion and OJK equations. Finally, we observe a fractal morphology for persistence clusters and extract their universal dimension. Given its accuracy and possibilities, this experimental setup may work as a prototype to address further universality issues in the realm of nonequilibrium systems.

Self-propelled particle model for cell-sorting phenomena

A self-propelled particle model is introduced to study cell sorting occurring in some living organisms. This allows us to evaluate the influence of intrinsic cell motility separately from differential adhesion with fluctuations, a mechanism previously shown to be sufficient to explain a variety of cell rearrangement processes. We find that the tendency of cells to actively follow their neighbors greatly reduces segregation time scales. A finite-size analysis of the sorting process reveals clear algebraic growth laws as in physical phase-ordering processes, albeit with unusual scaling exponents.

Effect of hydrodynamic interactions on the evolution of chemically reactive ternary mixtures

We investigate the structural evolution of an A/B/C ternary mixture in which the A and B components can undergo a reversible chemical reaction to form C. We developed a lattice Boltzmann model for this ternary mixture that allows us to capture both the reaction kinetics and the hydrodynamic interactions within the system. We use this model to study a specific reactive mixture in which C acts as a surfactant, i.e., the formation of C at the A/B interface decreases the interfacial tension between the A and B domains. We found that the dynamics of the system is different for fluids in the diffusive and viscous regimes. In the diffusive regime, the formation of a layer of C at the interface leads to a freezing of the structural evolution in the fluid; the values of the reaction rate constants determine the characteristic domain size in the system. In the viscous regime, where hydrodynamic interactions are important, interfacial reactions cause a slowing down of the domain growth, but do not arrest the evolution of the mixture. The results provide guidelines for controlling the morphology of this complex ternary fluid.

Mechanism and kinetics of phase separation in a gelatin/maltodextrin mixture studied by small-angle light scattering

Phase separation mechanisms and kinetics were studied using small-angle light scattering in a gelatin/maltodextrin system where phase separation could be studied in both liquid and gelled states. Nucleation and growth or spinodal decomposition occurred, depending on the quench depth. The transition between the two mechanisms occurred relatively sharply. The different mechanisms were distinguishable by the different behavior of the scattering function even though a peak was observed in both cases. Particular differences were the different evolution of the peak intensity and position, the absence of dynamic scaling of the nucleation and growth scattering function, and the final coarsening exponent of 1/3 that was measured when spinodal decomposition occurred but not for nucleation and growth. Gelation severely reduced the coarsening rate and initially placed the phase compositions far from their equilibrium values. Despite the loss of molecular mobility caused by gelation, the gelled systems did continue to evolve, albeit much more slowly than in the liquid case. Multiple coarsening rates were observed for some of the gelled samples, which were ascribed to the gradual movement of these systems toward the equilibrium compositions.

Phase separation in gelatin/maltodextrin and gelatin/maltodextrin/gum arabic mixtures studied using small-angle light scattering, turbidity, and microscopy

The kinetics of phase separation were observed in the gelatin/maltodextrin and gelatin/maltodextrin/gum arabic systems, where gum arabic was added as a minority component, using small-angle light scattering, turbidity measurement, and confocal scanning laser microscopy. Phase separation occurred by spinodal decomposition for quenches both above and below the temperature at which gelatin gelled. Coarsening of the phase-separated microstructure was hindered by gelation, and a hydrodynamic mechanism, observed when the gelatin remained in the liquid state, was suppressed. Gum arabic, containing both polysaccharide and polypeptide components, was hypothesized to be potentially interfacially active in the gelatin/maltodextrin system, in analogy with synthetic block copolymer compatibilizers in demixed synthetic polymer systems. The hypothesis was experimentally refuted under the chosen experimental conditions, as no evidence was found to suggest that it altered the phase separation behavior.