Aging and crossovers in phase-separating fluid mixtures

Kinetics of phase separation and aging dynamics of segregating fluid mixtures in the presence of quenched disorder

Quenched or frozen-in structural disorder is ubiquitous in real experimental systems. Much of the progress is achieved in understanding the phase separation of such systems using the diffusion-driven coarsening in an Ising model with quenched disorder. But there is a paucity of research on the phase-separation kinetics in fluids with quenched disorder. In this paper, we present results from a detailed molecular dynamics simulation, showing the effects of randomly placed localized impurities on the phase separation kinetics of binary fluid mixtures. Two different models are offered for representing the impurities. We observe a dramatic slowing down in the pattern formation with increasing impurity concentration. This sluggish domain growth kinetics follows a power-law with a disorder-dependent exponent. The correlation function and structure factor show a non-Porod behavior, indicating the roughening of the domain interfaces. We have also studied the effect of quenched disorder on the aging dynamics by calculating the two-time order parameter auto correlation function and find that the Fisher and Huse scaling law holds good in the presence of quenched disorder.

Accelerated inertial regime in the spinodal decomposition of magnetic fluids

Furukawa predicted that at late times, the domain growth in binary fluids scales as (t) ∼ t^2/3, and the growth is driven by fluid inertia. The inertial growth regime has been highly elusive in molecular dynamics (MD) simulations. We perform coarsening studies of the (d = 3) Stockmayer (SM) model comprising of magnetic dipoles that interact via long-range dipolar interactions as well as the usual Lennard-Jones (LJ) potential. This fascinating polar fluid exhibits a gas-liquid phase coexistence, and magnetic order even in the absence of an external field. From comprehensive MD simulations, we observe the inertial scaling [(t) ∼ t^2/3] in the SM fluid for an extended time window. Intriguingly, the fluid inertia is overwhelming from the outset - our simulations do not show the early diffusive regime [(t) ∼ t^1/3] and the intermediate viscous regime [(t) ∼ t] prevalent in LJ fluids.

Effect of annealed disorder on phase separation kinetics and aging phenomena in fluid mixtures

We use state-of-the-art molecular dynamics simulations to study the effects of annealed disorder on the phase-separating kinetics and aging phenomena of a segregating binary fluid mixture. In the presence of disorder, we observe a dramatic slowing down in the phase separation dynamics. The domain growth follows the power law with a disorder-dependent exponent. Due to the energetically favorable positions, the domain boundary roughens, which modifies the correlation function and structure factor to a non-Porod behavior. The correlation function and structure factor provide clear evidence that superuniversality does not hold in our system. The role of annealed disorder on the nonequilibrium aging dynamics is studied qualitatively by computing the two-time order-parameter autocorrelation function. The decay of the correlation function slows down significantly with the disorder. This quantity exhibits scaling laws with respect to the ratio of the domain length at the observation time and the age of the system. We find the scaling laws hold good for the disordered system and are therefore robust and generic to such segregating fluid mixtures.

The Interplay between Phase Separation and Gene-Enhancer Communication: A Theoretical Study

The phase separation occurring in a system of mutually interacting proteins that can bind on specific sites of a chromatin fiber is investigated here. This is achieved by means of extensive molecular dynamics simulations of a simple polymer model that includes regulatory proteins as interacting spherical particles. Our interest is particularly focused on the role played by phase separation in the formation of molecule aggregates that can join distant regulatory elements, such as gene promoters and enhancers, along the DNA. We find that the overall equilibrium state of the system resulting from the mutual interplay between binding molecules and chromatin can lead, under suitable conditions that depend on molecules concentration, molecule-molecule, and molecule-DNA interactions, to the formation of phase-separated molecular clusters, allowing robust contacts between regulatory sites. Vice versa, the presence of regulatory sites can promote the phase-separation process. Different dynamical regimes can generate the enhancer-promoter contact, either by cluster nucleation at binding sites or by bulk spontaneous formation of the mediating cluster to which binding sites are successively attracted. The possibility that such processes can explain experimental live-cell imaging data measuring distances between regulatory sites during time is also discussed.

Initial correlation dependence of aging in phase separating solid binary mixtures and ordering ferromagnets

Following quenches of initial configurations having long range spatial correlations, prepared at the demixing critical point, to points inside the miscibility gap, we study aging phenomena in solid binary mixtures. Results on the decay of the two-time order-parameter autocorrelation functions, obtained from Monte Carlo simulations of the two-dimensional Ising model, with Kawasaki exchange kinetics, are analyzed via state-of-the art methods. The outcome is compared with that obtained for the ordering in uniaxial ferromagnets. For the latter, we have performed Monte Carlo simulations of the same model using the Glauber mechanism. For both types of systems we provide comparative discussion of our results with reference to those concerning quenches with configurations having no spatial correlation. We also discuss the role of structure on the decay of these correlations.

Aging phenomena during phase separation in fluids: decay of autocorrelation for vapor-liquid transitions

We performed molecular dynamics simulations to study relaxation phenomena during vapor-liquid transitions in a single component Lennard-Jones system. Results from two different overall densities are presented: one in the neighborhood of the vapor branch of the coexistence curve and the other being close to the critical density. The nonequilibrium morphologies, growth mechanisms and growth laws in the two cases are vastly different. In the low density case growth occurs via diffusive coalescence of droplets in a disconnected morphology. On the other hand, the elongated structure in the higher density case grows via advective transport of particles inside the tube-like liquid domains. The objective in this work has been to identify how the decay of the order-parameter autocorrelation, an important quantity to understand aging dynamics, differs in the two cases. In the case of the disconnected morphology, we observe a very robust power-law decay, as a function of the ratio of the characteristic lengths at the observation time and at the age of the system, whereas the results for the percolating structure appear rather complex. To quantify the decay in the latter case, unlike the standard method followed in a previous study, here we have performed a finite-size scaling analysis. The outcome of this analysis shows the presence of a strong preasymptotic correction, while revealing that in this case also, albeit in the asymptotic limit, the decay follows a power-law. Even though the corresponding exponents in the two cases differ drastically, this study, combined with a few recent ones, suggests that power-law behavior of this correlation function is rather universal in coarsening dynamics.

Pattern, growth, and aging in aggregation kinetics of a Vicsek-like active matter model

Via molecular dynamics simulations, we study kinetics in a Vicsek-like phase-separating active matter model. Quantitative results, for isotropic bicontinuous pattern, are presented on the structure, growth, and aging. These are obtained via the two-point equal-time density-density correlation function, the average domain length, and the two-time density autocorrelation function. Both the correlation functions exhibit basic scaling properties, implying self-similarity in the pattern dynamics, for which the average domain size exhibits a power-law growth in time. The equal-time correlation has a short distance behavior that provides reasonable agreement between the corresponding structure factor tail and the Porod law. The autocorrelation decay is a power-law in the average domain size. Apart from these basic similarities, the overall quantitative behavior of the above-mentioned observables is found to be vastly different from those of the corresponding passive limit of the model which also undergoes phase separation. The functional forms of these have been quantified. An exceptionally rapid growth in the active system occurs due to fast coherent motion of the particles, mean-squared-displacements of which exhibit multiple scaling regimes, including a long time ballistic one.

Ballistic aggregation in systems of inelastic particles: Cluster growth, structure, and aging

We study far-from-equilibrium dynamics in models of freely cooling granular gas and ballistically aggregating compact clusters. For both the cases, from event-driven molecular dynamics simulations, we have presented detailed results on structure and dynamics in space dimensions d=1 and 2. Via appropriate analyses it has been confirmed that the ballistic aggregation mechanism applies in d=1 granular gases as well. Aging phenomena for this mechanism, in both the dimensions, have been studied via the two-time density autocorrelation function. This quantity is demonstrated to exhibit scaling property similar to that in the standard phase transition kinetics. The corresponding functional forms have been quantified and the outcomes have been discussed in connection with the structural properties. Our results on aging establish a more complete equivalence between the granular gas and the ballistic aggregation models in d=1.

Dimensionality dependence of aging in kinetics of diffusive phase separation: Behavior of order-parameter autocorrelation

Behavior of two-time autocorrelation during the phase separation in solid binary mixtures is studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via state-of-the-art methods, including the finite-size scaling technique. Full forms of the autocorrelation in space dimensions 2 and 3 are obtained empirically. The long-time behavior is found to be power law, with exponents unexpectedly higher than the ones for the ferromagnetic ordering. Both Cahn-Hilliard and Ising models provide consistent results.

Aging in ferromagnetic ordering: full decay and finite-size scaling of autocorrelation

Nonequilibrium dynamics in Ising and Ginzburg-Landau models were studied for a nonconserved order parameter that mimics ordering in ferromagnets. The focus was on the understanding of the decay of the two time (t, t(w); t > tw) order-parameter correlation function. For this quantity, a full form has been obtained empirically which, for t ≫ t(w), provides a power-law ∼ (ℓ/ℓ(w))(-λ), ℓ and ℓ(w) being the characteristic lengths at t and tw, respectively. This empirical form was used for a finite-size scaling analysis to obtain the exponent λ in space dimensions d = 2 and 3. Our estimates of λ and understanding of the finite-size effects, for the models considered, provide useful information on the relevance of thermal noise. The values of λ obtained are in good agreement with the predictions of a theory based on Gaussian auxiliary field ansatz.

Fragmentation and limits to dynamical scaling in viscous coarsening: an interrupted in situ x-ray tomographic study

X-ray microtomography was used to follow the coarsening of the structure of a ternary silicate glass experiencing phase separation in the liquid state. The volumes, surfaces, mean, and Gaussian curvatures of the domains of minority phase were measured after reconstruction of the 3D images and segmentation. A linear growth law of the characteristic length scale ℓ∼t was observed. A detailed morphological study was performed. While dynamical scaling holds for most of the geometrical observables under study, a progressive departure from scaling invariance of the distributions of local curvatures was evidenced. The latter results from a gradual fragmentation of the structure in the less viscous phase that also leads to a power-law size distribution of isolated domains.

Effects of density conservation and hydrodynamics on aging in nonequilibrium processes

Aging in kinetics of three different phase transitions, viz., magnetic, a binary solid, and a single component fluid, are studied via Monte Carlo and molecular dynamics simulations in three space dimensions with the objective of identifying the effects of order-parameter conservation and hydrodynamics. We observe that the relevant autocorrelations exhibit power-law decay in a ferromagnet and binary solid but with different exponents. At early time the fluid autocorrelation function nicely follows that of the binary solid, the order parameter being conserved for both of them, as opposed to a ferromagnet. At a late time the fluid data crosses over to an exponential decay which we identify as a hydrodynamic effect and we provide analytical justification for this behavior.