Droplet formation and growth inside a polymer network: A molecular dynamics simulation study

Kinetics of domain growth and aging in a two-dimensional off-lattice system

We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single-component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we have analyzed simulation data on structure, growth, and aging for nonequilibrium evolutions in the model. These data were obtained following quenches of well-equilibrated homogeneous configurations, with density close to the critical value, to various temperatures inside the miscibility gap, having vapor-"liquid" as well as vapor-"solid" coexistence. For the vapor-liquid phase separation we observe that ℓ, the average domain length, grows with time (t) as t^{1/2}, a behavior that has connection with hydrodynamics. At low-enough temperature, a sharp crossover of this time dependence to a much slower, temperature-dependent, growth is identified within the timescale of our simulations, implying "solid"-like final state of the high-density phase. This crossover is, interestingly, accompanied by strong differences in domain morphology and other structural aspects between the two situations. For aging, we have presented results for the order-parameter autocorrelation function. This quantity exhibits data collapse with respect to ℓ/ℓ_{w}, ℓ, and ℓ_{w} being the average domain lengths at times t and t_{w} (≤t), respectively, the latter being the age of a system. Corresponding scaling function follows a power-law decay: ∼(ℓ/ℓ_{w})^{-λ} for t≫t_{w}. The decay exponent λ, for the vapor-liquid case, is accurately estimated via the application of an advanced finite-size scaling method. The obtained value is observed to satisfy a bound.

Tracer Diffusion in Tightly-Meshed Homogeneous Polymer Networks: A Brownian Dynamics Simulation Study

We report Brownian dynamics simulations of tracer diffusion in regularly crosslinked polymer networks in order to elucidate the transport of a tracer particle in polymer networks. The average mesh size of homogeneous polymer networks is varied by assuming different degrees of crosslinking or swelling, and the size of a tracer particle is comparable to the average mesh size. Simulation results show subdiffusion of a tracer particle at intermediate time scales and normal diffusion at long times. In particular, the duration of subdiffusion is significantly prolonged as the average mesh size decreases with increasing degree of crosslinking, for which long-time diffusion occurs via the hopping processes of a tracer particle after undergoing rattling motions within a cage of the network mesh for an extended period of time. On the other hand, the cage dynamics and hopping process are less pronounced as the mesh size decreases with increasing polymer volume fractions. The interpretation is provided in terms of fluctuations in network mesh size: at higher polymer volume fractions, the network fluctuations are large enough to allow for collective, structural changes of network meshes, so that a tracer particle can escape from the cage, whereas, at lower volume fractions, the fluctuations are so small that a tracer particle remains trapped within the cage for a significant period of time before making infrequent jumps out of the cage. This work suggests that fluctuation in mesh size, as well as average mesh size itself, plays an important role in determining the dynamics of molecules and nanoparticles that are embedded in tightly meshed polymer networks.

Quantification of Ostwald Ripening in Emulsions via Coarse-Grained Simulations

Ostwald ripening is a diffusional mass transfer process that occurs in polydisperse emulsions, often with the result of threatening the emulsion stability. In this work, we design a simulation protocol that is capable of quantifying the process of Ostwald ripening at the molecular level. To achieve experimentally relevant time scales, the dissipative particle dynamics (DPD) simulation protocol is implemented. The simulation parameters are tuned to represent two benzene droplets dispersed in water. The coalescence between the two droplets is prevented via the introduction of membranes, which allow diffusion of benzene from one droplet to the other. The simulation results are quantified in terms of the changes in the droplet volume as a function of time. The results are in qualitative agreement with experiments. The agreement with the Lifshitz-Slyozov-Wagner theory becomes quantitative when the simulated solubility and diffusion coefficient of benzene-in-water are considered. The effect of two different surfactants was also investigated. In agreement with both experimental observations and theory, the addition of surfactants at moderate concentrations decreased the Ostwald ripening rate because of the reduction in the interfacial tension between benzene and water; as the surfactant film becomes dense, other phenomena are likely to further delay the Ostwald ripening. In fact, the results suggest that the surfactant that yields higher density at the benzene-water interface delayed more effectively Ostwald ripening. The formation of micelles can also affect the ripening rate, in qualitative agreement with experiments, although our simulations are not conclusive on such effects. Our simulations show that the coarse-grained DPD formalism is able to capture the molecular phenomena related to Ostwald ripening and reveal molecular level features that could help to understand experimental observations. The results could be useful for predicting and eventually controlling the long-term stability of emulsions.

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.

Droplet growth during vapor-liquid transition in a 2D Lennard-Jones fluid

Results for the kinetics of vapor-liquid phase transition have been presented from the molecular dynamics simulations of a single component two-dimensional Lennard-Jones fluid. The phase diagram for the model, primary prerequisite for this purpose, has been obtained via the Monte Carlo simulations. Our focus is on the region very close to the vapor branch of the coexistence curve. Quenches to such region provide morphology that consists of disconnected circular clusters in the vapor background. We identified that these clusters exhibit diffusive motion and grow via sticky collisions among them. The growth follows power-law behavior with time, exponent of which is found to be in nice agreement with a theoretical prediction.