State-dependent diffusion coefficients and free energies for nucleation processes from Bayesian trajectory analysis.

The rate of nucleation processes such as the freezing of a supercooled liquid or the condensation of supersaturated vapour is mainly determined by the height of the nucleation barrier and the diffusion coefficient for the motion across it. Here, we use a Bayesian inference algorithm for Markovian dynamics to extract simultaneously the free energy profile and the diffusion coefficient in the nucleation barrier region from short molecular dynamics trajectories. The specific example we study is the nucleation of vapour bubbles in liquid water under strongly negative pressures, for which we use the volume of the largest bubble as a reaction coordinate. Particular attention is paid to the effects of discretisation, the implementation of appropriate boundary conditions and the optimal selection of parameters. We find that the diffusivity is a linear function of the bubble volume over wide ranges of volumes and pressures, and is mainly determined by the viscosity of the liquid, as expected from the Rayleigh-Plesset theory for macroscopic bubble dynamics. The method is generally applicable to nucleation processes and yields important quantities for the estimation of nucleation rates in classical nucleation theory.

Crystallization and flow in active patch systems.

Based upon recent experiments in which Janus particles are made into active swimmers by illuminating them with laser light, we explore the effect of applying a light pattern on the sample, thereby creating activity inducing zones or active patches. We simulate a system of interacting Brownian diffusers that become active swimmers when moving inside an active patch and analyze the structure and dynamics of the ensuing stationary state. We find that, in some respects, the effect of spatially inhomogeneous activity is qualitatively similar to a temperature gradient. For asymmetric patches, however, this analogy breaks down because the ensuing stationary state is specific to partial active motion.

Molecular mechanism for cavitation in water under tension.

Despite its relevance in biology and engineering, the molecular mechanism driving cavitation in water remains unknown. Using computer simulations, we investigate the structure and dynamics of vapor bubbles emerging from metastable water at negative pressures. We find that in the early stages of cavitation, bubbles are irregularly shaped and become more spherical as they grow. Nevertheless, the free energy of bubble formation can be perfectly reproduced in the framework of classical nucleation theory (CNT) if the curvature dependence of the surface tension is taken into account. Comparison of the observed bubble dynamics to the predictions of the macroscopic Rayleigh-Plesset (RP) equation, augmented with thermal fluctuations, demonstrates that the growth of nanoscale bubbles is governed by viscous forces. Combining the dynamical prefactor determined from the RP equation with CNT based on the Kramers formalism yields an analytical expression for the cavitation rate that reproduces the simulation results very well over a wide range of pressures. Furthermore, our theoretical predictions are in excellent agreement with cavitation rates obtained from inclusion experiments. This suggests that homogeneous nucleation is observed in inclusions, whereas only heterogeneous nucleation on impurities or defects occurs in other experiments.

S-shooting: a Bennett-Chandler-like method for the computation of rate constants from committor trajectories.

Mechanisms of rare transitions between long-lived stable states are often analyzed in terms of commitment probabilities, determined from swarms of short molecular dynamics trajectories. Here, we present a computer simulation method to determine rate constants from such short trajectories combined with free energy calculations. The method, akin to the Bennett-Chandler approach for the calculation of reaction rate constants, requires the definition of a valid reaction coordinate and can be applied to both under- and overdamped dynamics. We verify the correctness of the algorithm using a one-dimensional random walker in a double-well potential and demonstrate its applicability to complex transitions in condensed systems by calculating cavitation rates for water at negative pressures.

Effect of entropy on the nucleation of cavitation bubbles in water under tension.

Water can exist in a metastable liquid state under tension for long times before the system relaxes into the vapor via cavitation, i.e., bubble nucleation. Microscopic information on the cavitation process can be extracted from experimental data by the use of the nucleation theorem, which relates measured cavitation rates to the size of the critical bubble. To apply the nucleation theorem to experiments performed along an isochoric path, for instance, in cavitation experiments in mineral inclusions, knowledge of the bubble entropy is required. Using computer simulations, we compute the entropy of bubbles in water as a function of their volume over a wide range of tensions from free energy calculations. We find that the bubble entropy is an important contribution to the free energy that significantly lowers the barrier to bubble nucleation, thereby facilitating cavitation. Furthermore, the bubble entropy per surface area depends on the curvature of the liquid-vapor interface, decreasing approximately linearly with its mean curvature over the studied range of bubble volumes. At room temperature, the entropy of a flat liquid-vapor interface at ambient pressure is very similar to that of critical bubbles over a wide range of tensions, which justifies the use of the former as an approximation when interpreting data from experiments. Based on our simulation results, we obtain an estimate for the volume of the critical bubble from experimentally measured cavitation rates.

Detecting vapour bubbles in simulations of metastable water.

The investigation of cavitation in metastable liquids with molecular simulations requires an appropriate definition of the volume of the vapour bubble forming within the metastable liquid phase. Commonly used approaches for bubble detection exhibit two significant flaws: first, when applied to water they often identify the voids within the hydrogen bond network as bubbles thus masking the signature of emerging bubbles and, second, they lack thermodynamic consistency. Here, we present two grid-based methods, the M-method and the V-method, to detect bubbles in metastable water specifically designed to address these shortcomings. The M-method incorporates information about neighbouring grid cells to distinguish between liquid- and vapour-like cells, which allows for a very sensitive detection of small bubbles and high spatial resolution of the detected bubbles. The V-method is calibrated such that its estimates for the bubble volume correspond to the average change in system volume and are thus thermodynamically consistent. Both methods are computationally inexpensive such that they can be used in molecular dynamics and Monte Carlo simulations of cavitation. We illustrate them by computing the free energy barrier and the size of the critical bubble for cavitation in water at negative pressure.

Phase transition and interpore correlations of water in nanopore membranes.

Using computer simulations, we study a membrane of parallel narrow pores filled with one-dimensional wires of hydrogen-bonded water molecules. We show that such a membrane is equivalent to a system of effective charges located at opposite sides of the membrane offering a computationally efficient way to model correlation effects in water-filled nanopore membranes. Based on our simulations we predict that membranes with square pore lattices undergo a continuous order-disorder transition to an antiferroelectric low-temperature phase in which water wires in adjacent pores are oriented in opposite directions. Strong antiferroelectric correlations exist also in the disordered phase far above the critical temperature or in membranes with geometric frustration, leading to a dielectric constant that is reduced considerably with respect to the case of uncoupled water wires. These correlations are also expected to hinder proton translocation through the membrane.