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Register a new userThe solid-liquid interfacial free energy out of equilibrium
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The properties of the interface between solid and melt are key to solidification and melting, as the interfacial free energy introduces a kinetic barrier to phase transitions. This makes solidification happen below the melting temperature, in out-of-equilibrium conditions at which the interfacial free energy is ill-defined. Here we draw a connection between the atomistic description of a diffuse solid- liquid interface and its thermodynamic characterization. This framework resolves the ambiguities in defining the solid-liquid interfacial free energy above and below the melting temperature. In addition, we introduce a simulation protocol that allows solid-liquid interfaces to be reversibly created and destroyed at conditions relevant for experiments. We directly evaluate the value of the interfacial free energy away from the melting point for a simple but realistic atomic potential, and find a more complex temperature dependence than the constant positive slope that has been generally assumed based on phenomenological considerations and that has been used to interpret experiments. This methodology could be easily extended to the study of other phase transitions, from condensation to precipitation. Our analysis can help reconcile the textbook picture of classical nucleation theory with the growing body of atomistic studies and mesoscale models of solidification.
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The curvature dependence of interfacial free energy, which is crucial in quantitatively predicting nucleation kinetics and the stability of bubbles and droplets, can be described in terms of the Tolman length {delta}. For solid-liquid interfaces, however,{delta} has never been computed directly due to various theoretical and practical challenges. Here we present a general method that enables the direct evaluation of the Tolman length from atomistic simulations of a solid-liquid planar interface in out-of-equilibrium conditions. This method works by first measuring the surface tension from the amplitude of thermal capillary fluctuations of a localized version of Gibbs dividing surface, and bythen computing the free energy difference between the surface of tension and the equimolar dividing surface. For benchmark purposes, we computed {delta}for a model potential, and compared the results to less rigorous indirect approaches.
In this paper, we propose a new derivation for the Green-Kubo relationship for the liquid-solid friction coefficient, characterizing hydrodynamic slippage at a wall. It is based on a general Langevin approach for the fluctuating wall velocity, involving a non-markovian memory kernel with vanishing time integral. The calculation highlights some subtleties of the wall-liquid dynamics, leading to superdiffusive motion of the fluctuating wall position.
We introduce a scheme for deriving an optimally-parametrised Langevin dynamics of few collective variables from data generated in molecular dynamics simulations. The drift and the position-dependent diffusion profiles governing the Langevin dynamics are expressed as explicit averages over the input trajectories. The proposed strategy is applicable to cases when the input trajectories are generated by subjecting the system to a external time-dependent force (as opposed to canonically-equilibrated trajectories). Secondly, it provides an explicit control on the statistical uncertainty of the drift and diffusion profiles. These features lend to the possibility of designing the external force driving the system so to maximize the accuracy of the drift and diffusions profile throughout the phase space of interest. Quantitative criteria are also provided to assess a posteriori the satisfiability of the requisites for applying the method, namely the Markovian character of the stochastic dynamics of the collective variables.
A compressed knotted ring polymer in a confining cavity is modelled by a knotted lattice polygon confined in a cube in ${mathbb Z}^3$. The GAS algorithm [17] is used to sample lattice polygons of fixed knot type in a confining cube and to estimate the free energy of confined lattice knots. Lattice polygons of knot types the unknot, the trefoil knot, and the figure eight knot, are sampled and the free energies are estimated as functions of the concentration of monomers in the confining cube. The data show that the free energy is a function of knot type at low concentrations, and (mean-field) Flory-Huggins theory [12,15] is used to model the free energy as a function of monomer concentration. The Flory interaction parameter of knotted lattice polygons in ${mathbb Z}^3$ is also estimated.
We investigate the possibility of extending the notion of temperature in a stochastic model for the RNA/protein folding driven out of equilibrium. We simulate the dynamics of a small RNA hairpin subject to an external pulling force, which is time-dependent. First, we consider a fluctuation-dissipation relation (FDR) whereby we verify that various effective temperatures can be obtained for different observables, only when the slowest intrinsic relaxation timescale of the system regulates the dynamics of the system. Then, we introduce a different nonequilibrium temperature, which is defined from the rate of heat exchanged with a weakly-interacting thermal bath. Notably, this kinetic temperature can be defined for any frequency of the external switching force. We also discuss and compare the behavior of these two emerging parameters, by discriminating the time-delayed nature of the FDR temperature from the instantaneous character of the kinetic temperature. The validity of our numerics are corroborated by a simple 4-state Markov model which describes the long-time behaviour of the RNA molecule.
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