Caroline Desgranges

Phase equilibria of molecular fluids via hybrid Monte Carlo Wang–Landau simulations: Applications to benzene and n-alkanes

In recent years, powerful and accurate methods, based on a Wang-Landau sampling, have been developed to determine phase equilibria. However, while these methods have been extensively applied to study the phase behavior of model fluids, they have yet to be applied to molecular systems. In this work, we show how, by combining hybrid Monte Carlo simulations in the isothermal-isobaric ensemble with the Wang-Landau sampling method, we determine the vapor-liquid equilibria of various molecular fluids. More specifically, we present results obtained on rigid molecules, such as benzene, as well as on flexible chains of n-alkanes. The reliability of the method introduced in this work is assessed by demonstrating that our results are in excellent agreement with the results obtained in previous work on simple fluids, using either transition matrix or conventional Monte Carlo simulations with a Wang-Landau sampling, and on molecular fluids, using histogram reweighting or Gibbs ensemble Monte Carlo simulations.

Polymorph selection during the crystallization of Yukawa systems

Using molecular-dynamics simulations, we study the crystallization of supercooled liquids of charge-stabilized colloidal suspensions, modeled by the Yukawa (screened-Coulomb) potential. By modifying the value of the screening parameter lambda, we are able to invert the stability of the body-centered cubic (bcc) and face-centered cubic (fcc) polymorphs and study the crystal nucleation and growth in the domain of stability of each polymorph. We show that the crystallization mechanism strongly depends on the value of lambda. When bcc is the stable polymorph (lambda=3), the crystallization mechanism is straightforward. Both kinetics and thermodynamics favor the formation of the bcc particles and polymorph selection takes place early during the nucleation step. When fcc is the stable polymorph (lambda=10), the molecular mechanism is much more complex. First, kinetics favor the formation of bcc particles during the nucleation step. The growth of the post-critical nucleus proceeds through the successive cross-nucleation of the stable fcc polymorph on the metastable hcp polymorph as well as of the hcp polymorph on the fcc polymorph. As a result, polymorph selection occurs much later, i.e., during the growth step, than for lambda=3. We then extend our findings established in the case of homogeneous crystal nucleation to a situation of practical interest, i.e., when a seed of the stable polymorph is used. We demonstrate that the growth from the (111) face of a perfect fcc crystal into the melt proceeds through the same mechanisms.

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. I. Thermodynamic properties in the bulk and at the liquid-vapor phase boundary.

The Wang-Landau sampling is a powerful method that allows for a direct determination of the density of states. However, applications to the calculation of the thermodynamic properties of realistic fluids have been limited so far. By combining the Wang-Landau method with expanded grand-canonical simulations, we obtain a high-accuracy estimate for the grand-canonical partition function for atomic and molecular fluids. Then, using the formalism of statistical thermodynamics, we are able to calculate the thermodynamic properties of these systems, for a wide range of conditions spanning the single-phase regions as well as the vapor-liquid phase boundary. Excellent agreement with prior simulation work and with the available experimental data is obtained for argon and CO(2), thereby establishing the accuracy of the method for the calculation of thermodynamic properties such as free energies and entropies.

Molecular simulation of the crystallization of aluminum from the supercooled liquid

We report hybrid Monte Carlo molecular simulation results on the crystallization of aluminum from the supercooled liquid. We simulate the entire crystallization process at P=1 atm and at temperatures 20% and 15% below the melting temperature. We demonstrate that crystallization takes place according to the same mechanism for the two degrees of supercooling considered in this work. We show that both nucleation and growth proceed into a random mixing of the hexagonal close packed structure and of the face centered cubic (fcc) phase, with a predominance of the stable fcc form. The concentration of icosahedral (Ih)-like atoms in the supercooled liquid is found to remain constant throughout nucleation and growth, showing that Ih-like atoms do not play an active role in the crystallization process. We also find that the crystallization mechanism of aluminum differs from that observed for simple fluids. While nucleation of simple fluids first proceeds into the metastable body centered cubic (bcc) phase, the fraction of bcc-like atoms in aluminum crystallites always remains very low.

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. II. Adsorption of atomic and molecular fluids in a porous material

We propose to apply expanded Wang-Landau simulations to study the adsorption of atomic and molecular fluids in porous materials. This approach relies on a uniform sampling of the number of atoms and molecules adsorbed. The method consists in determining a high-accuracy estimate of the grand-canonical partition function for the adsorbed fluids. Then, using the formalism of statistical mechanics, we calculate absolute and excess thermodynamic properties relevant to adsorption processes. In this paper, we examine the adsorption of argon and carbon dioxide in the isoreticular metal-organic framework (IRMOF-1). We assess the reliability of the method by showing that the predicted adsorption isotherms and isosteric heats are in excellent agreement with simulation results obtained from grand-canonical Monte Carlo simulations. We also show that the proposed method is very efficient since a single expanded Wang-Landau simulation run at a given temperature provides the whole adsorption isotherm. Moreover, this approach provides a direct access to a wide range of thermodynamic properties, such as, e.g., the excess Gibbs free energy and the excess entropy of adsorption.

Role of Liquid Polymorphism during the Crystallization of Silicon

Using molecular simulation, we establish the pivotal role played by liquid polymorphs during the crystallization of silicon. When undercooled at a temperature 20% below the melting point, a silicon melt is under the form of the highly coordinated, high-density liquid (HDL) polymorph. We find that crystallization starts with the formation, within the HDL liquid, of a nanosized droplet of the least stable liquid polymorph, known as the almost tetracoordinated low-density liquid (LDL) polymorph. We then show that the crystalline embryo forms within the LDL droplet, close to the interface with the surrounding HDL liquid, thereby following a pathway associated with a much lower free energy barrier than the direct formation of the crystalline embryo from the HDL liquid would have required. This implies that, for substances exhibiting liquid polymorphs, theories, like the classical nucleation theory, and empirical rules, like Ostwalds rule, should be modified to account for the role of liquid polymorphs in the nucleation process.

Phase equilibria of polyaromatic hydrocarbons by hybrid Monte Carlo Wang–Landau simulations

Using a combination of hybrid Monte Carlo simulations in the isothermal–isobaric ensemble with a Wang–Landau sampling, we parametrise a force field for polyaromatic hydrocarbons (PAHs). The proposed force field gives an accurate description of the vapour–liquid equilibria of naphthalene, phenanthrene and anthracene. In particular, the model yields a better account of the dependence of the vapour pressure on temperature than existing models. The strategy adopted in this work is markedly different from that followed in previous work, which relied on Gibbs Ensemble Monte Carlo (GEMC) simulations combined with configurational bias (CB) moves. The accuracy of the GEMC-CB method hinges on a reasonably high acceptance rate of the transfer of molecules from one phase to another, a condition difficult to achieve for large molecules like PAHs. Our approach avoids these transfers, allows for a direct determination of the coexistence data in the isothermal–isobaric ensemble and provides a promising alternative to the GEMC-CB approach.

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. III. Impact of combining rules on mixtures properties

Combining rules, such as the Lorentz-Berthelot rules, are routinely used to calculate the thermodynamic properties of mixtures using molecular simulations. Here we extend the expanded Wang-Landau simulation approach to determine the impact of the combining rules on the value of the partition function of binary systems, and, in turn, on the phase coexistence and thermodynamics of these mixtures. We study various types of mixtures, ranging from systems of rare gases to biologically and technologically relevant mixtures, such as water-urea and water-carbon dioxide. Comparing the simulation results to the experimental data on mixtures of rare gases allows us to rank the performance of combining rules. We find that the widely used Lorentz-Berthelot rules exhibit the largest deviations from the experimental data, both for the bulk and at coexistence, while the Kong and Waldman-Hagler provide much better alternatives. In particular, in the case of aqueous solutions of urea, we show that the use of the Lorentz-Berthelot rules has a strong impact on the Gibbs free energy of the solute, overshooting the value predicted by the Waldman-Hagler rules by 7%. This result emphasizes the importance of the combining rule for the determination of hydration free energies using molecular simulations.

Optimisation of multiple time-step hybrid Monte Carlo Wang-Landau simulations in the isobaric-isothermal ensemble for the determination of phase equilibria

We discuss the optimisation as well as the convergence of a recently developed molecular simulation method using a Wang–Landau sampling scheme, combined with multiple time-step hybrid Monte Carlo (MC) simulations in the isothermal–isobaric ensemble, to determine vapour–liquid equilibria. This method has the advantage of being simple to use, as only a single simulation run at a given temperature directly gives the coexistence properties, and of being transferable to any kind of fluid, since the method is readily applicable to any molecular architecture. We apply this method to two branched alkanes, isopentane and isobutane, and discuss how we optimise the various simulation parameters. The vapour–liquid coexistence curve as well as the critical point obtained in this work are in excellent agreement with those found experimentally and in previous work using a combination of the Gibbs ensemble MC method with the configurational bias technique.

Wang–Landau configurational bias Monte Carlo simulations: vapour–liquid equilibria of alkenes

We propose to combine the Wang–Landau (WL) sampling scheme with configurational-bias Monte Carlo (CBMC) simulations to study the phase behaviour of chain molecules. We apply the resulting WL–CBMC method to calculate an estimate for the canonical and isothermal–isobaric partition function for a series of alkene molecules. We assess the accuracy of the proposed method by showing that the phase equilibria and the critical properties of four alkenes (propene, butene, pentene and hexene) determined from the WL–CBMC simulations are in excellent agreement with the experimental data and simulation results from Gibbs ensemble Monte Carlo simulations.