Entropy Multiparticle Correlation Expansion for a Crystal.

As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a given order. By revisiting the combinatorial derivation of the entropy formula, we argue that a similar correlation expansion holds for the entropy of a crystalline system. We discuss how one- and two-body entropies scale with the size of the crystal, and provide fresh numerical data to check the expectation, grounded in theoretical arguments, that both entropies are extensive quantities.

Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres.

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δs, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), sex, and the pair-correlation contribution, s2. Thus, the RMPE represents the net contribution to sex due to spatial correlations involving three, four, or more particles. A heuristic "ordering" criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension 1

Ionic diffusion and proton transfer in aqueous solutions of alkali metal salts.

We report on a series of ab initio molecular dynamics investigations on LiCl, NaCl, and KCl aqueous solutions under the effect of static electric fields. We have found that although in low-to-moderate field intensity regimes the well-known sequence of cationic mobilities µ(K+) > µ(Na+) > µ(Li+) (i.e., the bigger the cation the higher the mobility) is recovered, from intense field strengths this intuitive rule is no longer verified. In fact, field-induced water molecular dissociations lead to more complex phenomena regulating the standard migration properties of the simplest monovalent cations. The water dissociation threshold is lowered from 0.35 V Å-1 to 0.25 V Å-1 by the presence of charged species in all samples. However, notwithstanding a one-stage process of water ionization and proton conduction takes place at 0.25 V Å-1 in the electrolyte solutions where "structure maker" cations are present (i.e., LiCl and NaCl), the KCl aqueous solution shows some hindrance in establishing a proton conductive regime, which is characterized by the same proton conduction threshold of neat water (i.e., 0.35 V Å-1). In addition, it turns out that protons flow easily in the LiCl (σp = 3.0 S cm-1) solution and then - in descending order - in the NaCl (σp = 2.5 S cm-1) and KCl (σp = 2.3 S cm-1) electrolyte solutions. The protonic conduction efficiency is thus inversely proportional to the ionic radii of the cations present in the samples. Moreover, Cl- anions act as a sort of "protonic well" for high field intensities, further lowering the overall proton transfer efficiency of the aqueous solutions. As a consequence, all the recorded protonic conductivities are lower than that for neat water (σp = 7.8 S cm-1), which strongly indicates that devices exploiting the proton transfer ability should be designed so as to minimize the presence of ionic impurities.

Ab initio molecular dynamics study of an aqueous NaCl solution under an electric field.

We report on an ab initio molecular dynamics study of an aqueous NaCl solution under the effect of static electric fields. We found that at low-to-moderate field intensity regimes chlorine ions have a greater mobility than sodium ions which, being a sort of "structure makers", are able to drag their own coordination shells. However, for field strengths exceeding 0.15 V Å(-1) the mobility of sodium ions overcomes that of chlorine ions as both types of ions do actually escape from their respective hydration cages. The presence of charged particles lowers the water dissociation threshold (i.e., the minimum field strength which induces a transfer of protons) from 0.35 V Å(-1) to 0.25 V Å(-1); moreover, a protonic current was also recorded at the estimated dissociation threshold of the solution. The behaviour of the current-voltage diagram of the protonic response to the external electric field is Ohmic as in pure water, with a resulting protonic conductivity of about 2.5 S cm(-1). This value is approximately one third of that estimated in pure water (7.8 S cm(-1)), which shows that the partial breaking of hydrogen bonds induced by the solvated ions hinders the migration of protonic defects. Finally, the conductivity of Na(+) and Cl(-) ions (0.2 S cm(-1)) is in fair agreement with the available experimental data for a solution molarity of 1.7 M.

On the determination of phase boundaries via thermodynamic integration across coexistence regions.

Specialized Monte Carlo methods are nowadays routinely employed, in combination with thermodynamic integration (TI), to locate phase boundaries of classical many-particle systems. This is especially useful for the fluid-solid transition, where a critical point does not exist and both phases may notoriously go deeply metastable. Using the Lennard-Jones model for demonstration, we hereby investigate on the alternate possibility of tracing reasonably accurate transition lines directly by integrating the pressure equation of state computed in a canonical-ensemble simulation with local moves. The recourse to this method would become a necessity when the stable crystal structure is not known. We show that, rather counterintuitively, metastability problems can be alleviated by reducing (rather than increasing) the size of the system. In particular, the location of liquid-vapor coexistence can exactly be predicted by just TI. On the contrary, TI badly fails in the solid-liquid region, where a better assessment (to within 10% accuracy) of the coexistence pressure can be made by following the expansion, until melting, of the defective solid which has previously emerged from the decay of the metastable liquid.

Liquid methanol under a static electric field.

We report on an ab initio molecular dynamics study of liquid methanol under the effect of a static electric field. We found that the hydrogen-bond structure of methanol is more robust and persistent for field intensities below the molecular dissociation threshold whose value (≈0.31 V/Å) turns out to be moderately larger than the corresponding estimate obtained for liquid water. A sustained ionic current, with ohmic current-voltage behavior, flows in this material for field intensities above 0.36 V/Å, as is also the case of water, but the resulting ionic conductivity (≈0.40 S cm(-1)) is at least one order of magnitude lower than that of water, a circumstance that evidences a lower efficiency of proton transfer processes. We surmise that this study may be relevant for the understanding of the properties and functioning of technological materials which exploit ionic conduction, such as direct-methanol fuel cells and Nafion membranes.

Supercooled water escaping from metastability.

The return of supercooled water to a stable equilibrium condition is an irreversible process which, in large enough samples, takes place adiabatically. We investigated this phenomenon in water by fast imaging techniques. As water freezes, large energy and density fluctuations promote the spatial coexistence of solid and liquid phases at different temperatures. Upon synchronously monitoring the time evolution of the local temperature, we observed a sharp dynamic transition between a fast and a slow decay regime at about 266.6 K. We construe the observed phenomenon in terms of the temperature dependence of heat transfers from solid and liquid volumes already at their bulk coexistence temperature towards adjacent still supercooled liquid regions. These findings can be justified by observing that convective motions induced by thermal gradients in a supercooled liquid near coexistence are rapidly suppressed as the nucleated solid fraction overcomes, at low enough temperatures, a characteristic percolation threshold.

Effect of electric field orientation on the mechanical and electrical properties of water ices: an ab-initio study.

We present a first-principles study of the properties of ordinary hexagonal ice (phase I(h)) and of its proton-ordered version (phase XI) under the action of static electric fields. We compute the mechanical response to the field in addition to the ionic current-voltage diagrams; we also analyze several other microscopic aspects of the proton transfer mechanism, with particular emphasis on the role played by the oxygen sublattice in driving molecular dissociation. We further study the topological aspects of the mechanical and electrical responses by orienting the external field along two different crystalline directions in both ice samples. At variance with ice Ih, ice XI displays an anisotropic behavior in the range of explored field intensities. In fact, when the direction of the field coincides with the ferroelectric axis, sustained molecular dissociation and proton transfer events are both observed just beyond a given field intensity; instead, the two processes exhibit different activation thresholds when the field is oriented along another symmetry axis. The underlying mechanism of molecular dissociation appears to be the same in solid and liquid water independently of the direction of the field.

Phase behavior of a fluid with a double Gaussian potential displaying waterlike features.

Pair potentials that are bounded at the origin provide an accurate description of the effective interaction for many systems of dissolved soft macromolecules (e.g., flexible dendrimers). Using numerical free-energy calculations, we reconstruct the equilibrium phase diagram of a system of particles interacting through a potential that brings together a Gaussian repulsion with a much weaker Gaussian attraction, close to the thermodynamic stability threshold. Compared to the purely repulsive model, only the reentrant branch of the melting line survives, since for lower densities solidification is overridden by liquid-vapor separation. As a result, the phase diagram of the system recalls that of water up to moderate (i.e., a few tens of MPa) pressures. Upon superimposing a suitable hard core on the double-Gaussian potential, a further transition to a more compact solid phase is induced at high pressure, which might be regarded as the analog of the ice I-to-ice III transition in water.

Proton conduction in water ices under an electric field.

We report on a first-principles study of the effects produced by a static electric field on proton conduction in ordinary hexagonal ice (phase Ih) and in its proton-ordered counterpart (phase XI). We performed ab initio molecular dynamics simulations of both phases and investigated the effects produced by the field on the structure of the material, with particular attention paid to the phenomenon of proton transfer. We observed that in ice Ih molecules start to dissociate for field intensities around 0.25 V/Å, as in liquid water, whereas fields stronger than 0.36 V/Å are needed to induce a permanent proton flow. In contrast, in ice XI, electric fields as intense as 0.22 V/Å are already able to induce and sustain, through correlated proton jumps, an ionic current; this behavior suggests, somewhat counterintuitively, that the ordering of protons favors the autoprotolysis phenomenon. However, the same is not true for static conductivities. In fact, both crystalline phases show an ohmic behavior in the conduction regime, but the conductivity of ice Ih turns out to be larger than that of ice XI. We finally discuss the qualitative and quantitative importance of the conspicuous concentration of ionic defects generated by intense electric fields in determining the value of the conductivity, also through a comparison with the experimental data available for saline ices.

Twofold reentrant melting in a double-Gaussian fluid.

Isotropic pair potentials that are bounded at the origin have been proposed from time to time as models of the effective interaction between macromolecules of interest in the chemical physics of soft matter. We present a thorough study of the phase behavior of point particles interacting through a potential which combines a bounded short-range repulsion with a much weaker attraction at moderate distances, both of Gaussian shape. Notwithstanding the fact that the attraction acts as a small perturbation of the Gaussian-core model potential, the phase diagram of the double-Gaussian model (DGM) is far richer, showing two fluid phases and four distinct solid phases in the case that we have studied. Using free-energy calculations, the various regions of confluence of three distinct phases in the DGM system have all been characterized in detail. Moreover, two distinct lines of reentrant melting are found, and for each of them a rationale is provided in terms of the elastic properties of the solid phases.

Fluids in porous media: the case of neutral walls.

The bulk phase behavior of a fluid is typically altered when the fluid is brought into confinement by the walls of a random porous medium. Inside the porous medium, phase-transition points are shifted, or may disappear altogether. A crucial determinant is how the walls interact with the fluid particles. In this work, we consider the situation whereby the walls are neutral with respect to the liquid and vapor phases. In order to realize the condition of strict neutrality, we use a symmetric binary mixture inside a porous medium that interacts identically with mixture species. Monte Carlo simulations are then used to obtain the phase behavior. Our main finding is that, in the presence of the porous medium, a liquid-vapor critical point still exists. At the critical point, the distribution of the order parameter remains scale invariant, but self-averaging is violated. These findings provide further evidence that random confinement by neutral walls induces critical behavior of the random Ising model (i.e., Ising models with dilution type disorder, where the disorder couples to the energy).

Spontaneous freezing of supercooled water under isochoric and adiabatic conditions.

The return of a supercooled liquid to equilibrium usually begins with a fast heating up of the sample which ends when the system reaches the equilibrium freezing temperature. At this stage, the system is still a microsegregated mixture of solid and liquid. Only later is solidification completed through the exchange of energy with the surroundings. Using the IAPWS-95 formulation, we investigate the adiabatic freezing of supercooled water in a closed and rigid vessel, i.e., under thermally and mechanically isolated conditions, which captures the initial stage of the decay of metastable water to equilibrium. To improve realism further, we also account for a fixed amount of foreign gas in the vessel. Under the simplifying assumption that the system is at equilibrium immediately after the nominal freezing temperature has been attained, we determine-as a function of undercooling and gas mole number-the final temperature and pressure of the system, the fraction of ice at equilibrium, and the entropy increase. Assuming a nonzero energy cost for the ice-water interface, we also show that, unless sufficiently undercooled, perfectly isolated pure-water droplets cannot start freezing in the bulk.

Volume crossover in deeply supercooled water adiabatically freezing under isobaric conditions.

The irreversible return of a supercooled liquid to stable thermodynamic equilibrium often begins as a fast process which adiabatically drives the system to solid-liquid coexistence. Only at a later stage will solidification proceed with the expected exchange of thermal energy with the external bath. In this paper we discuss some aspects of the adiabatic freezing of metastable water at constant pressure. In particular, we investigated the thermal behavior of the isobaric gap between the molar volume of supercooled water and that of the warmer ice-water mixture which eventually forms at equilibrium. The available experimental data at ambient pressure, extrapolated into the metastable region within the scheme provided by the reference IAPWS-95 formulation, show that water ordinarily expands upon (partially) freezing under isenthalpic conditions. However, the same scheme also suggests that, for increasing undercoolings, the volume gap is gradually reduced and eventually vanishes at a temperature close to the currently estimated homogeneous ice nucleation temperature. This behavior is contrasted with that of substances which do not display a volumetric anomaly. The effect of increasing pressures on the alleged volume crossover from an expanded to a contracted ice-water mixture is also discussed.

Hexatic phase and water-like anomalies in a two-dimensional fluid of particles with a weakly softened core.

We study a two-dimensional fluid of particles interacting through a spherically symmetric and marginally soft two-body repulsion. This model can exist in three different crystal phases, one of them with square symmetry and the other two triangular. We show that, while the triangular solids first melt into a hexatic fluid, the square solid is directly transformed on heating into an isotropic fluid through a first-order transition, with no intermediate tetratic phase. In the low-pressure triangular and square crystals, melting is reentrant provided the temperature is not too low, but without the necessity of two competing nearest-neighbor distances over a range of pressures. A whole spectrum of water-like fluid anomalies completes the picture for this model potential.

Ab initio molecular dynamics study of dissociation of water under an electric field.

The behavior of liquid water under an electric field is a crucial phenomenon in science and engineering. However, its detailed description at a microscopic level is difficult to achieve experimentally. Here we report on the first ab initio molecular-dynamics study on water under an electric field. We observe that the hydrogen-bond length and the molecular orientation are significantly modified at low-to-moderate field intensities. Fields beyond a threshold of about 0.35 V/Å are able to dissociate molecules and sustain an ionic current via a series of correlated proton jumps. Upon applying even more intense fields (∼1.0 V/Å), a 15%-20% fraction of molecules are instantaneously dissociated and the resulting ionic flow yields a conductance of about 7.8 Ω-1 cm-1, in good agreement with experimental values. This result paves the way to quantum-accurate microscopic studies of the effect of electric fields on aqueous solutions and, thus, to massive applications of ab initio molecular dynamics in neurobiology, electrochemistry, and hydrogen economy.

Hexatic phase in the two-dimensional Gaussian-core model.

We present a Monte Carlo simulation study of the phase behavior of two-dimensional classical particles repelling each other through an isotropic Gaussian potential. As in the analogous three-dimensional case, a reentrant-melting transition occurs upon compression for not too high temperatures, along with a spectrum of waterlike anomalies in the fluid phase. However, in two dimensions melting is a continuous two-stage transition, with an intermediate hexatic phase which becomes increasingly more definite as pressure grows. All available evidence supports the Kosterlitz-Thouless-Halperin-Nelson-Young scenario for this melting transition. We expect that such a phenomenology can be checked in confined monolayers of charge-stabilized colloids with a softened core.

Entropy from Correlations in TIP4P Water.

We use molecular dynamics to compute the pair distribution function of liquid TIP4P water as a function of the intermolecular distance and of the five angles that are needed to specify the relative position and orientation of two water molecules. We also calculate the translational and orientational contributions to the two-body term in the multiparticle correlation expansion of the configurational entropy at three selected thermodynamic states, where we also test various approximations for the angular dependence of the pair distribution function. We finally compare the results obtained for the pair entropy of TIP4P water with the experimental values of the excess entropy of ordinary water.

Comment on "Residual multiparticle entropy does not generally change sign near freezing" [J. Chem. Phys. 128, 161101 (2008)].

Does the vanishing of the residual multiparticle entropy, a quantity defined as the cumulative contribution of more-than-two-particle density correlations to the excess entropy of a fluid, have physical significance? We address this question in the light of the arguments presented in the paper that is being commented on and of the phenomenology thus far explored in a variety of model systems undergoing thermodynamic or structural transformations into more ordered (but not necessarily crystalline) states or regimes.

Liquid-solid coexistence via the metadynamics approach.

The metadynamics method, recently proposed by Laio and Parrinello as a general tool to map multidimensional free-energy landscapes [A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)], has been exploited with the aim of illustrating the properties of generalized thermodynamic potentials across a discontinuous phase transition. Virtues and limitations of the method are discussed in the exemplifying case of the freezing of a Lennard-Jones fluid in two dimensions.