arXiv subjects

E. Sanz

Publications and source records attributed to E. Sanz.

12 recordsLinked to original sources

arXiv2025

Homogeneous nucleation rate of carbon dioxide hydrate formation under experimental condition from Seeding simulations

We investigate the nucleation of carbon dioxide (CO$_2$) hydrates from carbon dioxide aqueous solutions by means of molecular dynamics simulations using the TIP4P/Ice and the TraPPE models for water and CO$_2$ respectively. We work at 400 bar and different temperatures and CO$_2$ concentrations. We use brute force molecular dynamics when the supersaturation or the supercooling are so high so that nucleation occurs spontaneously and Seeding otherwise. We used both methods for a particular state and we get a rate of 10$^{25}\,\text{m}^{-3}\text{s}^{-1}$ for nucleation in a CO$_2$ saturated solution at 255 K (35 K of supercooling). By comparison with our previous work on methane hydrates, we conclude that nucleation of CO$_2$ hydrates is several orders of magnitude faster due to a lower interfacial free energy between the crystal and the solution. By combining our nucleation studies with a recent calculation of the hydrate-solution interfacial free energy at coexistence, we obtain a prediction of the nucleation rate temperature dependence for CO$_{2}$-saturated solutions (the experimentally relevant concentration). On the one hand, we open the window for comparison with experiments for supercooling larger than 25 K. On the other hand, we conclude that homogeneous nucleation is impossible for supercooling lower than 20 K. Therefore, nucleation must be heterogeneous in typical experiments where hydrate formation is observed at low supercooling. To assess the hypothesis that nucleation occurs at the solution-CO$_2$ interface we run spontaneous nucleation simulations in two-phase systems and find, by comparison with single-phase simulations, that the interface does not affect hydrate nucleation, at least at the deep supercooling at which this study was carried out (40 and 45 K). Overall, our work sheds light on molecular and thermodynamic aspects of hydrate nucleation.

cond-mat.soft↗

arXiv2024

The Young-Laplace equation for a solid-liquid interface

The application of the Young-Laplace equation to a solid-liquid interface is considered. Computer simulations show that the pressure inside a solid cluster of hard spheres is smaller than the external pressure of the liquid (both for small and large clusters). That would suggest a negative value for the interfacial free energy. We show that in a Gibbsian description of the thermodynamics of a curved solid-liquid interface in equilibrium, the choice of the thermodynamic (rather than mechanical) pressure is required, as suggested by Tolman for the liquid-gas scenario. With this definition, the interfacial free energy is positive, and the values obtained are in excellent agreement with previous results from nucleation studies. Although for a curved fluid-fluid interface there is no distinction between mechanical and thermal pressures (for a sufficiently large inner phase), in the solid-liquid they do not coincide, as hypothesized by Gibbs.

cond-mat.soft↗

arXiv2021

Equivalence between condensation and boiling in a Lennard Jones fluid

Condensation and boiling are phase transitions highly relevant to industry, geology or atmospheric science. These phase transitions are initiated by the nucleation of a drop in a supersaturated vapor and of a bubble in an overstretched liquid respectively. The surface tension between both phases, liquid and vapor, is a key parameter in the development of such nucleation stage. Whereas the surface tension can be readily measured for a flat interface, there are technical and conceptual limitations to obtain it for the curved interface of the nucleus. On the technical side, it is quite difficult to observe a critical nucleus in experiments. From a conceptual point of view, the interfacial free energy depends on the choice of the dividing surface, being the surface of tension the one relevant for nucleation. We bypass the technical limitation by performing simulations of a Lennard Jones fluid where we equilibrate critical nuclei (both drops and bubbles). Regarding the conceptual hurdle, we find the relevant cluster size by searching the radius that correctly predicts nucleation rates and nucleation free energy barriers when combined with Classical Nucleation Theory. With such definition of the cluster size we find the same value of the surface tension for drops and bubbles of a given radius. Thus, condensation and boiling can be viewed as two sides of the same coin. Finally, we combine the data coming from drops and bubbles to obtain, via two different routes, estimates of the Tolman length, a parameter that allows describing the curvature dependence of the surface tension in a theoretical framework.

cond-mat.soft↗

arXiv2014

The mold integration method for the calculation of the crystal-fluid interfacial free energy from simulations

The interfacial free energy between a crystal and a fluid, γ cf, is a highly relevant parameter in phenomena such as wetting or crystal nucleation and growth. Due to the difficulty of measuring γ cf experimentally, computer simulations are often used to study the crystal-fluid interface. Here, we present a novel simulation methodology for the calculation of γ cf . The methodology consists in using a mold composed of potential energy wells to induce the formation of a crystal slab in the fluid at coexistence conditions. This induction is done along a reversible pathway along which the free energy difference between the initial and the final states is obtained by means of thermodynamic integration. The structure of the mold is given by that of the crystal lattice planes, which allows to easily obtain the free energy for different crystal orientations. The method is validated by calculating γ cf for previously studied systems, namely, the hard spheres and the Lennard-Jones systems. Our results for the latter show that the method is accurate enough to deal with the anisotropy of γ cf with respect to the crystal orientation. We also calculate γ cf for a recently proposed continuous version of the hard sphere potential and obtain the same γ cf as for the pure hard sphere system. The method can be implemented both in Monte Carlo and Molecular Dynamics. In fact, we show that it can be easily used in combination with the popular Molecular Dynamics package GROMACS.

cond-mat.stat-mech↗

arXiv2014

Homogeneous ice nucleation evaluated for several water models

In this work, we evaluate by means of computer simulations the rate for ice homogeneous nucleation for several water models such as TIP4P, TIP4P/2005,TIP4P/ICE, and mW (following the same procedure as in Sanz et al. [J. Am. Chem. Soc.135, 15008 (2013)]) in a broad temperature range. We estimate the ice-liquid interfacial free-energy, and conclude that for all water models γ decreases as the temperature decreases. Extrapolating our results to the melting temperature, we obtain a value of the interfacial free-energy between 25 and 32 mN/m in reasonable agreement with the reported experimental values. Moreover, we observe that the values of γ depend on the chosen water model and this is a key factor when numerically evaluating nucleation rates, given that the kinetic prefactor is quite similar for all water models with the exception of the mW (due to the absence of hydrogens). Somewhat surprisingly the estimates of the nucleation rates found in this work for TIP4P/2005 are slightly higher than those of the mW model, even though the former has explicit hydrogens. Our results suggest that it may be possible to observe in computer simulations spontaneous crystallization of TIP4P/2005 at about 60 K below the melting point.

cond-mat.stat-mech↗

arXiv2013

Homogeneous ice nucleation at moderate supercooling from molecular simulation

Among all the freezing transitions, that of water into ice is probably the most relevant to biology, physics, geology or atmospheric science. In this work we investigate homogeneous ice nucleation by means of computer simulations. We evaluate the size of the critical cluster and the nucleation rate for temperatures ranging between 15K and 35K below melting. We use the TIP4P/2005 and the TIP4P/Ice water models. Both give similar results when compared at the same temperature difference with the model's melting temperature. The size of the critical cluster varies from $\sim$8000 molecules (radius$ = 4$nm) at 15K below melting to $\sim$600 molecules (radius$ = 1.7$nm) at 35K below melting. We use Classical Nucleation Theory (CNT) to estimate the ice-water interfacial free energy and the nucleation free energy barrier. We obtain an interfacial free energy of 29(3)mN/m from an extrapolation of our results to the melting temperature. This value is in good agreement both with experimental measurements and with previous estimates from computer simulations of TIP4P-like models. Moreover, we obtain estimates of the nucleation rate from simulations of the critical cluster at the barrier top. The values we get for both models agree within statistical error with experimental measurements. At temperatures higher than 20K below melting we get nucleation rates slower than the appearance of a critical cluster in all the water of the hydrosphere in the age of the universe. Therefore, our simulations predict that water freezing above this temperature must necessarily be heterogeneous.

cond-mat.soft↗

arXiv2012

Calculation of the melting point of alkali halides by means of computer simulations

In this manuscript we study the liquid-solid coexistence of NaCl-type alkali halides, described by interaction potentials such as Tosi-Fumi (TF), Smith-Dang (SD) and Joung-Cheatham (JC), and compute their melting temperature (Tm) at 1 bar via three independent routes: 1) liquid/solid direct coexistence, 2) free-energy calculations and 3) Hamiltonian Gibbs-Duhem integration. The melting points obtained by the three routes are consistent with each other. The calculated Tm of the Tosi-Fumi model of NaCl is in good agreement with the experimental value as well as with other numerical calculations. However, the other two models considered for NaCl, SD and JC, overestimate the melting temperature of NaCl by more than 200 K. We have also computed the melting temperature of other alkali halides using the Tosi-Fumi interaction potential and observed that the predictions are not always as close to the experimental values as they are for NaCl. It seems that there is still room for improvement in the area of force-fields for alkaline halides, given that so far most models are still unable to describe a simple yet important property such as the melting point.

cond-mat.stat-mech↗

arXiv2011

Irreducible finite-size effects in surface free energies from crystal-nucleation data

In this Letter we report a simulation study in which we compare the solid-liquid interfacial free energy of NaCl at coexistence, with the value that follows from the height of the homogeneous nucleation barrier. We find that the two estimates differ by more than 100%. Similar, although smaller discrepancies are found for crystals of hard-sphere colloids and of Lennard-Jones ("argon") particles. We consider a variety of possible causes for this discrepancy and are forced to conclude that it is due to a finite-size effect that cannot be corrected for by any simple thermodynamic procedure. Importantly, we find that the surface free energies that follow from real nucleation experiments should be subject to large finite size effects. Taking this in to account, we obtain quantitative agreement between the simulation data and the surface free energy of NaCl that follows from nucleation experiments. Our finding suggests that most published solid-liquid surface free energies derived from nucleation experiments will have to be revised.

cond-mat.mtrl-sci↗

arXiv2009

Crystallization of hard-sphere glasses

We study by molecular dynamics the interplay between arrest and crystallization in hard spheres. For state points in the plane of volume fraction ($0.54 \leq phi \leq 0.63$) and polydispersity ($0 \leq s \leq 0.085$), we delineate states that spontaneously crystallize from those that do not. For noncrystallizing (or precrystallization) samples we find isodiffusivity lines consistent with an ideal glass transition at $ϕ_g \approx 0.585$, independent of $s$. Despite this, for $s<0.05$, crystallization occurs at $ϕ> ϕ_g$. This happens on time scales for which the system is aging, and a diffusive regime in the mean square displacement is not reached; by those criteria, the system is a glass. Hence, contrary to a widespread assumption in the colloid literature, the occurrence of spontaneous crystallization within a bulk amorphous state does not prove that this state was an ergodic fluid rather than a glass.

cond-mat.soft↗

arXiv2009

Hard Spheres: Crystallization and Glass Formation

Motivated by old experiments on colloidal suspensions, we report molecular dynamics simulations of assemblies of hard spheres, addressing crystallization and glass formation. The simulations cover wide ranges of polydispersity s (standard deviation of the particle size distribution divided by its mean) and particle concentration. No crystallization is observed for s > 0.07. For 0.02 < s < 0.07, we find that increasing the polydispersity at a given concentration slows down crystal nucleation. The main effect here is that polydispersity reduces the supersaturation since it tends to stabilise the fluid but to destabilise the crystal. At a given polydispersity (< 0.07) we find three regimes of nucleation: standard nucleation and growth at concentrations in and slightly above the coexistence region; "spinodal nucleation", where the free energy barrier to nucleation appears to be negligible, at intermediate concentrations; and, at the highest concentrations, a new mechanism, still to be fully understood, which only requires small re-arrangement of the particle positions. The cross-over between the second and third regimes occurs at a concentration, around 58% by volume, where the colloid experiments show a marked change in the nature of the crystals formed and the particle dynamics indicate an "ideal" glass transition.

cond-mat.mtrl-sci↗

arXiv2009

Rate of Homogeneous Crystal Nucleation in molten NaCl

We report a numerical simulation of the rate of crystal nucleation of sodium chloride from its melt at moderate supercooling. In this regime nucleation is too slow to be studied with "brute-force" Molecular Dynamics simulations. The melting temperature of ("Tosi-Fumi") NaCl is $\sim 1060$K. We studied crystal nucleation at $T$=800K and 825K. We observe that the critical nucleus formed during the nucleation process has the crystal structure of bulk NaCl. Interestingly, the critical nucleus is clearly faceted: the nuclei have a cubical shape. We have computed the crystal-nucleation rate using two completely different approaches, one based on an estimate of the rate of diffusive crossing of the nucleation barrier, the other based on the Forward Flux Sampling and Transition Interface Sampling (FFS-TIS) methods. We find that the two methods yield the same result to within an order of magnitude. However, when we compare the extrapolated simulation data with the only available experimental results for NaCl nucleation, we observe a discrepancy of nearly 5 orders of magnitude. We discuss the possible causes for this discrepancy.

physics.chem-ph↗

arXiv2009

Determination of phase diagrams via computer simulation: Methodology and applications to water, electrolytes and proteins

In this review we focus on the determination of phase diagrams by computer simulation with particular attention to the fluid-solid and solid-solid equilibria. The calculation of the free energy of solid phases using the Einstein crystal and Einstein molecule methods are described in detail. It is shown that for the hard spheres solid both methods yield the same results and that free energies of solid phases present noticeable finite size effects. Finite size corrections can be introduced, although in an approximate way, to correct for the dependence of the free energy on the size of the system. The computation of free energies of solid phases can be extended to molecular fluids. The procedure to compute free energies of solid phases of water (ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI and XII) using the SPC/E and TIP4P models will be described.Other methods to estimate the melting point of a solid, as the direct fluid-solid coexistence or simulations of the free surface of the solid will be discussed. It will be shown that the melting points of ice Ih for several water models, obtained from these two methods and from free energy calculations agree within statistical uncertainty. Phase diagram calculations can help to improve potential models of molecular fluids; for water, the TIP4P/2005 model can be regarded as an improved version of TIP4P. We will also review some recent work on the phase diagram of the simplest ionic model, the restricted primitive model. Although originally devised to describe ionic liquids, the model is becoming quite popular to describe charged colloids. Besides the possibility of obtaining fluid-solid equilibria for simple protein models will be discussed. In these primitive models, the protein is described by a spherical potential with certain anisotropic bonding sites.

cond-mat.stat-mech↗