(436j) NaCl Nucleation from Aqueous Solution By a Seeded Simulation Approach

Nucleation is scientifically and technologically exceptionally important. However, ascertaining mechanisms and kinetics remains extremely difficult for both simulations and experiments even when supposedly simple systems are considered. Conventional rare-event methods typically face a problem related to the nucleus size coordinate n (the measure of nucleation progress). The dynamics of n are so slow that sufficient sampling of the free-energy landscape is not achievable [1]. To overcome this limitation we highlight a seeding approach for molecular dynamics simulations to predict nucleation rates [1] and for ascertaining attachment kinetics [2]. We apply the approach to sodium chloride nucleation from aqueous solution because there are rate measurements for this system in the literature [3â??5]. Furthermore, force fields exist that reliably reproduce experimental data on important input data to the approach: the solution chemical potential and the solubility limit [6].

The key idea of the approach is to carefully merge compact clusters cut from a well-equilibrated crystal lattice with a quasi-equilibrated supersaturated solution box. The transient evolution of the nucleus size is then recorded for various seed sizes. The resulting nucleus drift data are then used in the framework of classical nucleation theory (CNT) together with the assumption of over-damped Langevin dynamics for n(t) to estimate the nucleation rate, J. The procedure to calculate J comprises three conceptual steps: (1) estimation of the critical nucleus size from nucleus drift data, (2) determination of the attachment frequency to the critical nucleus from short swarms of trajectories, and (3) fitting of the interfacial free-energy, γ, to reproduce the drift data from step (1).

In step (2), we have tested two models of the attachment kinetics, which reflect diffusion limitation and ion-desolvation limitation, respectively. The diffusion analysis required the calculation of mutual electrolyte diffusivities at varying concentration, which agree well with experimental results from interferometry [7,8]. The diffusion model grossly overestimates the attachment frequency compared with a standard analysis of the mean square change in nucleus size [9]. Therefore, ion-desolvation is identified as the limiting resistance to attachment. A second independent analysis, based on approach-to-coexistence data [10], confirms the negligible influence of diffusion.

Accurate data on the model-inherent solution chemical potential and solubility limit are critical for rate predictions because they define the (thermodynamic) driving force for nucleation in the simulations. The solubility limit of the chosen NaClâ??water model has been intensely debated until recently [6,10], for which reason we systematically investigate its influence on the nucleation rate [11]. We find that an error of 30% in the solubility, which reflects the ranges from recent literature [6,10], can cause the rate to differ by ten orders of magnitudes. Our seeded simulations are performed at experimentally relevant concentrations [3]. However, electrolyte chemical potentials, µ, are typically not available at these conditions for the force field chosen. Therefore, we also address the issue of reliably extrapolating µ [11]. Finally, we assess the uncertainty in the rate [11] due to the remaining uncertainty in the solubility [6].

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[11] Zimmermann et al., in preparation