Molecular dynamic studies of the solubility of sodium chloride: fast calculations using seed crystalline cluster probe

Abstract

Theoretical predictions of solubility, typically accomplished by comparing the chemical potential of pure solid and solution, currently suffer from a lack of accuracy. We suggest an alternative method for predicting solubility based on molecular dynamics simulations of the behaviour of a small seed crystalline cluster probe in solutions of varying concentrations. The size dynamics of a properly chosen seed cluster that dissolves in unsaturated solutions and grows in size in supersaturated solutions is indicative of the saturation point. This approach is illustrated by its application to NaCl in water. IntroductionThe first attempt to 'observe' the Arrhenius theory of electrolytic dissociation in action apparently belongs to Ohtaki and co-workers [1], who used for this purpose molecular dynamics (MD) simulations of dissolution of a 32-ion-pair perfect crystal of sodium chloride (NaCl) in a 216 water molecule solvent. The rapid progress of computer technology over the subsequent 20 years has made MD and Monte Carlo simulations possible for substantially more complex electrolyte systems [2][3][4][5][6][7][8]. Nevertheless, solubility calculations at the level of accuracy comparable to that of the experiment remain a challenge [3][4][5][6][7][8].Theoretical solubility predictions are typically accomplished by calculating the chemical potential of the solution and of the pure solid. In accordance with thermodynamics, the saturation point is defined as the concentration at which these chemical potentials are equal. While the methodology for performing this type of calculation is well established and widely used, solubility predictions from chemical potentials suffer from a lack of accuracy [9]. Recently, an effort was made to obtain solubilities from MD simulations directly, by following the dynamics of a supersaturated solution crystallising onto a solid crystal interface [7,8]. However, these calculations required extremely long simulations, and are thus quite expensive computationally. As a cheaper alternative, we here propose a method based on observing the behaviour of a small crystal probe in solutions of various concentrations. Properly chosen, this probe crystal will quickly dissolve in unsaturated solutions and grow in size in supersaturated solutions. These transforma-

Direct Coexistence Methods to Determine the Solubility of Salts in Water from Numerical Simulations. Test Case NaCl

“…As to the latter, when studying the coexistence of a saturated aqueous solution of a salt with its solid, the experimentally determined solubility would be expected to constitute a reasonable guess for the initial condition. However, that concentration is the property to be determined from the simulation, thus a different initial value should be 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 proposed by Wiebe et al, 11 that consists of a seed crystalline cluster probe. When they used the JC-SPC/E parameters for Na + and Cl − , combined with a flexible version of the SPC water model, they found a solubility of 5.7m.…”

On the calculation of solubilities via direct coexistence simulations: Investigation of NaCl aqueous solutions and Lennard-Jones binary mixtures

“…Even though DCM simulations have been widely used in the past, [13][14][15] and their agreement with free energy based calculations has been demonstrated for many systems, [16][17][18][19][20] there are significant unresolved discrepancies between DCM and CPR for calculating the solubility of NaCl in water. 11 The solubility obtained by DCM is generally higher than the corresponding value obtained by CPR, and different implementations of DCM yield different values for the solubility, [21][22][23][24] while multiple groups have obtained similar values for the solubility of NaCl in water using CPR. 9,[25][26][27][28][29][30][31][32] To cite a specific example, the solubility of the Joung-Cheatham NaCl model in SPC/E water (JC-SPC/E) 6,33 at 298.15 K and atmospheric pressure is 3.7m ± 0.2m, as reported from independent CPR calculations by different groups, 25,27,28,32 while the solubility of the same model obtained by the DCM approach ranges from 5.5m to 8.1m.…”

“…9,[25][26][27][28][29][30][31][32] To cite a specific example, the solubility of the Joung-Cheatham NaCl model in SPC/E water (JC-SPC/E) 6,33 at 298.15 K and atmospheric pressure is 3.7m ± 0.2m, as reported from independent CPR calculations by different groups, 25,27,28,32 while the solubility of the same model obtained by the DCM approach ranges from 5.5m to 8.1m. [21][22][23][24] The main aim of the present work is to understand the origin of such discrepancies between the DCM and CPR approaches and thereby to determine a reliable methodology to obtain salt solubilities. We choose to use the JC-SPC/E 6,33 force fields since the solubility of the model has been well established by CPR calculations, as stated in the previous paragraph.…”

Concentrated aqueous sodium chloride solution in clays at thermodynamic conditions of hydraulic fracturing: Insight from molecular dynamics simulations

“…We first prepared a cubic NaCl nanocrystal consisting of 216 ions, which is above a critical nucleus size, 5 by running isothermal-isobaric MD simulations at a temperature of 365 K and a pressure of 275 bar, resulting in the nanocrystal size of about 17.5 Å × 17.5 Å × 17.5 Å. For the cases with an initial rectangular parallelepiped NaCl nanocrystal, we similarly prepared the nanocrystal with 432 ions of the size of about 35 Å × 17.5 Å × 17.5 Å.…”

“…On the other hand, an increase in the system temperature speeds up the dissolution process. For instance, a cubic NaCl nanocrystal containing ∼2400 ions dissolved within about 500 ns at 300 K and the dissolution time reduced to about 100 ns when the temperature raised to 340 K. 4,5 In confined media, the dissolution of salt nanocrystals in aqueous solutions can be strongly affected by the interactions of water and ions with the wall surfaces. 6,7 Shale is comprised of two distinct parts: clay minerals and organic material.…”