Towards accurate force fields for electrolytes:
crystalline NaCl, aqueous NaCl, and hydrohalite
Filip Moučka and Jan Dočkal
Motivation
Conclusions
Faculty of Science, J. E. Purkyně University in Ústí nad Labem, Czech Republic
Radial distribution functions and thermodynamics
Model
Smith-Dang
Joung-Cheatham Dang
Horinek Madrid AH/BK3 MAH/BK3 Experiment
Density (g/cm3) 1.93
2.01 1.82 2.23 2.17 2.12 2.16 2.17
Chem. pot. (kJ/mol) -384.28
-384.37 -366.83 -413.32 -200.01 -399.00 -388.34 -384.02
Solubility (mol/kg) 0.6
3.7 0.2 0.0 5.7 1.0 4.7 6.14
Thermodynamic properties are related to radial distribution functions (RDF), gij(r):
Internal energy:
Pressure:
The interionic potential, , can be expressed as a sum of short-ranged (SR) and long- ranged (LR) contributions, and corresponding the SR contributions to U and P are:
and
Models based on the Lennard-Jones (LJ) potential:
Models based on the Buckingham (EXP) potential:
Only one free parameter but two target properties! Impossible to simultanously fit U and P without significantly affecting also the LR interaction. It seems unreasonable to adjust the LR attractive part (fitting the term of the LJ interaction) in order to change the behavior of the SR repulsive part.
U and P can be easily simultaneously fitted without significantly affecting the LR interaction. Desired changes in U and P aiming at target experimental values can be approximately found by solving these two simple equations.
RDFs at specified density and temperature are insensitive to details of interionic interactions and are characterised by narrow separate peaks. The first peaks at experimental ambient density are located at ≈0.2775 nm for gNaCl, and ≈0.3975 nm for gNaNa and gClCl.
SR contributions to U and P come from the 6 nearest neighbours in the lattice located almost exactly at the distances corresponding to the first peaks of RDFs, where the ClCl contribution is marginal and NaNa is negligible due to the small size of Na+ and greater like-ion distances:
and
LJ based models:
EXP based models:
Entropy should not significantly change when RDFs don't change. Changes in the chemical potential, μ, are almost completely ruled by changes in U.
We can thus target a value of chemical potential by changing a value of an initial model by
Radial distribution functions of crystalline NaCl and their consequences
Currently available ion-ion interaction models of electrolytes do not predict well properties of the crystalline phase. For example, none of different 13 NaCl models studied in our previous work simultaneously yields reasonable values of density and chemical potential, and the incorrect chemical potential values of crystals result in wrong predictions of electrolyte solubility. Wrong solubility predictions may cause spurious precipitation and thus limit usability of the models.
Resulting NaCl interaction model
A Gaussian-on-spring polarizable model which reparametrizes Kolafa's MAH/BK3 model and targets experimental values of ambient crystalline density and chemical potential:
Crystal properties:
New NaCl model Experiment
Density (g/cm3) 2.163 2.163
Chem. pot.
(kJ/mol) -384.01 -384.024
Solubility (mol/kg) 7.0
6.14 Bulk modulus
(GPa) 23.5 24.6
(MPa/K) 2.9
2.99 Shear modulus
(GPa) 12.5 12.7
Melting T (K)
1030 1074
perfect crystal density
good melt
density
perfect solution density
very good solution
permittivity
very good
solution NaCl
chemical potential
Correct hydrohalite structure
We have proposed and tested a method for adjusting ion-ion interaction models targeting simultaneously experimental values of crystalline density and chemical potential. The method is simple, cheap, provides significant insight to crystalline salts, and can be easily extended to consider multiple target properties at different thermodynamic conditions.
We have explained the origin of the general failure of alkali metal halide elecrolyte models based on the Lennard-Jones potential. The Lennard-Jones-based models cannot be fitted to a value of energy and pressure simultaneously without unreasonable changes in the London's attraction term or in the Coulombic electrostatics. Models based on exponential repulsion terms are more suitable for interactions between charged particles.
We have used the method to reparametrize the MAH/BK3 force field of Kolafa to yield correct predictions of density and chemical potential of crystalline NaCl. The resulting model predicts also all of the studied properties very well including properties of aqueous solutions and structure of hydrohalite.
In the future work, the ion-water interactions will be reparametrized to slightly improve predictions of NaCl chemical potential in aqueous solutions, solubility, faster self diffusion, and slightly higher permittivity at high concentrations. We believe that the AH/BK3 ion-water FF can be corrected by slightly weakening the ion-water short-ranged interactions.
Pot. energy (kJ/mol)
-781.5 -781.55
Ueq Na+ (Å2)
0.02 0.02
Ueq Cl- (Å2) 0.018 0.018
This work has received funding from the Internal Grant Agency of J. E. Purkyně University (Project No. UJEP-SGS-2019-53-005-3).
Acknowledgement
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