THE JOURNAL OF CHEMICAL PHYSICS 145, 046101 (2016)
Note: Activity coefficients and solubilities for the NaCl/ϵ force field
Hao Jiang and Athanassios Z. Panagiotopoulosa)
Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
(Received 4 June 2016; accepted 12 July 2016; published online 25 July 2016)
[http://dx.doi.org/10.1063/1.4959789]
Understanding the properties of salt-H2O mixture is of
great significance to biochemistry, separation technology,
and CO2 geologic sequestration. Molecular simulation is a
promising approach to provide predictions for the physical
and chemical properties of salts and their mixtures with H2O,
but the accuracy of these predictions depends sensitively on
the quality of the underlying intermolecular potential models.
There have been concerted research efforts in developing
force fields for salts, especially for NaCl and its aqueous
solutions.1–10 Prior studies have shown that non-polarizable
NaCl force fields do not represent accurately the properties of
the NaCl+H2O mixture over a wide range of conditions.11,12
Polarizable force fields have also been developed for this
system.13–18 Even though inclusion of polarizability may
improve the model performance, the computational cost of
polarizable force fields is generally 5-10 times higher than
their non-polarizable counterparts.
Recently, Leontyev, and Stuchebrukhov showed that
polarizable force fields can be approximated by nonpolarizable
ones with scaled charges.19 Using this idea, Fuentes-Azcatl
and Barbosa developed a force field for NaCl, namely NaCl/ϵ,
using screening factors in the Coulombic interactions to
account for the effect of polarization.20 The resulting NaCl/ϵ
force field, in conjunction with the TIP4P/ϵ 21 and SPC/ϵ 22
water force fields, was parameterized to density and radial
distribution function of the NaCl crystal as well as density
and dielectric constant of the NaCl+H2O mixture at salt
concentration of 4 mol/kg. The NaCl/ϵ force field yields
accurate calculation for properties of pure NaCl, including
density and surface tension, as well as properties for the
NaCl+H2O mixture including solution density, dielectric
constant, ion solvation structure, shear viscosity, and diffusion
coefficient. Using direct coexistence molecular dynamics
(MD) simulation, Fuentes-Azcatl and Barbosa calculated the
solubility of NaCl in H2O and found it to be in good agreement
with experimental data at 298.15 K. In this work, we obtain the
activity coefficients for the NaCl/ϵ and TIP4P/ϵ (and SPC/ϵ)
H2O force field combinations from 298.15 K to 473.15 K,
quantities which have not been obtained previously. We also
estimate the solubility of NaCl/ϵ force field by calculating
the electrolyte and crystal chemical potentials in bulk systems
without interfaces present.
The mean ionic activity coefficient of NaCl, which is
related to electrolyte chemical potential, was obtained from
a)Author to whom correspondence should be addressed. Electronic mail:
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MD simulations in the isothermal-isobaric ensemble, and the
electrolyte chemical potential of NaCl was estimated from
the free energy change of adding a pair of Na+ and Cl− ions
into the system, as in prior work.24,25 The solubility of NaCl
was estimated by finding the salt concentration where the
electrolyte chemical potential is equal to the crystal chemical
potential, which was obtained using the Einstein molecule
method.23,25
The mean ionic activity coefficients for the NaCl/ϵ and
TIP4P/ϵ force fields are given in Figure 1 and compared
with the prediction from the SPC/E+SD force fields. We
confirmed the thermodynamic consistency of the mean
ionic activity coefficient from Gibbs-Duhem calculation
of the water activity; the details of such calculation
are given in the supplementary material.26 As shown in
the Figure 1, the combination of NaCl/ϵ and TIP4P/ϵ
force fields underestimates the activity coefficients at all
temperatures studied. The activity coefficients predicted by
the NaCl/ϵ+TIP4P/ϵ force fields decrease almost linearly
with salt concentration, failing to follow the experimental
trend. Although the dielectric constant of NaCl+H2O mixture
at high salt concentration (4 mol/kg) was included in the
model development, the prediction of activity coefficient
from intermediate to high salt concentration is not improved
compared to the SPC/E+SD models, which suggests that
inclusion of dielectric constant in the parametrization is not
sufficient for reproducing the activity coefficients. We also
calculated the activity coefficients using the NaCl/ϵ and SPC/ϵ
force fields (results given in the supplementary material26),
and found a similarly inadequate representation of the activity
coefficients and their temperature dependence.
The solubility of NaCl in H2O from the NaCl/ϵ and
TIP4P/ϵ force fields is given in Figure 2 and compared
to the results from the SPC/E+SD force fields. Both the
TIP4P/ϵ+NaCl/ϵ and SPC/E+SD force fields underestimate
the solubility at all temperatures investigated. Fuentes-Azcatl
and Barbosa reported a NaCl solubility of 6 mol/kg for
the TIP4P/ϵ+NaCl/ϵ force fields at 298.15 K using direct
coexistence MD simulation; however, our free energy based
calculation yields a solubility around 0.1 mol/kg, which is
significantly lower than the experimental data. It is recognized
that the solubility of salt calculated from direct coexistence
simulation differs from the results obtained from free energy
based calculation.27,28 The reason of the discrepancy is not
clear at this point and is the subject of ongoing research.
Although the solubility of NaCl is underestimated, the NaCl/ϵ
and TIP4P/ϵ force fields predict correctly an increase in
145, 046101-1
Published by AIP Publishing.
046101-2
H. Jiang and A. Z. Panagiotopoulos
J. Chem. Phys. 145, 046101 (2016)
structure. Although the NaCl/ϵ force field gives accurate
description for many mixture and crystal properties, it is
unable to represent the activity coefficient and solubility of
NaCl in H2O, and its performance is not improved relative to
the SPC/E+SD force field. The unsatisfactory representation
of activity coefficient and solubility from NaCl/ϵ force field
suggests that it may be inadequate to develop an ion force
field by only including simple properties such as density
and dielectric constant in the model parameterization. This
coincides with a similar conclusion in the recent review of
Nezbeda et al.28
Financial support for this work was provided by the Office
of Basic Energy Sciences, U.S. Department of Energy, under
Award No. DE-SC0002128, and by the Carbon Mitigation
Initiative at Princeton University.
FIG. 1. Activity coefficient (γ) of NaCl as a function of salt concentration (m) for the TIP4P/ϵ+NaCl/ϵ (open symbols) and SPC/E+SD (filled
symbols) force fields compared to experiments (solid lines). Results for the
SPC/E+SD force field are taken from the work of Mester and Panagiotopoulos.25 Statistical uncertainties from the simulations are approximately twice
the symbol size.
FIG. 2. Solubility of NaCl in H2O calculated from the TIP4P/ϵ+NaCl/ϵ and
SPC/E+SD force fields. The results of SPC/E+SD force fields are taken from
Mester and Panagiotopoulos.25
solubility with temperature. The solubilities calculated from
the NaCl/ϵ and SPC/ϵ force fields are also much lower
than experimental data, and these values are given in the
supplementary material.26
To conclude, we studied the mean ionic activity coefficient
and solubility of the recently developed NaCl/ϵ force
field, which uses scaled charges to account indirectly for
polarization effects. The NaCl/ϵ force field, in conjunction
with TIP4P/ϵ or SPC/ϵ H2O force fields, was parameterized
against the density, structure, and dielectric constant of
NaCl+H2O mixture as well as NaCl crystal density and
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