arXiv:1001.2648v1  [physics.chem-ph]  15 Jan 2010
Models of electrolyte solutions from molecular descriptions: The example of NaCl
solutions
John Jairo Molina 1, 2, 3,∗ Jean-Fran¸ cois Dufrˆ eche1, 2, 3,† Mathieu
Salanne1, 2, Olivier Bernard 1, 2, Marie Jardat 1, 2, and Pierre Turq 1, 2
1 UPMC-Universit´ e Paris 06, UMR 7195, PECSA, F-75005 Paris, France
2 CNRS, UMR 7195, PECSA, F-75005 Paris, France
3 Institut de Chimie S´ eparative de Marcoule (ICSM),
UMR 5257 CEA–CNRS–Universit´ e Montpellier 2, Site de Marco ule,
Bˆ atiment 426, BP 17171, 30207 Bagnols-sur-C` eze Cedex, Fr ance
We present a method to derive implicit solvent models of elec trolyte solutions from all-atom
descriptions; providing analytical expressions of the the rmodynamic and structural properties of
the ions consistent with the underlying explicit solvent re presentation. Eﬀective potentials between
ions in solution are calculated to perform perturbation the ory calculations, in order to derive the
best possible description in terms of charged hard spheres. Applying this method to NaCl solutions
yields excellent agreement with the all-atom model, provid ed ion association is taken into account.
Since the pioneering works of Debye, H¨ uckel, and
Onsager, electrolyte solutions have been commonly
described by continuous solvent models, for which
the McMillan-Mayer theory [1] provides a rigorous
statistical-mechanical foundation. Within that level of
description, simple phenomenological models such as the
primitive model (PM), for which the ions are assimi-
lated to charged hard spheres [2], can lead to explicit
formulas for the thermodynamic and structural proper-
ties (e.g., with the help of the mean spherical approxima-
tion (MSA) [3] or the binding MSA (BIMSA) [4]). These
models are the most practical to use [5], since they allow
for a direct link between the experimental measurements
and the microscopic parameters of the system. Never-
theless, they ignore the molecular structure of the sol-
vent. Consequently, they cannot properly account for
the complex speciﬁc eﬀects of the ions, which appear in
numerous biological, chemical, and physical interfacial
phenomena [6, 7], without further developments.
An alternative procedure consists in carrying out
molecular simulations, where both the solvent and solute
are treated explicitly. After a rigorous averaging over
the solvent conﬁgurations, a coarse-grained description
of the ions, which still includes the eﬀect of the solvent
structure, can be obtained [8–11]. However, this set of
methods is purely numeric; they do not provide any an-
alytical expression for thermodynamic quantities. They
are therefore restricted to simple geometries [12, 13] (bulk
solutions or planar interfaces). The description of com-
plex systems, such as porous or electrochemical materi-
als, is still based on continuous solvent models [14].
In this letter we present a method aimed at bridging
the gap between analytical and numerical approaches. It
is based on the application of liquid perturbation theory
(LPT) [15] to eﬀective ion-ion potentials extracted from
∗ Electronic address: john.molina@etu.upmc.fr
† Electronic address: jean-francois.dufreche@upmc.fr
molecular dynamics (MD) results. Diﬀerent approxima-
tions of the PM are employed for the case of NaCl elec-
trolyte solutions: a two component model (MSA2), that
only takes free ions into account, and two diﬀerent three
component models (MSA3 and BIMSA3), which include
a third species (the contact ion pair). As we proceed
to show, LPT allows us to select the best simple model
which accurately accounts for the thermodynamics and
the physical-chemistry of the system.
The ﬁrst stage consists in calculating the McMillan-
Mayer eﬀective ion-ion interaction potentials V eﬀ
ij (r), by
inverting the radial distribution functions (RDF) gij(r)
obtained by MD. The simulations were carried out on
a box of 2000 water molecules and 48 NaCl pairs us-