Connecting local structure to interface formation: a molecular scale van der Waals theory of nonuniform liquids

This article reviews a new and general theory of nonuniform fluids that naturally incorporates molecular scale information into the classical van der Waals theory of slowly varying interfaces. The method optimally combines two standard approximations, molecular (mean) field theory to describe interface formation and linear response (or Gaussian fluctuation) theory to describe local structure. Accurate results have been found in many different applications in nonuniform simple fluids and these ideas may have important implications for the theory of hydrophobic interactions in water.Comment: 30 pages; 4 figures; to be published in Annual Reviews of Physical Chemistry, Vol. 5

External fields, density functionals, and the Gibbs inequality

By combining the upper and lower bounds to the free energy as given by the Gibbs inequality for two systems with the same intermolecular interactions but with external fields differing from each other only in a finite region of space Gamma, we show that the corresponding equilibrium densities must also differ from each other somewhere in Gamma. We note that the basic equations of density functional theory arise naturally from a simple rearrangement and reinterpretation of the terms in the upper bound Gibbs inequality for such systems and briefly discuss some of the complications that occur when the intermolecular interactions of the two systems also differ.Comment: 5 pages, no figures. To be published in Journal of Statistical Physic

Incorporating molecular scale structure into the van der Waals theory of the liquid-vapor interface

We have developed a new and general theory of nonuniform fluids that naturally incorporates molecular scale information into the classical van der Waals theory of slowly varying interfaces. Here the theory is applied to the liquid-vapor interface of a Lennard-Jones fluid. The method combines a molecular field treatment of the effects of unbalanced attractive forces with a locally optimal use of linear response theory to approximate fluid structure by that of the associated (hard sphere like) reference fluid. Our approach avoids many of the conceptual problems that arise in the classical theory and shows why capillary wave effects are not included in the theory. The general theory and a simplified version gives results for the interface profile and surface tension for states with different temperatures and potential energy cutoffs that compare very favorably with simulation data.Comment: 9 pages, 5 figures; to be published in Journal of Physical Chemistr

Acetonitrile on silica surfaces and at its liquid-vapor interface: structural correlations and collective dynamics

Solvent structure and dynamics of acetonitrile at its liquid-vapor (LV) interface and at the acetonitrile-silica (LS) interface are studied by means of molecular dynamics simulations. We set up the interfacial system and treat the long-ranged electrostatics carefully to obtain both stable LV and LS interfaces within the same system. Single molecule (singlet) and correlated density orientational profiles and singlet and collective reorientational dynamics are reported for both interfaces. At the LS interface acetonitrile forms layers. The closest sublayer is dominated by nitrogen atoms bonding to the hydrogen sites of the silica surface. The singlet molecular reorientation is strongly hindered when close to the silica surface, but at the LV interface it relaxes much faster than in the bulk. Antiparallel correlations between acetonitrile molecules at the LV interface are even stronger than in the bulk liquid phase. This strong antiparallel correlation disappears at the LS interface. The collective reorientational relaxation of the first layer acetonitrile is much faster than the singlet reorientational relaxation but it is still slower than in the bulk. These results are interpreted with reference to a variety of recent experiments. We found that defining interface properties based on the distribution of positions of different choices of atoms or sites within the molecule leads to apparently different orientational profiles, especially at the LV interface. We provide a general formulation showing that this ambiguity arises when the size of the molecule is comparable to the interfacial width and is particularly significant when there is a large difference in density at the upper and lower boundaries of the interface. We finally analyze the effect of electrostatics to show the necessity of properly treating long-ranged electrostatics for simulations of interfacial systems

Determining liquid structure from the tail of the direct correlation function

In important early work, Stell showed that one can determine the pair correlation function h(r) of the hard sphere fluid for all distances r by specifying only the "tail" of the direct correlation function c(r) at separations greater than the hard core diameter. We extend this idea in a very natural way to potentials with a soft repulsive core of finite extent and a weaker and longer ranged tail. We introduce a new continuous function T(r) which reduces exactly to the tail of c(r) outside the (soft) core region and show that both h(r) and c(r) depend only on the "out projection" of T(r): i.e., the product of the Boltzmann factor of the repulsive core potential times T(r). Standard integral equation closures can thus be reinterpreted and assessed in terms of their predictions for the tail of c(r) and simple approximations for its form suggest new closures. A new and very efficient variational method is proposed for solving the Ornstein-Zernike equation given an approximation for the tail of c. Initial applications of these ideas to the Lennard-Jones and the hard core Yukawa fluid are discussed.Comment: in press, J.Stat.Phy

On the mean field treatment of attractive interactions in nonuniform simple fluids

We study thermodynamic and structural properties of a Lennard-Jones liquid at a state very close to the triple point as the radius of a hard sphere solute is varied. Oscillatory profiles arise for small, molecular sized radii while for large radii smooth interfaces with a ``drying layer'' of low vapor density near the solute are seen. We develop a quantitative theory for this process using a new mean field treatment where the effects of attractive interactions are described in terms of a self-consistently chosen effective single particle field. We modify the usual simple molecular field approximation for the effective field in a very natural way so that exact results (consistent with a given accurate equation of state for the uniform fluid) arise in the ``hydrostatic limit'' of very slowly varying interfaces. Very good agreement with the results of computer simulations for a wide range of solute radii are found.Comment: to be published in J.Phys.Che

Exact relations between charge-density functions determining the total Coulomb energy and the dielectric constant for a mixture of neutral and charged site-site molecules

We extend results developed by Chandler [J. Chem. Phys. 65, 2925 (1976)] for the dielectric constant of neutral site-site molecular models to mixtures of both charged and uncharged molecules. This provides a unified derivation connecting the Stillinger-Lovett moment conditions for ions to standard results for the dielectric constant for polar species and yields exact expressions for the small-k expansion of the two-point intermolecular charge-density function used to determine the total Coulomb energy. The latter is useful in determining corrections to the thermodynamics of uniform site-site molecular models simulated with spherically truncated Coulomb interactions

Structure of nonuniform hard sphere fluids from shifted linear truncations of functional expansions

Percus showed that approximate theories for the structure of nonuniform hard sphere fluids can be generated by linear truncations of functional expansions of the nonuniform density rho (r) about that of an appropriately chosen uniform system. We consider the most general such truncation, which we refer to as the shifted linear response (SLR) equation, where the density response rho (r) to an external field phi (r) is expanded to linear order at each r about a different uniform system with a locally shifted chemical potential. Special cases include the Percus-Yevick (PY) approximation for nonuniform fluids, with no shift of the chemical potential, and the hydrostatic linear response (HLR) equation, where the chemical potential is shifted by the local value of phi (r) The HLR equation gives exact results for very slowly varying phi (r) and reduces to the PY approximation for hard core phi (r), where generally accurate results are found. We try to develop a systematic way of choosing an optimal local shift in the SLR equation for general phi (r) by requiring that the predicted rho (r) is insensitive to small variations about the appropriate local shift, a property that the exact expansion to all orders would obey. The resulting insensitivity criterion (IC) gives a theory that reduces to the HLR equation for slowly varying phi (r), and is much more accurate than HLR both for very narrow slits, where the IC agrees with exact results, and for fields confined to ``tiny'' regions that can accomodate at most one particle, where the IC gives very accurate (but not exact) results.Comment: Accepted for publication in Journal of Physical Chemistry

Hydrophobicity Scaling of Aqueous Interfaces by an Electrostatic Mapping

An understanding of the hydrophobicity of complex heterogeneous molecular assemblies is crucial to characterize and predict interactions between biomolecules. As such, uncovering the subtleties of assembly processes hinges on an accurate classification of the relevant interfaces involved, and much effort has been spent on developing so-called "hydrophobicity maps." In this work, we introduce a novel electrostatics-based mapping of aqueous interfaces that focuses on the collective, long-wavelength electrostatic response of water to the presence of nearby surfaces. In addition to distinguishing between hydrophobic and hydrophilic regions of heterogeneous surfaces, this electrostatic mapping can also differentiate between hydrophilic regions that polarize nearby waters in opposing directions. We therefore expect this approach to find use in predicting the location of possible water-mediated hydrophilic interactions, in addition to the more commonly emphasized hydrophobic interactions that can also be of significant importance.Comment: 11 pages, 7 figures in J. Phys. Chem. B (2014

Dissecting Hydrophobic Hydration and Association

We use appropriately defined short ranged reference models of liquid water to clarify the different roles local hydrogen bonding, van der Waals attractions, and long ranged electrostatic interactions play in the solvation and association of apolar solutes in water. While local hydrogen bonding in- teractions dominate hydrophobic effects involving small solutes, longer ranged electrostatic and dis- persion interactions are found to be increasingly important in the description of interfacial structure around large solutes. The hydrogen bond network sets the solute length scale at which a crossover in solvation behavior between these small and large length scale regimes is observed. Unbalanced long ranged forces acting on interfacial water molecules are also important in hydrophobic association, illustrated here by analysis of the association of model methane and buckminsterfullerene solutes.Comment: 14 page