Dipole density

There is, of course, a mass of rather direct evidence on orientation at the liquid-vapor interface, much of which is at least implicit in this chapter and in Chapter IV. The methods of statistical mechanics are applicable to the calculation of surface orientation of assymmetric molecules, usually by introducing an angular dependence to the inter-molecular potential function (see Refs. 67, 68, 77 as examples). Widom has applied a mean-held approximation to a lattice model to predict the tendency of AB molecules to adsorb and orient perpendicular to the interface between phases of AA and BB [78]. In the case of water, a molecular dynamics calculation concluded that the surface dipole density corresponded to a tendency for surface-OH groups to point toward the vapor phase [79]. 

The oscillating electric dipole density, P (the polarization), that is induced by the total incident electric field,... 

Pc- (c) Dipole density p. (d) Water contribution to the surface potential x calculated from the charge density Pc by means of Eq. (1). All data are taken from a 150 ps simulation of 252 water molecules between two mercury phases with (111) surface structure using Ewald summation in two dimensions for the long-range interactions. 

The dipole density profile p (z) indicates ordered dipoles in the adsorbate layer. The orientation is largely due to the anisotropy of the water-metal interaction potential, which favors configurations in which the oxygen atom is closer to the surface. Most quantum chemical calculations of water near metal surfaces to date predict a significant preference of oxygen-down configurations over hydrogen-down ones at zero electric field (e.g., [48,124,141-145]). The dipole orientation in the second layer is only weakly anisotropic (see also Fig. 7). 

Figure 2. (a) Density of water oxygens and hydrogens, (b) The water dipole density profile and the associated potential drop, (c) The total charge density profile and the potential drop, as a function of the distance between two parallel slabs of the Pt( 100) surface at T = 300 K. 

Figure 6. The water-dipole density pioflle for various external electric field strengths. Other details are as in Fig. 5.

One of the models that has had considerable success for predicting solvation processes of dipoles in non-hydrogen-bonded solvents is the dielectric continuum model [5,14]. In this model, the amount of solvation will depend on the dipole density— that is, the molar concentration and strength of dipoles. While the position of the absorption maximum is not directly related to the energy of solvation that a molecule experiences, one would expect the two to be very strongly correlated. However, for the three different... 

Much like the RISM method, the LD approach is intermediate between a continuum model and an explicit model. In the limit of an infinite dipole density, the uniform continuum model is recovered, but with a density equivalent to, say, the density of water molecules in liquid water, some character of the explicit solvent is present as well, since the magnitude of the dipoles and their polarizability are chosen to mimic the particular solvent (Papazyan and Warshel 1997). Since the QM/MM interaction in this case is purely electrostatic, other non-bonded interaction terms must be included in order to compute, say, solvation free energies. When the same surface-tension approach as that used in many continuum models is adopted (Section 11.3.2), the resulting solvation free energies are as accurate as those from pure continuum models (Florian and Warshel 1997). Unlike atomistic models, however, the use of a fixed grid does not permit any real information about solvent structure to be obtained, and indeed the fixed grid introduces issues of how best to place the solute into the grid, where to draw the solute boundary, etc. These latter limitations have curtailed the application of the LD model. 

In order to relate these molar quantities to properties of the single molecule we can apply arguments of statistical classical mechanics. At moderate intensity, the electric field gives rise to a dipole density by electronic and atomic translation (or deformation) effects and by rotation (or orientation) effects. We recall that the rotation effects are counteracted by the thermal movement of the molecules and thus they are strongly dependent on the temperature T whereas the translation effects are only slight dependent on T because they are intramolecular phenomena. The general expression to be used to define the Fourier amplitudes (2.165)-(2.167) is ... 

The label in on the integration symbol means that integration is limited to the region occupied by the solute from which solvent dipole density is expelled. The inverse jj-" 1 is defined as... 

In the applications of the PCM approach to SD, the focus so far has been mainly on the comparison with experiment [45,46] and very good agreement with experimental results has been obtained for C153 in several polar liquids [45], In the case of SD in water, the theory was implemented using two different approaches to obtain e(w), either a fit to experimental data [45] or a calculation of the dipole density time correlation from molecular dynamics simulation [46], While the results for S(t) that use experimental dielectric permittivity as input look quite similar to those shown in Figure 3.16, the results based on the simulation data exhibit more pronounced oscillatory features at the characteristic frequency of the hydrogen bond librations. 

In the case of a polar liquid at low k(k = k ), these components can be related to Fourier-Laplace transforms of the time correlations of the appropriate components of the collective dipole density... 

Thus the formulation of the dielectric susceptibility in terms of the charge rather than the dipole density extends the theory to molecules that are nondipolar, but have high enough higher electric moments to exhibit a predominantly electrostatic solvation dynamics mechanism. 

Figure 3.18 Transverse (a) and (b) longitudinal dipole density time correlations for SPC/E water at 308 K. Results for several k values, ranging from k= 0.2545 A-1 to /c10 = VTo k are shown. Data are from B. M. Ladanyi and B.-C. Perng, in L. R. Pratt and C. Hummer (eds) Simulation and Theory of Electrostatic Interactions in Solution, AIP Conf. Proc., Melville, NY, 1999, Vol. 492, pp. 250-264.

In nonprotic polar solvents, hydrogen bond librations are absent and the librational features appearing in charge and longitudinal dipole density TCFs have lower characteristic frequencies. This is illustrated for acetonitrile in Figure 3.20. Also shown is a comparison between [Pg.379]

The Gruen—Marcelja model could relate the hydration force to the physical properties of the surfaces by assuming that the polarization of water near the interface is proportional to the surface dipole density.9 This assumption led to the conclusion that the hydration force is proportional to the square of the surface dipolar potential of membranes (in agreement with the Schiby—Ruckenstein model),6 a result that was confirmed by experiment.10 However, subsequent molecular dynamics simulations revealed that the polarization of water oscillated in the vicinity of an interface, instead of being monotonic.11 Because the Gruen—Marcelja model was particularly built to explain the exponential decay of the polarization, it was clearly invalidated by the latter simulations. Other conceptual difficulties of this model have been also reported.12 13... 

It will be shown in what follows that the oscillations of the polarization are due to the structuring of water in a particular form, the coupling interactions between neighboring dipoles, the electrolyte concentration, and the boundary conditions (surface charge and surface dipole density). 

To examine the effect of the surface dipole density, we consider that the polarization on the surface acquires the value... 

There are two main reasons for the departure of the present model from the DLVO theory. First, the constitutive equations, which relate the polarization to the electric potential, are different. Second, the boundary conditions are different, since the average polarization in the DLVO theory is directly related to the surface charge, while in the present treatment it depends also on the surface dipole density. 

The polarization model predicts that the interaction between nanoparticles depends not only on the surface charge density, but also on the surface dipole density. As the concentration of electrolyte increases, the surface charge density decreases, due to the recombination of ions with surface groups, but the density of surface dipoles increases. At relatively low salt concentrations, the repulsion due to the dou-... 

---