Water density profile

I bulk membrane I membrane interface I vapor interface 

MembraneA apor Interfacial Width at Various Water Contents 

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The major difference of the water structure between the liquid/solid and the liquid/liquid interface is due to the roughness of the liquid mercury surface. The features of the water density profiles at the liquid/liquid interface are washed out considerably relative to those at the liquid/solid interface [131,132]. The differences between the liquid/solid and the liquid/liquid interface can be accounted for almost quantitatively by convoluting the water density profile from the Uquid/solid simulation with the width of the surface layer of the mercury density distribution from the liquid/liquid simulation [66]. 

Bostrom—Kunz—Ninham (BKN) Model for Ion-Solvation Forces. A new model for the short-ranged ion-solvation forces has been proposed recently.12 It is based on the observation that the air/water interface is not sharp, the water density increasing gradually, over a distance of a few angstroms, from zero (in air) to the density of bulk water. The water density profile was obtained by fitting the results of the molecular dynamics simulations with the empirical expression12... 

Figure 16. Water density profile along the z direction in the membrane/vapor interface (system 11) at X = 4.4, 6.4, 9.6 and 12.8. Hyperbolic tangents have been fitted to determine the interface thickness.

The molecular-level stmcture of the electrode/electrolyte interface was studied using two- and three- phase systems, including membrane/vapor, membrane/vapor/catalyst and membraneAfapor/ graphite systems. The simulations of a membraneAfapor interface show a region of dehydration near the interface. The interfacial thickness measured from the water density profile was found to decrease in width with increasing humidity. Hydronium ions displayed a preferential orientation at the interface, with the oxygen exposed to the vapor phase. 

It is tempting to try to estimate the characteristic density for water within the first peak of the water density profile. Such estimations are difficult, however, because this layer is significantly narrower than the diameter of a water molecule (roughly 2.8 A) and the density varies rapidly over this range, making the results somewhat ill-defined. Instead, it is more appropriate to estimate the... 

Fig. 7 Water density profile perpendicular to the pore wall depending on the temperature (black, 450 K gray, 300 K) and the relative humidity inside the pore. 100% equals the maximal water uptake at 1 bar pressure. The sulfur atoms of the S03 groups are marked as spheres and the water molecules are shown in ball and stick presentation. The point of origin to the distance perpendicular to the surface is the first layer of Si atoms, which are situated inside the pore surface. Reprinted with permission from Ref. 50. Copyright 2009, American Chemical Society.

Figure 49 Left the local diameter Pd M) at T = 550 K (solid line) and water density profile in one-phase region at about the bulk critical temperature T K 580 K (dashed line). Right the profiles of local diameters at several temperatures (T = 490,500,510,520,525,530,535,540,545, and 550 K) normalized by the respective bulk values as functions of the rescaled distance to the surface in pore with Hp = 30 k (data from [262]).

So, the water density profiles near the surfaces and their temperature evolution follow the laws of the surface critical behavior, which are universal for fluids and Ising magnets [254]. Nothing peculiar can be found in the surface critical behavior of water in comparison with LJ fluid (see Section 3.1). Many questions concerning the surface critical behavior of fluids and Ising magnets remain open [262] and should be studied. This may provide the possibility to describe the density profiles of water and other fluids analytically in a wide range of thermodynamic conditions near various surfaces. 

Figure 89 Water hexagon density profiles near the surface of the cylindrical pore with i = 20 A and Uo = -4.62 kcal/mol at T = 300 K. Water density profile is shown hy the dashed line in arbitrary scale.

Figure 126 Water density profiles near the surface of ELP (upper panel), Snase (middle panel), and near a smooth hydrophilic surface (lower panel). The vertical dashed lines show the most realistic width of hydration shell D = 4.5 A. Reprinted, with permission, from [566].

However, the general conclusion is that MPBE is in many cases a good approximation as compared to mean-field MC simulations or HNC calculations that account for ion size. This motivates us to use MPBE in improved calculations that account for monovalent ion potentials of mean force and water density profiles near surfaces. 

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