Liquid surface, density profile

Density profiles are the central quantity of interest in computer simulation studies of interfacial systems. They describe the correlation between atom positions in the liquid and the interface or surface . Density profiles play a similarly important role in the characterization of interfaces as the radial distribution functions do in bulk liquids. In integral equation theories this analogy becomes apparent when formalisms that have been established for liquid mixtures are employed. Results for interfacial properties are obtained in the simultaneous limit of infinitesimally small particle concentration and infinite radius for one species, the wall particle (e.g., Ref. 125-129). Of course, this limit can only be taken for a smooth surface that does not contain any lateral structure. Among others, this is one reason why, up to now, integral equation theories have not been able to move successfully towards realistic models of the double layer. 

FIGURE 6.17 Schematic representation of liquid number density profiles (a) at a vapor-liquid interface 2 is a measure of the molecular-scale surface roughness (b) in the vicinity of a wall-liquid interface (c) between two hard walls at a distance d. (Reprinted from Intermolecular and Surface Forces, 3rd ed., Israelachvili, J.N. Copyright 2010, with permission from Elsevier.)... 

Surface Density Profile in Liquid Metals A Semi-empirical Treatment of the Screening Effect, in Proc. 6th Int. Conf. on Liquid and Amorphous Metals, Z. Phys. C 1S6S, 445-450. 

Fig. ni-7. (a) Interfacial density profile for an argonlike liquid-vapor interface (density in reduced units) z is the distance normal to the surface, (b) Variations of P-p of Eq. ni-40 (in reduced units) across the interface. [From the thesis of J. P. R. B. Walton (see Ref. 66).]... 

It was noted in connection with Eq. III-56 that molecular dynamics calculations can be made for a liquid mixture of rare gas-like atoms to obtain surface tension versus composition. The same calculation also gives the variation of density for each species across the interface [88], as illustrated in Fig. Ill-13b. The density profiles allow a calculation, of course, of the surface excess quantities. 

Equilibration of the interface, and the establislnnent of equilibrium between the two phases, may be very slow. Holcomb et al [183] found that the density profile p(z) equilibrated much more quickly than tire profiles of nonnal and transverse pressure, f yy(z) and f jfz), respectively. The surface tension is proportional to the z-integral of Pj z)-Pj z). The bulk liquid in the slab may continue to contribute to this integral, indicatmg lack of equilibrium, for very long times if the initial liquid density is chosen a little too high or too low. A recent example of this kind of study, is the MD simulation of the liquid-vapour surface of water at temperatures between 316 and 573 K by Alejandre et al [184]. 

The simulated free surface of liquid water is relatively stable for several nanoseconds [68-72] because of the strong hydrogen bonds formed by liquid water. The density decrease near the interface is smooth it is possible to describe it by a hyperbolic tangent function [70]. The width of the interface, measured by the distance between the positions where the density equals 90% and 10% of the bulk density, is about 5 A at room temperature [70,71]. The left side of Fig. 3 shows a typical density profile of the free interface for the TIP4P water model [73]. 

The principal effect of the presence of a smooth wall, compared to a free surface, is the occurrence of a maximum in the density near the interface due to packing effects. The height of the first maximum in the density profile and the existence of additional maxima depend on the strength of the surface-water interactions. The thermodynamic state of the liquid in a slit pore, which has usually not been controlled in the simulations, also plays a role. If the two surfaces are too close to each other, the liquid responds by producing pronounced density oscillations. 

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]. 

Fig. 10 shows the radial particle densities, electrolyte solutions in nonpolar pores. Fig. 11 the corresponding data for electrolyte solutions in functionalized pores with immobile point charges on the cylinder surface. All ion density profiles in the nonpolar pores show a clear preference for the interior of the pore. The ions avoid the pore surface, a consequence of the tendency to form complete hydration shells. The ionic distribution is analogous to the one of electrolytes near planar nonpolar surfaces or near the liquid/gas interface (vide supra). 

Stelzer et al. [109] have studied the case of a nematic phase in the vicinity of a smooth solid wall. A distance-dependent potential was applied to favour alignment along the surface normal near the interface that is, a homeotropic anchoring force was applied. The liquid crystal was modelled with the GB(3.0, 5.0, 2, 1) potential and the simulations were run at temperatures and densities corresponding to the nematic phase. Away from the walls the molecules behave just as in the bulk. However, as the wall is approached, oscillations appear in the density profile indicating that a layered structure is induced by the interface, as we can see from the snapshot in Fig. 19. These layers are... 

We shall illustrate the applicability of the GvdW(S) functional above by considering the case of gas-liquid surface tension for the Lennard-Jones fluid. This will also introduce the variational principle by which equilibrium properties are most efficiently found in a density functional theory. Suppose we assume the profile to be of step function shape, i.e., changing abruptly from liquid to gas density at a plane. In this case the binding energy integrals in Ey can be done analytically and we get for the surface tension [9]... 

The eorresponding result for the surface tension [9] provides quite reasonable accuracy for a Leonard Jones fluid or an inert gas fluid, except helium whieh displays large quantum effeets. Thus we ean eonelude that the leading mechanisms of surface tension in a simple fluid is the loss of binding energy of the liquid phase at the gas-liquid interface and the seeond most important meehanism is likely to be the adsorption-depletion at the interface whieh ereates a moleeularly smooth density profile instead of an abrupt step in the density. 

Modern theories of electronic structure at a metal surface, which have proved their accuracy for bare metal surfaces, have now been applied to the calculation of electron density profiles in the presence of adsorbed species or other external sources of potential. The spillover of the negative (electronic) charge density from the positive (ionic) background and the overlap of the former with the electrolyte are the crucial effects. Self-consistent calculations, in which the electronic kinetic energy is correctly taken into account, may have to replace the simpler density-functional treatments which have been used most often. The situation for liquid metals, for which the density profile for the positive (ionic) charge density is required, is not as satisfactory as for solid metals, for which the crystal structure is known. 

A quantity of central importance in the study of uniform liquids is the pair correlation function, g r), which is the probability (relative to an ideal gas) of finding a particle at position r given that there is a particle at the origin. All other structural and thermodynamic properties can be obtained from a knowledge of g r). The calculation of g r) for various fluids is one of the long-standing problems in liquid state theory, and several accurate approaches exist. These theories can also be used to obtain the density profile of a fluid at a surface. 

The study of liquids near solid surfaces using microscopic (atomistic-based) descriptions of liquid molecules is relatively new. Given a potential energy function for the interaction between liquid molecules and between the liquid molecules and the solid surface, the integral equation for the liquid density profile and the liquid molecules orientation can be solved approximately, or the molecular dynamics method can be used to calculate these and many other structural and dynamic properties. In applying these methods to water near a metal surface, care must be taken to include additional features that are unique to this system (see later discussion). 

The results for the density profile of water near other metals are also similar to the one discussed above. Howeva, the density profile of water near liquid mercury is significantly less pronounced than that of water near the Pt surface or the solid mercury surface, reflecting the fluidity of the metal, which smears out the profile. The oscillatory density profile of the mercury atoms is consistent with many theoretical and experimental studies of liquid metals and their surfaces. 

Retaining the approximations of an incompressible liquid phase, a discontinuous density profile and curvature independent surface tension the conditions are those studied by Rao, Berne and Kalos (2). The essential physics was unchanged from the usual treatment in an open system, except that a minimum in the free energy of formation is found which corresponds to the unique equilibrium phase separated state whose symmetry, in the absence of an external field, is spherical. 

Often the liquid structure close to an interface is different from that in the bulk. For many fluids the density profile normal to a solid surface oscillates about the bulk density with a periodicity of about one molecular diameter, close to the surface. This region typically extends... 

As we have seen in Section 6.6.1 such confined liquids may behave quite differently from the bulk lubricant. Near the surfaces, the formation of layered structures can lead to an oscillatory density profile (see Fig. 6.12). When these layered structures start to overlap, the confined liquid may undergo a phase transition to a crystalline or glassy state, as observed in surface force apparatus experiments [471,497-500], This is correlated with a strong increase in viscosity. Shearing of such solidified films, may lead to stick-slip motions. When a critical shear strength is exceeded, the film liquefies. The system relaxes by relative movement of the surfaces and the lubricant solidifies again. 

Vinyl acetate is a colorless, flammable liquid having an initially pleasant odor which quickly becomes sharp and irritating. Table 1 lists the physical properties of the monomer. Information on properties, safety, and handling of vinyl acetate has been published (5—9). The vapor pressure, heat of vaporization, vapor heat capacity, liquid heat capacity, liquid density, vapor viscosity, liquid viscosity, surface tension, vapor thermal conductivity, and liquid thermal conductivity profile over temperature ranges have also been published (10). Table 2 (11) lists the solubility information for vinyl acetate. Unlike monomers such as styrene, vinyl acetate has a significant level of solubility in water which contributes to unique polymerization behavior. Vinyl acetate forms azeotropic mixtures (Table 3) (12). 

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