Density profiles at the interface

When the two phases separate the distribution of the solvent molecules is inhomogeneous at the interface this gives rise to an additional contribution to the free energy, which Henderson and Schmickler treated in the square gradient approximation [36]. Using simple trial functions, they calculated the density profiles at the interface for a number of system parameters. The results show the same qualitative behavior as those obtained by Monte Carlo simulations for the lattice gas the lower the interfacial tension, the wider is the interfacial region in which the two solvents mix (see Table 3). 

Figure 12.8 Density profile at the interface between two immiscible solutions the labelling indicates the values of a.

The term electrosteric stabilization is often used to describe how polyelectrolytes act as dispersants. Electrosteric stabilization is a combination of a pure electrostatic repulsion and a polymeric repulsion where the relative importance of the respective contributions is closely related to the segment density profile at the interface. If the polyelectrolyte adsorbs in a flat conformation, the polymeric repulsion is short-range in nature, and the stabilization mechanism is mainly... 

Fig. 6.7. The predicted, one-dimensional, mean-bulk temperatures versus location at various times are shown for a typical powder compact subjected to the same loading as in Fig. 6.5. It should be observed that the early, low pressure causes the largest increase in temperature due to the crush-up of the powder to densities approaching solid density. The "spike in the temperature shown on the profiles at the interfaces of the powder and copper is an artifact due to numerical instabilities (after Graham [87G03]).

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. 9 Simulated electrical potential and space charge density profiles at the water-1,2-DCE interface polarized at/= 5 in the absence (a) and in the presence (b) of zwitterionic phospholipids. The supporting electrolyte concentrations are c° = 20 mM and c = 1000 mM. The molecular area of the phospholipids is 150 A, and the corresponding surface charge density is a = 10.7 xC/cm. The distance between the planes of charge associated with the headgroups is d = 3 A. 

Fig. 10.11 The calculated (a) Nemst potential profile and (b) current density profile at the electro-lyte/anode interface for the standard case ( 1) in Table 10.2.

The computational efficiency of the simulation with the coarse-grained model permits the study of the process hy which cohesion of two thin films is obtained with n-alkanes Three different time scales are observed for healing of the density profile at the initial interface between the two films, redistribution of chain ends, and complete intermixing of the chains, with the time scale increasing in the order stated. 

The problem of the number density profile at the liquid/vapor interface, p z, 9), along the direction z perpendicular to the surface and as function of the molecular orientation 9, has been dealt with by Yang et al. (1991) in the case of water. It was concluded that there is a slight preference of the water dipoles at the surface to be directed downwards (i.e., with the hydrogen atoms towards the bulk liquid). This confirms earlier conclusions of Stillinger and Ben-Naim (1967), among others, who stressed the importance of the permanent quadrupole moment of the water molecules for the breaking of the symmetry in the direction of the dipole moment. 

The first information eoming from the application of the method regards the density profile across the interface. Density may be assumed to be constant in bulk liquids at the equilibrium, with local deviations around some solutes (these deviations belong to the family of cybotactic effects, on which something will be said later). At each type of liquid surface there will be some deviations in the density, of extent and nature depending on the system. 

According to this model, the concentration is equal to the initial concentration beyond a distance to the electrode equal to nebnst- At steady state this model leads to a mathematical discontinuity in the concentration profiles at this 5nernst distance from the electrode. The actual steady-state profile does not show any angular point. Therefore the model gives incorrect results in the area surrounding 5nh,nst- However, it makes it easy to describe the exact characteristics of the concentration profile at the interface, and therefore it gives a correct value for the current density. 

Grahame equation and also as the contact theorem [6]. This, fundamentally, is a relationship between the surface charge density, (Tq (which is defined as o-q = — Jpedy, with a SI unit of C/m ), and the limiting value of the ionic density profile at the substrate-fluid interface. For a single fiat surface with an infinite extent of the adjacent liquid, an expression for co can be obtained from the Poisson-Boltzmann equation as... 

Figure 1.1 Molecular layers of liquid molecules at a smooth solid surface, fa] The molecules close to the Interface form layers due to the geometrical boundary of the solid wall. This leads to an oscillation in the density profile near the interface, which decays within a few molecular diameters, a, toward the bulk of the disordered liquid, Pbuik- [b] The layered structure is enhanced in a thin film of the liquid confined between two such interfaces separated by the distance, D. [Figure adapted from Israelachvili. )...

Capillary wave theory considers the density variation at the interface to be the result of the superposition of thermally excited density fluctuations on a bare intrinsic profile. Mathematically, the instantaneous local density at a... 

The density profiles across the interface are depicted in Fig. 10(b). At low pressure the coexisting phases differ in the density of polymers. The density of the volatile solvent is almost equal in both phases, and very low. At the center of the interface there is a small excess of solvent. Upon increasing pressure, the density of solvent increases both in the vapor and in the liquid. The density of the polymer in the liquid decreases in turn. The interfacial excess of solvent increases and the profile becomes asymmetric most of the excess is found on the vapor side of the interface. The interfacial excess per unit area can be defined by... 

Lennard-Jones-de Boer-Michels form we have used. The exploration of inhomogeneous systems is a logical next step. At the moment only GFMC offers an unambiguous approach to the calculation of the density profile at an interface, for example. 

Fig. Ill-13. (a) Plots of molecular density versus distance normal to the interface a is molecular diameter. Upper plot a dielectric liquid. Lower plot as calculated for liquid mercury. (From Ref. 122.) (b) Equilibrium density profiles for atoms A and B in a rare-gas-like mixmre for which o,bb/ o,aa = 0.4 and q,ab is given by Eq. III-56. Atoms A and B have the same a (of Eq. m-46) and the same molecular weight of SO g/mol the solution mole fraction is jcb = 0.047. Note the strong adsorption of B at the interface. [Reprinted with permission from D. J. Lee, M. M. Telo de Gama, and K. E. Gubbins, J. Phys. Chem., 89, 1514 (1985) (Ref. 88). Copyright 1985, American Chemical Society.]...

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