Solid-liquid interface computer simulation

Over the last two decades the exploration of microscopic processes at interfaces has advanced at a rapid pace. With the active use of computer simulations and density functional theory the theory of liquid/vapor, liquid/liquid and vacuum/crystal interfaces has progressed from a simple phenomenological treatment to sophisticated ah initio calculations of their electronic, structural and dynamic properties [1], However, for the case of liquid/crystal interfaces progress has been achieved only in understanding the simplest density profiles, while the mechanism of formation of solid/liquid interfaces, emergence of interfacial excess stress and the anisotropy of interfacial free energy are not yet completely established [2],... 

We now turn to the prediction of the suspension mechanism of the ballotini versus the speed ratio in the coaxial mixer. The average volume concentration is 1%, and the solids are initially at rest in the tank bottom. The first case investigated corresponds to the motion of the sole anchor arm at a speed of 40 rpm. Simulations are carried out in the Lagrangian frame of reference (fixed anchor, rotating vessel). Fig. 12 shows the predicted and experimental solid volume fraction at equilibrium. The computation of the solid-liquid interface at the bottom is fairly well... 

One of the recent successes in computCT simulation of clay mina-al hydrates is that the structure of interlayer wate in toms of quantitatively obtainable content called total radial distributionfunction was achieved by both Monte Carlo simulations and neutron diffraction methods (111,112). The accuracy of the method and the predicting power of the molecular simulation of this complex solid-liquid interface was first confirmed for the intolayCT structure of 2 1 clay mineral smectite. Computational studies on the clay mina-al-water interface using quantum mechanics, molecular mechanics, Monte Carlo, and molecular dynamics simulations are summarized in Table 5. 

While the Navier-Stokes equation is a fundamental, general law, the boundary conditions are not at all dear. In fluid mechanics, one usually relies on the assumption that when liquid flows over a solid surface, the liquid molecules adjacent to the solid are stationary relative to the solid and that the viscosity is equal to the bulk viscosity. We applied this no-slip boundary condition in Eq. (6.18). Although this might be a good assumption for macroscopic systems, it is questionable at molecular dimensions. Measurements with the SFA [644—647] and computer simulations [648-650] showed that the viscosity of simple liquids can increase many orders of magnitude or even undergo a liquid to solid transition when confined between solid walls separated by only few molecular diameters water seems to be an exception [651, 652]. Several experiments indicated that isolated solid surfaces also induce a layering in an adjacent liquid and that the mechanical properties of the first molecular layers are different from the bulk properties [653-655]. An increase in the viscosity can be characterized by the position of the plane of shear. Simple liquids often show a shear plane that is typically 3-6 molecular diameters away from the solid-liquid interface [629, 644, 656-658]. 

The interface between a solid electrode and a liquid electrolyte is a complicated many-particle system, in which the electrode ions and electrons interact with solute ions and solvent ions or molecules through several chatmels of interaction, including forces due to quantum-mechanical exchange, electrostatics, hydrodynamics, and elastic deformation of the substrate. Over the last few decades, surface electrochemistry has been revolutionized by new techniques that enable atomic-scale observation and manipulation of solid-liquid interfaces, yielding novel methods for materials analysis, synthesis, and modification. This development has been paralleled by equally revolutionary developments in computer hardware and algorithms that by now enable simulations with millions of individual particles, so there is now significant overlap between system sizes that can be treated computationally and experimentally. 

The thickness of the gas-liquid interface is set as 3A based on the parameters used in the case of Sussman (1998), with the same density-ratio on the interface and similar Reynolds number. An interface thickness of 5A is also examined in the simulation and no significant improvement is observed. The accurate prediction of the bubble shape (shown in Figs. 3 and 4) can be attributed, in part, to the manner in which the surface-tension force is treated as a body force in the computation scheme. Specifically, since the surface-tension force acting on a solid particle is considered only when a solid particle crosses the gas-liquid interface and the solid particle is considered as a point, the accuracy of the calculation of this force can be expected if the surface tension is interpreted as a body force acting on each grid node near the interface. 

One of the fundamental problems in chemistry is understanding at the molecular level the effect of the medium on the rate and the equilibrium of chemical reactions which occur in bulk liquids and at surfaces. Recent advances in experimental techniques[l], such as frequency and time-resolved spectroscopy, and in theoretical methods[2,3], such as statistical mechanics of the liquid state and computer simulations, have contributed significantly to our understanding of chemical reactivity in bulk liquids[4] and at solid interfaces. These techniques are also beginning to be applied to the study of equilibrium and dynamics at liquid interfaces[5]. The purpose of this chapter is to review the progress in the application of molecular dynamics computer simulations to understanding chemical reactions at the interface between two immiscible liquids and at the liquid/vapor interface. 

Figure 10. Electronic absorption line shape of N,N -diethyl-p-nitroaniline in several bulk and interfacial systems, calculated by molecular dynamics computer simulation at 300K. (a) The spectrum in bulk water (solid line) and at the water liquid/vapor interface (dashed line), (b) The spectrum in bulk 1,2-dichloroethane (solid line) and at the water/1,2-dichloroethane interface.

The first computer simulation of liquid-solid coexistence, carried out by Hiwatari et al. was the molecular dynamics study of the fee (100) surface of a system of atoms interacting through truncated Lennard-Jones repulsive potentials. Subsequent molecular dynamics studies have looked at the same interface for Lennard-Jones and repulsive potentials, at the fee (111)... 

This name covers all polymer chains (diblocks and others) attached by one end (or end-block) at ( external ) solid/liquid, liquid/air or ( internal ) liquid/liq-uid interfaces [226-228]. Usually this is achieved by the modified chain end, which adsorbs to the surface or is chemically bound to it. Double brushes may be also formed, e.g., by the copolymers A-N, when the joints of two blocks are located at a liquid/liquid interface and each of the blocks is immersed in different liquid. A number of theoretical models have dealt specifically with the case of brush layers immersed in polymer melts (and in solutions of homopolymers). These models include scaling approaches [229, 230], simple Flory-type mean field models [230-233], theories solving self-consistent mean field (SCMF) equations analytically [234,235] or numerically [236-238]. Also first computer simulations have recently been reported for brushes immersed in a melt [239]. 

The behavior of polymers at a solid substrate is closely related to the behavior of maaomolecules in thin films. Either such a thin film can be fabricated by confining a polymer layer between two solid substrates or one can consider a polymer film that wets a solid substrate in contact with air orvacuum. As the liquid-vapor interface that constitutes the free surface of the supported film resembles the interface between a polymer liquid and a hard, nonattractive solid substrate at the coexistence pressure, both situations are qualitatively similar. The former situation is often employed in computer simulations, whereas the latter setup is of great praaical interest owing to applications of thin polymer films as protective coating layers that control wettability, adhesion, or friction. 

Well-defined flow characteristics in a microfluidic device can also reveal new aspects of mass transfer. For example, it was possible to elucidate the relative rates of the mass transfer at the bubble cups and at the lubricating fluid interface between the gas bubble and the solid wall (see the sidebar figure). Van Eaten and Krishna (2004) have demonstrated through computational flnid dynamics (CFD) simulations that the mass transfer rates at the hemispherical babble cups and the lubricating liquid interfaces of the rising Taylor gas flows contribute differently to the rates of the mass transfer. 

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