Phase multicomponent system surfaces

We consider a two-phase, multicomponent system in which there is one planar surface. The state of the system is defined by assigning values to the entropy and volume of the system, the area of the surface, and the mole numbers of the components. The differential of the energy of the system is... 

We choose the total system to be the condenser and the entire dielectric medium. The condenser is immersed in the medium which, for purposes of this discussion, is taken to be a single-phase, multicomponent system. The pressure on the system is the pressure exerted by the surroundings on a surface of the dielectric. In setting up the thermodynamic equations we omit the properties of the metal plates, because these remain constant except for a change of temperature. The differential change of energy of the system is expressed as a function of the entropy, volume, and mole numbers, but with the addition of the new work term. Thus,... 

A curious example is that of the distribution of benzene in water benzene will initially spread on water, then as the water becomes saturated with benzene, it will round up into lenses. Virtually all of the thermodynamics of a system will be affected by the presence of the surface. A system containing a surface may be considered as being made up of three parts two bulk phases and the interface separating them. Any extensive thermodynamic property will be apportioned among these parts. For example, in a two-phase multicomponent system, the extra amount of an i component that can be accom-mondated in the system due to the presence of the interface ( ) may be expressed as Qi Qii where is the total number of molecules of i in the whole system, Vj and Vjj are the volumes of phases I and II, respectively, and Q and Qn are the concentrations of i in phases I and II, respectively. The surface (excess) concentration of i is defined as Fj = A, where A is the surface area. At equilibrium, the chemical potential of any component is the same in each bulk phase and at the surface. The Gibbs adsorption equation, which is one of the most widely used expression in surface and colloid science is shown in Eq. (2) ... 

We consider a multicomponent system consisting of two phases separated by a planar surface in a container of fixed volume. The surface has some thickness, as shown by the slant lines in Figure 13.1. We have already stated that some properties, such as the density or the concentration of the components, change rapidly but continuously across the surface. Such behavior is illustrated by the curve in Figure 13.2, where l is measured along a line normal to the surface. Imaginary boundaries (a and b in Figs. 13.1 and 13.2) are placed in the system so that each boundary lies close to the real surface but at a position within the bulk phases where the properties are those of the bulk phases. The system is thus made to consist of three... 

The second subject is the effect of the surface on the chemical potential of a component contained in a small drop. We consider a multicomponent system in which one phase is a bulk phase and the second phase is kept constant with the conditions that the interface between the two phases is contained wholly within the bulk phase and does not affect the external pressure. The differential of the Gibbs energy of a two-phase system may be written as... 

The interfacial layer is the inhomogeneous space region intermediate between two bulk phases in contact, and where properties are notably different from, but related to, the properties of the bulk phases (see Figure 6.1). Some of these properties are composition, molecular density, orientation or conformation, charge density, pressure tensor, and electron density [2], The interfacial properties change in the direction normal to the surface (see Figure 6.1). Complex profiles of interfacial properties take place in the case of multicomponent systems with coexisting bulk phases where attractive/repulsive molecular interactions involve adsorption or depletion of one or several components. 

In all experiments, a constant silver layer thickness of three monolayers was initially deposited. In the multicomponent system, Cd diffuses towards S under thin layer conditions" established by a 2D CdxAgy surface alloy. In the one-component systems, Cd diffuses towards S under semi-infinite conditions. A phase transition... 

In addition to its capability of imaging the topography of polymer surfaces with virtually eliminated shear forces, intermittent contact (tapping) mode AFM, can also be useful to probe various surface properties, such as adhesive or surface mechanical properties. Thereby AFM can help to identify and quantify the abundance and distribution of the phases present in multicomponent systems. As shown already... 

The a and P phases have a favorable balance of these two sites necessary to effect the rate-determining first hydrogen abstraction. The multicomponent system possesses the greatest number of active surface sites having the proper structure and composition and a solid state structure with the ability to rapidly reconstitute these surface sites with bulk lattice oxygen. 

Several formalisms have been developed leading to what may be called practical thermodynamics. These treatments include the analog of solution thermodynamics, where the adsorbent and the adsorbate are considered as components in a two-phase equilibrium [6]. Another way to study the system is to use the surface excess approach, whereby the properties of the adsorbed phase are determined in terms of the properties of the real two-phase multicomponent... 

However, in normal phase adsorption systems (or liquid-solid chromatography) the interaction of the mobile phase solvent with the solute is often less Important than the competing Interactions of the mobile phase solvent and the solute with the stationary phase adsorption sites. Solute retention is based upon a displacement mechanism. Multicomponent mobile phases and their combination to optimize separations in liquid-solid chromatography have been studied in detail (31-35). Here, solvents are classified as to their interaction with the adsorption surface (Reference 32, in particular) ... 

For non-porous catalyst pellets the reactants are chemisorbed on their external surface. However, for porous pellets the main surface area is distributed inside the pores of the catalyst pellets and the reactant molecules diffuse through these pores in order to reach the internal surface of these pellets. This process is usually called intraparticle diffusion of reactant molecules. The molecules are then chemisorbed on the internal surface of the catalyst pellets. The diffusion through the pores is usually described by Fickian diffusion models together with effective diffusivities that include porosity and tortuosity. Tortuosity accounts for the complex porous structure of the pellet. A more rigorous formulation for multicomponent systems is through the use of Stefan-Maxwell equations for multicomponent diffusion. Chemisorption is described through the net rate of adsorption (reaction with active sites) and desorption. Equilibrium adsorption isotherms are usually used to relate the gas phase concentrations to the solid surface concentrations. 

Rates of Diffusion. When the solid and liquid of a multicomponent system are in thermodynamic equilibrium, the composition of the solid wul usually differ from that of the liquid. When the system is submitted to further melting or crystallization, the composition of at least one of the phases will change in the vicinity of the contact surface. Diffusion tends to equalize the concentration differences occurring both in the solid and in the liquid phases and should, therefore, be promoted. 

The following is a summary, based on Ref. 1, of the types of molecular interactions that are important in understanding the structure and phase behavior of surfaces and interfaces. Because they are multicomponent, the interactions in systems with surfaces and interfaces are often related to the interactions between molecules in a particular type of medium. This is particularly important for self-assembling systems composed of surfactants or polymers, where the interactions and the subsequent equilibrium structures are strongly influenced by the type of solvent. 

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