Surface, chemical potential excess concentration

If the species is neutral, its chemical potential p% can be varied by changing its concentration and hence its activity ay. dpt — RT d nat. In this case the determination of the surface excesses offers no difficulty in principle. However, if a species is charged, its concentration cannot be varied independently from that of a counterion, since the solution must be electrically neutral. To be specific, we consider the case of a 1-1 electrolyte composed of monovalent ions A and D+. The electro capillary equation then takes the form ... 

Thus, in principle, we could determine the adsorption excess of one of the components from surface tension measurements, if we could vary ii independently of l2. But the latter appears not to be possible, because the chemical potentials are dependent on the concentration of each component. However, for dilute solutions the change in p for the solvent is negligible compared with that of the solute. Hence, the change for the solvent can be ignored and we obtain the simple result that... 

Any electrons which reach the oxide—oxygen interface will be quickly utilized in the formation of 0" ions, and similarly, any positive holes which manage to reach the metal—oxide interface will be quickly annihilated by electrons from the parent metal. The asymmetrical surface reactions thus lead us to expect widely different electron concentrations in the oxide at the two interfaces of the oxide. This difference in electron concentration is equivalent to a difference in the chemical potential for the electronic species at the two interfaces. As in the case of the ionic defect species, such differences in concentration (and chemical potential) can be expected to produce particle currents of the defect species in question. If the primary electronic defects are excess electrons, then we can expect an electron particle current from metal to oxygen if the primary electron defects are the positive holes, then we can expect a positive-hole particle current from oxygen to metal. Of course, an intermediate situation is also possible in which electrons flow from the metal towards the oxygen while simultaneously a positive-hole current flows from the oxygen towards the metal, with recombination [8] (partial or total) occurring within the oxide film. 

Long ago, Langmuir suggested that the rate of deposition of particles on a surface is proportional to the density of particles in the vicinity of the surface and to the available area on the surface [1], However, the calculation of the available area is still an open problem. In a first approximation, one can assume that the available area is the total area of the surface minus the area already occupied by the adsorbed particles [1]. A better approximation can be obtained if the adsorbed particles, assumed to have the shape of a disk, are in thermal equilibrium on the surface, either because of surface diffusion and/or of adsorption/desorption kinetics. In this case, one can use one of the empirical equations available for the compressibility of a 2D gas of hard disks, calculate the chemical potential in excess to that of an ideal gas [2] and then use the Widom relation between the area available to one particle and its excess chemical potential on the surface (the particle insertion method) [3], The method is accurate at low densities of adsorbed particles, where the equations of state are accurate, but, in general, poor at high concentrations. The equations of state for hard disks are based on the virial expansion and only the first few coefficients of this... 

Let us suppose that under conditions of equilibrium a reversible change is made in the gas pressure and surface excess concentration of dp and dr, respectively, and that the corresponding change in the spreading pressure is ATI. Since the chemical potential must change by the same amount throughout the system, we may write ... 

When the two phases, gas and liquid, are in contact, component 1, the solvent, is present in large excess compared to component 2, the surfactant. In accordetnce with the Gibb s assumption, we choose a plane where the surface excess concentration of the solvent is equal to zero (Ff = 0) so that the changing surface tension is given only by the second term in the preceding equation. Because the chemical potential of the surfactant is given by... 

It follows from [4.6.8ff] that the Interfacicd excess entropy cem in principle be obtained from the temperature dependence of the surface tension. Such experiments require some scrutiny both technically (how to prevent evaporation ) and interpretationally (now to account for the temperature coefficients of chemical potentials at fixed concentrations ). Detailed studies are welcome. However, one striking trend may be mentioned ). Adsorption of (at least some) non-ionics is accompanied by an increase of entropy, whereas for the cationic Cj TMA Br" a decrease is observed. Again, more systematic study seems appropriate, before... 

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) ... 

The excess concentration Ti of the adsorbed component i may also be called the surface coverage of i in imits of molecitles/cm. Eqiration (8) shows that the specific sitrface free energy is only equal to the sitrface energy y, if the sum over all chemical potentials on the r.h.s. of Eq. (8) is zero for a one-component system this reqitires Tj = 0. In other words, for a clean sitrface, free of adsorbates, the first layer of the substrate has no surface excess, hence f = y. 

For a two-component Uquid-vapor system where the Gibbs dividing surface is defined so that the surface excess concentration of the solvent is zero (F = 0), the summation in Equation (9.12) is no longer necessary and a simple relationship between the surface tension of the liquid phase, o, and the surface excess concentration of solute i, F is obtained. It is therefore possible to employ experimentally accessible quantities such as surface tension and chemical potential to calculate the surface excess concentration of a solute species and to use that information to make other indirect observations about the system and its components. 

J. Willard Gibbs showed by thermodynamics that if a mixture of vapours, or a solution, is in contact with a surface, a change of concentration of a component occurs at the interface if the interfacial tension (surface tension) a is altered by such a change. If F is the excess of concentration at the interface above that in the body of the solution, and fi is the chemical potential of the component concerned F= - dajdfM (7). If the solute obeys the gas laws, and r and the concentration c are in mols per unit volume, (7) becomes ... 

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