Surface equilibrium concentration

Jv,Q is the exchange current density in the valence hand at equilibrium, ps denotes the equilibrium surface concentration of holes, ps represents the dynamic surface concentration of holes related to bulk surface hole concentration po by ... 

Poskus and Agafonovas [483] have applied radioactive Tl-204 to study its UPD on a polycrystalline gold electrode in alkaline solutions. The potential dependence of the equilibrium surface concentration obtained from the radiometric method has been compared to that calculated from CV. Surface concentration of Tl decreased monotonically as the potential was changed from the more positive Nern-stian values. This dependence exhibited a minimum without reaching zero. At more positive potentials (with respect to the minimum), adsorption of T1+ induced by specifically adsorbed hydroxyl anions occurred. 

Standard state free energies (AG°,js) and entropies (ASacjs) may also be determined from GSC retention data if ideal conditions are assumed. For the adsorbate behaving as an ideal gas in the mobile phase, the standard state is defined as a partial pressure of 1 atm. The adsorbed standard state is defined as a two-dimensional perfect gas at 1 atm where the mean distance between adsorbed molecules is the same as in the three dimensional gas phase standard state. Thus, the sorbate equilibrium surface concentration Cg becomes 4.07 x 10 9/T (moles/cm2) and the gas phase sorbate concentration becomes 4.07 x 10- /TK ,. 

The equilibrium surface concentrations on the solid phase qsl and qS2 are given by equation (3). To obtain the concentrations Cs and CS2 In the fluid phase, the two equations in equation (3) must be solved at each time step. This was done using the Newton-Raphson Method for solving nonlinear equations. 

The subscript G specifies elasticity determined from isothermal equilibrium measurements, such as for the spreading pressure-area method, which is a thermodynamic property and is termed the Gibbs surface elasticity, EG. EG occurs in very thin films where the number of molecules is so low that the surfactant cannot restore the equilibrium surface concentration after deformation. 

Kinetic models for crystal growth usually quantify the interface velocity, which is a direct measure of the crystal growth rate. The rate of stable cluster formation on a surface is proportional to the equilibrium surface concentration of clusters (of critical radius rc), nrc, and the frequency of addition of adatoms to these clusters, va (Howe, 1997) ... 

Note. V is the molar volume, JVyi is Advogadro s number, is the equilibrium concentration, D is the diffusion coefficient, sub-s surface, hHfiB the heat of fusion, t) is the Damkohler number. Ah is the thermal conductivity, i die area shape factor for surface nuclei , y, is the distance between steps, n is the equilibrium surface concentration, p = 1 - o-JS is one minus the maximum surface supersaturation divided by the solution supersaturation, and p is the density. ihG - pl- fPMpAkBT In S)... 

Before utilizing equation (92) in equation (88), let us consider the equilibrium surface concentration of an adsorbed gas as predicted by equation (92). Suppose that N — 1 and no surface reaction occurs. Equation (92) then reduces to... 

Equations 9 and 10 assume instantaneous establishment of equilibrium surface concentration as a result of sudden change in the ambient environment in the sample chamber. However, it was observed experimentally from the time derivative trace (dM/dt) that a finite response time is required to establish new equilibrium conditions see Figure 7). Under ideal conditions, the rate of sorption or desorption should, to a good approximation, be represented by Curve X. The actual observed curve. Curve R, has a distinct maximum. The position of the maximum... 

Meads equilibrium surface concentration on native substrate mol cm actual concentration of species i at the interface S/El concentration of species i bulk concentration of species i adsorption capacitance (adatom pseudo-capacitance) double layer capacitance... 

Disharmonies in the Conception of the Direct 0 /Antiozonant Reaction Importance. Four antiozonant theories have been formulated within the last 25 years. Ozone scavenging theory suggests a preferential direct reaction of an antiozonant with ozone on the rubber surface as a decisive process (26-27). As the antiozonant is depleted via direct ozonation on the surface, fresh antiozonant diffuses rapidly from the rubber bulk to reestablish the equilibrium surface concentration. At a comparable additive concentration and migration rate, the antiozonant efficiency of an additive should be therefore dependent on its ozonation rate and the vulcanizate will be protected until the antiozonant is depleted below the lowest critical concentration. From this point of view, the ozonation rate seems to be a more important factor than the total amount of ozone scavenged by one mole of an antiozonant (this latter phenomenon may be called ozonation factor). Relations between antiozonant efficiency in vulcanizate and antiozonant ozonation rate or antiozonant surface concentration have been indeed reported in some papers and an appreciable higher ozonation rate of PD in comparison with rubber unsaturation, a preferential consumption of an antiozonant in model olefin solution or in rubber were observed. The rubber surface was not attacked by ozone until the antiozonant was almost completely consumed (28). ... 

The times involved in foam production are in the range of 0.001-0.1 s the value of D/n for the usual surface-active solute (with a hydrocarbon chain of 12-18 carbon atoms) is of the order of 1 x 10-6 cm2/s equilibrium surface concentrations for this same type of material are about 2 x 1014 molecules/cm2. Thus, if the time needed to replace the solute at a new surface is to be no shorter than the time... 

Many surfactant solutions show dynamic surface tension behavior. That is, some time is required to establish the equilibrium surface tension. If the surface area of the solution is suddenly increased or decreased (locally), then the adsorbed surfactant layer at the interface would require some time to restore its equilibrium surface concentration by diffusion of surfactant from or to the bulk liquid. In the meantime, the original adsorbed surfactant layer is either expanded or contracted because surface tension gradients are now in effect, Gibbs—Marangoni forces arise and act in opposition to the initial disturbance. The dissipation of surface tension gradients to achieve equilibrium embodies the interface with a finite elasticity. This fact explains why some substances that lower surface tension do not stabilize foams (6) They do not have the required rate of approach to equilibrium after a surface expansion or contraction. In other words, they do not have the requisite surface elasticity. 

A plot of this equation is shown in Figure 1.4.3. When i = 0,E = gq and the system is at equilibrium. Surface concentrations are then equal to the bulk values. When current flows. 

Surfaces are heterogeneous on the atomic scale. Atoms appear in flat terraces, at steps, and at kinks. There are also surface point defects, vacancies, and adatoms. These various surface sites achieve their equilibrium surface concentrations through an atom-transport process along the surface that we call surface diffusion. Adsorbed atoms and molecules reach their equilibrium distribution on the surface in the same way. This view of surface diffusion as a site-to-site hopping process leads to the random-walk picture, in which the mean-square displacement of the adsorbed particle along the. r-component of the coordinate is given by... 

By accepting that there is a maximum surface concentration (Loo) and given an equilibrium constant Kl which relates the rates of adsorption vs. desorption, we may write the equilibrium surface concentration as... 

The stability of a single foam film can be explained by the Gibbs elasticity E, which results from the reduction in equilibrium surface concentration of adsorbed surfactant molecules when the film is extended (20). This produces an increase in equilibrium surface tension that acts as a restoring force. The Gibbs elasticity... 

Next we estimate the ratio between the characteristic rate of kinetic flux to the rate of convection. To obtain the former, we linearize the kinetic flux j around the equilibrium surface concentration Fq and sublayer concentration (i.e. write F = Fq H- AF and Cg = Co 4- AC and linearize the leading order is zero by definition of equilibrium). We find... 

Here cOi is the frequency of vibrations of an ion in the potential well, and is the equilibrium surface concentration of ions in phase 1. 

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