Concentration surface

Gibbs equation of surface concentration This equation relates the surface tension (y) of a solution and the amount (T) of the solute adsorbed at unit area of the surface. For a single non-ionic solute in dilute solution the equation approximates to... 

Qualitatively the equation shows that solutes which lower the surface tension have a positive surface concentration, e.g. soaps in water or amyl alcohol in water. Conversely solutes which increase the surface tension have a negative surface concentration. 

If the spreading is into a limited surface area, as in a laboratory experiment, the film front rather quickly reaches the boundaries of the trough. The film pressure at this stage is low, and the now essentially uniform film more slowly increases in v to the final equilibrium value. The rate of this second-stage process is mainly determined by the rate of release of material from the source, for example a crystal, and the surface concentration F [46]. Franses and co-workers [47] found that the rate of dissolution of hexadecanol particles sprinkled at the water surface controlled the increase in surface pressure here the slight solubility of hexadecanol in the bulk plays a role. 

Customarily, it is assumed that e is unity and that ]l = p,cos 9, where 0 is the angle of inclination of the dipoles to the normal. Harkins and Fischer [86] point out the empirical nature of this interpretation and prefer to consider only that AV is proportional to the surface concentration F and that the proportionality constant is some quantity characteristic of the film. This was properly cautious as there are many indications that the surface of water is structured and that the structure is altered by the film (see Ref. 37). Accompanying any such structural rearrangement of the substrate at the surface should be a change in its contribution to the surface potential so that AV should not be assigned too literally to the film molecules. 

It is perhaps fortunate that both versions lead to the same algebraic formulations, but we will imply a preference for the two-dimensional solution picture by expressing surface concentrations in terms of mole fractions. The adsorption process can be written as... 

In addition to Q and r, a quantity of interest is the surface concentration F, where... 

Here, if Z is expressed in moles of collisions per square centimeter per second, r is in moles per square centimeter. We assume the condensation coefficient to be unity, that is, that all molecules that hit the surface stick to it. At very low Q values, F as given by Eq. XVII-3 is of the order expected just on the basis that the gas phase continues uniformly up to the surface so that the net surface concentration (e.g., F2 in Eq. XI-24) is essentially zero. This is the situation... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

In many cases, however, well-designed catalysts provide intrinsically different reaction paths, and the specific nature of the catalyst surface can be quite important. This is clearly the case with unimolecular reactions for which the surface concentration effect is not applicable. 

The course of a surface reaction can in principle be followed directly with the use of various surface spectroscopic techniques plus equipment allowing the rapid transfer of the surface from reaction to high-vacuum conditions see Campbell [232]. More often, however, the experimental observables are the changes with time of the concentrations of reactants and products in the gas phase. The rate law in terms of surface concentrations might be called the true rate law and the one analogous to that for a homogeneous system. What is observed, however, is an apparent rate law giving the dependence of the rate on the various gas pressures. The true and the apparent rate laws can be related if one assumes that adsorption equilibrium is rapid compared to the surface reaction. 

Figure A3.10.18 Surface concentration of nitrogen on different Fe single crystals following N2 exposure at elevated temperatures in UHV [48],...

Figure A3.10.19 Variation of the initial sticking codFicient of N2 with increasing potassium surface concentration on Fe(lOO) at 430 K [50],...

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

The Ru surface is one of the simplest known, but, like virtually all surfaces, it includes defects, evident as a step in figure C2.7.6. The observations show that the sites where the NO dissociates (active sites) are such steps. The evidence for this conclusion is the locations of the N and O atoms there are gradients in the surface concentrations of these elements, indicating that the transport (diffusion) of the O atoms is more rapid than that of the N atoms thus, the slow-moving N atoms are markers for the sites where the dissociation reaction must have occurred, where their surface concentrations are highest. 

Therefore, in tire limiting case—tire surface concentration of tire reacting species is zero as all tire arriving ions immediately react—tire current density becomes voltage independent and depends only on diffusion, specifically, on tire widtli of tire Nerstian diffusion layer S, and of course tire diffusion coefficient and tire bulk concentration of anions (c). The limiting current density (/ ) is tlien given by... 

Fig. 5.16 Surface concentration of hydroxyl groups of silica, as a function of the temperature of dehydration. Data are +, from Fripiat and Uytterhoeven A, from Kiselev and Zhuralev O, from Taylor (cf.

The relationship between the BET monolayer capacity of physically adsorbed water and the hydroxyl content of the surface of silica has been examined by Naono and his co-workers in a systematic study, following the earlier work by Morimoto. Samples of the starting material—a silica gel—were heated for 4 hours in vacuum at a succession of temperatures ranging from 25 to 1000°C, and the surface concentration of hydroxyl groups of each sample was obtained from the further loss on ignition at 1100°C combined with the BET-nitrogen area. Two complete water isotherms were determined at 20°C on each sample, and to ensure complete... 

Perhaps the most common type of problem encountered in the analytical lab is a quantitative analysis. Examples of typical quantitative analyses include the elemental analysis of a newly synthesized compound, measuring the concentration of glucose in blood, or determining the difference between the bulk and surface concentrations of Cr in steel. Much of the analytical work in clinical, pharmaceutical, environmental, and industrial labs involves developing new methods for determining the concentration of targeted species in complex samples. Most of the examples in this text come from the area of quantitative analysis. 

The stabihty of a single foam film can be explained by the Gibbs elasticity E which results from the reduction ia equiUbrium surface concentration of adsorbed surfactant molecules when the film is extended (15). This produces an iacrease ia equiUbrium surface tension that acts as a restoring force. The Gibbs elasticity is given by equation 1 where O is surface tension and is surface area of the film. 

In a foam where the films ate iaterconnected the related time-dependent Marangoni effect is mote relevant. A similar restoring force to expansion results because of transient decreases ia surface concentration (iacteases ia surface tension) caused by the finite rate of surfactant adsorption at the surface. 

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