Surface excess specific

Besides helping to obtain some feeling for the accuracy of data, the above exercise serves a physical purpose the coefficients A and B are, or are closely related to, the surface excess entropy S and the surface excess specific heat. Regjirding the former, it may be recalled from [l.A.5.3] that... 

Tajima and co-workers [108] determined the surface excess of sodium dode-cyl sulfate by means of the radioactivity method, using tritiated surfactant of specific activity 9.16 Ci/mol. The area of solution exposed to the detector was 37.50 cm. In a particular experiment, it was found that with 1.0 x 10" Af surfactant the surface count rate was 17.0 x 10 counts per minute. Separate calibration showed that of this count was 14.5 X 10 came from underlying solution, the rest being surface excess. It was also determined that the counting efficiency for surface material was 1.1%. Calculate F for this solution. 

The surface excess per square centimeter F is just n/E, where n is the moles adsorbed per gram and E is the specific surface area. By means of the Gibbs equation (111-80), one can write the relationship... 

We have also discussed two applications of the extended ab initio atomistic thermodynamics approach. The first example is the potential-induced lifting of Au(lOO) surface reconstmction, where we have focused on the electronic effects arising from the potential-dependent surface excess charge. We have found that these are already sufficient to cause lifting of the Au(lOO) surface reconstruction, but contributions from specific electrolyte ion adsorption might also play a role. With the second example, the electro-oxidation of a platinum electrode, we have discussed a system where specific adsorption on the surface changes the surface structure and composition as the electrode potential is varied. 

Double integration with respect to EA yields the surface excess rB+ however, the calculation requires that the value of this excess be known, along with the value of the first differential 3TB+/3EA for a definite potential. This value can be found, for example, by measuring the interfacial tension, especially at the potential of the electrocapillary maximum. The surface excess is often found for solutions of the alkali metals on the basis of the assumption that, at potentials sufficiently more negative than the zero-charge potential, the electrode double layer has a diffuse character without specific adsorption of any component of the electrolyte. The theory of diffuse electrical double layer is then used to determine TB+ and dTB+/3EA (see Section 4.3.1). 

The quantity dyl3 In a2 at the potential of the electrocapillary maximum is of basic importance. As the surface charge of the electrode is here equal to zero, the electrostatic effect of the electrode on the ions ceases. Thus, if no specific ion adsorption occurs, this differential quotient is equal to zero and no surface excess of ions is formed at the electrode. This is especially true for ions of the alkali metals and alkaline earths and, of the anions, fluoride at low concentrations and hydroxide. Sulphate, nitrate and perchlorate ions are very weakly surface active. The remaining ions decrease the surface tension at the maximum on the electrocapillary curve to a greater or lesser degree. 

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 ... 

The definition of the electrosorption valence involves the total surface excess, not only the amount that is specifically adsorbed. It is common to correct the surface excess F, for any amount that may be in the diffuse double layer in order to obtain the amount that is specifically adsorbed. This can be done by calculating the excess in the... 

Another possible factor for the decrease of If is adsorption that is excess of G on a surface of H. According to Gibbs, the isotherm of adsorption (the specific surface excess of /th guest) has a form ... 

H specific surface charge calculated from surface excess of H+ C m... 

The capacitance-potential dependences of Cd(OOOl) in dilute solutions of Cl04, N02, and NOs" were also studied [6]. A weak specific adsorption of anions increasing in the order Cl04 < N02 < N03 was observed. The adsorption of halides on the Cd(OOOl) single crystal electrode was studied [7], and was found to increase in the sequence Cl < Br < 1 [8]. Analysis of the impedance data does not point to the specific adsorption of Cl ions, and shows that the surface excess (T) of halide ions changes with potential and increases from Br to 1 (Fig. 1) [7]... 

For example, if the property in Figure 7.13 was G and the dividing surface was placed so that the two shaded regions would be equal, then there would be no surface excess G The last term in Equation (30) would be zero. The Gibbs free energy is convenient to work with, however, so such a choice for x0 would not be particularly helpful. Until now we have not had any reason to identify the surface of physical phases with any specific mathematical surface. We had not, that is, until Equation (44) was reached. Now things are somewhat different. 

Such NACs do not exhibit linear isotherms when they sorb under certain conditions with aluminosilicate clays (Fig. 11.66 Haderlein and Schwarzenbach, 1993 Hader-lein et al., 1996). Rather they show saturation behavior indicating an association with specific sites on the solid surfaces. This specific site interaction is also indicated by the observations of competitive effects among different NACs in sorption experiments. Further, the sorption enthalpies have been found to be much greater than excess enthalpies of aqueous solution of these sorbates (e.g., 4-methyl-2-nitro-phenol exhibits a sorption enthalpy of-41.7 kJ-mol"1). These data all indicate that there is a strong specific interaction of NACs with the aluminosilicate clay surfaces. 

The specific surface excess amount is what is typically measured in practical adsorption studies (see Section 6.4). This parameter is almost equal to the amount adsorbed, a, and is dependent on the equilibrium adsorption pressure, P, at constant adsorbent temperature, T. Accordingly, gas adsorption data is, in practice, expressed by the adsorption isotherm ... 

The intrinsic surface charge density reflects particle charge developed from either isomorphic substitutions or adsorption involving H+ or OH-. A widely used technique for measuring intrinsic surface charge density is the Schofield method. In this method [3], clay mineral particles are reacted with an electrolyte solution (e.g., NaCl) at a given pH value and ionic strength the specific surface excess of the cation and the anion adsorbed from the electrolyte is determined and the value of is calculated with the equation... 

What is usually measured and recorded is the specific surface excess amount na/ms, where... 

For the sake of simplicity in some later sections of this book, we adopt the symbol n to denote the specific surface excess amount n°lm. Also, for convenience, this quantity will be often referred to as amount adsorbed. 

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