Boltzmann factor surfaces

The data of Loukidou et al. (2004) for the equilibrium biosorption of chromium (VI) by Aeromonas caviae particles were well described by the Langmuir and Freundlich isotherms. Sorption rates estimated from pseudo second-order kinetics were in satisfactory agreement with experimental data. The results of XAFS study on the sorption of Cd by B. subtilis were generally in accord with existing surface complexation models (Boyanov et al. 2003). Intrinsic metal sorption constants were obtained by correcting the apparent sorption constants by the Boltzmann factor. A 1 2 metal-ligand stoichiometry provides the best fit to the experimental data with log K values of 6.0 0.2 for Sr(II) and 6.2 0.2 for Ba(II). 

Further, for planes 1 and M the segment/surface interactions will necessitate the introduction of the Boltzmann factor in the probability equation. Thus ... 

The energy term in the Boltzmann factor may be considered as the size of the barrier along a potential energy surface for a system of reactants going to products, as shown schematically in Fig. 2.1. The state of the reacting species at this activated energy can be regarded as some intermediate complex that... 

In Chapter 11 (Sections 11.4 and 11.6) we implicitly anticipated that the ion opposite in charge from the wall plays the predominant role in the double layer, the central observation of the Schulze-Hardy rule. This enters the mathematical formalism of the Gouy-Chapman theory in Equation (11.52), in which a Boltzmann factor is used to describe the relative concentration of the ions in the double layer compared to the bulk solution. For those ions that have the same charge as the surface (positive), the exponent in the Boltzmann factor is negative. This reflects the Coulombic repulsion of these ions from the wall. Ions with the same charge as the surface are thus present at lower concentration in the double layer than in the bulk solution. 

From Figure 17 it is apparent that the molecules evaporate by a two-step process. The atoms evaporate to the plane which passes through P and is parallel to the surface. Any atoms which collide with one another can form a molecule. Any molecule thus formed has a high probability of evaporating. Hence to get an expression for the evaporation rate E we calculate the numbers which pass through 1 cm. of this plane in 1 sec. and multiply this by the probability that they will collide with an atom in this plane. The number of atoms per square centimeter in this plane is equal to Na (the number of atoms per square centimeter at the minimum) times the Boltzmann factor where tph/2 is nearly... 

H+]iocai is the local proton concentration in the solution directly at the surface. This local concentration can differ from the concentration in the volume phase if the surface is charged it either attracts protons (by negative surface charge) or it repels protons (by positive surface charge). A relation between the local concentration and the bulk concentration can be found with the help of the Boltzmann factor ... 

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