Fixed electrostatic model

Another extreme is to neglect the exponential term in Eq. (5.24) at all. This leads to overestimated effect of the pH on tjo (assuming a fixed value). A model neglecting the surface potential is physically unrealistic, but non-electrostatic models of adsorption at solid-aqueous solution interface can be found even in very recent literature. According to the prevailing opinion the actual surface potential is between the above two extremes (Nemst potential and 0 = 0). The electrostatic models of oxide - inert electrolyte solution interface were discussed in detail by Westall and Hohl [25]. In this section the most common electrostatic models are combined with the 1-pK model in order to illustrate their ability to simulate the actual surface charging data. 

Figures 5.2-5.5 show that the non-electrostatic model completely fails for alumina (one example of relatively good agreement between the calculated and experimental charging curve in Fig, 5.5 is probably a fortuitous coincidence). On the other hand the sigmoidal model curves roughly reflect the charging behavior of silica, especially at low ionic strengths. For silica, the number of adjustable parameters in the model can be reduced to one by fixing the K or N, . Figures 5.11-5.15 show the model curves calculated for log K (reaction 5.25) = 8 (fixed value). The best-fit values are summarized in Table 5.6.

This leads to unique definition of the stability constants of monodentate surface complexes involved in the specific adsorption of cations. Thus, reaction (5.65) rather than reactions (5.66)-(5.68) should be chosen as a standard definition, according to the above standards. The exact definition of the stability constant of the =TiOCd species in the present example depends on the electrostatic position of Cd in the surface complex. It should be also emphasized that even with fixed electrostatic position of Cd, the numerical value of the equilibrium constant of reaction (5.65) depends on the choice of the model of primary surface charging. The details on the models of primary surface charging are not given in the tables in Chapter 4, and the reader is referred to the original publications. 

Errors (/>(calc)-/ (expt)) in the relaxed crystal structures using a fixed repulsion-dispersion potential (as in Table 11.2) and various electrostatic models derived from a DMA of a 6-31G SCF wave function DMA, full multipoles up to hexadecapole SDMA, all multipoles scaled by 0.9 CHAR, just the charge component of the DMA. The r.m.s. % errors were calculated over the three cell lengths. The electrostatic contribution, (7estat, to the total lattice energy, Us, is given at both the experimental (for the SDMA model) and relaxed crystal structures. This can be compared with the experimental heat of sublimation Af/sutl (Chickos 1987), where available. 

The compression and stretching modes of actuation are mechanically coupled for most elastomers because, at the stresses of interest, the elastomer volume is essentially fixed (the bulk modulus is much higher than the modulus of elasticity T). We can use our electrostatic model to show that the effective compressive stress, p, compressing the film in thickness [13] is... 

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