Lateral interaction parameter

This formula is derived in Appendix 3). With regard to various cubic and quartic anharmonic interactions, the quantity ft is characterized by a certain combination of these anharmonic contributions and becomes dependent on k (see Eq. (4.3.14) for a related quantity and Ref. 140). However, this dependence is insignificant compared to the k-dependence appearing in the denominators of Eqs. (4.3.32) and (4.3.34). Therefore, spectral characteristics defined by formulae (4.3.32) can with good reason be regarded as proportional to certain functions of lateral interaction parameters and of the resonance width 77 ... 

Figure2.17 Formal Os(lll)/Os(ll) redox potential as a function of the average fraction of oxidized osmium sites for Qai,= 1 mM (dashed lines) or 1.2 M (solid line). From the slope it is possible to predict the lateral interaction parameters in Brown and Anson model, Equation 2.8. Taken from Ref [120].

Figure 15 The leave-one-out error (in kJjmol) as a function of the model of the lateral interactions. The numbers indicate the different lateral interactions triangie( 5), and (pbent(=6). The Uncs are guides to the eye. They connect models that differ by one lateral interactions parameter. A fat line indicates that adding a parameter improves the model...

Figure 1.21. Distinguishing between localized (drawn lines) and mobile (dashed curves) adsorbates. Figure (a), adsorption isotherms. Figure (b), two-dimensional equations of state. In figure (a) K[ =Kv=100 m N figure (b) is independent of K. The lateral interaction parameter (in units of kT] is indicated.

The good definition of these systems implies that the models of sec. 2.4 apply. Kern and Flndenegg ) fitted the experimental results for the adsorption of n-docosane from n-heptane on Vulcan 3G graphite at 25, 35 and 45°C with 12.4.34b] assuming 0 and r = 2.67. A good fit was obtained with a lateral Interaction parameter 2° of 1.16, 1.10 and 0.91 and equilibrium constants of 13.9, 10.6 and 8.2 for the three temperatures, respectively. The standard enthalpy of displacement of r moles of n-heptane by 1 mole of n-docosane was calculated from the temperature dependence of K. The value of -54.4 kJ mole obtained compared very well with the calorimetric result at monolayer coverage, -58.8 kJ mole L... 

The FFG and quasi-chemical equations of state are both based on a lattice model, with the inclusion of a lateral interaction parameter w. For attraction w < 0, for repulsion w > 0. Equation 13.4.37] is in the Bragg-Williams approximation, where it is assumed that lateral interaction has no consequences for the configurational entropy. The quasi-chemiccd approximation is better in this respect, see sec. 1.3.8a, as is inferred from the fact that it can better account for phase equilibria. 

TTie degree of coverage, 6, is related to the surface excess concentration, F, by 6= /yrwL where /ml denotes the surface excess concentration of a Meads monolayer. The parameter c represents the number of first nearest neighbors in the compact Meads monolayer. The lateral interaction parameter, a, is related to the lateral interaction energy, i Meads-Meads. by = l Meads-Meads electrode potentials E... 

S mean binding energy of Meads on S step binding energy of Meads at a step atom-substrate binding energy lateral interaction parameter angular frequency, deposition frequency of atoms to a site x dissolution frequency of atoms from a site x phonon frequency area of an adsorption site... 

Ordinarily, electrochemical adsorption isotherms would have to be written (e.g., a Frumkin-like isotherm) as given in, for example, Eq. (36), which includes a lateral interaction parameter, g ... 

T i is a lateral interaction parameter for component i. It is an additional empirical coefficient that can be determined from multicomponent data. 

From the fit of AG/jj vs. ( . within the linear region, the values of AG°jj are obtained from the intercept (Eqs. 14 and 30), while the value of the lateral interaction parameter, .., at low-medium coverages is obtained from the slope (Eqs. 15 and 31). The results of this calculation are shown in Fig. 4. 

Table 1 summarizes some of the most relevant results from thermodynamic studies on platinum single-crystal surfaces. In order to facilitate the comparison of thermodynamic data corresponding to different adsorption reactions, values of the thermodynamic properties at the standard state ( AG , A/T and AS ) are provided. Values of the lateral interaction parameter (a>), and its temperature dependence (dm/dT) are also given in Table 1. While the lateral interaction parameter measures the magnitude of the lateral interactions, its temperature dependence reflects the entropic contributions to the lateral interactions. Therefore, the enthalpic contribution to the lateral interaction energy, can be obtained from - T da/dT.

In order to calculate the lateral interaction parameters, DFT calculations are performed on species i in the presence of different coverages of species k, 0. Equation (8.13) is used repeatedly, at each value of to compute the effective adsorption energy of species i in the presence of a coverage... 

Lateral interaction parameters calculated according to Equation (8.13). 

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