Jovanovic equations

Jovanovic [83] derived two equations for monolayer and multilayer adsorption. 

For isotherms having sharp knees, exp(-ox) 1, and the equation for multilayer adsorption simplifies to  

These equations have been used to interpret experimental data with some success [84]. 

Several attempts have been made to extend the scope of the BET equation. Hiittig [85] assumed that the evaporation of the ith layer molecule was unimpeded by the presence of molecules in the (/-l)th layer whereas in the BET derivation it is assumed that they are completely effective in preventing the evaporation of underlying molecules. Hiittig s final equation is  

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The Jovanovic Equation. In the kinetic derivation of the Langmuir equation the rate of desorption is proportional to the adsorbate surface coverage and independent of the equilibrium bulk gas pressure. Jovanovic derived a general equation for monolayer adsorption by taking account of the mechanical contact between the adsorbed and bulk phases. After a complex kinetic derivation he obtained the equation ... 

Jaroniec presented a statistical thermodynamic derivation of the Jovanovic equation using generalized ensemble theory. The final result may be written in the form ... 

Le. p = 0 in equation (120). To assume no correlation between the adsorption energies seems a gross approximation. Nonetheless, it does lead to simplifications if the mixed gas Jovanovic equation is adopted as B pu pa, t/i, I/2) in equation (119). " A number of other approaches to the solution of equation... 

The function T (p) is convex from below and its initial (to zero extrapolated) value is equal to unity. This type of function /(p) represents the modified Jovanovic equation and extensive interactions between molecules adsorbed. Since the equation fulfils both conditions of thermodynamic consistence it can be applied to both the determination of the Henry section the isotherm and to the calculation of the total monolayer capacity (see Fig. 10). 

The Fowler-Guggenheim-Jovanovic model [3] assumes (as it was the earlier case also) the occurrence of intermolecular interactions among the molecules adsorbed as a monolayer but is based on the Jovanovic isotherm. The single-component isotherm is represented by the equation ... 

This relationship was then used to calculate the BDE for a-Toc, giving a value of 77.2 kcalmor, in excellent agreement with the experimental value of 77.3 kcalmoP. This empirical method does depend on the electronic effects of groups (methyls and para-ether) around the phenyl ring and provides some confirmation of the role these play in weakening the O—H bond and thus raising the antioxidant activity. In a similar manner, Jovanovic and coworkers obtained a correlation between the measured reduction potentials and the a+ constants for twenty-one substituted phenols at pH 7 (equation 59) and pH 0 (equation 60) ". ... 

Graham and Jovanovic (1999) pointed out that the degradation of chlorinated compounds by reacting with Pd/Fe bimetal includes the following reactions (i) surface reactions, (ii) solution reactions, and (iii) a dechlorination reaction. The relevant schematic diagram (see Rg. 21.1) and reaction equations are given as follows I. Surface reactions... 

The prediction of multicomponent equilibria based on the information derived from the analysis of single component adsorption data is an important issue particularly in the domain of liquid chromatography. To solve the general adsorption isotherm, Equation (27.2), Quinones et al. [156] have proposed an extension of the Jovanovic-Freundlich isotherm for each component of the mixture as local adsorption isotherms. They tested the model with experimental data on the system 2-phenylethanol and 3-phenylpropanol mixtures adsorbed on silica. The experimental data was published elsewhere [157]. The local isotherm employed to solve Equation (27.2) includes lateral interactions, which means a step forward with respect to, that is, Langmuir equation. The results obtained account better for competitive data. One drawback of the model concerns the computational time needed to invert Equation (27.2) nevertheless the authors proposed a method to minimize it. The success of this model compared to other resides in that it takes into account the two main sources of nonideal behavior surface heterogeneity and adsorbate-adsorbate interactions. The authors pointed out that there is some degree of thermodynamic inconsistency in this and other models based on similar -assumptions. These inconsistencies could arise from the simplihcations included in their derivation and the main one is related to the monolayer capacity of each component [156]. 

The equations based on the double-barrier model were utilized by Damjanovic and Jovanovic to account for their experimental results for OER on Pt in H2SO4 solutions and particularly to explain the reaction order with respect to as equal to -1/2, i.e.,... 

Results of the Numerical Iterative Methods.—The application of more sophisticated local isotherms than the Langmuir or Jovanovic dictates the use of numerical iterative methods. The advantages of these methods are they do not require curve fitting of the experimental data to establish a total isotherm equation, nor assumptions regarding the general form of the adsorption energy distribution. However they generally necessitate extensive and reliable experimental data, the measurement of which has been made possible by the more... 

Statistical mechanics is not the xmique frame for the theory of adsorption. A description in kinetic terms of the equilibrium of the adsorbent with a gas was proposed by Jovanovic, who assuming desorption-hindering collisions as the unique cause for deviation from ideality of the gas and modeling the adphase as formed by localized molecules without lateral interactions, eventually obtained the equation... 

The original Jovanovic (J) equation is a semiconsistent relationship because of the two conditions only one is met ... 

By inserting Eq. (110) into Eq. (55) after integration we obtain the consistent modified Jovanovic (MJ) equation ... 

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