Toth model

It consists of three parameters, which are C (i. e., the equilibrium concentration of the chemical compound of interest in solution), Q (i.e., the maximum number of moles of a pollutant adsorbed per mass adsorbent), and q (i.e., the number of moles of adsorbate per mass adsorbent at equilibrium). The Toth model (Eq. 17) reduces to Henry s law at very low concentrations and exhibits saturation at high concentrations. 

The best results to describe the adsorption isotherm by the selected isotherm equations were achieved by the Toth model. The Freundlich model showed in some cases a lack of flexibility in describing the region were the linear behaviour changed to saturation behaviour (22 MPa) and the Langmuir-model in some cases had difficulties in describing the region were the adsorbate is saturated (16 MPa). 

The competitive equilibrium isotherm model best fitting the FA experimental data for the R and S enantiomers of 1-phenyl-l-propanol on cellulose tiibenzoate was the Toth model. This model was used to calculate the elution profiles of samples of mixtures of the two enantiomers [29]. The General Rate model combined with the Generalized Maxwell-Stefan equation (GR-GMS) was used to model and describe surface diffusion (see Chapter 5). The mass transfer kinetics is slow and this model fits the experimental data well over a wide concentration range with one single set of numerical parameters to account for the band profiles in a wide range of concentrations, as shown in Figure 16.24. 

Martinez-Basmadjian model is a further extension to include lateral interactions in the adsorbed phase. The Toth model is developed to describe adsorption of equal-sized molecules on an energetically heterogenous adsorbent. The variables of Eqs. (l)-(4) are the fractional coverage of component i of the gas mixture (9i = at P, r, and y, the number of adsorption... 

The selectivity of adsorption (S = niyj/njyi) of water vapour (component 1, mole fraction yi) on aluminas over component j (mole fraction yj) of a gas mixture can be complex functions of adsorbate loadings (ni,nj), system temperature and pressure. There is a scarcity of published data on water adsorption from multicomponent gas mixtures on alumina. Typically, it is assumed that water is exclusively adsorbed on aluminas (S — oo,nj —> 0) from non- polar gases such as air or natural gas. The assumption may not be valid when the gas mixture contains polar components. The mixed gas Langmuir or Toth models may be used to describe multicomponent Type I equilibria on aluminas [6,7]. No isotherm model is available to describe adsorption of water from gas mixtures when there is partial condensation of water in the mesopores of the alumina. 

The isotherm data of 12DCP adsorbed on Cat-I are presented in Fig. 2. The isotherms were reversible over the complete pressure range investigated. For the sake of clarity, the desorption data are omitted. For adsorption on heterogeneous adsorbents such as activated carbon, the Toth model is often used to fit isotherm data [14-15]. 

The TEOM is a unique technique that is suitable for simultaneous measurements of adsorption, reaction, and coke formation. The adsorption isotherms of 12DCP on activated carbon and catalysts have been accurately determined. The isotherm data can be described by the Toth model. Only minor differences exist between the adsorption on activated carbon and fresh catalysts. The reduction of catalysts can lead to the chemisorption of 12DCP on metallic species, which enhances the adsorption capacity. 

Another three-parameter expression which has been widely used to represent equilibrium data for activated carbon adsorbents is the Toth model [6] ... 

Fundamentals of sorption and sorption kinetics by zeohtes are described and analyzed in the first Chapter which was written by D. M. Ruthven. It includes the treatment of the sorption equilibrium in microporous sohds as described by basic laws as well as the discussion of appropriate models such as the Ideal Langmuir Model for mono- and multi-component systems, the Dual-Site Langmuir Model, the Unilan and Toth Model, and the Simphfied Statistical Model. Similarly, the Gibbs Adsorption Isotherm, the Dubinin-Polanyi Theory, and the Ideal Adsorbed Solution Theory are discussed. With respect to sorption kinetics, the cases of self-diffusion and transport diffusion are discriminated, their relationship is analyzed and, in this context, the Maxwell-Stefan Model discussed. Finally, basic aspects of measurements of micropore diffusion both under equilibrium and non-equilibrium conditions are elucidated. The important role of micropore diffusion in separation and catalytic processes is illustrated. 

Fig. 2.16 CO2 adsorption evaluation of the PCNs. a, b CO2 adsorption isotherms for high and low CO2 partial pressures at 25 °C, where the solid line represents a Toth model fit to the CO2 isotherms, c The number of CO2 molecules adsorbed per nm pore volume and d per nm surface area for PCNs with different thickness, e, f CO2 separation evaluation of PCN-17 in dynamic breakthrough tests, e Breakthrough curves and f cycling of CO2 separation from a stream of CO2/H2O/ N2 of 4/3/93 v% at 25 °C, following a regeneration by an Ar purge at 50 °C. Reproduced from Ref. [71] by permission of The Royal Society of Chemistry...

The multicomponent Toth model is thermodynamically consistent only when the variables m, and k for all components are equal [13,14]. The mixed gas adsorption model is based on the criteria that the local site selectivity of adsorption for component i—j pairs (5 y = bj/bj) is constant for all adsorption sites, but the gas-sohd interaction parameters of component /(/>,) vary from site to site. The functions 7 (0/) and F(0) of Tables 3 and 4, respectively, are identical except that the independent variables are 9, and 9. 

The Toth model describes the adsorption isotherms of pure C2H4 (component 1) and CH4 (component 2) as well as those for their binary mixtures on Nuxit charcoal fairly well [14,30], The multicomponent Toth model was used to calculate the binary gas isosteric heats of adsorption for a C2H4-CH4 mixture as functions of C2H4 gas-phase mole fraction (j i) at a total as pressure of 99.2 kPa and at a temperature of 293 K [14]. Figure 10 show the results, qc,Hi decreases as the mole fraction of that component in the gas phase increases. ch4 increases as the mole fraction of that component in the gas phase increases. This is a typical characteristic of the T oth model. 

Fig. 2. Comparison of the isotherms of the alkanes with those of the corresponding alkenes. Lines are the Toth model correlations. (A) Ethane and (A) ethene at 194 K. (O) propane and ( ) propene at 273 K.

Table 2. Estimated parameter values for the combined fitting of the adsorption data by the Toth model...

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