Van Bemmelen-Freundlich isotherm

Equation 4.27 has the form of the generalized Freundlich isotherm equation.11 If the product A[C]cb < < 1, it reduces to the van Bemmelen-Freundlich isotherm equation and, ifb 1, it becomes the Langmuir isotherm equation (cf. Eq. 3.50b).M Thus Eq. 4.18 and a gamma distribution of the two rate coefficients it contains are sufficient to generate three very common adsorption... 

The weighting factor m( y) is very similar to a gaussian function centered on y, as illustrated in Fig. 4.3. Thus the van Bemmelen-Freundlich isotherm can be thought of as the result of a log-normal distribution of Langmuir parameters iC (i.e, a normal distribution of In K) in a soil. The parameter (3 determines the narrowness of this distribution, in that ° ... 

Figure 4.3. A graph of the distribution of In K values, w(y) (y = In K), that leads to the van Bemmelen-Freundlich isotherm. Each curve corresponds to the same value of yni but to different values of /3 in Eq. 4.18.

Loukidou et al. (2005) fitted the data for the equilibrium sorption of Cd from aqueous solutions by Aeromonas caviae to the Langmuir and Freundlich isotherms. They also conducted, a detailed analysis of sorption rates to validate several kinetic models. A suitable kinetic equation was derived, assuming that biosorption is chemically controlled. The so-called pseudo second-order rate expression could satisfactorily describe the experimental data. The adsorption data of Zn on soil bacterium Pseudomonas putida were fit with the van Bemmelen-Freundlich model (Toner et al. 2005). 

The L-curve isotherm is by far the one most commonly encountered in the literature of soil chemistry. The mathematical description of this isotherm almost invariably involves either the Langmuir equation or the van Bemmelen-Freundlich equation. Ths Langmuir equation has the form... 

As pointed out by Sposito (1984) this equation initiated the surface chemistry of naturally occurring solids. Maarten van Bemmelen published this equation (now referred to as the Freundlich isotherm) more than 100 years ago and distilled from his results, that the adsorptive power of ordinary soils depends on the colloidal silicates, humus, silica, and iron oxides they contain. 

There was not any theory enabling interpretations of adsorption isotherms till 1914. The Freundlich equation [107] was used but is was not theoretically justified. According to McBain [108], the empirical equation mentioned above was proposed by J.M. van Bemmelen in 1888. 

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