Sips isotherm temperature dependence

This three-parameter equation behaves linearly in the Henry s law region and reduces to the Langmuir isotherm for m = 1. Other well-known isotherms include the Langmuir-Freundlich isotherm or Sips isotherm [Sips,/. Chem. Phys., 16, 490 (1948) Koble and Corrigan, Ind. Eng. Chem., 44,383 (1952)] or loading ratio correlation with prescribed temperature dependence [Yon and Turnock, AlChE Symp. Sen, 67(117), 75 (1971)]... 

For useful description of adsorption equilibrium data at various temperatures, it is important to have the temperature dependence form of an isotherm equation. The temperature dependence of the Sips equation... 

Take the example of propane on activated carbon, we plot the isosteric heat (eq. 3.2-19f) versus the fractional loading for the Toth equation using the parameters obtained in Table 3.2-6 (Figure 3.2-11). Just like the case of the Sips isotherm, the isosteric heat decreases with loading, and it shows a weak temperature dependence. 

The temperature dependence of the Unilan equation is shown in eqs.(3.2-23) assuming the maximum and minimum energies are not dependent on temperature. Like the last two empirical isotherm equations (Sips and Toth), we assume that the saturation capacity follows the following temperature dependence ... 

Because the exponential term a 1, the Sips equation does not have a correct low pressure limit, which is contrary to experimental observations. To overcome this problem and extend the range of applicability of isotherms of this type, Staudt et al. [77] introduced the pressure- and temperature-dependent exponents to ensure that Henry s law holds when pressure is sufficiently low. The new generalized form of Eq. (48) is... 

If Bdistribution function is translated to lower adsorption energies.A difficulty arises when using the Sips procedure since the distribution function so determined is temperature dependent. Honig and Hill have repeated the analysis but with a constraint requiring the distribution to be independent of temperature thus leading to severe restrictions on the form of the total isotherm function that can be handled by the Stieltjes transform method. 

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