Henry-like isotherm

In any case, Langmuir model did not hold in describing species—A thermodynamic features and Eq. 1.26 employed for species B did not apply. So, the entropy of CO adsorption at A sites was obtained by considering that, in the very early stage of adsorption, the coverage 0 increased linearly with the pco [18]. By employing the Eq. 1.29, based on the Henry-like isotherm ... 

Equation (2.207), like Henry s isotherm, is applicable for relatively low concentrations. At such kinetics there may be no difference between the adsorption and desorption rates. With increase in concentration the effect of a limited munber of active sites begins to appear. A consequence is that the adsorption rate law becomes nonlinear and equation (2.206) assiunes the following format... 

Assuming a linear Henry-like absorption isotherm, for polymer membranes the permeability P. (molmm h Pa ) can be expressed as product of solubility S (mol Pa" m" ) and diffusivity D (m h ). For pore membranes, however, this simple relation is not valid because the limited pore volume the amount adsorbed does not increase linearly with the pressure (Henry-like behavior only for permanent gases at relative high temperatures) and the adsorption isotherm is usually curved (Langmuir-like). 

The adsorption isotherm —Equation (8) —associated with this surface equation of state is called the Henry law limit, in analogy with the equation that describes the vapor pressure of dilute solutions. The constant m, then, is the adsorption equivalent of the Henry law constant. When adsorption is described by the Henry law limit, the adsorbed state behaves like a two-dimensional ideal gas. 

From the scientific point of view, however, all approaches in the sense of the Kd concept (Henry, Freundlich or Langmuir isotherm) are unsatisfactory, since the complex processes on surfaces cannot be described by empirical fitting parameters. Boundary conditions like pH value, redox potential, ionic strength, competition reactions for binding sites are not considered. Thus results from laboratory and field experiments are not transferable to real systems. They are only advisable to provide a suitable prognosis model, if no changes concerning boundary conditions are to be expected and if no parameters for deterministic or mechanistic approach can be determined. 

Of these shapes, long linear isotherms are uncommon for adsorption on solids (Just like type c in fig. 2.8) and occur only if penetration into the solid takes place, leading to a Nemst-type distribution law as in liquid-liquid partitioning, see (1.2.20.1]. Linearity is also found for the (relatively short) initial parts of all isotherms on homogeneous surfaces. We shall call them, as before, Henry isotherms or the Henry parts of curved Isotherms. 

Studies on the sorption of some hydrocarbons have shown that above the transition temperature of EBBA (331 K) the isotherms obey Henry s law and the solubility coefficients S can be calculated. The sorption and desorption curves are similar in shape which indicates that these systems follow Fickian sorption. This fact indicates that steady state surface equilibrium is reached and that the diffusion coefficient for hydrocarbons is a function of concentration only. It follows that the membranes containing 60 wt.% of EBBA are homogeneous from the view point of gas permeation at the temperature above transition in EBBA. The permeability coefficients P show a distinct jump in the vicinity of transition temperature from crystal to nematic phase. This phenomenon was observed for hydrocarbon gases, noble gases like He, and for inert gases like N2. 

The product iqmibi) corresponds to the initial slope of the isotherm, or Henry s constant K), for component i. Hence, the adsorbent selectivity is equivalent to the ratio of the initial slopes of the isotherms of the two components, or K1/K2. It should be noted that the selectivity has resulted in a constant value simply because of the nature of the Langmuir isotherm. If, however, a different model such as the loading ratio correlation (Eq. 3.5) is used, the selectivity is likely to be dependent on the operating pressures of the PSA cycle. 

Fig. 7.11 Grapliic determination of adsorption enthalpy and entropy from isothermal adsorption data measured at various temperatures, a Van t Hoff method applied to the adsorption equilibrium constant deduced from the parameter of a thermodynamic model like Henry or Langmuir fitting well the adsorption isotherms, h Clausius-Clapeyron or isosteric method the isosters he below a limit Une, which corresponds to the liquefaction equihbrium of the adsorptive...

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