Nonequilibrium adsorption isotherm

Adsorption can be classified into two types (1) the equilibrium adsorption isotherm in which the reaction process is in equilibrium, and (2) the nonequilibrium adsorption isotherm in which the reaction rate is important. Since classical thermodynamics treats only the equilibrium state, the nonequilibrium adsorption isotherm is commonly described in a phenomenological sense (cf. Appendices E.8 and E.9). 

Here we list some examples of the equilibrium and nonequilibrium adsorption isotherms. Let the current area of an adsorbed layer be S, and let the final area of the layer after completion of the reaction be S. Then the fractional coverage 0 is expressed as... 

For the case of nonequilibrium adsorption where the rate of reaction cannot be ignored, Langmuir s nonequilibrium adsorption isotherm corresponding to (5.112) is given by... 

Figure 2. Adsorption isotherms for equilibrium (top curve) and nonequilibrium conditions. Molecular weight 1x10, charge density 95%. Nonequilibrium, open symbols G = 1800 s 1, closed symbol G = 8000 s-1.

Consider now adsorbed molecular or ionic species that are, practically speaking, immobilized in the soil. Unless the soil is extremely acid, metals such as Cu, Cr, and Pb fall into this category. Also, certain anions such as phosphate bond so strongly on minerals that they too behave as immobile elements. The property that all of these ions have in common is that their sorption isotherms are not reversible within a time scale relevant to soil processes the adsorption (forward) isotherm is usually approximated closely by a Langmuir function of the strong-affinity type, but the desorptioii (backward) isotherm deviates markedly from the adsorption isotherm. This kind of nonequilibrium behavior, depicted in Figure 9.6, is sometimes referred to as hysteresis. Possible reasons for hysteresis in chemisorption are discussed in Chapter 4. 

In the past when the nonequilibrium characteristics of the anodic layers were not well recognized, premature conclusions were reached concerning the adsorption isotherms based on only the anodic branch of the Q vs. E curves. This dependence is almost rectilinear and corresponds to the flat part... 

As previously shown, this equation in the absence of chemical reactions gives adsorption isotherm for immovable adsorbate (Gm(Pm) = 0). For movable adsorbate (Gm(pm) 7 0) the condition (14.1.13) gives partially equilibrium thermodynamic states, i.e., there is an equilibrium between the adsorbate and the gas phase, but the adsorbate itself is nonequilibrium. The reverse situation is possible, when Gm(Pm) = 0 but jm 0. When complete material balance and chemical equilibrium over components at the boundary take place, one has to determine equilibrium values of 0c, ric from (14.1.13). 

Sun, W., and Costa, C.A.V., Fast method for solving nonequilibrium fixed-bed adsorption models with variable velocity and linear isotherm, Comput. Chem. Eng., 16(6), 535-544 (1992). 

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