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At sufficiently low adsorbate concentration (or partial pressure), adsorption isotherm at- tains a linear form, called Henry’s Law: qi∗ =kiHPi i=1,...,Nc (2.8) Here kH is Henry’s constant and is inversely related to temperature (kH = k e∆Hads/RT). i i0i In general, nonlinear equlibrium relationship is described in numerous different mathemati- cal forms, some of which are based on a simplified physical picture of adsorption/desorption phenomena while others are purely empirical and intended to correlate the experimental data. Commonly used mathematical models include single- and dual-site Langmuir model, Freundlich model, and Langmuir- Freundlich model. • Langmuir adsorption isotherm The Langmuir isotherm model is derived from mass action considerations and by bal- ancing the occupied and unoccupied sites on the surface. It shows correct asymptotic behavior as it reduces to Henry’s Law in the low-concentration region, and approaches saturation limit at high concentrations, which is a requirement for thermodynamic con- sistency in any physisorption-based system [156]. Single-site model ∗ qisbiPi qi = 1+ b P where s 1 2 qi =ki +kiT 3 4 i=1,...,Nc (2.9) (2.10) m = 1, 2 18 and dual-site model q1si b1i Pi qi =1+ b P +1+ b P ∗ q2si b2i Pi j 2j j i=1,...,Nc 2.3 PSA Modeling jjj bi =kiexp(ki/T) j 1j j where qs = k1 + k2 T b = k3 mi mi exp(k4 mi /T ) mi mi mi are the commonly used formulations for Langmuir model. • Freundlich and Langmuir-Freundlich isotherms Chapter 2. Pressure Swing AdsorptionPDF Image | Design and Operation of Pressure Swing Adsorption Processes
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