Effect of pore size distribution on the surface diffusivity in activated carbon: Hybrid Dubinin-Langmuir isotherm

The concentration dependence of the observed surface diffusivity for activated carbon due to the pore size distribution is theoretically investigated. The mathematical model is derived based on the assumption of a local hybrid adsorption isotherm (proposed recently by Shethna and Bhatia, 1994) and a local surface diffusive flux for a particular pore of half widthr. Using those local quantities and assuming a Gamma pore size distribution, the observed surface diffusivity is obtained. This observed surface diffusivity was found to increase rapidly with loading if the chemical potential is the driving force for surface flow. Furthermore, this observed surface diffusivity,D/D(0), was found to be the same as the Darken thermodynamic correction factor, using only the macroscopic isotherm information. This indicates that the thermodynamic correction factor contains information on the averaging of the surface heterogeneity.Nomenclature a coefficient for surface diffusivity - A adsorbate molecular area - c affinity parameter of the surface adsorption isotherm - C(P, T) concentration - C_max maximum adsorbed concentration - D_obs observed surface diffusivity - D_s intrinsic surface diffusivity - D_s0 coefficient of intrinsic surface diffusivity - E₀ characteristic energy of Dubinin isotherm - F(r) pore size distribution - J local flux - J_obs observed flux - k empirical constant of Dubinin isotherm - K Langmuir affinity parameter - K_m Langmuir affinity parameter at maximum micropore half width - m structural parameter defined in Eq. (13) - n Dubinin variable exponent - q structural parameter defined in Eq. (13) - Q function ofr andT defined in Eq. (4) - Q_m function ofn defined in Eq. (8) - P pressure - P⁰ vapour pressure - P_t threshold pressure defined in Eq. (3) - P₀,P_L pressure at two end of the slab - P minimum pressure for Dubinin isotherm - P_m threshold pressure at maximum micropore half width - S₁,S₂ scaling factors defined in Eq. (15) - r pore half width - r₀ smallest micropore half width - r_t threshold micropore half width demarcates Dubinin and Langmuir mechanisms - r_m maximum micropore half width - v_M liquid molar volume of adsorbate - V pore volume - R gas constant - T temperature - x axial variable - parameter defined in Eq. (A-7) - affinity factor of Dubinin isotherm - _L constant defined in Eq. (A-7) - small number - pore variance - non dimensional local isotherm - _D non dimensional Dubinin isotherm - _L non dimensional Langmuir isotherm - _S non dimensional surface isotherm - _obs non dimensional overall adsorption isotherm