Henry's Law Behavior and Density Functional Theory Analysis of Adsorption Equilibrium
Schindler, Bryan Joseph
This work focuses on three different aspects of adsorption equilibrium: the measurement of adsorption equilibrium into the Henry's law region for n-pentane, the calculation of the maximum isosteric heat of adsorption achievable in the Henry's law region for slit-shaped pores, and the incorporation into density functional theory of statistical associating fluid theory to treat the adsorption of chain molecules in slit-shaped pores and analyze data for nitrogen and pentane adsorbed in activated carbon. In the first section experimental data for n-pentane adsorbed on BPL activated carbon in a nitrogen environment are reported at ultra-low concentrations into the Henry's law region. We introduce two methods to prepare pre-equilibrated samples at known loadings. The samples were analyzed by a purge and trap method. Adsorption data were measured at loadings from 1.0 down to 0.0001 mol/kg and pressures of 6 down to 5*10^-10 kPa. The transition into the Henry's law region occurs over a range of loadings near 0.01 mol/kg for all temperatures. The data are compared with the DR, Langmuir, and Toth equations. We discuss how the three equations transition into the Henry's law region, and how well they describe the data. Since the DR equation does not have a proper Henry's law region, we show where this equation no longer applies. The Toth equation describes the data better than the Langmuir equation. The second section discusses the isosteric heat of adsorption in the Henry's law region calculated as a function of the width of slit-shaped pores. We determine the pore width where the isosteric heat is a maximum, which is shown to be a strong function of the solid-fluid collision diameter sigma_sf and a weak function of the solid-fluid well depth potential epsilon_sf. Thus, general results are reported for the pore size where the isosteric heat of adsorption is a maximum that apply to a wide variety of gases. We compare our values of isosteric heat with those in the Henry's law region determined from adsorption data for nitrogen, argon, carbon dioxide, and methane on various activated carbons. The isosteric heats of adsorption for helium and hydrogen in carbon slit pores are also calculated, but are not compared with experimental data. Reasons for differences between the theoretical maximum and the experimental values are discussed. In the third section density functional theory is modified to include the statistical associating fluid theory equation of state in order to describe chain fluids. First-order non-mean field and second-order perturbation attractive terms are included in the model. The interaction parameters for both nitrogen and n-pentane with a carbon parallel slit pore are determined. The monolayer transition, pore condensation, and a clear freezing transition are observed for nitrogen. The effects of the pore size on when the transitions occur is discussed. The pore size distribution for BPL activated carbon is calculated from an experimental nitrogen isotherm and the model. The monolayer transition and pore condensation for n-pentane are found. An isotherm for n-pentane is calculated using the nitrogen pore size distribution and the n-pentane model.