In the first of this two-paper series, a new model is presented that simulates the effects of a temperature perturbation on the rate of slow desorption as a function of mass remaining. The model assumes slow desorption is controlled by one-dimensional diffusion from a single or many hydrophobic micropores and that the micropores of a geosorbent are defined by a γ distribution of diffusion rate constants. Simulation results indicate that during slow desorption the relative increase in flux upon heating increases with decreasing micropore width. Simulation results also indicate that the relative increase in flux upon heating increases with desorption time when diffusion occurs from successively smaller width micropores with decreasing mass remaining. In paper 2, the model is tested and used to examine micropore geometry in natural and model solids by simulating results from temperature stepped desorption (TSD) experiments.
Results from temperature stepped desorption (TSD) experiments are presented and compared with simulations from the TSD model presented in the first of this two-paper series. TSD columns were filled with a sand, a sediment, a soil, or a silica gel, all at 100% relative humidity. Next, TSD columns were equilibrated with trichloroethene (TCE), initially purged at 30 °C, and then heated to 60 °C after 100, 1000, or 10 000 min of slow desorption. One γ distribution of diffusion rate constants at 30 °C and one γ distribution of diffusion rate constants at 60 °C were used to simulate column results at all three heating times for a single solid. At each heating time, diffusion rate constants of the γ distributions at 30 °C and 60 °C were used to calculated an effective activation energy, Eact,eff. Values of Eact,eff for all solids were between 47 and 94 kJ/mol, on the order of activation energy values found for diffusion in microporous solids. Between 100 and 10 000 min heating times, the value of Eact,eff increased by a factor of 1.7 for the sand and by a factor of ∼1.1 for the sediment and the soil. This suggests that diffusion occurs from micropores with a wider distribution of widths in the sand than in the other solids and that with decreasing mass remaining diffusion occurs from successively smaller width micropores. For the sediment, values of Eact,eff and 〈D/lm2〉 were lower than those in the other solids. For a given sorbate, larger width micropores are associated with smaller values of Eact,eff and larger values of D. Hence, it is likely that micropores in the sediment are both wider and longer (i.e. larger value of lm2) than those in the other solids. These results suggest that micropore geometry varies between natural solids, and it is an important parameter that must be quantified to predict rates of slow desorption.
Isothermal desorption rates were measured at 15, 30, and 60 °C for trichloroethylene (TCE) on a silica gel, an aquifer sediment, a soil, a sand fraction, and a clay and silt fraction, all at 100% relative humidity. Temperature-stepped desorption (TSD) rates were measured for these solids in columns prepared and equilibrated at 30 °C, but heated instantaneously to 60 °C after ∼1000 min of slow desorption. Fast and slow elution rates are observed for all solids. Modeling results for the fast eluting fraction of TCE show that fast desorption is controlled by diffusion through aqueous filled mesopores. Rates predicted from diffusion and surface-barrier models are compared to slow isothermal and TSD rates. Diffusion model fits are superior to surface-barrier model fits in all cases. Slow diffusion coefficients and a high activation energy calculated from silica gel data (∼34 kJ/mol) indicate that slow desorption is controlled by activated diffusion in micropores. Initial amounts of slow desorbing TCE do not affect these rates and are found to obey Polanyi's equation. The mass adsorbed in non-Freundlich isotherm regions, where micropores are hypothesized to control adsorption, is 10 times greater than the mass adsorbed at the onset of slow desorption, suggesting that these pores are undulating in nature. TSD column results are consistent with a mechanism where slow diffusion rates are controlled by sorptive forces at hydrophobic micropore constrictions.
Aqueous phase isotherms were calculated from vapor phase desorption isotherms measured at 15, 30, and 60 °C for trichloroethylene on a silica gel, an aquifer sediment, a soil, a sand fraction, and a clay and silt fraction, all at 100% relative humidity. Isosteric heats of adsorption (Qst(q)) were calculated as a function of the sorbed concentration, q, and examined with respect to the following mechanisms: adsorption on water wet mineral surfaces, sorption in amorphous organic matter (AOM), and adsorption in hydrophobic micropores. Silica gel, sand fraction, and clay and silt fraction 60 °C isotherms are characterized by a Freundlich region and a region at very low concentrations where isotherm points deviate from log-log linear behavior. The latter is designated the non-Freundlich region. For the silica gel, values of Qst(q) (9.5−45 kJ/mol) in both regions are consistent with adsorption in hydrophobic micropores. For the natural solids, values of Qst(q) in the Freundlich regions are less than or equal to zero and are consistent with sorption on water wet mineral surfaces and in AOM. In the non-Freundlich regions, diverging different temperature isotherms with decreasing q and a Qst(q) value of 34 kJ/mol for the clay and silt fraction suggest that adsorption is occurring in hydrophobic micropores. The General Adsorption Isotherm is used to capture this adsorption heterogeneity.