Determining Maximum Chemico-Osmotic Pressure Difference across Clay Membranes

Significant research conducted over the last 20 years has shown that engineered clay barriers for chemical containment applications can behave as semipermeable membranes that restrict the migration of aqueous-phase chemicals (solutes), thereby enhancing the containment function of the barriers. The ability of such clays to restrict solute migration is characterized by a membrane efficiency coefficient, $\omega$, that typically ranges from zero for no solute restriction (i.e., no membrane behavior) to unity for complete solute restriction ($0\le \omega \le 1$). Measurement of $\omega$ for such clays requires an estimate of the maximum chemico-osmotic pressure difference across the clay, $\mathrm{\Delta }\pi$. To date, estimates of $\mathrm{\Delta }\pi$ and $\omega$ have been determined almost exclusively using the van’t Hoff equation, which is based on the difference in the molar concentrations of simple salts (e.g., KCl and NaCl) in electrolyte solutions bounding the clay specimen. However, the van’t Hoff equation is limited by the assumption that the electrolyte solutions are ideal (i.e., infinitely dilute), such that some error typically is incurred when the van’t Hoff equation is used to estimate $\mathrm{\Delta }\pi$ and $\omega$ for real (nonideal) electrolyte solutions. Therefore, the purposes of this paper are to describe the use of the more fundamental method for estimating $\mathrm{\Delta }\pi$ and $\omega$ based on the differences in water (${\mathrm{H}}_2\mathrm{O}$) activity and to quantify the error associated with the use of the van’t Hoff equation in determining $\omega$. The results indicate that the error in the calculated $\omega$ based on the use of the van’t Hoff equation relative to the use of the water activity method is $\le 9.3\%$ for KCl or NaCl concentrations less than $\sim 2\mathrm{M}$. Also, previously reported values of $\omega$ for bentonite-based membranes based on the van’t Hoff equation were reevaluated using the water activity method. The resulting error in $\omega$ based on the use of the van’t Hoff equation was $\le 8.0\%$, and the $\omega$ resulting from the use of the van’t Hoff equation was more conservative (lower) than that based on the use of water activity, resulting in a slight underestimate of the effect of $\omega$ on transport.