Modeling multi-component vapor sorption in a poly(dimethyl siloxane) membrane

This study establishes a mathematical model that describes the vapor sorption level as a function of its activity in poly(dimethyl siloxane) (PDMS) membrane in multi-component systems. The investigated vapors included polar (methanol, water) and non-polar (m-xylene, toluene, and isopentane) permeants. The sorption experiments were carried out using the gravimetric method. The sorption isotherms in the binary (polymer þ vapor) systems were obtained from the equilibrium weights gains at various activity levels. The Flory-Huggins equation and the UNIQUAC model were used to fit the parameters based on the experimental results. For binary systems, the UNIQUAC model gave better prediction power, especially at high activity levels. The sorption concentrations for the ternary (polymer þ 2 vapors) systems were measured after the individual sorbed constituents were purged and analyzed using gas chromatography. The predicted sorption levels from multi-component models for the ternary systems were compared with the experimental results. The two models fit the experimental data satisfactorily for the ternary systems. In this modeling procedure, only the interaction parameters (12 for Flory-Huggins equation and  12 and  21 for UNIQUAC model) between any two components are needed to estimate the sorption levels for multi-component systems. No ternary interaction parameters is required. The modeling process is therefore simplified and the prediction power greatly enhanced.

3.2.3. UNIQUAC models for multi-component vapor systems Table 4 listed the interaction parameters ( 12 and  21) calculated from the vapor-liquid equilibrium data. Figs. 11 and 12 demonstrate that for methanolÀtoluene and tolueneÀm-xylene systems, the predicted sorption volume fraction agreed very well with the experimental data. Some deviated data points in Figs. 10 and 12 may be attributed from the experimental error arising from different PDMS batches used for polymer This research demonstrated that vapor sorption in PDMS can be described using the FloryHuggins or UNIQUAC models. For multicomponent feed systems, the parameter obtained from the single vapor sorption experiments can be used to predict the sorption behavior of multiple vapors. That is to say only the interaction parameters (12 for Flory-Huggins equation and  12 and  21 for UNIQUAC model) between any two components are needed to estimate sorption levels for multi-component systems. No ternary interaction parameter is required. The modeling process is therefore simplified and the prediction power greatly enhanced. For a ternary system, the Flory-Huggins equation required one interaction parameter between any two constituents and offered the advantage of easier calculation. The UNIQUAC models yielded better prediction power at high vapor activity levels but involved a complex non-linear regression procedure.