The determination of interaction parameters in the characterization of polyetherimide gas separation membranes using the Horvath-Kawazoe model

The Horvath-Kawazoe (HK) model is widely used to characterize microporous carbons and zeolites. The use of the HK model in this application has been extensively studied and interaction parameters exist to relate gas adsorption isotherms to the microporosity of these materials. However, interaction parameters for the HK model do not exist for polymeric materials, which limits its use in characterizing such systems. In this work, the HK parameters for the nitrogen-polyetherimide system were determined from molecular properties and computational chemistry. The interaction energy coefficients required to calculate interaction parameters in the HK model were determined from the polarizability and diamagnetic susceptibility of PEI using the Kirkwood-Muller equations. The parameters were used in the HK method to model a nitrogen adsorption isotherm at 77.2°K and determine the micropore size distribution of a PEI gas separation membrane. The relation between the differential heat of adsorption and pore size distribution, which is the basis of the HK model, was studied for nitrogen adsorption on PEI using different interaction parameters and estimates of the diameter of the PEI chain. The influences of these parameters on the calculated pore size distribution were discussed. The validity of the pore size distribution was examined by comparing the dominant pore size with the d-spacing obtained from X-ray diffraction on PEI. Good agreement was obtained between these values on using a suitable structural model that represents the wall thickness of the adsorbent and includes the polar property of PEI in determining HK parameters.

The parameters required in the HK model were determined for the adsorption of nitrogen on PEI. These parameters predict pore sizes that are in agreement with X-ray diffraction measurements of PEI. The polar nature of polyetherimide should be included in determining IP as this affects the resulting pore size distribution. The atomic/ molecular representation of the surface is critical in estimating the value of the structural parameter ds for inclusion in the HK model. The HyperChem program was helpful in determining this value. Larger pore sizes are predicted by the HK model when the parameters for carbon are used. The results indicate the importance of parameter deter-