Mathematical Models for Estimating Diffusion Coefficients in Concentrated Polymer Solutions from Experimental Data

Abstract

Diffusion processes in operations involving polymeric materials are of significant interest. Determining experimental values for diffusion coefficients is often challenging. Estimating these coefficients in concentrated polymer solution, polymer films, and membranes relies on experimental tests where the polymer is brought into contact with certain components/solvents. The diffusion coefficient values depend on the diffusion type, which is affected mainly by the nature of the polymer, concentration, and temperature. The literature presents an extensive amount of information regarding the diffusion phenomenon. This paper makes a particular contribution by showing how experimental data obtained from different applications can be processed to determine diffusion coefficients. The manuscript addresses some aspects regarding solvent diffusion in polymers, and illustrates how to determine the diffusion coefficients from experimental data. For specific cases of diffusion, several models for the predictive estimation of diffusion coefficients are also presented. Polymer–solvent systems such as polyvinyl alcohol (PVA)–water, cellulose acetate (CA)–tetrahydrofuran (THF) and cellulose triacetate (CTA)–dichloromethane (DCM) are investigated, with their diffusion mechanisms influenced by changes in structure caused by variations in concentration and temperature. The experimental data obtained through a gravitational technique allow for the highlighting of the diffusion mechanism and the selection of an appropriate mathematical model. A change in the structure of the polymer during the experiment leads to diffusion anomalies. Modeling the experimental data yielded diffusion coefficient values that vary based on the type of system investigated, composition and temperature. Thus, in the case of the CTA-DCM system, the diffusion coefficient at 303 K, at various concentration values, is in the range of 4.5 and 8·10−11 m2/s; for the PVA-H2O system, D = 4.1·10−12 m2/s at 303 K, and D = 6.5·10−12 m2/s at 333 K; while for the CA-THF system, the solvent–polymer diffusion coefficient has a value of 2.5∙10−12 m2/s at 303 K, and D = 1.75∙10−11 m2/s at 323 K. Mathematical models can be useful in studies regarding the drying of polymer films with complex structures, providing knowledge for designing or selecting suitable equipment.