UNSTEADY-STATE DIFFUSION IN BLOCK-COPOLYMERS WITH LAMELLAR DOMAINS

An unsteady-state model has been developed to predict the diffusion coefficients of small molecules in copolymers having a lamellar morphology. The model incorporates simplifications which are valid when the diffusion in one of the components or phases of the polymer is much faster than in the other phase. This behavior is realized in many systems such as block copolymers in which styrene constitutes one segment of the polymer molecule attached to a rubber segment such as polybutadiene. Three solutions for the model equations are presented: an analytical. solution valid for the initial stage of the sorption process, a numerical solution of the complete model equations, and a simple approximate model which will be shown to be valid when there is essentially a dynamic equilibrium between the two phases. This lamellar copolymer model is then evaluated with experimental diffusivity data obtained with the capillary column inverse gas chromatography method and the sorption data obtained by Rein et al. (1990, 1992). The most significant result of this work is that sorption behavior in many block copolymer systems with lamellar structure can be described by a simple model which assumes dynamic equilibrium between adjacent lamellae.