UNSTEADY-STATE DIFFUSION IN BLOCK-COPOLYMERS WITH LAMELLAR DOMAINS

An unsteady-state model has been developed to predict the diffusion co efficients of small molecules in copolymers having a lamellar morpholo gy. The model incorporates simplifications which are valid when the di ffusion in one of the components or phases of the polymer is much fast er than in the other phase. This behavior is realized in many systems such as block copolymers in which styrene constitutes one segment of t he 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 nume rical solution of the complete model equations, and a simple approxima te model which will be shown to be valid when there is essentially a d ynamic equilibrium between the two phases. This lamellar copolymer mod el is then evaluated with experimental diffusivity data obtained with the capillary column inverse gas chromatography method and the sorptio n data obtained by Rein et al. (1990, 1992). The most significant resu lt of this work is that sorption behavior in many block copolymer syst ems with lamellar structure can be described by a simple model which a ssumes dynamic equilibrium between adjacent lamellae.