An interpretation of gaseous diffusion through polymers using fluctuation theory

An amorphous polymer is visualized as an ensemble of N independent, n ‐center polymer segments. An ergodic hypothesis and a canonical ensemble are utilized in determining the probability of a given volume fluetuation within the polymer. The thermal energy change associated with a given volume fluctuation is calculated and related to the activation energy for gaseous diffusion. Polymer segment lengths were in the range of 6–20 A. and appeared to decrease with increasing temperature in the case of natural rubber. The results were interpreted to show that the activation energy for gaseous diffusion in rubbery polymers went into the breaking of cohesive bonds between parallel polymer segments while in glassy polymers it went into both the breaking of cohesive bonds and the compressing of the surrounding segments. It is felt that it may be possible to relate gaseous diffusion, self‐diffusion, and viscous flow to the thermodynamic and molecular properties of an amorphous polymer.