Transition-state theory model for the diffusion coefficients of small penetrants in glassy polymers

Previous molecular dynamics simulations have shown that the diffusion of a penetrant in a glassy polymer involves occasional jumps between cavities through the opening of a ''neck'', and thus, because this is a rare event, the diffusion coefficient can be estimated using transition-state theory, We treat this process as a unimolecular rearrangement and develop semiempirical means of estimating the activation energy, frequency factor and jump length. The activation energy is obtained by treating the polymer as a continuous solid and calculating the energy required to expand a neck in that continuum. The model for the frequency factor uses the result from simulations that the distribution of frequencies of the modes in the transition is very similar to that distribution for the reactant state. The frequency factor is estimated by considering only the motion of the penetrant. These motions are treated as harmonic oscillators. The jump length is obtained from simple geometric considerations of the polymer chain. The parameters are readily evaluated from bulk properties of the polymer such as the isothermal compressibility. The model reproduces experimental trends semiquantitatively and could be used to interpolate and extrapolate experimental diffusion data.