A Cumulant Expansion Approach to Predict the Service Lifetime of Polymers and Polymer Composites

The lifetime prediction of polymers and polymer composites has traditionally been approached by constructing an Arrhenius plot of the measured rate constants, as determined from mechanical failure experiments over an elevated temperature range, and extrapolating the best-fit line to low temperatures. This approach is fundamentally inaccurate for polymeric systems because kinetic rate constants cannot be accurately extrapolated through phase transitions that may occur at elevated temperatures, and the data are seldom linear at lower temperatures which are relevant to predicting service lifetime. In fact, the empirical results for even the simplest chemical systems are shown to deviate from linearity when extrapolated to low temperatures, which generally indicates that the rate constants being measured are a combination of rate constants for elementary processes with different activation energies. Therefore, the method of linear extrapolation of kinetic rate constants can not be expected to provide a meaningful prediction of service lifetime for complex systems such as polymers and polymer composites. The present work demonstrates an approach by which a cumulant expansion is used to determine the mean, variance, and higher moments of the probability distribution of activation energies that are inherent to complex polymeric systems. The coefficients of the cumulant expansion function are determined subsequent to non-linear regression analysis of the temperature dependence of the rate constants. This method provides a direct and more accurate means of equating the desired service temperature of a polymeric system to its lifetime prediction.