The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T₀ only affects the relaxation up to T₀ + T_Lag, where T_Lag is proportional to the logarithm of the annealing time t_A. A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E = (317 + 1.17ξ)×10³ J/mol, and therefore must have a characteristic relaxation time τ which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t) = N(ξ)e^-t/τ(T,ξ)dξ, in which both the relaxation time τ(T,ξ) and the distribution function N(ξ) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.