Small and large scale segmental motion in polymers: Estimating cooperativity length by ordinary relaxation experiments

We derive a suitable expression for estimating the size of the cooperatively rearranging regions (CRRs) in supercooled polymer melts by fitting data worked out by ordinary relaxation experiments carried out in isothermal conditions. As an example, the average CRR size in poly(n-butyl methacrylate) in proximity to the glass transition temperature is derived from a stress relaxation experiment performed by means of an atomic force microscopy setup. Good agreement is found with results in the literature derived from measurements of temperature fluctuations (the so-called Donth method). The temperature dependence of the CRR size is explored for poly(butadiene); in this case the segmental relaxation function is derived through a novel method for the analysis of the efficiency with which free induction decay echoes are refocused in 1 H NMR experiments. It is found that the CRR size increases upon cooling. The results derived from the analysis of the NMR data are found to be in satisfactory agreement with those worked out from broadband dielectric spectroscopy data in the literature.