From Rouse to Fully Established Entanglement Dynamics: A Study of Polyisoprene by Dielectric Spectroscopy

Polyisoprenes (PI) covering a wide range of molecular weights (M in g/mol) from 652 <= M <= 4.36 x 10 are investigated by dielectric spectroscopy. Normal mode (tau(n)) and segmental (or alpha-) relaxation (tau(alpha)) are considered. The normal mode spectra are singled out by subtracting the spectra of the segmental relaxation. This yields the full spectrum including its high-frequency cutoff. Regarding the Rouse regime (1040 < M < 9910 congruent to M-c congruent to 2M(c)), we are able to construct a master curve which is quantitatively reproduced by the Rouse theory provided that a weak stretching (beta(K) = 0.8) of the correlation function is introduced for each mode. In the low M limit (M < 1040) the normal mode can not any longer be clearly identified. In the entanglement regime (M > M-c) the normal mode spectrum exhibits a power-law behavior epsilon '' proportional to nu(-gamma) at high frequencies with an exponent continuously changing until it saturates around M congruent to 10(5), yielding gamma = 0.26 +/- 0.01. Moreover, the M dependence of the ratio tau(n)/tau(alpha) changes from M-4.0 at M-c < M < M-r to M-3.0 at M > M-r. The latter exponent is that of pure tube reptation; yet, the exponent gamma = 0.26 is not compatible with the reptation model. Nevertheless, both findings we take as evidence for another characteristic molecular weight, namely, M-r congruent to 20M(c), beyond which entanglement dynamics are fully established. Analyzing the strength of the normal mode relaxation as a function of M yields Gaussian statistics of the chains at M > 2000, i.e., well below M. Including data from field cycling NMR. we provide master curves for both the segmental as well as the terminal relaxation time as a function of T - T-g, where T-g denotes the glass transition temperature.