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

Abstract

Polyisoprenes (PI) covering a wide range of molecular weights (M in g/mol) from 652 ≤ M ≤ 4.36 × 105 are investigated by dielectric spectroscopy. Normal mode (τn) and segmental (or α-) relaxation (τα) 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 ≅ Mc ≅ 2Me), we are able to construct a master curve which is quantitatively reproduced by the Rouse theory provided that a weak stretching (βK = 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 > Mc) the normal mode spectrum exhibits a power-law behavior ε′′ ∝ ν−γ at high frequencies with an exponent continuously changing until it saturates around Mr ≅ 105, yielding γ = 0.26 ± 0.01. Moreover, the M dependence of the ratio τn/τα changes from M4.0 at Mc < M < Mr to M3.0 at M > Mr. The latter exponent is that of pure tube reptation; yet, the exponent γ = 0.26 is not compatible with the reptation model. Nevertheless, both findings we take as evidence for another characteristic molecular weight, namely, Mr ≅ 20Me, 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 Mc. 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 − Tg, where Tg denotes the glass transition temperature.