Breakdown of time–temperature superposition: From experiment to the coupling model and beyond A.P. Sokolov * , Y. Hayashi 1 Department of Polymer Science, The University of Akron, 170 University Avenue, Akron, 44325-3909 OH, USA Available online 20 August 2007 Abstract We studied chain and segmental relaxation in polyisoprene using broadband dielectric and light scattering spectroscopy. Our results demonstrate different temperature dependence of these processes (i.e. failure of the time–temperature superposition) in the entire tem- perature range studied. Segmental relaxation varies with temperature faster than chain relaxation at low temperatures while reverse is observed at high T. The transition between two regimes seems to occur around the dynamic crossover temperature. It appears that non-entangled and slightly entangled polymers exhibit the same behavior. The results are compared to predictions of the coupling model. We emphasize that current models cannot describe the data consistently. Ó 2007 Elsevier B.V. All rights reserved. PACS: 83.80.Sg; 64.70.Pf; b3.80.k Keywords: Glass transition; Polymers and organics; Fragility; Rheology 1. Introduction Time–temperature superposition (or equivalence) (TTS) principle is widely used in analysis of dynamics of glass forming systems and especially in polymer rheology. It assumes that all relaxation processes of interest have the same temperature dependence. Use of TTS allows study of relaxation behavior in a broad frequency range using rather narrow frequency range accessible for many experi- mental techniques. This approach is traditionally used in polymer dynamics where relevant relaxation processes, seg- mental and chain relaxations, can span over more than ten decades in frequency. There is no particular theoretical jus- tification for TTS in polymers. The chain relaxation theo- ries usually assume that the same friction mechanism controls chain and segmental modes [1]. This leads to the expectation that both chain and segmental relaxation have the same temperature dependence. Detailed studies by Plazek performed four decades ago showed that TTS breaks down at temperatures approach- ing the glass transition temperature T g [2]. A nice overview of the experimental evidences of TTS breakdown has been published by Ngai and Plazek [3]. The problem became especially obvious when broadband dielectric spectroscopy has been applied to polymers that exhibit chain relaxation in the dielectric spectra. For example, analysis of poly(pro- pylene glycol) (PPG) and poly(isoprene) (PIP) demonstrates significant difference in the temperature dependence of chain and segmental modes [4–6]. Also, detailed analysis of relaxation processes in atactic poly(propylene) (a-PP) demonstrates that segmental relaxation varies with temper- ature significantly stronger than the chain relaxation [7]. The authors, however, concluded that TTS seems to hold at high temperatures and breaks down only when T approaches T g . Comparison of relaxation behavior in different polymers reveals that the difference in temperature variations of chain and segmental relaxation is stronger in fragile poly- 0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.02.063 * Corresponding author. Tel.: +1 330 972 8409; fax: +1 330 972 5290. E-mail address: alexei@uakron.edu (A.P. Sokolov). 1 Present address: Life Science Laboratory, Materials Laboratories, Sony Corporation, Sony Bioinformatics Center, Tokyo Medical and Dental University, Bunkyo-ku, Tokyo 113-8510, Japan. www.elsevier.com/locate/jnoncrysol Journal of Non-Crystalline Solids 353 (2007) 3838–3844