arXiv:1003.6015v2 [cond-mat.soft] 1 Oct 2010 From caging to Rouse dynamics in polymer melts with intramolecular barriers: a critical test of the Mode Coupling Theory Marco Bernabei, 1 Angel J. Moreno, 2, ∗ Emanuela Zaccarelli, 3 Francesco Sciortino, 3 and Juan Colmenero 1, 2, 4 1 Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20018 San Sebasti´ an, Spain. 2 Centro de F´ ısica de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebasti´ an, Spain. 3 Dipartimento di Fisica and CNR-ISC, Universit` a di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185, Roma, Italy 4 Departamento de F´ ısica de Materiales, Universidad del Pa´ ıs Vasco (UPV/EHU), Apartado 1072, E-20080 San Sebasti´ an, Spain. (Dated: October 4, 2010) By means of computer simulations and solution of the equations of the Mode Coupling Theory (MCT), we investigate the role of the intramolecular barriers on several dynamic aspects of non- entangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question, provide new results and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However a progressive discrepancy is revealed as the limit of stiff chains is approached. This disagreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed devations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and non-monotonous wavelength dependence of the mode correlators. PACS numbers: 64.70.pj, 64.70.qj, 61.20.Ja, 83.10.Mj, 83.10.Rs, 83.80.Sg I. INTRODUCTION The different dynamic processes present in amorphous polymers cover a extremely broad range of characteristic time scales, spanning from about 100 femtoseconds up to years. There are two main reasons for this. First, polymers are usually good glass-formers, which inher- ently exhibit a dramatic increase of the viscosity and structural (α-) relaxation times on approaching the glass transition temperature T g . As in non-polymeric glass- formers, localized dynamic processes are also present be- low T g [1]. Second, their macromolecular character in- troduces relaxation processes related to the dynamics of the internal chain degrees of freedom. In the case of low- molecular weight, nonentangled, polymer chains a sub- linear increase (Rouse-like) arises in the mean squared displacement prior to the linear diffusive regime. In the case of high-molecular weight, strongly entangled, chains further sublinear regimes are found between the Rouse and linear regimes, which are usually interpreted in terms of reptation dynamics [2–4]. Such processes are inherent to chain connectivity, and extend over more time decades on increasing chain length. This broad time window for chain dynamics is observed even for temperatures far * Corresponding author: wabmosea@ehu.es above T g , when the structural relaxation extends over just a few picoseconds. Another particular ingredient of polymer systems is that, apart from fast librations or methyl group rotations [5], every motion involves jumps over carbon-carbon ro- tational barriers and/or chain conformational changes. The corresponding map of relaxation processes is largely influenced by the barrier strength. Intramolecular barri- ers play a decisive role in, e.g., crystallization [6, 7], ad- sorption onto surfaces [8, 9], viscoelastic properties [10], or phase behavior of block copolymers [11]. Models for semiflexible and stiff polymers are of great interest in biophysics, since they can be applied to many impor- tant biopolymers as DNA, rodlike viruses, or actin fila- ments [12–14]. Thus, an understandig of the role of the intramolecular barriers on structural and dynamic prop- erties of polymer systems is of practical as well as of fundamental interest in many fields of research. A possible theroretical approach to this problem is provided by the Mode Coupling Theory (MCT) [15]. MCT introduces a closed set of coupled Mori-Zwanzig equations for the time dependence of density correlators. Static correlations enter the memory kernel as external input. Since the former can be related to the interaction potential through liquid state theories, MCT constitutes a first-principle theory for slow dynamics in complex sys- tems. MCT has been developed over the last years to include systems with intramolecular structure (see e.g., Typeset by REVT E X