Structural and dynamic heterogeneity in a telechelic polymer solution Dmitry Bedrov a, * , Grant Smith a , Jack F. Douglas b a Department of Materials Science and Engineering, University of Utah, 122 South Central Campus Drive, Room 304, Salt Lake City, UT 84112-0560, USA b Polymers Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Received 23 July 2003; received in revised form 8 January 2004; accepted 8 January 2004 Abstract We utilize molecular dynamics simulations to investigate the implications of micelle formation on structural relaxation and polymer bead displacement dynamics in a model telechelic polymer solution. The transient structural heterogeneity associated with incipient micelle formation is found to lead to a ‘caging’ of the telechelic chain end-groups within dynamic clusters on times shorter than the structural relaxation time governing the cluster (micelle) lifetime. This dynamical regime is followed by ordinary diffusion on spatial scales larger than the inter-micelle separation at long times. As with associating polymers, glass-forming liquids and other complex heterogeneous fluids, the structural t s relaxation time increases sharply upon a lowering temperature T ; but the usual measures of dynamic heterogeneity in glass- forming liquids (non-Gaussian parameter a 2 ðtÞ; product of diffusion coefficient D and shear viscosity h; non-Arrhenius T-dependence of t s Þ all indicate a return to homogeneity at low T that is not normally observed in simulations of these other complex fluids. The greatest increase in dynamic heterogeneity is found on a length scale that lies intermediate to the micellar radius of gyration and intermicellar spacing. We suggest that the limited size of the clusters that form in our (low concentration) system limit the relaxation time growth and thus allows the fluid to remain in equilibrium at low T : q 2004 Published by Elsevier Ltd. Keywords: Intermicellar spacing; Telechelic solution; Homogeneous fluid 1. Introduction There have been many recent experimental and compu- tational studies indicating the existence of ‘dynamic heterogeneity’ in polymeric and other glass-forming liquids [1]. Recent molecular dynamics (MD) simulation studies [2–5] have further expounded upon the important role of dynamic heterogeneity (defined below) in governing relaxation behavior in polymer melts as the temperature is reduced toward T g : Experimental and MD simulations studies of polymer dynamics at attractive interfaces [6–9] have shown that the dynamics of polymers new interfaces can be significantly slowed down and that this slowing down of polymer dynamics is accompanied by an increasing dynamic heterogeneity even at temperatures ðT Þ much higher than T g [6]. Dynamic heterogeneity has been also reported in associating polymer solutions that form thermoreversible gels [10]. Evidently, dynamic hetero- geneity is not restricted to glass-forming liquids and it is interesting to inquire if, how and why it is exhibited in other ‘complex’ fluids. Dynamic heterogeneity is a phenomenon that can arise in both the spatial and time domains and is recognizable by deviations from the properties of ‘homogeneous’ solutions and fluids. In idealized homogeneous fluids, the distribu- tion of dynamical events approach simple limiting forms governed by the independence of successive dynamical events and by the finiteness of the averages and variances of the times separating these events. For example, the distribution of waiting times between conformational transitions in a polymer at high temperatures is expected to be Poissonian [11–14] because the transition events are described by an independent random process with finite variance and mean time. Upon lowering T towards the glass transition of the polymer melt, the conformational tran- sitions become increasingly intermittent and conformational transition distribution become distinctly non-Poissonian. [11,12,15] Similarly, the deviation of the distribution of atom displacements from a Gaussian distribution (or 0032-3861/$ - see front matter q 2004 Published by Elsevier Ltd. doi:10.1016/j.polymer.2004.01.082 Polymer 45 (2004) 3961–3966 www.elsevier.com/locate/polymer * Corresponding author. Tel.: þ 1-801-585-3949; fax: þ1-801-581-4816. E-mail address: bedrov@tacitus.mse.utah.edu (D. Bedrov).