Dynamics of Chain Molecules in Disordered Materials Rakwoo Chang Department of Chemistry, Kwangwoon University, Seoul, 139-701, Republic of Korea Arun Yethiraj Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, USA (Received 27 October 2005; published 14 March 2006) The dynamic behavior of hard chains in disordered materials composed of fixed hard spheres is studied using discontinuous molecular dynamics simulations. The matrix induces entanglements in the chain fluid, i.e., for high matrix densities the diffusion coefficient D scales with the chain length N as D  N 2 . At high matrix densities the rotational relaxation time becomes very large but the translational diffusion is not affected significantly; i.e., the chains display a dynamic heterogeneity reminiscent of probe diffusion in supercooled liquids and glasses. We show that this is because some chains are trapped, and move via a hopping mechanism. There are no signatures of this dynamic heterogeneity in the matrix static structure, however, which is identical to that of a hard-sphere liquid. DOI: 10.1103/PhysRevLett.96.107802 PACS numbers: 61.20.Lc, 61.43.j, 66.30.Pa A central question in soft matter is how complex fluids move in complex environments. Practical examples are the diffusion of macromolecules in crowded living cells [1,2], gels [3,4], or glasses [5]. Often on the time scale of interest for solute transport the matrix is essentially static, and it is of considerable importance to be able to relate the structure of the matrix to the dynamic properties of the solutes. While this is an area of active experimental research, what has been lacking is a set of dynamical models with structural complexity that could play the same role that Ising and lattice models did for critical phenomena. In this Letter we present molecular dynamics simulations of a simple model, namely, hard chains in a matrix of fixed hard spheres, and show that this simple model has very interesting dynamics and captures much of the phenome- nology seen in the dynamics of probes in structural glasses [6]. The heterogeneous nature of the dynamics of probes in glasses is a topic of continuing interest. NMR [7] and dynamic hole burning [8] experiments on the rotational dynamics of probes in glasses and supercooled liquids have shown that a subset of probe molecules have rotational relaxation times that are orders of magnitude greater than the average. More recently, single molecule experiments [9] have demonstrated that the rotational dynamics of probes in supercooled liquids is strikingly heterogeneous, i.e., different probes rotate at very different rates, with single probes switching from ‘‘fast’’ to ‘‘slow’’ or vice versa almost instantaneously. The molecular origin of these spatially heterogeneous dynamics remains an open ques- tion of considerable current interest [6]. Computer simulations have played an important role in our understanding of supercooled liquids. In fact, spa- tial heterogeneity is observed in simulations of binary (noncrystallizable) mixtures of Lennard-Jones particles [10,11], although this occurs at temperatures much above the glass transition. As the liquid is cooled, however, the relaxation times become prohibitively large, preventing the simulation of the glass transition itself. In this work, we take a different approach to the problem and focus on the dynamics of probes in glasses by con- struction rather than trying to create a structural glass by cooling. We model the matrix as a collection of spheres fixed in space and investigate the dynamics of chainlike probe molecules in these matrices. We find that the dy- namic behavior can be very interesting and can reproduce much of the phenomenology observed in experiment. There is no signature of this in the average static structure factor of the matrix, however, which is (by construction) identical to that of a hard-sphere liquid. The main challenge in the computational study of dis- ordered materials is that the positions of the matrix parti- cles are quenched. An average over realizations of the matrix is necessary, which make the simulations computa- tionally intensive. Consequently, although there have been a number of computational studies of lattice and/or two dimensional models or single chains [12 –16], to our knowledge there have been no studies of the dynamics of solutions of macromolecules in random media except for solutions of chains [17] and rods [18] in two dimensions. We overcome the problems associated with simulations by employing a model with only impulsive forces that allows us to use the efficient discontinuous molecular dynamics (DMD) algorithm [19]. Monte Carlo (MC) simulations [13–16] provide useful insight into chain behavior, but there is a worry that the dynamics might be influenced by the MC moves used to propagate the system, and MD simulations are therefore important. The solute molecules are modeled as chains of N hard spheres of diameter , where N is the number of mono- mers (or sites) in a chain. The bond length between adja- cent beads is allowed to vary freely between 1   B  and 1   B , with  B  0:05 [20]. The static properties of this model are identical to the tangent hard-sphere chain PRL 96, 107802 (2006) PHYSICAL REVIEW LETTERS week ending 17 MARCH 2006 0031-9007= 06=96(10)=107802(4)$23.00 107802-1  2006 The American Physical Society