Equilibrium Dynamics of an Associating Polymer Melt in Narrow Slits by Computer Simulation Marco Malvaldi, ² Samantha Bruzzone, ² Guido Raos,* ,‡ and Giuseppe Allegra ‡ Dipartimento di Chimica e Chimica Industriale, UniVersita ` degli Studi di Pisa, Via Risorgimento 35, 56126 Pisa, Italy, and Dipartimento di Chimica, Materiali e Ingegneria Chimica “G. Natta, Politecnico di Milano, Via L. Mancinelli 7, 20131 Milano, Italy ReceiVed: December 20, 2006; In Final Form: February 15, 2007 Molecular dynamics simulations have been used to study the dynamics of a coarse-grained model of a melt of polymer chains with associating terminal groups, confined in a narrow slit by two layers of Lennard-Jones sites. Simulations were carried out as a function of wall separation and attracting strength. We found that confinement has an important effect on the overall dynamics of the system. Strongly attracting walls can significantly modify the dynamics of the melt, giving an aggregation structure with extremely long relaxation times. A noticeable degree of anisotropy was found for the dynamics of both the individual chains and the aggregates formed by the associating terminal groups. 1. Introduction Macromolecules containing groups capable of reversible association represent an important class of self-organizing soft materials. 1-6 Their applications as lubricants, adhesives, rhe- ology modifiers, and surfactants exploit their amphiphilic self- associating character and the peculiar mechanical properties deriving therefrom. The specific chemical natures of the polymers and of the associating groups and the physical mechanisms responsible for their aggregation can vary widely, including, for example, polar or hydrophobic interactions. These systems are characterized by clusters of associating groups that, depending on their chemical structure, concentration, and temperature, can include from two to a few hundred. In the latter case, a microphase-separated structure results. In a sufficiently concentrated solution, from semidilute to the melt state, the clusters formed by the associating groups are interconnected by bridging chains, resulting in an infinite three-dimensional physical gel or transient network. Provided that the interactions are sufficiently strong, the temperature- or concentration-driven transition from the sol to the gel state is accompanied by a sudden change in mechanical properties, from fluidlike to solidlike. Thus, there is an intriguing interplay of microphase separation and dynamical slowing: the competition between cluster breakup and chain relaxation results in the formation of an effectively reversible network if the clusters have a mean lifetime longer than the terminal relaxation time of the corre- sponding homopolymer (i.e., without associating terminal groups). A number of theoretical studies have addressed the equilibrium and viscoelastic properties of these systems, using both mean-field calculations and scaling arguments. 7-18 More recently, the matter has been increasingly studied with simula- tion techniques such as Monte Carlo (MC) and molecular dynamics (MD). 19-31 In numerous applications, such as adhesion or colloid precipitation/stabilization, associating polymer systems are used in situations of geometric confinement between two surfaces. The present simulation study was motivated by these applica- tions and by the general observation that, when this confinement occurs on the nanometer scale, it is known to affect strongly both the structural and dynamical properties of polymeric systems. 32-42 We present the results of MD simulations on a model polymer bearing two associating units at its ends (telechelic polymer) at meltlike densities. The polymer was confined between two infinite parallel walls, represented by two slabs of closely packed Lennard-Jones sites. This relatively simple system can already display a rich behavior, depending on the ratio of chain size to wall-to-wall distance, in terms of the interaction strength among the associating terminal groups and the terminal group-wall adsorption energy. There is competition between chain-end aggregation and adsorption on the confining walls. The chains can bridge the two walls, but they can also form loops and tails. The clusters can be preferentially located near the surfaces or away from them. Unlike our previous studies, which mainly considered static structural properties of the polymer in the bulk 30 or in thin films 31 (cluster size distribution or chain conformation, for example), the main focus of the present work is on dynamical equilibrium properties: cluster formation and breakup, diffusion of macromolecules and of associative units, and macromolecular chain motion. 2. Model and Computational Methods We provide a concise description of our model system and simulation methods: more detailed information can be found in our previous publications. 30,31 All simulations were conducted with the coarse-grained molecular dynamics code COGNAC, version 4.2. 43 We adopted a standard bead-and-spring repre- sentation of flexible polymer chains. 44 Because this is a generic coarse-grained model, it was convenient to adopt reduced units, whereby the bead diameter (entering the Lennard-Jones interac- tion potential) was σ ) 1, the energy and temperature units were such that k B T ) 1, and the mass of the beads was m ) 1. The units of all other quantities, such as time [τ ) σ(m/k B T) 1/2 ], number density (1/σ 3 ), and pressure (k B T/σ 3 ) derive from these * Corresponding author. Phone: +39-02-2399-3051. Fax: +39-02-2399- 3080. E-mail: guido.raos@polimi.it. ² Universita ` degli Studi di Pisa. ‡ Politecnico di Milano. 4141 J. Phys. Chem. B 2007, 111, 4141-4149 10.1021/jp0687596 CCC: $37.00 © 2007 American Chemical Society Published on Web 03/30/2007