Investigation of Transition States in Bulk and Freestanding Film Polymer Glasses Tushar S. Jain and Juan J. de Pablo * Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA (Received 26 August 2003; published 15 April 2004) We have performed transition state searches on the potential energy landscape for bulk and freestanding film polymer glasses and identified connected minima. An analysis of the displacements between minima shows that the sites that undergo the greatest displacement are highly localized in space for both the bulk and the thin-film systems studied. In the case of the thin film, the clusters originate at the surface and penetrate into the center of the film thereby coupling the relaxation in the center of the film to the mobile surface layer. Furthermore, the energy barriers between minima are lower in the thin film than in the bulk system. These findings can rationalize the experimentally observed depression of the glass transition temperature in freestanding polymer films. DOI: 10.1103/PhysRevLett.92.155505 PACS numbers: 61.43.Fs, 64.70.Pf Over the past few years, the glass transition of thin polymeric films has received considerable attention. Partly because thin films have a large surface area to volume ratio, they appear to exhibit thermodynamic, structural, and dynamic properties that are different from those of the bulk material. In particular, the glass transition temperature of thin freestanding polymer films (T g ) changes with film thickness and, in the case of supported films, also with the nature of substrate polymer interactions [1–5]. Various arguments have been proposed to explain the depression of T g ; many of these have been based on a higher concentration of chain ends [6 –8] and a depression of the density near the free interface [9–11]. It has also been proposed that a ‘‘sliding motion’’ mecha- nism dominates the dynamics in thin films leading to the observed reduction of T g [12]. Recently, Herminghaus [13] has proposed a model based on the coupling of capillary waves at the surface of a polymer film to the dynamics of the films. Several workers have used layer models [14,15] to explain the anomalous properties ob- served in thin films. However, direct evidence of dynamic cooperativity between the interfacial and bulk regions of confined systems has not been presented in the literature. A useful theoretical framework for the investigation of glassy behavior is the potential energy landscape (PEL) [16,17]. In this framework, the PEL is partitioned into energy basins connected by saddle points that lead the system from one basin to another. One view of the dy- namics in glassy systems assumes that the motion over short time occurs via intrabasin vibrations, and that long- time relaxation occurs via infrequent activated jumps over saddle points into neighboring basins. Previous stud- ies have demonstrated the influence of the PEL on the dynamics of glass formers, with the appearance of a dynamical regime exhibiting a separation of intrabasin and interbasin motion below a certain crossover tempera- ture [18,19]. Several studies have tried to identify a tem- perature dependent length scale for cooperative motion [20–22], thereby hoping to explain the heightened acti- vation barriers encountered in glassy systems as the tem- perature is lowered towards the glass transition. A calculation of the actual activation events and the corre- sponding barriers could provide useful insights into the dynamics of the glassy regime. Calculations of this nature have been performed for model systems in the bulk or in small clusters [23–26] and have elucidated the mecha- nisms involved in such events. However, studies of this nature have not been pursued for glass forming polymers, and computational studies detailing the influence of con- finement on the PEL have not been conducted. In this work, we have simulated a glass forming polymer in the bulk and in freestanding film geometries. We have explic- itly calculated the true first order saddle points starting from potential energy minima. In all of the systems studied here, we find that highly localized clusters are responsible for the transitions between minima. In the case of freestanding films, the clusters originate at the free surfaces of the film but, interestingly, they penetrate well into the center of the film, thereby aiding rearrange- ment of the overall system. The model employed in this work consists of polymer chains of spherical interaction sites of diameter . Nonbonded sites interact through the 6–12 Lennard- Jones potential with characteristic energy , and bonded sites interact through a harmonic potential with a spring constant k h  2000"= 2 and an equilibrium bond length of . These parameters were chosen to prevent crystal- lization and facilitate trapping of the system in an amor- phous glassy state. The chains used in this work have length L  32, which is close to one entanglement length for this model. All of the results are reported in reduced variables, i.e., temperature T   kT=" and density    N 3 =V. Two systems are considered in this work; a bulk glass and a freestanding film glass of thickness 12. The equilibration of these systems was carried out using advanced Monte Carlo moves [27,28] and molecular dy- namics in the NPT ensemble at zero pressure. The two systems were first equilibrated at T   1:0, which is well PHYSICAL REVIEW LETTERS week ending 16 APRIL 2004 VOLUME 92, NUMBER 15 155505-1 0031-9007= 04=92(15)=155505(4)$22.50  2004 The American Physical Society 155505-1