Structure and dynamics of thin polymer films: a case study with the bond-fluctuation model☆
Introduction
Interfacial properties of polymeric films represent an interesting field of applied and fundamental research [1], [2], [3], [4], [5]. Even if one ignores complications occurring at the interface between polymer and substrate in real materials, such as corrugation on atomistic scale, roughness on mesoscopic scale or adsorbed impurities, and models the underlying substrate as a completely smooth wall, the properties of the chains close to the wall substantially deviate from the established bulk behavior [2], [3], [4]. The deviations depend on the polymer–substrate interaction and external control parameters, such as film thickness, pressure or temperature.
If the interaction between the wall and all monomers of the polymers is attractive, the chains adsorb below the adsorption temperature Ta[5], [6]. Above Ta, the reduction of orientational freedom leads to a depletion of chains near the wall, whereas the gain in interaction energy outweighs this loss in entropy below Ta. The adsorbed chains have strongly flattened, almost two-dimensional configurations contrary to the random coil structure in the bulk [7], [8], [9], [10], [11], [12], [13]. The thermodynamic properties of the adsorbed layer has been extensively studied both numerically [6], [12], [13], [14], [15] and analytically [2], [16], [17], [18], [19], [20].
On the other hand, if there is no preferential attraction between the monomers and the wall, but the wall merely represents an impenetrable obstacle, the situation resembles the aforementioned attractive case for T>Ta. In dilute solution, the loss of orientational entropy makes the monomer and chain concentrations vanish at the wall. As the bulk density increases, the packing constraints of all chains gradually compensate the loss in entropy. At melt-like densities, the monomer profile develops pronounced oscillations, which are damped out after a few interparticle distances and can be interpreted similarly to those of the pair-distribution function in bulk fluids. These oscillations are observed in simulations [4], [7], [10], [11], [21], [22] and can also be rationalized analytically [23], [24], [25], [26], [27], [28], [29], [30].
Whereas these static features of polymer films are well established, a similar level of understanding for the dynamic properties has not yet been reached. However, one would expect the influence of confinement on the polymer structure to carry over to the dynamic properties of the melt. In fact, computer simulations suggest that the mobility of chains close to a hard wall increases in parallel, but decreases in perpendicular direction, relative to the isotropic bulk value [4], [7], [10], [11], [31], [32]. This anisotropy is usually rationalized as a consequence of those chain portions which are in immediate contact with the wall. Their mobility should be facilitated in parallel direction due to both the preferentially parallel alignment of the chains and the smooth walls. In agreement with this interpretation, one finds that the motion of the polymers approaches the isotropic bulk behavior on the same length scale as the chain density profile (on the scale of the bulk radius of gyration Rg) [4], [7], [10], [11], [31].
These findings are not limited to polymer films confined between two solid walls. Recent Monte Carlo simulations for a coarse-grained lattice model, suitably adapted to efficiently simulate polyethylene [33], [34], [35], illustrate the same dynamic anisotropy between parallel and perpendicular motions also for free-standing film (two vacuum-polymer surfaces) [36], nanofibers [37] and supported films (free surface on one side and solid (partially attractive) substrate on the other side) [38].
From a theoretical point of view, it would also be interesting to test to what extent widely studied models, such as the Rouse model [39], can be applied to the polymer dynamics in confined geometry. In the bulk, this model is often suggested as a viable approximation to the dynamics of short chains [39], [40], [41] and furthermore underlies the reptation theory for the dynamics of long chains [39]. So, a more detailed test of its applicability in confined geometry might be beneficial.
The present paper describes results of such an application of the Rouse model to Monte Carlo simulations of a simple lattice model for a non-entangled polymer melt which is embedded between two impenetrable walls. Special attention is paid to the influence of film thickness on the dynamics (and statics) of the melt. The thickness D is varied from D≈1.5Rg to D≈1.5Rg, thus encompassing the regime of strong to weak spatial confinement. The paper is organized as follows: Section 2 introduces the model of the simulation; the following two sections summarize the results. Section 3 discusses some static properties, whereas Section 4 is devoted to the dynamics of the films. Section 5 contains our conclusions.
Section snippets
Simulation model
The model of the simulation has been described in detail in [22], [42]. Here, we only give a brief outline of its properties. The present approach uses a lattice model: the bond-fluctuation model [43], [44], [45], [46]. A monomer of this model does not correspond to a single lattice site, but to a whole unit cell of a simple cubic lattice. This enlarged size of a monomer allows the bond vectors to fluctuate both in length and direction. The fluctuation of the bond length b is limited to the
Static properties of the polymer films
Theoretical studies [2], [5], [17], [23], [24], [25], [26], [27], [28], [29], [30], computer simulations [4], [6], [7], [9], [21], [32], [54], and some recent experiments [55] (see however Ref. [56] for different experimental observations) suggest that the structure of a melt close to an impenetrable interface is different from that of the bulk. Since the interface restricts the number of accessible configurations, the chains prefer to stay away from it. This repulsive force has to compete with
Dynamic properties of the polymer films
This section deals with the dynamic properties of the simulated polymer films. For the analysis, we consider two kinds of quantities: Translational motion is studied by various mean-square displacements, whereas reorientational relaxation is probed on the length scale of both the bond and the chain by time-displaced correlation functions. Both quantities are analyzed parallel and perpendicular to the wall and compared to predictions of the Rouse model.
Summary
The purpose of this paper was to study the influence of spatial confinement on the properties of a polymer melt in an idealized situation. The simulation model consists of short (non-entangled) monodisperse chains, which are embedded between two completely smooth and impenetrable walls. Only excluded volume interactions are taken into account between the monomers and between the monomers and the walls. With this model, we investigated both static and dynamic features of polymer films of various
Acknowledgements
We are indebted to F. Eurich, T. Kreer, P. Maass, M. Müller, W. Paul and F. Varnik for helpful discussions on various aspects of this work. This study would not have been possible without a generous grant of simulation time by the HLRZ Jülich, the RHRK Kaiserslautern, the IDRIS Orsay and the computer center at the University of Mainz. Financial support by the ESF Programme on ‘Experimental and Theoretical Investigation of Complex Polymer Structures’ (SUPERNET) is gratefully acknowledged.
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This paper was originally submitted to Computational and Theoretical Polymer Science and received on 22 November 2000; received in revised form on 23 February 2001; accepted on 25 February 2001. Following the incorporation of Computational and Theoretical Polymer Science into Polymer, this paper was consequently accepted for publication in Polymer.