We present results of molecular dynamics simulations for free-standing and supported thin films of a nonentangled polymer melt using a coarse-grained (beadspring) model. Our discussion is mainly concerned with the equilibrium properties of the films above the critical temperature (T c ) of mode-coupling theory, although we also determine the glass-transition temperature (T g ) by measurements of the film thickness h upon cooling. We explore the influence of confinement on the structure and dynamics of the polymer films. We find that the dynamics in the films is accelerated compared to the bulk, that this enhanced mobility originates from the surfaces, and that the effect is larger at the free than at the supported surface. Thus, the films have lower T c values relative to the bulk. T c depends on film thickness h; this dependence can be well parametrized by T c (h) = T bulk c /(1 + h 0 /h), a function proposed by experiments on supported polystyrene films.

We employ molecular dynamics simulations to explore the influence that the surface of a free-standing polymer film exerts on its structural relaxation when the film is cooled toward the glass transition. Our simulations are concerned with the features of a coarse-grained bead-spring model in a temperature regime above the critical temperature T c of mode-coupling theory. We find that the film dynamics is spatially heterogeneous. Monomers at the free surface relax much faster than they would in the bulk at the same temperature T . The fast relaxation of the surface layer continuously turns into bulk-like relaxation with increasing distance y from the surface. This crossover remains smooth for all T , but its range grows on cooling. We show that it is possible to associate a gradient in critical temperatures T c (y) with the gradient in the relaxation dynamics. This finding is in qualitative agreement with experimental results on supported polystyrene (PS) films (Ellison and Torkelson 2003 Nat. Mater. 2 695). Furthermore we show that the y dependence of T c (y) can be expressed in terms of the depression of T c (h)-the global T c for a film of thickness hif we assume that T c (h) is the arithmetic mean of T c (y) and parameterize the depression of T c (h) by T c (h) = T c /(1 + h 0 / h), a formula suggested by Herminghaus et al (2001 Eur. Phys. J. E 5 531) for the reduction of the glass transition temperature in supported PS films. We demonstrate the validity of this formula by comparing our simulation results to results from other simulations and experiments.

We perform molecular dynamics simulations to study the dielectric relaxation of a bead-spring model for a polymer melt in the bulk and in supported films. By assigning dipole moments parallel and perpendicular to the backbone of all chains in the completed simulation trajectories, we calculate the dielectric spectra of so-called type-A polymers which exhibit relaxation processes due to the local motion of chain segments ("segmental mode") and due to fluctuations of the end-to-end vector ("normal mode"). We investigate the dependence of both processes on film thickness and chain length and for the segmental mode also on temperature T. We find that the relaxation of both modes is enhanced in the films relative to the bulk. For the segmental mode this difference between film and bulk dynamics increases on cooling toward the glass transition. By a layerresolved analysis of the segmental relaxation, we show that the acceleration of the average film dynamics is a consequence of a smooth gradient in relaxation, originating from both interfaces where the segmental dipoles relax much faster than in the bulk. Additionally, near the interfaces the segmental relaxation is more strongly stretched than in the center of the film where bulk behavior prevails. As the average film dynamics comprises contributions from all layers, the dielectric spectra of the films are broader than in the bulk at the same T. Finally, starting from the layer-resolved analysis which associates a dielectric function and so a capacitance with each layer, we suggest to think of a film as being a system of capacitors. The capacitors are arranged in series, if the electric (E) field is perpendicular to the plane of the film (the usual experimental situation), and in parallel, if the field is parallel to the plane. Because of these different arrangements of the capacitors, the resulting dielectric spectra depend on the direction of the E-field. For instance, we find that, although the segmental relaxation in each layer is taken to be the same for both field directions, the average dielectric spectra differ because the layer-dependent dielectric strength and the limiting high-frequency permittivity (ε ∞ ) enter into the average dielectric response in different ways for the E-field being perpendicular or parallel to the film plane.

We report on results of molecular dynamics simulations for supported polymer films with explicit solvent. The simulation represents the polymers by bead-spring chains and the solvent particles by monomers. The interaction between polymer and solvent favors mixing. We find that the solvent acts as a plasticizer. The glass transition temperature T(g) is reduced relative to the pure polymer film. Near T(g) we explore equilibrium properties as a function of temperature and solvent concentration. We find that the structure and dynamics of the films are spatially heterogeneous. The solvent density is enriched at the supporting wall and at the free surface where the film is in equilibrium with solvent vapor. At both interfaces the solvent dynamics is fast, but smoothly crosses over to bulk dynamics when moving from the interfaces toward the center of the film. A smooth gradient from enhanced dynamics at the interfaces to bulk behavior in the film center is also found for the monomers. We show that the same formula used to parametrize the spatial gradient of the dynamics in the pure polymer film may also be applied here. Furthermore, we determine the concentration dependence of the relaxation time of the solvent in the center of film and compare this dependence to models proposed in literature.

We examine by molecular dynamics simulations the relaxation of polymer-solvent mixtures close to the glass transition. The simulations employ a coarse-grained model in which polymers are represented by bead-spring chains and solvent particles by monomers. The interaction parameters between polymer and solvent are adjusted such that mixing is favored. We find that the mixtures have one glass transition temperature T(g) or critical temperature T(c) of mode-coupling theory (MCT). Both T(g) and T(c) (> T(g)) decrease with increasing solvent concentration φ(S). The decrease is linear for the concentrations studied (up to φ(S) = 25%). Above T(c) we explore the structure and relaxation of the polymer-solvent mixtures on cooling. We find that, if the polymer solution is compared to the pure polymer melt at the same T, local spatial correlations on the length scale of the first peak of the static structure factor S(q) are reduced. This difference between melt and solution is largely removed when comparing the S(q) of both systems at similar distance to the respective T(c). Near T(c) we investigate dynamic correlation functions, such as the incoherent intermediate scattering function φ(q)(s)(t), mean-square displacements of the monomers and solvent particles, two non-Gaussian parameters, and the probability distribution P(ln r; t) of the logarithm of single-particle displacements. In accordance with MCT we find, for instance, that φ(q)(s)(t) obeys the time-temperature superposition principle and has α relaxation times τ(q)(s) which are compatible with a power law increase close (but not too close) to T(c). In divergence to MCT, however, the increase of τ(q)(s) depends on the wavelength q, small q values having weaker increase than large ones. This decoupling of local and large-length scale relaxation could be related to the emergence of dynamic heterogeneity at low T. In the time window of the α relaxation an analysis of P(ln r; t) reveals a double-peak structure close to T(c). The first peak corresponds to "slow" particles (monomer or solvent) which have not moved much farther than 10% of their diameter in time t, whereas the second occurs at distances of the order of the particle diameter. These "fast" particles have succeeded in leaving their nearest-neighbor cage in time t. The simulation thus demonstrates that large fluctuations in particle mobility accompany the final structural relaxation of the cold polymer solution in the vicinity of the extrapolated T(c).

The determination of the elements of the S-matrix within the framework of time-dependent density-functional theory (TDDFT) has remained a widely open question.We explore two different methods to calculate state-to-state transition probabilities. The first method closely follows the extraction of the S-matrix from the time-dependent Hartree-Fock approximation. This method suffers from cross-channel correlations resulting in oscillating transition probabilities in the asymptotic channels. An alternative method is proposed which corresponds to an implicit functional in the time-dependent density. It gives rise to stable and accurate transition probabilities. An exactly solvable two-electron system serves as benchmark for a quantitative test.As a matter of principle, time-dependent density functional theory [1] provides a highly efficient method to solve the time-dependent quantum many-body problem. It yields directly the time-dependent one-particle density n( r, t) of the many-body system. All physical observables of the quantum system can, in principle, be determined from the density. In practice there a two essential ingredients to a TDDFT calculation. First an approximation to the time-dependent exchange-correlation potential V xc [n]( r, t) has to be found which via the non-interacting Kohn-Sham system determines the evolution of the density. The second ingredient are functionals that allow the extraction of physical observables from the density.For some of the observables such as the ground-state energy extraction is straight forward within ground-state density functional theory [2]. Excited-state spectra have been obtained from linear-response functionals [3,4]. Beyond linear response, the time-dependent dipole moment which governs the emission of high-harmonic radiation can be directly determined from n( r, t). Ionization probabilities can be approximately extracted by identifying the integrated density beyond a certain critical distance from the bound system with the flux of ionized particles [5,6]. However, in general, on the most fundamental level, state-to-state transition probabilities contain the full information on the response of a many-body system

We perform molecular dynamics simulations of a coarse-grained model of a polymer-solvent mixture to study solvent evaporation from supported and freestanding polymer films near the bulk glass transition temperature T(g). We find that the evaporation process is characterized by three time (t) regimes: An early regime where the initially large surplus of solvent at the film-vapor interface evaporates and the film thickness h varies little with t, an intermediate regime where h decreases strongly, and a final regime where h slowly converges toward the asymptotic value of the dry film. In the intermediate regime the decrease of h goes along with an increase of the monomer density at the retracting interface. This polymer-rich "crust" is a nonequilibrium effect caused by the fast evaporation rate in our simulation. The interfacial excess of polymer gradually vanishes as the film approaches the dry state. In the intermediate and final time regimes it is possible to describe the simulation data for h(t) and the solvent density profile phi(L)(y,t) by the numerical solution of a one-dimensional diffusion model depending only on the y direction perpendicular to the interface. The key parameter of this model is the mutual diffusion coefficient D(L) of the solvent in the film. Above T(g) we find that a constant D(L) allows to describe the simulation data, whereas near T(g) agreement between simulation and modeling can only be obtained if the diffusion coefficient depends on y through two factors: A factor describing the slowing down of the dynamics with decreasing solvent concentration phi(L)(y,t) and a factor parametrizing the smooth gradient toward enhanced dynamics as the film-vapor interface is approached.

An analytically solvable model of multilevel condensed-phase quantum dynamics relevant to vibrational relaxation and electron transfer is presented. Exact solutions are derived for the reduced system density matrix dynamics of a degenerate N-level quantum system characterized by nearest-neighbor hopping and off-diagonal coupling (which is linear in the bath coordinates) to a harmonic oscillator bath. We demonstrate that for N> 2 the long-time steady-state system site occupation probabilities are not the same for all sites; that is, they are distributed in a non-Boltzmann manner, which depends on the initial conditions and the number of levels in the system. Although the system-bath Hamiltonian considered here is restricted in form, the availability of an exact solution enables us to study the model in all regions of an extensive parameter space.