J. Baschnagel

Reduction of the glass transition temperature in polymer films: a molecular-dynamics study.

We present results of molecular-dynamics simulations for a nonentangled polymer melt confined between two completely smooth and repulsive walls, interacting with inner particles via the potential U(wall)=(sigma/z)(9), where z=/z(particle)-z(wall) and sigma is (roughly) the monomer diameter. The influence of this confinement on the dynamic behavior of the melt is studied for various film thicknesses (wall-to-wall separations) D, ranging from about 3 to about 14 times the bulk radius of gyration. A comparison of the mean-square displacements in the film and in the bulk shows an acceleration of the dynamics due to the presence of the walls. This leads to a reduction of the critical temperature T(c) of the mode coupling theory with decreasing film thickness. Analyzing the same data by the Vogel-Fulcher-Tammann (VFT) equation, we also estimate the VFT temperature T0(D). The ratio T0(D)/T(bulk)(0) decreases for smaller D similarly to T(c)(D)/T(bulk)(c). These results are in qualitative agreement with that of the glass transition temperature observed in some experiments on supported polymer films.

Molecular dynamics results on the pressure tensor of polymer films

Polymeric thin films of various thicknesses, confined between two repulsive walls, have been studied by molecular dynamics simulations. Using the anisotropy of the perpendicular, PN(z), and parallel components, PT(z), of the pressure tensor the surface tension of the system is calculated for a wide range of temperature and for various film thicknesses. Three methods of determining the pressure tensor are compared: the method of Irving and Kirkwood (IK), an approximation thereof (IK1), and the method of Harasima (H). The IK- and the H-methods differ in the expression for PT(z) (z denotes the distance from the wall), but yield the same formula for the normal component PN(z). When evaluated by molecular dynamics (or Monte Carlo)-simulations PN(z) is constant, as required by mechanical stability. Contrary to that, the IK1-method leads to strong oscillations of PN(z). However, all methods give the same expression for the total pressure when integrated over the whole system, and thus the same surface tension, w...

On the construction of coarse‐grained models for linear flexible polymer chains: Distribution functions for groups of consecutive monomers

Coarse‐grained models for linear flexible polymers are constructed defining effective segments by taking together n successive chemical monomers of a polymer chain, for n=1,2,3,...u2009. The distribution function Pn(l) for the length l of such effective segments is studied as well as the distribution function Pn(ϑ) of the angle between successive effective segments. If n is large enough, all these distribution functions tend towards universal limiting functions. For small n, information on chemical structure and effective potentials for the various degrees of freedom of the polymer chains is still preserved. Using polyethylene (PE) as one example, it is shown that these distribution functions for small n depend somewhat on the choice of the model for the effective potential (and the degrees of freedom included). Bisphenol‐A‐polycarbonate (BPA‐PC) as a second example, serves to study to which extent these distribution functions Pn(l) and Pn(ϑ) differ for chemically different polymers, such as PE and BPA‐PC. Co...

Intramolecular long-range correlations in polymer melts: the segmental size distribution and its moments.

We present theoretical arguments and numerical results to demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers, which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion u(s) approximately s/rho R3(s) approximately c(e)/sqrt[s] when connecting two segments together where s denotes the curvilinear length of a segment, R(s) its typical size, c(e) approximately 1/rho b(e)3 the swelling coefficient, b(e) the effective bond length, and rho the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to u(s). The analysis of different moments of this distribution allows for a precise determination of the effective bond length b(e) and the swelling coefficient c(e) of asymptotically long chains. At striking variance to the short-range decay suggested by Florys ideality hypothesis the bond-bond correlation function of two bonds separated by s monomers along the chain is found to decay algebraically as 1/s(3/2). Effects of finite chain length are briefly considered.

Long range bond-bond correlations in dense polymer solutions

The scaling of the bond-bond correlation function P1(s) along linear polymer chains is investigated with respect to the curvilinear distance s along the flexible chain and the monomer density rho via Monte Carlo and molecular dynamics simulations. Surprisingly, the correlations in dense three-dimensional solutions are found to decay with a power law P1(s) approximately s(-omega) with omega=3/2 and the exponential behavior commonly assumed is clearly ruled out for long chains. In semidilute solutions, the density dependent scaling of P1(s) approximately g(-omega(0))(s/g)(-omega) with omega(0)=2-2nu=0.824 (nu=0.588 being Florys exponent) is set by the number of monomers g(rho) in an excluded volume blob. Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains caused by the chain connectivity and the incompressibility of the melt.

Static properties of end-tethered polymers in good solution: a comparison between different models.

We present a comparison between results, obtained from different simulation models, for the static properties of end-tethered polymer layers in good solvent. Our analysis includes data from two previous studies--the bond fluctuation model of Wittmer et al. [J. Chem. Phys. 101, 4379 (1994)] and the off-lattice bead-spring model of Grest and Murat [Macromolecules 26, 3108 (1993)]. Additionally, we explore the properties of a similar off-lattice model simulated close to the Theta temperature. We show that the data for the bond fluctuation and the Grest-Murat model can be analyzed in terms of scaling theory because chains are swollen inside the Pincus blob. In the vicinity of the Theta point the structure of the chains is essentially Gaussian in the Pincus blob. Therefore, the data for the second off-lattice model can be compared quantitatively to the self-consistent field theory. Different ways to determine the parameters of the self-consistent field theory are discussed.

Polymer films in the normal-liquid and supercooled state: a review of recent Monte Carlo simulation results

Abstract The present paper reviews recent attempts to study the development of glassy behavior in thin polymer films by means of Monte Carlo simulations. The simulations employ a version of the bond-fluctuation lattice model, in which the glass transition is driven by the competition between an increase of the local volume requirement of a bond, caused by a stiffening of the polymer backbone and the dense packing of the chains in the melt. The melt is geometrically confined between two impenetrable walls separated by distances that range from once to approximately fifteen times the bulk radius of gyration. The confinement influences static and dynamic properties of the films: Chains close to the walls preferentially orient parallel to it. This orientation tendency propagates through the film and leads to a layer structure at low temperatures and small thicknesses. The layer structure strongly suppresses out-of-plane reorientations of the chains. In-plane reorientations have to take place in a high density environment which gives rise to an increase in the corresponding relaxation times. However, local density fluctuations are enhanced if the film thickness and the temperature decrease. This implies a reduction of the glass transition temperature with decreasing film thickness.

Static properties of polymer melts in two dimensions

Self-avoiding polymers in strictly two-dimensional (d=2) melts are investigated by means of molecular dynamics simulation of a standard bead-spring model with chain lengths ranging up to N=2048. The chains adopt compact configurations of typical size R(N)∼Nν with ν=1/d. The precise measurement of various distributions of internal chain distances allows a direct test of the contact exponents Θ0=3/8, Θ1=1/2, and Θ2=3/4 predicted by Duplantier. Due to the segregation of the chains the ratio of end-to-end distance Re(N) and gyration radius Rg(N) becomes Re2(N)/Rg2(N)≈5.3<6 for N⪢100 and the chains are more spherical than Gaussian phantom chains. The second Legendre polynomial P2(s) of the bond vectors decays as P2(s)∼1/s1+νΘ2, thus measuring the return probability of the chain after s steps. The irregular chain contours are shown to be characterized by a perimeter length L(N)∼R(N)dp of fractal line dimension dp=d−Θ2=5/4. In agreement with the generalized Porod scattering of compact objects with fractal contou...

Why polymer chains in a melt are not random walks

A cornerstone of modern polymer physics is the Flory ideality hypothesis which states that a chain in a polymer melt adopts ideal random-walk–like conformations. Here we revisit theoretically and numerically this pivotal assumption and demonstrate that there are noticeable deviations from ideality. The deviations come from the interplay of chain connectivity and the incompressibility of the melt, leading to an effective repulsion between chain segments of all sizes s. The amplitude of this repulsion increases with decreasing s where chain segments become more and more swollen. We illustrate this swelling by an analysis of the form factor F(q), i.e. the scattered intensity at wave vector q resulting from intramolecular interferences of a chain. A Kratky plot of q2F(q) vs. q does not exhibit the plateau for intermediate wave vectors characteristic of ideal chains. One rather finds a conspicuous depression of the plateau, δ(F−1(q))=|q|3/32ρ, which increases with q and only depends on the monomer density ρ.

Polymer-brush lubrication in the limit of strong compression

Abstract.By means of molecular dynamics simulations we demonstrate power laws for macroscopic transport properties of strongly compressed polymer-brush bilayers to stationary shear motion beyond the Newtonian response. The corresponding exponents are derived from a recently developed scaling theory, where the interpenetration between the brushes is taken as the relevant length scale. This allows to predict the dependence of the critical shear rate, which separates linear and non-linear behavior, on compression and molecular parameters of the bilayer. We present scaling plots for chain extension (R , viscosity (