This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the theta-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of "good solvents" and "theta-solvents" in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types.

Results of molecular dynamics simulations for systems with two flexible, oppositely charged polymer chains are presented. The lengths N and interaction strength of the chains are varied. We find that the chains remain separated for small values of . For large interaction strengths, i.e., large Bjerrum lengths, we find glasslike structures and order on the length scale of a few monomer diameters. Between these two limits of the interaction strengths, the chains of various lengths collapse into compact complexes that exhibit self-similar structures. The scaling behavior of the radius of gyration is discussed as a function of chain length and interaction strength. In addition, the local structure of the collapsed systems is analyzed and the dependence of the density of the aggregate on the interaction strength is discussed.

We discuss the hydrodynamic radius RH of polymer chains in good solvent, and show that the leading order correction to the asymptotic law RH ∝ N ν (N degree of polymerization, ν ≈ 0.59) is an "analytic" term of order N −(1−ν) , which is directly related to the discretization of the chain into a finite number of beads. This result is further corroborated by exact calculations for Gaussian chains, and extensive numerical simulations of different models of good-solvent chains, where we find a value of 1.591 ± 0.007 for the asymptotic universal ratio RG/RH , RG being the chain's gyration radius. For Θ chains the data apparently extrapolate to RG/RH ≈ 1.44, which is different from the Gaussian value 1.5045, but in accordance with previous simulations. We also show that the experimentally observed deviations of the initial decay rate in dynamic light scattering from the asymptotic Benmouna-Akcasu value can partly be understood by similar arguments.

This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment.