Computer simulations of polymeric systems

Two polymeric systems that deviate from the usual scaling limit were studied by two simulation techniques. Scaling concepts are often applied to polymeric systems to understand their underlying natures. But when anisotropies or different length scales have to be included in the model, the application of scaling concepts is no longer straight forward. The use of simulations circumvents this problem and gives exact solutions to the model.; Monte Carlo umbrella sampling has been used to study the effects of randomly distributed surface disorders on the adsorption of linear polymers with excluded volume interactions on a 3-d lattice model. The monomers and the surface defects are assumed to interact with an attractive short-range potential. Analysis of the free-energy profiles reveal that an adsorbed phase sets in above a certain critical surface disorder. Using the theory of self-averaging, this critical surface disorder can be related to the density and energy of the defects using a simple universal relationship. Various scaling exponents describing the equilibrium geometries of the adsorbed chains as well as the adsorption energy were also obtained.; Constant temperature molecular dynamics simulations were used to study solutions of flexible polyelectrolyte chains at nonzero concentrations with explicit counterions and unscreened Coulombic interactions. Counterion condensation, measured via the self-diffusion coefficient of the counterions, is found to increase with polymer concentration, but contrary to the prediction of Manning theory, the renormalized charge fraction on the chains decreases with increasing Bjerrum length without showing any saturation. Scaling analyses of the radius of gyration show that the chains are extended at low polymer concentrations and small Bjerrum lengths, while at sufficiently large Bjerrum lengths, the chains shrink to produce compact structures with exponents smaller than a gaussian chain, suggesting the presence of attractive intrachain interactions. A careful study of the radial distribution function of the center-of-mass of the polyelectrolyte chains shows clear evidence that effective interchain attractive interactions also exist in solutions of flexible polyelectrolytes, similar to what has been found for rodlike polyelectrolytes.