Marvin Bishop

Investigation of the end‐to‐end distance distribution function for random and self‐avoiding walks in two and three dimensions

Monte Carlo simulations employing the pivot algorithm are used to generate random and self‐avoiding walks on two‐ and three‐dimensional lattices. The moments of the end‐to‐end distance distribution function are calculated from the resulting configurations. It is found that the moments and the shape of the vector distribution function are in excellent agreement with the scaling form derived by des Cloizeaux.

Brownian dynamics study of the shape of star and linear polymers in different regimes

Brownian dynamics computer simulations are used to investigate the shape of linear and star polymers in three regimes: (1) excluded volume, (2) θ, (3) collapsed. It is found that the mean‐square radius of gyration 〈S2〉 displays a different power law exponent in the different regimes: 〈S2〉∼(1) (N−1)1.2 (2) (N−1)1.0, and (3) (N−1)2/3 where N is the number of chain units. The pair‐correlation function using the central vertex bead as the origin reveals the polymer structure. In the collapsed regime the structure resembles face‐centered‐cubic (FCC) packing. The g ratio of star/linear chains as well as the asphericity of the polymers have been determined for the three regimes.

The shape of linear and star polymers with and without excluded volume

The shape of isolated linear and star polymers, with and without excluded volume, has been determined by Monte Carlo simulations using a pivot algorithm. Stars with 3, 4, 5, and 6 arms are studied. The high efficiency of the pivot algorithm has allowed us to obtain accurate data for long chains. Good agreement is found with existing analytical expressions for nonexcluded volume chains and with other computer simulations for excluded volume chains.

Investigation of the end-to-end vector distribution function for linear polymers in different regimes

Monte Carlo simulations employing the pivot algorithm are used to generate off‐lattice three‐dimensional linear polymers in three regimes: nonexcluded volume, theta, and excluded volume. The end‐to‐end vector distribution function is calculated from the resulting configurations. It is found that the shape of the distribution function is Gaussian for nonexcluded volume chains, nearly Gaussian for theta chains, and that the scaling form derived by des Cloizeaux fits the data for excluded volume chains well.

System size dependence and time convergence in molecular dynamics simulations of monolayer films

The sample size dependence and time convergence of property values of simple hydrocarbon monolayers has been investigated by performing molecular dynamics simulations at four surface coverages for systems ranging in size from 16 to 100 chains and for trajectories as long as 200 ps. Detailed studies of the tilt angle indicate that systems with 64 chains simulated for 40 ps (in addition to a 40 ps equilibration stage) are large enough to obtain statistically meaningful results. The equilibrium tilt angle is slightly sensitive to the boundary conditions.

The shape of two-dimensional linear and star polymers with and without excluded volume

The shape of isolated two‐dimensional linear and star polymers, with and without excluded volume, have been determined by Monte Carlo simulations using a pivot algorithm. Stars with 3, 4, 5, and 6 arms are studied. The high efficiency of the pivot algorithm has allowed us to obtain accurate data for long chains. Good agreement is found with existing analytical expressions for nonexcluded volume chains and with other computer simulations for excluded volume chains.

Brownian dynamics study of surface adsorption of a linear polymer in different regimes

Brownian dynamics computer simulations are used to investigate the properties of isolated, terminally attached polymers interacting with a surface. Three regimes of the polymer chains are studied: excluded volume, θ, and self‐collapsed. It is found that chains are progressively adsorbed to the surface as the surface attraction is increased. The mean‐square radius of gyration power law exponent for excluded volume chains changes from 1.2 (the three‐dimensional excluded volume value) to 1.5 (the two‐dimensional excluded volume value) when the chains are completely adsorbed and the exponent for the θ chains changes from 1.0 (the three‐dimensional θ value) to 1.5 in agreement with previous lattice simulations. The collapsed chain exponent remains at 2/3 throughout the transition. The density profile as a function of the distance from the surface, the asphericity, and computer graphics snapshots of typical configurations reveal more details about the polymer structure. The self‐collapsed chain forms a multilay...

The distribution function of the radius of gyration of linear polymers in two and three dimensions

Monte Carlo simulations employing the pivot algorithm are used to generate excluded‐volume chains on two‐ and three‐dimensional lattices. The radius of gyration distribution function is calculated from the resulting configurations. The distributions are in excellent agreement with the scaled form postulated by Lhuillier.

Structure function of linear polymers in the ideal and excluded volume regime

Monte Carlo simulations employing the pivot algorithm are used to generate ideal and excluded‐volume chains on two‐ and three‐dimensional lattices. The second, fourth, sixth, and eighth moments of the average monomer–monomer separation are calculated from the resulting configurations. The coefficients in the expansion of the structure factor are computed from universal ratios of these. The values found for excluded‐volume chains are smaller than the ideal chain values and the differences are greater in two dimensions than in three dimensions.

Brownian dynamics study of the end‐to‐end distribution function of two‐dimensional linear chains in different regimes

Brownian dynamics computer simulations are used to investigate the shape of the mean‐squared end–to–end distance distribution function for two‐dimensional linear chains in three regimes: (1) excluded volume, (2) θ, (3) collapsed. It is found that Mazur’s function fits regime (1), that the Gaussian function fits regime (3), and that the changeover in behavior between these two functional forms appears to occur at temperatures well above the expected θ point.