Search results for "statistical [methods]"

Direct evaluation of the electron density correlation function of partially crystalline polymers

1980

A discussion of the general properties of the one-dimensional electron density correlation function K(z) of a partially crystalline polymer with lamellar structure shows that application of a graphical extrapolation procedure permits direct determination of the crystallinity, the specific inner surface, and the electron density difference ηc − ηa. The procedure is based upon the occurrence of a straight section in the “self-correlation” range of K(z). Curved and nonparallel lamellae do not invalidate the concept. In the case of heterogeneous samples composed of partially crystalline and totally amorphous regions, some of the parameters of the experimentally obtained correlation function, as…

Statistical Mechanics of Polymers: New Developments - International Workshop

2007

Dragging a Polymer Chain into a Nanotube and Subsequent Release

2008

We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method. The nanotube is a long channel opened at one end and its diameter $D$ is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position $x$ inside the tube: the free energy of confinement, the average end-to-end distance, the averag…

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

2001

We present results of molecular dynamics (MD) simulations for a non-entangled polymer melt confined between two completely smooth and repulsive walls, interacting with inner particles via the potential $U_{\rm wall}\myeq (\sigma/z)^9$, where $z \myeq |z_{\rm particle}-z_{\rm wall}|$ 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. %Consistent…

Structure of bottle-brush brushes under good solvent conditions: a molecular dynamics study.

2011

We report a simulation study for bottle-brush polymers grafted on a rigid backbone. Using a standard coarse-grained bead-spring model extensive molecular dynamics simulations for such macromolecules under good solvent conditions are performed. We consider a broad range of parameters and present numerical results for the monomer density profile, density of the untethered ends of the grafted flexible backbones and the correlation function describing the range that neighboring grafted bottle-brushes are affected by the presence of the others due to the excluded volume interactions. The end beads of the flexible backbones of the grafted bottle-brushes do not access the region close to the rigid…

Calculation of the Phase Behavior of Lipids

1998

The self-assembly of monoacyl lipids in solution is studied employing a model in which the lipid's hydrocarbon tail is described within the Rotational Isomeric State framework and is attached to a simple hydrophilic head. Mean-field theory is employed, and the necessary partition function of a single lipid is obtained via a partial enumeration over a large sample of molecular conformations. The influence of the lipid architecture on the transition between the lamellar and inverted-hexagonal phases is calculated, and qualitative agreement with experiment is found.

Scaling theory of star polymers and general polymer networks in bulk and semi-infinite good solvents

1988

Theorie d'echelle utilisant l'equivalence entre la fonction generatrice du nombre total de configuration et la fonction de correlation a plusieurs spins du modele de Heisenberg classique a n composantes dans la limite n→0

Third virial coefficient for 4-arm and 6-arm star polymers

2008

We discuss the computation of the third virial coefficient in polymer systems, focusing on an additional contribution absent in the case of monoatomic fluids. We determine the interpenetration ratio and several quantities that involve the third virial coefficient for star polymers with 4 and 6 arms in the good-solvent regime, in the limit of a large degree of polymerization.

Polymer dynamics in time-dependent periodic potentials.

2008

Dynamics of a discrete polymer in time-dependent external potentials is studied with the master equation approach. We consider both stochastic and deterministic switching mechanisms for the potential states and give the essential equations for computing the stationary state properties of molecules with internal structure in time-dependent periodic potentials on a lattice. As an example, we consider standard and modified Rubinstein-Duke polymers and calculate their mean drift and effective diffusion coefficient in the two-state non-symmetric flashing potential and symmetric traveling potential. Rich non-linear behavior of these observables is found. By varying the polymer length, we find cur…

Scaling behavior of topologically constrained polymer rings in a melt

2014

Large scale molecular dynamics simulations on graphic processing units (GPUs) are employed to study the scaling behavior of ring polymers with various topological constraints in melts. Typical sizes of rings containing $3_1$, $5_1$ knots and catenanes made up of two unknotted rings scale like $N^{1/3}$ in the limit of large ring sizes $N$. This is consistent with the crumpled globule model and similar findings for unknotted rings. For small ring lengths knots occupy a significant fraction of the ring. The scaling of typical ring sizes for small $N$ thus depends on the particular knot type and the exponent is generally larger than 0.4.