Search results for " statistical mechanics"
showing 10 items of 557 documents
Methods to Compute Pressure and Wall Tension in Fluids containing Hard Particles
2011
Colloidal systems are often modelled as fluids of hard particles (possibly with an additional soft attraction, e.g. caused by polymers also contained in the suspension). in simulations of such systems, the virial theorem cannot be straightforwardly applied to obtain the components of the pressure tensor. In systems confined by walls, it is hence also not straightforward to extract the excess energy due to the wall (the "wall tension") from the pressure tensor anisotropy. A comparative evaluation of several methods to circumvent this problem is presented, using as examples fluids of hard spheres and the Asakura-Oosawa model of colloid-polymer mixtures with a size ratio $q=0.15$ (for which th…
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.
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.
Anomalous Structure and Scaling of Ring Polymer Brushes
2011
A comparative simulation study of polymer brushes formed by grafting at a planar surface either flexible linear polymers (chain length $N_L$) or (non-catenated) ring polymers (chain length $N_R=2 N_L$) is presented. Two distinct off-lattice models are studied, one by Monte Carlo methods, the other by Molecular Dynamics, using a fast implementation on graphics processing units (GPUs). It is shown that the monomer density profiles $\rho(z)$ in the $z$-direction perpendicular to the surface for rings and linear chains are practically identical, $\rho_R(2 N_L, z)=\rho_L(N_L, z)$. The same applies to the pressure, exerted on a piston at hight z, as well. While the gyration radii components of ri…
Structure of bottle-brush polymers in solution: A Monte Carlo test of models for the scattering function
2008
Extensive Monte Carlo results are presented for a lattice model of a bottle-brush polymer under good solvent or Theta solvent conditions. Varying the side chain length, backbone length, and the grafting density for a rigid straight backbone, both radial density profiles of monomers and side chain ends are obtained, as well as structure factors describing the scattering from a single side chain and from the total bottle-brush polymer. To describe the structure in the interior of a very long bottle-brush, a periodic boundary condition in the direction along the backbone is used, and to describe effects due to the finiteness of the backbone length, a second set of simulations with free ends of…