Structure of a bidisperse polymer brush: Monte Carlo simulation and self-consistent field results

Using the bond-fluctuation model, Monte Carlo simulations are performed for polymer brushes composed of chains of two different chain lengths under good solvent condition. Profiles of monomer density and free end density, chain linear dimensions, and average monomer position along a chain are studied. Quantities measured in the simulations are derived from the analytic self-consistent field (SCF) theory and compared with the simulation data. The structural properties can be quite accurately described by the theory only when both the long and short chains are stretched

Structure and dynamics of grafted polymer layers: A Monte Carlo simulation

The bond fluctuation model of polymer chains on lattices is used to study layers of polymers anchored with one end at a hard wall, assuming good solvent conditions and repulsive interactions between the monomers and the wall. Chain lengths from N=10 to N=80 and grafting densities σ from 0.025 to 0.20 are considered, both for the ‘‘quenched’’ case, where the anchor points are kept fixed at randomly chosen surface sites, and the ‘‘annealed’’ case, where lateral diffusion of the anchored ends at the wall is considered. Profiles of monomer density and free end density, chain linear dimensions parallel and perpendicular to the wall, as well as corresponding mean square displacements of inner and…

Structure and dynamics of polymer brushes near the Θ point: A Monte Carlo simulation

Grafted polymer layers under variable solvent conditions are studied by Monte Carlo simulations using the bond fluctuation model. Structural information such as monomer density profiles, brush thickness, mean‐square displacement of monomers, and positions of the monomers along the chain are obtained for temperatures above, at, and below the Θ point. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. At the Θ point, more extensive simulations are performed to investigate the structural and dynamical properties. While the brush thickness at the Θ point agrees very well with the scaling and self‐consistent field predictions, the latter deviate …

Quantum vector spin-glass in a field: results for general spin

Abstract In this paper we investigate the infinite-ranged quantum Heisenberg spin-glass in an applied field for a general spin s without the use of the static approximation. The Suzuki-Trotter method is used to map the system into a classical one for general spin s. Results for spin 1 2 and spin 1 are explicitly obtained and the phase diagram agrees qualitatively but not exactly with previous results obtained by us using the static approximation.

Grafted polymer layers under variable solvent conditions: A Monte Carlo simulation

Polymer chains anchored with one end at a hard wall under variable solvent conditions are investigated by Monte Carlo simulations using the bond- fluctuation model. Detail information on the structural properties are obtained above, at, and below the Θ-point and discussed in terms of the appropriate theories. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. For the dynamics at the Θ-point, both the relaxation time of the chain configuration and the mean-square time displacement are studied. At temperatures distinctly below the Θ-point, we find that the layer develops considerable lateral inhomogeneity in its density, which has not been pre…

Monte Carlo test of the self-consistent field theory of a polymer brush

Grafted polymer layers under shear: A Monte Carlo simulation

Endgrafted polymers at surfaces exposed to a shear flow are modeled by a nonequilibrium Monte Carlo method where the jump rate of effective monomers to neighboring lattice sites against the flow direction is smaller than in the flow direction, assuming that this difference in jump rates is proportional to the local velocity of the flowing fluid. In the dilute case of isolated chains, the velocity profile is assumed linearly increasing with the distance from the surface, while for the case of polymer brushes the screening of the velocity field is calculated using a parabolic density profile for the brush whose height is determined self‐consistently. Linear dimensions of isolated chains are o…

Monte Carlo simulations of chain dynamics in polymer brushes

The bond-fluctuation model of polymer chains has been used to study layers of end-grafted polymers anchoring at repulsive walls for a broad range of chain length, grafting densities and solvent quality. The dynamics of monomers and associated relaxation times are investigated and interpreted by phenomenological theories and scaling arguments. The case is also considered where a chain is cut off from its anchor point and the chain is subsequently expelled from the brush. Both the velocity with which the chain leaves the brush and the associated conformational changes (chain contraction etc.) are analysed and interpreted in terms of recent theoretical concepts.

Ising Spin-Glass on a Lattice with Small Loops

We consider the Ising spin-glass on a special lattice containing small loops with finite coordination number c. We derive the equation for the effective field distribution. With zero external field, we calculate the spin-glass transition temperature and obtain the lower critical dimension of the system. We investigate the system near and below the spin-glass transition and find that the replica symmetric solution is unstable in the low-temperature phase. Our results indicate that the replica symmetry breaking (RSB) effects are stronger than that of the Bethe lattice and furthermore, RSB is enhanced as the dimension (c/2) is decreased. Comparison with recent results of the 1/d expansion is a…

Linear chain surfactants at a planar interface: a comparative Monte Carlo study of several lattice models

Linear chain surfactants in a densely packed arrangement (such as alkane chains in lipid monolayers in the “uniform tilt” structures) are described by a crude coarse-grained model where the endgroups grafted on the interface form a regular lattice and the chains are described by the bond fluctuation model with chains containing N = 4 effective monomers only. Square-well interactions between the monomers are studied for both the attractive and repulsive case for three choices of the interaction range. None of these models exhibits a structure with uniform tilt. For attractive interactions the last bond has a strong tendency to fold back thus leading to a very high density close to the interf…