Search results for "Scaling"
showing 10 items of 754 documents
Osmotic pressure, atomic pressure and the virial equation of state of polymer solutions: Monte Carlo simulations of a bead-spring model
1994
A recently introduced coarse-grained model of polymer chains is studied analyzing various contributions to the pressure as obtained from the virial theorem as a function of chain length N, temperature T and density ϕ. The off-lattice model of the polymer chains has anharmonic springs between the beads, but of finite extensibility, and the Morse-type interaction between beads is repulsive at very short distances and attractive at intermediate distances. Solvent molecules are not explicitly included. It is found that the covalent forces along the chain (modelled by the spring potentials) contribute a negative term to the pressure, irrespective of temperature, which vanishes linearly in ϕ as ϕ…
Adsorption Transition of a Polymer Chain at a Weakly Attractive Surface: Monte Carlo Simulation of Off-Lattice Models
2002
A bead-spring model of a polymer chain with one end attached to a wall is studied by Monte Carlo simulations for chain lengths 16 ≤ N ≤ 256. Two types of adsorption potentials, 9-3 and 10-4 Lennard-Jones (LJ) potentials, between the effective monomers and the wall are assumed. For both cases the adsorption transition where the chain changes its asymptotic statistical properties from a three-dimensional to a two-dimensional configuration is located using a scaling analysis. It is shown that the crossover exponent φ = 0.50 ± 0.02 is the same for both LJ potentials. This value is compatible with recent theoretical predictions and simulation results for lattice models with short-range wall pote…
On the first-order collapse transition of a three-dimensional, flexible homopolymer chain model
2005
We present simulation results for the phase behavior of flexible lattice polymer chains using the Wang-Landau sampling idea. These chains display a two-stage collapse through a coil-globule transition followed by a crystallization at lower temperatures. Performing a finite-size scaling analysis on the two transitions, we show that they coincide in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil-globule transition.
Structure and dynamics of grafted polymer layers: A Monte Carlo simulation
1991
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…
Monte Carlo simulations of chain dynamics in polymer brushes
1994
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.
Osmotic pressure of catenanes in solution
1989
We propose a nonuniversal scaling for the osmotic pressure in the case of concatenating ring polymers. The size exponent depends on the molecular weight of the catenans. The effect is more significant the shorter and the stiffer the molecules are.
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…
Selfdiffusion of polymer chains in solutions and melts
2005
Anomalous diffusion of monomers of polymer chains, as well as motion of these chains as a whole, is discussed with an emphasis on Monte Carlo simulations and simple scaling concepts. While the behavior of isolated chains in good solvents or Theta-solvents without excluded volume interactions is fully accounted for by the Rouse model, the behavior is less clear both for isolated chains in bad solvents and for chains in dense melts. Collapsed chains are shown to diffuse as g3(t) = <([rCM (t) -rCM(0)]2〉 ∝ tξ3 where the (effective?) exponent ξ3 simply seems to be linearly temperature-dependent for temperatures T lower than the Σ-temperature, ξ3 T/Θ. A relaxation time τ oc N3 is found, and scali…
Anomalous Diffusion and Relaxation of Collapsed Polymer Chains
1994
Time-dependent displacement of monomers and the centre-of-gravity motion of a polymer chain at various temperatures below the theta-temperature are studied by Monte Carlo simulation of an off-lattice model. While inner monomers diffuse Rouse-like, [ri(t) − ri(0)]2 t1/2, the centre of mass exhibits pronounced anomalous diffusion, [rc.m.(t) − rc.m.(0)]2 ta, where the exponent a seems to depend on temperature. The resulting anomalous dependence of the relaxation times on chain length is discussed in terms of scaling ideas. A possible relation to a glasslike freezing in of the collapsed globules is pointed out.
Scaling concepts for polymer brushes and their test with computer simulation
2004
After a brief review of the scaling concepts for static and dynamic properties of polymer brushes in good solvents and Theta solvents, the Monte Carlo evidence is discussed. It is shown that under typical conditions the diameter of the last blob is of the order of 10-20% of the brush height, and therefore pronounced deviations from the self-consistent field predictions occur. In bad solvents, lateral microphase separation occurs leading to an irregular pattern of "dimples". Particularly interesting is the response of brushes to shear deformation, and the interaction between two interpenetrating brushes. Recent attempts to understand the resulting shear forces via molecular-dynamics simulati…