Molecular dynamics simulation bead-spring model

Since this behavior is universal, it is obvious that the simplest simulation models which contain the essential aspects of polymers are sufficient to study these phenomena. Two typical examples of such models are the bond fluctuation Monte Carlo model and the simple bead-spring model employed in molecular dynamics simulations. Both models are illustrated in Fig. 6. 

So far, we have demonstrated that the MC simulation (lattice-based SRS model and off-lattice bead-spring model) results are in qualitative agreement with the experiments. A complementary approach is molecular dynamics (MD) simulation using the bead-spring model. Since MD study for PFPE is still the infant stage, we will discuss it only briefly. The equation of motion can be expressed in... 

Now that we have settled on a model, one needs to choose the appropriate algorithm. Three methods have been used to study polymers in the continuum Monte Carlo, molecular dynamics, and Brownian dynamics. Because the distance between beads is not fixed in the bead-spring model, one can use a very simple set of moves in a Monte Carlo simulation, namely choose a monomer at random and attempt to displace it a random amount in a random direction. The move is then accepted or rejected based on a Boltzmann weight. Although this method works very well for static and dynamic properties in equilibrium, it is not appropriate for studying polymers in a shear flow. This is because the method is purely stochastic and the velocity of a mer is undefined. In a molecular dynamics simulation one can follow the dynamics of each mer since one simply solves Newton s equations of motion for mer i,... 

On the basis of our results using scanning force microscopy such as S VM and LFM, we claim that the mobility at the surface of PS films is not the same as that in the bulk. However, in such measurements, a probe tip made of silicon or silicon nitride makes contact with the surface to be measured. This may induce some artifacts in the results. If an effect of tip contact on the surface dynamics cannot be negligible, our conclusion must be reconsidered. Thus, T is here discussed on the basis of coarse-grained molecular dynamics simulation using a bead-spring model of Grest... 

Figure 9 Molecular dynamics simulation of a Lennard-Jones, bead-spring model, (a) Slip length, 8, as a function of the strength, [ an, of attraction between a hard, corrugated substrate and liquid for temperature, kgT/ [ =. 2. The solid line with circles is obtained from the Couette and Poiseuille profiles (NEMO) according toeqn [37], whereas the dashed line with squares, from the Green-Kubo (GK) relation, eqn [39]. The curve marks the behavior 1/ [ jii in accord with eqn [40]. The inset illustrates the velocity profiles of the Couette and Poiseuille flows, from which the slip length has been estimated for [mii = 0.6, measured in units of the Lennard-Jones parameter, [. Adapted from Servantie, J. Muller, M. Phys. Rev. Lett. 2008, 101,...

The LB method and its improved versions are widely used for the effident treatment of polymer solution dynamics. In the application to polymer solution dynamics, the polymer itself is still treated on a partide-based CG level using, for example, a bead-spring model, while the solvent is treated on the level of a discretized Boltzmann equation. The two parts are coupled by a simple dissipative point-partide force, and the system is driven by Langevin stochastic forces added to both the fluid and the polymers. In this approach, the hydrodynamics of the low-molecular-weight solvent is correctly captured, and the HI between polymer segments, which is mediated by the hydrodynamic flow generated within the solvent through the motion of the polymer, is present in the simulation without explidt... 

Figure 1.9 illustrates the variation of these mean-square displacements with time and the estimation of the resulting relaxation times n, t2, ts, T4 for three different models the bond fluctuation model, the off-lattice bead-spring model of Gerroff et al. and the molecular dynamics simulation of a realistic model for short polyethylene chains Np = 50) in the melt... 

The Zimm model apphes to dilute solutions, and, therefore, to the dynamics of a single solvated chain. It has become a benchmark system, used to test the validity of mesoscopic simulation methods. A single chain, modeled by bead-spring interactions, coupled to a surrounding solvent to account for hydrodynamic interactions, has been successfully simulated via (1) Molecular Dynamics [180-182], (2) Dissipative Particle Dynamics [183,184], Multi-Particle Collision Dynamics [185,186],... 

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