Simulation polymer chain

The RIS-MC scheme allows the positions of all segments in a particular simulated molecule to be specified. The solution adjacent to the wall was divided into a series of layers, all of equal thickness and all parallel to the surface (see Fig. 17.4). The layer thickness typically was chosen to be, say, one-twentieth of the rms end-to-end distance of the free polymer. Halving or doubling the thickness of the layer did not significantly alter the results obtained. Each simulated polymer chain was also divided into layers of the same thickness. The number of segments in each layer of each simulated chain was found using the RIS-MC scheme. 

EDMD and thermodynamic perturbation theory. Donev et developed a novd stochastic event-driven molecular dynamics (SEDMD) algorithm for simulating polymer chains in a solvent. This hybrid algorithm combines EDMD with the direa simulation Monte Carlo (DSMC) method. The chain beads are hard spheres tethered by square-wells and interact with the surrounding solvent with hard-core potentials. EDMD is used for the simulation of the polymer and solvent, but the solvent-solvent interaction is determined stochastically using DSMC. 

Fig. 3. MD simulation of a polymer chain of 100 CH2 groups due to [10], The dynamics of the distance between two CHj-groups ( 12 and 36). The series of plots illustrates the oscillations of the distance at time scales increasing by a zoom factor of 10 at each level.

The property to be predicted must be considered when choosing the method for simulating a polymer. Properties can be broadly assigned into one of two categories material properties, primarily a function of the nature of the polymer chain itself, or specimen properties, primarily due to the size, shape, and phase... 

Many simulations attempt to determine what motion of the polymer is possible. This can be done by modeling displacements of sections of the chain, Monte Carlo simulations, or reptation (a snakelike motion of the polymer chain as it threads past other chains). These motion studies ultimately attempt to determine a correlation between the molecular motion possible and the macroscopic flexibility, hardness, and so on. 

Once a rubberband is stretched beyond its elastic region, it becomes much harder to stretch and soon breaks. At this point, the polymer chains are linear and more energy must be applied to slide chains past one another and break bonds. Thus, determining the energy required to break the material requires a different type of simulation. 

Finally, we want to describe two examples of those isolated polymer chains in a sea of solvent molecules. Polymer chains relax considerably faster in a low-molecular-weight solvent than in melts or glasses. Yet it is still almost impossible to study the conformational relaxation of a polymer chain in solvent using atomistic simulations. However, in many cases it is not the polymer dynamics that is of interest but the structure and dynamics of the solvent around the chain. Often, the first and maybe second solvation shells dominate the solvation. Two recent examples of aqueous and non-aqueous polymer solutions should illustrate this poly(ethylene oxide) (PEO) [31]... 

Another important characteristic aspect of systems near the glass transition is the time-temperature superposition principle [23,34,45,46]. This simply means that suitably scaled data should all fall on one common curve independent of temperature, chain length, and time. Such generahzed functions which are, for example, known as generalized spin autocorrelation functions from spin glasses can also be defined from computer simulation of polymers. Typical quantities for instance are the autocorrelation function of the end-to-end distance or radius of gyration Rq of a polymer chain in a suitably normalized manner ... 

Generally, the models used for simulation of living polymers can be divided roughly into two classes, focused on static or dynamic properties of the LP or GM. The static models are mainly designed to study equilibrium conformational properties of the polymer chains, critical behavior at the polymerization transition, and molecular weight distribution... 

These models are designed to reproduce the random movement of flexible polymer chains in a solvent or melt in a more or less realistic way. Simulational results which reproduce in simple cases the so-called Rouse [49] or Zimm [50] dynamics, depending on whether hydrodynamic interactions in the system are neglected or not, appear appropriate for studying diffusion, relaxation, and transport properties in general. In all dynamic models the monomers perform small displacements per unit time while the connectivity of the chains is preserved during the simulation. 

The bond fluctuation model (BFM) [51] has proved to be a very efficient computational method for Monte Carlo simulations of linear polymers during the last decade. This is a coarse-grained model of polymer chains, in which an effective monomer consists of an elementary cube whose eight sites on a hypothetical cubic lattice are blocked for further occupation (see... 

K. Binder, P. Y. Lai, J. Wittmer. Monte Carlo simulations of chain dynamics in polymer brushes. Faraday Discuss Chem Sci 95 97-109, 1994. 

A. Milchev, W. Paul, K. Binder. Polymer chains confined into tubes with attractive walls A Monte Carlo simulation. Macromol Theory Simul 5 305-323, 1994. 

V. Yamakov, A. Milchev. Polymer chain in a flow through a porous medium A Monte Carlo simulation. Phys Rev E 5(5 7043-7052, 1997. 

P. Y. Lai. Statics and dynamics of a polymer chain adsorbed on a surface Monte Carlo simulation using the bond fluctuation model. Phys Rev E 49 5420-5430, 1994. 

K. Kremer, K. Binder. Dynamics of polymer chains confined into tubes Scaling theory and Monte Carlo simulations. J Chem Phys 7 6381-6394, 1984. 

Whenever the polymer crystal assumes a loosely packed hexagonal structure at high pressure, the ECC structure is found to be realized. Hikosaka [165] then proposed the sliding diffusion of a polymer chain as dominant transport process. Molecular dynamics simulations will be helpful for the understanding of this shding diffusion. Folding phenomena of chains are also studied intensively by Monte Carlo methods and generalizations [166,167]. 

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

Mapping Atomistically Detailed Models of Flexible Polymer Chains in Melts to Coarse-Grained Lattice Descriptions Monte Carlo Simulation of the Bond Fluctuation Model... 

All the simulations described so far refer to strictly monodisperse polymer melts, i. e. all polymer chains have strictly the same chain length N. For most... 

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