Polymer simulations

Fig. 18 Schematic picture of the system for simulating polymer crystallization from the dense melt. Polymer chains that should be crystallized are sandwiched between parallel side surfaces of the lamellae made of the same polymer chains. The z-axis is taken normal to the substrate, while the y-axis is along the chain direction of the substrate crystals...

One of the interests in confined polymers arises from adsorption behavior— that is, the intake or partitioning of polymers into porous media. Simulation of confined polymers in equilibrium with a bulk fluid requires simulations where the chemical potentials of the bulk and confined polymers are equal. This is a difficult task because simulations of polymers at constant chemical potential require the insertion of molecules into the fluid, which has poor statistics for long chains. Several methods for simulating polymers at constant chemical potential have been proposed. These include biased insertion methods [61,62], novel simulation ensembles [63,64], and simulations where the pore is physically connected to a large bulk reservoir [42]. Although these methods are promising, so far they have not been implemented in an extensive study of the partitioning of polymers into porous media. This is a fruitful avenue for future research. 

Ramesh, N. S., Rasmussen, D. H., and Campbell, G. A., The Heterogeneous Nucleation of Microcellular Foams Assisted by the Survival of Microvoids in Polymers Containing Low Glass Transition Particles. Part 1 Mathematical Modeling and Numerical Simulation, Polym. Eng. ScL, 34, 1685 (1994)... 

Moysey, P.A. and Thompson, M.R., Investigation of Solids Transport in a Single-Screw Extruder Using a 3-D Discrete Particle Simulation, Polym. Eng. ScL, 44, 2203 (2004)... 

Henstenburg, R.B. and Phoenix, S.L. (1989). Interfaeial shear strength studies using the single-filament-compositc test, part II, A probability model and Monte Carlo simulation. Polym. Composites 10, 389-408. 

Figure 16 shows G(D) of a simulated polymer mixture at two scattering angles ("Q", 14° and 17°). The mixture consists of two polystyrene standards having distinctly different weight average molar masses (3.Ox 105 and 5.9x 106 g/mol) and a high mass polystyrene which is used to simulate the polymer cluster [66]. The area ratio Ar of the two peaks is expressed by... 

Ramesh NS, Rasmussen DH, Campbell GA (1994) The heterogeneous nucleation of microcellular foams assisted by the survival of microvoids in polymers containing low glass-transition particles. 1. Mathematical-modeling and numerical-simulation. Polym Eng Sci 34 1685-1697... 

The constants in eqn. (2.73) are defined in Table 2.7 for various viscoelastic models commonly used to simulate polymer flows. 

Fig. 12.36 Capillary viscosity data and Sabia equation fit. [Reprinted by permission from H. Mavridis and R. N. Shroff, Multilayer Extrusion Experiments and Computer Simulation, Polym. Eng. Sci., 34, 559 (1994).]...

To conclude this section, it may be interesting to mention what was concluded recently in (17) on the future of the free-volume diffusion models . .. However, phenomenological transport models based on free-volume concepts are likely to become obsolete during the coming decade, due to the development of computational techniques of simulating polymer microstructures . The development of such techniques and their results are discussed in Section 5.2. 

The difficulties in simulating polymer systems stem from the long relaxation times these systems display. Long runs are needed in order to ensure adequate equilibration. We have employed the method of Wall and Mandel (21) as modified for continuum three dimensional polymers by Webman, Ceperley, Kalos and Lebowitz (22). Each chain is considered in order and one end is chosen randomly as a bead. Suppose the initial chain coordi-nates are C = X, .. Xn A new position of that bead, X, is selected such that X = X + Ax where Xn is the initial head position and Ax is a vector randomly chosen via a rejection technique from the probability distribution exp(-BUfl(AX))(3=l/kBT, kfi Boltzmann s constant, T the temperature) and Ujj is iv< n in Eq. 

Parameter Values Used for Simulations (Polymer is Dextran)... 

This paper describes a finite element formulation designed to simulate polymer melt flows in which both conductive and convective heat transfer may be important, and illustrates the numerical model by means of computer experiments using Newtonian extruder drag flow and entry flow as trial problems. Fluid incompressibility is enforced by a penalty treatment of the element pressures, and the thermal convective transport is modeled by conventional Galerkin and optimal upwind treatments. 

There are two main approaches used to simulate polymer materials molecular dynamics and Monte Carlo methods. The molecular dynamics approach is based on numerical integration of Newton s equations of motion for a system of particles (or monomers). Particles follow dctcr-ministic trajectories in space for a well-defined set of interaction potentials between them. In a qualitatively different simulation technique, called Monte Carlo, phase space is sampled randomly. Molecular dynamics and Monte Carlo simulation approaches are analogous to time and ensemble methods of averaging in statistical mechanics. Some modern computer simulation methods use a combination of the two approaches. 

Kipper, M.J. Seifert, S. Thiyagarajan, P. Narasimhan, B. Understanding polyanhydride blend phase behavior using scattering, microscopy, and molecular simulations. Polymer 2004, 45 (10), 3329-3340. 

Soldera, A. Energetic analysis of the two pmma chain tacticities and pma through molecular dynamics simulations. Polymer 43, 4269-4275 (2002)... 

After having simulated the components of the chemical process individually, a simulation of the overall process is performed. To this end, different kinds of simulators have to be coupled to form a heterogeneous simulator. We have shown that MOREX has been used for ID simulation of the extruder. Furthermore, reaction and separation simulations have been performed with the help of the commercial simulators Polymers Plus and gPROMS, respectively. 

Part of the difficulty of simulating polymers resides in the fact that both intra- and intermolecular interactions play a role on the behavior of a molecule. Some of the methods mentioned above have circumvented this... 

Figure 4.6-2 Characteristic features of the PLP-SEC measurement (a) the pulsed laser-induced free-radical concentration (cr) versus time profile, where v is the pulse repetition rate (b) the resulting (simulated) polymer molecular weight distribution, wClogio M).

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. 

PART 3 Bulk Polymerization Process Simulation-Polym.Eng.Science, 31,886-903 (1991) ... 

To estimate Lc more accurately Yamakawa and Shimada [52] computed (5 ) of polymethylene-like rotational isomeric state models with excluded volume by a Monte Carlo method. They considered that bead-bead interactions higher than ones leading to the pentane effect contribute to excluded-volume effects. They found that the simulated polymer in the unperturbed state can be modeled by a wormlike chain and that (5 )/(4 rtK) of perturbed chains begins to deviate from those of unperturbed ones at uk of 3—5. Thus, the Lc by Yamakawa and... 

Boussoum, M. O. Atek, D. Belhaneche-Bensemra, N. Interactions between poly(viny 1 chloride) stabilised with epoxidised sunflower oil and food simulants. Polymer Degradation and Stability, 2006,91, 579-584. 

The study of static and dynamic properties of polymer liquids and glasses is one of the central topics of research in polymer science. A variety of experimental and theoretical techniqi s have been mobilized for this purpose. In recent years the techniques of computer simulations are increasingly finding application toward this goal. AU the various methods of simulating polymer molecules on computers, such as Monte Carlo, molecular mechanics. Brownian dynamics, and molecular dynamics simulation techniques have been utilized. Early works relied mostly on Monte Carlo techniques apfdied to schematic models of polymer Uquid built on a lattice. With increased capabilities of computers available in recent years, the use of more computationally intensive methods has become feasible, allowing simulations of more realistic, off-latdce models of bulk polymers by Brownian and molecular dynamics simulation techniques as well as by Monte Carlo methods. 

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