Search results for "Monte Carlo method."
showing 10 items of 1217 documents
Monte Carlo Simulations of Polymer Systems
1988
The impact of Monte Carlo “computer experiments” in polymer physics is described, emphasizing three examples taken from the author’s research group. The first example is a test of the classical Flory—Huggins theory for polymer mixtures, including a discussion of cricital phenomena. Also “technical aspects” of such simulations (“grand-canonical” ensemble, finite—size scaling, etc.) are explained briefly. The second example refers to configurational statistics and dynamics of chains confined to cylindrical tubes; the third example deals with the adsorption of polymers at walls. These simulations check scaling concepts developed along the lines of de Gennes.
Monte Carlo Simulations in Polymer Science
2012
Monte Carlo methods are useful for computing the statistical properties of both single macromolecules of various chemical architectures and systems containing many polymers (solutions, melts, blends, etc.). Starting with simple models (lattice models such as the self-avoiding walk or the bond fluctuation model, as well as coarse-grained or chemically realistic models in the continuum) various algorithms exist to generate conformations typical for thermal equilibrium, but dynamic Monte Carlo methods can also model diffusion and relaxation processes (as described by the Rouse and the reptation models for polymer melt dynamics). Limitations of the method are explained, and also the measures to…
Monte Carlo Simulation of Langmuir Monolayer Models
1998
We study a coarse grained, continuum model for Langmuir monolayers, i.e., monolayers of amphiphilic molecules on a polar substrate. The amphiphiles are represented by stiff chains of beads with one end grafted to a planar surface. Monte Carlo Simulations at constant pressure have been performed, using simulation boxes of variable size and variable shape. A number of techniques have been explored in order to obtain an efficient simulation algorithm. We discuss the resulting phase diagram, characterize the different phases, and analyze the conditions, under which they can be found.
Symmetric diblock copolymers confined into thin films: A Monte Carlo investigation on the CRAY T3E
2000
We present the results of large scale computer simulations targeted at investigating the phase stability and the structure of symmetric AB diblock copolymers in thin films. The connectivity of the two different monomer species A and B in the diblock copolymer prevents macrophage separation and the molecules assemble into A-rich and B-rich domains on the scale of the molecule’s extension. This large length scale of the ordering phenomena makes these polymeric systems a promising candidate for revealing the universal features of self-assembling in amphiphilic molecules. However, the widely spread length and time scales impart protracted long relaxation times to the systems and pose a challeng…
Theory of glass transition in spin glasses, orientational glasses and structural glasses
2008
Theoretical concepts about the glass transition are briefly reviewed, and the test of these ideas by Monte Carlo simulations of simple lattice models is described, with an emphasis on isotropic and anisotropic orientational glasses, and the bond fluctuation model of polymer melts. It is suggested that orientational glasses do have an equilibrium phase transition at zero temperature (in d = 3 dimensions!) only, in contrast to the Ising spin glass which orders at nonzero temperature. A diverging glass correlation length is identified that is responsible for the anomalous slowing down. For the Potts glass, the divergence seems to be exponential, implying that the model is at its lower critical…
Small-Angle Excess Scattering: Glassy Freezing or Local Orientational Ordering?
1996
We present Monte Carlo simulations of a dense polymer melt which shows glass-transition-like slowing-down upon cooling, as well as a build up of nematic order. At small wave vectors q this model system shows excess scattering similar to that recently reported for light-scattering experiments on some polymeric and molecular glass-forming liquids. For our model system we can provide clear evidence that this excess scattering is due to the onset of short-range nematic order and not directly related to the glass transition.
Computer Simulations for Polymer Dynamics
1991
In this paper we review recent work on the dynamics of polymeric systems using computer simulation methods. For a two-dimensional polymer melt, we show that the chains segregate and the dynamics can be described very well by the Rouse model. This simulation was carried out using the bond fluctuation Monte Carlo method. For three-dimensional (3d) melts and for the study of hydrodynamic effects, we use a molecular dynamics simulation. For 3d melts our results strongly support the concept of reptation. A detailed comparison to experiment shows that we can predict the time and length scales for the onset of reptation for a variety of polymeric liquids. For a single chain, we find the expected h…
Monte Carlo Simulations of Growth Kinetics and Phase Transitions at Interfaces: Some Recent Results
1991
ABSTRACTIn the first part Monte Carlo studies of the kinetics of multilayer adsorption (without screening) are described. The approach to the jamming coverage in each layer is asymptotically exponential. The jamming coverages approach the infinite-layer limit value according to a power law. In the second part, studies of phase transitions in two dimensional fluids are reviewed. With a combination of Monte Carlo and finite size scaling block analysis techniques, accurate values are obtained for the critical temperatures, coexistence densities and the compressibilities of an adsorbed fluid layer in an NVT ensemble.
Anomalous diffusion of polymers in supercooled melts near the glass transition
2007
Two coarse-grained models for polymer chains in dense melts near the glass transition are investigated: the bond fluctuation lattice model, where long bonds are energetically favored, is studied by dynamic Monte Carlo simulation, and an off-lattice bead-spring model with Lennard-Jones forces between the beads is treated by Molecular Dynamics. We compare the time-dependence of the mean square displacements of both models, and show that they become very similar on mesoscopic scales (i.e., displacements larger than a bond length). The slowing down of motions near the glass transition is discussed in terms of the mode coupling theory and other concepts.
Isotropic–isotropic phase separation in mixtures of rods and spheres: Some aspects of Monte Carlo simulation in the grand canonical ensemble
2008
Abstract In this article we consider mixtures of non-adsorbing polymers and rod-like colloids in the isotropic phase, which upon the addition of polymers show an effective attraction via depletion forces. Above a certain concentration, the depletant causes phase separation of the mixture. We performed Monte Carlo simulations to estimate the phase boundaries of isotropic–isotropic coexistence. To determine the phase boundaries we simulated in the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120 (2004) 10925]. The location of the critical point was estimated by a finite size scaling analysis. In order to equilibrate the system efficiently, we used a cluster move…