Off-lattice Monte Carlo Method Research Articles

First-principle simulations of electronic structure in semicrystalline polyethylene.

In order to increase our fundamental knowledge about high-voltage cable insulation materials, realistic polyethylene (PE) structures, generated with a novel molecular modeling strategy, have been analyzed using first principle electronic structure simulations. The PE structures were constructed by first generating atomistic PE configurations with an off-lattice Monte Carlo method and then equilibrating the structures at the desired temperature and pressure using molecular dynamics simulations. Semicrystalline, fully crystalline and fully amorphous PE, in some cases including crosslinks and short-chain branches, were analyzed. The modeled PE had a structure in agreement with established experimental data. Linear-scaling density functional theory (LS-DFT) was used to examine the electronic structure (e.g., spatial distribution of molecular orbitals, bandgaps and mobility edges) on all the materials, whereas conventional DFT was used to validate the LS-DFT results on small systems. When hybrid functionals were used, the simulated bandgaps were close to the experimental values. The localization of valence and conduction band states was demonstrated. The localized states in the conduction band were primarily found in the free volume (result of gauche conformations) present in the amorphous regions. For branched and crosslinked structures, the localized electronic states closest to the valence band edge were positioned at branches and crosslinks, respectively. At 0 K, the activation energy for transport was lower for holes than for electrons. However, at room temperature, the effective activation energy was very low (∼0.1 eV) for both holes and electrons, which indicates that the mobility will be relatively high even below the mobility edges and suggests that charge carriers can be hot carriers above the mobility edges in the presence of a high electrical field.

Prediction of thermal resistances and heat conduction of carbon nanotube aerogels in various permeated gases

Heat conduction in single-walled carbon nanotube (SWNT) aerogels is investigated by an off-lattice Monte Carlo method. Thermal boundary resistances (TBRs) between the SWNT and four permeated gases of argon, nitrogen, neon and hydrogen are reported from fitting simulation results with experimental data. It is found that the TBRs between the SWNT and the permeated gases decrease with larger gas molecular masses. Effects of volume fractions and complex morphologies of SWNTs on thermal conductivities of SWNT aerogels are also quantified. The effective thermal conductivities of SWNT aerogels increase with the larger volume fraction, the greater length and the smaller diameter of the SWNTs.

Inter-Carbon Nanotube Contact and Thermal Resistances in Heat Transport of Three-Phase Composites

Single-walled carbon nanotubes (SWNTs) tend to aggregate into bundles due to van der Waals forces during the fabrication of the composite. A computational model using an off-lattice Monte Carlo method is developed to systematically investigate the effects of SWNT bundles, the number of SWNTs per bundle and the thermal boundary resistance (TBR) at the SWNT–SWNT interfaces on the effective thermal conductivity (Keff) of three-phase composites. It is found that the aggregation of the SWNTs in bundles can reduce significantly the Keff of the composites with SWNTs oriented parallel or randomly to the heat flux direction, but it enhances slightly the Keff of those with SWNTs perpendicular to the heat flux direction. The Keff of the composites also decreases when more individual SWNTs aggregate in each bundle and with larger SWNT–SWNT TBR values. The thermal transport mechanism within the composites is dominated by a critical SWNT–SWNT TBR of 0.155 × 10–8 m2K/W.

Following atomistic kinetics on experimental timescales with the kinetic Activation–Relaxation Technique

The properties of materials, even at the atomic level, evolve on macroscopic time scales. Following this evolution through simulation has been a challenge for many years. For lattice-based activated diffusion, kinetic Monte Carlo has turned out to be an almost perfect solution. Various accelerated molecular dynamical schemes, for their part, have allowed the study on long time scale of relatively simple systems. There is still a need, however, for methods able to handle complex materials such as alloys and disordered systems. Here, we review the kinetic Activation–Relaxation Technique (k-ART), one of a handful of off-lattice kinetic Monte Carlo methods, with on-the-fly cataloging, that have been proposed in the last few years.

Coil–helix transition of biopolymer confined in finite cylinder

An off-lattice dynamic Monte Carlo method is used to study the conformations of biopolymers confined in finite cylinders. The coil–helix transition is observed with the increase of bending energy b for the polymer chain confined in small cylinder, and helical structure becomes more perfect for larger b. Periodicity of tangent–tangent correlation function C(s) begins to disappear when the cylinder height H increases, and the influence of R and b on the ability of helix formation of polymer chain weakens significantly. Therefore, the semiflexible and stiff polymer chains can fold into helix in small cylinder.

Monte Carlo Study of Patchy Nanostructures Self-Assembled from a Single Multiblock Chain

We present a lattice Monte Carlo simulation for a multiblock copolymer chain of length N=240 and microarchitecture $(10-10)_{12}$.The simulation was performed using the Monte Carlo method with the Metropolis algorithm. We measured average energy, heat capacity, the mean squared radius of gyration, and the histogram of cluster count distribution. Those quantities were investigated as a function of temperature and incompatibility between segments, quantified by parameter {\omega}. We determined the temperature of the coil-globule transition and constructed the phase diagram exhibiting a variety of patchy nanostructures. The presented results yield a qualitative agreement with those of the off-lattice Monte Carlo method reported earlier, with a significant exception for small incompatibilities,{\omega}, and low temperatures, where 3-cluster patchy nanostructures are observed in contrast to the 2-cluster structures observed for the off-lattice $(10-10)_{12}$ chain. We attribute this difference to a considerable stiffness of lattice chains in comparison to that of the off-lattice chains.

The Activation-Relaxation Technique: ART Nouveau and Kinetic ART

The evolution of many systems is dominated by rare activated events that occur on timescale ranging from nanoseconds to the hour or more. For such systems, simulations must leave aside the full thermal description to focus specifically on mechanisms that generate a configurational change. We present here the activation relaxation technique (ART), an open-ended saddle point search algorithm, and a series of recent improvements to ART nouveau and kinetic ART, an ART-based on-the-fly off-lattice self-learning kinetic Monte Carlo method.

Off-lattice pattern recognition scheme for kinetic Monte Carlo simulations

We report the development of a pattern-recognition scheme for the off-lattice self-learning kinetic Monte Carlo (KMC) method, one that is simple and flexible enough that it can be applied to all types of surfaces. In this scheme, to uniquely identify the local environment and associated processes involving three-dimensional (3D) motion of an atom or atoms, space around a central atom is divided into 3D rectangular boxes. The dimensions and the number of 3D boxes are determined by the accuracy with which a process needs to be identified and a process is described as the central atom moving to a neighboring vacant box accompanied by the motion of any other atom or atoms in its surrounding boxes. As a test of this method to we apply it to examine the decay of 3D Cu islands on the Cu(100) and to the surface diffusion of a Cu monomer and a dimer on Cu(111) and compare the results and computational efficiency to those available in the literature.

Aggregation behavior of two separate polymers confined between two membranes

An off-lattice Monte Carlo method is used to study the aggregation behavior of two separate confined polymer chains induced by membranes. A separation-to-combination transition occurs when the two separate chains are induced to combine and become a sphere by membranes for large surface tension σ at the critical distance dc. However, they still remain separate and each chain adopts a globular conformation for small surface tension σ at dc. For d dc, they keep separate and each chain becomes a sphere under compression of membranes for all σ. Formation of a membrane tunnel between two separate chains and entropy lead to the aggregation of separate polymer chains. In addition, dc and chain length N satisfy the relation: dc ∼ N0.46. This investigate can provide insights into the chromosome segregation/aggregation between two biological membranes, or single polymer manipulation through a membrane.

Helical Conformations of Semiflexible Polymers Confined between Two Concentric Cylinders

An off-lattice Monte Carlo method was used to study the conformational properties of semiflexible chains confined between two concentric cylinders. The conformations of confined semiflexible chains depend on the bending energy as well as the size of confinement, and the semiflexible chains with particular rigidities confined in the appropriate spaces can form helical structures under entropically driven. The inner cylinder plays a key role in the formation of helical conformations, whereas the outer cylinder affects the size of confinement. Furthermore, the helical structures keep fluctuating like a harmonic oscillation, and the clockwise or counterclockwise helical conformations will appear with the same possibility in the processes of relaxation-helix transitions. This study can help us understand the conformational behaviors of biological macromolecules in confined space.

Monte Carlo simulation of pore blocking phenomena in cross-flow microfiltration

An off-lattice Monte Carlo method was developed to examine the pore blocking phenomena in cross-flow microfiltration. Membranes were generated by randomly distributed pores with a given pore size distribution on a two-dimensional plane. The permeability of particles through the membrane pores was calculated, and the effects of crucial factors on the reduction of permeability were discussed. Reasonable fouling rules for simulations were examined and selected. At the initial stage the flux decreases sharply as the filtration time increases and then a steady state is reached. The results fit the pore blocking mechanism well. The simulation model developed in this study can be effectively used for analyzing a number of factors influencing physical fouling of membranes.

Local coil–helix transition of semiflexible polymers confined in spheres

An off-lattice Monte Carlo method is used to study the conformations of semiflexible polymer chains confined in spheres. The local coil–helix transition is observed for the chains with moderate rigidity confined in small spheres, and the helical structures can be identified by the combination of the dihedral angles and the correlation functions between the tangent vectors. Through calculating the average number of monomers per helix turn, the average number of helix turns per chain, and the ratio of average helix pitch to average helix radius, we find that the radius of the confining sphere and the bending energy are the key factors in the formation of helical structures. This study can help us understand how DNA chains fold in confined spaces, such as viruses and cells.

Kinetic Monte Carlo method for simulating reactions in solutions

We present an off-lattice kinetic Monte Carlo method, which is useful to simulate reactions in solutions. We derive the method from first-principles. We assume that diffusion leads to a Gaussian distribution for the position of the particles. This allows us to deal with the diffusion analytically, and we only need to simulate the reactive processes. The rate constants of these reactions can be computed before a simulation is started, and need not be computed on-the-fly as in other off-lattice kinetic Monte Carlo methods. We show how solvent molecules can be removed from the simulations, which minimizes the number of particles that have to be simulated explicitly. We present the relation with the customary macroscopic rate equations, and compare the results of these equations and our method on a variation of the Lotka model.

Monte Carlo simulation of the interchain exchange reaction in a blend of incompatible polymers

The interchain exchange reaction in a blend composed of two contacting layers of incompatible A and B homopolymers was simulated by means of the dynamic off-lattice Monte Carlo method. The evolution of local molecular-mass and block mass distributions, depending on the effective temperature and the reaction rate, was studied for the first time. It was shown that the components interpenetrate as the copolymer forms in the interphase layer and the average block length decreases below a certain, temperature-dependent value. The state of dynamic equilibrium, whose characteristics are determined mainly by temperature, is established in the system. The time of establishment of equilibrium and the intensity of compatibilization at the early steps of the process are controlled by the rate of the reaction. The results of the study allow the contribution of the reaction to the interchange processes to be evaluated.

Structural crossover in dense irreversibly aggregating particulate systems.

Cluster-cluster aggregation has been simulated by off-lattice Monte Carlo methods for diffusion-limited (DLCA), ballistic-limited, and reaction-limited cluster aggregation classes. We find that as the system evolves and becomes dense, the largest cluster develops a hybrid structure with mass fractal dimension D(f) approximately 2.6 over large length scales, while at smaller length scales, the early time dilute-limit fractal structure is frozen in. The largest cluster is thus an aggregate of smaller aggregates with a different fractal dimension, and we call it a "superaggregate." The crossover length separating the two morphologies, which we call the critical radius of gyration, can be calculated based on a simple theory that assumes a monodisperse cluster size distribution. This agrees well with simulation results for DLCA. However, for other classes we find that the increasing polydispersity in cluster size pushes the simulated crossover length radius of gyration to values systematically larger than the predicted value.

Monte Carlo Simulation of Polymers Confined Between Two Surfaces in the Presence of Diluent

Structure and surface properties of polymers confined between two surfaces are studied in the presence of diluent by using an off-lattice Monte Carlo method. When the diluent–chain interaction is weak, the density of diluent beads near the surface increases sharply with increasing the diluent–surface interaction while the chain bead density near the surface decreases gradually. The total bead density near the surface increases with increasing the diluent–surface interaction until it exceeds the total bulk density. This is mainly due to a large increase in the diluent bead density near the surface. Because of the increase of diluent at the surface, chains near the surface change their conformation, i.e., long tails become abundant while short trains and loops are relatively depleted. On the other hand, when the diluent–chain interaction becomes strong, the total bead density near the surface increases slightly, but it exceeds the total bulk density only when the diluent–surface interaction is strong enough, because the diluents approaching the surface induce chain beads to move to the surface due to strong interaction between the chain and diluent.

Off-lattice Monte Carlo methods for coarse-grained models of polymeric materials and selected applications

This brief review presents a general introduction to the Monte Carlo simulation of coarse-grained models for flexible macromolecules under various conditions: from the solution to the melt, in the bulk as well as in geometries confined by walls etc. In the first part, the general concepts for the construction of such coarse-grained models for the simulation of cooperative phenomena in multi-chain systems and `technical' aspects of Monte Carlo simulations are discussed, as well as the limitations that this methodology still has to face. In the second part, typical applications are briefly reviewed, including the dynamics of chains adsorbed on surfaces or confined between plates, the scattering function from semidilute polymer solutions, and the formation of micelles from solutions of short block copolymers in the bulk and at the surface. Finally, a brief comparison to related but somewhat different approaches (Monte Carlo simulation of lattice models, Molecular Dynamics of bead-spring models) is given.

Off-Lattice Monte Carlo Simulation of Hyperbranched Polymers, 2. Effect of the Reactivity Ratio of Linear to Terminal Unit on the Microstructure of Hyperbranched Polymers Based on AB2 Monomers

The polycondensation of hyperbranched polymers was simulated using an off-lattice Monte Carlo method in order to investigate the effect of reactivity ratio (x) of linear to terminal unit on the microstructure of hyperbranched polymers based on AB 2 type monomers. The polydispersity index (PI) shows a maximum when the reactivity ratio is 1.0 and decreases as the reactivity ratio deviates from unity. Fractions of dendritic, linear and terminal units were determined from simulation and com pared with theoretical predictions. As the reactivity ratio increases, the formation of the dendritic unit is more favored. The relative Wiener indices, free from the poly dispersity effects, were newly defined in this simulation. The relative Wiener indices increases with increasing the reactivity ratio, indicating that the more branched structures are formed as the reactivity ratio increases.

Conformational Dynamics of Subtilisin-Chymotrypsin Inhibitor 2 Complex by Coarse-Grained Simulations

An off-lattice dynamic Monte Carlo (MC) method is used to investigate the conformational dynamics of chymotrypsin inhibitor 2 (CI2) and subtilisin in both free and complex forms over two time windows, referring to short and long time scales. The conformational dynamics of backbone bonds analysed from several independent trajectories reveal that: Both the inhibitor and the enzyme are restricted in their bond rotations, excluding a few bonds, upon binding; the effect being greatest for the loop regions, and for the inhibitor. A cooperativity in the near-neighbor bond rotations are observed on both time scales, whereas the cooperative rotations of the bonds far along the sequence appear only in the long time window, and the latter time window is where most of the interactions between the inhibitor and the enzyme are observed. Upon binding, the cooperatively rotating parts of the inhibitor and the enzyme are readjusted compared to their free forms, and new correlations appear. The binding loop, although it is the closest contact region, is not the only part of the inhibitor involved in the interactions with the enzyme. Loops 3 and 8 and the helices F and G in bound enzyme and the binding loop of the inhibitor contribute at the most to the collective motions of whole structure on the slow time scale and are apparently important for enzyme-inhibitor interactions and function. The results in general provide evidence for the contribution of the loops with cooperative motions to the extensive communication network of the complex.

Off-lattice Monte Carlo simulation of hyperbranched polymers, 1 Polycondensation of AB2 type monomers

The polycondensation of hyperbranched polymers, based on AB2 type monomers, was simulated using an off-lattice Monte Carlo method in order to investigate the polymerization kinetics and microstructures of hyperbranched polymers. The effects of temperature and activation energy of reaction on the conversion rate seem qualitatively acceptable, indicating that our simulation model properly describes the polymerization reaction of hyperbranched polymers. Number average degree of polymerization and polydispersity index were calculated as a function of conversion and compared with Flory's expectation. Fractions of dendritic, linear and terminal unit were also determined from simulation and compared with theoretical predictions. As the hyperbranched polymer grows, it is observed that the molecular shape changes from a regular fan-shape structure to an edge-curled up structure.