A Monte Carlo lattice model for chain diffusion in dense polymer systems and its interlocking with molecular dynamics simulation

The paper reports the development of a Monte Carlo lattice model (cubic F) of polymer chains which is able to access times where the diffusion of the centre-of-mass of the chains is the dominant process, even though the chain lengths are well above that for entanglement. The volume of the model is large when compared with the volume of gyration of the individual molecules. The model incorporates an algorithm, which allows for the possibility of co-operative motions over sections of the chains and increases the time efficiency of the simulation. Both the model and the modifying algorithm have been tested against the known scaling laws.The model, for shorter chains, is ‘reverse mapped’ into full atomic detail as polyethylene and the shorter time processes simulated using molecular dynamics (MD). The MD model is tested against experimental diffusion data for polyethylene, of the same molecular weight and at the same temperature, and then used to time-calibrate the lattice model.Both the fine grained MD model and the coarse grained MC model are thus interlocked to cover a time range from the individual atomic motions of MD up to the order of a microsecond, a range of six orders of magnitude.     

Elastoviscous properties of polyisobutylene. IV. Relaxation time spectrum and calculation of bulk viscosity

The elastoviscous behavior of polyisobutylene may be interpreted in terms of a mechanical model consisting of a distribution of Maxwell elements connected in parallel. The structure of this “generalized Maxwell model” is specified by the distribution of relaxation times of the component elements. The relaxation of stress curve of the material is directly related to the distribution of relaxation times, and general expressions for the bulk viscosities (tensile and shear) of such a system in terms of the distribution of relaxation times are readily obtained. A simple “box distribution” of relaxation times is described which can be used to approximate the relaxation behavior of polyisobutylene at the long-time end of the relaxation time spectrum, and in terms of which the expressions for bulk viscosity reduce to very simple form. The parameters specifying this distribution may be determined from experimental relaxation curves by a simple graphical method. Values of these parameters as a functions of molecular weight and temperature are computed, by use of these data. It is shown that bulk viscosity values calculated from relaxation data by this method are in good agreement with experimental values for both tensile and shear deformations, and for both unfractionated and fractionated polymers. Measurements of viscosity and of relaxation of stress can thus be directly correlated, and could be used in combination to characterize elastoviscous properties over wide ranges of molecular weight and temperature.     

Study of simulation method of time evolution of atomic and molecular systems by quantum electrodynamics

We discuss a method to follow step‐by‐step time evolution of atomic and molecular systems based on quantum electrodynamics. Our strategy includes expanding the electron field operator by localized wavepackets to define creation and annihilation operators and following the time evolution using the equations of motion of the field operator in the Heisenberg picture. We first derive a time evolution equation for the excitation operator, the product of two creation or annihilation operators, which is necessary for constructing operators of physical quantities such as the electronic charge density operator. We, then, describe our approximation methods to obtain time differential equations of the electronic density matrix, which is defined as the expectation value of the excitation operator. By solving the equations numerically, we show “electron‐positron oscillations,” the fluctuations originated from virtual electron‐positron pair creations and annihilations, appear in the charge density of a hydrogen atom and molecule. We also show that the period of the electron‐positron oscillations becomes shorter by including the self‐energy process, in which the electron emits a photon and then absorbs it again, and it can be interpreted as the increase in the electron mass due to the self‐energy. © 2014 Wiley Periodicals, Inc.     

An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping

Stochastic simulation of reaction-diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies.     

Understanding diffusion in confined systems: methane in a ZK4 molecular sieve. A molecular dynamics simulation study

The equilibrium probability distribution of N methane molecules adsorbed in the interior of n alpha cages of the ZK4 zeolite, the all-silica analogue of zeolite A, is modeled by a modified hypergeometric distribution where the effects of mutual exclusion between particles are extracted from long molecular dynamics simulations. The trajectories are then analyzed in terms of time-correlation functions for the fluctuations in the occupation number of the alpha cages. The analysis digs out the correlations induced by the spatial distribution of the adsorbed molecules coupled with a migration mechanism where a molecule can pass from one alpha cage to another, one-by-one. These correlations lead to cooperative motion, which manifests itself as a nonexponential decay of the correlators. Our results suggest ways of developing improved lattice approaches that may be useful for studying diffusion in much larger systems and for a much longer observation time.     

Relaxation characteristics and intrinsic birefringence and viscosity of polystyrene solutions for a wide range of molecular weights

A comparison is made between measurements on polystyrene solutions and the relaxation characteristics and intrinsic birefringence and viscosity given by the theory for the flexible Gaussian chain of variable number of segments and with internal viscosity and internal hydrodynamic interaction. This is done in order to determine the applicability of the theory to polymers over a wide range of molecular weights, including the low molecular weight range in which there may be conflict with the theoretical assumption of chains having a large number of segments. The longest, terminal relaxation time and the number of chain segments are determined from measurements of the frequency dependence of oscillatory flow birefringence while the intrinsic birefringence and viscosity are determined from steady flow measurements. The range of molecular weights studied is from approximately 900 at 10⁶. It is found that the segment weight is approximately 1000 and the number of segments is in direct proportion to the molecular weight for the range from 1 to 1000 segments. The terminal relaxation time has a molecular weight dependence of the type given by the theory but with better agreement for higher molecular weights. While the measured dependences of the intrinsic viscosity and birefringence are in agreement with theory for molecular weights greater than 5 × 10⁴, they deviate significantly for molecular weights below 1 × 10⁴. The ratio of the intrinsic birefringence to intrinsic viscosity, which in theory is a constant independent of molecular weight, is found to change at the lower molecular weights.     

Thermal and viscosity characterization of two asphalt emulsions

Journal of Thermal Analysis and Calorimetry - Asphalt emulsion is a versatile product that can be used for different waterproofing applications in civil construction and highway constructions....     

Brownian dynamics simulation of polyelectrolyte dilute solutions: Relaxation time and elongational flow

The authors used the bead‐and‐spring model and the Brownian dynamics simulation technique including hydrodynamic interaction to study the behavior of dilute polyelectrolyte solutions under elongational flow. First they carried out simulations to determine the longest relaxation time of a polyelectrolyte, finding that the relaxation time depends on the ionic strength of the solution. Then, they studied the coil‐stretch transition of polyelectrolyte molecules in elongational flow and determined the critical value of the elongational rate necessary in order this transition to occur. In this way, they could compute the value of the Deborah number at which coil‐stretch transition sets in for polyelectrolyte dilute solutions. Finally, they studied the power law relationship that relates the critical elongational rate with the molecular weight of the polyelectrolyte. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 714–722, 2007     

Prediction of viscosity for molecular fluids at experimentally accessible shear rates using the transient time correlation function formalism

Nonequilibrium molecular dynamics (NEMD) simulations were performed and the transient time correlation function (TTCF) method applied to calculate the shear viscosity of n-decane. Using the TTCF method we were able to calculate the viscosity at shear rate orders of magnitude lower than is possible by direct NEMD simulation alone. For the first time for a molecular fluid, we were able to simulate shear rates accessible by experimental measurements, which are typically performed at shear rates well below those accessible by NEMD simulation. The TTCF method allows us to close the gap between the lowest shear rates accessible by MD simulation and the highest shear rates possible in experimental studies. Additionally a multiple time step method for Gaussian thermostatted SLLOD equations of motion was developed following earlier work [G. A. Pan et al., J. Chem. Phys. 122, 4114 (2005)] for atomic fluids.     

Relaxation time measurements and molecular dynamics of dipalmitoyl-α-lecithin in the solid phase

The relaxation times T₁ and T_D were measured for dipalmitoyl-L-α-lecithin and dipalmitoyl-DL-α-lecithin at various temperatures. It was possible to separate the contribution of the slow motions to the relaxation rates from the fast ones. For some types of motions the activation energies could be estimated.     

Structure,thermodynamics and diffusion in asymmetric binary mixtures: a molecular dynamics simulation study

Structural and thermodynamic properties as well as diffusion coefficients of binary fluid mixtures with asymmetry in mass, size, charge and their combinations have been studied using classical molecular dynamics simulations. The fluid mixture is modelled as spherical particles interacting via the Weeks–Chandler–Andersen and Coulomb potential. The diameter, charge and mass of the fluid particles are in the range 6–60 Å, 1–10e and 1—500 amu, respectively. Systematic variations in pair-correlation functions, thermodynamic properties as well as the self-diffusion coefficient are found with the size, charge and mass ratio of the particles. The self-diffusion coefficient for systems having more than one type of asymmetry is calculated and expressed in terms of diffusion coefficients of systems with only one type of asymmetry.     

Studies of translational diffusion in the smectic A phase of a Gay-Berne mesogen using molecular dynamics computer simulation

Molecular dynamics computer simulations are used to determine the self-diffusion coefficients for a Gay-Berne model mesogen GB (4.4,20,1,1) in the isotropic, nematic and smectic A phases along two isobars. The values of the parallel and perpendicular diffusion coefficients, D(parallel) and D(perpendicular), are calculated and compared in the different phases. For the phase sequence isotropic-smectic A, D(perpendicular)*> or =D(parallel)* over the whole smectic A range with the ratio D(parallel)*/D(perpendicular)* decreasing with decreasing temperature. At a higher pressure, a nematic phase is observed between these two phases and we find that D(parallel)*>D(perpendicular)* throughout the nematic region and the inequality D(parallel)*>D(perpendicular)* remains on entering the smectic A phase. However, the ratio D(parallel)*/D(perpendicular)* decreases with decreasing temperature within the smectic A range and eventually this ratio inverts such that D(perpendicular)*>D(parallel)* at low temperatures. The temperature dependence of the parallel diffusion coefficient in the smectic A phase for this model mesogen is compared to that predicted by a theoretical model for diffusion subject to a cosine potential.     

Diffusion and viscosity of a calamitic liquid crystal model studied by computer simulation

We report a molecular dynamics simulation study on an ensemble of rod-like particles, each composed of nine soft spheres held rigidly along a line. We have calculated translational mean square displacements and velocity autocorrelation functions in the fluid phases exhibited by the model, i.e., smectic A, nematic and isotropic. These quantities have then been used to compute diffusion coefficients. In addition, we have calculated viscosities in the nematic and isotropic phases. Despite its crude nature, the model is capable of providing a faithful reproduction of many features of the transport behavior observed in real liquid-crystalline materials. The simulation results have been compared with the predictions of the modified affine transformation theory, finding only a fair agreement.     

Finite time thermodynamics: limiting performance of diffusion engines and membrane systems

In this paper, the limiting performance of membrane systems with inhomogeneous composition is studied within the class of fixed rate processes. The problem of maintaining a nonequilibrium state in such a system using minimal power (separation problem) and the problem of extracting maximal power from such a system (diffusion engine problem) are formulated and solved. Results are obtained for diffusion engines with constant and periodic contact between the working body and the reservoirs.     

A systematic molecular simulation study of ionic liquid surfaces using intrinsic analysis methods

In this paper, we apply novel intrinsic analysis methods, coupled with bivariate orientation analysis, to obtain a detailed picture of the molecular-level structure of ionic liquid surfaces. We observe pronounced layering at the interface, alternating non-polar with ionic regions. The outermost regions of the surface are populated by alkyl chains, which are followed by a dense and tightly packed layer formed of oppositely charged ionic moieties. We then systematically change the cation chain length, the anion size, the temperature and the molecular model, to examine the effect of each of these parameters on the interfacial structure. Increasing the cation chain length promotes orientations in which the chain is pointing into the vapor, thus increasing the coverage of the surface with alkyl groups. Larger anions promote a disruption of the dense ionic layer, increasing the orientational freedom of cations and increasing the amount of free space. The temperature had a relatively small effect on the surface structure, while the effect of the choice of molecular model was clearly significant, particularly on the orientational preferences at the interface. Our study demonstrates the usefulness of molecular simulation methods in the design of ionic liquids to suit particular applications.     

Prediction of CO2 and H2 solubility,diffusion, and permeability in MFI zeolite by molecular dynamics simulation

Structural Chemistry - Molecular dynamics simulation has been employed to calculate the amounts of solubility, diffusion coefficient, and permeability for the pure and volumetric binary mixture of...     

Estimation of viscosity of liquid mixtures using Hildebrand's fluidity model

The fluidity model presented by Hildebrand has been extended to liquid mixtures containing two, three or four components. Semiempirical methods are pre     

Relaxation of chemical potential and a generalized diffusion equation

The effect of slow structural relaxation in a solvent of high viscosity on the chemical potential driving the diffusion of penetrant molecules is described by a generalized diffusion equation with a memory term. The linearized version of this equation is solved for some special cases, and the correlation function of concentration fluctuations in thermodynamic equilibrium is calculated. As a result of the memory term, for very slow relaxation two different stages of the diffusion process can be distinguished.     

Electrolysis of water in the diffusion layer: first-principles molecular dynamics simulation

With Car-Parrinello molecular dynamics simulations the elementary reaction steps of the electrolysis of bulk water are investigated. To simulate the reactions occurring near the anode and near the cathode, electrons are removed or added, respectively. The study focuses on the reactions in pure water. Effects depending on a particular electrode surface or a particular electrolyte are ignored. Under anodic conditions, the reaction continues till molecular oxygen is formed, under cathodic conditions the formation of molecular hydrogen is observed. In addition the formation of hydrogen peroxide is observed as an intermediate of the anodic reaction. The simulations demonstrate that the electrochemistry of oxygen formation without direct electrode contact can be explained by radical reactions in a solvent. These reactions may involve the intermediate formation of ions. The hydrogen formation is governed by rapid proton transfers between water molecules.     

Uncovering molecular processes in crystal nucleation and growth by using molecular simulation

Exploring nucleation processes by molecular simulation provides a mechanistic understanding at the atomic level and also enables kinetic and thermodynamic quantities to be estimated. However, whilst the potential for modeling crystal nucleation and growth processes is immense, there are specific technical challenges to modeling. In general, rare events, such as nucleation cannot be simulated using a direct "brute force" molecular dynamics approach. The limited time and length scales that are accessible by conventional molecular dynamics simulations have inspired a number of advances to tackle problems that were considered outside the scope of molecular simulation. While general insights and features could be explored from efficient generic models, new methods paved the way to realistic crystal nucleation scenarios. The association of single ions in solvent environments, the mechanisms of motif formation, ripening reactions, and the self-organization of nanocrystals can now be investigated at the molecular level. The analysis of interactions with growth-controlling additives gives a new understanding of functionalized nanocrystals and the precipitation of composite materials.