Positron backscattering from an Al target: analytical calculation and Monte Carlo simulation

Positron backscattering coefficients are analytically calculated and numerically simulated for an Al target in the positron energy range 0.50–4 keV and for incident angles between 0° and 80° . The differential elastic scattering cross section has been obtained using the Bentabet and Bouarissa approximation (Phys. Lett. 2006; A 355: 390). Both the analytical and simulated results show good agreement with the experiment and previous theoretical work. Copyright © 2007 John Wiley & Sons, Ltd.     

Monte Carlo analyses of multiple backscattering of gamma rays

We have written a Monte Carlo code to simulate the experimental results of a previously reported study. We were able to analyse the energy distributions of photons that reached the detector system after suffering several successive Compton scatterings in the target. We have also investigated how the number of multiply backscattered events depends on the target thickness and the energy of the primary photons.     

Monte Carlo simulation of AB diblock copolymer between surface and substrate and comparison of experimental results

The morphologies of AB diblock copolymer film between the substrate and surface were investigated via Monte Carlo simulations on simple cubic lattices. The morphological dependence of the diblock copolymer thin film on the thickness, as well as the composition and interactive intensity has been mainly studied. With the increase of A‐segments fraction, various microdomain morphologies including regular parallel stripe‐like, mesh‐like, and normal lamella near the region of the surface were generated in this work. The morphology of thin films of asymmetric diblock copolymer was found to form cylinders in a bulk system when L_z was equal to 30. The morphologies of PS‐b‐PDMS diblock copolymer films have been studied via atomic force microscopy (AFM) and transition electron microscopy (TEM) measurements. The surface morphology of the PS‐b‐PDMS copolymer thin film shows a mesh‐like microphase separated structure, and PDMS continuous phase protruded on the PS dispersed phase. The surface composition of PS‐b‐PDMS copolymer thin films was measured by means of X‐ray photoelectron spectroscopy (XPS) and ATR‐IR. The comparison results show that the experimental observations are in good agreement with the simulation results. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1835–1845, 2006     

Density functional theory for encapsidated polyelectrolytes: A comparison with Monte Carlo simulation

Genome packaging inside viral capsids is strongly influenced by the molecular size and the backbone structure of RNA∕DNA chains and their electrostatic affinity with the capsid proteins. Coarse-grained models are able to capture the generic features of non-specific interactions and provide a useful testing ground for theoretical developments. In this work, we use the classical density functional theory (DFT) within the framework of an extended primitive model for electrolyte solutions to investigate the self-organization of flexible and semi-flexible linear polyelectrolytes in spherical capsids that are permeable to small ions but not polymer segments. We compare the DFT predictions with Monte Carlo (MC) simulation for the density distributions of polymer segments and small ions at different backbone flexibilities and several solution conditions. In general, the agreement between DFT and MC is near quantitative except when the simulation results are noticeably influenced by the boundary effects. The numerical efficiency of the DFT calculations makes it promising as a useful tool for quantification of the structural and thermodynamic properties of viral nucleocapsids in vivo and at conditions pertinent to experiments.     

A comparison between two massively parallel algorithms for Monte Carlo computer simulation: An investigation in the grand canonical ensemble

We present a comparison between two different approaches to parallelizing the grand canonical Monte Carlo simulation technique (GCMC) for classical fluids: a spatial decomposition and a time decomposition. The spatial decomposition relies on the fact that for short-ranged fluids, such as the cut and shifted Lennard-Jones potential used in this work, atoms separated by a greater distance than the reach of the potential act independently, and thus different processors can work concurrently in regions of the same system which are sufficiently far apart. The time decomposition is an exactly parallel approach which employs simultaneous (GCMC) simulations, one per processor, identical in every respect except the initial random number seed, with the thermodynamic output variables averaged across all processors. While scaling characteristics for the spatial decomposition are presented for 8–1024 processor systems, the comparison between the two decompositions is limited to the 8–128 processor range due to the warm-up time and memory imitations of the time decomposition. Using a combination of speed and statistical efficiency, the two algorithms are compared at two different state points. While the time decomposition reaches a given value of standard error in the system's potential energy more quickly than the spatial decomposition for both densities, the warm-up time demands of the time decomposition quickly become insurmountable as the system size increases. © 1996 by John Wiley & Sons, Inc.     

A Monte Carlo simulation study of branched polymers

Monte Carlo simulations are presented for the static properties of highly branched polymer molecules. The molecules consist of a semiflexible backbone of hard-sphere monomers with semiflexible side chains, also composed of hard-sphere monomers, attached to either every backbone bead or every other backbone bead. The conformational properties and structure factor of this model are investigated as a function of the stiffness of the backbone and side chains. The average conformations of the side chains are similar to self-avoiding random walks. The simulations show that there is a stiffening of the backbone as degree of crowding is increased, for example, if the branch spacing is decreased or side chain length is increased. The persistence length of the backbone is relatively insensitive to the stiffness of the side chains over the range investigated. The simulations reproduce most of the qualitative features of the structure factor observed in experiment, although the magnitude of the stiffening of the backbone is smaller than in experiment.     

A Monte Carlo simulation of the inhomogeneous Lebwohl-Lasher lattice model

A Monte Carlo computer simulation of a modified Lebwohl-Lasher model is presented. The model consists of a set of interaction centres placed at the sites of a cubic lattice. The angular part of the pair potential is a second Legendre polynomial of the relative orientation between the two particles, like that of the Lebwohl-Lasher model. Each particle interacts with its six nearest neighbours with an attractive anisotropic potential differing in strength for the four horizontal and the two vertical neighbours. Various values of the in-plane to out-of-plane coupling ratio δ have been considered, i.e. δ = 0.75, 0.5, 0.1, 0.0. The latter case corresponds to the limiting situation of a two-dimensional lattice. Systems with a 1000 particles have been simulated for δ = 0.75, 0.5 and 0.1 while a sample of 3600 particles has been investigated for the two-dimensional lattice. Comparisons are made with available simulations and with mean field theory. We find that the molecular field theory predictions worsen as the effective coordination number is decreased. Energy, specific heat, second and fourth rank order parameters have been evaluated for the various models. We also present, for the first time, a way of approximately reconstructing the pair distribution, G(r₁₂, ω₁₂), using maximum entropy and second and fourth rank two particle order parameters.     

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.     

Monte Carlo simulation of osmotic equilibria

We present a Metropolis Monte Carlo simulation algorithm for the Tpπ-ensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.     

Monte Carlo simulation of polymer welding

Monte Carlo Modelling of random polymer chains, course grained onto a cubic F lattice, provides the ability to monitor the long range relaxation processes and the dynamic parameters of chains up to 400 units long. The model, described and verified by Haire et al. (Haire KR, Carver TJ, Windle AH. A Monte Carlo model for dense polymer systems and its interlocking with molecular dynamics simulation. Computational and Theoretical Polymer Science 2000; in press), is here applied to the study of molecular parameters in the vicinity of different types of surface and also to the process of polymer welding, whereby adhesion between two adjacent surfaces is achieved by the interpenetration of chains which are across the surface.The model demonstrates that a surface distorts the conformation of chains adjacent to it to give an oblate molecular envelope, that the concentration of vacant sites and chain ends increases near to the surface and that the density of points representing the centres of mass of the chains increases in the sub-surface regions. These results confirm earlier predictions and provide additional confidence in the model.Modelling of the welding process leads to the parameter intrinsic weld time, t_w, which is the time from initial perfect contact of the surfaces to the achievement of a weld within which the chain conformation is indistinguishable from the bulk. After the initial period in which the mating surfaces roughen, the welding proceeds according to the t^1/4 law predicted by reptation theory. The time to a given level of interdiffusion across the boundary is proportional to the chain length l, a comparatively weak dependence, while t_w is proportional to l³, a strong dependence. This is the same dependence on length as for the relaxation time of the chain end-to-end vectors. In fact, the agreement between the relaxation time, measured on the model of the bulk, and t_w is surprisingly close, at least for the monodisperse polymers investigated here.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

The interaction between charged aggregates in electrolyte solution. A Monte Carlo simulation study

The Monte Carlo simulation technique has been used to calculate the electrostatic force acting upon a charged aggregate outside a similarly charged wall. Contrary to intuition and existing electrostatic theories, the force is found to be attractive for some realistic values of the parameters determining the system. High surface charge density, low temperature, low relative permitivity and polyvalent neutralizing counterions are all factors that favour a net attraction between the wall and the aggregate. In some cases the resulting electrostatic attractive force is found to be an order of magnitude larger than the ordinary van der Waals attraction applied in the DLVO theory of colloidal stability. The attractive interaction is interpreted as being due to currelations between the counterions in the electric double layers.     

Order-parameter-based Monte Carlo simulation of crystallization

A Monte Carlo simulation method is presented for simulation of phase transitions, with emphasis on the study of crystallization. The method relies on a random walk in order parameter Phi(q(N)) space to calculate a free energy profile between the two coexisting phases. The energy and volume data generated over the course of the simulation are subsequently reweighed to identify the precise conditions for phase coexistence. The usefulness of the method is demonstrated in the context of crystallization of a purely repulsive Lennard-Jones system. A systematic analysis of precritical and critical nuclei as a function of supercooling reveals a gradual change from a bcc to a fcc structure inside the crystalline nucleus as it grows at large degrees of supercooling. The method is generally applicable and is expected to find applications in systems for which two or more coexisting phases can be distinguished through one or more order parameters.     

Monte Carlo simulation of hard spheroids

We present Monte Carlo simulations of the equation of state and radial distribution function for a model fluid composed of hard spheroids.     

Monte Carlo simulation of block copolymers

Monte Carlo simulations deal with crudely simplified but well-defined models and have the advantage that they treat the statistical thermodynamics of the considered model exactly (apart from statistical errors and problems due to finite size effects). Therefore, these simulations are well suited to test various approximate theories of block copolymer ordering, e.g. the self-consistent field theory. Recent examples of this approach include the study of block copolymer ordering at melt surfaces and confinement effects in thin films, adsorption of block copolymers at interfaces of unmixed homopolymer blends, the phase behavior of ternary mixtures of two homopolymers and their block copolymer, and micelle formation in selective solvents.     

A Monte Carlo simulation of diffusion-controlled reactions in inhomogeneous systems

A random-walk model has been developed to treat the kinetics of reactions taking place in spurs at different solute concentrations. The dependence of the molecular yields on solute concentration has been studied using Monte Carlo techniques for simulation of the formation of spurs and of the random movement of the reactive species.     

Collective-variable Monte Carlo simulation of DNA

Monte Carlo simulations have been carried out on DNA oligomers using an internal coordinate model associated with a pseudorotational representation of sugar repuckering. It is shown that when this model is combined with the scaled collective variable approach of Noguti and Go, much more efficient simulations are obtained than with simple single variable steps. Application of this method to a DNA oligomer containing a recognition site for the TATA-box binding protein leads to striking similarities with results recently obtained from a 1-ns molecular dynamics simulation using explicit solvent and counterions. In particular, large amplitude bending fluctuations are observed directed toward the major groove. Conformational analysis of the Monte Carlo simulation shows clear base sequence effects on conformational fluctuations and also that the DNA energy hypersurface, like that of proteins, is complex with many local, conformational substates. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2001–2011, 1997     

Self-assembly of patchy particles into polymer chains: a parameter-free comparison between Wertheim theory and Monte Carlo simulation

The authors numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory. This comparison offers a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameters and liquid state correlation functions. The Wertheim theory has not been previously subjected to stringent tests against simulation data for ordering across the polymerization transition. The authors numerically determine many of the thermodynamic properties governing this basic form of self-assembly (energy per particle, order parameter or average fraction of particles in the associated state, average chain length, chain length distribution, average end-to-end distance of the chains, and the static structure factor) and find that predictions of the Wertheim theory accord remarkably well with the simulation results.     

Grand canonical Monte Carlo simulation study of capillary condensation between nanoparticles

Capillary condensation at the nanoscale differs from condensation in the bulk phase, because it is a strong function of surface geometry and gas-surface interactions. Here, the effects of geometry on the thermodynamics of capillary condensation at the neck region between nanoparticles are investigated via a grand canonical Monte Carlo simulation using a two-dimensional lattice gas model. The microscopic details of the meniscus formation on various surface geometries are examined and compared with results of classical macromolecular theory, the Kelvin equation. We assume that the system is composed of a lattice gas and the surfaces of two particles are approximated by various shapes. The system is modeled on the basis of the molecular properties of the particle surface and lattice gas in our system corresponding to titania nanoparticles and tetraethoxy orthosilicate molecules, respectively. This system was chosen in order to reasonably emulate our previous experimental results for capillary condensation on nanoparticle surfaces. Qualitatively, our simulation results show that the specific geometry in the capillary zone, the surface-surface distance, and the saturation ratio are important for determining the onset and broadening of the liquid meniscus. The meniscus height increases continuously as the saturation ratio increases and the meniscus broadens faster above the saturation ratio of 0.90. The change of the radius of curvature of the particle surface affects the dimensions of the capillary zone, which drives more condensation in narrow zones and less condensation in wide zones. The increase of surface-surface distance results in the decrease of the meniscus height or even the disappearance of the meniscus entirely at lower saturation ratios. These effects are significant at the nanoscale and must be carefully considered in order to develop predictive relationships for meniscus height as a function of saturation conditions.     

A Monte Carlo simulation of radiation-induced conductivity of disordered solids

The Monte Carlo method was used to perform a theoretical study of the kinetics of radiation-induced conductivity under pulsed irradiation of a disordered solid with traps having different energy distributions. The kinetics of radiation-induced conductivity in a weak electric field was satisfactorily described by the Rose-Fowler-Vaisberg model. In a strong field, radiation-induced conductivity became a nonlinear field strength function because of distortions of the energy spectrum of trap centers.