Monte Carlo simulation for the formation of a mixed crystal from two solids in contact

The study focuses on nucleation and growth of a binary mixed crystal phase from two pure crystals in contact. Monte Carlo simulations of this process are conducted, with the dynamics proceeding via activated atom-vacancy exchanges. Intermolecular interactions, ranging up to next-nearest neighbors, are of size typical of hydrogen bonded systems. The process is driven by the formation of strong AB bonds at the expense of weaker AA and BB bonds. In the resulting model, the material is channeled and transported through the mixed phase crust along antiphase boundaries. The flow of molecules through the channels is directed, due to molecular energy lowering via gradual acquisition of an increasing number of nearest neighbors of the second species. On the other hand, defect motion is quasirandom. The model accounts partially for the t(1/alpha) (alpha>3) time dependence observed for conversion of nanoparticles of HBr dihydrate to monohydrate, by exposure to acid adsorbate.     

A multiple chain Monte Carlo method for atomistic simulation of high molecular weight polymer melts

A new Monte Carlo method is proposed for the simulation of bulk systems of atomistically detailed polymers. Each move consists of a configurational rearrangement of the atoms in a specified region of the material, rather than a specified molecule. Thus atoms within different chains may be displaced cooperatively in each Monte Carlo move. Here, the method is implemented for the case of melts of linear chains, where the bond lengths and bond angles are held constant during the move. The performance of the algorithm is examined for linear polyethylene systems with chain lengths of 100 and 1000 backbone atoms, under a range of conditions. The method shows a considerable potential as a very general and flexible tool for simulating realistic polymer materials, subject to a number of performances limiting factors which are described in detail.     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

Cassandra: An open source Monte Carlo package for molecular simulation

Cassandra is an open source atomistic Monte Carlo software package that is effective in simulating the thermodynamic properties of fluids and solids. The different features and algorithms used in Cassandra are described, along with implementation details and theoretical underpinnings to various methods used. Benchmark and example calculations are shown, and information on how users can obtain the package and contribute to it are provided. © 2017 Wiley Periodicals, Inc.     

Monte Carlo simulation of electrical double-layer formation from mixtures of electrolytes inside nanopores

The formation of the electrical double layer (EDL) in the presence of trivalent and monovalent ions inside a slit-type nanopore was simulated via the canonical Monte Carlo method using a primitive model. In large pores, the distribution of ionic species is similar to that observed in an isolated planar double layer. Screening of surface charge is determined by the competitive effects between ion size and charge asymmetry of the counterions. On the other hand, as the pore size approaches the dimension of the ionic species, phenomena such as EDL overlapping become enhanced by ion-size effects. Simulation results demonstrate that EDL overlapping is not only a function of such parameters as ionic strength and surface charge density, but also a function of the properties of the ionic species involved in the EDL. Furthermore, charge inversion can be observed under certain conditions when dealing with mixtures of asymmetric electrolytes. This phenomenon results from strong ion-ion correlation effects and the asymmetries in size and charge of ionic species, and is most significant in the case of trivalent counterions with larger diameters. The simulation results provide insights into the fundamental mechanisms behind the formation of EDL within nanopores as determined by pore size and by the properties of ionic species present in solution. The findings of this work are relevant to ion sorption and transport within nanostructured materials.     

Spontaneous formation of vesicles

his review highlights the relevant issues of spontaneous formation of vesicles. Both the common characteristics and the differences between liposomes and vesicles are given. The basic concept of the molecular packing parameter as a precondition of vesicles formation is discussed in terms of geometrical factors, including the volume and critical length of the amphiphile hydrocarbon chain. According to theoretical considerations, the formation of vesicles occurs in the systems with packing parameters between 1/2 and 1. Using common as well as new methods of vesicle preparation, a variety of structures is described, and their nomenclature is given. With respect to sizes, shapes and inner structures, vesicles structures can be formed as a result of self-organisation of curved bilayers into unilamellar and multilamellar closed soft particles. Small, large and giant uni-, oligo-, or multilamellar vesicles can be distinguished. Techniques for determination of the structure and properties of vesicles are described as visual observations by optical and electron microscopy as well as the scattering techniques, notably dynamic light scattering, small angle X-ray and neutron scattering. Some theoretical aspects are described in short, viz., the scattering and the inverse scattering problem, angular and time dependence of the scattering intensity, the principles of indirect Fourier transformation, and the determination of electron density of the system by deconvolution of p(r) function. Spontaneous formation of vesicles was mainly investigated in catanionic mixtures. A number of references are given in the review.     

Monte Carlo simulation of micelle formation in block copolymer solutions

Short block copolymers in selective solvents (bad for A-block, good for B-block) are modeled by flexible bead-spring chains, where beads interact with short range Morse potentials of variable strength. It is shown that already very short chains (N_A = N_B = 2) exhibit a rather well-defined critical micelle concentration (cmc). The mass distribution of the micelles and their gyration tensor components as well as their internal structure are studied. It is shown that the relaxation time increases exponentially with the strength E_AA of the attractive energy between the A-monomers, and thus frozen-in micelles of medium size are obtained when E_AA is chosen too large. Our results are compared to studies of related but somewhat different models.     

MCDOCK: A Monte Carlo simulation approach to the molecular docking problem

Prediction of the binding mode of a ligand (a drug molecule) to its macromolecular receptor, or molecular docking, is an important problem in rational drug design. We have developed a new docking method in which a non-conventional Monte Carlo (MC) simulation technique is employed. A computer program, MCDOCK, was developed to carry out the molecular docking operation automatically. The current version of the MCDOCK program (version 1.0) allows for the full flexibility of ligands in the docking calculations. The scoring function used in MCDOCK is the sum of the interaction energy between the ligand and its receptor, and the conformational energy of the ligand. To validate the MCDOCK method, 19 small ligands, the binding modes of which had been determined experimentally using X-ray diffraction, were docked into their receptor binding sites. To produce statistically significant results, 20 MCDOCK runs were performed for each protein–ligand complex. It was found that a significant percentage of these MCDOCK runs converge to the experimentally observed binding mode. The root-mean-square (rms) of all non-hydrogen atoms of the ligand between the predicted and experimental binding modes ranges from 0.25 to 1.84 Å for these 19 cases. The computational time for each run on an SGI Indigo2/R10000 varies from less than 1 min to 15 min, depending upon the size and the flexibility of the ligands. Thus MCDOCK may be used to predict the precise binding mode of ligands in lead optimization and to discover novel lead compounds through structure-based database searching.     

Parallelization strategies for molecular simulation using the Monte Carlo algorithm

We describe the development of Metropolis Monte Carlo algorithms for a general network of multiple instruction multiple data (MIMD) parallel processors. The implementation of farm, event, and systolic parallel algorithms on transputer-based computers is detailed and their relative performance discussed. Although the emphasis is on methodology, the application of such parallel algorithms will be important for addressing computational problems such as the determination of free energy differences in complex biologically important molecular systems. © 1993 John Wiley & Sons, Inc.     

Effect of interchange reactions on the molecular weight distribution of poly(ethylene terephthalate): A Monte Carlo simulation

The effect of the interchange reactions of poly(ethylene terephthalate) (PET) on its molecular weight distribution (MWD) was analyzed using a Monte Carlo simulation method. Three kinds of motions, which correspond to the direct ester(SINGLEBOND)ester interchange reaction, alcoholysis, and internal alcoholysis in polyester, were performed in this simulation: bond flip, end attack, and backbite. Two systems with two different types of nonequilibrium distribution (monodisperse and bimodal distribution) were initially prepared. The initial biases from equilibrium MWD are rapidly relaxed to an equilibrium MWD as the reaction progresses. The MWD at equilibrium is well described by the most probable MWD proposed by Flory. From the polydispersity data, it is concluded that about 0.3 interchanges per segment are sufficient to equilibrate the nonequilibrium system. For the validity of the simulation, the variation of MWD of the mixtures of two PETs having different molecular weights were monitored using gel permeation chromatography. The agreement between simulation and experiment is remarkably good. © 1996 John Wiley & Sons, Inc.     

Spontaneous formation of nanoparticle vesicles from homopolymer polyelectrolytes

Nanoparticle vesicles were spontaneously assembled from homopolymer polyamine polyelectrolytes and water-soluble, citrate-stabilized quantum dots. The further addition of silica nanoparticles to a solution of quantum dot vesicles generated stable micrometer-sized hollow spheres whose walls were formed of a thick, inner layer of close-packed quantum dots followed by an outer layer of silica. The method employed here to assemble both the nanoparticle vesicles and the hollow spheres is in direct contrast to previous syntheses that use either tailored block copolymers or oil-in-water emulsion templating. We propose that the formation of charge-stabilized hydrogen bonds between the positively charged amines of the homopolymer polyelectrolytes and the negatively charged citrate molecules stabilizing the quantum dots is responsible for the macroscopic phase separation in this completely aqueous system. The ease and processibility of the present approach gives promise for the production of a diverse array of materials ranging in applications from drug delivery to catalysis to micrometer-scale optical devices.     

A Monte Carlo simulation study of lipid bilayer formation on hydrophilic substrates from vesicle solutions

A general lattice Monte Carlo model is used for simulating the formation of supported lipid bilayers (SLBs) from vesicle solutions. The model, based on a previously published paper, consists of adsorption, decomposition, and lateral diffusion steps, and is derived from fundamental physical interactions and mass transport principles. The Monte Carlo simulation results are fit to experimental data at different vesicle bulk concentrations. A sensitivity analysis reveals that the process strongly depends on the bulk concentration C(0), adsorption rate constant K, and all vesicle radii parameters. A measure of "quality of coverage" is proposed. By this measure, the quality of the formed bilayers is found to increase with vesicle bulk concentration.     

Monte Carlo simulation of transport from an electrothermal vaporizer

Monte Carlo simulations were developed to elucidate the time and spatial distribution of analyte during the transport process from an electrothermal vaporizer to an inductively coupled plasma. A time-of-flight mass spectrometer was employed to collect experimental data that was compared with the simulated transient signals. Consideration was given to analyte transport as gaseous species as well as aerosol particles. In the case of aerosols, the simulation assumed formation of 5 nm particles and used the Einstein–Stokes equation to estimate the aerosol's diffusion coefficient, which was ca. 1% of the value for free atom diffusion. Desorption conditions for Cu that had been previously elucidated for electrothermal atomic absorption spectrometry were employed for the release processes from the electrothermal vaporizer. The primary distinguishing feature in the output signal to differentiate between gas and aerosol transport was a pronounced, long lived signal after the transient peak if aerosols were transported. Time and spatial distributions of particles within the transport system are presented. This characteristic was supported by independent atomic absorption measurements using a heated (or unheated) quartz T-tube with electrothermal vaporizer introduction.     

Monte Carlo molecular simulation of the hydration of Na-montmorillonite at reservoir conditions

The hydration of Na-saturated Wyoming-type montmorillonite is investigated by Monte Carlo simulations at constant stress in the NP(zz)T ensemble and at constant chemical potential in the microVT ensemble, at the sedimentary basin temperature of 353 K and pressure of 625 bar, equivalent to 2-4 km depth. The simulations use procedures established in Chavez-Paez et al. [J. Chem. Phys. 114, 1405 (2001)]. At these conditions, simulations predict a single stable form of 1,2-water layer Na-montmorillonite, containing 164.38 mg/g or 53.37 molecules/layer of adsorbed water and having a spacing of 12.72 A. The corresponding density is 0.32 g/ml. Sodium ions are coordinated with six molecules of water separated 2.30-2.33 A. Water molecules are closer to the central interlayer plane and the spacing is larger than that at 300 K and 1 bar. The interlayer configuration consists of two symmetrical layers of oriented water molecules 1.038 A from the central plane, with the hydrogen atoms in two outermost layers, 3.826 A apart, and the sodium ions on the central plane located between the water layers. The interlayer configuration can be considered to be a stable two-layer intermediate between the one- and two-layer hydrates. Our simulations do not predict formation of other hydrates of Na-montmorillonite at 353 K and 615 bar.     

Nanoparticle formation in water-in-oil microemulsions: experiments, mechanism, and Monte Carlo simulation

The dynamics of nanoparticle formation in water-in-oil microemulsions via temporal size evolution has been followed from UV-visible absorption spectra of CdS nanoparticles. Existing Monte Carlo (MC) simulations of nanoparticle formation are primarily based on the mechanism of nuclei formation and their growth by coalescence-exchange of drops, which alone do not predict particles of large size as observed in some experiments. Hence, we have included an additional size enlargement process, namely coagulation of nanoparticles during drop coalescence. We find that particle coagulation, constrained by microemulsion drop size, shows very good agreement with our experimental data on CdS nanoparticle size evolution, for different drop sizes. Thus a combined approach of spectroscopy and MC simulation is helpful in elucidating the mechanism of nanoparticle formation in these confined systems, leading to prediction of size-controlled nanoparticle synthesis.     

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 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.     

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.     

Structure of ABCA tetrablock copolymer vesicles and their formation in selective solvents: a Monte Carlo study

Vesicles formed by ABCA tetrablock copolymers in solvents that are selective for block A are studied using the Monte Carlo simulation. Simulation results show that the chain length ratio and hydrophobicity of blocks B and C are key factors determining the hydrophobic layer structure of the vesicles. If the B and C blocks are of the same hydrophobicity, the longer block C tends to form the closed hydrophobic layer, whereas the shorter block B is located on the outer surface of the closed hydrophobic layer. However, if the hydrophobicity difference between blocks B and C is high enough, the reverse will occur given that block B has a higher hydrophobicity and block C has a lower hydrophobicity. The kinetics of vesicle formation is also studied. Simulation results reveal that the hydrophobic layer structure is formed through the migration of the polymer chain within the vesicle membrane after the formation of the vesicle profile. This migration is independent of the differences in chain length ratio and the hydrophobicity between the blocks B and C. The packing mode and the migration of polymer chains within the vesicle membrane are also presented and discussed.