Discontinuous Molecular Dynamics Simulations Research Articles

Investigation of the Microstructure of Micelles Formed by Hard-Sphere Chains Interacting via Size Nonadditivity by Discontinuous Molecular Dynamics Simulation

Micelle formation by short nonadditive hard surfactant chains was investigated at different size ratios, reduced densities, and nonadditivity parameters using molecular dynamics simulation. It was found that spherical, cylindrical, lamellar, and reverse micelles can form in systems with different head, tail, and solvent characteristics. Hard-core surfactant chains composed of a head segment and three tail segments were simulated in a solvent of hard spheres. The formation of micelles was found to be a strong function of the packing fraction and nonadditivity parameter. Micelles were more stable at higher densities and larger nonadditivity parameters. At lower densities, micelles tended to break into small, dynamic globules.

Effect of substrate-water interaction on the wetting behavior in water-oil and substrate-water-oil systems

The effects of the substrate water interaction on the wetting behavior in water-oil and surfactant-water-oil systems confined by one substrate which has the preferential interaction to one species of particles have been investigated by using the free energy analysis and discontinuous molecular dynamic simulations. As the preferential interaction between the substrate and water particles varies from small repulsion to large attraction, the partial drying, partial wetting and complete wetting state are observed in sequence. In addition, the wetting behavior of surfactant aqueous solution on the substrate is not only dependent on the interaction, but also limited by the maximum equilibrium concentration of surfactants at the interface.

Influence of monomer sequence on microstructure of nonadditive hard chain copolymers: Simulation and equation of state

Influence of copolymer structure on self-assembly of the copolymer was investigated by introducing nonadditive size interactions among different type segments in copolymers composed of touching hard spheres. The copolymer structures investigated are diblock, alternating, multiblock, and random. The copolymers were simulated using discontinuous molecular dynamics simulation. Equations of state of the different model copolymers were developed using the TPT1 theory. Diblock copolymers were found to self assemble readily at high values of the nonadditivity parameter Δ and at high densities. Multiblock and random copolymers self assembled to a smaller extent and the alternating copolymer self-assembled only at very high Δ and densities. The TPT1 equation of state provided good prediction of the compressibilities of the different copolymer systems at negative and small positive values of Δ. Deviations between the model and simulation results were observed at high Δ and high densities. Deviations were associated with self-assembly of the copolymers.

EFFECT OF DISC-WATER INTERACTION ON THE WETTING BEHAVIOR OF WATER PHASE BETWEEN TWO DISCS

The effect of the interaction between a disc and water-like particle on the wetting behavior of water-like phase between two discs has been investigated by free energy analysis and discontinuous molecular dynamic simulations. A detailed description for the partial wetting-complete wetting transition is provided and the analytical expressions describing the wetting behavior are obtained.

Temperature dependence of the distribution of the first passage time: results from discontinuous molecular dynamics simulations of an all-atom model of the second beta-hairpin fragment of protein G.

More than 22 000 folding kinetic simulations were performed to study the temperature dependence of the distribution of first passage time (FPT) for the folding of an all-atom Gō-like model of the second beta-hairpin fragment of protein G. We find that the mean FPT (MFPT) for folding has a U (or V)-shaped dependence on the temperature with a minimum at a characteristic optimal folding temperature T(opt). The optimal folding temperature T(opt) is located between the thermodynamic folding transition temperature and the solidification temperature based on the Lindemann criterion for the solid. Both the T(opt) and the MFPT decrease when the energy bias gap against nonnative contacts increases. The high-order moments are nearly constant when the temperature is higher than T(opt) and start to diverge when the temperature is lower than T(opt). The distribution of FPT is close to a log-normal-like distribution at T > or = T(opt). At even lower temperatures, the distribution starts to develop long power-law-like tails, indicating the non-self-averaging intermittent behavior of the folding dynamics. It is demonstrated that the distribution of FPT can also be calculated reliably from the derivative of the fraction not folded (or fraction folded), a measurable quantity by routine ensemble-averaged experimental techniques at dilute protein concentrations.

Computer simulation of copolymer phase behavior

Discontinuous molecular dynamics simulation is used to study the phase behavior of diblock copolymers modeled as chains of tangent hard spheres with square shoulder repulsions between unlike species as a function of chain length, volume fraction and interaction strength (χ). The location of the order–disorder transition for a symmetric copolymer is close to the predictions of Fredrickson and Helfand. Our simulation results for packing fractions of 0.35, 0.40, and 0.45 and chain lengths 10 and 20 are summarized in phase diagrams which display disordered, lamellae, perforated lamellae (PL), cylindrical, and BCC spherical (S) phases in the χN versus f plane. These phase diagrams are consistent with phase diagrams from other simulation studies. Contrary to theoretical predictions we observe the PL phase near regions of predicted gyroid stability, and the S phase only in the systems with high packing fraction and long chain length. These discrepancies may be due to the short chain lengths considered, as they are less evident in the 20-bead chains than the 10-bead chains. We examine the structural spacing of the microphases and the variation of that spacing with χN. We also examine the internal energy and entropy and their variation with χN. Our results are consistent with self-consistent field theory results for the strong segregation limit.

Global phase diagram for monomer/dimer mixtures

The basic features of the global phase diagram associated with the generalized Flory dimer (GFD) equation of state for mixtures of square-well monomers and dimers are calculated. We first extend the GFD theory to square-well monomer/chain mixtures. Theoretical predictions for the compressibility factor as a function of volume fraction are in good agreement with discontinuous molecular dynamics simulation results for monomer/dimer and monomers/8-mer mixtures. The GFD-predicted global phase diagram for square-well monomer/dimer mixtures is estimated using a brute force method. The locus of critical points in the P– T plane is calculated over a grid of points in the Λ– ζ plane, where ζ is a measure of the difference between the monomer and dimer well depths and Λ is a measure of the strength of the attraction between monomers and dimers. The major topographical features of our global phase diagram are similar to those predicted for other equations of state.

Protein Folding Pathways and Kinetics: Molecular Dynamics Simulations of β-Strand Motifs

The folding pathways and the kinetic properties for three different types of off-lattice four-strand antiparallel β-strand protein models interacting via a hybrid Go-type potential have been investigated using discontinuous molecular dynamics simulations. The kinetic study of protein folding was conducted by temperature quenching from a denatured or random coil state to a native state. The progress parameters used in the kinetic study include the squared radius of gyration R g 2, the fraction of native contacts within the protein as a whole Q, and between specific strands Q ab. In the time series of folding, the denatured proteins undergo a conformational change toward the native state. The model proteins exhibit a variety of kinetic folding pathways that include a fast-track folding pathway without passing through an intermediate and multiple pathways with trapping into more than one intermediate. The kinetic folding behavior of the β-strand proteins strongly depends on the native-state geometry of the model proteins and the size of the bias gap g, an artificial measure of a model protein's preference for its native state.

Effects of properties of the surfactant on its aggregate behavior.

The effects of the solvent-surfactant interaction, chain length and stiffness of surfactants on the formation of aggregates and the aggregation degree of surfactants in the two-dimension solution have been investigated using discontinuous molecular-dynamics simulations. When the tail-water repulsion increases or the head-water attraction decreases, the aggregation degree increases. Increasing the chain length and raising the stiffness of surfactants lead to the increment of the aggregation degree.

The effect of position along the chain on the dynamic properties of hard chain segments

Discontinuous molecular dynamics simulations are performed on systems containing 32 hard chains of length 192 at three volume fractions, φ=0.40, 0.45, and 0.50, to investigate the effect of position on the segmental mean squared displacement. The mean squared displacements of various sized blocks of segments at different positions along the chain are calculated. First, the effect of block size on the dynamics of end and middle blocks is considered. It is found that small blocks provide a greater difference between the mean squared displacements of middle blocks, end blocks, and the whole chain than larger equal-sized blocks. Next, the portions of the chain exhibiting end and middle behavior are determined. It is found that a large portion of the chain displays middle behavior, while a small portion displays end behavior. Finally, the dynamics of segment relaxation along the chain are studied. The relaxation of small blocks of segments at different positions along the chain starts at the chain ends and progresses toward the chain middle with time, as the tube model predicts. The minor chain length, the portion of the chain that has relaxed, follows a power law with time, but the power is somewhat less than predicted.

Entanglement Relaxation and Release in Hard Chain Fluids during Molecular Dynamics Simulations

Discontinuous molecular dynamics simulations are performed on systems containing 32 hard chains of length 192 at three volume fractions, φ = 0.40, 0.45, and 0.50, to investigate entanglement relaxation and release in model polymer melts. The relaxation behavior of the systems is compared to that predicted by the tube model and to that suggested for the release of interchain entanglements, or knots. The mean squared displacement of the chain center of mass, the mean squared displacements of inner, outer, and intermediate segments along the chain, the end-to-end vector autocorrelation function, and the apparent self-diffusion coefficient are calculated over the course of the simulations. The three relaxation times (τe, τR, and τd) predicted by the tube model are estimated in order to determine the extent to which the results exhibit tube confinement. The initial relaxation of chain segments occurs from the ends toward the middle as the tube model predicts. However, different methods for predicting the longe...

Evidence for size-dependent mechanical properties from simulations of nanoscopic polymeric structures

Discontinuous molecular dynamics simulations of a model polymer have been conducted to investigate the glass transition of ultrathin films and the mechanical properties of nanoscopic structures. Continuum mechanics models have been applied to interpret simulation data and extract apparent Young’s Moduli. Consistent with experiments, the results of simulations indicate that the glass transition temperature of thin films can be higher or lower than that of the bulk, depending on the nature of polymer–substrate interactions. Simulations also indicate that the mechanical properties of nanoscopic structures can be considerably different from those of the bulk. An analysis of molecular strain distributions in nanostructures undergoing a deformation indicate that significant stress relaxation occurs at air–polymer interfaces. A comparison of these distributions to the results of continuum, finite-element calculations reveal pronounced differences between the continuum and molecular approaches.

Phase diagrams for a multistep potential model of n-alkanes by discontinuous molecular dynamics and thermodynamic perturbation theory

Discontinuous molecular dynamics simulations and thermodynamic perturbation theory have been used to study thermodynamic properties for chain molecules. A multistep potential model is considered in this work through characterization of the vapor pressure and saturated liquid density for the n-alkanes from ethane to octane. The multistep potential model provides ∼4% accuracy for the entire molecular weight range. By contrast, previous studies of the square-well potential showed that the range of the square-well needed to vary with molecular weight to provide comparable accuracy. Therefore, having multiple steps with different depths for each functional group appears to be an essential part of making the potential model transferable. The depths of the wells vary such that the CH2 potential appears flatter than the CH3 potential, in an apparent attempt to moderate the overlaps implicit in the interaction site model.

Folding Thermodynamics of Model Four-Strand Antiparallel β-Sheet Proteins

The thermodynamic properties for three different types of off-lattice four-strand antiparallel β-strand protein models interacting via a hybrid Go-type potential have been investigated. Discontinuous molecular dynamic simulations have been performed for different sizes of the bias gap g, an artificial measure of a model protein’s preference for its native state. The thermodynamic transition temperatures are obtained by calculating the squared radius of gyration R g 2, the root-mean-squared pair separation fluctuation Δ B, the specific heat C v, the internal energy of the system E, and the Lindemann disorder parameter Δ L. Despite these models’ simplicity, they exhibit a complex set of protein transitions, consistent with those observed in experimental studies on real proteins. Starting from high temperature, these transitions include a collapse transition, a disordered-to-ordered globule transition, a folding transition, and a liquid-to-solid transition. The high temperature transitions, i.e., the collapse transition and the disordered-to-ordered globule transition, exist for all three β-strand proteins, although the native-state geometry of the three model proteins is different. However the low temperature transitions, i.e., the folding transition and the liquid-to-solid transition, strongly depend on the native-state geometry of the model proteins and the size of the bias gap.

Optimized step potential models for n-alkanes and benzene

Vapor pressure, density, and internal energy data from the literature are correlated in terms of the intermolecular interactions as represented by stepwise potential energies. Discontinuous molecular dynamics simulations are performed for united atom hard chain models of ethane, n-butane, n-hexane, n-octane, and benzene. Assuming square-well attractions ending at r/ σ=1.2, 1.5, 1.8, and 2.0, the depths of each well are regressed by computing the physical properties from thermodynamic perturbation theory at each set of trial depths and minimizing the deviations from experimental observation. The result is an equation-of-state for each fluid derived directly from the intermolecular potential model. Because molecular dynamics form the basis for the reference fluid simulations, transport properties may also be derived. Vapor pressure, density, and internal energy are correlated to roughly 1% average absolute deviation. The trends in the resulting potential models suggest that the change in disperse attractions with distance may vary from one functional group to another. For example, the optimized potential model for benzene diminishes to zero more slowly than the model for ethane.

Assembly of a tetrameric alpha-helical bundle: computer simulations on an intermediate-resolution protein model.

Discontinuous molecular dynamics (DMD) simulation on an intermediate-resolution protein model is used to study the folding of an isolated, small model peptide to an amphipathic alpha-helix and the assembly of four of these model peptides into a four-helix bundle. A total of 129 simulations were performed on the isolated peptide, and 50 simulations were performed on the four-peptide system. Simulations efficiently sample conformational space allowing complete folding trajectories from random initial configurations to be observed within 15 min for the one-peptide system and within 15 h for the four-peptide system on a 500-MHz workstation. The native structures of both the alpha-helix and the four-helix bundle are consistent with experimental characterization studies and with results from previous simulations on these model peptides. In both the one- and four-peptide systems, the native state is achieved during simulations within an optimal temperature range, a phenomenon also observed experimentally. The ease with which our simulations yield reasonable estimates of folded structures demonstrates the power of the intermediate-resolution model developed for this work and the DMD algorithm and suggests that simulations of very long times and of multiprotein systems may be possible with this model.

Alpha-helix formation: discontinuous molecular dynamics on an intermediate-resolution protein model.

An intermediate-resolution model of small, homogeneous peptides is introduced, and discontinuous molecular dynamics simulation is applied to study secondary structure formation. Physically, each model residue consists of a detailed three-bead backbone and a simplified single-bead side-chain. Excluded volume and hydrogen bond interactions are constructed with discontinuous (i.e., hard-sphere and square-well) potentials. Simulation results show that the backbone motion of the model is limited to realistic regions of Phi-Psi conformational space. Model polyalanine chains undergo a locally cooperative transition to form alpha-helices that are stabilized by backbone hydrogen bonding, while model polyglycine chains tend to adopt nonhelical structures. When side-chain size is increased beyond a critical diameter, steric interactions prevent formation of long alpha-helices. These trends in helicity as a function of residue type have been well documented by experimental, theoretical, and simulation studies and demonstrate the ability of the intermediate-resolution model developed in this work to accurately mimic realistic peptide behavior. The efficient algorithm used permits observation of the complete helix-coil transition within 15 min on a single-processor workstation, suggesting that simulations of very long times are possible with this model.

Phase envelopes for variable width square well chain fluids

Discontinuous Molecular Dynamics (DMD) and Thermodynamic Perturbation Theory (TPT) have been used to study square-well (SW) chain molecules with variable well-width SW potentials. Well widths of 1.5, 1.8, and 2.0 are considered for united atom models of ethane, n-hexane, and n-octane. The properties studied are the acentric factor, vapor pressure, and liquid density. DMD of purely repulsive potentials was applied to record the number of interaction sites in different wells, giving estimates of the TPT contributions from the attractive potential. DMD simulations of the complete potential near the coexistence condition were used to refine estimates of the derivative quantities related to the compressibility factor. Evaluations of this approach indicate that it is accurate and efficient at βε>0 and η>0.28. Phase diagrams of pure fluids also indicate quantitative accuracy for DMD/TPT at reduced temperatures less than 0.9. The results show that wider wells improve the representation of thermodynamic properties for longer chains. The well width becomes a function of the molecular weight, however.

Vapor–liquid equilibria of vibrating square well chains

Vibrating square well (SW) 2-mer, 4-mer, and 8-mer with average reduced bond lengths of 0.97±0.03, 0.60±0.03, and 0.40±0.03 were studied by discontinuous molecular dynamics (DMD) simulation in the NVE ensemble. Average bond angles for the reduced bond length of 0.4 were constrained to 127±16° while the longer bond lengths were freely jointed. Vapor–liquid equilibria of the vibrating SW fluids were determined based on DMD simulation by isochoric integration and compared to that of rigid SW chains from Gibbs ensemble Monte Carlo (MC) simulation. The binodals of vibrating chains show a shift to higher temperatures relative to rigid chains, reflecting their less repulsive (more attractive) nature. Vapor pressures of the vibrating chains were computed through isochoric integration with Clausius–Clapeyron consistency to 5% or better. Vapor pressure behavior for each chain model was characterized in terms of critical temperature, critical pressure, and acentric factor. The trend in acentric factor vs. chain length showed that shorter bond lengths gave improved agreement with the experimental trend for n-alkanes. Nevertheless, the trends in acentric factor did not support any molecular model for alkanes which represented methylene segments as individual SW interaction sites. If SW chains are to be applied as models of alkanes, each interaction site must be assigned more than one methylene segment.

Discontinuous Molecular Dynamics Studies of End-Linked Polymer Networks

Discontinuous molecular dynamics simulations are used to study the structure and relaxation of large, off-lattice, near-perfect, tri- and tetrafunctional polymer networks at a packing fraction of 0.43. The networks are constructed by end-linking freely jointed, tangent hard-sphere chains ranging in length from N = 20 to N = 150 and are then relaxed for 5−20 billion collisions. The simulation trajectories are used to calculate the radius of gyration and end-to-end distance of the network chains, the static structure factor of the cross-links, the mean-squared displacement of the cross-links and chain inner segments, the intermediate scattering function of the chains, and the elastic modulus of the network. The structure and properties of the networks are shown to depend heavily on the manner in which the network is initially constructed. The dynamics of the network cross-links and chain inner segments are similar to those of melt chains at short times and show evidence of spatial localization at long times...