Monte Carlo Simulation of Thin Film Polymer Melts

We present Monte Carlo simulation data on conformations and dynamics of polymer melts confined in narrow slits of different widths and compare with data of bulk systems. We find that in confined geometries the chains swell laterally; they retain and even expand their spatially long-range correlations compared to bulk polymers and in contrast to the assumption of a complete screening of excluded volume. Long chains in bulk melts show entangled dynamics with a clear signature of a t^1/4-power law for the mean square displacements of innermost monomers at intermediate time scales. This behavior is gradually lost by confining the melts in slits with decreasing width. For ultra-thin films, the dynamics appears to follow a Rouse-like behavior over the entire subdiffusive regime. However, the terminal relaxation time is significantly increased compared to Rouse relaxation. This interesting observation was not reported previously and is the focus of our ongoing research.     

Compressed exponential relaxation in liquid silicon: universal feature of the crossover from ballistic to diffusive behavior in single-particle dynamics

We report a first-principles molecular-dynamics study of the relaxation dynamics in liquid silicon (l-Si) over a wide temperature range (1000-2200 K). We find that the intermediate scattering function for l-Si exhibits a compressed exponential decay above 1200 K including the supercooled regime, which is in stark contrast to that for normal "dense" liquids which typically show stretched exponential decay in the supercooled regime. The coexistence of particles having ballistic-like motion and those having diffusive-like motion is demonstrated, which accounts for the compressed exponential decay in l-Si. An attempt to elucidate the crossover from the ballistic to the diffusive regime in the "time-dependent" diffusion coefficient is made and the temperature-independent universal feature of the crossover is disclosed.     

Rotational relaxation in simple chain models

The rotational dynamics of chemically similar systems based on freely jointed and freely rotating chains are studied. The second Legendre polynomial of vectors along chain backbones is used to investigate the rotational dynamics at different length scales. In a previous study, it was demonstrated that the additional bond-angle constraint in the freely rotating case noticeably perturbs the character of the translational relaxation away from that of the freely jointed system. Here, it is shown that differences are also apparent in the two systems' rotational dynamics. The relaxation of the end-to-end vector is found to display a long time, single-exponential tail and a stretched exponential region at intermediate times. The stretching exponents beta are found to be 0.75+/-0.02 for the freely jointed case and 0.68+/-0.02 for the freely rotating case. For both system types, time-packing-fraction superposition is seen to hold on the end-to-end length scale. In addition, for both systems, the rotational relaxation times are shown to be proportional to the translational relaxation times, demonstrating that the Debye-Stokes-Einstein law holds. The second Legendre polynomial of the bond vector is used to probe relaxation behavior at short length scales. For the freely rotating case, the end-to-end relaxation times scale differently than the bond relaxation times, implying that the behavior is non-Stokes-Einstein, and that time-packing-fraction superposition does not hold across length scales for this system. For the freely jointed case, end-to-end relaxation times do scale with bond relaxation times, and both Stokes-Einstein and time-packing-fraction-across-length-scales superposition are obeyed.     

Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study

Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond fluctuation model, where differences in the interaction energies between nonbonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a no bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long time dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths N(c) are calculated from the packing length of the chains. These are combined with a local mobility mu determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients D(c)=muN(c). We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients DD(c) as a function of reduced chain length NN(c). The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length N=20 at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends.     

Dynamics of Bond‐Fluctuation Model Chains in Good and Theta Solvents

The dynamic Monte Carlo algorithm is employed to explore the dynamics of flexible linear chains. The chains are represented by the bond‐fluctuation model with and without attractions between non‐bonded units placed at close distances. This mimics the behavior of real chains in the good and poorer solvents. We obtain the chain sizes, diffusion coefficients, Rouse modes, and their relaxation times. We also evaluate the time correlation function of the end‐to‐end vector at different concentrations. Subsequently, we compare the dependence of the simulation results on chain length, solvent quality, concentration, and mode order with the corresponding theoretical predictions. We observe a retardation of diffusion for non‐dilute systems close to the theta state. This retardation is too high to be exclusively attributed to the increase of global friction and can be caused by temporary adherence of the chains to transient clusters.     

Simple model for grafted polymer brushes

The first theories of grafted polymer brushes assumed a step profile for the monomer density. Later, the real density profile was obtained from Monte Carlo or molecular dynamics simulations and calculated numerically using a self-consistent field theory. The analytical approximations of the solutions of the self-consistent field equations provided a parabolic dependence of the self-consistent field, which in turn led to a parabolic distribution for the monomer density in neutral brushes. As shown by numerical simulations, this model is not accurate for dense polymer brushes, with highly stretched polymers. In addition, the scaling laws obtained from the analytical approximations of the self-consistent field theory are identical to those derived from the earlier step-profile-approximation and predict a vanishing thickness of the brush at low graft densities, and a thickness exceeding the length of the polymer chains at high graft densities. Here a simple model is suggested to calculate the monomer density and the interaction between surfaces with grafted polymer brushes, based on an approximate calculation of the partition function of the polymer chains. The present model can be employed for both good and poor solvents, is compatible with a parabolic-like profile at moderate graft densities, and leads to an almost steplike density for highly stretched brushes. While the thickness of the brush depends strongly on solvent quality, it is a continuous function in the vicinity of the temperature. In good and moderately poor solvents, the interactions between surfaces with grafted polymer brushes are always repulsive, whereas in poor solvents the interactions are repulsive at small separations and become attractive at intermediate separation distances, in agreement with experiment. At large separations, a very weak repulsion is predicted.     

Grafted polymer layers under variable solvent conditions: A Monte Carlo simulation

Polymer chains anchored with one end at a hard wall under variable solvent conditions are investigated by Monte Carlo simulations using the bond- fluctuation model. Detail information on the structural properties are obtained above, at, and below the Θ-point and discussed in terms of the appropriate theories. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. For the dynamics at the Θ-point, both the relaxation time of the chain configuration and the mean-square time displacement are studied. At temperatures distinctly below the Θ-point, we find that the layer develops considerable lateral inhomogeneity in its density, which has not been predicted by previous theories.     

Energy relaxation of intermolecular motions in supercooled water and ice: a molecular dynamics study

We investigate the energy relaxation of intermolecular motions in liquid water at temperatures ranging from 220 K to 300 K and in ice at 220 K using molecular dynamics simulations. We employ the recently developed frequency resolved transient kinetic energy analysis, which provides detailed information on energy relaxation in condensed phases like two-color pump-probe spectroscopy. It is shown that the energy cascading in liquid water is characterized by four processes. The temperature dependences of the earlier three processes, the rotational-rotational, rotational-translational, and translational-translational energy transfers, are explained in terms of the density of states of the intermolecular motions. The last process is the slow energy transfer arising from the transitions between potential energy basins caused by the excitation of the low frequency translational motion. This process is absent in ice because the hydrogen bond network rearrangement, which accompanies the interbasin transitions in liquid water, cannot take place in the solid phase. We find that the last process in supercooled water is well approximated by a stretched exponential function. The stretching parameter, β, decreases from 1 to 0.72 with decreasing temperature. This result indicates that the dynamics of liquid water becomes heterogeneous at lower temperatures.     

Quantum Monte Carlo simulations of selected ammonia clusters (n = 2-5): isotope effects on the ground state of typical hydrogen bonded systems

Variational Monte Carlo, diffusion Monte Carlo, and stereographic projection path integral simulations are performed on eight selected species from the (NH(3))(n), (ND(3))(n), (NH(2)D)(n), and (NH(3))(n-1)(ND(3)) clusters. Each monomer is treated as a rigid body with the rotation spaces mapped by the stereographic projection coordinates. We compare the energy obtained from path integral simulations at several low temperatures with those obtained by diffusion Monte Carlo, for two dimers, and we find that at 4 K, the fully deuterated dimer energy is in excellent agreement with the ground state energy of the same. The ground state wavefunction for the (NH(3))(2-5) clusters is predominantly localized in the global minimum of the potential energy. In all simulations of mixed isotopic substitutions, we find that the heavier isotope is almost exclusively the participant in the hydrogen bond.     

Orientational dynamics for an amphiphilic-solvent solution

In this work, we performed Monte Carlo simulations on a lattice model for spontaneous amphiphilic aggregation, in order to study the orientational and hydrogen-bonding dynamics of water on different regions inside the micellar solution. We employed an associating lattice gas model that mimics the aqueous solvent, which presents a rich phase diagram with first- and second-order transition lines. Even though this is a simplified model, it makes possible to investigate the orientational dynamics of water in an equilibrium solution of amphiphiles, as well as the influence of the different phases of the solvent in the interfacial and bulk water dynamics. By means of extensive simulations, we showed that, at high temperatures, the behavior of the orientational relaxation and hydrogen bonding of water molecules in the bulk, first, and second hydration shells are considerable different. We observe the appearance of a very slow component for water molecules in the first hydration shell of micelles when the system reaches a high-density phase, consistent with previous theoretical and experimental studies concerning biological water. Also, at high temperatures, we find that water molecules in the second hydration shell of micelles have an orientational decay similar to that of bulk water, but with a generally slower dynamics. Otherwise, at low temperatures, we have two components for the orientational relaxation of bulk water in the low density liquid phase, and only a single component in the high density liquid (HDL) phase, which reflect the symmetry properties of the different phases of the solvent model. In the very dense region of water molecules in the first hydration shell of micelles at low temperatures, we find two components for the orientational relaxation on both liquid phases, one of them much slower than that in the single component of bulk water in the HDL phase. This happens even though our model does not present any hindrance to the water rotational freedom caused by the presence of the amphiphiles.     

New phase for one-component hard spheres

A completely new phase for one-component hard spheres is reported in an unexpected region of the phase diagram. The new phase is observed at compressibility factors intermediate between the solid and the metastable branches. It can be obtained from either Monte Carlo simulations alone or a combination of Monte Carlo and molecular dynamics calculations. An analysis of the intermediate scattering function data shows that the new phase is in a stable equilibrium. Radial distribution function data, configurational snapshots, bond order parameters, and translational order parameters obtained from molecular simulations indicate that the new phase is significantly different from the isotropic liquid, metastable, or crystalline phases traditionally observed in hard sphere systems. This result significantly changes our previous understanding of the behavior of hard spheres.     

Apparent glassy dynamics of an adsorbed polymer chain in the bond-fluctuation model

The dynamics of a single homopolymer chain strongly adsorbed on a flat surface is investigated by Monte Carlo simulation using the bond-fluctuation model. Previously observed anomalous glassy dynamics at low temperatures [Phys. Rev. E 49 , 5420 (1994)] is revisited in detail. We also study the dynamics of a polymer chain confined in a narrow slit of width of a monomer and a modified bond-fluctuation model in three dimensions to include more relevant bond vectors. We show that the previously observed glassy dynamics is due to an artifact of the bond-fluctuation model in three dimensions in that it does not cross-over to the two dimensional bond-fluctuation model with the correct Rouse dynamics. With the proper inclusion of the extra bond vectors P(2,2,0) and P(3,2,0), no glassy behavior appears for the strongly adsorbed chain.     

Nonlinear Viscoelasticity Raised at Low Temperatures by Intermolecular Cooperation of Bulk Amorphous Polymers

We performed dynamic Monte Carlo simulations of stress relaxation in parallel-aligned and uniaxially stretched bulk amorphous polymers at low temperatures.We observed an extra-slowing down in the early stage of stress relaxation,which causes nonlinear viscoelasticity as deviated from Debye relaxation and Arrhenius-fluid behaviors observed previously at high temperatures.Meanwhile,fluctuation analysis of stress relaxation revealed a substantial increase in the stretch fractions of polymers at the transient periods of high-temperature Debye relaxation.Structural analysis of free volume further revealed the scenario that,at low temperatures,the modulus of polymer entropy elasticity decreases with temperature and eventually loses its competition to the imposed modulus (Deborah number becomes larger than one),and hence upon stress relaxation under constant strains,monomers are firstly accumulated nearby two stretching ends of polymers,resulting in tentative global jamming like physical cross-linking there,and thus retarding the coming transient state of stress relaxation.We concluded that intermolecular cooperation raises physical crosslinking for nonlinear viscoelasticity of polymer stress relaxation as well as the rubbery states unique to bulk amorphous polymers.The new microscopic mechanism of the fluid-rubbery transition of polymers may bring insights into the intermolecular cooperation mechanism of glass transition of small molecules,if the fluid-rubbery transition is regarded as an extrapolation of glass transition from low to high molecular weights.     

Local Transient Jamming in Stress Relaxation of Bulk Amorphous Polymers

Bulk amorphous polymers become stretched and parallel-aligned under loading stress, and their intermolecular cooperation slows down the subsequent stress relaxation process. By means of dynamic Monte Carlo simulations, we employed the linear viscoelastic Maxwell model for stress relaxation of single polymers and investigated their intermolecular cooperation in the stress relaxation process of stretched and parallel-aligned bulk amorphous polymers. We carried out thermal fluctuation analysis on t...     

Statics and dynamics of dense polymer systems studied by monte carlo simulation

Monte Carlo simulations of coarse–grained models of macromolecules offer a unique tool to study the interplay between coil conformations, thermodynamic properties, and chain configurational relaxation and diffusion. Two examples are discussed where the chain conformation strongly differs from a gaussian coil: (i) collapsed chains in a bad solvent, where anomalous diffusion occurs in the Rouse limit and the relaxation time increases at least with the third power of chain length. (ii) Expulsion of a chain from a semidilute polymer brush. The initially stretched chain contracts to a gaussian coil and the center of mass moves outward with constant velocity until it reaches the region of the “last blob” where crossover to diffusive behavior occurs.     

On the equation of state for thermal polymer solutions and melts with attractive interaction

We perform Monte Carlo simulations of a lattice model for polymer melts, i. e., the bond fluctuation model in three dimensions. By using an energy parameter that prefers relatively long bonds, the model exhibits a glass transition at low temperatures, in close qualitative similarity to experiment. We modify this model by adding an attractive interaction of variable strength. We demonstrate that a small interaction strength has only a very small effect on the static properties of the melt. For a fixed strength of the potential, the chemical potential is measured by a modified particle-insertion method over a large range of temperatures and densities. The osmotic pressure is obtained by thermodynamic integration. In contrast to the original version our extended model exhibits a positive thermal expansion.     

Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte Carlo simulations

We use replica exchange Monte Carlo simulations to measure the equilibrium equation of state of the disordered fluid state for a binary hard sphere mixture up to very large densities where standard Monte Carlo simulations do not easily reach thermal equilibrium. For the moderate system sizes we use (up to N = 100), we find no sign of a pressure discontinuity near the location of dynamic glass singularities extrapolated using either algebraic or simple exponential divergences, suggesting they do not correspond to genuine thermodynamic glass transitions. Several scenarios are proposed for the fate of the fluid state in the thermodynamic limit.     

Dynamic distance disorder in proteins is caused by trapping

Dynamic disorder in proteins, as demonstrated by variations in single-molecule electron transfer rates, is investigated by molecular dynamics simulations. The potential of mean force for the fluctuating donor-acceptor distance is calculated for the NAD(P)H:flavin oxidoreductase (Fre) complex with flavin adenine dinucleotide (FAD) and is found to be in agreement with that estimated from electron transfer experiments. The calculated autocorrelation function of the distance fluctuations has a simple exponential behavior at low temperatures and stretched exponential behavior at higher temperatures on femtosecond to nanosecond time scales. This indicates that the calculated dynamic disorder arises from a wide range of trapping times in potential wells on the protein energy landscape and suggests a corresponding origin for the stretched exponential behavior observed experimentally on longer time scales.