Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations

A method of statistical estimation is applied to the problem of one-dimensional internal rotation in a hindering potential of mean force. The hindering potential, which may have a completely general shape, is expanded in a Fourier series, the coefficients of which are estimated by fitting an appropriate statistical-mechanical distribution to the random variable of internal rotation angle. The function of reduced moment of inertia of an internal rotation is averaged over the thermodynamic ensemble of atomic configurations of the molecule obtained in stochastic simulations. When quantum effects are not important, an accurate estimate of the absolute internal rotation entropy of a molecule with a single rotatable bond is obtained. When there is more than one rotatable bond, the "marginal" statistical-mechanical properties corresponding to a given internal rotational degree of freedom are reduced. The method is illustrated using Monte Carlo simulations of two public health relevant halocarbon molecules, each having a single internal-rotation degree of freedom, and a molecular dynamics simulation of an immunologically relevant polypeptide, in which several dihedral angles are analyzed.     

Elastic and dynamical properties of alkali-silicate glasses from computer simulations techniques

This paper shows recent progresses in the field of computer simulations of inorganic glasses. Molecular dynamics simulations and energy minimization methods have been applied to calculate the elastic and transport properties of alkali silicate glasses of compositions xM₂O · (100 ? x)SiO₂ (with x = 0, 10, 15, 20, 25, 30 % mol for M = Li, Na and K) and of a soda-lime glass with composition 15Na₂O · 10CaO · 75SiO₂, which has been employed to ascertain the effect of the replacement of CaO for Na₂O. The excellent agreement of the computed results with the experimental data highlights the important predictive and interpretative role reached by computer simulations techniques.     

Multiscale modeling of viscoelastic properties of polymer nanocomposites

A methodology for simple multiscale modeling of mechanical properties of polymer nanocomposites has been developed. This methodology consists of three steps: (1) obtaining from molecular dynamics simulations the viscoelastic properties of the bulklike polymer and approximating the position-dependent shear modulus of the interfacial polymer on the basis of the polymer-bead mean-square displacements as a function of the distance from the nanoparticle surface, (2) using bulk- and interfacial-polymer properties obtained from molecular dynamics simulations and performing stress–relaxation simulations of the nanocomposites with material-point-method simulations to extract the nanocomposite viscoelastic properties, and (3) performing direct validation of the average composite viscoelastic properties obtained from material-point-method simulations with those obtained from the molecular dynamics simulations of the nanocomposites. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1005-1013, 2005     

A topology preserving method for generating equilibrated polymer melts in computer simulations

A new method for generating equilibrated configurations of polymer melts is presented. In this method, the molecular weight of an equilibrated melt of polymers is successively doubled by affinely scaling the simulation box and adding beads along the contour of the chains. At each stage of molecular weight doubling, compressive deformations are produced on all length scales, while the random walk nature of the polymers is preserved, thereby requiring relaxation times significantly smaller than the reptation time to fully equilibrate the melt. This method preserves the topological state of individual polymers in the melt and its effectiveness is demonstrated for linear polymers with molecular weight N up to 1024, and cyclic polymers with N up to 8192. For the range of N studied, the method requires simulation time that scales as N(2) and is thought to be applicable to a variety of polymer architectures.     

Linear viscoelastic characteristics of in situ compatiblized binary polymer blends with viscoelastic properties of components variable

By Friedel‐Crafts alkylation reaction, catalyzed by a Lewis acid of anhydrous aluminum chloride (AlCl₃), binary polymer blends of polypropylene (PP)/polystyrene (PS) with volume proportion of 80/20 were in situ compatiblized and prepared in an XSS‐30 melt mixer at 210 °C. The linear viscoelastic characteristics of the blends were investigated by checking the variations of storage modulus, loss modulus, complex modulus, and complex viscosity of the in situ compatiblized blends, which were dependent on AlCl₃ content. In addition, Han plots of the in situ compatiblized blends with different AlCl₃ content were also used to characterize the linear viscoelastic properties of the blends. The results showed that both the dynamic rheological parameters and the Han plots were obviously influenced by the rheological properties of the matrix and slightly influenced by the rheological properties of the dispersed phase. Further investigations revealed that phase geometry contributions to the dynamic rheological parameters of the blends could be ignored in comparison with the contributions of the components and the interfacial modification, which were defined and obtained according to log‐linear‐additivity rule. The linear viscoelastic characteristics of the blends were mainly controlled by the combination of the effects of interfacial modification between phases and the rheological properties of the matrix. Storage modulus is the most sensitive dynamic rheological parameter to characterize the interfacial compatiblization effects in the in situ compatiblized binary polymer blends with rheological properties of components variable. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1349–1362, 2010     

Estimation of the liquid-vapor spinodal from interfacial properties obtained from molecular dynamics and lattice Boltzmann simulations

Interfacial pressure and density profiles are calculated from molecular dynamics and lattice Boltzmann simulations of a liquid film in equilibrium with its vapor. The set of local values of tangential pressure and density along an interface exhibits a van der Waals-type loop; starting from the stable vapor bulk phase one passes through metastable and unstable states to the stable liquid bulk phase. The minimum and maximum values of the profile of tangential pressure are related to the liquid and vapor spinodal states, respectively. The spinodal pressures turn out to be linearly related to the extreme values of the tangential pressure in the interface. The comparison with equations of state shows good agreement with the simulation results of the spinodals. In addition the properties of the metastable region are obtained. Based on this investigation a method is proposed for the estimation of the liquid spinodal from experimentally obtained interfacial properties. Estimations for water and helium are presented.     

Estimation of protein folding probability from equilibrium simulations

The assumption that similar structures have similar folding probabilities (p(fold)) leads naturally to a procedure to evaluate p(fold) for every snapshot saved along an equilibrium folding-unfolding trajectory of a structured peptide or protein. The procedure utilizes a structurally homogeneous clustering and does not require any additional simulation. It can be used to detect multiple folding pathways as shown for a three-stranded antiparallel beta-sheet peptide investigated by implicit solvent molecular dynamics simulations.     

The role of intermolecular interactions in the viscoelastic properties of polymer melts

The exact microscopic expression for the stress tensor in polymer liquids contains a tensor product of the the segment position vector with the total, intra- plus inter-chain, force acting on the segment. On the other hand, the widely accepted theory of viscoelasticity of polymer melts¹⁾ is based on the assumption, that contributions from interchain interactions to the viscosity of polymer melts is negligible relative to the effectively intrachain entropic interactions. Starting from the exact Green-Kubo formula for the viscosity, the Rouse dynamic correlation functions, and Newton's second law, we show that the intrachain assumption is inadequate. Rather, the intrachain and interchain forces acting on polymer segments cancel each other largely. The intrachain contribution therefore cannot be dominant as anticipated in the usual treatment¹⁾, or, in other words, the interchain contribution cannot be ignored. The main contribution to viscoelastic properties of polymer melts can only arise from a part of the total stress tensor as already suggested by M. Fixman based on a different argument²⁾. It is concluded that the viscosity is of a purely interchain nature, and is determined by the tensor product of the vector connecting the centers-of-mass of neighboring macromolecules on the one hand, and the total force by which macromolecules interact, on the other, just in the case of simple liquids.     

A new instrument for measuring the viscoelastic properties of dilute polymer solutions

A new oscillating capillary viscometer has been developed and used for measuring viscoelastic flow properties of dilute polymer solutions. These flow properties are determined from measurements of the pressure to volume flow relationships for sinusoidal flow in cylindrical glass capillaries. The theory for this measurement procedure is based upon the known theory for oscillatory flow of a viscoelastic fluid in circular tubes and which is presented with a few supplementations in this paper.The oscillatory flow is generated by a piezoelectric driver which is dipped directly into the aqueous solution. The advantage of this driver is that the excitation voltage for the piston is a direct measure of the motion of the piston. Changes in pressure are measured with a sensitive low-pressure quartz tranducer.The viscometer was tested with aqueous glycerol solutions and a gelatin gel. The viscoelastic flow properties of dilute polymer solutions (gelatin, gelatin/color-coupler, polyacrylamide) were then investigated in the frequency range 5 Hz to 150 Hz at very small volume flow amplitudes. The results presented illustrate the suitability of the method. The results are also evaluated with regard to the stabilizing action of slightly viscoelastic gelatinous coating liquids in the high-speed coating process in the manufacture of photographic materials.     

Liquid-phase structure of dialkylimidazolium ionic liquids from computer simulations

We present a detailed computational study of the structure of ionic liquids based on the imidazolium cation. Both imidazolium-ring stacking and hydrogen bonding behavior are investigated from radial and spatial orientational distribution functions, as well as orientational correlation functions. The alkyl chain size and anion effect on the liquid structure are provided and discussed. Our results support models for liquid organization comparable to those formulated on the basis of experimental observations.     

Phase equilibrium in polymer systems

The topological analysis of phase equilibria in polymer systems, which was developed by S.P. Papkov; the classification of the types of phase equilibrium; the principle of mutual independence of the two types of equilibrium; the concept of the generality of the phase equilibrium in polymer-solvent, polymer-plasticizer, polymer-oligomer, and polymer-polymer systems; and the processes of water sorption by polymers are considered. It is shown that the problems that Papkov dealt with remain topical and the concepts that he elaborated can underlie new studies in the field of phase equilibria in polymer systems.     

Monte Carlo simulations of single crystals from polymer solutions

A novel "anisotropic aggregation" model is proposed to simulate nucleation and growth of polymer single crystals as functions of temperature and polymer concentration in dilute solutions. Prefolded chains in a dilute solution are assumed to aggregate at a seed nucleus with an anisotropic interaction by a reversible adsorption/desorption mechanism, with temperature, concentration, and seed size being the control variables. The Monte Carlo results of this model resolve the long-standing dilemma regarding the kinetic and thermal roughenings, by producing a rough-flat-rough transition in the crystal morphology with increasing temperature. It is found that the crystal growth rate varies nonlinearly with temperature and concentration without any marked transitions among any regimes of polymer crystallization kinetics. The induction time increases with decreasing the seed nucleus size, increasing temperature, or decreasing concentration. The apparent critical nucleus size is found to increase exponentially with increasing temperature or decreasing concentration, leading to a critical nucleus diagram composed in the temperature-concentration plane with three regions of different nucleation barriers: no growth, nucleation and growth, and spontaneous growth. Melting temperatures as functions of the crystal size, heating rate, and concentration are also reported. The present model, falling in the same category of small molecular crystallization with anisotropic interactions, captures most of the phenomenology of polymer crystallization in dilute solutions.     

Determining equilibrium constants for dimerization reactions from molecular dynamics simulations

With today's available computer power, free energy calculations from equilibrium molecular dynamics simulations "via counting" become feasible for an increasing number of reactions. An example is the dimerization reaction of transmembrane alpha-helices. If an extended simulation of the two helices covers sufficiently many dimerization and dissociation events, their binding free energy is readily derived from the fraction of time during which the two helices are observed in dimeric form. Exactly how the correct value for the free energy is to be calculated, however, is unclear, and indeed several different and contradictory approaches have been used. In particular, results obtained via Boltzmann statistics differ from those determined via the law of mass action. Here, we develop a theory that resolves this discrepancy. We show that for simulation systems containing two molecules, the dimerization free energy is given by a formula of the form ΔG ∝ ln(P(1) /P(0) ). Our theory is also applicable to high concentrations that typically have to be used in molecular dynamics simulations to keep the simulation system small, where the textbook dilute approximations fail. It also covers simulations with an arbitrary number of monomers and dimers and provides rigorous error estimates. Comparison with test simulations of a simple Lennard Jones system with various particle numbers as well as with reference free energy values obtained from radial distribution functions show full agreement for both binding free energies and dimerization statistics.     

Electrostatics of phosphatidic acid monolayers: Insights from computer simulations

In this paper, we argue that many of the fascinating electrostatic effects that take place in amphiphilic systems are strongly related to the particular organization of the oxygen atoms within each individual molecule. In particular, we focus on two effects: charge inversion and dielectric overscreening. For that purpose, we present molecular dynamics simulations of phosphatidic acid (DMPA²⁻) in the presence of divalent counterions. Our results show that the many oxygens present in DMPA²⁻ cooperatively create strong binding sites for counterions, which in some cases lead to charge inversion. We also present an analysis of the role of interfacial water and relate our analysis to the phenomenon of dielectric overscreening. Several experimental implications are discussed in the conclusions.     

Structures of neat and hydrated 1-octanol from computer simulations

Molecular dynamics computer simulations of 1-octanol and its mixtures with water have been performed. The liquid is composed of regions enriched in either hydrocarbons or hydroxyl groups. In neat octanol, the hydroxyl groups form clusters of long, thin chains. Upon the addition of water, the clusters become longer and more spherical, forming a structure that can be described as consisting of "overlapping elongated inverse micelles". The structures of the mixtures obtained at different hydration levels are consistent with those of experimental diffraction studies of water/octanol mixtures and previous computer simulations of neat and water-saturated octanol. The saturation point of the model has been calculated using the cavity-bias particle insertion method. The solubility of water in octanol is slightly too low compared to experimental results, and suggestions for possible improvements to the force field are made.     

Calculation of free energy differences for water from computer simulations

Free energy differences for water at different temperatures have been calculated from Monte Carlo computer simulations using both ratio overlap and umbrella sampling methods. The problems of calculating precise values from these methods are discussed. Three models for water (ST2, TIPS2 and PE) have been used in these calculations which have been compared with experimental estimates for the configurational free energy. The importance of being able to predict accurate mean potential energies as well as accurate energy distributions is emphasised.     

Inkjet printing of viscoelastic polymer inks

The droplet formation, the rheological properties of jettable ink and polymer inks in inkjet printing are summarized.     

Thermal conductivity of molten alkali halides from equilibrium molecular dynamics simulations

The thermal conductivity of molten sodium chloride and potassium chloride has been computed through equilibrium molecular dynamics Green-Kubo simulations in the microcanonical ensemble (N,V,E). In order to access the temperature dependence of the thermal conductivity coefficient of these materials, the simulations were performed at five different state points. The form of the microscopic energy flux for ionic systems whose Coulombic interactions are calculated through the Ewald method is discussed in detail and an efficient formula is used by analogy with the methods used to evaluate the stress tensor in Coulombic systems. The results show that the Born-Mayer-Huggins-Tosi-Fumi potential predicts a weak negative temperature dependence for the thermal conductivity of NaCl and KCl. The simulation results are in agreement with part of the experimental data available in the literature with simulation values generally overpredicting the thermal conductivity by 10%-20%.