Coarse-grained polyethylene: 1. The simplest model for the orthorhombic crystal

The coarse-grained model of polyethylene and alkanes (the united-atom model, in which each CH₂ group is represented by a single bead) was proposed several decades ago. It is widely applied in molecular dynamics simulations. For different tasks, the models with different geometrical and force parameters are used. Until now, it was thought that the coarse-grained model of polyethylene cannot reproduce the orthorhombic crystalline phase, which is typical of this polymer. In the present study, we analyze the simplest coarse-grained model of polyethylene. In this model, the Lennard-Jones potential (6–12) is adopted for van der Waals interactions between the beads of different chains. Of the bonded interactions, only the “valence” bonds between beads and the “bond” and “torsion” angles are taken into account, whereas the cross terms between them are disregarded. We consider the model variation in which the bead (the force center with the mass of a CH₂ group) is displaced from the center of the carbon atom and all the interactions, both bonded and nonbonded, are defined by the positions of these beads. For this model, we find the area of geometrical parameters (the displacement value and the van der Waals radius of the bead) in which all the three known crystalline phases of polyethylene are at equilibrium at low temperatures. We choose the force field constants for the model so that its oscillation spectrum reproduces the low-frequency part of the inelastic neutron scattering spectrum of the orthorhombic polyethylene. It proved to be that this choice can be made unambiguously. We compare the dispersion curves in the terahertz range with experimental data on the Raman scattering and infrared spectroscopy, and discuss the advantages and disadvantages of the analyzed simplest coarse model.     

A coarse-grained model for polyethylene glycol polymer

A coarse-grained (CG) model of polyethylene glycol (PEG) was developed and implemented in CG molecular dynamics (MD) simulations of PEG chains with degree of polymerization (DP) 20 and 40. In the model, two repeat units of PEG are grouped as one CG bead. Atomistic MD simulation of PEG chains with DP = 20 was first conducted to obtain the bonded structural probability distribution functions (PDFs) and nonbonded pair correlation function (PCF) of the CG beads. The bonded CG potentials are obtained by simple inversion of the corresponding PDFs. The CG nonbonded potential is parameterized to the PCF using both an inversion procedure based on the Ornstein-Zernike equation with the Percus-Yevick approximation (OZPY(-1)) and a combination of OZPY(-1) with the iterative Boltzmann inversion (IBI) method (OZPY(-1)+IBI). As a simple one step method, the OZPY(-1) method possesses an advantage in computational efficiency. Using the potential from OZPY(-1) as an initial guess, the IBI method shows fast convergence. The coarse-grained molecular dynamics (CGMD) simulations of PEG chains with DP = 20 using potentials from both methods satisfactorily reproduce the structural properties from atomistic MD simulation of the same systems. The OZPY(-1)+IBI method yields better agreement than the OZPY(-1) method alone. The new CG model and CG potentials from OZPY(-1)+IBI method was further tested through CGMD simulation of PEG with DP = 40 system. No significant changes are observed in the comparison of PCFs from CGMD simulations of PEG with DP = 20 and 40 systems indicating that the potential is independent of chain length.     

Conformational and packing stability of crystalline polymers. VI. Stable chain packing of polyethylene

The stable packings of polyethylene chains were investigated by intermolecular potential energy calculations based on various chain-assembly models. The structures of the two crystal modifications of polyethylene (i.e., orthorhombic and the monoclinic), together with their cell constants and the setting angles, were well reproduced. The packing modes of polymethylene chains found in various alkane derivatives were also explained by the energy minima of the chain-assembly models. In these calculations, several sets of potential functions were tried and three sets of functions were found to reproduce conformations of single polymer chains, the cell constants of polyethylene at low temperature, and those at room temperature.     

Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor.     

The lattice and rotational dynamics of the methyl halides described by pair potentials based on universal force fields

A systematical computational study of the lattice and rotational dynamics of the methyl halides, which belong to the most simple organic molecules containing CH(3) groups, was done. Because of their simplicity there might be a chance to understand and model the dynamics of these systems by combining nonbonded pair interactions and crystallographic information. Based on the experimentally determined crystal structure, which was not relaxed during the calculations, interactions were modeled using the transferable parameters of the universal force fields. The lattice dynamical calculation can reproduce with reasonable accuracy the low-energy regime of the lattice excitations as well as the single-particle rotational potential of the CH(3) group of the respective halide.     

Comparison of structural,thermodynamic, kinetic and mass transport properties of Mg2+ ion models commonly used in biomolecular simulations

The prevalence of Mg²⁺ ions in biology and their essential role in nucleic acid structure and function has motivated the development of various Mg²⁺ ion models for use in molecular simulations. Currently, the most widely used models in biomolecular simulations represent a nonbonded metal ion as an ion‐centered point charge surrounded by a nonelectrostatic pairwise potential that takes into account dispersion interactions and exchange effects that give rise to the ion's excluded volume. One strategy toward developing improved models for biomolecular simulations is to first identify a Mg²⁺ model that is consistent with the simulation force fields that closely reproduces a range of properties in aqueous solution, and then, in a second step, balance the ion–water and ion–solute interactions by tuning parameters in a pairwise fashion where necessary. The present work addresses the first step in which we compare 17 different nonbonded single‐site Mg²⁺ ion models with respect to their ability to simultaneously reproduce structural, thermodynamic, kinetic and mass transport properties in aqueous solution. None of the models based on a 12‐6 nonelectrostatic nonbonded potential was able to reproduce the experimental radial distribution function, solvation free energy, exchange barrier and diffusion constant. The models based on a 12‐6‐4 potential offered improvement, and one model in particular, in conjunction with the SPC/E water model, performed exceptionally well for all properties. The results reported here establish useful benchmark calculations for Mg²⁺ ion models that provide insight into the origin of the behavior in aqueous solution, and may aid in the development of next‐generation models that target specific binding sites in biomolecules. © 2015 Wiley Periodicals, Inc.     

Quasiharmonic treatment of infrared and raman vibrational frequency shifts induced by tensile deformation of polymer chains. II. Application to the polyoxymethylene and isotactic polypropylene single chains and the three-dimensional orthorhombic polyethylene crystal

Quasiharmonic equations are derived for stress-induced vibrational frequency shifts in the infrared and Raman spectra of polymer chains subjected to a tensile stress. The expressions are applied to the helical chains of polyoxymethylene and isotactic polypropylene. Observed frequency shifts can be reproduced well by using reasonable anharmonic force constants. A semiquantitative interpretation is given for the close relationship between stress-induced vibrational frequency shifts and the deformation mechanism of the polymer chains. Stress-induced frequency shifts are also calculated for an orthorhombic polyethylene crystal subjected to uniaxial tension along the chain axis or to hydrostatic pressure. The results consistently and reasonably reproduce observed data, not only for the intramolecular vibrational modes but also for the external lattice modes. © 1992 John Wiley & Sons, Inc.     

Molecular dynamics calculation to clarify the relationship between structure and mechanical properties of polymer crystals: the case of orthorhombic polyethylene

The molecular dynamics (MD) technique was used to calculate the temperature dependence of the structure, molecular motion, and mechanical property of the orthorhombic polyethylene (PE) crystal. The potential functional parameters reported by Karasawa et al. (J Phys Chem, 95 (1991) 2260) were refined further so that the vibrational frequencies of infrared and Raman bands, measured by us at ultra-low temperatures for the normal and fully deuterated PE, could be reproduced well. The flip-flop motion around the chain axis and the torsional motion of the skeletal chains were found to start above ca. 350 K and increase the amplitude of these motions progressively. Coupling these two types of chain motion resulted in a steep increase of the thermal vibration parameters or the mean-square-displacements of carbon and hydrogen atoms, corresponding well with the X-ray data. The lattice constants and the related linear thermal expansion coefficients were also found to be in good agreement with the observed data. The calculated Young's modulus along the chain axis decreased gradually with the increasing temperature: 330 GPa at 0 K to 280 GPa at room temperature. The latter was in good agreement with the value of 280–305 GPa evaluated from the Raman measurement of the longitudinal acoustic mode. Young's modulus was found to relate intimately with the chain contraction caused by the skeletal torsional motion. Only 0.3% contraction of the chain resulted in the reduction of the modulus by ca. 35%. A similar behavior was also seen in the trigonal polyoxymethylene and nylon 6 α forms.     

Multiscale coarse-graining of monosaccharides

A systematic multiscale coarse-graining (MS-CG) algorithm is applied to build coarse-grained models for monosaccharides in aqueous solution. The methodology is demonstrated for the example of alpha-D-glucopyranose. The nonbonded interactions are directly derived from the force-matching approach, whereas the bonded interactions are obtained through Boltzmann statistical analyses of the underlying atomistic trajectory. The MS-CG model is shown to reproduce many structural and thermodynamic properties in the constant NPT ensemble. Although the model is derived at a single temperature, pressure, and concentration, it is shown to be reasonably transferable to other thermodynamic states. In this model, long-range interactions are effectively mapped into short-range forces with a moderate cutoff and are evaluated by table look-up. As a result, molecular dynamics employing the MS-CG model is approximately 3 orders of magnitude more efficient than its atomistic counterpart. Consequently, the model is particularly suitable for simulating carbohydrate systems at large length and long time scales. Results for an alpha-(1-->4)-d-glucan with 14 glucose units are also presented, demonstrating that the MS-CG algorithm is also applicable to the coarse-graining of other saccharide systems.     

Pressure and temperature effects on the vibrational frequencies of crystalline polymethylenes. I. Infrared-active rocking modes

The energy level dispersion, along the chain wave vector, of infrared-active methylene rocking modes has been measured as a function of pressure to 40 kbar for a number of polymethylenes. They are crystalline polyethylene and n-paraffins C₂₃H₄₈, C₂₄H₅₀, C₂₈H₅₈, and C₂₉H₆₀. The crystalline factor-group splitting of each chain mode is observed at various pressures, for those polymethylenes which have orthorhombic or monoclinic structures. The effects of crystal structure, intermolecular force field and intramolecular force field on the observed energy levels as well as on the crystalline factor-group splittings are discussed A hydrogen–hydrogen nonbonded repulsion potential has been calculated as a function of interatomic distance r_H??H for 2.3 Å < r_H??H < 3.0 Å from the observed volume dependence of the factor-group splittings of methylene rocking modes. It is shown that the dynamic potential wells along the normal coordinates of the rocking modes are harmonic up to room temperature.     

磷脂微滴囊泡化的介观模拟

发展了一种非显示溶剂的粗粒化三粒子磷脂模型,该模型明确反映磷脂分子的双尾结构．模型分别采用变形的MIE作用势和Harmonic作用势描述分子间非成键和分子内成键相互作用,粗粒化力场参数通过拟合DPPC双分子层的结构和力学性质获得．该粗粒化模型成功重现了磷脂分子从随机初始态到双分子层和从盘状结构到囊泡的形成过程．应用该模型系统研究了球形和柱形磷脂微滴囊泡化的过程,结果表明此模型能有效地模拟介观尺度下复杂磷脂囊泡的形成及演化．     

Development of force field parameters for molecular simulation of polylactide

Polylactide is a biodegradable polymer that is widely used for biomedical applications, and it is a replacement for some petroleum based polymers in applications that range from packaging to carpeting. Efforts to characterize and further enhance polylactide based systems using molecular simulations have to this point been hindered by the lack of accurate atomistic models for the polymer. Thus, we present force field parameters specifically suited for molecular modeling of PLA. The model, which we refer to as PLAFF3, is based on a combination of the OPLS and CHARMM force fields, with modifications to bonded and nonbonded parameters. Dihedral angle parameters were adjusted to reproduce DFT data using newly developed CMAP dihedral cross terms, and the model was further adjusted to reproduce experimentally resolved crystal structure conformations, melt density, volume expansivity, and the glass transition temperature of PLA. We recommend the use of PLAFF3 in modeling PLA in its crystalline or amorphous states and have provided the necessary input files required for the publicly available molecular dynamics code GROMACS.     

Modeling the structure of amorphous MoS3: a neutron diffraction and reverse Monte Carlo study

A model for the structure of amorphous molybdenum trisulfide, a-MoS3, has been created using reverse Monte Carlo methods. This model, which consists of chains of MoS6 units sharing three sulfurs with each of its two neighbors and forming alternate long, nonbonded, and short, bonded, Mo-Mo separations, is a good fit to the neutron diffraction data and is chemically and physically realistic. The paper identifies the limitations of previous models based on Mo3 triangular clusters in accounting for the available experimental data.     

Simulation of Polymer Melts: From Spherical to Ellipsoidal Beads

In a previous work^[1] we presented a coarse‐graining procedure for bonded interactions, while spherical, purely repulsive 6–12 interactions were used to account for the excluded‐volume of the beads of the phantom chains. Here we extend this approach towards ellipsoidal beads whose shapes are extracted from the geometry of the underlying atomistic chains. The influence of the bead shapes on the static and dynamical properties of melts are studied in detail for two modifications of polycarbonates, from 2mers up to 20mers. The results obtained in both cases are discussed in the context of corresponding experiments and atomistic simulations.     

A new force field (ECEPP-05) for peptides, proteins, and organic molecules

Parametrization and testing of a new all-atom force field for organic molecules and peptides with fixed bond lengths and bond angles are described. The van der Waals parameters for both the organic molecules and the peptides were taken from J. Phys. Chem. B 2003, 107, 7143 and J. Phys. Chem. B 2004, 108, 12181. First, the values of the 1-4 nonbonded and electrostatic scale factors appropriate to the new force field were determined by computing the conformational energies of six model molecules, namely, ethanol, ethylamine, propanol, propylamine, 1,2-ethanediol, and 1,3-propanediol with different values of these factors. The partial atomic charges of these molecules were obtained by fitting to the electrostatic potentials calculated with the HF/6-31G quantum-mechanical method. Two different charge models (single- and multiple-conformation-derived) were also considered. We demonstrated that the charge model has a stronger effect on the conformational energies than the 1-4 scaling. The choice of a charge model affected the conformational energies of even the smallest molecules considered, whereas the effect of the 1-4 electrostatic or nonbonded scaling was apparent only for 1,3-propanediol. The best agreement with high-level ab initio data was obtained with the multiple-conformation-derived charges and with no scaling of the 1-4 nonbonded or electrostatic interactions (scale factors of 1.0). Next, the torsional parameters of a large number of neutral and charged organic molecules, assumed to be models of the side chains of the 20 naturally occurring amino acids, were computed by fitting to rotational energy profiles obtained from ab initio MP2/6-31G calculations. The quality of the fits was high with average errors for torsional profiles of less than 0.2 kcal/mol. To derive the torsional parameters for the peptide backbone, the partial atomic charges of the 20 neutral and charged amino acids were obtained by fitting to the electrostatic potentials of terminally blocked amino acids using the HF/6-31G quantum-mechanical method. Then, the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe were computed using MP2/6-31G//HF/6-31G quantum-mechanical methods. The phi-psi energy map of Ac-Ala-NMe was used for refinement of the nonbonded parameters for the backbone nitrogen and hydrogen bonded to it. Subsequently, the main-chain torsional parameters were obtained by fitting the molecular mechanics energies to the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe. The transferability of the entire force field was demonstrated by reproducing the main energy minima of terminally blocked Ala3 from the literature. The performance of the force field was also evaluated by simulating crystal structures of small peptides. By comparison of simulated and experimental data, examination of the torsional-angle and atom-positional root-mean-square deviations of the energy-minimized crystal structures from the corresponding X-ray model structures demonstrated high accuracy of the force field.     

Ab initio calculation of polyethylene deformation including electron correlation effects

The longitudinal acoustic elastic modulus of polyethylene has been calculated with the aid of the ab initio crystal orbital method applying corrections also for electronic correlation effects. The basis set and correlation dependence of the elastic modulus have been investigated. The best theoretical value of 305 GPa of this modulus is in reasonable agreement with the published experimental values. At an elongation of ca. 0.1 the deviation from Hooke's law is found to be substantial.     

Structure and mechanical properties of poly(L‐lactic acid) crystals and fibers

The elastic constants of poly(L ‐lactic acid) (PLLA) crystals are reported on the basis of a commercial software package and the published crystal structure of the α form. A chain modulus of 36 GPa and a shear modulus of 3 GPa have been obtained for cylindrically symmetric aggregates of perfectly oriented crystals. The helical conformation of the PLLA molecule reduces the stiffness in the chain axis direction because bond rotation plays a significant role in the deformation. X‐ray crystal strain measurements suggest that shear of the α crystal parallel to the helix axis is the easiest mode of deformation, in agreement with the expectations obtained from the low shear modulus of 3 GPa obtained from the theoretical calculations. A combination of small‐ and wide‐angle X‐ray scattering, differential scanning calorimetry, dynamic mechanical thermal analysis, and shrinkage measurements has been used to characterize the structure that develops and the crystal transformation that occurs during fiber processing. The structure that develops during processing very much depends on the crystal transformation, and a structural model is proposed for fibers at different degrees of plastic deformation. The transformation of the α crystal into the β form and vice versa is governed primarily by shear along the helix axis because the chains must shear past each other during the crystal transformation, disrupting the lamellar packing. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 892–902, 2007     

Conformational and energetic effects of truncating nonbonded interactions in an aqueous protein dynamics simulation

In a previous aqueous protein dynamics study, we compared the rms deviation relative to the crystal structure for distance-dependent and constant dielectric models with and without a nonbonded cutoff. The structures obtained from a constant dielectric simulation with a cutoff were substantially different from the structures obtained from a distance-dependent dielectric simulation, with and without cutoff, and a constant dielectric model without a cutoff. In fact, structures from the distance-dependent dielectric simulations were insensitive to the nonbonded cutoff and in good agreement with the structures generated from the constant dielectric simulation without a cutoff. In addition, the solute-solvent temperature differential and solvent evaporation artifacts, characteristic of the constant dielectric simulation with a cutoff, were not present for the distance-dependent dielectric simulations. In this current work, we explore whether this dielectric-dependent cutoff-sensitive behavior for a constant dielectric model arises from the discontinuities in the forces at the nonbonded cutoff or from neglecting the structure-stabilizing interactions beyond the nonbonded cutoff. We also examine the origin of the dielectric-dependent artifacts, and its potential influence on the structural disparity. Several protocols for protein dynamics simulations are compared using both constant and distance-dependent dielectric models, including implementation of a switching function and a nonbonded cutoff and two different temperature coupling algorithms. We show that the distance-dependent dielectric model conserves energy in the SPASMS molecular mechanics and dynamics software for the time steps and nonbonded cutoffs commonly used in macromolecule simulations. Although the switching function simulation also conserved energy over a range of commonly used cutoffs, the constant dielectric model with a switching function yielded conformational results more similar to a constant dielectric simulation without a switching function than to a constant dielectric model without a nonbonded cutoff. Therefore, the conformational disparity between the dielectric models arises from neglecting important structure-stabilizing interactions beyond the cutoff, rather than differences in energy conservation. © 1993 John Wiley & Sons, Inc.     

Effective force field for liquid hydrogen fluoride from ab initio molecular dynamics simulation using the force-matching method

A recently developed force-matching method for obtaining effective force fields for condensed matter systems from ab initio molecular dynamics (MD) simulations has been applied to fit a simple nonpolarizable two-site pairwise force field for liquid hydrogen fluoride. The ab initio MD in this case was a Car-Parrinello (CP) MD simulation of 64 HF molecules at nearly ambient conditions within the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure included a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The performance of the force-match potential was examined for the gas-phase dimer and for the liquid phase at various temperatures. The model was able to reproduce correctly the bent structure and energetics of the gas-phase dimer, while the results for the structural properties, self-diffusion, vibrational spectra, density, and thermodynamic properties of liquid HF were compared to both experiment and the CP MD simulation. The force-matching model performs well in reproducing nearly all of the liquid properties as well as the aggregation behavior at different temperatures. The model is computationally cheap and compares favorably to many more computationally expensive potential energy functions for liquid HF.