Relation between Energy Contribution to Elastic Force and Strain Dependence of Modulus for Polybutadiene Vulcanizates

It is well known that the modulus G = r/(λ - λ^?2) varies with deformation, thus deviating from the predictions of statistical theories of rubber elasticity which require it to be constant. It has also been found that there is a nonnegligible energy contribution to the elastic force. It is postulated that these two phenomena are related because both arise from energetic interaction between chains.

Based on the lateral order of chains indicated by x-ray fiber diagrams of elongated noncrystallizable elastomers, it is suggested that energetic interaction of chains is induced by strain orientation. Proportionality between these two is assumed. The orientation distribution functions of end-to-end vectors and of statistical chain segments are considered. The proportionality constants are determined from the energy contribution to the strain dependence of the coefficient of thermal expansion. With the aid of these constants the modulus, corrected for energy contribution, is calculated. The observed and calculated elongation dependence of G agree reasonably well.

It is concluded that an energy interaction between aligned chains can account for the deviation of the observed stress elongation relation from the predictions of entropy elasticity theories.     

Elastic properties of the (001) face of xenon crystals

In this work we investigated the elastic properties of the (001) face of xenon crystal. The slabs (twodimensional crystals) defined by (001) planes are generated, their structures are optimized and the slabs thermodynamic functions in excess to the crystal bulk calculated. The calculations are based on the Lennard-Jones 6?12 force field, classical elasticity theory and surface thermodynamics. In this work, the number of planes undergoing relaxation is not a priori constrained but it follows from the minimization of the free energy of the slabs and of the bulk, in respect to atomic positions. The value of the surface free energy is calculated as a function of the homogeneous strain of the 2D (001) cell measured relatively to the cell of the stable 3D crystal. At 0 K, when strain is not applied, the specific surface free energy is about 0.064 Jm^-2 and decreases by about 6% at 50 K. The surface stress is positive amounting to 0.010 Jm^-2 at 0 K, and it decreases by about 50% at 50 K. We find that the surface stress can be released by a reorganization of the interatomic distances at the crystal surfaces. The surface excess mean value of the slab elastic constants at 0 K is small (0.012 GPa) and it decreases by about 35% at 50 K. The method proposed can be alternative to molecular dynamics simulations in order to assess the excess surface properties of materials having a complex structure.     

高分子熔体和浓溶液流变性能的研究

基于多重缠结网络结构模型和高分子链上缠结点在流动中可进行动态解缠和再缠结的多重蠕动机理,用统计力学和动力学相结合的方法,分别计算出了缠结链组的末端距分布函数;处于缠结状态下高分子链构象统计分布函数;受力下聚合物熔体粘弹性形变自由能和解除外力下高分子挤出体可回复性粘弹性形变自由能,提出了高分子挤出体可回复形变的粘弹性分子理论。推导出的高分子熔体的回忆函数、简单剪切流下的本构方程和物料函数,并采用一种新的方法测定出物料的四种参数： η0、 GN0、 n′和 a。对于高分子挤出体,可回复性粘弹性形变由快速弹性形变和慢速粘弹性形变两者组成,当把两种形变量的复合结构参数－分子链的反式构象分数引入两种形变自由能表达式后,就从理论上得到了可回复形变量同挤出胀大比间的定量表达式,从而建立起一个具有分子链结构参数的新的挤出胀大比方程,可回复形变量同挤出条件（温度、挤出速率和量以及口模长径比不同的挤出机）和树脂结构特征（分子量及分布）的关系式以及在特殊情形下的简化表达式,并用几种高分子熔融体系的挤出胀大比和可回复性形变量的实验数据对理论进行验证,理论方程同实验数据较好的符合。     

Computer simulation study of a nematogenic lattice model based on an elastic energy mapping of the pair potential

Director configurations in a nematic liquid crystal can be determined by minimizing its total elastic free energy, for given elastic constants and specific boundary conditions. In some cases, these configurations have been obtained by numerical procedures where the elastic free energy density plays the same role as the overall potential energy in a standard Metropolis Monte Carlo simulation. The interaction energies or potentials used in these studies are short ranged but, in general, not pairwise additive, unless the three elastic constants are set to a common value, thus reducing the potential to that in the well-known Lebwohl-Lasher lattice model. On the other hand, we can construct, in different ways, a lattice model with pairwise additive interactions, which approximately reproduces the elastic free energy density, where the parameters defining the pair potential are expressed as linear combinations of elastic constants. An anisotropic nematogenic pair interaction of this kind, originally proposed by Gruhn and Hess (T. Gruhn and S. Hess, Z. Naturforsch. A51, 1 (1996)), has recently been investigated by one of us, using a Monte Carlo simulation (S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998)). Here we propose another approximate procedure for the mapping, and study the resulting pair potential model with the aid of Monte Carlo simulations. The behaviour of the nematic phases formed by the two models is compared together with the predictions of molecular field theory and the properties of the Lebwohl-Lasher model.     

New potential-energy functions for Cu, Ag and Au solids and their applications to computer simulations on metallic surfaces

Ｓｕｒｆａｃｅｓｉｍｕｌａｔｉｏｎｃｏｎｔｉｎｕｅｓｔｏｂｅｏｎｅｏｆｔｈｅｍａｉｎｔｏｐｉｃｓｏｆｃｕｒｒｅｎｔｉｎｔｅｒｅｓｔ,ａｎｄｎｏｂｌｅｍｅｔａｌｓｈａｖｅｂｅｅｎｔｈｅｓｕｂｊｅｃｔｏｆｅｘｔｅｎｓｉｖｅｅｘｐｅｒｉｍｅｎｔｓａｎｄｔｈｅｏｒｅｔｉｃａｌｉｎｖｅｓｔｉｇａｔｉｏｎｓｆｏｒｍａｎｙｙｅａｒｓ.Ｉｔｈａｓｂｅｅｎｋｎｏｗｎｗｅｌｌｔｈａｔｍｅｔａｌｓｕｒｆａｃｅｓｕｓｕａｌｌｙｄｉｆｆｅｒｆｒｏｍｔｈｅｅｘｔｅｎｄｅｄｓｏｌｉｄｓｉｎｔｈｅｉｒｓｔｒｕｃｔｕｒｅｐａｒａｍ…     

Exact on-event expressions for discrete potential systems

The properties of systems composed of atoms interacting though discrete potentials are dictated by a series of events which occur between pairs of atoms. There are only four basic event types for pairwise discrete potentials and the square-well/shoulder systems studied here exhibit them all. Closed analytical expressions are derived for the on-event kinetic energy distribution functions for an atom, which are distinct from the Maxwell-Boltzmann distribution function. Exact expressions are derived that directly relate the pressure and temperature of equilibrium discrete potential systems to the rates of each type of event. The pressure can be determined from knowledge of only the rate of core and bounce events. The temperature is given by the ratio of the number of bounce events to the number of disassociation/association events. All these expressions are validated with event-driven molecular dynamics simulations and agree with the data within the statistical precision of the simulations.     

Stress and heat flux for arbitrary multibody potentials: a unified framework

A two-step unified framework for the evaluation of continuum field expressions from molecular simulations for arbitrary interatomic potentials is presented. First, pointwise continuum fields are obtained using a generalization of the Irving-Kirkwood procedure to arbitrary multibody potentials. Two ambiguities associated with the original Irving-Kirkwood procedure (which was limited to pair potential interactions) are addressed in its generalization. The first ambiguity is due to the nonuniqueness of the decomposition of the force on an atom as a sum of central forces, which is a result of the nonuniqueness of the potential energy representation in terms of distances between the particles. This is in turn related to the shape space of the system. The second ambiguity is due to the nonuniqueness of the energy decomposition between particles. The latter can be completely avoided through an alternate derivation for the energy balance. It is found that the expressions for the specific internal energy and the heat flux obtained through the alternate derivation are quite different from the original Irving-Kirkwood procedure and appear to be more physically reasonable. Next, in the second step of the unified framework, spatial averaging is applied to the pointwise field to obtain the corresponding macroscopic quantities. These lead to expressions suitable for computation in molecular dynamics simulations. It is shown that the important commonly-used microscopic definitions for the stress tensor and heat flux vector are recovered in this process as special cases (generalized to arbitrary multibody potentials). Several numerical experiments are conducted to compare the new expression for the specific internal energy with the original one.     

Pressure calculation in hybrid particle-field simulations

In the framework of a recently developed scheme for a hybrid particle-field simulation techniques where self-consistent field (SCF) theory and particle models (molecular dynamics) are combined [J. Chem. Phys. 130, 214106 (2009)], we developed a general formulation for the calculation of instantaneous pressure and stress tensor. The expressions have been derived from statistical mechanical definition of the pressure starting from the expression for the free energy functional in the SCF theory. An implementation of the derived formulation suitable for hybrid particle-field molecular dynamics-self-consistent field simulations is described. A series of test simulations on model systems are reported comparing the calculated pressure with those obtained from standard molecular dynamics simulations based on pair potentials.     

An analytical bond‐order potential for carbon

Carbon is the most widely studied material today because it exhibits special properties not seen in any other materials when in nano dimensions such as nanotube and graphene. Reduction of material defects created during synthesis has become critical to realize the full potential of carbon structures. Molecular dynamics (MD) simulations, in principle, allow defect formation mechanisms to be studied with high fidelity, and can, therefore, help guide experiments for defect reduction. Such MD simulations must satisfy a set of stringent requirements. First, they must employ an interatomic potential formalism that is transferable to a variety of carbon structures. Second, the potential needs to be appropriately parameterized to capture the property trends of important carbon structures, in particular, diamond, graphite, graphene, and nanotubes. Most importantly, the potential must predict the crystalline growth of the correct phases during direct MD simulations of synthesis to achieve a predictive simulation of defect formation. Because an unlimited number of structures not included in the potential parameterization are encountered, the literature carbon potentials are often not sufficient for growth simulations. We have developed an analytical bond order potential for carbon, and have made it available through the public MD simulation package LAMMPS. We demonstrate that our potential reasonably captures the property trends of important carbon phases. Stringent MD simulations convincingly show that our potential accounts not only for the crystalline growth of graphene, graphite, and carbon nanotubes but also for the transformation of graphite to diamond at high pressure. © 2015 Wiley Periodicals, Inc.     

Monte Carlo simulations of fluids whose particles interact with a logarithmic potential

Monte Carlo simulations of a model fluid in which the particles interact via a continuous potential that has a logarithmic divergence at a pair separation of sigma, which we introduced in J. G. Powles et al., Proc. R. Soc. London, Ser. A 455, 3725 (1999), have been carried out. The potential has the form, phi(r)= -epsilon ln(fr), where epsilon sets the energy scale and fr=1-(sigma/r)m. The value of m chosen was 12 but the qualitative trends depend only weakly on the value of m, providing it is greater than 3. The potential is entirely repulsive and has a logarithmic divergence as approximately -ln(r/sigma-1) in the r-->sigma limit. Predictions of the previous paper that the internal energy can be computed at all temperatures using the standard statistical mechanics formula for continuous potentials are verified here. The pressure can be calculated using the usual virial expression for continuous potentials, although there are practical limitations in resolving the increasingly important contribution from the r-->sigma limit at reduced temperatures greater than approximately 5. The mean square force F2 and infinite frequency shear Ginfinity and bulk Kinfinity moduli are only finite for T*=kBT/epsilon<1. The logarithmic fluid's physical properties become increasingly more like that of the hard sphere fluid with increasing temperature, showing a sharp transition in the behavior of the mean square force and infinite frequency elastic constants at T*=1. The logarithmic fluid is shown to exhibit a solid-fluid phase transition.     

Gradients of the polarization energy in the effective fragment potential method

The effective fragment potential (EFP) method is an ab initio based polarizable classical method in which the intermolecular interaction parameters are obtained from preparative ab initio calculations on isolated molecules. The polarization energy in the EFP method is modeled with asymmetric anisotropic dipole polarizability tensors located at the centroids of localized bond and lone pair orbitals of the molecules. Analytic expressions for the translational and rotational gradients (forces and torques) of the EFP polarization energy have been derived and implemented. Periodic boundary conditions (the minimum image convention) and switching functions have also been implemented for the polarization energy, as well as for other EFP interaction terms. With these improvements, molecular dynamics simulations can be performed with the EFP method for various chemical systems.     

The elastic constants of solid Ar

An interatomic potential for Ar₂ derived from high resolution elastic differential scattering cross sections, second virial coefficients and vibrational level spacings, by Parson et al. is used to calculate, by Monte Carlo methods, the elastic constants of solid Ar at 80°K and near zero pressure. The calculated solid state properties are compared with those of two other recently proposed Ar₂ potentials. Comparison with experiments confirm the presence of many body forces in the solid. Moreover, these appear to be almost quantitatively accounted for by the three body triple-dipole force.     

Transferable pair potentials for CdS and ZnS crystals

A set of interatomic pair potentials is developed for CdS and ZnS crystals. We show that a simple energy function, which has been used to describe the properties of CdSe [E. Rabani, J. Chem. Phys. 116, 258 (2002)], can be parametrized to accurately describe the lattice and elastic constants, and phonon dispersion relations of bulk CdS and ZnS in the wurtzite and rocksalt crystal structures. The predicted coexistence pressure of the wurtzite and rocksalt structures as well as the equation of state are in good agreement with experimental observations. These new pair potentials enable the study of a wide range of processes in bulk and nanocrystalline II-VI semiconductor materials.     

On fitting a gold embedded atom method potential using the force matching method

We fit a new gold embedded atom method (EAM) potential using an improved force matching methodology which included fitting to high-temperature solid lattice constants and liquid densities. The new potential shows a good overall improvement in agreement to the experimental lattice constants, elastic constants, stacking fault energy, radial distribution function, and fcc/hcp/bcc lattice energy differences over previous potentials by Foiles, Baskes, and Daw (FBD) [Phys. Rev. B 33, 7983 (1986)] Johnson [Phys. Rev. B 37, 3924 (1988)], and the glue model potential by Ercolessi et al. [Philos. Mag. A 50, 213 (1988)]. Surface energy was improved slightly as compared to potentials by FBD and Johnson but as a result vacancy formation energy is slightly inferior as compared to the same potentials. The results obtained here for gold suggest for other metal species that further overall improvements in potentials may still be possible within the EAM framework with an improved fitting methodology. On the other hand, we also explore the limitations of the EAM framework by attempting a brute force fit to all properties exactly which was found to be unsuccessful. The main conflict in such a brute force fit was between the surface energy and the liquid lattice constant where both could not be fitted identically. By intentionally using a very large number of spline sections for the pair potential, electron-density function, and embedding energy function, we eliminated a lack of functional freedom as a possible cause of this conflict and hence can conclude that it must result from a fundamental limitation in the EAM framework.     

Solubility of methane in water: the significance of the methane-water interaction potential

The influence of the methane-water interaction potential on the value of the Henry constant obtained from molecular dynamics simulations was investigated. The SPC, SPC/E, MSPC/E, and TIP3P potentials were used to describe water and the OPLS-UA and TraPPE potentials for methane. Nonbonding interactions between unlike atoms were calculated both with one of four mixing rules and with our new methane-water interaction potential. The Henry constants obtained from simulations using any of the mixing rules differed significantly from the experimental ones. Good agreement between simulation and experiment was achieved with the new potential over the whole temperature range.     

Study on Non-Newtonian Behaviors of Lennard-Jones Fluids via Molecular Dynamics Simulations

Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rheological behaviors of a monoatomic fluid governed by the Lennard-Jones potential. Both steady Couette and oscillatory shear flows are investigated. Shear thinning and normal stress effects are observed in the steady Couette flow simulations. The radial distribution function is calculated at different shear rates to exhibit the change of the microscopic structure of molecules due to shear. We observe that for a larger shear rate the repulsion between molecules is more powerful while the attraction is weaker, and the above phenomena can also be confirmed by the analyses of the potential energy. By applying an oscillatory shear to the system, several findings are worth mentioning here:First, the phase difference between the shear stress and shear rate increases with the frequency. Second, the real part of complex viscosity first increases and then decreases while the imaginary part tends to increase monotonically, which results in the increase of the proportion of the imaginary part to the real part with the increasing frequency. Third, the ratio of the elastic modulus to the viscous modulus also increases with the frequency. These phenomena all indicate the appearance of viscoelasticity and the domination of elasticity over viscosity at high oscillation frequency for Lennard-Jones fluids.     

ANiN(A=Li,Na,Mg,Ca)的结构、热力学、弹性和电子性质的第一性原理研究

三元过渡金属氮化物ANiN(A=Li,Na,Mg,Ca)是潜在的可充放电池的电极材料.物理性质,比如热稳定性、电子能隙以及弹性稳定性等,对于这些材料的电池应用都是非常重要的.本文使用第一原理方法,对比研究了 ANiN这些材料的结构、动力学、弹性和电子结构性质.对状态方程和声子谱的计算被用来确定体系的稳定结构.对最稳定结...     

平板型高电位胶粒双电层的相互作用

利用线性迭加法,提出了平行平板型高电位颗粒之间的弱相互作用的近似表达式.结合文献[3]给出的强相互作用表达式,对高电位平行平板型颗粒的相互作用给出了完整的描述,和精确数值解吻合相当好.强弱相互作用的接合点在κh=4,误差在接合点处最大,～10％.根据Derjaguin法和改进的Derjaguin法,求出了高电位球颗粒在恒电位条件下的相互作用能.     

Interaction of elastic bodies via surface forces. 2. Exponential decay

Our goal is to study theoretically the effect of deformation on the exponentially decaying interaction of two elastic solids separated by a thin liquid film. The deformed shape of the surfaces and the contribution of the elasticity to the total force, i.e., an additional term present between elastic bodies, are calculated from continuum elastic theory via a new asymptotic technique. Both the deformation and the contribution of the elasticity to the force are found to be significant on the length scale over which the surface force acts. The surface deformation is exponentially decaying with a decay length equal to that of the original surface interaction. It is especially important for large and/or rapidly changing force. The contribution of the elasticity is also exponentially decaying, but with half the decay length. Its strength depends on the elastic constants and size of the solids and on the magnitude and gradient of the original surface force. Depending on how the separation is detected, it can appear either as an attractive or as a repulsive contribution to the force. Our results open the possibility of recalculating the measured force to the interaction free energy.     

Simulation of tunneling in enzyme catalysis by combining a biased propagation approach and the quantum classical path method: application to lipoxygenase

The ability of using wave function propagation approaches to simulate isotope effects in enzymes is explored, focusing on the large H/D kinetic isotope effect of soybean lipoxygenase-1 (SLO-1). The H/D kinetic isotope effect (KIE) is calculated as the ratio of the rate constants for hydrogen and deuterium transfer. The rate constants are calculated from the time course of the H and D nuclear wave functions. The propagations are done using one-dimensional proton potentials generated as sections from the full multidimensional surface of the reacting system in the protein. The sections are obtained during a classical empirical valence bond (EVB) molecular dynamics simulation of SLO-1. Since the propagations require an extremely long time for treating realistic activation barriers, it is essential to use an effective biasing approach. Thus, we develop here an approach that uses the classical quantum path (QCP) method to evaluate the quantum free energy change associated with the biasing potential. This approach provides an interesting alternative to full QCP simulations and to other current approaches for simulating isotope effects in proteins. In particular, this approach can be used to evaluate the quantum mechanical transmission factor or other dynamical effects, while still obtaining reliable quantized activation free energies due to the QCP correction.