Transient ordering in a quasi-two-dimensional liquid near freezing

We report the results of a theoretical study of locally ordered fluctuations in a quasi-two-dimensional colloid fluid. The fluctuations in the equilibrium state are monitored by the aperture cross-correlation function of radiation scattered by the fluid, as calculated from molecular dynamics simulations of near hard spheres with diameter sigma confined between smooth hard walls. These locally ordered fluctuations are transient; their decay can be monitored as a function of the time between the cross-correlated scattered radiation signals, but only the single-time cross-correlated signals are discussed in this paper. Systems with thicknesses less than two hard sphere diameters were studied. For wall separation H in the range 1 sigma/=1.57 sigma, hexagonal fluctuations persist in the dense liquid up to H=1.75 sigma, and fluctuations with square ordered symmetry, that of the solid to which the liquid freezes, only emerge at densities approximately 2% below freezing. For H=1.8 sigma and 1.85 sigma, hexagonal ordered flucuations are no longer found, and the square ordered fluctuations dominate the dense liquid region as the system freezes into a two layer square solid. For H=1.9 sigma and 1.95 sigma, where the liquid freezes into a two layer hexagonal solid, both square and hexagonal ordered fluctuations are observed. At lower densities, the ordered fluctuations only exhibit square symmetry. Hexagonal ordered fluctuations appear at densities approximately 7% below freezing and become more dominant as the density is increased, but the square ordered fluctuations persist until the system is converted into the solid.     

Accurate freezing and melting equations for the Lennard-Jones system

Analyzing three approximate methods to locate liquid-solid coexistence in simple systems, an observation is made that all of them predict the same functional dependence of the temperature on density at freezing and melting of the conventional Lennard-Jones (LJ) system. The emerging equations can be written as T=Aρ(4)+Bρ(2) in normalized units. We suggest to determine the values of the coefficients A at freezing and melting from the high-temperature limit, governed by the inverse 12th power repulsive potential. The coefficients B can be determined from the triple point parameters of the LJ fluid. This produces freezing and melting equations which are exact in the high-temperature limit and at the triple point and show remarkably good agreement with numerical simulation data in the intermediate region.     

An accurate expression for radial distribution function of the Lennard-Jones fluid

A simple and accurate expression for radial distribution function (RDF) of the Lennard-Jones fluid is presented. The expression explicitly states the RDF as a continuous function of reduced interparticle distance, temperature, and density. It satisfies the limiting conditions of zero density and infinite distance imposed by statistical thermodynamics. The distance dependence of this expression is expressed by an equation which contains 11 adjustable parameters. These parameters are fitted to 353 RDF data, obtained by molecular dynamics calculations, and then expressed as functions of reduced distance, temperature and density. This expression, having a total of 65 constants, reproduces the RDF data with an average root-mean-squared deviation of 0.0152 for the range of state variables of 0.5  T^*  5.1 and 0.35  ρ^*  1.1 (T^*=kT/ε and ρ^* = ρσ³ are reduced temperature and density, respectively). The expression predicts the pressure and the internal energy of the Lennard-Jones fluid with an uncertainty that is comparable to that obtained directly from the molecular dynamics simulations.     

Application of the extended RSA models in studies of particle deposition at partially covered surfaces

This paper reviews the application of the extended random sequential adsorption (RSA) approaches to the modeling of colloid-particle deposition (irreversible adsorption) on surfaces precovered with smaller particles. Hard (noninteracting) particle systems are discussed first. We report on the numerical simulations we performed to determine the available surface function, jamming coverage, and pair-correlation function of the larger particles. We demonstrate the effect of the particle size ratio and the small particle surface coverage. We found that the numerical results were in reasonable agreement with the formula stemming from the scaled-particle theory in 2D with a modification for the sphere geometry. Next, we discuss three approximate models of adsorption allowing electrostatic interaction of colloid particles at a charged interface, employing a many-body superposition approximation. We describe two approaches of the effective hard-particle approximation next. We demonstrate the application of the effective hard-particle concept to the bimodal systems and present the effect of electrolyte concentration on the effective particle size ratio. We present the numerical results obtained from the theoretical models of soft-particle adsorption at precovered surfaces. We used the effective hard-particle approximation to determine the corresponding simpler systems of particles, namely the system of hard spheres and the system of hard discs at equilibrium. We performed numerical computations to determine the effective minimum particle surface-to-surface distance, available surface function, jamming coverage, and pair-correlation function of the larger particles at various electrolyte ionic strengths and particle size ratios. The numerical results obtained in the low-surface coverage limit were in good agreement with the formula stemming from the scaled-particle theory with a modification for the sphere geometry and electrostatic interaction. We compared the results of numerical computations of the effective minimum particle surface-to-surface distance obtained using the 2D, 3D, and curvilinear trajectory model. The results obtained with the 3D and curvilinear trajectory models indicate that large-particle/substrate attractive interaction significantly reduces the kinetic barrier to large, charged-particle adsorption at a surface precovered with small, like-charged particles. The available surface function and jamming-coverage values predicted using the simplified 3D and the more sophisticated curvilinear trajectory models are similar, while the results obtained with the 2D model differ significantly. The pair-correlation function suggests different structures of monolayers obtained with the three models. Unlike the three models of the electrostatic interaction, both effective hard-particle approximations give almost identical results. Results of this research clearly suggest that the extended RSA approaches can fruitfully be exploited for numerical simulations of colloid-particle adsorption at precovered surfaces, allowing the investigation of both hard and soft-particle systems.     

A classical polarizable model for simulations of water and ice

We develop a classical rigid polarizable model of water for molecular simulations of water and ice. The model uses the Rowlinson five-site geometry: oxygen bearing the Lennard-Jones interaction and linearly polarizable point dipole, two positively charged hydrogens, and two massless negative charges placed symmetrically off oxygen so that the experimental dipole moment is reproduced. The target properties are the densities of water and ice Ih, diffusivity, enthalpies of fusion and vaporization, and the ice Ih melting point. The surface tension at lower temperatures is by 7% underestimated whereas the dielectric constant by 6% overestimated. Diffusivity and viscosity worsen at higher temperatures, although the Stokes radius is overestimated only by 2-7%. The ice Ih melting temperature is 260 K and the temperature of maximum density is 269 K. Rescaling the charges by a factor of 1.01 and Lennard-Jones energy by 1.0201 improves the melting point and energy-related quantities but shifts the agreement of kinetic properties to higher temperatures. For the model we propose abbreviation POL4D.     

Precise simulation of the freezing transition of supercritical Lennard-Jones

The fluid-solid transition of the Lennard-Jones model is analyzed along a supercritical isotherm. The analysis is implemented via a simulation method which is based on a modification of the constrained cell model of Hoover and Ree. In the context of hard-sphere freezing, Hoover and Ree simulated the solid phase using a constrained cell model in which each particle is confined within its own Wigner-Seitz cell. Hoover and Ree also proposed a modified cell model by considering the effect of an external field of variable strength. High-field values favor configurations with a single particle per Wigner-Seitz cell and thus stabilize the solid phase. In previous work, a simulation method for freezing transitions, based on constant-pressure simulations of the modified cell model, was developed and tested on a system of hard spheres. In the present work, this method is used to determine the freezing transition of a Lennard-Jones model system on a supercritical isotherm at a reduced temperature of 2. As in the case of hard spheres, constant-pressure simulations of the fully occupied constrained cell model of a system of Lennard-Jones particles indicate a point of mechanical instability at a density which is approximately 70% of the density at close packing. Furthermore, constant-pressure simulations of the modified cell model indicate that as the strength of the field is reduced, the transition from the solid to the fluid is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the Lennard-Jones system is obtained by analyzing the field-induced fluid-solid transition of the modified cell model in the high-pressure, zero-field limit. The simulations are implemented under constant pressure using tempering and histogram reweighting techniques. The coexistence pressure and densities are determined through finite-size scaling techniques for first-order phase transitions which are based on analyzing the size-dependent behavior of susceptibilities and dimensionless moment ratios of the order parameter.     

Modeling of 2‐D DNA display

2‐D display is a fast and economical way of visualizing polymorphism and comparing genomes, which is based on the separation of DNA fragments in two steps, first according to their size and then to their sequence composition. In this article, we present an exhaustive study of the numerical issues associated with a model aimed at predicting the final absolute locations of DNA fragments in 2‐D display experiments. We show that simple expressions for the mobility of DNA fragments in both dimensions allow one to reproduce experimental final absolute locations better than experimental uncertainties. However, our simulations also point out that the results of 2‐D display experiments are not sufficient to determine the best set of parameters for the modeling of fragments separation in the second dimension and that additional detailed measurements of the mobility of a few sequences are necessary to achieve this goal. We hope that this work will help in establishing simulations as a powerful tool to optimize experimental conditions without having to perform a large number of preliminary experiments and to estimate whether 2‐D DNA display is suited to identify a mutation or a genetic difference that is expected to exist between the genomes of closely related organisms.     

Determination of the solid-fluid coexistence of the n - 6 Lennard-Jones system from free energy calculations

The solid-fluid coexistence properties of the n - 6 Lennard-Jones system, n from 7 to 12, are reported. The procedure relies on determining Helmholtz free energy curves as a function of volume for each phase independently, from several NVT simulations, and then connecting it to points of known absolute free energy. For n = 12 this requires connecting the simulated points to states of very low densities on the liquid phase, and to a harmonic crystal for the solid phase, which involves many extra simulations for each temperature. For the reference points of the remaining systems, however, the free energy at a given density and temperature can be calculated relative to the n = 12 system. The method presented here involves a generalization of the multiple histogram method to combine simulations performed with different potentials, provided they visit overlapping regions of the phase space, and allows for a precise calculation of relative free energies. The densities, free energies, average potential energies, pressure, and chemical potential at coexistence are presented for up to T? = 5.0 and new estimations of the triple points are given for the n - 6 Lennard-Jones system.     

Phase diagram and universality of the Lennard-Jones gas-liquid system

The gas-liquid phase transition of the three-dimensional Lennard-Jones particles system is studied by molecular dynamics simulations. The gas and liquid densities in the coexisting state are determined with high accuracy. The critical point is determined by the block density analysis of the Binder parameter with the aid of the law of rectilinear diameter. From the critical behavior of the gas-liquid coexisting density, the critical exponent of the order parameter is estimated to be β = 0.3285(7). Surface tension is estimated from interface broadening behavior due to capillary waves. From the critical behavior of the surface tension, the critical exponent of the correlation length is estimated to be ν = 0.63(4). The obtained values of β and ν are consistent with those of the Ising universality class.     

离子液体[emim]Br熔点的分子动力学模拟

运用分子动力学模拟, 采用直接加热法和微正则(NVE)系综法计算离子液体[emim]Br的熔点, 以期获得较好的熔点预测方法. 直接加热法通过分析体系的非键合能、密度、径向分布函数、扩散系数和平动序参数随温度的变化关系判断熔点; NVE系综法则通过获得固液共存体系判断熔点. 直接加热法中, 体系易出现过热问题; NVE系综法则能有效克服过热问题, 是在模拟研究中应优先选择的离子液体熔点预测方法.     

Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. II. Simulation results and analyses

In the first paper of this series [S. Torquato, J. Chem. Phys. 136, 054106 (2012)], analytical results concerning the continuum percolation of overlapping hyperparticles in d-dimensional Euclidean space R(d) were obtained, including lower bounds on the percolation threshold. In the present investigation, we provide additional analytical results for certain cluster statistics, such as the concentration of k-mers and related quantities, and obtain an upper bound on the percolation threshold η(c). We utilize the tightest lower bound obtained in the first paper to formulate an efficient simulation method, called the rescaled-particle algorithm, to estimate continuum percolation properties across many space dimensions with heretofore unattained accuracy. This simulation procedure is applied to compute the threshold η(c) and associated mean number of overlaps per particle N(c) for both overlapping hyperspheres and oriented hypercubes for 3 ≤ d ≤ 11. These simulations results are compared to corresponding upper and lower bounds on these percolation properties. We find that the bounds converge to one another as the space dimension increases, but the lower bound provides an excellent estimate of η(c) and N(c), even for relatively low dimensions. We confirm a prediction of the first paper in this series that low-dimensional percolation properties encode high-dimensional information. We also show that the concentration of monomers dominate over concentration values for higher order clusters (dimers, trimers, etc.) as the space dimension becomes large. Finally, we provide accurate analytical estimates of the pair connectedness function and blocking function at their contact values for any d as a function of density.     

A 3D-analysis of cluster formation and dynamics of the X(-)-benzene (X = F, Cl, Br, I) ionic dimer solvated by Ar atoms

The specific influence of X(-) ions (X = F,Cl, Br, I) in the solvation process of halide-benzene (X(-)-Bz) ionic heterodimers by Ar atoms is investigated by means of molecular dynamic (MD) simulations. The gradual evolution from cluster rearrangement to solvation dynamics is discussed by considering ensembles of n (n = 1-15 and n = 30) Ar atoms around the X(-)-Bz stable ionic dimers. The potential energy surfaces employed are based on an atom/ion-atom and atom/ion-bond decomposition, which has been developed previously by some of the authors. The outcome of the dynamics is analyzed by employing radial distribution functions (RDF) and tridimensional (3D) probability densities.     

Attractive and repulsive interactions among methanol molecules in supercritical state investigated by Raman spectroscopy and perturbed hard-sphere theory

The short-range structure of supercritical methanol (CH(3)OH) is investigated by measuring the spontaneous Raman spectra of the C-O stretching mode. The spectra are obtained at a reduced temperature, T(r)=T/T(c)=1.02 (522.9 K), which permits the neat fluid to be studied isothermally as a function of density. As the density increases, the spectral peaks shift toward the lower energy side and the spectra broaden. In the supercritical region, the amount of shifting shows nonlinear density dependence and the width becomes anomalously large. We use the perturbed hard-sphere model to analyze these density dependencies along the vibrational coordinate. The amount of shifting is decomposed into attractive and repulsive components, and the changes in attractive and repulsive energies are evaluated as functions of density and packing fraction, both of which are continuously varied by a factor of 120. Here we show that the shift amount consists principally of the attractive component at all densities, since the attractive energy is about eight times the repulsive energy. The density dependence of the widths is analyzed by calculating homogeneous and inhomogeneous widths as a function of density. The results show that, although vibrational dephasing and density inhomogeneity contribute similarly to the width at low and middle densities, at high density the main contributor turns out to be the vibrational dephasing. We estimate the local density enhancements of supercritical CH(3)OH as function of bulk density by two methods. The results of these analyses show common features, and both the estimated local density enhancements of CH(3)OH are considerably larger than the local density enhancements of simple fluids, i.e., those having nonhydrogen bonding. It is revealed that the local density of supercritical CH(3)OH is 40%-60% greater than the local densities of the simple fluids. We also estimate the local density fluctuation using the obtained values of attractive shift, inhomogeneous width, and local density. The density fluctuation in the vicinity of a vibrating molecule is compared to the fluctuation of bulk density, which is obtained from the thermodynamic calculation.     

Structure factor for hard hyperspheres in higher dimensions

The structure factor for hard hyperspheres in two to eight dimensions is computed by Fourier transforming the pair correlation function obtained by computer simulation at a variety of densities. The resulting structure factors are compared to the known Percus-Yevick equations for odd dimensions and to the model proposed by Leutheusser [J. Chem. Phys. 84, 1050 (1986)] and Rosenfeld [J. Chem. Phys. 87, 4865 (1987)] in even dimensions. It is found that there is fine agreement among all these approaches at low to moderate densities but that the accuracy of the analytical models breaks down as the freezing transition is approached. The structure factor gives another insight into the decrease in the ordering of the hyperspheres as the dimension is increased.     

Pair correlation function of soft-sphere fluids

A closed-form analytic formula for the radial distribution function (RDF) or g(r) of inverse power fluids is proposed. The RDF is expressed as a sum of separate component functions, one monotonic and a series of exponentially damped oscillatory functions. Unlike previous treatments in the literature, this formula does not rely on patching different functional forms at arbitrary crossover distances. This expression, which we refer to as g(M)(r), yields the expected asymptotic behavior at large distance and reproduces the main features of the RDF generated by molecular dynamics (MD) simulations. The g(M) is applied to the soft n = 4 inverse power fluid, and it is shown that in this case seven or fewer terms are sufficient to represent accurately the MD-generated RDF over the entire fluid domain. The relative contributions of the separate terms of the g(M) as a function of density are analyzed and discussed. The key role played by the monotonic component function and two oscillatory terms is demonstrated. The origin of the crossover from the oscillatory to the monotonic behavior is shown to be the same as that recently proposed by Evans and Henderson [R. Evans and J. R. Henderson, J. Phys.: Condens. Matter 21, 474220 (2009)] for the dispersion interactions.     

Molecular dynamics simulations of vapor/liquid coexistence using the nonpolarizable water models

The surface tension, vapor-liquid equilibrium densities, and equilibrium pressure for common water models were calculated using molecular dynamics simulations over temperatures ranging from the melting to the critical points. The TIP4P/2005 and TIP4P-i models produced better values for the surface tension than the other water models. We also examined the correlation of the data to scaling temperatures based on the critical and melting temperatures. The reduced temperature (T/T(c)) gives consistent equilibrium densities and pressure, and the shifted temperature T + (T(c, exp) - T(c, sim)) gives consistent surface tension among all models considered in this study. The modified fixed charge model which has the same Lennard-Jones parameters as the TIP4P-FQ model but uses an adjustable molecular dipole moment is also simulated to find the differences in the vapor-liquid coexistence properties between fixed and fluctuating charge models. The TIP4P-FQ model (2.72 Debye) gives the best estimate of the experimental surface tension. The equilibrium vapor density and pressure are unaffected by changes in the dipole moment as well as the surface tension and liquid density.     

Determination of the melting point of hard spheres from direct coexistence simulation methods

We consider the computation of the coexistence pressure of the liquid-solid transition of a system of hard spheres from direct simulation of the inhomogeneous system formed from liquid and solid phases separated by an interface. Monte Carlo simulations of the interfacial system are performed in three different ensembles. In a first approach, a series of simulations is carried out in the isothermal-isobaric ensemble, where the solid is allowed to relax to its equilibrium crystalline structure, thus avoiding the appearance of artificial stress in the system. Here, the total volume of the system fluctuates due to changes in the three dimensions of the simulation box. In a second approach, we consider simulations of the inhomogeneous system in an isothermal-isobaric ensemble where the normal pressure, as well as the area of the (planar) fluid-solid interface, are kept constant. Now, the total volume of the system fluctuates due to changes in the longitudinal dimension of the simulation box. In both approaches, the coexistence pressure is estimated by monitoring the evolution of the density along several simulations carried out at different pressures. Both routes are seen to provide consistent values of the fluid-solid coexistence pressure, p=11.54(4)k(B)T/sigma(3), which indicates that the error introduced by the use of the standard constant-pressure ensemble for this particular problem is small, provided the systems are sufficiently large. An additional simulation of the interfacial system is conducted in a canonical ensemble where the dimensions of the simulation box are allowed to change subject to the constraint that the total volume is kept fixed. In this approach, the coexistence pressure corresponds to the normal component of the pressure tensor, which can be computed as an appropriate ensemble average in a single simulation. This route yields a value of p=11.54(4)k(B)T/sigma(3). We conclude that the results obtained for the coexistence pressure from direct simulations of the liquid and solid phases in coexistence using different ensembles are mutually consistent and are in excellent agreement with the values obtained from free energy calculations.     

无机聚合絮凝剂的结构研究

本文用广角度Ｘ射线散射（ＷＡＸＳ）和径向分布函数（ＲＤＦ）方法对聚合硅硫酸铝钾ＴＸ２０３絮凝剂的结构进行了分析。ＷＡＸＳ和ＲＤＦ分析指出：该絮凝剂是一种有序尺寸（Ｄ）约为２２～２５Ａ非晶固体。它是由有序周期（ｒ、）≌１２－１４Ａ的中程有序畴组成的,而这些有序畴又是由三种结构单元,即四面体「ＳＯ４」,「ＡｌＯ４」（０＝Ｏ,ＯＨ）和八面体「ＡｌＯ６」（Ｏ＝Ｏ,ＯＨ）组成的。Ｄ／ｒ１＝２～３,因此ＴＸ２     

Auswertung von erstarrungs-und schmelzkurven zur berechnung des reinheitsgrades mittels maschinenlochkarten

Assuming thermal equilibrium and constant heat withdrawal from the system or constant heat supply (constant rate of crystallization or melting), the time-dependent function of the freezing or melting point of a two-phase liquid-solid saystem is approximately a hyperbola. The time-temperature curves were recorded with the help of a special measuring apparatus. In order to evaluate these curves it is necessary: (i) to determine the freezing point of a given substance, at which the first (or last) crystal nucleus is exactly in equilibrium with the liquid phase, (2) to ascertain the extrapolated freezing point of the completely pure substance, and (3) to check whether the measured curve really corresponds to the phase equilibrium. One searches for, for example, ten pairs of values of temperature and time, the hyperbola of the general function T=TF$\text{b}\text{1-cZ}$ that best renders the measured course of the curve, i.e. the one that makes the sum of the squares of the deviations of the measured temperatures from that calculated from the hyperbola function a minimum. In this way, the freezing point of a given substance, as well as the standard deviation of the measured curve from the hyperbola is better obtained than with the analytical or geometrical methods of evaluating via 3 points on the equilibrium curve. Since the numerical calculation of a hyperbola trend is very time-consuming, it is accomplished with the help of machine punch-cards in an electronic computer. The determination of the degree of purity of substances can be routinely carried out in this way.     

三元体系H3BO3-MgCl2-H2O在308.15K和323.15K稳定相平衡研究

采用等温溶解法研究了三元体系H3BO3 - MgCl2 - H2O在308.15 K和323.15 K的稳定相平衡;测定了上述体系液相中各组分的平衡溶解度及液相密度,并绘制了相应相图和平衡溶液密度组成图.结果表明,该体系在308.15 K和323.15 K时有一个共饱点、两条饱和溶解度曲线和两个结晶相区,无复盐及固溶体...