Subcritical and Supercritical Water Radial Distribution Function

A theoretical and analytic expression for the first shell, and an analytic empirical expression for the whole radial distribution function (RDF) of water are introduced. All the asymptotic limits and functionalities of the RDF with temperature and density are incorporated in these expressions. An effective Kihara pair potential function is presented for water intermolecular interactions which incorporates the hydrogen bonding by using the chain association theory. The intermolecular pair potential parameters are adjusted to the experimental x-ray diffraction data of water RDF at various temperatures. The predicted first-shell results for water near critical and in supercritical conditions compare satisfactorily with the available neutron diffraction RDF data, with the simulation RDF results, and with the empirical RDF curves. The empirical expression initially proposed for the RDF of the Lennard–Jones fluid is extended to predict the RDF and the isothermal compressibility of water to conditions where experimental or simulated data are not available. Comparison with the Lennard–Jones fluid shows that the height of the first peak of water RDF changes much less at subcritical and supercritical conditions compared to that of the Lennard–Jones fluid which decreases appreciably going from subcritical to supercritical conditions.     

Strain energy density – a molecular appraisal

Abstract

The interaction potential between two clusters simulating the crack tip on the lattice level is derived in this work. Employing molecules as the building blocks and the Lennard‐Jones potential as the Green's function, the close‐form solution shows that the 1/r‐type of singularity is an intrinsic behavior of the energy field when mutual attraction dominates the lattice interactions. This behavior is now proven, explicitly, to be independent of the constitutive equation of the material.     

Consistency conditions for the integral equations of liquid structures

A thermodynamic consistency principle is established for the closure relations in integral equations that can yield accurate correlation functions as well as accurate thermodynamic properties, A brief lour d'horizon is given for existing consistency approaches. In addition to the common pressure consistency and the pressure energy consistency, we introduce a third requirement based on the Gibbs-Duhem relation. We found that Gibbs Duhem relation, mediated through the chemical potential, is instrumental in procuring accurate behavior of the bridge function and cavity Junction in the overlapping region (0 <r < ). We test the Lennard Jones fluid over wide ranges ofT ^* andp ^* (T ^* as low as 0.72 andp ^* up to 11,90(, For more than IS state points we obtain excellent agreement in internal energy, pressure, and chemical potential. Comparison with Monte Carlo data on the bridge Junction and the radial distribution function also shows that the present approach is highly accurate.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

A New Simplified Local Density Model for Adsorption of Pure Gases and Binary Mixtures

Adsorption modeling is an important tool for process simulation and design. Many theoretical models have been developed to describe adsorption data for pure and multicomponent gases. The simplified local density (SLD) approach is a thermodynamic model that can be used with any equation of state and offers some predictive capability with adjustable parameters for modeling of slit-shaped pores. In previous studies, the SLD model has been utilized with the Lennard–Jones potential function for modeling of fluid–solid interactions. In this article, we have focused on application of the Sutherland potential function in an SLD–Peng–Robinson model. The advantages and disadvantages of using the new potential function for adsorption of methane, ethane, carbon dioxide, nitrogen, and three binary mixtures on two types of activated carbon are illustrated. The results have been compared with previous models. It is shown that the new SLD model can correlate adsorption data for different pressures and temperatures with minimum error.     

Adhesive force between a spherical rigid particle and an incompressible elastic substrate

Adhesion between a spherical rigid particle and an incomprssible elastic substrate is studied on the basis of the Lennard–Jones (L–J) potential, and the aim is to explore limitations of the well-known Derjaguin approximation. A new expression of the adhesive force is derived, in which the contribution from the elastic deformation of the substrate is incorporated naturally. Numerical results show that the Derjaguin approximation is valid down to particle radii of the order of the interaction range.     

Theoretical Equation of State for Highly Anharmonic Solids

Thermodynamic properties of Lennard–Jones (LJ) face-centered cubic crystals are calculated in a wide range of temperatures along sublimation and melting lines on the basis of statistical mechanical theory which accounts for anharmonicity, pair and triple correlations in the displacements of atoms. Results are compared with the most accurate Monte Carlo data available. Excellent agreement was found. Anharmonic and correlation contributions to entropy, internal energy, and the compressibility factor of LJ solids are computed and their relative importance analyzed. An analytical equation of state approximating the theoretical results is developed.     

Thermodynamic Properties of Sutherland Fluids from an Analytical Perturbation Theory

Analytical expressions are obtained for the thermodynamic properties of fluids with potentials consisting of a spherical hard core plus an attractive tail of the form 1/r (Sutherland fluids). To this end, use is made of the Barker–Henderson perturbation theory together with an analytical expression for the first coordination shell of the radial distribution function of the reference hard-sphere fluid. This expression was derived previously on the basis of the analytical solution of the Percus–Yevick integral equation theory. The results are compared with available simulation data for a wide range of densities, temperatures, and values of the potential parameter . The overall agreement is good, and the accuracy is similar to that obtained using more accurate solutions for the radial distribution function of the hard-sphere fluid leading to nonanalytical expressions for the thermodynamic properties of the fluid considered.     

Persistence of supersonic periodic solutions for chains with anharmonic interaction potentials between neighbours and next to nearest neighbours

We consider an infinite chain of particles with nearest neighbour (NN) and next to nearest neighbour (NNN) being coupled by nonlinear springs. To mimic the Lennard–Jones potential, the NN and NNN springs act against each other. We prove that in contrast to the NN interaction case, there are supersonic periodic solutions.     

Mechanics of concentric carbon nanotubes: Interaction force and suction energy

Based on the continuum approximation together with Lennard–Jones potential, a new semi-analytical method is developed to determine the van der Waals interaction between two single-walled carbon nanotubes. Neglecting the frictional effects, acceptance condition and suction energy for an inner tube entering semi-infinite outer ones are obtained and nature of interaction force is investigated. The maximum suction energy configurations are found by netting analysis. Using this procedure, the optimum configurations are obtained to minimize the potential energy. Also, a universal potential curve is presented for an inner tube entering various semi-infinite outer ones. Finally, on the basis of the direct method, suction energy and acceptance condition are obtained for multi-walled carbon nanotubes.     

Encapsulation of a benzene molecule into a carbon nanotube

Aromatic hydrocarbon molecules encapsulated in carbon nanotubes have been proposed for applications as semiconductors. They can be formed by exploiting the van der Waals interaction as a simple method to incorporate molecules into carbon nanotubes. However, the existence of energy barriers near the open ends of carbon nanotubes may be an obstacle for molecules entering carbon nanotubes. In this paper, we investigate the encapsulation mechanism of a typical aromatic hydrocarbon, namely a benzene molecule, into a carbon nanotube in order to determine the dependence on radius of the tube. A continuous approach which assumes that the molecular interactions can be approximated using average atomic densities together with the semi-empirical Lennard–Jones potential function is adopted, and an analytical expression for the interaction energy is obtained which may be readily evaluated by algebraic computer packages. In particular, we determine the threshold radius of the carbon nanotube for which the benzene molecule will enter the carbon nanotube. The analytical approach adopted here provides a computationally rapid procedure for the determination of critical numerical values.     

Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory

Axial buckling analysis of double-walled Boron Nitride nanotubes (DWBNNTs) embedded in an elastic medium under combined electro-thermo-mechanical loadings is presented in this article. Virtual displacement method based on nonlocal cylindrical piezoelasticity continuum shell theory is employed to derive the equilibrium equations. Boron Nitride nanotube (BNNT) is assumed to be surrounded by a bundle of carbon nanotubes (CNTs) as elastic medium for reinforcement. The elastic medium is simulated as Winkler–Pasternak foundation, and adjacent layers interactions are assumed to have been coupled by van der Walls (vdW) force evaluated based on the Lennard–Jones model. The effects of parameters such as electric and thermal loads, elastic medium and small scale are investigated on the buckling behavior of the DWBNNTs. The electric field and its direction are found to have affected the magnitude of the critical buckling load. Moreover, an analysis is carried out to estimate the nonlocal critical electro-thermo-mechanical load for the axial buckling of embedded DWBNNTs.     

Thermal conductivity of nitrogen at high pressures

The results of the measurements of the thermal conductivity coefficients of nitrogen at 298.15 K from atmospheric pressure up to 1 GPa are reported. The experimental values are used to test the Modified Enskog Theory and the corresponding state principle. The experimental values are also compared with the results of computer simulation of the thermal conductivity of a Lennard Jones fluid.     

Direct imaging the upconversion nanocrystal core/shell structure at the subnanometer level: shell thickness dependence in upconverting optical properties

Lanthanide-doped upconversion nanoparticles have shown considerable promise in solid-state lasers, three-dimensional flat-panel displays, and solar cells and especially biological labeling and imaging. It has been demonstrated extensively that the epitaxial coating of upconversion (UC) core crystals with a lattice-matched shell can passivate the core and enhance the overall upconversion emission intensity of the materials. However, there are few papers that report a precise link between the shell thickness of core/shell nanoparticles and their optical properties. This is mainly because rare earth fluoride upconversion core/shell structures have only been inferred from indirect measurements to date. Herein, a reproducible method to grow a hexagonal NaGdF(4) shell on NaYF(4):Yb,Er nanocrystals with monolayer control thickness is demonstrated for the first time. On the basis of the cryo-transmission electron microscopy, rigorous electron energy loss spectroscopy, and high-angle annular dark-field investigations on the core/shell structure under a low operation temperature (96 K), direct imaging the NaYF(4):Yb,Er@NaGdF(4) nanocrystal core/shell structure at the subnanometer level was realized for the first time. Furthermore, a strong linear link between the NaGdF(4) shell thickness and the optical response of the hexagonal NaYF(4):Yb,Er@NaGdF(4) core/shell nanocrystals has been established. During the epitaxial growth of the NaGdF(4) shell layer by layer, surface defects of the nanocrystals can be gradually passivated by the homogeneous shell deposition process, which results in the obvious enhancement in overall UC emission intensity and lifetime and is more resistant to quenching by water molecules.     

Structural investigation of boron-containing metallic glasses

Structural investigations have been made of high boron-containing alloy glasses of compositions Co_100–x B _x withx=34, 36, 38 and 40 at % measured by X-ray diffraction. The characteristic second-peak splitting in the radial distribution function (RDF) is found for all samples presently investigated. The shoulders are also observed near the distances of 0.20 and 0.34 nm. The partial radial distribution functions of Co-Co and Co-B pairs have been derived from the measured total RDF data by applying the concentration method with the anomalous scattering technique, and the contributions from different atomic pairs to total RDF have been discussed. The calculation by the relaxed dense random packing model has been made for Fe-B alloy glasses with three different boron concentrations, i.e., 15, 25, and 40 at % boron and a comparison between the calculated and experimentally determined data is presented. The present model calculation could give the possible representation for the compositional dependence of the X-ray RDF for amorphous Fe-B alloys with boron contents of up to 40 at % as well as the different peak profile observed in the total RDF of X-ray data between Fe-B and Fe-P glasses.     

Effects of the angle of deposition on short-range order in amorphous germanium

A comparison of the atomic arrangements in germanium films deposited at normal and oblique incidence is made. It is shown that the parameters of short-range order are sensitive to the angle ? of deposition. The oblique incidence effects manifest themselves both in the intensity function and in the radial distribution function (RDF). The RDF of a film deposited at oblique incidence has an additional correlation peak at r₀ = 0.174 nm which is not observed for normal incidence. Its location corresponds to the length of the GeO bond. It arises because of the increase in the oxygen content of the filn with increasing obliqueness. The coordination number consistent with the GeO correlations is proportional to the oxygen content of the film as estimated by Auger electron spectroscopy. The incorporated oxygen and the structural anisotropy of obliquely deposited films also influence the shape of the second structural peak of the RDF. The reasons for the different oxygen contents in films prepared under the same vacuum conditions are discussed.     

Molluscan biomineralization: The proteinaceous shell constituents of Pinna nobilis L.

The shell of molluscs is a remarkable example of a natural composite biomaterial, synthesized at ambient temperature. Consequently, many consider it as a model for trying to develop at little cost new biomimetic materials of superior mechanical properties. The peculiar resistance of shells to fracture lies in an organic matrix, which is closely associated with the mineral phase. This matrix regulates the crystal growth, by allowing nucleation of the crystals only where appropriate, by favoring crystal elongation in privileged directions, and by inhibiting their growth. This matrix is a mixture of glycoproteins and polysaccharides, the primary structure and function of which are poorly known. Pinna nobilis, the Mediterranean fan mussel, is one of the few molluscs for which molecular data on shell proteins are available. In the present paper, we review what is known, at molecular level, on the macromolecular constituents of the shell of P. nobilis by describing three proteins, the characterization of which is still going on: the first one, mucoperlin, is specific of the nacreous layer. The two others were obtained from the calcitic prismatic layer and one of them was localized by immunogold and further tested to check its ability to modify the shapes of CaCO3 crystals. The data shown here, together with data obtained from the pearl oyster or the abalone, put into question some common ideas about molluscan mineralization.     

Fracture mechanics analysis of asperity cracking due to adhesive normal contact

A two-dimensional linear-elastic fracture mechanics analysis of asperity cracking induced by adhesive normal contact was performed with the finite element method. Normal contact between two elastic asperities was analyzed with the equivalent contact system of an elastic asperity with equivalent radius of curvature and effective elastic modulus compressed by a rigid plane. Surface adhesion was modeled by nonlinear springs obeying a constitutive force-distance law derived from the Lennard–Jones potential. The maximum ranges of the tensile and shear stress intensity factors were used to determine the crack-growth direction and the dominant mode of asperity fracture in terms of the Maugis parameter (a function of the equivalent radius of curvature, work of adhesion, effective elastic modulus, and intermolecular equilibrium distance), friction coefficient at the crack interface, maximum surface interference, and crack position. Finite element simulation results indicate that the direction and the rate of crack growth are mostly affected by the Maugis parameter and the maximum surface interference. A transition from shear to tensile dominant mode of crack growth is encountered with the increase of the Maugis parameter and/or the decrease of the maximum surface interference. Opening, slip, and stick between the crack faces during loading and unloading are discussed in the context of crack mechanism maps.     

Particle modeling of dynamic fragmentation-I: theoretical considerations

This paper series adopts particle modeling (PM) to simulation of dynamic fracture phenomena in homogeneous and heterogeneous materials, such as encountered in comminution processes in the mining industry. This first paper is concerned with the setup of a lattice-type particle model having the same functional form as the molecular dynamics (MD) model (i.e., the Lennard–Jones potential), yet on centimeter length scales. We formulate four conditions to determine four key parameters of the PM model (also of the Lennard–Jones type) from a given MD model. This leads to a number of properties and trends of resulting Young’s modulus in function of these four parameters. We also investigate the effect of volume, at fixed lattice spacing, on the resulting Young modulus. As an application, we use our model to revisit the dynamic fragmentation of a copper plate with a skew slit [J. Phys. Chem. Solids, 50(12) (1989) 1245].     

A structural study of glassy polystyrene

X-ray scattering from three polystyrene glasses and from a partially devitrified specimen has been measured. The intensity data are identical for quenched and slowly cooled atactic polystyrene but differ for isotactic polystyrene quenched to the glassy state. Radial Distribution Functions (RDF) exhibit five principal peaks centred at 1.5, 2.5, 5, 6, and 10Å for all of the glasses. A model RDF based on the published crystal structure is shown to compare well with the RDF obtained experimentally for devitrified isotactic polystyrene. On the basis of this model, peaks in the RDFs are assigned. It is shown that both inter- and intramolecular scattering contributes to the polystyrene RDF at distances beyond 3.7Å. The structure is dominated by steric interaction of the phenyl groups, affecting both chain conformation and molecular packing.