Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles

Athermal lattice gases of particles with first neighbor exclusion have been studied for a long time as simple models exhibiting a fluid-solid transition. At low concentration the particles occupy randomly both sublattices, but as the concentration is increased one of the sublattices is occupied preferentially. Here, we study a mixed lattice gas with excluded volume interactions only in the grand-canonical formalism with two kinds of particles: small ones, which occupy a single lattice site and large ones, which, when placed on a site, do not allow other particles to occupy its first neighbors also. We solve the model on a Bethe lattice of arbitrary coordination number q. In the parameter space defined by the activities of both particles, at low values of the activity of small particles (z(1)) we find a continuous transition from the fluid to the solid phase as the activity of large particles (z(2)) is increased. At higher values of z(1) the transition becomes discontinuous, both regimes are separated by a tricritical point. The critical line has a negative slope at z(1) = 0 and displays a minimum before reaching the tricritical point, so that a re-entrant behavior is observed for constant values of z(2) in the region of low density of small particles. The isobaric curves of the total density of particles as a function of the density or the activity of small particles show a minimum in the fluid phase.     

On the Electride Nature of Na-hP4

Early quantum mechanical models suggested that pressure drives solids towards free-electron metal behavior where the ions are locked into simple close-packed structures. The prediction and subsequent discovery of high-pressure electrides (HPEs), compounds assuming open structures where the valence electrons are localized in interstitial voids, required a paradigm shift. Our quantum chemical calculations on the iconic insulating Na-hP4 HPE show that increasing density causes a 3s→3pd electronic transition due to Pauli repulsion between the 1s2s and 3s states, and orthogonality of the 3pd states to the core. The large lobes of the resulting Na-pd hybrid orbitals point towards the center of an 11-membered penta-capped trigonal prism and overlap constructively, forming multicentered bonds, which are responsible for the emergence of the interstitial charge localization in Na-hP4. These multicentered bonds facilitate the increased density of this phase, which is key for its stabilization under pressure.     

Electrical potentials of two identical particles with fixed surface charge density in a salt-free medium

The electrical potentials of two identical planar, cylindrical, and spherical particles immersed in a salt-free dispersion are solved analytically by a perturbation approach for the case of constant surface charge density. The system under consideration simulates, for example, micelles, where the ionic species in the liquid phase come mainly from the dissociation of the functional groups on the droplet surface. We show that for planar particles, the present zero-order perturbation solution is exact, and for cylindrical and spherical particles, the first-order perturbation solution provides sufficiently accurate results, with an averaged percentage deviation on the order of 1% under typical conditions. In general, the higher the surface charge density, the higher the valence of counterions, the smaller the separation distance between two particles, and the smaller the curvature of particle surface, the better the performance of the perturbation solution.     

Free volume properties of a linear soft polymer: a computer simulation study

Molecular dynamics simulation of a linear soft polymer has been performed and the free volume properties of the system have been analyzed in detail in terms of the Voronoi polyhedra of the monomers. It is found that there are only small density fluctuations present in the system. The local environment of the monomers is found to be rather spherical, even in comparison with liquids of atoms or small molecules. The monomers are found to be, on average, eight coordinated by their nearest geometric neighbors, including intra-chain and inter-chain ones. The packing of the monomers is found to be rather compact, in a configuration of 1900 monomers there are, on average, only three voids large enough to incorporate a spherical particle as large as a monomer, indicating that the density of the large vacancies in the system is considerably, i.e., by a few orders of magnitude lower than in molecular liquids corresponding to roughly the same reduced densities.     

六角形氧化锌超晶格粒子的控制制备

本文通过蒸发微乳液体系中的溶剂得到了六角形的氧化锌亚微米粒子，其具有超晶格结构。所得产物用红外(FT-IR)和透射电镜(TEM)进行了表征，并进行了热重分析(TGA)。通过监测反应过程，研究了该粒子的形成机制。实验观察到约7nm的纳米氧化锌粒子聚集成亚微米的球形超晶格粒子，该球形粒子随溶剂蒸发进行了自组装，并由于界面相互作用转换成六角形的超晶格粒子。     

Analytical solutions of nonlinear Poisson–Boltzmann equation for colloidal particles immersed in a general electrolyte solution by homotopy perturbation technique

We present the first application of the homotopy perturbation technique to analytically solve the nonlinear PB equation describing spherical and planar colloidal particles immersed in an arbitrary valence and mixed electrolyte solution. Analytical expressions for electrical potential distribution and surface charge density/surface potential relationship are acquired. Our analytical solutions contrast sharply with previous ones by two striking features: (1) the present ones apply irrespective of the types of electrolyte considered or whether single electrolyte or mixed electrolytes are being considered, and (2) the valid application scopes of present solutions are in small κa domain and thus are complementary with those of previous ones. Our expressions are considered to provide the constituents whose combinations with previous solutions may end up global valid expressions.     

Density functional theory of freezing of a system of conjugated oligomers parameterised via Gay–Berne potential

Density functional theory (DFT) of freezing is used to study the isotropic–nematic, isotropic–smectic A and nematic–smectic A phase transitions in a system of large, semi-flexible conjugated oligomers parameterised within Gay–Berne (GB) potential. The pair correlation functions of the isotropic fluid, used as structural inputs in the DFT, are calculated by solving the Percus–Yevick integral equation theory. Large number of spherical harmonic coefficients of each orientation-dependent functions has been considered to ensure the numerical accuracy at different densities and temperatures for the system of these model GB ellipsoids having large aspect ratio (length-to-breadth ratio). We found that the system of GB ellipsoids parameterised for conjugated oligomers shows stable isotropic, nematic and smectic A phases. At low temperatures, on increasing the density, isotropic fluid makes a direct transition to smectic A phase. Nematic phase get stabilised in between the isotropic and smectic A phases on increasing the temperature. Using the transition parameter obtained through the DFT, we have plotted the temperature–density and pressure–temperature phase diagrams which are found to be qualitatively similar to the one obtained in simulations for the systems with low aspect ratio GB particles.     

Non-Born-Oppenheimer electronic and nuclear densities for a Hooke-Calogero three-particle model: non-uniqueness of density-derived molecular structure

We consider the calculation of non-Born-Oppenheimer, nBO, one-particle densities for both electrons and nuclei. We show that the nBO one-particle densities evaluated in terms of translationally invariant coordinates are independent of the wavefunction describing the motion of center of mass of the whole system. We show that they depend, however, on an arbitrary reference point from which the positions of the vectors labeling the particles are determined. We examine the effect that this arbitrary choice has on the topology of the one-particle density by selecting the Hooke-Calogero model of a three-body system for which expressions for the one-particle densities can be readily obtained in analytic form. We extend this analysis to the one-particle densities obtained from full Coulomb interaction wavefunctions for three-body systems. We conclude, in view of the fact that there is a close link between the choice of the reference point and the topology of one-particle densities that the molecular structure inferred from the topology of these densities is not unique. We analyze the behavior of one-particle densities for the Hooke-Calogero Born-Oppenheimer, BO, wavefunction and show that topological transitions are also present in this case for a particular mass value of the light particles even though in the BO regime the nuclear masses are infinite. In this vein, we argue that the change in topology caused by variation of the mass ratio between light and heavy particles does not constitute a true indication in the nBO regime of the emergence of molecular structure.     

The chemical potential for dilute hard-sphere mixtures

Accurate Monte Carlo evaluation of the probability of inserting an additional particle of arbitrary size into a hard-sphere fluid at various densities allows a quantitative check on the scaled particle interpolation formula for this probability, which is rigorously known when the added particle is either very small or very large. The simple scaled particle formula is remarkably accurate due to a favorable choice of the functional dependence of the surface tension on curvature. The biggest deviation occurs at liquid-like densities where the insertion probability is about 20% larger for larger particles, indicating a larger probability of occurrence of larger density fluctuations, and resulting in a smaller (3%) excess chemical potential than the simple theory predicts. On the other hand, at lower densities the insertion probability for large particles is slightly smaller than the theory predicts.     

Conductivity percolation in loosely compacted microcrystalline cellulose: An in situ study by dielectric spectroscopy during densification

The present study aims at contributing to a complete understanding of the water-induced ionic charge transport in cellulose. The behavior of this transport in loosely compacted microcrystalline cellulose (MCC) powder was investigated as a function of density utilizing a new type of measurement setup, allowing for dielectric spectroscopy measurement in situ during compaction. The ionic conductivity in MCC was found to increase with increasing density until a leveling-out was observed for densities above approximately 0.7 g/cm3. Further, it was shown that the ionic conductivity vs density followed a percolation type behavior signifying the percolation of conductive paths in a 3D conducting network. The density percolation threshold was found to be between approximately 0.2 and 0.4 g/cm3, depending strongly on the cellulose moisture content. The observed percolation behavior was attributed to the forming of interparticulate bonds in the MCC and the percolation threshold dependence on moisture was linked to the moisture dependence of particle rearrangement and plastic deformation in MCC during compaction. The obtained results add to the understanding of the density-dependent water-induced ionic transport in cellulose showing that, at given moisture content, the two major parameters determining the magnitude of the conductivity are the connectedness of the interparticluate bonds and the connectedness of pores with a diameter in the 5-20 nm size range. At densities between approximately 0.7 and 1.2 g/cm3 both the bond and the pore networks have percolated, facilitating charge transport through the MCC compact.     

A chemically useful definition of electron difference densities

Molecular difference densities (DD ) are conventionally constructed using spherically averaged atomic densities at the appropriate positions. For atoms in degenerate ground states, this is an unphysical choice, and artifacts dominate the DD . We suggest the extraction of both the position and the orientation of an atom with an open valence shell from x-ray scattering or molecular density data. Subtracting the oriented atoms yields a uniquely defined, as well as chemically meaningful, DD. Covalent bonds to electronegative atoms such as O are no longer exceptional but show bond charges of normal magnitude. Lone pairs are characterized by a dipolar density shift from the bond to the back side of the atomic core.     

A chemically useful definition of electron difference densities

Molecular difference densities (DD ) are conventionally constructed using spherically averaged atomic densities at the appropriate positions. For atoms in degenerate ground states, this is an unphysical choice, and artifacts dominate the DD . We suggest the extraction of both the position and the orientation of an atom with an open valence shell from x-ray scattering or molecular density data. Subtracting the oriented atoms yields a uniquely defined, as well as chemically meaningful, DD . Covalent bonds to electronegative atoms such as O are no longer exceptional but show bond charges of normal magnitude. Lone pairs are characterized by a dipolar density shift from the bond to the back side of the atomic core.     

Large attractive depletion interactions in soft repulsive-sphere binary mixtures

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.     

Covalent bond orders and atomic anisotropies from iterated stockholder atoms

Iterated stockholder atoms are produced by dividing molecular electron densities into sums of overlapping, near-spherical atomic densities. It is shown that there exists a good correlation between the overlap of the densities of two atoms and the order of the covalent bond between the atoms (as given by simple valence rules). Furthermore, iterated stockholder atoms minimise a functional of the charge density, and this functional can be expressed as a sum of atomic contributions, which are related to the deviation of the atomic densities from spherical symmetry. Since iterated stockholder atoms can be obtained uniquely from the electron density, this work gives an orbital-free method for predicting bond orders and atomic anisotropies from experimental or theoretical charge density data.     

Mechanical and frictional properties of nanoparticle monolayers grafted on functionalized mica substrates

Normal and lateral forces between two opposing monolayers of grafted polymer nanoparticles (NPs) were measured using the Surface Forces Apparatus in a humid atmosphere. The NPs made of N, N-diethylacrylamide and 2-hydroxyethyl methacrylate have a hydrodynamic diameter of ca. 660 nm at 25 degrees C. The effect of surface roughness was studied by creating surface asperities using different NP grafting densities ranging from 0.41 to 2.63 NPs/mum (2). An increase in the NPs grafting density gave rise to an increase in surface roughness and to a deformation of the nanoparticles caused by the lateral pressure between neighboring particles. An elastoplastic behavior of the nanoparticles was observed for large grafting densities, while a purely elastic behavior was observed for small grafting densities. The lateral forces measured between two opposing NP monolayers sliding past each other followed Amontons' law for all grafting densities. The friction coefficient between the surfaces appeared to increase significantly with an increase in surface roughness, which was inherent to an increase in the elastoplastic behavior of the NP monolayers.     

Interactions between polymer brush-coated spherical nanoparticles: the good solvent case

The interaction between two spherical polymer brushes is studied by molecular dynamics simulation varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. A coarse-grained bead-spring model is used to describe the macromolecules, and purely repulsive monomer-monomer interactions are taken throughout, restricting the study to the good solvent limit. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to-end distance of the grafted chains, etc.). When the nanoparticles approach very closely, some chains need to be squeezed out into the tangent plane in between the particles, causing a very steep rise of the repulsive interaction energy between the particles. We consider as a complementary method the density functional theory approach. We find that the quantitative accuracy of the density functional theory is limited to large nanoparticle separation and short chain length. A brief comparison to Flory theory and related work on other models also is presented.     

Topological analysis of electron density distribution taken from a pseudopotential calculation

Theoretical studies of the electron density topology at the bond critical point for some small molecules, Ti, and Mo organometallic complexes were undertaken in order to understand the reason for the failure of the topological analysis of the coreless electron densities obtained from a pseudopotential calculation. We show that the absence of the core electron density is the main reason for such behavior. The erratic behavior of the effective core potentials electron densities can be corrected by adding atomic electron core density obtained from a single-atom Hartree-Fock calculation. The effect of orthogonalization of the core orbital with the valence orbitals was also investigated. © 1997 by John Wiley & Sons, Inc.     

Structure and size of spontaneously formed aggregates in Aerosol OT/PEG mixtures: effects of polymer size and composition

Dynamic light scattering and Cryo-TEM measurements have allowed us to obtain the size and structure of spontaneous aggregates formed by mixtures of Aerosol OT, AOT, and ethylene glycol polymers of different molecular mass. The results presented in this work show that small unilamellar vesicles predominate in pure Aerosol OT solutions and in dilute polymer solutions mixed with AOT. In the latter case, elongated micelles coexist with unilamellar vesicles. When polymer concentration increases above a certain concentration, the small vesicles disappear and the size of the elongated micelles decreases to a radius compatible with spherical micelles. For PEG concentrations above the overlapping ones, spherical micelles coexist with very large aggregates probably formed by large rod like micelles or by superstructures of elongated micelles embedded in a polymer network. This behavior is consistent with theoretical models based in molecular mean-field theory [M. Rovira-Bru, D.H. Thompson, I. Szleifer, Biophys. J. 83 (2002) 2419]. The properties of the different types of aggregates are obtained by fluorescence spectroscopy and electrophoretic mobility measurements.