Hard-sphere Model Research Articles

Equation of State for Molten Alkali Halides by Thermodynamic Perturbation Theory.

Several variants of the equation of state (EoS) for molten alkali halides are considered using the thermodynamic perturbation theory. Most attention is focused on taking into account the charge-induced dipole (or induction) term to pressure. The model of charged hard spheres of different diameters within the mean spherical approximation is used as a reference system. The value of the extra induction contribution to the pressure is about 5-10% of the Coulomb input and, thus, leads to a better agreement between the calculation results and experimental data. It is shown that the EoS through the energy gives superior results as compared to the experimental data on molten alkali halides near their melting points. Trends in density change with the ionic radii and the polarizabilities are analyzed.

Aerothermodynamics of a sphere in a monatomic gas based onab initiointeratomic potentials over a wide range of gas rarefaction: transonic, supersonic and hypersonic flows

Aerothermodynamic characteristics of a sphere such as drag and energy transfer coefficients are calculated for Mach numbers varying from 1 to 10 over a wide range of the gas rarefaction degree spanning the free molecular, transitional and near hydrodynamic flow regimes. The effects of major factors determining the gas flow are studied using the direct simulation Monte Carlo method. To reveal the effect of gas species, the simulations are performed based onab initiointeratomic potentials for helium, neon, argon and krypton, as well as based on the hard sphere model. The impact of the accommodation coefficients is evaluated by applying the Cercignani–Lampis model of gas–surface interaction. The calculations are carried out for several values of the free stream and sphere temperatures. It is found that the effects of gas species on the drag and energy transfer coefficients are approximately 3 % and 6 %, respectively. The accommodation coefficients in the Cercignani–Lampis model strongly affect all aerothermodynamic characteristics. The drag and energy transfer coefficients calculated for different accommodation coefficients vary within 30 % and 200 %, respectively. It is found that the variation of the tangential momentum and normal energy accommodation coefficients can induce an increase of the drag coefficient compared to the case of diffuse gas–surface interaction. In hypersonic flows, the drag coefficient varies within 30 % when the sphere temperature varies from the free stream temperature to the stagnation temperature. The drag and energy transfer coefficients are found to be non-monotonic functions of the free stream temperature.

Resonance distribution in the quantum random Lorentz gas

The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of scattering resonances in the complex plane of the wavenumber without finding them one by one. The method is applied to two collision models for the individual scatterers, namely a resonant model, and a non-resonant hard-sphere model. The results obtained with the former are compared to the literature. In particular, the spiral arms surrounding the single-scatterer resonance are identified as proximity resonances. Moreover, the hard-sphere model is used to reveal previously unknown structures in the resonance density. Finally, it is shown how Anderson localization affects the distribution of resonance widths, especially in the one-dimensional case.

A novel method for photon unfolding spectroscopy of protein ions in the gas phase.

In this study, a new experimental method for photon unfolding spectroscopy of protein ions based on a Fourier transform ion cyclotron resonance (FT ICR) mass spectrometer was developed. The method of short-time Fourier transform has been applied here to obtain decay curves of target ions trapped in the cell of the FT ICR mass spectrometer. Based on the decay constants, the collision cross sections (CCSs) of target ions were calculated using the energetic hard-sphere model. By combining a tunable laser to the FT ICR mass spectrometer, the changes of CCSs of the target ions were recorded as a function of the wavelengths; thus, the photon isomerization spectrum was obtained. As one example, the photon isomerization spectrum of [Cyt c + 13H]13+ was recorded as the decay constants relative to the applied wavelengths of the laser in the 410-480 nm range. The spectrum shows a maximum at 426 nm, where an unfolded structure induced by a 4 s irradiation can be deduced. The strong peak at 426 nm was also observed for another ion of [Cyt c + 15H]15+, although some difference at 410 nm between the two spectra was found at the same time. This novel method can be expanded to ultraviolet or infrared region, making the experimental study of wavelength-dependent photon-induced structural variation of a variety of organic or biological molecules possible.

Atomistic Simulation of Lysozyme in Solutions Crowded by Tetraethylene Glycol: Force Field Dependence.

The behavior of biomolecules in crowded environments remains largely unknown due to the accuracy of simulation models and the limited experimental data for comparison. Here we chose a small crowder of tetraethylene glycol (PEG-4) to investigate the self-crowding of PEG-4 solutions and molecular crowding effects on the structure and diffusion of lysozyme at varied concentrations from dilute water to pure PEG-4 liquid. Two Amber-like force fields of Amber14SB and a99SB-disp were examined with TIP3P (fast diffusivity and low viscosity) and a99SB-disp (slow diffusivity and high viscosity) water models, respectively. Compared to the Amber14SB protein simulations, the a99SB-disp model yields more coordinated water and less PEG-4 molecules, less intramolecular hydrogen bonds (HBs), more protein–water HBs, and less protein–PEG HBs as well as stronger interactions and more hydrophilic and less hydrophobic contacts with solvent molecules. The a99SB-disp model offers comparable protein–solvent interactions in concentrated PEG-4 solutions to that in pure water. The PEG-4 crowding leads to a slow-down in the diffusivity of water, PEG-4, and protein, and the decline in the diffusion from atomistic simulations is close to or faster than the hard sphere model that neglects attractive interactions. Despite these differences, the overall structure of lysozyme appears to be maintained well at different PEG-4 concentrations for both force fields, except a slightly large deviation at 370 K at low concentrations with the a99SB-disp model. This is mainly attributed to the strong intramolecular interactions of the protein in the Amber14SB force field and to the large viscosity of the a99SB-disp water model. The results indicate that the protein force fields and the viscosity of crowder solutions affect the simulation of biomolecules under crowding conditions.

Rheology Applied to Microgels: Brief (Revision of the) State of the Art.

The ability of polymer microgels to rapidly respond to external stimuli is of great interest in sensors, lubricants, and biomedical applications, among others. In most of their uses, microgels are subjected to shear, deformation, and compression forces or a combination of them, leading to variations in their rheological properties. This review article mainly refers to the rheology of microgels, from the hard sphere versus soft particles’ model. It clearly describes the scaling theories and fractal structure formation, in particular, the Shih et al. and Wu and Morbidelli models as a tool to determine the interactions among microgel particles and, thus, the viscoelastic properties. Additionally, the most recent advances on the characterization of microgels’ single-particle interactions are also described. The review starts with the definition of microgels, and a brief introduction addresses the preparation and applications of microgels and hybrid microgels.

Computation of Structure and Electrical Resistivity of Liquid Na-Rb Alloys

The structure and electrical resistivity of Na1-xRbx binary alloys (where x = 0, 0.1, 0.2,…,1) are computed using Percus-Yevick (PY) equation, hard-sphere model and Faber-Ziman formula respectively. The partial structure factors and total structure factor are computed using hard-sphere model for Na1-xRbx. In the calculation of resistivity using Faber-Ziman formula, we have employed Ashcroft empty-core pseudo-potential and Hartree dielectric screening. Calculated values of resistivity are compared with the experimental results and other theoretical values reported in literature. It is found that the electrical resistivity calculated using Faber-Ziman formula for binary alloy Na1-xRbx is in good agreement with the values reported experimentally.

Influence of Low Molecular Weight Salts on the Viscosity of Aqueous-Buffer Bovine Serum Albumin Solutions.

Pharmaceutical design of protein formulations aims at maximum efficiency (protein concentration) and minimum viscosity. Therefore, it is important to know the nature of protein-protein interactions and their influence on viscosity. In this work, we investigated the dependence of the viscosity of BSA in an aqueous 20 mM acetate buffer at pH = 4.3 on protein concentration and on temperature (5–45 °C). The viscosity of the solution increased with protein concentration and was 230% higher than the viscosity of the protein-free formulation at 160 mg/mL. The viscosity decreased by almost 60% in the temperature range from 5 to 45 °C. The agreement of the modified Arrhenius theory with experiment was quantitative, whereas a hard-sphere model provided only a qualitative description of the experimental results. We also investigated the viscosity of a 100 mg/mL BSA solution as a function of the concentration of added low molecular weight salts (LiCl, NaCl, KCl, RbCl, CsCl, NaBr, NaI) in the range of salt concentrations up to 1.75 mol/L. In addition, the particle size and zeta potential of BSA-salt mixtures were determined for solutions containing 0.5 mol/L salt. The trends with respect to the different anions followed a direct Hofmeister series (Cl− > Br− > I−), whereas for cations in the case of viscosity the indirect Hofmeister series was observed (Li+ > Na+ > K+ > Rb+ > Cs+), but the values of particle sizes and zeta potential did not show cation-specific effects. Since the protein is positively charged at pH = 4.3, anions are more attracted to the protein surface and shield its charge, while the interaction with cations is less pronounced. We hypothesize that salt surface charge shielding reduces protein colloidal stability and promotes protein aggregate formation.

Viscosity to entropy density ratio ($\\eta$/s) in nanoliquid

ABSTRACT We present the coefficient of viscosity (), entropy (S) and viscosity to entropy density (s) ratio () for aqueous silver nanoparticle (AgNP) solution at temperatures T = 273–300 K performing experiments and examining the same with discrete dipole approximation (DDA) simulation. The experimental UV-Visible dipole extinction spectra of the nanoliquid, matched with simulations, explore cluster morphologies. The latter is used for the calculation of (cluster volume fraction ~ 4–10%; NP, cluster radii 8–15 nm and 35–55 nm, respectively). In addition, dimer (AgNP-AgNP) formation free energy and S are explored at those T’s. We determine ratio exploiting nanoparticle behaviour. The value of is found lower than that of water and similar to strongly correlated liquid He4, owing to higher S for NP agglomeration. Our results of , S and are also corroborated from hard sphere model calculation. This, to the best of our knowledge, is the first attempt to determine in NP.

Correction to: Viscosities of Liquid Refrigerants from a Rough Hard-Sphere Theory-Based Semi-Empirical Model

Correction to: Viscosities of Liquid Refrigerants from a Rough Hard-Sphere Theory-Based Semi-Empirical Model

Mean scattering angle method for direct simulation Monte Carlo.

In order to predict the postcollision velocities in the binary collision, one needs the deflection angle given by the solution of the trajectory equation of classical mechanics. In the direct simulation Monte Carlo, it has been conventional to assume that the scattering is isotropic taking the hard sphere scattering law (the variable hard sphere model). Because the simulation carries out the ensemble average, and thus the collisional deflections should be averaged at the end, it is proposed to use the preaveraged deflection angle for each collision. This is a representative single deflection angle simulation. The present work postulates a method to estimate the mean deflection angles for arbitrary force models considering the differential cross section formula and the trajectory equation. For hard spheres, the representative single deflection simulation of normal shock waves recovers the conventional computations within 3%. For Maxwell molecules, the conventional simulation in which the isotropic scattering law is taken can exactly be reproduced by the single deflection when the representative angle is adjusted to the mean deflection angle together with the reference diameter obtained in the present method. It has been observed that the Maxwell-molecule-representative for the single angle simulation reproduces the conventional computations of any isotropic scattering models including hard spheres.

Density and molar volumes of liquid alloys of iron with C, B, Si, P, Cu, Al, Ni, Cr and Mn

The paper discusses density and molar volume of liquid alloys of iron with C, B, Si, P, Cu, Al, Ni, Cr and Mn. Liquid alloys of iron with other metals are considered as substitutional solutions using the hard-sphere model. Deviations of molar volumes of Fe-Cu and Fe-Al alloys from the ideal solutions were analysed using relationship between excess volume and entropy. Alloys of iron with Ni, Cr and Mn are close to the ideal solutions. Calculated volumes are in agreement with experimental data. Alloys of Fe with C, B, Si and P are considered as interstitial solutions using P. Gaskell�s model developed for amorphous alloys of transition metals with metalloids. Calculated partial molar volumes of C, B, Si and P in dilute binary solutions at 1823 K are (cm3/mol): 1.59, 3.37, 7.06 and 6.26 respectively. The model correctly describes the liquid alloys of iron with metalloids as interstitial solutions.

Планарные сверхструктурные дефекты в сплавах сверхструктуры L10

Planar superstructural defects have a great influence on the mechanical, functional properties of binary ordered alloys of the L10 superstructure based on the fcc lattice, but there is no complete analysis of their structure and energy in the literature. For the L10 superstructure alloys of the stoichiometric composition AB, the paper gives the expressions for calculating the sublimation energy and the energy of a planar superstructural defect in the model of hard coordination spheres and pair interatomic interactions. The crystal lattice tetragonality was not taken into account. The authors presented the ordered alloy structure as a union of four monoatomic simple cubic lattices, two of which are occupied by A atoms, and the other two by B atoms. This approach allows calculating the sublimation energy required for crystal evaporation. The first eight coordination spheres were taken into account in the work. The paper shows an algorithm for determining all possible geometrically different representations of the L10 superstructure with the same sublimation energy, gives an expression for finding the planes of occurrence of all possible conservative antiphase boundaries. The study identified that the conservative and nonconservative antiphase boundaries, as well as conservative and nonconservative boundaries of C-domains are observed in the binary ordered alloys of the L10 superstructure based on the fcc lattice. The algorithms described in this work make it possible to carry out a crystal-geometric analysis of planar defects in both binary and multicomponent ordered alloys with various superstructures.

On the Relationship Between Stickiness in DMRT Theory and Physical Parameters of Snowpack: Theoretical Formulation and Experimental Validation With SNOWPACK Snow Model and X-Band SAR Data

This study aims at relating the stickiness parameter (&#x03C4;) of the Dense Media Radiative Transfer theory integrated with Sticky Hard Sphere (SHS) model (DMRT-QMS), to the physical parameters of the layered snowpack. A relationship has been derived to express &#x03C4;, which modulates the attractive contact force between ice spheres, as a function of ice volume fraction (&#x03D5;) and coordination number (<i>n_c</i>). Since &#x03C4; is not a measurable parameter, this is a step forward with respect to what is commonly made in literature, where &#x03C4; is assumed as an arbitrary parameter, generally ranging between 0.1 and 0.3, to fit simulated backscattering data with those measured. As a first validation, DMRT-QMS was integrated with SNOWPACK model to simulate backscattering at X band (9.6 GHz) driven by nivo-meteorological data acquired on a test area located in Monti Alti di Ornella, Italy. The simulations were compared with Synthetic Aperture Radar COSMO-SkyMed (CSK) satellite observations. The results show a significant agreement (R²=0.68), although for a limited dataset of eight points in a unique winter season.

A Review on Contact and Collision Methods for Multi-Body Hydrodynamic Problems in Complex Flows

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the combustion process, to aerosol deposition in spray medication, along with many others. Due to their strongly nonlinear and multiscale nature, the above complex phenomena still raise a very steep challenge to the most computational methods. In this review, we provide comprehensive coverage of multibody hydrodynamic (MBH) problems focusing on particulate suspensions in complex fluidic systems that have been simulated using hybrid Eulerian-Lagrangian particulate flow models. Among these hybrid models, the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) provides mathematically simple and computationally-efficient algorithms for solid-fluid hydrodynamic interactions in MBH simulations. This paper elaborates on the mathematical framework, applicability, and limitations of various 'simple to complex' representations of close-contact interparticle interactions and collision methods, including short-range inter-particle and particle-wall steric interactions, spring and lubrication forces, normal and oblique collisions, and mesoscale molecular models for deformable particle collisions based on hard-sphere and soft-sphere models in MBH models to simulate settling or flow of nonuniform particles of different geometric shapes and sizes in diverse fluidic systems.

Estimation of the nucleation barrier in a multicomponent system with intermolecular potential.

The formation of a "critical nucleus" prior to phase change is a crucial step for new particle formation (NPF) in the atmosphere. However, the nucleation occurring below ∼1 nm is hard to observe directly. As an effective alternative, theoretical nucleation models have been widely studied. An energy barrier is involved in the nucleation and is the fundamental factor for the nucleation model. Typical atmospheric nucleation agents such as H2SO4, H2O and NH3 are dipole molecules, whose intermolecular interactions are non-ignorable. Herein, a dipole-dipole potential model is adopted to determine the interaction between molecules instead of the traditional hard sphere model, and graph theory is used to describe the structure of the cluster and the cluster-molecule interaction. The nucleation barriers (ΔEb) of H2SO4-H2SO4, H2SO4-H2O, H2SO4-NH3 and H2SO4-H2O-NH3 are derived and compared to each other. In the presence of H2O and NH3, the ΔEb value is decreased by 17-28% compared to that in the pure H2SO4 nucleation system. NH3 is identified to be a key factor for ternary nucleation based on an orthogonal test. Atmospheric concentrations of H2SO4, H2O and NH3 are considered to investigate the influence of [H2O + NH3]/[H2SO4] on ΔEb and the related effective collision coefficient (α). The α value in the ternary nucleation system reaches the range of (2.5-25) × 10-5, which is 3-4 orders of magnitude higher than that in the pure H2SO4 system. Due to a significant enhancement of α, NH3 and H2O should be focused on in future aerosol particle estimation and control.

Boundary layer effects on ionic flows via Poisson-Nernst-Planck systems with nonuniform ion sizes

&lt;p style='text-indent:20px;'&gt;We study a one-dimensional Poisson-Nernst-Planck model with two oppositely charged particles, zero permanent charges and nonuniform finite ion sizes through a local hard-sphere model. Of particular interest is to examine the boundary layer effects on ionic flows systematically in terms of individual fluxes, the total flow rate of charges (current-voltage relations) and the total flow rate of matter. This is particularly important because boundary layers of charge are particularly likely to create artifacts over long distances, and this could dramatically affect the behavior of ionic flows. Several critical potentials are identified, which play unique and critical roles in examining the dynamics of ionic flows. Some can be estimated experimentally. Numerical simulations are performed for a better understanding and further illustrating our analytical results. We believe the analysis can provide complementary information of the qualitative properties of ionic flows and help one better understand the mechanism of ionic flow through membrane channels.&lt;/p&gt;

Reaction Rate Theory-Based Mathematical Approximation for the Amount of Time it Takes For Cellular Respiration to Occur

Abstract The venerable process of cellular respiration is essential for cells to produce energy from glucose molecules, in order to carry out cellular work. The process is responsible for producing molecules of ATP, a molecule which is thermodynamically coupled with other biochemical and biophysical processes in order to provide energy for such processes to occur. While the process of cellular respiration is essential to biology, one cycle of the process occurs only in a matter of milliseconds, and so, it would be impractical to measure the time it takes for the process to occur through conventional means. Therefore, using concepts from reaction rate theory, particularly Marcus Theory of electron transfer, Michaelis-Menten kinetics for enzymatic catalysis, and the hard-sphere model of collision theory, I formulate and propose a mathematical approximation for the amount of time it takes for cellular respiration to occur. Through this heuristic approach, quantitatively knowing the amount of time it takes for one cycle of cellular respiration to occur could potentially have future applications in biological research.

Causes of the Unsolved Glassy State Problem: Incompleteness of the Atomic-Molecular Hard-Sphere Model

Causes of the Unsolved Glassy State Problem: Incompleteness of the Atomic-Molecular Hard-Sphere Model

Prediction of Temperature Dependence of Impurity Diffusion Coefficients in Liquid Metal Based on a Hard-Sphere Model from Measurements Using Shear Cell Technique and Stable Density Layering

Prediction of Temperature Dependence of Impurity Diffusion Coefficients in Liquid Metal Based on a Hard-Sphere Model from Measurements Using Shear Cell Technique and Stable Density Layering