Percus Yevick Research Articles

Approximating the nonlinear density dependence of electron transport coefficients and scattering rates across the gas–liquid interface

This study reviews the neutral density dependence of electron transport in gases and liquids and develops a method to determine the nonlinear medium density dependence of electron transport coefficients and scattering rates required for modeling transport in the vicinity of gas–liquid interfaces. The method has its foundations in Blanc’s law for gas-mixtures and adapts the theory of Garland et al (2017 Plasma Sources Sci. Technol. 26) to extract electron transport data across the gas–liquid transition region using known data from the gas and liquid phases only. The method is systematically benchmarked against multi-term Boltzmann equation solutions for Percus–Yevick model liquids. Application to atomic liquids highlights the utility and accuracy of the derived method.

PRISM Theory Study of Amphiphilic Block Copolymer Solutions with Varying Copolymer Sequence and Composition

We present a comparison of Polymer Reference Interaction Site Model (PRISM) theory and molecular dynamics (MD) simulations for studying amphiphilic block copolymers in solution. We use a generic coarse-grained model to represent amphiphilic A–B block copolymers in implicit solvent with the solvophobicity of the B segments captured using effective B–B pairwise attraction modeled using the Lennard-Jones potential. We study the assembly of the amphiphilic A–B block copolymer as a function of solvophobicity for varying copolymer sequences (diblock and triblock) and composition (solvophobic-rich or solvophilic-rich). The PRISM theory equation along with the atomic Percus–Yevick closure is solved to obtain the intermolecular pair correlations in real space, g(r), and structure factors in Fourier space, S(k), for block copolymer solutions at increasing values of solvophobicity. The real-space intermolecular pair correlation functions and structure factors from PRISM theory and from MD simulations are compared di...

Correction of Kovalenko-Hirata closure in Ornstein-Zernike integral equation theory for Lennard-Jones fluids

We have studied the accuracy of Ornstein-Zernike (OZ) integral equation theory in terms of the solvation free energy (SFE) for a two-component Lennard-Jones system at the infinite dilution limit. We have employed the hypernetted chain (HNC), Kovalenko-Hirata (KH), Kobryn-Gusarov-Kovalenko (KGK), and Percus-Yevick (PY) closure equations. Further, we have extended the Verlet-modified (VM) closure to the two-component system to examine the accuracy of this method in terms of the SFE. Molecular dynamics simulations were employed to compare the results with the above mentioned OZ theories. The HNC and KH approximations significantly overestimate the SFE, whereas the PY approximation tends to underestimate it. The overestimation of the SFE by the KGK approximation becomes significant when the solvent density is relatively high. In contrast, the VM approximation is found to be rather accurate at all studied conditions. An analysis of the integrand for the SFE reveals that, to improve the SFE, the first rising (FR) region in the radial distribution function (RDF) must be corrected. We have also tested the sigma-enlarging-bridge (SEB) function that we proposed previously [T. Miyata and Y. Ebato, J. Mol. Liq. 217 (2016) 75] for the correction of the FR region of the RDF. In this study, we applied the SEB function to both HNC-type and KH-type closures and found that these combinations (SEB-HNC and SEB-KH) improve the SFE significantly.

Reformulation of time-convolutionless mode-coupling theory near the glass transition

The time-convolutionless mode-coupling theory (TMCT) recently proposed is reformulated under the condition that one of two approximations, which have been used to formulate the original TMCT in addition to the MCT approximations done on a derivation of nonlinear memory function in terms of the intermediate-scattering function, is not employed because it causes unphysical results for intermediate times. The improved TMCT equation is then derived consistently under another approximation. It is first checked that the ergodic to non-ergodic transition obtained by a new equation is exactly the same as that obtained by an old one because the long-time dynamics of both equations coincides with each other. However, it is emphasized that a difference between them appears in the intermediate-time dynamics of physical quantities. Such a difference is explored numerically in the dynamics of a non-Gaussian parameter by employing the Percus–Yevick static structure factor to calculate the nonlinear memory function.

Structure and Dynamics of Bimodal Colloidal Dispersions in a Low-Molecular-Weight Polymer Solution.

We present an experimental study of the structural and dynamical properties of bimodal, micrometer-sized colloidal dispersions (size ratio ≈ 2) in an aqueous solution of low-molecular-weight polymer (polyethylene glycol 2000) using synchrotron ultra-small angle X-ray scattering (USAXS) and USAXS-based X-ray photon correlation spectroscopy. We fixed the volume fraction of the large particles at 5% and systematically increased the volume fraction of the small particles from 0 to 5% to evaluate their effects on the structure and dynamics. The bimodal dispersions were homogenous through the investigated parameter space. We found that the partial structure factors can be satisfactorily retrieved for the bimodal colloidal dispersions using a Percus-Yevick hard-sphere potential when the size distributions of the particles were taken into account. We also found that the partial structure factor between the large particles did not exhibit a significant variation with increasing volume fraction of the small particles, whereas the isothermal compressibility of the binary mixture was found to decrease with increasing volume fraction of the small particles. The dynamics of single-component large-particle dispersion obey the principles of de Gennes narrowing, where the wave vector dependence of the interparticle diffusion coefficient is inversely proportional to the interparticle structure factor. The dynamics of the bimodal dispersions demonstrate a strong dependence on the fraction of small particles. We also made a comparison between the experimental effective dynamic viscosity of the bimodal dispersion with the theoretical predictions, which suggest that the complex mutual interactions between the large and small particles have a strong effect on the dynamic behaviors of bimodal dispersions.

A comparison of the correlation functions of the Lennard–Jones fluid for the first-order Duh–Haymet–Henderson closure with molecular simulations

ABSTRACTFirst-order integral equation theories are much more computationally efficient than second-order theories, but the latter are usually much more accurate for computing correlation functions of fluids. We here test the accuracy of the Duh–Haymet–Henderson (DHH) integral equation theory by comparing radial distribution, cavity correlation and bridge functions computed from DHH, first-order and second-order Percus–Yevick theories, with molecular dynamics calculations for the Lennard–Jones fluid. We find that the DHH theory is almost as accurate as the second-order Percus–Yevick theory at liquid-like densities for both sub- and super-critical temperatures. However, the accuracy of the DHH theory decreases with decreasing density. The correlation functions computed from DHH theory are very similar to those computed from first-order Percus–Yevick theory at low densities. The cavity correlation and bridge functions at low densities computed from these two theories are qualitatively different from results computed from molecular simulations. However, the radial distribution functions computed from all three methods are essentially identical at low densities, indicating that errors in the cavity correlation and bridge functions at low densities cancel out to give high accuracy in the radial distribution function.

New SAFT-VR equation of state based on Morse potential

Abstract In this work, a new statistical associating fluid theory with variable range (SAFT-VR) equation of state (EOS) for the Morse fluids has been developed. Monte Carlo (MC) simulations have been performed to determine the first and second order perturbative contributions of Barker and Henderson (BH) perturbation theory over wide range of density, temperature and potential ranges. In addition to perturbative terms, pressure and internal energy of Morse fluid have been simulated and compared with theoretical results. In development of new EOS, an exact analytic solution of the Percus-Yevick (PY) integral equation for hard sphere radial distribution function (RDF) has been implemented into calculation of the first and second terms of BH theory. Our results showed that there are good agreement between MC simulation data and analytical solution of hard sphere RDF. In the case of BH first order term, excellent agreement was obtained. It is found that, the new EOS is able to predict the perturbative Helmholtz free energy, pressure and residual internal energy of Morse fluids over wide range of thermodynamic conditions. Finally, the new EOS has been utilized to correlate vapor pressure and saturated liquid density of pure components. Obtained results in this work prove that considering Morse as potential function can lead us to achieve an accurate SAFT-based EOS.

A multi-term solution of the space–time Boltzmann equation for electrons in gases and liquids

In this study we have developed a full multi-term space–time solution of Boltzmann’s equation for electron transport in gases and liquids. A Green’s function formalism is used that enables flexible adaptation to various experimental systems. The spatio-temporal evolution of electrons in liquids in the non-hydrodynamic regime is benchmarked for a model Percus–Yevick (PY) liquid against an independent Monte Carlo simulation, and then applied to liquid argon. The temporal evolution of Franck–Hertz oscillations in configuration and energy space are observed for the model liquid with large differences apparent when compared to the dilute gas case, for both the velocity distribution function components and the transport quantities. The packing density in the PY liquid is shown to influence both the magnitude and wavelength of Franck–Hertz oscillations of the steady-state Townsend (SST) simulation. Transport properties are calculated from the non-hydrodynamic theory in the long time limit under SST conditions which are benchmarked against hydrodynamic transport coefficients. Finally, the spatio-temporal relaxation of low-energy electrons in liquid argon was investigated, with striking differences evident in the spatio-temporal development of the velocity distribution function components between the uncorrelated gas and true liquid approximations, due largely to the presence of a Ramsauer minimum in the former and not in the latter.

Modeling and optimizing the performance of plasmonic solar cells using effective medium theory

In this paper, the effects of random Ag nanoparticle used within the active layer of Si based thin film solar cell are investigated. To avoid the complexity of taking into account all random nanoparticles, an effective dielectric function for random Ag nanoparticles and Si nanocomposites is used that is the Maxwell–Garnet theory along with Percus–Yevick correction term. Considering the energy reservation law and using the effective dielectric function, the absorbance of the active layer, therefore, the solar cell's maximum short current density is obtained. Also, the maximum external quantum efficiency of the solar cell is obtained using the optimum values for the radius and filling fraction of Ag nanoparticles.

Multiple and dependent scattering by densely packed discrete spheres: Comparison of radiative transfer and Maxwell theory

The radiative transfer equation (RTE) has been widely used to deal with multiple scattering of light by sparsely and randomly distributed discrete particles. However, for densely packed particles, the RTE becomes questionable due to strong dependent scattering effects. This paper examines the accuracy of RTE by comparing with the exact electromagnetic theory. For an imaginary spherical volume filled with randomly distributed, densely packed spheres, the RTE is solved by the Monte Carlo method combined with the Percus–Yevick hard model to consider the dependent scattering effect, while the electromagnetic calculation is based on the multi-sphere superposition T-matrix method. The Mueller matrix elements of the system with different size parameters and volume fractions of spheres are obtained using both methods. The results verify that the RTE fails to deal with the systems with a high-volume fraction due to the dependent scattering effects. Apart from the effects of forward interference scattering and coherent backscattering, the Percus–Yevick hard sphere model shows good accuracy in accounting for the far-field interference effects for medium or smaller size parameters (up to 6.964 in this study). For densely packed discrete spheres with large size parameters (equals 13.928 in this study), the improvement of dependent scattering correction tends to deteriorate. The observations indicate that caution must be taken when using RTE in dealing with the radiative transfer in dense discrete random media even though the dependent scattering correction is applied.

Density functional theory of freezing of a system of highly elongated ellipsoidal oligomer solutions

ABSTRACTWe have used the density functional theory of freezing to study the liquid crystalline phase behavior of a system of highly elongated ellipsoidal conjugated oligomers dispersed in three different solvents namely chloroform, toluene and their equimolar mixture. The molecules are assumed to interact via solvent-implicit coarse-grained Gay–Berne potential. Pair correlation functions needed as input in the density functional theory have been calculated using the Percus–Yevick (PY) integral equation theory. Considering the isotropic and nematic phases, we have calculated the isotropic–nematic phase transition parameters and presented the temperature–density and pressure–temperature phase diagrams. Different solvent conditions are found not only to affect the transition parameters but also determine the capability of oligomers to form nematic phase in various thermodynamic conditions. In principle, our results are verifiable through computer simulations.

Size effects of solvent molecules on the phase behavior and effective interaction of colloidal systems with the bridging attraction

There has been much recent research interest towards understanding the phase behavior of colloidal systems interacting with a bridging attraction, where the small solvent particles and large solute colloidal particles can be reversibly associated with each other. These systems show interesting phase behavior compared to the more widely studied depletion attraction systems. Here, we use Baxter’s two-component sticky hard sphere model with a Percus–Yevick closure to solve the Ornstein–Zernike equation and study the size effect on colloidal systems with bridging attractions. The spinodal decomposition regions, percolation transition boundaries and binodal regions are systematically investigated as a function of the relative size of the small solvent and large solute particles as well as the attraction strength between the small and large particles. In the phase space determined by the concentrations of small and large particles, the spinodal and binodal regions form isolated islands. The locations and shapes of the spinodal and binodal regions sensitively depend on the relative size of the small and large particles and the attraction strength between them. The percolation region shrinks by decreasing the size ratio, while the binodal region slightly expands with the decrease of the size ratio. Our results are very important in understanding the phase behavior for a bridging attraction colloidal system, a model system that provides insight into oppositely charged colloidal systems, protein phase behavior, and colloidal gelation mechanisms.

A thermodynamic self-consistent theory of asymmetric hard-core Yukawa mixtures

We perform structural and thermodynamic calculations in the framework of the modified hypernetted chain (MHNC) integral equation closure to the Ornstein–Zernike equation for binary mixtures of size-different particles interacting with hard-core Yukawa pair potentials. We use the Percus–Yevick (PY) bridge functions of a binary mixture of hard-sphere (HSM) particles. The hard-sphere diameters of the PY bridge functions of the HSM system are adjusted so to achieve thermodynamic consistency between the virial and compressibility equations of state. We show the benefit of thermodynamic consistency by comparing the MHNC results with the available computer simulation data reported in the literature, and we demonstrate that the self-consistent thermodynamic theory provides a better reproduction of the simulation data over other microscopic theories.

Fabrication and Structural Characterization of Module-Assembled Amphiphilic Conetwork Gels

Structural analysis of inhomogeneity-free poly(ethylene glycol)–poly(dimethylsiloxane) (PEG–PDMS) amphiphilic conetwork gels has been performed by the complementary use of small-angle X-ray and neutron scattering. Because of the hydrophobicity of PDMS units, the PEG–PDMS gels exhibit a microphase-separated structure in water. Depending on the volume fraction of PDMS, the microphase-separated structure varies from core–shell to lamellar. The obtained X-ray and neutron scattering profiles are reproduced well using a core–shell model together with a Percus–Yevick structure factor when the volume fraction of PDMS is small. The domain size is much larger than the size of individual PEG and PDMS unit, and this is explained using the theory of block copolymers. Reflecting the homogeneous dispersion conditions in the as-prepared state, scattering peaks are observed even at a very low PDMS volume fraction (0.2%). When the volume fraction of PDMS is large, the microphase-separated structure is lamellar and is demon...

Accuracy of temperature-derivative of radial distribution function calculated under approximations in Ornstein-Zernike theory for one-component Lennard-Jones fluid

The accuracy of the temperature derivative of radial distribution function obtained under hypernetted chain (HNC), Kovalenko-Hirata (KH), Percus-Yevick (PY) and Verlet-modified (VM) closure approximations is examined for one-component Lennard-Jones fluid. As relevant thermodynamic quantities, constant-volume heat capacity and thermal pressure coefficient are investigated in terms of their accuracy under the above four approximations. It is found that HNC and KH closures overestimate these quantities, whereas PY closure tends to underestimate them. VM closure predicts rather accurately the quantities. A significant cancellation is observed along the integration for the above quantities under HNC and KH closures, especially at high density state.

Microwave Scattering and Medium Characterization for Terrestrial Snow With QCA–Mie and Bicontinuous Models: Comparison Studies

Comparison studies are made between the QCA–Mie model and the bicontinuous model in microwave scattering from terrestrial snow. Both the scattering properties and the medium characterization are compared. For QCA, we use the multisize and the sticky particle models. For the bicontinuous model, we use the probability distribution function for the wavenumber. We compare the scattering rate and the angular distribution of scattering using the mean cosine of scattering and show that the two models have similar properties. In medium characterization, we use the pair distribution functions used in QCA to derive the correlation functions. We show that both the Percus–Yevick pair functions and the bicontinuous model have tails in the correlation functions that are distinctly different from the traditional exponential correlation functions. The methodologies of using ground measurements of grain size distributions and correlation functions to obtain model parameters are addressed.

Cavity correlation and bridge functions at high density and near the critical point: a test of second-order Percus–Yevick theory

ABSTRACTCavity correlation functions, pair correlation functions, and bridge functions for the Lennard-Jones fluid are calculated from first Percus–Yevick (PY) theory and second-order Percus– Yevick (PY2) theory, molecular dynamics, and grand canonical Monte Carlo techniques. We find that the PY2 theory is significantly more accurate than the PY theory, especially at high density and near the critical point. The pair correlation function near the critical point has the expected slowly decaying long-range behaviour. However, we do not observe any long-range behaviour in the bridge function for the state points near the critical point we have simulated. However, we do note that the bridge function, which is usually negative near r = 0, becomes positive as r → 0. This behaviour is seen for the bridge functions computed from both PY2 and molecular dynamics, but not from PY.

Phase behaviour and correlations of parallel hard squares: from highly confined to bulk systems

We study a fluid of two-dimensional parallel hard squares in bulk and under confinement in channels, with the aim of evaluating the performance of fundamental-measure theory (FMT). To this purpose, we first analyse the phase behaviour of the bulk system using FMT and Percus–Yevick (PY) theory, and compare the results with molecular dynamics and Monte Carlo simulations. In a second step, we study the confined system and check the results against those obtained from the transfer matrix method and from our own Monte Carlo simulations. Squares are confined to channels with parallel walls at angles of 0° or 45° relative to the diagonals of the parallel hard squares, respectively, which allows for an assessment of the effect of the external-potential symmetry on the fluid structural properties. In general FMT overestimates bulk correlations, predicting the existence of a columnar phase (absent in simulations) prior to crystallization. The equation of state predicted by FMT compares well with simulations, although the PY approach with the virial route is better in some range of packing fractions. The FMT is highly accurate for the structure and correlations of the confined fluid due to the dimensional crossover property fulfilled by the theory. Both density profiles and equations of state of the confined system are accurately predicted by the theory. The highly non-uniform pair correlations inside the channel are also very well described by FMT.

Long-range weight functions in fundamental measure theory of the non-uniform hard-sphere fluid

We introduce long-range weight functions to the framework of fundamental measure theory (FMT) of the non-uniform, single-component hard-sphere fluid. While the range of the usual weight functions is equal to the hard-sphere radius R, the modified weight functions have range 3R. Based on the augmented FMT, we calculate the radial distribution function g(r) up to second order in the density within Percus’ test particle theory. Consistency of the compressibility and virial routes on this level allows us to determine the free parameter γ of the theory. As a side result, we obtain a value for the fourth virial coefficient B4 which deviates by only 0.01% from the exact result. The augmented FMT is tested for the dense fluid by comparing results for g(r) calculated via the test particle route to existing results from molecular dynamics simulations. The agreement at large distances (r > 6R) is significantly improved when the FMT with long-range weight functions is used. In order to improve agreement close to contact (r = 2R) we construct a free energy which is based on the accurate Carnahan–Starling equation of state, rather than the Percus–Yevick compressibility equation underlying standard FMT.

Time domain finite element estimates of dynamic stiffness of viscoelastic composites with stiff spherical inclusions

A weighted residual time domain unstructured mesh finite element approach was used to obtain numerical estimates for the dynamic stiffness of medium and high stiffness contrast composites consisting of viscoelastic epoxy matrix filled with stiff spherical inclusions. Both random and regular microstructure composites were studied. It was shown that over the broad temperature and inclusion fraction ranges studied, the generalized self-consistent model ( Christensen and Lo, 1979 ) provided accurate predictions for the effective dynamic stiffness of random composites obeying classical Percus–Yevick hard sphere statistics. Assuming sphere flocculation, we have studied the role of microstructural effects and found that upon increasing stiffness contrast, they become progressively more important for both the effective storage and loss moduli. As a consequence, for the reliable predictions of effective stiffness of high contrast composites with rubber like matrices, one should necessarily use homogenization models accounting not only for the inclusion concentration but also for the finer microstructural details. However, it was also found that for such high stiffness contrast viscoelastic composites, the ratio of their effective storage and loss shear moduli (the damping factor) remains essentially unchanged as compared to that of pure unfilled matrix so it is the invariability of the damping factor that can be viewed as a special signature of underlying micromechanical mechanism of reinforcement.