Virial Pressure Research Articles

The variation of the temperature of maximum density of non-polar solutes in water: insights from the pressure change in a constant volume solution process

The effects of non-polar solutes on the temperature of maximum density (T MD) of water are revisited by means of a molecular dynamics study of TIP4P/2005 water and two examples of spherically symmetric non-polar solutes modelled by same size single Lennard-Jones sites, with weak and strong solute–water dispersive interactions. We have adopted a two-stage strategy to model the solution process at constant pressure to reduce the analysis to the description of the pressure variation in the solution process at constant volume. To this end, the Reaction Field treatment of the Coulombic forces was used so as to be able to decompose the different molecular components to the virial pressure and their spatial variation in terms of the distance to the solute molecule. In this way, we have been able to separate which factors induce the increase of water’s T MD observed for weakly interacting non-polar solutes and the decrease that occurs when the solute is strongly interacting.

Pressure of Coulomb systems with volume-dependent long-range potentials

In this work, we consider the pressure of Coulomb systems, in which particles interact via a volume-dependent potential (in particular, the Ewald potential and its angular-averaged version (Demyanov and Levashov 2022 J. Phys. A: Math. Theor. 55 385202)). We confirm that the expression for the virial pressure should be corrected in this case. We show that the corrected virial pressure coincides with the formula obtained by differentiation of free energy if the potential energy is a homogeneous function of particle coordinates and a cell length. As a consequence, we find out that the expression for the pressure in the recent paper by Liang et al (2022 J. Chem. Phys. 157 144102) is incorrect.

Theoretical study of interactions and structural and thermodynamical properties of nanopores within bilayer-membranes: Experimental inspiration

In this work, we consider a bilayer-membrane which is crossed by an assembly of (parallel) nanopores formed generally by peptide molecules. The deformations and thermal fluctuations of this bilayer-membrane give rise to repulsive effective pair-interactions between the parallel nanopores. Some recent experiment has revealed that the repulsive effective pair-potentials, as function of distance between adjacent nanopores, are of Born-Mayer type (soft-potential). Beside the repulsive forces, the nanopores mutually attract through the van der Waals forces. Our main goal is an extensive theoretical study of the structural and thermodynamical properties of the nanopores we consider as a dense gas system. When the bath temperature is fixed to some value (room temperature), the only remaining pertinent parameter of discussion is the nanopore-density, denoted as n, or equivalently, the peptide-molar-fraction, P/L. First, we propose a closer expression of the effective pair-potentials taking into account recent experimental measurements dealt with many lipid-bilayers (Gramicidin/DLPC, Gramicidin/C12EO5...). Second, we classify these effective pair-potentials in terms of the nanopore-density, and in particular, we show the existence of a typical nanopore-density, nc, below which the total pair-potential exhibits an energy-barrier which prevents the coagulation of the nanopores. When the nanopore-density reaches threshold, nc, the energy-barrier ceases to exist, and beyond this threshold, one assists to a complete coagulation of the nanopores. Third, we determine an exact theoretical expression of the structure factor of the nanopores, as a function of the wave-vector, within the framework of Random Phase Approximation, using a hard-disk model as a reference system. Finally, from the obtained structure factor, we extract the thermodynamical properties of the integrated nanopores, such as the virial pressure (state of equation), the isothermal compressibility and the chemical potential which are nanopore-density dependent.

Phase behavior of active and passive dumbbells.

We report phase separation in a mixture of "hot" and "cold" three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of "hot" and "cold" dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity χ of the system. From constant density simulations of symmetric dumbbells, we observe that the "hot" and "cold" dumbbells phase separate at higher activity ratio (χ>5.80) compared to that of a mixture of hot and cold Lennard-Jones monomers (χ>3.44). We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.

Global Existence of Weak Solutions for Compresssible Navier—Stokes—Fourier Equations with the Truncated Virial Pressure Law

Abstract This paper concerns the existence of global weak solutions á la Leray for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.

Force density functional theory in- and out-of-equilibrium.

When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description of inhomogeneous (classical) many-body systems, based explicitly on the two-body correlation functions. By consideration of local Noether-invariance against spatial distortion of the system we demonstrate the fundamental status of the Yvon-Born-Green (YBG) equationas a local force-balance within the fluid. Using the inhomogeneous Ornstein-Zernike equationwe show that the two-body correlations are density functionals and, thus, that the average interparticle force entering the YBG equationis also a functional of the one-body density. The force-based theory we develop provides an alternative to standard density functional theory for the study of inhomogeneous systems both in- and out-of-equilibrium. We compare force-based density profiles to the results of the standard potential-based (dynamical) density functional theory. In-equilibrium, we confirm both analytically and numerically that the standard approach yields profiles that are consistent with the compressibility pressure, whereas the force-density functional gives profiles consistent with the virial pressure. For both approaches we explicitly prove the hard-wall contact theorem that connects the value of the density profile at the hard-wall with the bulk pressure. The structure of the theory offers deep insights into the nature of correlation in dense and inhomogeneous systems.

The primitive model in classical density functional theory: beyond the standard mean-field approximation

The primitive model describes ions by point charges with an additional hard-core interaction. In classical density-functional theory (DFT) the mean-field electrostatic contribution can be obtained from the first order of a functional perturbation of the pair potential for an uncharged reference system of hard spheres. This mean-field electrostatic term particularly contributes at particle separations that are forbidden due to hard-core overlap. In this work we modify the mean-field contribution such that the pair potential is constant for distances smaller than the contact distance of the ions. We motivate our modification by the underlying splitting of the potential, which is similar to the splitting of the Weeks–Chandler–Andersen potential and leads to higher-order terms in the respective expansion of the functional around the reference system. The resulting formalism involves weighted densities similar to the ones found in fundamental measure theory. To test our modifications, we analyze and compare density profiles, direct and total correlation functions, and the thermodynamic consistency of the functional via a widely established sum rule and the virial pressure formula for our modified functional, for established functionals, and for data from computer simulations. We found that our modifications clearly show improvements compared to the standard mean-field functional, especially when predicting layering effects and direct correlation functions in high concentration scenarios; for the latter we also find improved consistency when calculated via different thermodynamic routes. In conclusion, we demonstrate how modifications toward higher order corrections beyond mean-field functionals can be made and how they perform, by this providing a basis for systematic future improvements in classical DFT for the description of electrostatic interactions.

Isothermal-isobaric algorithm to study the effects of rotational degrees of freedom-Benz water model

We have developed isothermal-isobaric algorithm for non-equilibrium Monte Carlo simulations. As first we have shown that the new method correctly predict density by comparing it to the density determined in canonical Monte Carlo simulations through the virial pressure. The new method was then used to study the effect of translational and rotational degrees of freedom on the structural and thermodynamic properties of the simple Mercedes-Benz water model. By holding one of the temperatures constant and varying the other one, we investigated how the position of the density maxima changes. We have observed that upon increase of rotational temperature the fluid become more Lennard-Jones like and the density maxima disappears.

The stress in a dispersion of mutually polarizable spheres.

Dispersions of dielectric and paramagnetic nanoparticles polarize in response to an external electric or magnetic field and can form chains or other ordered structures depending on the strength of the applied field. The mechanical properties of these materials are of interest for a variety of applications; however, computational studies in this area have so far been limited. In this work, we derive expressions for two important properties for dispersions of polarizable spherical particles with dipoles induced by a uniform external field-the isothermal stress tensor and the pressure. Numerical calculations of these quantities, evaluated using a spectrally accurate Ewald summation method, are validated using thermodynamic integration. We also compare the stress obtained using the mutual dipole model, which accounts for the mutual polarization of particles, to the stress expected from calculations using a fixed dipole model, which neglects mutual polarization. We find that as the conductivity of the particles increases relative to the surrounding medium, the fixed dipole model does not accurately describe the dipolar contribution to the stress. The thermodynamic pressure, calculated from the trace of the stress tensor, is compared to the virial expression for the pressure, which is simpler to calculate but inexact. We find that the virial pressure and the thermodynamic pressure differ, especially in suspensions with a high volume fraction of particles.

Inertial self-propelled particles.

We study how inertia affects the behavior of self-propelled particles moving through a viscous solvent by employing the underdamped version of the active Ornstein-Uhlenbeck model. We consider both potential-free and harmonically confined underdamped active particles and investigate how the single-particle trajectories change as the drag coefficient is varied. In both cases, we obtain the matrix of correlations between the position, velocity, and self-propulsion and the explicit form of the steady-state probability distribution function. Our results reveal the existence of marked equal-time correlations between velocity and active force in the non-equilibrium steady state. Inertia also affects the time-dependent properties of the active particles and leads to non-monotonic decay of the two-time correlation functions of particle positions and velocities. We also study how the virial pressure of particles confined to harmonic traps changes as one goes from the overdamped to the underdamped regime. Finally, the study of the correlations in the underdamped regime is extended to the case of a chain of active particles interacting via harmonic springs.

Properties of the circumgalactic medium in cosmic ray-dominated galaxy haloes

ABSTRACT We investigate the impact of cosmic rays (CRs) on the circumgalactic medium (CGM) in FIRE-2 simulations, for ultra-faint dwarf through Milky Way (MW)-mass haloes hosting star-forming (SF) galaxies. Our CR treatment includes injection by supernovae, anisotropic streaming and diffusion along magnetic field lines, and collisional and streaming losses, with constant parallel diffusivity $\kappa \sim 3\times 10^{29}\, \mathrm{cm^2\ s^{-1}}$ chosen to match γ-ray observations. With this, CRs become more important at larger halo masses and lower redshifts, and dominate the pressure in the CGM in MW-mass haloes at z ≲ 1–2. The gas in these ‘CR-dominated’ haloes differs significantly from runs without CRs: the gas is primarily cool (a few ${\sim}10^{4}\,$ K), and the cool phase is volume-filling and has a thermal pressure below that needed for virial or local thermal pressure balance. Ionization of the ‘low’ and ‘mid’ ions in this diffuse cool gas is dominated by photoionization, with O vi columns ${\gtrsim}10^{14.5}\, \mathrm{cm^{-2}}$ at distances ${\gtrsim}150\, \mathrm{kpc}$. CR and thermal gas pressure are locally anticorrelated, maintaining total pressure balance, and the CGM gas density profile is determined by the balance of CR pressure gradients and gravity. Neglecting CRs, the same haloes are primarily warm/hot ($T\gtrsim 10^{5}\,$K) with thermal pressure balancing gravity, collisional ionization dominates, O vi columns are lower and Ne viii higher, and the cool phase is confined to dense filaments in local thermal pressure equilibrium with the hot phase.

Virial theorem, boundary conditions, and pressure for massless Dirac electrons

The virial and the Hellmann–Feynman theorems for massless Dirac electrons in a solid are derived and analyzed using generalized continuity equations and scaling transformations. Boundary conditions imposed on the wave function in a finite sample are shown to break the Hermiticity of the Hamiltonian resulting in additional terms in the theorems in the forms of boundary integrals. The thermodynamic pressure of the electron gas is shown to be composed of the kinetic pressure, which is related to the boundary integral in the virial theorem and arises due to electron reflections from the boundary, and the anomalous pressure, which is specific for electrons in solids. Connections between the kinetic pressure and the properties of the wave function on the boundary are drawn. The general theorems are illustrated by examples of uniform electron gas, and electrons in rectangular and circular graphene samples. The analogous consideration for ordinary massive electrons is presented for comparison.

Global existence of weak solutions for compressible Navier--Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor

We prove global existence of appropriate weak solutions for the compressible Navier–Stokes equations for more general stress tensor than those covered by P.–L. Lions and E. Feireisl’s theory. More precisely we focus on more general pressure laws which are not thermodynamically stable; we are also able to handle some anisotropy in the viscous stress tensor. To give answers to these two longstanding problems, we revisit the classical compactness theory on the density by obtaining precise quantitative regularity estimates: This requires a more precise analysis of the structure of the equations combined to a novel approach to the compactness of the continuity equation. These two cases open the theory to important physical applications, for instance to describe solar events (virial pressure law), geophysical flows (eddy viscosity) or biological situations (anisotropy).

Virial series expansion and Monte Carlo studies of equation of state for hard spheres in narrow cylindrical pores.

In this paper, the virial series expansion and constant pressure Monte Carlo method are used to study the longitudinal pressure equation of state for hard spheres in narrow cylindrical pores. We invoke dimensional reduction and map the model into an effective one-dimensional fluid model with interacting internal degrees of freedom. The one-dimensional model is extensive. The Euler relation holds, and longitudinal pressure can be probed with the standard virial series expansion method. Virial coefficients B_{2} and B_{3} were obtained analytically, and numerical quadrature was used for B_{4}. A range of narrow pore widths (2R_{p}), R_{p}<(sqrt[3]+2)/4=0.9330... (in units of the hard sphere diameter) was used, corresponding to fluids in the important single-file formations. We have also computed the virial pressure series coefficients B_{2}^{'}, B_{3}^{'}, and B_{4}^{'} to compare a truncated virial pressure series equation of state with accurate constant pressure Monte Carlo data. We find very good agreement for a wide range of pressures for narrow pores. These results contribute toward increasing the rather limited understanding of virial coefficients and the equation of state of hard sphere fluids in narrow cylindrical pores.

Addressing the temperature transferability of structure based coarse graining models.

Systematically derived coarse grained (CG) models for molecular liquids do not inherently guarantee transferability to a state point different from its reference, especially when derived on the basis of structure based CG methods like Inverse Monte Carlo (IMC). Several efforts made in the past years to improve the transferability of these models focused on including thermodynamic constraints or on the application of multistate parametrization. Das and Andersen (DA) [Das et al., J. Chem. Phys., 2010, 132, 164106.] proposed a different Ansatz. They derived a correction term added to the system's Hamiltonian to reproduce the virial pressure and the volume fluctuations of the reference system in the CG resolution which does not require further adjustment of the effective pair potential. Herein, we discuss the possibility to achieve temperature transferability with IMC models for selected alkanes following the optimization of the DA approach as proposed by Dunn and Noid (DN) [Dunn et al., J. Chem. Phys., 2015, 143, 243148.]. The work focuses on a novel approach to determine the DN correction term for different state points by linear interpolation.

Pressure in an exactly solvable model of active fluid.

We consider the pressure in the steady-state regime of three stochastic models characterized by self-propulsion and persistent motion and widely employed to describe the behavior of active particles, namely, the Active Brownian particle (ABP) model, the Gaussian colored noise (GCN) model, and the unified colored noise approximation (UCNA) model. Whereas in the limit of short but finite persistence time, the pressure in the UCNA model can be obtained by different methods which have an analog in equilibrium systems, in the remaining two models only the virial route is, in general, possible. According to this method, notwithstanding each model obeys its own specific microscopic law of evolution, the pressure displays a certain universal behavior. For generic interparticle and confining potentials, we derive a formula which establishes a correspondence between the GCN and the UCNA pressures. In order to provide explicit formulas and examples, we specialize the discussion to the case of an assembly of elastic dumbbells confined to a parabolic well. By employing the UCNA we find that, for this model, the pressure determined by the thermodynamic method coincides with the pressures obtained by the virial and mechanical methods. The three methods when applied to the GCN give a pressure identical to that obtained via the UCNA. Finally, we find that the ABP virial pressure exactly agrees with the UCNA and GCN results.

Systematic and simulation-free coarse graining of multi-component polymeric systems: Structure-based coarse graining of binary polymer blends

We proposed a systematic and simulation-free strategy for the structure-based coarse graining of multi-component polymeric systems using the polymer reference interaction site model theory, and as an example applied it to a simple model system of binary polymer blends. Our structure-based coarse graining ensures that the original and coarse-grained (CG) systems have the same intra- and intermolecular pair correlation functions involving the CG segments (each representing the center-of-mass of a group of consecutive monomers on the same chain in the original system). When applied to binary polymer blends, it does not change the spinodal curve (thus also the critical point), regardless of the original model system and closure used. We also quantitatively examined how the effective non-bonded pair potentials between CG segments and the thermodynamic properties of CG systems vary with the coarse-graining level. As expected, the structure-based coarse graining cannot give thermodynamic consistency (i.e., the same interchain internal energy per chain and virial pressure) between the original and CG systems at any coarse-graining level.

Applicability of effective pair potentials for active Brownian particles.

We have performed a case study investigating a recently proposed scheme to obtain an effective pair potential for active Brownian particles (Farage et al., Phys. Rev. E 91, 042310 (2015)). Applying this scheme to the Lennard-Jones potential, numerical simulations of active Brownian particles are compared to simulations of passive Brownian particles interacting by the effective pair potential. Analyzing the static pair correlations, our results indicate a limited range of activity parameters (speed and orientational correlation time) for which we obtain quantitative, or even qualitative, agreement. Moreover, we find a qualitatively different behavior for the virial pressure even for small propulsion speeds. Combining these findings we conclude that beyond linear response active particles exhibit genuine non-equilibrium properties that cannot be captured by effective pair interaction alone.

A pressure consistent bridge correction of Kovalenko-Hirata closure in Ornstein-Zernike theory for Lennard-Jones fluids by apparently adjusting sigma parameter

Ornstein-Zernike (OZ) integral equation theory is known to overestimate the excess internal energy, Uex, pressure through the virial route, Pv, and excess chemical potential, μex, for one-component Lennard-Jones (LJ) fluids under hypernetted chain (HNC) and Kovalenko-Hirata (KH) approximatons. As one of the bridge correction methods to improve the precision of these thermodynamic quantities, it was shown in our previous paper that the method to apparently adjust σ parameter in the LJ potential is effective [T. Miyata and Y. Ebato, J. Molec. Liquids. 217, 75 (2016)]. In our previous paper, we evaluated the actual variation in the σ parameter by using a fitting procedure to molecular dynamics (MD) results. In this article, we propose an alternative method to determine the actual variation in the σ parameter. The proposed method utilizes a condition that the virial and compressibility pressures coincide with each other. This method can correct OZ theory without a fitting procedure to MD results, and possesses characteristics of keeping a form of HNC and/or KH closure. We calculate the radial distribution function, pressure, excess internal energy, and excess chemical potential for one-component LJ fluids to check the performance of our proposed bridge function. We discuss the precision of these thermodynamic quantities by comparing with MD results. In addition, we also calculate a corrected gas-liquid coexistence curve based on a corrected KH-type closure and compare it with MD results.

Water liquid-vapor equilibrium by molecular dynamics: Alternative equilibrium pressure estimation

Abstract The molecular dynamics simulations of the liquid-vapor equilibrium of water including both water phases — liquid and vapor — in one simulation are presented. Such approach is preferred if equilibrium curve data are to be collected instead of the two distinct simulations for each phase separately. Then the liquid phase is not restricted, e.g. by insufficient volume resulting in too high pressures, and can spread into its natural volume ruled by chosen force field and by the contact with vapor phase as vaporized molecules are colliding with phase interface. Averaged strongly fluctuating virial pressure values gave untrustworthy or even unreal results, so need for an alternative method arisen. The idea was inspired with the presence of vapor phase and by previous experiences in gaseous phase simulations with small fluctuations of pressure, almost matching the ideal gas value. In presented simulations, the first idea how to calculate pressure only from the vapor phase part of simulation box were applied. This resulted into very simple method based only on averaging molecules count in the vapor phase subspace of known volume. Such simple approach provided more reliable pressure estimation than statistical output of the simulation program. Contrary, also drawbacks are present in longer initial thermostatization time or more laborious estimation of the vaporization heat. What more, such heat of vaporization suffers with border effect inaccuracy slowly decreasing with the thickness of liquid phase. For more efficient and more accurate vaporization heat estimation the two distinct simulations for each phase separately should be preferred.