Van Der Waals Approximation Research Articles

Thermodynamic analysis of the difference in adsorption characteristics of CH4 and CO2 on continental shale

In order to explain the difference in adsorption characteristics of CH4 and CO2 on continental shale from the perspective of thermodynamics, the isothermal adsorption experiments of CH4 and CO2 adsorbed by shale in Yanchang Formation in Ordos Basin were carried out, and the excess adsorption capacity was corrected to absolute adsorption capacity. Then the Clausius-Clapeyron equation was used to analyze the isosteric heat of adsorption of CH4 and CO2 on shale. The results show that, for calculating the absolute adsorption capacity, Ozawa empirical formula or Van der Waals approximation method should be used to calculate the adsorption phase density. The absolute adsorption capacity should be selected as the basic data for calculating the isosteric heat of adsorption. The reason is that the excess isosteric heat of adsorption has a negative value in the low adsorption capacity stage, which is contradictory to the fact that the adsorption process is exothermic, and is significantly higher than the absolute isosteric heat of adsorption. There is a good linear positive correlation between the isosteric heat of adsorption and the adsorption amount of CH4 and CO2 adsorbed by continental shale, and the isosteric heat of adsorption of CH4 is greater than that of CO2. The absolute initial isosteric heat of adsorption of CH4 and CO2 adsorbed by shale is 52.04 kJ/mol and 27.71 kJ/mol, indicating that the adsorption force of CH4 on Yanchang Formation shale is stronger than that of CO2.

Understanding delivery and adsorption of Flutamide drug with ZnONS based on: Dispersion-corrected DFT calculations and MD simulations

The unique features of zinc oxide nanosheet (ZnONS) as an appropriate platform for Flutamide molecule was considered by means of density functional theory (DFT) framework with van der Waals (vdW) approximation via Perdew–Burke–Ernzerhof variant of the generalized gradient approximation (PBE-GGA) method along with double zeta polarization (DZP) basis set. The most stable model of interaction between Flutamide molecule and ZnONS is specified and adsorption energies (Eads) are assessed. In energetically favorable configuration, O atoms of –NO2 group of Flutamide interacts with a Zn atom of the ZnONS at 2.11 Å with Eads of −20.616 kcal mol−1. We have scrutinized charge analysis between species involved through famous Mulliken, Hirshfeld and Voronoi approaches. Furthermore, we have examined the density of states (DOS) and the projected density of states (PDOS) for the energetically favorable model to explore the interaction of the drug molecule with the ZnONS. Besides, quantum molecular descriptors (QMD) are also analyzed upon interaction of drug molecule on ZnONS. To deeper knowledge the details of the interaction between the Flutamide and the ZnONS, Quantum Theory of Atoms in Molecules (QTAIM) calculations are implemented. The values of ▽2ρ(BCP) and H(BCP) for (Flutamide)O⋯Zn(ZnONS) at the most stable configuration are positive and G/|V| is greater than 1, it denotes the non-covalent interaction between Flutamide with ZnONS. The DFT calculation based on molecular dynamics (MD) approach are utilized to acquire a better understand into the nature of the Flutamide drug and ZnONS interactions. The MD outcomes demonstrate that when the Flutamide molecule takes longer time to link with ZnONS, the Flutamide/ZnONS complex becomes stable. Moreover, after Flutamide molecule adsorption phenomenon the electrical conductivity generates an electrical signal. The outcomes affirmed the potential of a ZnONS as a drug delivery system (DDS) for drug molecule to remedy cancer and may be an appropriate sensor for the Flutamide drug detection.

Gas Transport across Carbon Nitride Nanopores: A Comparison of van der Waals Functionals against the Random-Phase Approximation

C2N is an ordered two-dimensional carbon nitride with a high density (1.7 × 1014 cm–2) of 3.1 Å-sized nanopores, making it promising for high-flux gas sieving for energy-efficient He and H2 purification. Herein, we discuss the accurate calculation of potential energy surfaces for He, H2, N2, and CO2 across C2N nanopores, to characterize the gas-sieving potential of C2N. We compare the potential energy surface derived from density-functional theory calculations using five commonly used van der Waals (vdW) approximations. While all five functionals point that the C2N nanopore yields He/N2 and H2/N2 selectivities over 1000, adsorption energies and energy barriers vary remarkably depending on the approximation chosen. To make progress, we compare the calculations against the results from the adiabatic connection fluctuation dissipation theory, with random-phase approximation, known to be accurate in capturing vdW interactions. The comparison indicates that the interaction energy is less accurate with vdW density functional theory. On the other hand, more empirical corrections work reasonably well, a finding that we also confirm for another carbon nitride lattice, poly(triazine imide). Overall, we recommend these for screening carbon nitride materials for gas separation, but also comparing functionals with higher-order approaches when dealing with different materials.

Alternative formulation of the induced surface and curvature tensions approach

We develop a novel method to analyze the excluded volume of the multicomponent mixtures of classical hard spheres in the grand canonical ensemble. The method is based on the Laplace–Fourier transform technique and allows one to account for the fluctuations of the particle number density for the induced surface and curvature tensions equation of state. As a result one can go beyond the Van der Waals (VdW) approximation by obtaining the suppression of the induced surface and curvature tensions coefficients at moderate and high packing fractions. In contrast to the standard induced surface and curvature tensions equation of state the suppression of these coefficients is not the exponential, but a power-like one. The obtained alternative equation of state is further generalized to account for higher virial coefficients. This result is straightforwardly generalized to the case of quantum statistics.

The concept of induced surface and curvature tensions for EoS of hard discs and hard spheres

Mathematically rigorous derivation of the hadron matter equation of state within the induced surface and curvature tensions approach is worked out. Such an equation of state allows one to go beyond the Van der Waals approximation for the interaction potential of hard spheres. The compressibility of a single- and two-component hadron mixtures are found for two- and three-dimensional cases. The obtained results are compared to the well known one- and two-component equations of state of hard spheres and hard discs. The values of the model parameters which successfully reproduce the above-mentioned equations of state on different intervals of packing fractions are determined from fitting their compressibility factors. It is argued that after some modification the developed approach can be also used to describe the mixtures of gases of convex hard particles of different sizes and shapes.

Bose–Einstein Condensation as a Deposition Phase Transition of Quantum Hard Spheres and New Relations between Bosonic and Fermionic Pressures

We investigate the phase transition of Bose–Einstein particles with the hard-core repulsion in the grand canonical ensemble within the Van der Waals approximation. It is shown that the pressure of non-relativistic Bose–Einstein particles is mathematically equivalent to the pressure of simplified version of the statistical multifragmentation model of nuclei with the vanishing surface tension coefficient and the Fisher exponent тF = 5/2 , which for such parameters has the 1-st order phase transition. The found similarity of these equations of state allows us to show that within the present approach the high density phase of Bose-Einstein particles is a classical macro-cluster with vanishing entropy at any temperature which, similarly to the system of classical hard spheres, is a kind of solid state. To show this we establish new relations which allow us to identically represent the pressure of Fermi–Dirac particles in terms of pressures of Bose–Einstein particles of two sorts.

Self-consistent analysis of quantum gases of hard spheres beyond the Van der Waals approximation

The necessary conditions to derive the quantum VdW EoS with hard-core repulsion from the quantum partition are discussed. On a plausible example it is shown that an alternative way to account correctly for the 3-rd virial coefficient of classical hard spheres leads to inconsistencies. The multicomponent formulation of the quantum VdW EoS with hard-core repulsion is derived within a self-consisting approximation. For practical applications it is simplified, extended to higher densities and generalized to the case of hard convex bodies of any dimension $D\ge 2$.

Hard-Core Radius of Nucleons within the Induced Surface Tension Approach

We review the recent approach to model the hadronic and nuclear matter equations of state using the induced surface tension concept, which allows one to go far beyond the usual Van der Waals approximation. Since the obtained equations of state, classical and quantum, are among the most successful ones in describing the properties of low density phases of strongly interacting matter, they set strong restrictions on the possible value of the hard-core radius of nucleons, which is widely used in phenomenological equations of state. We summarize the latest results obtained within this novel approach and perform a new detailed analysis of the hard-core radius of nucleons, which follows from hadronic and nuclear matter properties. Such an analysis allows us to find the most trustworthy range of its values: the hard-core radius of nucleons is 0.3–0.36 fm. A comparison with the phenomenology of neutron stars implies that the hard-core radius of nucleons has to be temperature and density dependent. Such a finding is supported when the eigenvolume of composite particles like hadrons originates from their fermionic substructure due to the Pauli blocking effect.

Equation of State of Quantum Gases Beyond the Van der Waals Approximation

A recently suggested equation of state with the induced surface tension is generalized to the case of quantum gases with mean-field interaction. The self-consistency conditions of such a model and the conditions necessary for the Third Law of thermodynamics to be satisfied are found. The quantum virial expansion of the van der Waals models of such a type is analyzed, and its virial coefficients are given. In contrast to traditional beliefs, it is shown that an inclusion of the third and higher virial coefficients of a gas of hard spheres into the interaction pressure of the van der Waals models either breaks down the Third Law of thermodynamics or does not allow one to go beyond the van der Waals approximation at low temperatures. It is demonstrated that the generalized equation of state with the induced surface tension allows one to avoid such problems and to safely go beyond the van der Waals approximation. In addition, the effective virial expansion for the quantum version of the induced surface tension equation of state is established, and all corresponding virial coefficients are found exactly. The explicit expressions for the true quantum virial coefficients of an arbitrary order of this equation of state are given in the low-density approximation. A few basic constraints on such models which are necessary to describe the nuclear and hadronic matter properties are discussed.

Going beyond the second virial coefficient in the hadron resonance gas model

We develop a novel formulation of the hadron resonance gas model which, besides a hard-core repulsion, explicitly accounts for the surface tension induced by the interaction between the particles. Such an equation of state allows us to go beyond the Van der Waals approximation for any number of different hard-core radii. A comparison with the Carnahan–Starling equation of state shows that the new model is valid for packing fractions 0.2–0.22, while the usual Van der Waals model is inapplicable at packing fractions above 0.1–0.11. Moreover, it is shown that the equation of state with induced surface tension is softer than the one of hard spheres and remains causal at higher particle densities. The great advantage of our model is that there are only two equations to be solved and neither their number nor their form depend on the values of the hard-core radii used for different hadronic resonances. Such an advantage leads to a significant mathematical simplification compared to other versions of truly multi-component hadron resonance gas models. Using this equation of state we obtain a high-quality fit of the ALICE hadron multiplicities measured at the center-of-mass energy 2.76 TeV per nucleon and we find that the dependence of χ2/ndf on the temperature has a single global minimum in the traditional hadron resonance gas model with the multi-component hard-core repulsion. Also we find two local minima of χ2/ndf in the model in which the proper volume of each hadron is proportional to its mass. However, it is shown that in the latter model a second local minimum located at higher temperatures always appears far above the limit of its applicability.

Coupled electron-ion Monte Carlo simulation of hydrogen molecular crystals.

We performed simulations for solid molecular hydrogen at high pressures (250 GPa ≤ P ≤ 500 GPa) along two isotherms at T = 200 K (phase III) and at T = 414 K (phase IV). At T = 200 K, we considered likely candidates for phase III, the C2c and Cmca12 structures, while at T = 414 K in phase IV, we studied the Pc48 structure. We employed both Coupled Electron-Ion Monte Carlo (CEIMC) and Path Integral Molecular Dynamics (PIMD). The latter is based on Density Functional Theory (DFT) with the van der Waals approximation (vdW-DF). The comparison between the two methods allows us to address the question of the accuracy of the exchange-correlation approximation of DFT for thermal and quantum protons without recurring to perturbation theories. In general, we find that atomic and molecular fluctuations in PIMD are larger than in CEIMC which suggests that the potential energy surface from vdW-DF is less structured than the one from quantum Monte Carlo. We find qualitatively different behaviors for systems prepared in the C2c structure for increasing pressure. Within PIMD, the C2c structure is dynamically partially stable for P ≤ 250 GPa only: it retains the symmetry of the molecular centers but not the molecular orientation; at intermediate pressures, it develops layered structures like Pbcn or Ibam and transforms to the metallic Cmca-4 structure at P ≥ 450 GPa. Instead, within CEIMC, the C2c structure is found to be dynamically stable at least up to 450 GPa; at increasing pressure, the molecular bond length increases and the nuclear correlation decreases. For the other two structures, the two methods are in qualitative agreement although quantitative differences remain. We discuss various structural properties and the electrical conductivity. We find that these structures become conducting around 350 GPa but the metallic Drude-like behavior is reached only at around 500 GPa, consistent with recent experimental claims.

The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect.

In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.

Application of a Dual-Hybrid Direct Random Phase Approximation to Water Clusters

In water clusters, there is a delicate balance of van der Waals interactions and hydrogen bonds. Although semilocal and nonlocal density functional approximations have been recently routinely applied to water in various phases, the accurate description of hydrogen bonds remains a challenge. The most popular density functional approaches fail to predict the correct ordering of the energies of water clusters. To illustrate the required accuracy, the CCSD(T) complete basis set extrapolated dissociation energy difference between the two lowest energy hexamer structures is 0.06 kcal mol(-1) per monomer. In this work, we assessed interaction energies in neutral and ionic water clusters with various density functionals with or without van der Waals correction. Generally, van der Waals approximations play a significant role in clusters with increasing size, while hybrid functionals improve the description of hydrogen bonds. Despite these general trends, none of the tested density functional approximations with or without van der Waals correction and exact exchange mixing can lead to a uniform performance for neutral and ionic water clusters. The recently constructed dual-hybrid dRPA75 approximation is a successful combination of exact and semilocal exchange, and nonlocal correlation in its energy, while utilizing a high fraction of exact exchange. We have shown that the dRPA75 method has a systematic error, which can be efficiently compensated for by the aug-cc-pVTZ basis set for small- and medium-sized water clusters.

Development of Porosity Measurement Method in Shale Gas Reservoir Rock

The pore scales have impacts on transport mechanisms in shale gas reservoirs. In this research, digital helium porosity meter is used for porosity measurement by considering real condition. Accordingly it is necessary to obtain a good approximation for gas filled porosity. Shale has the typical effective porosity that is changing as a function of time. Effective porosity values for three different shale rocks are analyzed by this proposed measurement. We develop the new measurement method for characterizing porosity phenomena in shale gas as a time function by measuring porosity in a range of minutes using digital helium porosity meter. The porosity of shale rock measured in this experiment are free gas and adsorbed gas porosoty. The pressure change in time shows that porosity of shale contains at least two type porosities: macro scale porosity (fracture porosity) and fine scale porosity (nano scale porosity). We present the estimation of effective porosity values by considering Boyle-Gay Lussaac approximation and Van der Waals approximation.

Methods for constructing gas laws near critical temperatures by means of molecular dynamics

Various methods for constructing gas laws by means of molecular dynamics are considered. A model with a thermostat is shown to yield correct parameters of the Lennard-Jones gas law. Results near the condensation point are verified using the LAMMPS program on a hybrid high-performance computer cluster. Parameters of a Van der Waals approximation for the Lennard-Jones gas law are found.

Theoretical study of amino derivatives and anticancer platinum drug grafted on various carbon nanostructures

Density functional theory calculations with van der Waals approximation have been conducted to analyze the functionalization of various carbon-based nanostructures (fullerene, metallic, and semi-conducting nanotubes) with amino derivative groups. The results obtained with azomethine, show the formation of a five membered ring on fullerenes, and on nanotubes consistent with experimental observations. The attachment of an azomethine plus subsequent drug like a Pt(IV) complex does not perturb the cycloaddition process. Moreover, all theoretical results show that the length of different amino derivatives with subsequent Pt(IV) complex does not affect the complexed therapeutic agent when it is attached onto these carbon-based nanostructures.

Segregation surface in binary solid solutions

Analytic equations describing the concentration profile, surface energy, and adsorption for a binary solid solution with the emergence of one of the components to the surface (surface segregation) were obtained using a unique approach, a modified van der Waals approximation. The calculation results were compared with the experimental secondary ion mass spectrometry data on Cu-Ge and Cu-Al metallic binary solutions; agreement was satisfactory.

Bridging the gap between phenomenology and microscopic theory: Asymptotes in nematic colloids

The Ornstein-Zernike equation is applied to nematic colloids with up-down symmetry to determine how the electrostatic analogy and other phenomenological results appear in molecular theory. In contrast to phenomenological approaches, the molecular theory does not assume particular boundary conditions (anchoring) at colloidal surfaces. For our molecular parameters the resulting anchoring appears to be realistic, neither rigid nor infinitely weak. For this case, the effective force between a colloidal pair at large separation remains essentially constant over the entire region of nematic stability. We show that a simple van der Waals approximation gives a potential of mean force that in some important aspects is similar to the phenomenological results obtained in the limit of weak anchoring; at large separations the potential varies as Sigma8, where Sigma is the colloidal diameter. In contrast, the more sophisticated mean spherical approximation yields a Sigma6 dependence consistent with phenomenological calculations employing rigid boundary conditions. We show that taking proper account of the correlation (or magnetic coherence) length xi inherent in the nematic sample is essential in an analysis of the Sigma dependence. At infinite xi the leading Sigma dependence is Sigma6, but this shifts to Sigma8 when xi is finite. The correlation length also influences the orientational behavior of the effective interaction. The so-called quadrupole interaction that determines the long-range behavior at infinite xi transforms into a superposition of screened "multipoles" when xi is finite. The basic approach employed in this paper can be readily applied to a broad range of physically interesting systems. These include patterned and nonspherical colloids, colloids trapped at interfaces, and nematic fluids in confined geometries such as droplets.

Interfacial properties of liquid-vapor interfaces with planar, spherical, and cylindrical geometries in mean field

Following the route of the stress tensor we study the free energy of a fluid liquid-vapor interface in the van der Waals approximation for planar, cylindrical and spherical interfaces. By performing a systematic expansion in powers of the inverse of the curvature radii, and appropriately defining the Gibbs dividing surface, we find unambiguous expressions for the surface tension, the spontaneous curvature, the bending rigidity and the Gaussian rigidity.

Generalized equation of state for square-well potentials of variable range

An equation of state for square-well fluids of short and long potential range λ is presented and compared with Gibbs ensemble and canonical Monte Carlo simulation data; vapour–liquid coexistence densities, vapour pressures, internal energies and contact radial distribution functions are examined. The equation is an extension of that presented in previous work for the reference monomer fluid in the SAFT-VR approach [GIL-VILLEGAS et al., 1997, J. chem. Phys., 106, 4168]. The Helmholtz free energy is written as a high-temperature expansion up to second order, where simple expressions are obtained for the mean attractive energy and the fluctuation term using the mean-value theorem and a mapping of radial distribution functions. In previous work the range of the square-well potential was limited to λ ≤ 1.8. In this work we show that the phase behaviour of such a fluid is far from the expected long-range limits given by the mean-field and van der Waals approximations. We extend the applicability of the equation of state to ranges up to λ = 3, and show that, in this case, the phase behaviour of the fluid is essentially that of a fluid of infinite potential range (van der Waals limit). At short ranges (λ < 1.8) the calculated coexistence is virtually identical to that of the previous approach, hence ensuring that its application within a SAFT-VR framework is consistent with previous work. The extension of the approach to longer ranges is of interest in the context of modelling of polar fluids, and in the implementation of cross-over approaches to treat the critical region.