Thermodynamic consistency by a modified Perkus–Yevick theory using the Mittag-Leffler function

Carvalho, Felipe Silva; Braga, J. P.

doi:10.1016/j.physa.2021.126065

Cited by 7 publications

(2 citation statements)

References 31 publications

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“…For fluid thermodynamic systems, great progress [11][12][13][14][15] has been made for theoretical approaches based on continuous model in recent decades. Systematic liquid theories include Ornstein-Zernike integral equation theory [16][17][18][19], thermodynamic perturbation theory [20][21][22], and classical density functional theory (CDFT) [23][24][25][26][27][28]. The CDFT is originally designed for thermodynamic systems under external field(s), among which includes electrical double layer (EDL) system, which underlies much of the EDLSC.…”

Section: Introductionmentioning

confidence: 99%

Ultrananoporous supercapacitor with ionic liquid comprised of two-site cation: an Ising model study (II)

Zhou¹,

Zhou²

2022

J. Phys. D: Appl. Phys.

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A four-state one-dimension discrete spin model with the nearest neighbor and partial next nearest neighbor lattice interactions is proposed for describing electrical double layer formed by ionic liquid in cylindrical pore that can accommodate only one row of particles. The model, in which cation is modelled as a dimer formed by two hard spheres: one is positively charged with diameter , while the other is neutral with diameter , and anion is modeled by charged hard sphere with diameter , is designed to investigate effects of pore diameter , ion transfer free energy, ion size and electrical valence on behaviors of specific differential capacitance and specific energy storage and its saturation value . Relevant Kramers-Wannier transfer matrix is , which gives system partition function by numerically solving maximum real root of the relevant characteristic equation. Main findings are briefly described below. (i) The ion valence has little effect on the value, but does reduce the threshold voltage strength , beyond which the energy storage reaches . However, the ion valence (whether co- or counter-ion) raises both the and values as the relevant ion size decreases enough. (ii) Decreasing of the value weakly reduces the value, but raises the peak height and the value obviously; correlation between the value and value becomes stronger with the ions getting more pore hostile. (iii) With the counter-ion or co-ion charged site size decreasing, both the value and value rise. However, the effect of the co-ion charged site size is weakened as the co-ion gets more pore hostile, and the cation neutral site size influences on the value less than the cation charged site size does. (iv) Pore friendly co-ion or pore hostile counter-ion always helps in raising the value; the two have significant synergistic effect with the co-ion pore friendliness playing more important role than the counter-ion pore hostility.

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Section: Introductionmentioning

confidence: 99%

Ultrananoporous supercapacitor with ionic liquid comprised of two-site cation: an Ising model study (II)

Zhou¹,

Zhou²

2022

J. Phys. D: Appl. Phys.

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“…This approximation is used in solving the Ornstein-Zernike (OZ) equation as the approximation itself is a closure relation. This approximation method is also assigned as the Percus-Yevick equation [23]. To acquire the expression for the radial distribution function, g(r) this approximation can be frequently applied in the fluid theory.…”

Section: Methodology P-y Approximation Was Defined First By Percus Andmentioning

confidence: 99%

Radial Distribution Function of Hard Spheres at Different Densities

Khanal,

Gyawali,

Khati

et al. 2023

J. Nep. Phys. Soc.

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The model of hard sphere system has important part in modern theories of liquids. Hard sphere fluid is considered as the most intensively studied system among all model fluids. The thermodynamic and structural properties of real fluids can be studied with the help of hard spheres fluid. The exact solution of Ornstein-Zernike (OZ) equation with Percus-Yevick (PY) along with the equation of state provides an approximate analytical expression for radial distribution function (RDF). This work intends to study the radial distribution function of Hard sphere (HS) using the PY approximation for different densities ranging from low to high to find out their structural properties, packing behavior, phase transitions, and thermodynamics. We use FORTRAN program for this purpose. At low densities, the RDF has a single peak at a distance corresponding to the hard sphere diameter, indicating that the particles are well- separated and not interacting with each other like gaseous. As density increases, the peak becomes broader and shifts to smaller distances, indicating that the particles are coming into closer contact and interacting more strongly with each other. The height of the peak also increases, indicating that there is a greater probability of finding a particle at a certain distance from another particle.

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Physics Informed Neural Networks applied to liquid state theory

Carvalho

Braga

2022

Journal of Molecular Liquids

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Thermodynamic consistency by a modified Perkus–Yevick theory using the Mittag-Leffler function

Cited by 7 publications

References 31 publications

Ultrananoporous supercapacitor with ionic liquid comprised of two-site cation: an Ising model study (II)

Ultrananoporous supercapacitor with ionic liquid comprised of two-site cation: an Ising model study (II)

Radial Distribution Function of Hard Spheres at Different Densities

Physics Informed Neural Networks applied to liquid state theory

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