Critical Casimir effects in 2D Ising model with curved defect lines

Mostovoy, S. D.; Pavlovsky, Oleg

doi:10.1016/j.physleta.2017.11.030

Cited by 5 publications

(3 citation statements)

References 22 publications

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“…Although real fluid systems are most suitably described by continuous classical potential model, only if the potential is short-range, the discrete lattice model in its simplest nearest neighbor approximation gives at least qualitatively reliable results. Ising model [50][51][52][53][54][55][56][57][58][59] is well suitable for this purpose for many years. One-dimension Ising model with external field is in principle tractable theoretically by resorting to Kramers-Wannier transfer matrix method [60] whether only the nearest neighbor interaction is considered, or higher-order neighbors as well are considered.…”

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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“…Frequently, one would rather give up quantitative accuracy requirement and wishes the theoretical methods tractable and give qualitatively correct change tendency. Ising model [59][60][61][62][63][64][65][66][67][68] is well suitable for this purpose. Although the Ising model is essentially based on discrete lattice concept [69], it plays an important role in our understanding [69][70][71][72][73][74] of behaviors of the real systems which are usually modeled by continuous classical statistical model and are too complex to be treated in a friendly way.…”

Section: Introductionmentioning

confidence: 99%

Influence of ion structure and solvent electric dipole on ultrananoporous supercapacitor: a lattice model study

Zhou¹,

Zhou²

2022

Phys. Scr.

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A five-state modified BEG model is proposed for describing aqueous electrolyte in cylindrical pore so narrow that only one row of particles can be stationed. Two properties the closest to the actual situation of the aqueous electrolyte are integrated into the model: cation is dimer comprised of two tangentially tethered hard spheres of different diameters: one is charged, while the other is neutral, and solvent is modeled as neutral hard sphere with an electric dipole. The system partition function is obtained by numerically solving maximum real root of characteristic equation of Kramers-Wannier transfer matrix. The present theory reduces to that by the Rochester et al by making both the cation neutral sphere size and electric dipole moment of the solvent equal to zero. The model is used to investigate effects of cation shape and electric valence, solvent electric dipole moment, and cylindrical pore radius on specific differential capacitance and specific energy storage in electric double layer supercapacitor formed inside the cylindrical pore. Main findings are briefly described below. (i) With dimer counter-ion electric valence changing from 1 to 2, the peak becomes higher, and the peak position becomes nearer to the zero charge potential; as a comprehensive effect of these changes, the dimer counter-ion electric valence does not exert obvious influence on the saturation value , but reduces the threshold electrode potential strength , beyond which the value is just and approximately reached. (ii) Whether the dimer counter-ion is monovalent or bivalent, the peak height and the value tend to rise with the dimer neutral site size decreasing, but influence of the value on the value is very small. Only when the value is small enough, the value rises a little with decrease of the value. (iii) Increase of solvent electric dipole moment (wheth

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“…The first direct measurement of critical Casimir force [1,2] between a single colloidal sphere and a flat silica surface in a water-2,6-lutidine mixture was performed ten years ago [3]. It created a tremendous impulse for further experimental and theoretical studies of the critical behaviour of colloidal suspensions [4][5][6][7][8][9][10][11]. One of the most intensively researched issues is the aggregation transition originating from the confinement of the solvent critical fluctuations between the surfaces of distinct colloids [3,5,12].…”

Section: Introductionmentioning

confidence: 99%

Numerically Exact Approach to Ultra-Small Particles in Near-Critical Mixtures

Drzewiński

2019

Acta Phys. Pol. A

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The critical Casimir forces between solute particles in a solvent can arise from the medium fluctuations. The properties of ultra-small particles immersed in a binary liquid mixture close to its consolute point Tc are studied using the exact statistical-mechanical derivation based on the two-dimensional Ising model. Each solute particle is represented by a local magnetic field acting on an individual spin. The ensemble average for the distance between particles placed on the torus is determined as a temperature-dependent function. It has been shown how the presence of other particles modifies the separation distance for a pair of particles with the same or opposing preferential adsorption.

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Critical Casimir effects in 2D Ising model with curved defect lines

Cited by 5 publications

References 22 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)

Influence of ion structure and solvent electric dipole on ultrananoporous supercapacitor: a lattice model study

Numerically Exact Approach to Ultra-Small Particles in Near-Critical Mixtures

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