Inter-surface effective electrostatic interactions in the presence of surface charge discreteness and solvent granularity

Zhou, Shiqi

doi:10.1080/00268976.2020.1778807

Cited by 19 publications

(10 citation statements)

References 61 publications

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“…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. In fact, the CDFT and relevant statistical theories have been widely used in the EDL systems [29][30][31][32], the EDLSC [33,34], and other issues such as confined system phase transitions [35][36][37][38][39][40][41], solvation energy [42][43][44][45], surface forces [46][47][48][49], etc. Problems with the CDFT are that the CDFT is purely numerical and no analytical solution exists for it.…”

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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“…(ii) The nonlinear equations resulting from the discretized CDFT equation are solved by the Newton GMRES algorithm as implemented in the public-domain nonlinear Krylov solver NITSOL [ 70 ]. The examples [ 60 , 71 , 72 , 73 , 74 ] show that the GMRES algorithm is often effective in dealing with electrostatic systems.…”

Section: Model and Methodsmentioning

confidence: 99%

“…In theoretical studies, simpler coarse-grained models are used, but essential features can be captured. Usually, the aqueous electrolyte solution is modeled by so-called primitive model (PM) [ 20 , 22 , 50 , 51 , 52 ], in which a water solvent is considered as a structureless continuum and shows its existence only through a high dielectric constant completely neglecting its hard core; some researches [ 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 ] pick up the hard core missed in the PM and use an appropriately high dielectric constant to reflect the electric dipole moment of the water molecule (such a model is called the solvent primitive model abbreviated as SPM). There are studies [ 61 , 62 ] that consider a semi-primitive model where the solvent is represented by hard spheres with a Yukawa attraction and a dielectric permittivity is also introduced to reflect the electrostatic shielding effect of water molecules; in a very recent study [ 63 ], one Lennard–Jones (LJ) sphere with a higher energy parameter is used to model the water molecule to reflect its strong polarity, both the LJ energy and size parameters are determined by reproducing the two experimentally measured a and b parameters in the van der Waals equation of the state of water.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of the present work is to reproduce the experimentally observed capacitive behaviors of the aqueous EDLC with help from the classical density functional theory (CDFT) in which the water is modeled by a more realistic dipole dimer hard sphere model and the salt ions are approximated by charged hard spheres as in the PM. Compared with a large number of reports on the aqueous EDLC capacitance behaviors based on the PM [ 20 , 22 , 50 , 51 , 52 , 68 ] and SPM [ 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 ], the report of capacitance behaviors of the EDLC based on the dipole dimer hard sphere model for water is almost blank (instead of the EDLC capacitance behaviors, the literature [ 67 ] only reports the electrical double layer structure). So, the present report is necessary and urgent.…”

Section: Introductionmentioning

confidence: 99%

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Capacitive Behavior of Aqueous Electrical Double Layer Based on Dipole Dimer Water Model

2022

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The aim of the present paper is to investigate the possibility of using the dipole dimer as water model in describing the electrical double layer capacitor capacitance behaviors. Several points are confirmed. First, the use of the dipole dimer water model enables several experimental phenomena of aqueous electrical double layer capacitance to be achievable: suppress the differential capacitance values gravely overestimated by the hard sphere water model and continuum medium water model, respectively; reproduce the negative correlation effect between the differential capacitance and temperature, insensitivity of the differential capacitance to bulk electrolyte concentration, and camel–shaped capacitance–voltage curves; and more quantitatively describe the camel peak position of the capacitance–voltage curve and its dependence on the counter-ion size. Second, we fully illustrate that the electric dipole plays an irreplaceable role in reproducing the above experimentally confirmed capacitance behaviors and the previous hard sphere water model without considering the electric dipole is simply not competent. The novelty of the paper is that it shows the potential of the dipole dimer water model in helping reproduce experimentally verified aqueous electric double layer capacitance behaviors. One can expect to realize this potential by properly selecting parameters such as the dimer site size, neutral interaction, residual dielectric constant, etc.

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“…The CDFT is a convenient starting point for the microscopic structure and thermodynamic properties of inhomogeneous fluids [ 41 , 42 ]. It successfully accounts for the correlation and repulsive volume effects, and is widely applied to many fields of classical statistical mechanics, such as adsorption [ 43 , 44 , 45 , 46 ], phase transitions [ 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 ], inter-surface effective interactions [ 55 , 56 , 57 , 58 ], electrical double layer [ 6 , 59 , 60 , 61 , 62 , 63 ], polymer statistics [ 64 , 65 , 66 ], and solid [ 67 , 68 , 69 ].…”

Section: Introductionmentioning

confidence: 99%

On Capacitance and Energy Storage of Supercapacitor with Dielectric Constant Discontinuity

Zhou

2022

Nanomaterials

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The classical density functional theory (CDFT) is applied to investigate influences of electrode dielectric constant on specific differential capacitance Cd and specific energy storage E of a cylindrical electrode pore electrical double layer. Throughout all calculations the electrode dielectric constant varies from 5, corresponding to a dielectric electrode, to εwr = 108 corresponding to a metal electrode. Main findings are summarized as below. (i): By using a far smaller value of the solution relative dielectric constant εr = 10, which matches with the reality of extremely narrow tube, one discloses that a rather high saturation voltage is needed to attain the saturation energy storage in the ultra-small pore. (ii): Use of a realistic low εr = 10 value brings two obvious effects. First, influence of bulk electrolyte concentration on the Cd is rather small except when the electrode potential is around the zero charge potential; influence on the E curve is almost unobservable. Second, there remain the Cd and E enhancing effects caused by counter-ion valency rise, but strength of the effects reduces greatly with dropping of the εr value; in contrast, the Cd and E reducing effects coming from the counter-ion size enhancing remain significant enough for the low εr value. (iii) A large value of electrode relative dielectric constant εrw always reduces both the capacitance and energy storage; moreover, the effect of the εrw value gets eventually unobservable for small enough pore when the εrw value is beyond the scope corresponding to dielectric electrode. It is analyzed that the above effects take their rise in the repulsion and attraction on the counter-ions and co-ions caused by the electrode bound charges and a strengthened inter-counterion electrostatic repulsion originated in the low εr value.

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Inter-surface effective electrostatic interactions in the presence of surface charge discreteness and solvent granularity

Cited by 19 publications

References 61 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)

Capacitive Behavior of Aqueous Electrical Double Layer Based on Dipole Dimer Water Model

On Capacitance and Energy Storage of Supercapacitor with Dielectric Constant Discontinuity

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