Power law for frequency-dependence of double layer capacitance of graphene flakes

Wang, Hongxin; Aoki, Koichi; Chen, Jingyuan; Nishiumi, Toyohiko; Zeng, Xiangdong; Ma, Xiaoxing

doi:10.1016/j.jelechem.2015.01.008

Cited by 16 publications

(16 citation statements)

References 39 publications

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“…[34][35][36][37] This is based on the intuition that the concentration of the redox species in the voltammetry is much smaller than the concentration of the solvent molecules and/or supporting electrolyte. However, our experimental results on the frequency-dependence of the DL impedance indicate that (i) the DL capacitance is independent of the concentration of the salt, 38,39 the type of the salt, 40 and the dcpotential; 40,41 (ii) it is caused by the eld-driven orientation of the solvent molecules on the electrode; 42 and (iii) the interaction energy of the dipole-dipole of solvent molecules or hydrogen bonding energy is larger by one order in magnitude than the externally driven orientation energy such that a small molar concentration of the solvent molecules participate in the DL impedance. 43,44 The behavior (i) with regard to the frequency dispersion is in accordance with the results reported in the literature.…”

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confidence: 76%

Decrease in the double layer capacitance by faradaic current

Aoki¹,

Chen

Zeng

et al. 2017

RSC Adv.

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This study describes the reverse of the well-known double layer effects on charge transfer kinetics in the relationship between a cause and an effect. The reversible redox reaction of a ferrocenyl derivative decreased the capacitive values of the double layer impedance up to negative values, corresponding to an inductive component. This observation was disclosed by the subtraction of the real admittance from the imaginary admittance, which can extract the net double layer capacitance from the Warburg impedance. The inductance-like behavior is caused due to two reasons: (i) the double layer capacitance in the polarized potential domain is determined by the low concentrations of the fieldoriented solvent dipoles that are considered as the conventionally employed redox concentrations and (ii) the double layer capacitance is caused by the orientation of the dipoles in the same direction as that of the electric field, whereas the redox reaction generates charge in the direction opposite to the field. The faradaic effect was demonstrated via the ac-impedance data obtained for the ferrocenyl compound in a KCl solution in the unpolarized potential domain between 1 Hz and 3 kHz frequency. The negative admittance was proportional to the frequency. The theory of negative capacitance was presented by combining the mirror-image surface charge with the Nernst equation.

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confidence: 76%

Decrease in the double layer capacitance by faradaic current

Aoki¹,

Chen

Zeng

et al. 2017

RSC Adv.

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“…An experimental measure of the DL is the electrostatic capacitance, which is composed basically of two parts; the inner domain being caused by orientation of dipoles and/or adsorption; the outer domain being caused by distribution of diffusing ions, as illustrated with some models . Capacitance values conventionally determined result from properties in the inner domain , as has been demonstrated with the ionic concentration‐independence , kinds of ions and the dc‐potential dependence . The DL capacitance is provided by orientation of solvent molecules on the electrode, associated with the relaxation long enough of the seconds order .…”

Section: Introductionmentioning

confidence: 99%

“…Capacitance values conventionally determined result from properties in the inner domain , as has been demonstrated with the ionic concentration‐independence , kinds of ions and the dc‐potential dependence . The DL capacitance is provided by orientation of solvent molecules on the electrode, associated with the relaxation long enough of the seconds order . The relaxation has been quantitatively supported with the concept of the constant phase element (CPE) .…”

Section: Introductionmentioning

confidence: 99%

Double Layer Impedance in Mixtures of Acetonitrile and Water

Aoki¹,

Chen

Tang

2018

Electroanalysis

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Double layer (DL) impedances were evaluated in mixed solutions of water and acetonitrile at various ratios in the polarized potential domain in order to find competitive orientation of the two solvent molecules on the platinum electrode. The DL capacitance at any ratio of the mixture shows the common power law of the ac‐frequency. The capacitance at molar fractions of water less than 0.2 increases linearly with the fraction, and reaches the value for aqueous solution. This variation indicates accumulation of water molecules on the electrode excluding acetonitrile molecules. It is modelled on the concept of the Langmuir‐type isotherm in which water and acetonitrile molecules have competitive interaction with the electrode. The experimental variations by the use of the isotherm yield the difference in the interaction energy, 6 kJ mol−1. The accumulation of water in the DL is supported by the formation of the adsorbed layer by insoluble ferrocene.

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“…Aqueous solution of 1 M (= mol dm -3 ) KCl was filled into the two parallel-arranged electrodes, of which distance was increased so that the solution might be wet on the HOPG electrode (see Figure 1 of ref. 23). Then the contact area was evaluated by analyzing some photographs taken from some directions.…”

Section: Methodsmentioning

confidence: 99%

“…The frequency dispersion has been able to be formulated from the definition of capacitance, q = CV, where q is the charge preserved in the capacitance C at the voltage V [21][22][23][24]. The ac-current density responding to the ac voltage V = V 0 exp (iωt) is given through the differentiation of q by…”

Section: Introductionmentioning

confidence: 99%

Quantitative Relation of the Frequency Dispersion of Double Layer Capacitances to Surface Roughness

2018

ANN

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Frequency dispersion of double layer (DL) capacitances, which can be represented by the power law of the frequency or the constant phase element, is modeled by the Arrhenius equation with the activation energy which has a linear relation with the free energy change in the orientation of solvent dipoles. The Arrhenius equation has a form of a differential equation of the number of oriented dipoles. The solution is the power law of the time, being equivalent to the DL capacitance with the power law of the frequency. The power number is associated with the surface roughness of the electrode on the assumption that a dipole is oriented with the help of interaction on a given local area of the electrode. Then it has an approximately linear relation with the surface roughness. Surface roughness of highly oriented pyrolytic graphite electrodes is varied unintentionally by peeling-off processes and intentionally by electrochemical oxidation. The power numbers determined by acimpedance techniques are compared with surface roughness obtained by scanning probe microscopy. They are approximately proportional to the surface roughness factor when the scanned domain on the surface is less than (40nm), which is much smaller than the domain for the fractal structure.

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Power law for frequency-dependence of double layer capacitance of graphene flakes

Cited by 16 publications

References 39 publications

Decrease in the double layer capacitance by faradaic current

Decrease in the double layer capacitance by faradaic current

Double Layer Impedance in Mixtures of Acetonitrile and Water

Quantitative Relation of the Frequency Dispersion of Double Layer Capacitances to Surface Roughness

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