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Concentration dependence of resistancecomponents in solutions containing dissolved Fe2+/
Fe3+
Dai Inouea and Yutaka Moritomo*abc

Electrolyte solutions containing Fe2+/Fe3+ are suitable for liquid thermoelectric conversion devices (LTEs),
because they are inexpensive materials and exhibit a high electrochemical Seebeck coeﬃcient a. Here, weinvestigated the concentration (c) dependence of resistance components, i.e., solvent (Rs), charge-transfer

Received 15th November 2023
Accepted 8th February 2024

(Rct), and diﬀusion (Rdif) resistances, of dissolved-Fe2+/Fe3+-containing aqueous, methanol (MeOH),
acetone, and propylene carbonate (PC) solutions. We found that the c dependence of Rs and Rdif areccand Rdif 1 ¼ Cdif
well reproduced by empirical formulas, Rs 1 ¼ Cs
, where h(c) is viscosity at c.
hðcÞhðcÞ1=2

DOI: 10.1039/d3ra07829a

We further found that the magnitudes of Cs and Cdif are nearly independent of solvent, suggesting that hrsc.li/rsc-advancesis one of the signiﬁcant solution parameters that determine Rs and Rdif.

1

Introduction

Energy-harvesting devices are attracting the current attention ofresearchers from the viewpoint of a basic power source for theinternet of things (IoT) society as well as sustainable development goals (SDGs). Thermoelectric conversion devices (TEs) arepromising because they cover the eld from bioelectric andwearable electronics to industrial power generation. In particular, exible TEs using cellulose gel1 have excellent compatibility with various thermoelectric conversion materials. This isbecause cellulose can be used in the design of exible and ion/
electron conductive materials with robust mechanical properties. Flexible TEs are expected to be used not only for thermoelectric conversion but also for sensors and refrigeration units.
Among TEs, liquid thermoelectric conversion devices (LTEs)
are promising because they are made of inexpensive materials.
There is already a long history of LTE research.2 Nevertheless,vigorous research has become more active in recent years andmany research results have been reported.3–19 The performanceof LTEs is governed by the electrochemical Seebeck coeﬃcienta, eﬀective electric conductivity s, and eﬀective thermal
conductivity k of the electrolyte.20 Unlike solid thermoelectric
devices, s is related to the charge transfer and diﬀusion
processes of redox ions as well as the conventional ion migration. The magnitude of s depends on the microscopic structureaGraduate School of Pure & Applied Science, University of Tsukuba, Tennodai 1-1-1,
Tsukuba, Ibaraki 305-8571, Japan. E-mail: moritomo.yutaka.gf@u.tsukba.ac.jpbFaculty of Pure & Applied Science, University of Tsukuba, Tennodai 1-1-1, Tsukuba,
Ibaraki 305-8571, Japanc
Tsukuba Research Center for Energy Materials Science (TREMS), University ofTsukuba, Tsukuba, Ibaraki 305-8571, Japan6292 | RSC Adv., 2024, 14, 6292–6297

and material of the electrodes.16,17 In addition, eﬀective s and k
are inuenced by convection of the electrolyte induced by DT.
a2 sT, where T is
The dimensionless gure of merit (ZT ¼ktemperature) is a measure of the LTE performance. With theincrease of ZT, the thermal eﬃciency h increases toward theDT
Carnot eﬃciency ¼, which is the maximum eﬃciency ofTHa heat engine.21 To enhance ZT, it is eﬀective to increase(decrease) a and s (k).
In recent years, research on LTEs using an organic electrolyte18,19 has begun to attract attention, as has research on
conventional LTEs using an aqueous electrolyte.4–17 This isbecause the organic electrolytes exhibit both large a and small
k. In several organic solutions containing Fe2+/Fe3+, a is higher
than the value (= 1.4 mV K−1) of an aqueous solution. For
example, a is 3.6 mV K−1 in acetone solution and 1.8 mV K−1 inpropylene carbonate (PC) solution.22 In addition, k of a typicalorganic solvent is z 0.2 W K−1 m−1 and is approximately 33% of
the value (= 0.6 W K−1 m−1) of water. Recently, Wake et al.18,19
showed that LTEs composed of dissolved-Fe2+/Fe3+-containing
methanol (MeOH) and acetone solutions exhibit a large power
factor (PF = a2s) comparable to that of the corresponding
aqueous LTE. They also reported a and s against soluteconcentration c. The disadvantage of organic electrolytes isa small s value compared with that of an aqueous electrolyte.
Except for aqueous electrolyte,7 there exists no detailed investigation on the resistance components. Therefore, the origin of
the small s in organic electrolytes is still unclear. Here, we will
investigate the resistance components of several solutions
containing dissolved Fe2+/Fe3+ against c to deeply understand s
and to obtain guidelines for increasing s in organic electrolytes.

© 2024 The Author(s). Published by the Royal Society of ChemistryView Article OnlinePaperd, where d and s are thesselectrode distance and area, respectively) of an electrolyte
solution consists of the solution resistance Rs due to ion
migration, charge transfer resistance Rct due to electron transfer, and diﬀusion resistance Rdif due to reactant/product diﬀusion.23 Among them, Rs is derived from the balance between theelectric force (=jzjeEef; jzj, e, and Eef are the charge number,elementary charge, and electric eld, respectively) and frictional
force. According to Stokes’ law, the latter force is expressed as
6phrv, where h, r, and v are the viscosity, eﬀective radius, andvvelocity of the ion, respectively. Then, the mobility u h
of
Eef
jzje
and is inversely proportional toan ion is expressed as u ¼
6phr
h. On the other hand, Rct and Rdif are governed by the reaction
kinetics in the vicinity of the electrode surface and are independent of d. The reaction rate k is expressed aseDEkfexp , where DE (= E − Eeq; E and Eeq are the eleckB T
trode and equilibrium potentials, respectively) and kB are theoverpotential and Boltzmann constant, respectively. In the
kB T, the charge-transfer current Jct is expressedregion of DE ei0 e
DE,23 where i0 is the exchange current. Thus, Rct is
as Jct ¼
kB T
kB T
and is independent of d. The physicalproportional toi0 emeaning of Rdif is as follows. As the reaction progresses, theconcentration of reactants/products at the electrode surfacechanges in a way that prevents further reaction. For the reaction
to continue, the reactants/products must diﬀuse into/from thebulk region. Note that the diﬀusion current of reactants/
products is driven by the concentration gradient created by
the reaction at the electrode surface and is independent of d.
In this work, we investigated the c-dependence of Rs, Rct, andRdif of dissolved-Fe2+/Fe3+-containing aqueous, MeOH, acetone,
and PC solutions. We found that the c-dependence of Rs and Rdifcis well reproduced by empirical formulas, Rs 1 ¼ Cs
and
hðcÞ
c
. We further found that their coeﬃcients, Cs
Rdif 1 ¼ CdifhðcÞ1=2
and Cdif, are nearly independent of solvent, suggesting that h is
one of the signicant solution parameters that determine Rs
and Rdif.

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In general, the resistance R (¼2 Experimental methods
2.1

Solution preparation

In this study, water, MeOH, acetone, and PC were selected as thesolvents because they exhibit a high solubility of Fe(ClO4)2/Fe(ClO4)3. We prepared aqueous, MeOH, acetone, and PC
solutions containing c M Fe(ClO4)2$6.0H2O and c M Fe(ClO4)3$7.1H2O. Distilled water, MeOH, acetone, PC, and solutes werepurchased from FUJIFILM Wako Corp. and used as received.
Table 1 shows the solubility s and critical concentration c* ofFe(ClO4)2/Fe(ClO4)3 in the four solvents. c* is dened as the© 2024 The Author(s). Published by the Royal Society of Chemistry

RSC Advances
Table 1 Solubility s and critical concentration c* of Fe(ClO4)2$6.0H2O/Fe(ClO4)3$7.1H2O in several solvents at 298 K. c* is deﬁned as
the concentration at which one Fe ion is dissolved per six solvent
molecules. MeOH and PC represent methanol and propylene
carbonate, respectively

Solvents (M)c* (M)Water
MeOH
Acetone
PC

2.5
2.5
1.2
1.5

4.62
2.06
1.12
0.97

concentration at which one Fe ion is dissolved per six solvent
molecules. At c = c*, all solvent molecules are on averagecoordinated with Fe ions.
2.2

Total resistance

The total resistance Rtot of the electrolyte was measured ina two-pole cell at 298 K.24 The electrodes were produced froma 220 mm graphite sheet (PREMA-FOIL, TOYO TANSO). The
electrode distance d and area s are 1.0 cm and 0.42 cm2,
respectively. The voltage drop V was measured against thecurrent I (I # 0.4 mA) with a multimeter. I was changed ina stepwise manner at intervals of several minutes. V was stable
and no change over time was observed. The slope of the I–V plotcorresponds to Rtot.
2.3

Electrochemical impedance spectroscopy

Rct and Rdif were evaluated in the same cell with the same
electrodes. d and s are 1.0 cm and 0.42 cm2, respectively. Electrochemical impedance spectroscopy (EIS) was performed at
298 K with use of a potentiostat (Vertex.one.EIS, Ivium Technologies). The frequency range was from 50 mHz to 100 kHz,and the amplitude was 10 mV. V was stable and no change overtime was observed. It was conrmed that almost identical EIS
data were obtained through multiple measurements.
The EIS data were analyzed with a Randles equivalentcircuit,23 which consists of Rs, Rct, double layer capacitance Cd,
and Warburg impedance Zu. Zu is expressed as Zu = AW(u−1/2 −iu−1/2), where AW and u are the Warburg coeﬃcient and angularvelocity, respectively. It was diﬃcult to evaluate the magnitude
of Rdif from AW even though Zu describes the diﬀusion processof the reactants/products. In the present study, we tentatively
evaluate the Rdif values by subtraction of Rs and Rct from Rtot. Weconrmed a positive correlation between AW and Rdif (= Rtot −Rs − Rct), which strongly supports the correctness of our evaluation method of Rdif (vide infra).

3 Results
3.1

Total resistanceFig. 1 shows examples of the I–V plot of several solutions containing dissolved Fe2+/Fe3+ at 298 K: (a) water, (b) MeOH, (c)acetone, and (d) PC. For all solutions, V increases in proportion
to I. Rtot was evaluated from the slope of the plots, as indicatedby the straight lines. The obtained Rtot values are listed in Table

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Table 2 Total resistance Rtot, solution resistance Rs, charge-transfer
resistance Rct, diﬀusion resistance Rdif, and Warburg coeﬃcient AW in
solvents containing c M Fe(ClO4)2 and c M Fe(ClO4)3. Rdif was evaluated by subtraction of Rs and Rct from Rtot

Fig. 1 Voltage V against current I for several solutions containing
dissolved Fe2+/Fe3+ at 298 K: (a) water, (b) MeOH, (c) acetone, and (d)PC. Data for three typical solute concentrations are shown for eachsolution: below the resistance minimum (blue), near the resistanceminimum (green), and above the resistance minimum (red). The
straight lines are the results of least-squares ﬁts.

2. In (a) the aqueous solution, Rtot decreases from 65.0 U at
0.5 M to 28.5 U at 1.5 M, and then increases to 37.9 U at 2.5 M.
The decrease in Rtot in the low c region is due to the increase in
the number (f c) of charge carriers, such as Fe2+ and Fe3+. Thisbehavior is consistent with the literature.6 Similar local minima
structures in the c–Rtot plot are also observed for the MeOH,
acetone and PC solutions (Table 2).
Let us estimate the maximum value of ZT in the aqueous
electrolyte at 300 K with the use of Rtot shown in Table 2. Thedmaximum value of s ¼
is 86.0 mS cm−1 at c = 2.0 M.
SRtpt
Kim et al.6 reported c-dependence of a and k in an aqueous
solution containing Fe(ClO4)2/Fe(ClO4)3. From the extrapolationof the reported data, we evaluated a = 1.76 mV K−1 and k =0.4 W K−1 m−1 at 2.0 M. Then, we obtained ZT = 0.020 at 2.0 M.
The ZT value is smaller than the value (= 0.036 (ref. 6) at 0.8 M)
reported by Kim et al.,6 reecting the smaller s obtained in thepresent experiment. We note that eﬀective s of a LTE is inuenced by the microscopic structure of the electrodes as well as
the convection of the electrolyte.
3.2

Solventc (M)Rtot (U)Rs (U)

Rct (U)

Rdif (U)AW (U s−1/2)

Water
Water
Water
Water
Water
Water
Water
Water
MeOH
MeOH
MeOH
MeOH
MeOH
MeOH
MeOH
AcetoneAcetoneAcetoneAcetoneAcetoneAcetoneAcetone
PC
PC
PC
PC
PC
PC

0.10
0.20
0.50
0.80
1.00
1.50
2.00
2.50
0.05
0.10
0.50
1.00
1.50
2.00
2.50
0.05
0.10
0.20
0.40
0.80
1.00
1.20
0.05
0.10
0.20
0.50
1.00
1.50

351.0
236.0
65.0
42.6
39.4
28.5
27.7
37.9
906.0
314.0
95.6
95.2
98.2
110.0
115.0
692.0
333.0
225.0
172.0
192.0
254.0
251.0
1265.0
813.0
528.0
537.0
741.0
726.0

56.0
35.4
19.8
18.1
18.1
16.3
19.6
20.0
221.7
126.0
54.6
60.9
67.4
75.5
83.3
439.2
187.0
130.4
100.3
126.8
160.5
180.0
726.8
615.0
387.6
447.9
663.3
674.1

32.0
16.1
5.3
3.8
2.9
2.1
1.9
1.9
65.2
22.6
4.4
1.8
1.6
2.4
3.2
35.6
18.0
8.6
5.0
2.8
4.5
4.5
75.6
27.0
11.5
11.4
12.9
13.2

263.0
184.5
39.9
20.7
18.4
10.1
6.2
16.0
619.1
165.4
36.6
32.5
29.2
32,1
28.6
227.2
128.0
86.0
66.7
62.4
89.0
66.5
425.6
171.0
128.9
77.7
64.8
38.7

86.2
42.8
15.7
10.8
10.0
9.1
7.0
10.4
176.7
63.0
16.2
9.1
8.4
6.8
7.5
134.6
72.0
29.0
14.7
9.0
9.2
8.8
255.8
70.0
31.2
17.5
15.0
13.9

a straight line with an inclination of 45° on the right side. The
resistances on the le and right sides of the semicircle correspond to Rs and Rs + Rct, respectively. The intersection of theElectrochemical impedance spectroscopy

Fig. 2 shows examples of the Cole–Cole plots of complex
impedance for several solutions containing dissolved Fe2+/Fe3+
at 298 K: (a) water, (b) MeOH, (c) acetone, and (d) PC. The Cole–
Cole plot of 0.1 M MeOH solution (Fig. 2(b)) shows a prototypical shape. The plot shows a semicircle on the le side and6294 | RSC Adv., 2024, 14, 6292–6297

Fig. 2 Cole–Cole plots of complex impedance for several solutions
containing dissolved Fe2+/Fe3+ at 298 K: (a) water, (b) MeOH, (c)acetone, and (d) PC. The solid curves are the results of least-squares
ﬁts with a Randles equivalent circuit composed of Rs, Rct, Cd, and Zu(see text).

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Paperstraight line with the horizontal axis corresponds to Rs + Rct −2AW2Cd. Similar behaviors are also observed in the other solutions. The solid curves in Fig. 1 are the results of least-squares
ts with a Randles equivalent circuit composed of Rs, Rct, Cd,
and Zu. The Randles equivalent circuit well reproduces theobserved complex impedance. Thus, we obtained Rs, Rct, Cd,
and AW. We further evaluate Rdif (= Rtot − Rs − Rct) with the useof Rtot. The obtained Rs, Rct, Rdif, and AW values are listed inTable 2.
AW is expected to have a strong correlation with Rdif because
Zu [= AW(u−1/2 − iu−1/2)] describes the diﬀusion process of thereactants/products. We calculated the correlation coeﬃcient X
between AW and Rdif (= Rtot − Rs − Rct) for each solution system;
X = 0.976 for water, 0.995 for MeOH, 0.980 for acetone, and
0.988 for PC. The positive correlation (X $ 0.976) between AW
and Rdif strongly supports the correctness of our evaluation
method of Rdif.

3.3

Concentration dependence of resistivity components

Fig. 3 shows the c-dependence of (a) Rs−1, (b) Rct−1, (c) Rdif−1,and (d) Rtot−1 in several solutions containing dissolved Fe2+/Fe3+
at 298 K. For the convenience of explanation, the horizontal axis
is normalized by the critical concentration c* of each solvent. Atc = c*, all solvent molecules are on average coordinated with Fe
ions.

RSC AdvancesFirst, let us examine the solvent dependence of Rs−1, Rct−1,
and Rdif−1. Signicant solvent dependence is observed forc(a) Rs−1. Rs−1 values at¼ 0:1 are 69.5 × 10−3 U−1 in water,c*17.1 × 10−3 U−1 in MeOH, 6.7 × 10−3 U−1 in acetone, and1.4 × 10−3 U−1 in PC. The Rs−1 values in organic solutions aremuch smaller than those in aqueous solutions. In contrast,
Rct−1 and Rdif−1 have relatively small solvent dependence.
In this sense, reducing Rs is eﬀective to reduce Rtot in
organic solution. Shortening d is especially eﬀective becausek (z 0.2 W K−1 m−1) of an organic solvent is much smaller thank (= 0.6 W K−1 m−1) of water. Reecting the small k in organic
solvent, a suﬃcient DT is expected between the electrodes, evenin the cell with smaller d.
cNext, let us investigate the dependence of Rs−1, Rct−1, and
c*
c
c
as
Rdif−1. In the small region, Rs−1 increases linearly withc*c*−1
indicated by the straight lines in Fig. 3(a). The increase in Rs is
due to the increase in the number (f c) of charge carriers, suchc
as Fe2+ and Fe3+. Upon further increasing beyond ∼0.3, Rs−1c*ccbegins to decrease with . Similarly, in the small
region,c*c*c
as indicated by theRct−1 and Rdif−1 increase linearly withc*straight lines in Fig. 3(b) and (c), respectively. The increase in
Rct−1 and Rdif−1 is due to the increase (f c) of reactant/productcconcentration, i.e., Fe2+/Fe3+. Upon further increasing beyondc*∼0.5, Rct−1 and Rdif−1 begin to saturate. The saturation of Rct−1
can be ascribed to the nite reaction number (Nreaction) per unit
time at the electrode surface. The redox reaction cannot keep up
with the supply of reactants when the number (Nreactant f c) of
reaching reactants per unit time exceeds Nreaction. In sucha region, Nreaction becomes the rate-determining factor for the
charge-transfer current Jct, and hence, Rct−1. As a result, Rctbecomes constant at suﬃciently large c.

4 Discussion
4.1

Concentration dependence of Rs

Now, let us discuss the solution parameters that determine Rs.
 s 
sF X Rs 1 ¼ ss is expressed as Rs 1 ¼
zj uj Cj ,23 where F,dd jzj, uj, and Cj are the Faraday constant, charge number, mobility,
and molar concentration of the j-th ion, respectively. By  2z j esFec Xzj 
1, we obtain Rs ¼
. Notesubstituting uj ¼
6phrj
6pdh j rj

Solute concentration (c) dependence of (a) Rs−1, (b) Rct−1, (c)−1
Rdif , and (d) Rtot−1 in several solutions containing dissolved Fe2+/Fe3+
Fig. 3at 298 K. The horizontal axis is normalized by the critical concentration
c* of each solvent. The straight lines in (a), (b), and (c) represent theclinear relation with .
c*© 2024 The Author(s). Published by the Royal Society of Chemistrythat CFe2+ = CFe3+ = c in the present solutions. By assuming
 2Pzj 
is independent of c in each solution, we obtain thej rjcsimple relation Rs 1 fCs , where Cs is a constant. The tophpanels of Fig. 4(a)–(d) show h of each solution against c. The hvalues were evaluated at 298 K using a sine-wave vibro viscometer (SV-10; A&D Company Limited). In all solutions, h increases
nonlinearly with c. The solid curves are the results of least-

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RSC AdvancesPaperc
Coeﬃcients (Cs and Cdif) of empirical formulas, Rs 1 ¼ Cs
hðcÞcand Rdif 1 ¼ Cdif
, determined by least-squares ﬁts with thehðcÞ1=2
observed data. MeOH and PC represent methanol and propylene
carbonate, respectively

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Table 3

Solvent

Cs (mPa s M−1 U−1)

Cdif (mPa1/2 s1/2 M−1 U−1)

Water
MeOH
Acetone
PC

0.183
0.132
0.019
0.104

0.125
0.099
0.053
0.166

In (c) acetone solution, the shape of the c–Rs−1 plot (opencircles) is qualitatively diﬀerent from the shape of the empiricalformula (solid curve). In the region of c $ 0.5, the empiricalformula results decrease steeply while the observed Rs−1
decreases slowly. If Cs is set to ∼0.1, the agreement between thecalculated and observed values is improved in the region of c $0.5 even though the calculated value is much larger in theregion of c ∼ 0.3. This implies that an additional factor, e.g., therepulsive interaction between Fe ions, suppressed Rs in theregion of c ∼ 0.3.
4.2

Fig. 4 (a) Viscosity h (top), Rs−1 (middle), Rdif−1 (bottom) in aqueous
solutions containing dissolved Fe2+/Fe3+ at 298 K against soluteconcentration c. (b) h, Rs−1, and Rdif−1 in MeOH solutions containing
dissolved Fe2+/Fe3+ at 298 K against c. (c) h, Rs−1, and Rdif−1 in acetone
solutions containing dissolved Fe2+/Fe3+ at 298 K against c. (d) h, Rs−1,
and Rdif−1 in PC solutions containing dissolved Fe2+/Fe3+ at 298 K
against c. The solid curves in the upper panels are the results of leastsquares ﬁts with a quadratic function. The solid curves in the middlecfunction. The
panels are the results of least-squares ﬁts with thehðcÞsolid curves in the bottom panels are the results of least-squares ﬁtscfunction.
with thehðcÞ1=2

squares ts with a quadratic function. With use of the quadraticc, can befunction h(c), the empirical formula, Rs 1 ¼ Cs
hðcÞcalculated.
The middle panels of Fig. 4(a)–(d) show comparisons
between observed Rs−1 (open circles) and empirical formula(solid curves) against c. We note that there is only one tting
parameter (Cs) to adjust the magnitude but no parameter toadjust the shape. Nevertheless, the curve reproduces theobserved Rs−1 well, except for (c) acetone solution. In Table 3, welisted Cs. Except for the acetone solution, the solvent dependence of Cs is rather small, falling between 0.104 mPa s M−1 U−1
and 0.183 mPa s M−1 U−1. This is probably because the r value
does not change greatly depending on the solvent.

6296 | RSC Adv., 2024, 14, 6292–6297

Concentration dependence of Rdif

Finally, let us consider the relationship between Rdif−1 and h.
Rdif−1 is proportional to the diﬀusion current Jdif, which isdC
expressed as Jdif fD . Replacing the diﬀerential with thedx
DDC 23
diﬀerence, we get Jdif f, where Dx and DC are the diﬀuDx
sion length and concentration diﬀerence between electrodesurface and bulk solution, respectively. In one-dimensionalpﬃﬃﬃﬃﬃﬃﬃﬃ
diﬀusion, Dx is expressed as Dx ¼ 2DtfD1=2 , where t is theelapsed time. Then, Jdif is proportional to cD1/2 because DC f c.
kB T.
From the Stokes–Einstein equation, we obtain D ¼
6phrcFinally, we obtain an empirical relation Rdif 1 ¼ Cdif,hðcÞ1=2
where Cdif is a constant. We can calculate the empirical formulawith use of the quadratic function h(c).
The bottom panels of Fig. 4(a)–(d) show comparisons
between the observed Rdif−1 (open circles) and empiricalformula (solid curves) against c. We note that there is only one
tting parameter (Cdif) to adjust the magnitude. Nevertheless,the curve reproduces the observed Rdif−1 well. In Table 3, we list
the Cdif values. The solvent dependence of Cdif is rather small,falling between 0.053 mPa1/2 s1/2 M−1 U−1 and 0.166 mPa1/2 s1/2
M−1 U−1. This is probably because the r value does not change
greatly depending on the solvent.

5 Conclusions
In conclusion, we investigated the c-dependence of Rs, Rct, andRdif in dissolved-Fe2+/Fe3+-containing aqueous, MeOH, acetone,
and PC solutions. We found that the c-dependence of Rs and Rdifcis well reproduced by the empirical formulas Rs 1 ¼ Cs
andhðcÞ© 2024 The Author(s). Published by the Royal Society of ChemistryView Article Online

Paperc. We further found that the magnitudes of Cs
hðcÞ1=2
and Cdif are nearly independent of the solvent, suggesting that his one of the signicant solution parameters that determine Rs
and Rdif. Our ndings suggest that s of the electrolyte solution
can be increased through reducing h.

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Rdif 1 ¼ Cdif

Author contributions
Dai Inoue: data curation, formal analysis, and investigation.
Yutaka Moritomo: conceptualization, supervision, writing –original dra, and writing – review & editing.

Conﬂicts of interest
There are no conicts to declare.

Acknowledgements
This work was supported by JSPS KAKENHI (Grant No.
22KJ0413), Yazaki Memorial Foundation for Science and Technology, and joint research with Taisei Rotec Corporation.

Notes and references
1 Q. Long, G. Jiang, J. Zhou, D. Zhao, P. Jia and S. Nie, Nano
Energy, 2024, 120, 109130.
2 T. Ikeshoji, Bull. Chem. Soc. Jpn., 1987, 60, 1505;
I. Quickenden and Y. Mua, J. Electrochem. Soc., 1995, 142,
3985; Y. Mua and T. I. Quickenden, J. Electrochem. Soc.,
1996, 143, 2558; J. Kawamura, M. Shimoji and H. Hoshino,
J. Phys. Soc. Jpn., 1981, 50, 194; A. Schiraldi, E. Pezzati and
P. Baldini, J. Phys. Chem., 1985, 89, 1528; R. Hu, B. A. Cola,
N. Haram, J. N. Barisci, S. Lee, S. Stoughton, G. Wallace,
C. Too, M. Thomas, A. Gestos, M. Ed Cruz, J. P. Ferraris,
A. A. Zakhidov and R. H. Baughman, Nano Lett., 2010, 10,838; D. R. MacFarlane, N. Tachikawa, M. Forsyth,J. M. Pringle, P. C. Howlett, G. D. Elliott, J. F. Davis Jr,
M. Watanabe, P. Simon and C. A. Angell, Energy Environ.
Sci., 2014, 7, 232; M. Bonetti, S. Nakamae, M. Roger and
P. Guenoun, J. Chem. Phys., 2011, 134, 114513;
T. J. Abraham, D. R. MacFarlane and J. M. Pringle, Chem.
Commun., 2011, 47, 6260; M. Romano, S. Gambhir,
J. Razal, A. Gestos, G. Wallace, J. Chen and J. Therm, J.
Therm. Anal. Calorim., 2012, 109, 1229; M. S. Romano,
N. Li, D. Antiohos, J. M. Razal, A. Nattestad, S. Beirne,
S. Fang, Y. Chen, R. Jalili, G. G. Wallace, R. Baughman and
J. Chen, Adv. Mater., 2013, 25, 6602; T. J. Abraham,
D. R. MacFarlane and J. M. Pringle, Energy Environ. Sci.,
2013, 6, 2639; A. Gunawan, C.-H. Lin, D. A. Buttry,
V. Mujica, R. A. Taylor, R. S. Prasher and P. E. Phelan,
Nanoscale Microscale Thermophys. Eng., 2013, 17, 304;
N. Jiao, T. J. Abraham, D. R. MacFarlane and J. M. Pringle,© 2024 The Author(s). Published by the Royal Society of Chemistry

RSC Advances
J. Electrochem. Soc., 2014, 161, D3061; S. Uhl, E. Laux,
T. Journot, L. Jeandupeux, J. Charmet and H. Keppner, J.
Electron. Mater., 2014, 43, 3758; A. Gunawan, H. Li,
C.-H. Lin, D. A. Buttry, V. Mujica, R. A. Taylor, R. S. Prasher
and P. E. Phelan, Int. J. Heat Mass Transfer, 2014, 78, 423;
M. A. Lazar, D. Al-Masri, D. R. MacFarlane andJ. M. Pringle, Phys. Chem. Chem. Phys., 2016, 18, 1404.
3 Y. Liang, J. K.-H. Hui, M. Morikawa, H. Inoue, T. Yamada andN. Kimizuka, ACS Appl. Energy Mater., 2021, 4, 5326.
4 B. Yu, J. Duan, H. Cong, W. Xie, R. Liu, X. Ahuang, H. Wang,
B. Qi, M. Xu and L. Wan, Science, 2020, 370, 342.
5 Y. Xaing, X. Guo, H. Zhu, Q. Zhang and S. Zhu, Chem. Eng. J.,
2023, 461, 142018.
6 J. H. Kim, J. H. Lee, E. E. Palen, M.-S. Suh, H. H. Lee andR. J. Kang, Sci. Rep., 2019, 9, 8706.
7 M. A. Buckingham, F. Marken and L. Aldous, Sustainable
Energy Fuels, 2018, 2, 2717.
8 J. Duan, G. Feng, B. Yu, J. Li, M. Chen, P. Yang, J. Feng, K. Liu
and J. Zhou, Nat. Commun., 2018, 9, 5146.
9 T. Kim, J. S. Lee, G. Lee, H. Yoon, J. Yoon, T. J. Kangd andY. H. Kim, Nano Energy, 2017, 31, 160.
10 M. Sindhuja, B. Lohith, V. Sudha, G. R. Manjunath and
S. Harinipriya, Mater. Res. Express, 2017, 4, 075513.
11 H. Im, T. Kim, H. Song, J. Choi, J. S. Park, R. Ovalle-Robles,
H. D. Yang, K. D. Kihm, R. H. Baughman, H. H. Lee,T. J. Kang and Y. H. Kim, Nat. Commun., 2016, 7, 10600.
12 H. Zhou, T. Yamada and N. Kimizuka, J. Am. Chem. Soc.,
2016, 138, 10502.
13 A. H. Kazim and B. A. Cola, J. Electrochem. Soc., 2016, 163,
F867.
14 S. W. Lee, Y. Yang, H.-W. Lee, H. Ghasemi, D. Kraemer,
G. Chen and Y. Cui, Nat. Commun., 2014, 5, 3942.
15 Y. Tanaka, A. Wake, D. Inoue and Y. Moritomo, Jpn. J. Appl.
Phys., 2024, 63, 014002.
16 S.-M. Jung, S.-Y. Kang, B.-J. Lee, J. Kwon, D. Lee and
Y.-T. Kim, Adv. Funct. Mater., 2023, 33, 2304067.
17 B. Yu, H. Xiao, Y. Zeng, S. Liu, D. Wu, P. Liu, J. Guo, W. Xie,
J. Duan and J. Zhou, Nano Energy, 2022, 93, 106795.
18 A. Wake, D. Inoue and Y. Moritomo, Appl. Phys. Express,
2022, 15, 054002.
19 A. Wake, D. Inoue and Y. Moritomo, Jpn. J. Appl. Phys., 2023,
62, 014002.
20 J. Duan, B. Yu, L. Huang, B. Hu, M. Xu, G. Feng and J. Zhou,
Joule, 2021, 5, 768.
21 S. W. Angrist, Direct Energy Conversion, Allyn and Bacon, Inc.,
Boston, 1982.
22 D. Inoue, H. Niwa, H. Nitani and Y. Moritomo, J. Phys. Soc.
Jpn., 2021, 90, 033602.
23 A. J. Bard, L. R. Faulkner, and H. S. White, Electrochemical
Methods, Wiley, West Sussex, 2022.
24 Y. Fukuzumi, Y. Hinuma and Y. Moritomo, Jpn. J. Appl. Phys.,
2019, 58, 065501.

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