ANALYTICAL SCIENCES JULY 2011, VOL. 27 685

1 Introduction

The problem of the liquid junction potential (LJP)*1 between electrolyte solutions in different solvents is theoretically interesting. But its importance from the practical or experimental point is also considerable. In electrochemical measurements in nonaqueous solutions, it often happens that the solvent of the reference electrode is different from that of the solution under

study. Aqueous calomel and Ag/AgCl reference electrodes are often used with their tips being inserted into the salt bridge of the nonaqueous solvent under study. Besides these aqueous reference electrodes, calomel and Ag/AgCl electrodes in methanolic KCl and an Ag/Ag+ electrode in AN are sometimes used. In all these cases, a liquid junction between different solvents is formed and the LJP there gives a direct influence on the results of the potential measurements. Therefore, the magnitude of the LJP is of great concern to us. But, because the phenomena occurring at the junction between different solvents are complicated, the problem of the LJP was considered to be difficult to solve.

The first approach to this problem was to estimate the LJP using an extra-thermodynamic assumption. The followings are examples: Kolthoff1 discussed the magnitudes of the LJP between the solutions in AN and the aqueous saturated calomel electrode (SCE), which were estimated before 1965. Kolthoff and Thomas2 reported that the LJP between the solution in

2011 © The Japan Society for Analytical Chemistry

Present address: 4-31-6-208 Kichijoji-honcho, Musashino, Tokyo 180–0004, Japan.E-mail: izutsu@almond.ocn.ne.jp

1 Introduction 6852 Characteristics of the LJP between

Different Solvents 686 2·1 Components (a) and (b) 2·2 Component (c)3 Three-component Method for the

Estimation of the LJP 693

4 Stability of the LJP between Different Solvents 693

5 Assumption of the Negligible LJP between Different Solvents 694

6 Conclusion 6947 Acknowledgements 6948 References 694

Liquid Junction Potentials between Electrolyte Solutions in Different Solvents

Kosuke IZUTSU

Faculty of Science, Shinshu University, Matsumoto 390–8621, Japan

Many chemists are not familiar with the problem of the liquid junction potential (LJP) between electrolyte solutions in different solvents. Some even misunderstand it. Therefore, it seems worthwhile to write a review article on this subject. The LJP between electrolyte solutions in different solvents consists of three components: i.e., (a) a component related to electrolyte concentrations and ionic mobilities, (b) a component related to ion solvation (and ionic mobilities), and (c) a component related to solvent-solvent interactions. The characteristics of each of the three components have been discussed in detail, based on our old and new results. Components (a) and (b) are diffusion potentials but component (c) is a dipole potential.

(Received April 1, 2011; Accepted May 12, 2011; Published July 10, 2011)

Kosuke IZUTSU received his D.Sc. degree from Kyoto University in 1961 and became an Assistant Professor there in 1963. During 1961 – 1963, he worked under Prof. Kolthoff (University of Minnesota). He moved to Shinshu University, Matsumoto, as an Associate Professor in 1972, was promoted to Professor in 1975, and has been an Emeritus Professor since 1999. He served as the Chairman of the IUPAC Commission on Electroanalytical Chemistry and as the President of the Japan Society for Analytical Chemistry.

He is the author of the book Electrochemistry in Nonaqueous Solutions, 2nd edition, Wiley-VCH (2009).

*1 Abbreviations: Ac, acetone; AN, acetonitrile; γ-BL, γ-butyrolactone; DCE, 1,2-dichloroethane; DMA, N,N-dimethylacetamide; DMF, N,N-dimethylformamide; DMSO, dimethyl sulfoxide; EtOH, ethanol; EC ethylene carbonate; EG, ethylene glycol; FA, formamide; HMPA, hexamethylphosphoric triamide; LJP, liquid junction potential; MeOH, methanol; NB, nitrobenzene; NM, nitromethane; NMP, N-methyl-2-pyrrolidinone; PC, propylene carbonate; TMS, sulfolane; W, water.

Reviews

686 ANALYTICAL SCIENCES JULY 2011, VOL. 27

AN  and the aqueous SCE with a tip of an aqueous saturated KNO3-agar salt bridge was approximately 0.25 V,*2 assuming the solvent-independence of the potentials of ferricinium ion/ferrocene (Fc(+1/0)) and tris(o-phenanthroline)iron(III)/(II) couples. Coetzee and Campion3 obtained the value of 0.034 V between AN and aqueous SCE, after getting the transfer activity coefficient of rubidium ion by use of the modified Born equation. By a similar method, Matsuura et al.4 got the LJP-values between organic solvents other than AN and aqueous SCE (results: EC, –0.067 V; PC, –0.007 V; DMF, 0.081 V; DMSO, 0.090 V). Diggle and Parker5 used the extra-thermodynamic assumption of a reference electrolyte, which assumes ΔG°tr(Ph4As+) = ΔG°tr(BPh4

–) = (1/2)ΔG°tr(Ph4AsBPh4) (ΔG°tr: standard Gibbs energy of transfer), and got the LJPs between 0.1 M Et4NPic(S) (S: solvent) and aqueous saturated KCl (results: MeOH, 0.025 V; EtOH, 0.030 V; NM, 0.059 V; AN, 0.093 V; FA, 0.078 V; PC, 0.135 V; HMPA, 0.152 V; DMF, 0.172 V; DMSO, 0.174 V; TMS, 0.223 V). Datta et al.6 got somewhat different values using the same assumption. Kotocová7 assumed solvent-independence of the potential of bis(biphenyl)chromium(I)/(0) (BCr(+1/0)) couple and got the LJPs between 0.1 M Bu4NClO4(S) and aqueous 4.16 M KCl-AgCl/Ag (results: NM, 0.032 V; AN, 0.114 V; MeOH, 0.138 V; PC, 0.142 V; Ac, 0.200 V; DMF, 0.210 V; NMP, 0.223 V; DMA, 0.230 V; DMSO, 0.213 V; HMPA, 0.300 V). Krishtalik et al.8,9 assumed the solvent-independence of the potential of cobalticinium ion/cobaltocene (Co(+1/0)) couple and got the LJPs between 0.1 M Bu4NBF4(S) and aqueous saturated KCl (results: dichloromethane, 0.15 V; PC, 0.25 V; γ-BL, 0.27 V; monoglyme, 0.28 V; Ac, 0.30 V). The estimated LJPs varied considerably according to the extra-thermodynamic assumptions employed; it  means that the reliability of the estimated LJP depends on the reliability of the extra-thermodynamic assumption used.*3 Moreover, these estimations cannot clarify the details of the LJP between different solvents.

The LJP between different solvents is determined by both the solvents and the electrolyte(s) present at the junction. Thus, the factors composing the LJP were studied along with its estimation studies. Papers on this subject were reported by the groups of Alfenaar et al.,10 Cox et al.,11 Gaboriaud,12 Murray and Aikens,13 Popovych and his coworker,14–17 Senanayake and Muir18 and by our own.19–36 All of them expressed the LJP between different solvents (Ej) by:

E RTF

tz a

Ftzj

S

S i

ii

ions S

S i

iid d= − − +∫ ∫∑ °

1

2

1

21ln µ EE

E E

j,solvions

j,ion j,solv

∑

≡ +( ) (1)

where ti is the transport number of ion i, zi its charge, ai its activity, and μi° its standard chemical potential.*4 On the right-hand side of Eq. (1), the first and second terms show the contributions from ionic diffusion: the first term is due to the diffusion by the gradients in ionic concentrations and the second is due to the diffusion by the gradients in ionic standard chemical potentials or ionic solvation energies. The third term (Ej,solv) shows the contribution from the solvents, though Gaboriaud12 denied the existence of this term. For convenience, hereafter, the first, second and third terms of Eq. (1) are named components (a), (b), and (c), respectively. All research groups carried out experimental studies. The standpoints of the experimental studies were different from one group to another, but, in analyzing the experimental results, all of them used Eq. (1), by integrating the first and second terms under appropriate conditions. All groups except ours considered that the equations for components (a) and (b) were actually valid and got the value

of component (c) (= Ej,solv) as the difference between the sum of components (a) and (b) and the estimated value of the LJP. Here, the estimated value of the LJP was obtained from the measured emf of the cell and the theoretical potential difference between the electrodes on the two sides of the junction, which was determined by the use of an extra-thermodynamic assumption. As to component (c) obtained by this procedure, Alfenaar et al.10 concluded as follows: “The contribution of the transport of solvent molecules to the diffusion potential is not only a function of the solvent composition but also of the kind of electrolyte that participates in the diffusion process. This is to be expected as the flows of ions and uncharged particles are mutually dependent”. Cox et al.11 showed that there is a linear relation between component (c) and the total heats of transfer (more accurately, total heats of solution) of solvents, but they still considered that this component is due to the transport of solvent molecules across the boundary and that the flows of ions and solvent molecules are mutually dependent, the division of the LJP into Ej,ion (= the sum of components (a) and (b)) and Ej,solv being strictly not justified. All other groups, except ours, considered in nearly the same way, i.e., component (c) was determined by both the solvents and the ions and it was a diffusion potential. As described later, according to our study, the equation for component (b) is actually not valid, though that for component (a) is actually valid. The actual values of component (b) are usually much less (ca. 50% or less) than the theoretical values. Thus, if the theoretical value of component (b) is taken as its actual value, it is an overestimation. The overestimated part of component (b) is added (with a minus sign) to the actual value of component (c) and it gives an impression that component (c) is determined by the solvents and the ions as well. But these are not correct according to our results that component (c) is almost electrolyte-independent and it is determined by the solvent-solvent interaction at the junction and is a dipole potential. Thus, in the following, only the results of our own studies are reviewed.

2 Characteristics of the LJP between Different Solvents

The LJP between different solvents consists of three components: component (a) related to electrolyte concentrations and ionic mobilities, component (b) related to ion solvation (and ionic mobilities), and component (c) related to solvent-solvent interactions.

Here the simplest case is considered: it is a free-diffusion junction with the same electrolyte on the two sides

*2 According to our results, if aqueous saturated KCl instead of aqueous saturated KNO3 is directly in contact with the AN solution, a larger value of LJP should be obtained.

*3 As described later, the reliability of the assumption of reference electrolyte (Ph4AsBPh4) is considered to be the best among the extra-thermodynamic assumptions.

*4 In Refs. 10 and 11, Ej was expressed in the form like

E F t F t zjS

Sir

ii

S

Si i

io/ d / /

2 2= − = −∫ ∫∑( ) ( ) ( )1 11 1

µnns

i

S

Sir

unchargedspecies

i

d

/ d2

∑

∑

−

≡∫

µ

µ( )11

F t E jj,ion j,solv+ E

where μi is the chemical potential and, for ions, μi = μi° + RTln ai. ti

r  is the reduced transport number and tir for ions is equal to ti/zi,

while tir for uncharged species is defined by nF/Q where n is the

moles of uncharged species transported across the junction when a quantity of charge Q flows through the cell.

ANALYTICAL SCIENCES JULY 2011, VOL. 27 687

(c1 MX(S1)¦c2 MX(S2)). In order to get this type of junction(s), we constructed emf-cells by using dual four-way stopcock(s) for high performance liquid chromatography (Fig. 1). The cells were convenient for repeated measurements and gave junctions with LJPs reproducible within ±1 mV. We found that, by using appropriate cell constructions, we could experimentally measure the variation in each of the three components separately (Fig. 2). Thus, we could study the characteristics of each of the three components. The characteristics of the three components are schematically shown in Fig. 3.

2·1 Components (a) and (b)24,25,28–31,33

Components (a) and (b) are diffusion potentials. Component (a) is due to the ionic diffusion by the gradients in ionic

concentrations, while component (b) is due to the ionic diffusion by the gradients in ionic standard chemical potentials or ionic solvation energies. In order to get the theoretical equations for components (a) and (b), the first and second terms of Eq. (1) were integrated by assuming linear variations in a, t, and μ° at the interphase region from the values in S1 to the values in S2 (Fig. 4(a)). Equations (2) and (3) show the relations at the

c1 > c 2

t X

t M

＋

0

Ej(a)

Component (a)J

Component (b)J

Solvation: weaker

Solvation:stronger

＋M+

－X-

0 Ej(b)

Component (c)J

－ ＋ － ＋

－ ＋ － ＋

Lewisacidsolvent

Lewisbasesolvent

0

＋

Ej(c)

Fig. 3　Characteristics of the three components of the LJP between different solvents.

J2J1

j1 J j2

Cell (I)

Cell (II)Ag5mM AgClO425mM Et4NClO4(S2)

25 mM Et4N-ClO4(S2)

c MX(S1=AN)

c3 MX(S3)

c MX(S2)

25 mM Et4N-ClO4(S1=AN)

5mM AgClO4, 25mM Et4NClO4(S1=AN)Ag

Ag5mM AgClO420mM Et4NClO4(S2)

20mMEt4NClO4(S2)

c2MX(S2)

c1MX(S1)

20mM Et4NClO4(S1)

5mM AgClO420mM Et4NClO4(S1)

Ag

J2J1

Cell (II')Ag5mM AgClO425mM Et4NClO4(S2)

c (1mM)Et4NClO4(S2)

c3 (100mM)MX(S3)

c (1mM) Et4N-ClO4(S1=AN)

5mM AgClO4, 25mM Et4NClO4(S1=AN)Ag

Fig. 2　Cell constructions to get the actual variations of the three components. Component (a): the emf of Cell (I) is measured varying c1 and c2, and corrections are made for the LJPs at j1 and j2. Component (b): the emf of Cell (I) is measured varying MX, and corrections are made for the LJPs at j1 and j2 and component (a) at J. Component (c): the emf of Cell (II) or (II′) is measured varying S3, and corrections are made for the influence of components (a) and (b) at J1 and J2, if needed. The sum of the variations in component (c) at J1 and J2 is obtained.

Fig. 1　Schematic diagram of the cell for emf measurements in the study of the LJP between different solvents. The case of Cell (II′).

} }∆ϕ1

∆ϕi∆ϕ2

Interphaseregion

t1,µo1

c1

c2

t2,µo2

S1 S2

(Inter- face)

Inter-face

Interphaseregion

t1,µo1

c1

c2

t2,µo2

ci ,1

ci ,2

S1 S2

(b)(a)

Fig. 4　(a) The variations in c, t, and μ° at the interphase region of the miscible junction, assumed in deriving Eqs. (2) and (3), and (b) those at the immiscible junction, used to get the relation of Fig. 8. Δφi is the distribution potential and Δφ1 and Δφ2 are the LJPs in S1 and S2.

688 ANALYTICAL SCIENCES JULY 2011, VOL. 27

junction with the same electrolyte on the two sides (c1 MX(S1)/c2 MX(S2)).

E RTF

t t aa t tj M1 X1

MX2

MX1M2 Ma( ) ( – ) ln (= −

+ − 11 X2 X1

MX1

MX2 MX1

MX2

MX1

− +

×

−

t t

aa a

aa

)

– ln1

(2)

EF

t t G t tj M1 M2 to

X1 X2b M( ) [( ) ( ) ( )= −

+ − +12

∆ ∆∆Gto X( )] (3)

Here, Ej(a) = 0 for aMX1 = aMX2 in Eq. (2). ΔGto(M) and ΔGt

o(X) in Eq. (3) are the Gibbs energies of transfer of M+ and X– from solvent S1 to S2.*5 We can predict from Eq. (2) that component

(a) is a function of ionic activities (concentrations) and mobilities. We can predict the characteristics of component (b) from Eq. (3): (i) cation M+ makes the side on which the solvation is stronger more positive, while anion X– makes the side on which the solvation is stronger more negative (see component (b) in Fig. 3); (ii) this component is not influenced by electrolyte concentrations.

In order to get the variations in the actual (experimental) values for components (a) and (b), we used Cell (I) in Fig. 2. In the case of component (a), the actual (experimental) variations could be obtained by varying the ratio c1/c2 in Cell (I) and by making corrections for the LJPs at j1 and j2 (by use of the Henderson equation, because junctions j1 and j2 are between the same solvent). In the case of component (b), the actual (experimental) variations could be obtained by varying electrolyte MX in Cell (I), keeping the ratio (c1/c2) constant and by making corrections for the LJPs at j1 and j2 and for component (a) at J (nearly equal to zero when c1 = c2).

In the case of component (a), linear relations of unit slopes were generally observed between the actual variations and the values obtained from Eq. (2), as in Fig. 5. This shows that Eq. (2) is valid; thus, component (a) can be estimated by Eq. (2).

In the case of component (b), the independence from electrolyte concentrations was confirmed using concentrations of (c1 = c2 = 20 mM) and (c1 = 1 mM and c2 = 100 mM) for various solvent systems and MX and showing that the same results were observed for the two sets of concentrations (Fig. 6).25 However, the relations between the actual variations of component (b) and the values calculated by Eq. (3) are somewhat complicated.33 Figure 7 shows such relations for the junctions between water and organic solvents (H2O/S). For miscible junctions, although near-linear relations are observed, the slopes are much smaller than unity, i.e., 0.43 for H2O/AN, 0.45 for H2O/DMF, 0.47 for H2O/DMSO, and 0.50 for H2O/MeOH, and their average is 0.46 ± 0.029. For the junction H2O/PC, which is partially miscible, the slope is a little larger (0.57). For practically immiscible junctions of H2O/NB and H2O/DCE, the slopes are 1.06 and 1.00, respectively; such values are very near to unity.*6 For miscible junctions between ethylene glycol and organic solvents (EG/S), the average slope was 0.33 ± 0.025, while for slightly miscible EG/NB (NB is dissolved in EG by ca. 2%) the slope was 0.84, which is nearer to unity. For miscible FA/S, the average slope was 0.32 ± 0.031, while for slightly miscible FA/NB (NB is dissolved in FA by ca. 3%) the slope was 0.70. For MeOH/S which are miscible with all solvents used, the average slope was 0.26 ± 0.08. At the junctions between two aprotic solvents, on the other hand, the slopes were much smaller (Fig. 9) and, although some contributions of anions and tetraalkylammonium cations were

200 100 0 -100 -200 -300200

100

0

-100

-200

-300 0

100

200

300

400

500

0100200300400500

□ H2O/PC△ H2O/NB

◇ H2O/AN◎ H2O/DMF■ H2O/DMSO○ H2O/MeOH

Ecorrected/mV (c1=c2=20 mM)

Eco

rrec

ted/

mV

(c1=

1 m

M, c

2=10

0 m

M)

Fig. 6　Influence of electrolyte concentrations on component (b). Cell (I) with a junction c1 MX(H2O)/c2 MX(S) was used and, for H2O/S shown in the figure, MX (tetraalkylammonium salts) were varied. c1 = c2 = 20 mM for abscissa and c1 = 1 mM and c2 = 100 mM (10 mM for S = NB) for ordinate.

W/DS

Et/ClO4

Et/Cl

W/PC

Et/Cl

Et/Br

Et/I

Et/ClO4

DF/DS

Na/ClO4

M/AN

Li/ClO4

Na/ClO4

Li/ClO4

AN/DS

Na/ClO4

Li/ClO4Mg/ClO4

Ba/ClO4

Sr/ClO4

Sr/ClO4

Sr/ClO4

PC/DS

PC/M

PC/W

40 20 0 -20 -40 40 20 0 -20 -4040 20 0 -20 -40E j(a)calc / mV

20 mV

Eco

rre

cte

d

Fig. 5　Actual variation in component (a) versus component (a) calculated by Eq. (2). Junctions: c1 MX(S1)/c2 MX(S2); S1/S2 and M/X are shown on the lines and W, M, DF, DS, and Et show H2O, MeOH, DMF, DMSO and Et4N, respectively; (c1, c2)/mM are, from left to right, (100, 1), (10, 1), (1, 1), (1, 10), (1, 100); ◆ (25, 25). Lines have unit slopes. The relation for “W/DS, Et/ClO4” deviates from linearity but this is due to the influence of the electrolyte concentration on component (c) (see Fig. 12).

*5 Equations (2) and (3) are for the case c1 MX(S1)/c2 MX(S2) where MX is a 1:1 electrolyte. For the case when MX is z1:z2 type, see Ref. 31. For junctions with different 1:1 electrolytes on the two sides, see Ref. 30.

*6 The slopes of unity seem to show that Eq. (3) is valid. However, the phenomena at immiscible junctions are different from that at miscible junctions: ions are distributed at the abrupt interface (thickness ~1 nm) of an immiscible junction (Fig. 4(b)) and the distribution potential, Δφi, is generated. Moreover, on both sides of the interface, the LJPs between the same solvent, Δφ1 and Δφ2, are generated. Thus, the potential difference generated at the immiscible junction should be the sum of Δφi, Δφ1 and Δφ2. We compared this potential difference and the LJP calculated by Eq. (3). As shown by Fig. 8, the values by the two methods agreed fairly well, showing that Eq. (3) can be applied even at immiscible junctions.33

ANALYTICAL SCIENCES JULY 2011, VOL. 27 689

observed, the contributions of alkali metal and Ag+ ions were practically equal to zero. Although the slopes are always much less than unity, component (b) is actually nearly proportional to the calculated Ej(b) (see the positions of the “+” marks in Fig. 7).33 Thus, we can estimate the actual values of component (b) by multiplying the calculated Ej(b) and the slope. For the

-250 0 250 500

-250

0

250

500

E j(b)calc/ mV

Eco

rrec

ted/

mV

NB(1.06)

DCE(1.00)

PC(0.57)

MeOH(0.50)

DMF(0.45)

DMSO(0.47)

AN(0.43)

c1=c2=20 mM

Fig. 7　Component (b) of the LJP between different solvents: experimental results versus the values calculated by Eq. (3). The case of the junction between water and organic solvents, 10 mM MX(H2O)¦10 mM MX(S). Solvent S and the slope are shown on each line. The electrolyte MX are shown by the number as follows: 1, Bu4NCl; 2, Bu4NBr; 3, Bu4NI; 4, Bu4NClO4; 5, Bu4NPic; 6, Bu4NBPh4; 7, Pr4NClO4; 8, Me4NClO4; 9, Et4NCl; 10, Et4NBr; 11, Et4NI; 12, Et4NClO4; 13, Et4NPic; 14, LiCl; 15, LiBr; 16, LiI; 17, LiClO4; 18, LiPic; 19, NaBr; 20, NaI; 21, NaClO4; 22, NaPic; 23, NaBPh4; 24, KClO4; 25, RbClO4; 26, CsClO4. MX (from right to left): S = NB (1, 2, 9, 10, 3, 11, 4, 7, 12, 8, 13); DCE (1, 2, 9, 3, 10, 4, 7, 11, 12, 8, 13); PC (1, 2, 9, 14, 3, 19, 11, 15, 4, 7, 13, 20, 12, 26, 16, 8, 25, 24, 21, 17, 22, 18, 23); MeOH (1, 2, 3, 4, 9, 14, 10, 15, 11, 12, 16, 17, 20, 21, 24, 26, 25, 13, 18, 22, 23); DMF (1, 14, 9, 2, 15, 10, 19, 3, 16, 20, 11, 4, 7, 26, 24, 25, 21, 17, 12, 8, 22, 18, 13, 23); AN (1, 2, 9, 10, 3, 14, 11, 4, 15, 7, 12, 20, 13, 16, 8, 26, 25, 24, 21, 17, 22, 18, 23); DMSO (14, 9, 15, 19, 10, 16, 20, 11, 26, 24, 21, 17, 25, 12, 8). “+” marks show the estimated Ecorrected in the absence of component (b).

-250 0 250 500

-250

0

250

500

E j(b)calc/ mVE

corr

ect

ed/

mV

AN/PC

AN/NB

AN/DMF

AN/DMSO

PC/DMF

DMF/DMSO

PC/DMSO-500

-750

6,5,310

109,8 7 6 54 3

4,3,2,1

9,8,7,6,5 10

3 10 6 5

10,1,3,2

4 8,9,7.6.5

10 1,6,5 3.2 4

1,3,4,2

Fig. 9　Component (b) of the LJP between different solvents: experimental results versus the values calculated by Eq. (3). The case of the junction between two aprotic solvents. Solid marks are for MX of perchlorates. “M” is Bu4N for 1, Pr4N for 2, Et4N for 3, Me4N for 4, Li for 5, Na for 6, K for 7, Rb for 8, Cs for 9, and Ag for 10. “—” marks show the values of Ecorrected estimated in the absence of component (b).

0 50 100 150 200 2500

50

100

150

200

2501 Et4NPic2 Me4NClO43 Et4NClO44 Pr4NClO45 Bu4NClO46 Et4NI7 Et4NBr8 Et4NCl

12

3

45

6

7

8

Ej(b)/mV for Fig. 4(a)

Ej(b

)/m

V f

or F

ig.

4(b

)

Fig. 8　Relation between Ej(b) obtained for the model of Fig. 4(b) by Ej(b) = Δφ1 + Δφi + Δφ2 and Ej(b) obtained for Fig. 4(a) from Eq. (3). The case of c MX(H2O)/c MX(NB).

-3 -2 -1 0 1 2 3

(3)

(2)

(4)

(1)

x/(4Dt)1 /2

0

0.5

1.0

S2S1

φ2

and

( µo - µ

o 1)/(µ

o 2-µ

o 1)

Fig. 10　Volume fraction of S2 (f2) and ionic standard chemical potential (μ°). Curve (1) shows f2 and (μ° – μ°1)/(μ°2 – μ°1) in the absence of selective solvation, curve (2) (μ° – μ°1)/(μ°2 – μ°1) for selective solvation of S1, and curve (3) (μ° – μ°1)/(μ°2 – μ°1) for selective solvation of S2, at a miscible junction. Curve (4) shows f2 and (μ° – μ°1)/(μ°2 – μ°1) at an immiscible junction.

690 ANALYTICAL SCIENCES JULY 2011, VOL. 27

junctions of H2O/S, the actual values of component (b) vary considerably with the electrolyte species (Fig. 7): the largest variations at H2O/PC, H2O/AN, and H2O/DMF are between MX of NaPh4B and Bu4NCl and are 354, 254, and 192 mV, respectively. The largest variation at H2O/DMSO is between MX of Me4NClO4 and LiCl and is 172 mV. It should be noted that these variations are much larger than the magnitudes of component (c) described below.

Curve 1 in Fig. 10 schematically shows the volume fraction of solvent S2 (f2) at a miscible junction; the volume fraction of solvent S1 (f1) is equal to (1 – f2). The thickness of the interphase region varies with time but is usually between 0.05 to 2 mm. Theoretically, the variation in the standard chemical potential of M+ (or X–) from the value in S1 (μ°1) to that in S2 (μ°2) occurs along curve 1 if the ion solvation is not selective but deviates to the left or right side of curve 1 (curve 2 or 3) if the ion solvation is selective to S1 or S2.33 Anyway, the variation in μ° occurs gradually. This is in contrast to an immiscible junction, where abrupt variations in f2 and μ° occur at the interface (curve 4). Then, why is the slope between the actual variation in component (b) against the theoretical values much less than unity or near to zero at miscible junctions? This problem has been discussed in Ref. 33 and the relation to the ionic random-walk has been pointed out. The ionic diffusion occurs as the results of ionic random-walk, where the average time and distance of one step of the random-walk are extremely small. The diffusion due to the gradient of ionic concentrations occurs as theoretically expected by the random-walk, but the diffusion due to the gradient in μ° seems to be retarded because the solvation/desolvation processes, which determine the value of μ°, cannot catch up with the theoretically-expected μ°-value at each position and time.

(a) If we assume that the distance of one step of ionic random-walk is of the order of the diameter of solvent molecules (0.3 – 0.7 nm), it is so small that solvation/desolvation of ions does not seem to occur to catch up with the theoretical μ°-value at each position and time.

(b) For easily solvated ions like Na+ and Li+, the average life-time of solvent molecules to stay at the first solvation-sphere

is longer than the average time of one step of ionic random-walk.*7 Therefore, it seems kinetically difficult for these ions to catch-up with the theoretical μ°-value. This may be the reason why these ions do not contribute to component (b), especially between two aprotic solvents.

Ionic random-walk seems to be the cause for the small slopes for component (b). But, in contrast to the reasons that make the slopes smaller than unity or near to zero, a factor that may increase the slopes nearer to unity can be suspected. Amphiprotic solvents like H2O, FA, EG, and MeOH are known to form clusters when they are mixed with other solvents. When these amphiprotic solvents form junctions with aprotic solvents, some of the clusters generated at the junctions may have a tendency to form an immiscible-like interphase and work to increase the slopes. This might be responsible for the fact that the slopes at the junctions involving these amphiprotic solvents are moderately large (0.5 to 0.25).

2·2 Component (c)20–22,26,29,31,33–36

Component (c) can be investigated by using Cell (II) or (II′) in Fig. 2. In these cells, solvents S1(= AN) and S2, electrolyte MX and concentrations, c and c3, are fixed and the variation in the emf is measured by varying solvent S3 in various ways.*8 In this case, component (c) varies at junctions J1 and J2. For the variations in components (a) and (b), corrections are made if necessary. Thus, the variation in the sum of component (c) at J1 and J2 can be detected. Because component (c) at J1 (between AN and other aprotic solvents) is relatively small, the variations in the corrected emfs can be considered, in many cases, to be

*7 The average time for one step is of the order from 0.1 ps to 10 ps, though it is much influenced by the average distance of one step of the random-walk. On the other hand, for Na+ and Li+, the average life time of solvent molecules at the first solvation-sphere is of the order from 10 ps to 1 ns, though it is also influenced by the kind of solvent and by the measuring techniques.

*8 In Cell (II′) with c = 1 mM and c3 = 100 mM, components (b) and (c) at J1 and J2 are determined almost entirely by electrolyte MX, while the sum of component (a) at J1 and J2 is near to zero.

Lines: unit slopesLines: unit slopes

E(MX = Et4NClO4)

E(M

X =

R4N

X)

S3 =

(b)(a)

S3 =

20 m

V

20 mV

AC

DM

FD

MS

OA

NP

CN

M

MeO

H

AC

DM

FD

MS

OA

NP

CN

M

MeO

H

AC

DM

FD

MS

OA

NP

CN

M

MeO

H

01

2

3

4

5

678

91011

( )

( )

( ) ( )

( )

( )

( )

( )

( )

( )( )

( )

1

(1) (2) (3)

2

3

-160

-140

-120

-100

-80

-180

-160

-140

-120

-100

-200

-180

-160

-140

-120

-100-80 -100 -120 -140 -160

E /

mV

E(c=1 mM, c3=100 mM) / mV

Fig. 11　Emfs of Cell (II′) in which S1 = AN and S2 = DMSO (the data for S3 = MeOH are only for reference). (a) Influence of electrolyte species. The abscissa is for MX = Et4NClO4. MX for ordinate: 0, Et4NClO4; 1, Me4NClO4; 2, Pr4NClO4; 3, Bu4NClO4; 4, Hex4NClO4; 5, Et4NCl; 6, Et4NBr; 7, Et4NI; 8, Et4NNO3; 9, Et4NPic; 10, Et4NBF4; 11, Bu4NBPh4. In all cases, c = 1 mM and c3 = 100 mM. (b) Influence of electrolyte concentrations. MX = Et4NClO4. The abscissa is for c = 1 mM and c3 = 100 mM, and the ordinate: (1) c = 100 mM, c3 = 1 mM; (2) c = c3 = 50 mM; (3) c = c3 = 10 mM.

ANALYTICAL SCIENCES JULY 2011, VOL. 27 691

mainly due to the variation in component (c) at J2. Figure 11 shows examples of the results for the case S1 = AN and S2 = DMSO. In Fig. 11(a), the abscissa is for MX = Et4NClO4 and the ordinate is for other kinds of MX. The slopes of the lines have unit slopes, so, from this figure, it is apparent that component (c) is independent of electrolyte species. Figure 11(b) shows the influence of electrolyte concentrations for MX = Et4NClO4: the abscissa is for c = 1 mM and c3 = 100 mM, while the ordinate is for different concentrations of c and c3. The slopes of the lines are unity. From Fig. 11(b), it is apparent that component (c) is independent of electrolyte concentrations. Similar experiments to those in Fig. 11(a) were also carried out for S2 of H2O, FA, MeOH, Ac, PC, NM, DMF, NMP, and HMPA, and those as in Fig. 11(b) were also carried out for S2 of H2O, FA, and HMPA. When tetraalkylammonium salts were used as MX, the relations of unit slopes were obtained in all cases, irrespective of whether the corrections were made for component (b) at J1 and J2 or not. But, when H2O, EG, FA or MeOH was used as S2 and an alkali or an alkaline earth metal salt was used as MX, the slope was much larger than unity (1.5 to 2.2) if the values of component (b) at J1 and J2 were not corrected for. If corrections were made, however, the slope of

unity was obtained.29,31,33 Moreover, if the alkali and alkaline earth metal ions were complexed with cryptands or crown ethers, the slopes became almost unity even when the corrections for component (b) were not made.21 Thus, component (c) can be concluded to be always independent of electrolyte. Here, however, one should mention the small influences of electrolytes:26,36 the influences of electrolytes to component (c) at H2O/DMSO are shown in Fig. 12. With the increase in electrolyte concentrations from 1 to 100 mM, component (c) decreases slightly when MX = Et4NCl but by about 25% when MX = Et4NClO4. This influence of electrolyte concentrations does not mean the participation of electrolyte in the generation of component (c), rather, it seems to be the influence of an ionic atmosphere on the orientation of the solvent molecule (see below).

The characteristics of component (c) can be understood if we consider that the two solvents at the junction interact with each other as a Lewis acid and a Lewis base and some of the solvent molecules are oriented perpendicularly to the interphase (see component (c) in Fig. 3): the solvent side as a Lewis acid is more negative than that as a Lewis base and the value increases with the increase in the strength of the solvent-solvent interaction. The relations with the strength of the solvent-solvent interaction are apparent, for example, from Figs. 13 and 14.20 The variations in the emf of Cell (II′) are plotted in Fig. 13(a) for S2 of protic solvents as a function of donor number (scale of basicity) of solvent S3 and in Fig. 13(b) for S2 of basic aprotic solvents as a function of acceptor number (scale of acidity) of solvent S3. In Fig. 13(a), the emf decreases with the increase in donor number, while in Fig. 13(b) the emf increases with the increase in acceptor number. This shows that component (c) increases with the increase of the strength of interaction, with the side of the Lewis acid solvent being more negative. On the other hand, Fig. 14 shows some examples of the relations between ΔH(S1/S3/S2) and the emf of Cell (II′). Here, ΔH(S1/S3/S2) (≡ [k1/3ΔH(S1/S3) + k3/2ΔH(S3/S2)]) is the sum of the heat of mixing of solvents at S1/S3 and S3/S2, which considers the direction of the solvent orientations by interaction. The followings were assumed for junction S/S′: (i) ΔH(S/S′) is defined by [ΔHS′(S) + ΔHS(S′)], where ΔHS′(S) and ΔHS(S′) are the heats of solution of S into S′ and S′ into S, respectively, (ii)

100 mV

6

6

6

7

7

7

5

5

5

4

4

4

1

1

1

3

3

3

2

2

2

S2=H 2O

S2=FA

S2=MeOH

∆H(S1/S3/S2) / kJ mol-1

E /

mV

-20 -10 0 +10 +20

Fig. 14　Examples of the relation between the heat of mixing of solvents and the emf of Cell (II′) with S1 = AN, MX = Et4NClO4, and c = 1 mM and c3 = 100 mM (see text). Solvent S3: 1, AN; 2, NM; 3, PC; 4, Ac; 5, DMF; 6, DMSO; 7, NMP.

(b)(a)

E /

mV

Donor number Acceptor number

300

260

180

40

0

0 10 10-500

-600

-700

+50

150

100

-100

-150

50

0

20 30 40 50 6020 30

-40

140

100

H2O

FA

S2=DMSO

NMP

DMF

HMPA

S2=MeOH

=

=

=

S3 : Ac

DM

FP

CD

S

FA

Me

OH

H2ON

MA

N

NM

AN

PC

Ac

DM

FN

MP

DM

SO

Fig. 13　Relations between the emfs of Cell (II′) and the donor number (a) and acceptor number (b) of solvent S3. MX = Et4NClO4 and c = 1 mM and c3 = 100 mM. Solvent S2, shown on each line, is protic for (a) and basic aprotic for (b) (DS shows DMSO).

0

20

40

60

80

100

120

140

c / mM

Com

pone

nt (c

) / m

V

Pic-ClO4

-BF4

-I-Br-Cl-

X- of Et4NX

1 10 25 50 100

▽

◇

□

△

○

☆

Fig. 12　Influence of electrolyte concentrations on component (c). Junction: c Et4NX(H2O)/c Et4NX(DMSO).

692 ANALYTICAL SCIENCES JULY 2011, VOL. 27

component (c) is proportional to kΔH(S/S′), (iii) in the following series of solvents, k = +1 for S < S′ and k = –1 for S > S′.

H2O(<)FA(<)MeOH < Ac(<)NM(<)AN(<)PC < group 1 group 2

DMF(<)NMF(<)DMSO(<)HMPAgroup 3

The groups of solvents were arranged based on the Lewis acid-base interaction, but the order of the solvents in each group was somewhat arbitrary. Apparently, in Fig. 14, the increase in component (c) is observed with the increase in the heat of mixing.

From these characteristics, we can conclude that component (c) is not a diffusion potential but is a dipole potential.36 The dipole-potential mechanism can also explain the following important property of component (c). At a junction with a mixed solvent on one side or mixed solvents on two sides, component (c) often changes linearly or near-linearly with the volume fraction of the mixed solvent(s).21,22,34 Some examples are shown in Fig. 15. Here, component (c) generated at a mixed solvent junction, (S3 + S3′)/S2, is considered. If components S3 and S3′ of the mixed solvent interact with S2 independently and generate, by a dipole-potential mechanism, potential differences which are proportional to the densities of dipoles of S3 and S3′ at the junction, component (c) should be in linear relation with the volume fraction, since the density of the dipole of each of S3 and S3′ is proportional to the fraction of the area occupied by each of S3 and S3′ at the junction, which is theoretically equal to the volume fraction of each of S3 and S3′ in the bulk. This is true also at the mixed solvent/mixed solvent junction, (S3 + S3′)/(S2 + S2′). However, there are exceptional cases in which nonlinear (curved) relations against volume fraction are

observed.34 This occurs for the mixtures between an amphiprotic solvent (H2O, FA, or N-methylformamide) and an aprotic solvent of low acceptor number (DMF (16.0), DMA (13.6), NMP (13.3), Ac (12.5), or HMPA (10.6)) (see (d), (e) and (f) of Fig. 15). In contrast, for the mixtures between an amphiprotic solvent and an aprotic solvent of moderate acceptor number (NM (20.5), DMSO (19.3), or AN (18.9)), linear or near-linear relations are observed. The curved relations were explained by the fact that amphiprotic solvents which have structure-forming properties are more likely to settle and aprotic solvents of very low acceptor numbers are less likely to settle at the interphase region than in the bulk, because the dipolar molecules of aprotic solvents of very low acceptor numbers have vague positive charge-centers.34

The model of component (c) in Fig. 3, which assumes a direct interaction of the solvent molecules on the two sides, may seem inadequate, because solvent compositions vary gradually at the actual junction. But this direct-interaction model has been proved to be practically applicable.35 We proved this by dividing the interphase region of the junction S/S′ into many steps, i.e., {[(n – i + 1)/n]S + [(i – 1)/n]S′}¦{[(n – i)/n]S + (i/n)S′} (i = 1 to n), considering the magnitude of component (c) at each step, and summing them up (Fig. 16). The condition used is that component (c) varies linearly with the volume fraction at each step of mixed solvent; component (c) at each step is equal to (1/n) of component (c) at S/S′ (Fig. 16(b)). Here, however, it has also been shown that the direct-interaction model is applicable even when non-linear relations against volume fraction are observed.35

We have no theoretical way of estimating the magnitude of component (c), but from the experimental results and under some assumptions, estimation is possible.*9 Component (c) between strongly-interacting solvents, like H2O/DMF or H2O/DMSO, is estimated to be a little over 100 mV, with the

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

0.0 0.5 1.0-70

-90

-110

-130

-150

-170

-190

(a)W+MeOH! (c)W+AN(b)W+DMSO (d)W+DMF (e)W+NMP (f)W+Ac

(h)MeOH+AN!(g)MeOH+DMSO!

(i)MeOH+DMF! (j)MeOH+NMP! (k)MeOH+Ac!

(l)AN+DMSO (m)AN+PC (n)AN+DMF (o)AN+NMP (p)AN+Ac

Fig. 15　Variation in the emf of Cell (II′) (ordinate) with mixed solvent composition (abscissa) for the case S2 = DMSO. The emf (in mV) is plotted against volume fraction (○) and mole fraction (●) of S3′. (S3 + S3′) is shown on each figure, where “!” shows that the electrolyte MX was Et4NBF4. Otherwise MX = Et4NClO4. c = 1 mM and c3 = 100 mM.

ANALYTICAL SCIENCES JULY 2011, VOL. 27 693

H2O side more negative. However, it is usually within ±20 mV at a junction between two aprotic solvents, because these solvents interact only weakly, and especially between AN and other aprotic solvent, it is probably within ±10 mV.

3 Three-component Method for the Estimation of the LJP

The value of the total LJP can be obtained by summing up the values of the three components.27a Table 1 shows some examples  of the LJP estimated by this (three-component) method and they are compared with the values estimated by the traditional indirect method based on the reference electrolyte (Ph4AsBPh4)  assumption. The results obtained by the two methods agreed fairly well. Also for other liquid junctions, the results by the three-component method agreed fairly well with the results based on the Ph4AsBPh4 assumption as indicated in Fig. 17.27b The reference electrolyte (Ph4AsBPh4) assumption has been considered to be the most reliable among many extra-thermodynamic assumptions. The results that the values obtained by the method based on this assumption agreed well with the values by the three-component method may be considered to show that both methods are reliable.

4 Stability of the LJP between Different Solvents

According to the experimental studies at free-diffusion junctions between different solvents, the LJP reaches a steady value within a few seconds after the formation of the junction; it is reproducible within ±1 mV; and, although the thickness of the junction expands with time due to the mutual diffusion of both solvents and electrolytes, it is very stable provided the electrolytes on the two sides are the same, with the drift usually within ±1 mV/h even when the LJP is near to 200 mV.23 When the electrolytes on the two sides are different but their concentrations are the same, the LJP varies significantly with time (over 15 mV in 1 h). But if the concentration on one side is more than 20 times that on the other, the LJP is almost decided by the more concentrated electrolyte and it is stable

with time.23 This seems to justify, to some extent, the use of aqueous reference electrodes for the measurements in nonaqueous solutions. In reality, however, the junctions between different solvents are usually not free-diffusion type but are restrained with, for example, a sintered-glass disk. The situation is thus complicated: the composition of solvents and electrolytes in the diaphragm is indefinite and sometimes a clog of electrolyte is formed, making the LJP less reproducible and less stable.

*9 The values of component (c), estimated under the assumption that component (c) at H2O/NB and AN/other aprotic solvents are negligible, are 122 mV for H2O/DMF and H2O/DMSO, 44 mV for H2O/AN and 30 mV for H2O/PC at 1 mM Et4NPic(H2O)/1 mM Et4NPic(S). See Fig. 12 for an example of the influence of electrolyte concentrations.

Table 1　Comparison of the LJPs evaluated by the three-component method and the conventional method (mV)

S1/S2 MXThree component method Conv.

Ej(2)b

Ej(1) – Ej(2)(a) (b) (c) Ej(1)a

H2O/AN

H2O/DMF

H2O/MeOH

Et4NPicEt4NClO4

Et4NIEt4NClEt4NPicEt4NClO4

Et4NIEt4NClEt4NPicEt4NClO4

Et4NIEt4NCl

0–2–2–2 0–2–2–2 1–2–2–1

8 18 60131 2 30 73157–18 18 22 40

37 37 37 37103103103103 30 30 30 30

45 53 95166105131174258 13 46 50 69

39 55105169111131177252 6 40 49 81

6 –2–10 –3 –6 0 –3 6 7 6 1–12

Liquid junction: 25 mM MX(S1)¦25 mM MX(S2).a. Ej(1) = (a) + (b) + (c).b. Conv. Ej(2): Conventional method under the assumption of reference electrolyte (Ph4AsBPh4).

-200

-150

-100

-50

0

50

100

150

200AN

/DM

F

AN/D

MSO

MeO

H/AN

MeO

H/DM

F

MeO

H/DM

SO

H 2O

/AN

H 2O

/DM

F

H 2O

/MeO

HS1 / S2

Ej /

mV

(☆,◇)

(☆)

(△)

(□)

Fig. 17　Comparison of the LJPs estimated by three-component method and various extra-thermodynamic assumption methods. ○, Three-component method; △, reference electrolyte (Ph4AsBPh4) assumption; ▽, Fc(+1/0) assumption; □, BCr(+1/0) assumption; ☆, Co(+1/0) assumption; ◇, Co(0/–1) assumption; ◎, Co(+1/–1) assumption. At 25 mM Et4NPic(S1)/25 mM Et4NPic(S2), and S1/S2 is shown on the upper abscissa.

-3 -2 -1 0 1 2 3 0 1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.01

2

3

4

5

6

7

8

9

10

x/(4Dt)1 /2

0

0.5

1.0

S'S

φ S

(a) (b)

ΣE

j(c) [(

i-1)

/i]/E

j(c)

No. of steps

Fig. 16　(a) Transition layer at the junction between solvents S and S′; consideration by dividing in 10 steps. Linearity against volume fraction is assumed for component (c) at each step, {[(11 – i)/10]S + [(i – 1)/10]S′}¦{[(10 – i)/10]S + (i/10)S′} (i = 1 to 10). x is the distance from the original junction, t the time after the beginning of the junction, and D the diffusion coefficient of solvent molecules. (b) Summing up of component (c) at each step. ΣEj(c)[(i–1)/i] shows the sum of component (c) from the 1st step to the ith step.

694 ANALYTICAL SCIENCES JULY 2011, VOL. 27

This applies to the case when the tip of an aqueous reference electrode is inserted into a nonaqueous solution.

5 Assumption of the Negligible LJP between Different Solvents

Parker et al.37 employed, in studying ion solvation, the assumption of negligible LJP, considering that the LJP across Cell (III) is within ±20 mV.

Ag|10 mM AgNO3(AN)¦¦100 mM Et4NPic(AN)¦¦10 mM AgNO3(S)|Ag Cell (III)

The assumption is based on these conditions: (i) the mobilities of Et4N+ and Pic– are close to each other, (ii) ΔGt°(i,AN→S) (i:  ionic species) values of these ions are small, and (iii) AN interacts only weakly with other aprotic solvents. According to our new estimation method, the LJP at the AN/S junction in Cell (III) is, as reported by Parker et al., within ±20 mV if S is aprotic, though approx. –30 and –50 mV for S of MeOH and H2O, respectively. An Ag/Ag+ electrode in AN is sometimes used as the reference electrode for other aprotic solvents. If the electrolyte is either picrate or perchlorate, all of the three components of the LJP are relatively small and thus the LJP itself is small, perhaps within ±20 mV.

6 Conclusion

The problem of the LJP has been reviewed based mainly on our results. Some results are old, but, combined with new results, the whole picture of the LJP will become clear. The important points in this review are that the actual values of component (b) are smaller than the values theoretically expected and that component (c) is not a diffusion potential but is a dipole potential. It is known that the orientation of the dipoles gives dipole potentials at the interface between two phases;38 thus, it is not surprising that the dipole potential exists as a component of the LJP between different solvents. Contrarily, the opinion that component (c) is related to ionic species as well as solvents, i.e., it is a diffusion potential, is contradicted by the observation that the electrolyte composed of ionic species that are nearly solvation-free gives a value of component (c) which is similar in magnitude and direction to that for the electrolyte composed of strongly-solvated ions.

Usually the liquid junctions used in real experiments are constrained by some diaphragm, and, in such cases, the LJPs are less reproducible and less stable. But the knowledge at free-diffusion junctions, which have been discussed here, will be of help in understanding the behavior of the LJPs even at liquid junctions with such a diaphragm.

7 Acknowledgements

I am very grateful to Prof. Toshio Nakamura and to all those who worked with me on this subject at Shinshu University.

8 References

1. I. M. Kolthoff, J. Polarogr. Soc., 1965, 10, 22. 2. I. M. Kolthoff and F. G. Thomas, J. Phys. Chem., 1965, 69,

3049.

3. J. F. Coetzee and J. J. Campion, J. Am. Chem. Soc., 1967, 89, 2513 and 2517.

4. (a) N. Matsuura, K. Umemoto, M. Waki, Z. Takeuchi, and M. Omoto, Bull. Chem. Soc. Jpn., 1974, 47, 806; (b) N. Matsuura, K. Umemoto, and Z. Takeuchi, Bull. Chem. Soc. Jpn., 1974, 47, 813; (c) N. Matsuura and K. Umemoto, Bull. Chem. Soc. Jpn., 1974, 47, 1334.

5. J. W. Diggle and A. J. Parker, Aust. J. Chem., 1974, 27, 1617. 6. J. Datta, S. Bhattacharya, and K. K. Kundu, Aust. J. Chem.,

1983, 36, 1779. 7. A. Kotocová, Chem. Zvesti, 1980, 34, 56. 8. L. I. Krishtalik, N. M. Alpatova, and E. V. Ovsyannikova,

Electrochim. Acta, 1991, 36, 435. 9. L. V. Bunakova, L. A. Khanova, V. V. Topolev, and L. I.

Krishtalik, J. New Mat. Electrochem. Systems, 2004, 7, 241.10. M. Alfenaar, C. L. De Ligny, and A. G. Remijnse, Recl.

Trav. Chim. Pay-Bas, 1967, 86, 986.11. B. G. Cox, A. J. Parker, and W. E. Waghorne, J. Am. Chem.

Soc., 1973, 95, 1010.12. R. Gaboriaud, J. Chim. Phys., 1975, 72, 347.13. R. C. Murray, Jr. and D. A. Aikens, Electrochim. Acta,

1976, 21, 1045.14. S. S. Goldberg and O. Popovych, Aust. J. Chem., 1983, 36, 1767.15. A. Berne and O. Popovych, Aust. J. Chem., 1988, 41, 1523.16. A. Berne, C. Kahanda, and O. Popovych, Aust. J. Chem.,

1992, 45, 1633.17. C. Kahanda and O. Popovych, Aust. J. Chem., 1994, 47, 921.18. G. Senanayake and D. M. Muir, J. Electroanal. Chem.,

1987, 237, 149.19. K. Izutsu, T. Nakamura, T. Kitano, and C. Hirasawa, Bull.

Chem. Soc. Jpn., 1978, 51, 783.20. K. Izutsu, T. Nakamura, I. Takeuchi, and N. Karasawa, J.

Electroanal. Chem., 1983, 144, 391.21. K. Izutsu, T. Nakamura, and N. Gozawa, J. Electroanal.

Chem., 1984, 178, 165 and 171.22. K. Izutsu and N. Gozawa, J. Electroanal. Chem., 1984,

171, 373.23. K. Izutsu, T. Nakamura, and T. Yamashita, J. Electroanal.

Chem., 1987, 225, 255.24. K. Izutsu, T. Nakamura, and T. Yamashita, J. Electroanal.

Chem., 1988, 256, 43.25. K. Izutsu and T. Nakamura, “Ion-selective Electrodes”, ed.

E. Pungor, 1989, Vol. 5, Pergamon Press, 425.26. K. Izutsu, T. Nakamura, and M. Muramatsu, J. Electroanal.

Chem., 1990, 283, 435.27. (a) K. Izutsu, T. Nakamura, M. Muramatsu, and Y. Aoki,

Anal. Sci., 1991, 7(Suppl.), 1411; (b) K. Izutsu, T. Nakamura, T. Arai, and M. Ohmaki, Electroanalysis, 1995, 7, 884.

28. K. Izutsu, T. Nakamura, M. Muramatsu, and Y. Aoki, J. Electroanal. Chem., 1991, 297, 49.

29. K. Izutsu and Y. Aoki, J. Electroanal. Chem., 1992, 334, 213.30. K. Izutsu, M. Muramatsu, and Y. Aoki, J. Electroanal.

Chem., 1992, 338, 125.31. K. Izutsu, T. Arai, and T. Hayashijima, J. Electroanal.

Chem., 1997, 426, 91.32. K. Izutsu, Pure Appl. Chem., 1998, 70, 1873.33. (a) K. Izutsu and N. Kobayashi, J. Electroanal. Chem.,

2005, 574, 197; (b) K. Izutsu, Rev. Polarogr. (in Japanese), 2005, 51, 73.

34. K. Izutsu, Bull. Chem. Soc. Jpn., 2008, 81, 703.35. K. Izutsu, Bull. Chem. Soc. Jpn., 2010, 83, 39.36. K. Izutsu, Bull. Chem. Soc. Jpn., 2010, 83, 777.37. R. Alexander, A. J. Parker, J. H. Sharp, and W. E. Waghorne,

J. Am. Chem. Soc., 1972, 94, 1148.38. S. Trasatti and R. Parsons, Pure Appl. Chem., 1986, 58, 437.