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Electrolysis with electrolyte dropping electrode
J. Electroanal. Chem., 75 (1977) 211--228 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands
211
ELECTROLYSIS WITH ELECTROLYTE DROPPING ELECTRODE II. B A S I C P R O P E R T I E S O F T H E S Y S T E M *
J. KORYTA, P. VANYSEK and M. BREZINA
Czechoslovak Academy of Sciences, J. Heyrovsk~ Institute of Physical Chemistry and Electrochemistry, Opletalova 25, 110 O0 Prague 1 (Czechoslovakia) (Received 17th May 1976)
ABSTRACT In a theoretical discussion the conditions have been pointed out where an interface of two immiscible electrolyte solution behaves as an equilibrium system metal ion-metallic electrode, as an ideally polarized electrode and as an electrode under faradaic current flow. The basic equations for current-electrical potential difference across the interface have been deduced for the cases of ion as well as electron transfer. Experimentally, various base electrolyte systems were studied, the most advantageous among these are LiC1 in water ÷ tetrabutylammonium tetraphenylborate in nitrobenzene and MgC12 in water + tetrabutylammonium dicarbollyl cobaltate in nitrobenzene. S-shaped polarographic curves were observed with the tetramethylammonium ion. The limiting current is directly proportional to concentration. The limiting currents are somewhat higher than those predicted by the Ilkovi6 equation which has been ascribed to the tangential movement of the interface.
INTRODUCTION T h e i n t e r e s t on p o l a r i z a t i o n p h e n o m e n a a t e l e c t r o c h e m i c a l m e m b r a n e s - - a r t i f i c i a l a n d n a t u r a l - - has d a t e d since t h e e n d o f t h e p a s t c e n t u r y . T h e eff e c t o f e l e c t r o s t e n o l y s i s ( f o r a r e v i e w , see ref. 1) b a s e d on m e t a l d e p o s i t i o n on glass [ 2 , 3 ] , c o l l o d i o n [ 4 - - 6 ] o r b i o l o g i c a l [ 7 , 8 ] m e m b r a n e s , t h o u g h perh a p s in s o m e cases c a u s e d b y s p u r i o u s i n f l u e n c e s , has d o u b t l e s s a r e a l e x i s t e n c e On t h e o t h e r h a n d t h e r e has b e e n a v a s t m a t e r i a l p u b l i s h e d on p o l a r i z a t i o n o f a r t i f i c i a l , p a r t i c u l a r l y b i l a y e r l i p i d ( f o r reviews, see e.g. refs. 9---12) a n d b i o l o g ical ( f o r a r e v i e w , see e.g. ref. 13) m e m b r a n e s . H o w e v e r , t h e s i m p l e s t s y s t e m of this k i n d , an i n t e r f a c e o f t w o i m m i s c i b l e e l e c t r o l y t e s o l u t i o n s , h a s b e e n i n v e s t i g a t e d u n d e r f l o w of e l e c t r i c a l c u r r e n t r a t h e r r a r e l y . I o n t r a n s f e r a c r o s s an i n t e r f a c e o f t h a t k i n d was first s t u d i e d b y G u a s t a l l a [14]. The c o n c e n t r a t i o n changes due to the ion transfer were indicated by
* In honour of Dr. G.C. Barker's 60th birthday.
212
changes of the interfacial tension. Steady state polarization curves [15] were obtained with an aqueous KC1 solution and nitrobenzene solutions of dodecyltrimethylammonium dodecylsulphate or picrates of dodecyltrimethylammonium, tetradecyltrimethylammonium or h e x y d e c y l t r i m e t h y l a m m o n i u m . A similar system was also studied by means of slow triangular potential pulses [16] (for analogous experiments with the system of the calcium ion-selective electrode [17] see ref. 18). Gavach and coworkers used c h r o n o p o t e n t i o m e t r y for investigation of the system NaBr containing low concentration of tetrab u t y l a m m o n i u m ion in water + t e t r a b u t y l a m m o n i u m tetraphenylborate in nitrobenzene [19] and of some other systems [20]. The E--t curves showed characteristics analogous to those found with the same m e t h o d using metallic electrodes. A metal deposition at a liquid-liquid interface was observed by Gainazzi and coworkers [21] who studied the polarization of the cell CuICuSO4, H20[JBu4NV(CO)6, C1CH2 • CH2CliPt The overall reaction taking place at the interface during current flow is V(CO)~- + 2 Cu 2+ -+ V aq 3+ + 6 CO + 2 Cu Similarly as a mixed potential reflects the characteristics of processes taking place at a metallic electrode, there are reactions occurring at an interface of two immiscible solvents which are termed as phase-transfer catalysis [22,23] (see also refs. 24--27, for a review see ref. 28). The basic step in these reactions is ion transfer across the interface, of course in the absence of an outer electrical current. In a preliminary communication [29] the experimental assembly for the electrolyte dropping electrode (EDE) was described together with some polarization characteristics of this system. In the present paper, after discussing the theoretical foundations for the static and dynamic behaviour of the interface of two immiscible electrolytes, it will be shown that the basic results obtained with EDE resemble those supplied by polarography with DME. THEORETICAL
A non-polarized interface of two immiscible electrolyte solutions Let us consider two immiscible solvents ~ and ~ in contact. In both solvents a uni-univalent electrolyte B]A 1 is dissolved consisting of the cation B~ and anion A~-, in a graphical representation
BIA 1 JJ B1A 1
(1)
In equilibrium the electrochemical potentials of chemically identical corn-
213 ponents are equal, =
(/3)
]~A~.(0~) = ]~Al(/3)
(2)
or p ° +(a) + R T In as+' (a) + F ~ ( a ) = pO ~(/3) + R T In as~(/3) + F~(/3) (3) p°-(a)
+ R T In aA~(a ) -- F ~ ( a ) = p°-l (fi) + R T In aA~(/3) -- F~(/3)
where the ai's are the ion activities in the appropriate phases, the ~'s are the inner potentials of individual phases and the pi's are the standard chemical potentials which include the terms describing the ion-solvent interaction so that the ai's are functions only of concentration of the i-th ion and of interionic interactions. The p°'s are, of course, quantities which are not accessible to direct measurement. At the interface a Galvani potential difference A ~ is formed A ~ = ~(/3) -- ~(a) = [p°+'(a) - p ° ~ ( / 3 ) ] / F + ( R T / F )
ln[aB+' (a)/aB+1 (/3)] =
(4)
. . . . [p° i (a) -- p ° i ( / 3 ) ] / F - ( R T / F ) ln[aAi(a)/aAi(/3) ] From eqn. (3) we have ln(labs(/3) • aAi(fi)]/[aB+l(a ) • aA](a)], } = = + /2A1 0 (0~) - - po (/3) -- p ' A ~ ( a ) ] / R T = In kB1Al(a, fi)
[u°~(~)
(5)
which is the distribution coefficient of B1A1 between the phases ~ and/3. The differences of the standard chemical potentials in eqns. (3) will be identified with the negative values of standard Gibbs energies of transfer of the cation i from the phase ~ into the phase/3,
~tr,i
:
__
(6)
The values of these quantities can be obtained using various extrathermodynamical assumptions. The most frequently used is that of Parker [30] and Popovych [31] supposing that the standard Gibbs energies of transfer of tetraphenylarsonium cation and tetraphenylborate anion between any pair of solvents are equal. With the help of this assumption a scale of standard transfer Gibbs energies can be calculated for any pair of solvents since the sum of standard transfer Gibbs energies for a cation and an anion (multiplied by corre sponding stoichiometric coefficients for the given electrolyte) is in a simple relationship (eqn. (5)) to the distribution coefficient which is an experimentally accessible quantity. For the present purpose this kind of representation by means of relative scales is quite satisfactory and it is not necessary to account here for the influence of surface potentials (cf. ref. 32). The quantity A ~ cannot be determined by a direct measurement based on
214 a thermodynamic approach. Let us consider the system (1) complemented by two electrodes reversible to the cation B~,
(7)
B11B1A1 [[B1 A1 ]B1 which is in equilibrium. The e.m.f, of this cell E is given by the sum E = /~1 ~ + a ~
+ /~1~
(8)
where
A~l~ = [po ( B 1 ) _ p o ( a ) ] / F _ (RT/F) In aB~(~) and = [p~(fl)
p°~(B1)]/F + (RT/F) In aB+(fl)
Here po~ (B1) denotes the standard potential of the ion B~ in the (metallic, for example) phase B1 and A ~ is given by eqn. (4). The quantity E is obviously equal to zero which also results directly when considering that a system which is in equilibrium cannot expend work. However, by means of a suitable non-thermodynamic procedure it is possible to determine indeed not directly A ~ but the changes of this quantity when the composition of the solutions is varied which is, for the present purpose, quite sufficient. For example, if with the help of suitable electrolyte bridges the reference electrodes are joined to the phases a and fl under conditions that (i) both the bridge and the solution of the reference electrode contain the same solvent as the phase ~ or fl, respectively, (ii) that, with its composition, the bridge minimizes the liquid junction potentials A~L in the scheme (9), then the changes of EMF of this cell are approximately equal to the changes of A ~ when varying the composition of
and ft. reference electro- electroelectrode lyte so- lyte 1 lution bridge 5 of reference electrode 1
AIB1
electro-I electro', lyte soA1 B1 1I I lyte bridge e [ lution of reference electrode 2
(v)
reference electrode 2
(9)
(D
/x~(6,v) Ideally polarized interface of two electrolyte solutions Let us again consider a system consisting of two immiscible solvents a and /3 in one of which an electrolyte BIA1 and in the other one an electrolyte
215
B2A 2 is dissolved, B1A1 IIB2A2
(10)
We shall assume that for the standard Gibbs energies of transfer of ionic components of the system (10) the relationship is valid o,~ >> 0 min~A~O,c~-~ _ A p 0 , ~ - ~ ~.~t__A~0,~-~ (11) "--, ~ t r , A 1 ' L'a~'~tr, B~ ' - - ' " ° ' ~ t "~tr, B~ ' A e t r , A ~ / 3 ) This inequality has two consequences: (i) The equilibrium of distribution of both electrolytes between the solvents a and fi is shifted in the case of the electrolyte AIB1 almost completely on the side of the solvent a while in the case of the electrolyte A2B2 almost completely on the side of the solvent ft. In fact, from the inequality (11) we obtain Ap0,a-+~ ~Jtr B + '. 1
+ A~o,~-+~ --~tr,A 1
>> 0
(12)
~tr, B~ + _ v t r , A~ < < 0 With respect to eqn. (6) these inequalities characterize the corresponding distribution equilibria. (ii) The exchange equilibria B~(a) + B~(fi) ~ BI(fl) + B~(a)
(13)
and
A~(~) + A~-(~)~ A~-(/~)+ A2(a)
(14)
axe shifted to the left-hand side, since from the inequality (11) the following relationships result A~O,c~-+~ __ A ~ O , c ~ - ~ U t r , B~ ~.a~-*tr,B ~ > >
0
Aco,~--~
0
~ t r , A1
-
>>
(15)
For the purpose of calculation of A ~ we shall assume that for one pair of ions of opposite sign i and j (e.g. A2 and B~ or A~ and B~) it holds +A~O,~-~ _+ AGtr o J, ~ ----~tr,i
< < ±AG°~'~ , -~ + A ~t~,l ~ °,a~
(16)
The upper sign applies in the case that the ion is predomirmntly present in the phase ~, the lower one in the opposite case and the indices k and 1 denote the remaining pair of ions. Under these circumstances the ions i and j determine the quantity A ~ according to the relationship, for example for the ion i (cf. eqns. (4) and (6))
A ~ = ~- A G ° ; , 7 ~ / F + ( R T / F ) ln[ai(a)/ai(fi)]
(17)
where the upper sign applies in the case that i is a cation and the lower one in the case that it is an anion.
216 If, for example, the ion i is identical with B~, then in the case of a large shift of the equilibrium for the electrolyte AIB1 in favour of the phase a, the determination of A ~ by the activity a.+(fl) is fictitious. When a certain amount DI of charge is transported to the phase boundary, only a small fraction of this charge is consumed for the transfer of B~ across the phase b o u n d a r y while, from a major part, it is used for charging the double layer at this interface. Thus, at a phase boundary characterized in this way the exchange of charge does not take place, at least in a certain range of A ~ ; the phase boundary has therefore the properties of an ideally polarized interface. A phase boundary defined above is an analogy of an ideally polarized electrode, e.g. of a mercury electrode in a KF solution. Among reactions occurring at the interface which have been mentioned in this paragraph only an analogy to eqns. (13) and (14) can be considered, i.e. the exchange reaction Hg(electrode) + K+ (solution) ~ K(electrode) + Hg+(solution) The equilibrium of this reaction is shifted to the left-hand side so that, in view of their only statistically characterized concentrations, neither potassium dissolved in the electrode nor mercurous ions can influence the e]ectrode potential. Let us consider a cell analogous to (9) b u t with phases a and fl according to (10). Since the phase boundary between the electrolyte solutions a and/3 is ideally polarized the difference of electrical potentials of leads connected to reference electrodes 1 and 2 can be arbitrarily (i.e. in the range where the interface is indeed ideally polarized) varied by means of an external source. This electrical potential difference AV is equal to the difference of inner electrical potentials A ~ with an additional constant independent of A V.
An interface o f two immiscible electrolyte solutions under flow o f current Let us consider a system
B~, A1, BElIB,, A~, BE
(18)
The ions B~ and AT, B~ and A2- are practically present only in one phase as shown in (18). The ion BE, present at a low concentration compared with the other ions, can be transferred between the phases a and/3. At the phase boundary an electrical double layer is formed with the charge density on the side of and fl
q(a) = --q(fi)
(19)
Obviously q(c~)/F= I~B; ( a ) - PA~(a)+ l~B~(0t)=
(20)
If electrical current flows through the system (18) from the left to the right
217 then for the current density j we have j / F = JB~((~) -- JA~(~) + JB+3(~) = JB~(~) -- JA~ (~) + JB~(~)
(21)
where the Ji(a) or Ji(fi) are material fluxes of the components of the phase a or fi, respectively. In view of the small concentration of B~ in comparison with BIA 1 and B2A2, which function as base electrolytes, the charge is transported by BIA1 and BeA2 outside the diffusion layer while inside the diffusion layer the current depends only on the transport of B~, i.e. (22)
f f F = JB~(~) = JB~(fJ)
At the interface we have to consider the balance of adsorption of the components of the system and the transfer reactions of BE characterized by rate constants ktr and ktr. For this balance for the phase a- side of the interface (x -~ 0) we have (a similar relationship for the interface metal ion in solutionmetal amalgam was deduced by Delahay [33], see also ref. 34) j / F = dPB~ ( a ) / d t - - dFA~ (a)/dt + dPB~(~)/dt + ktr CB~((~) -- ktr eBb(/3)
For the flux JB~(a) we have at the same time JB;(~) = dFB;(~)/dt + ~t, cB~(~) -- kt, Cs~(~)
(24)
so that in view of eqn. (20) we obtain j / F = ( l / F ) d q ( a ) / d t - - dFB~(a)/dt
+ JB~((~)
(25)
Similarly for the phase fi-side of the interface it holds __~
j / r = --dFB~(~)/dt + dFA~(~)/dt -- dFB~(~)/dt + ktr
<--
CB~(I~ ) -- ktr CB~(/~)
(26)
and JB~(~) = --dFB~(~)/dt + ktr c.~(a) -- ktr CB+3(~)
(27)
SOthat
j/F = (l/F) dq(a)/dt + dFB~(~)/dt+ JB~(fi)
(28)
Let us assume, for the sake of simplicity, that the absolute value of dFB+(a)/ dt as well as dPs+(fi)/dt is much smaller than the absolute values of the dif~eren rials of FB+ -- F A-1 or of--> FB+ -- FA:2 with respect to time and than the absolute 1 2 +value of the difference ktr cB~(~) -- ktrCB+3(~). Then we have 3
J = Jn~ + J~
.
.
(29)
where
Jn~ = F[dFB~(a)/dt -- dFA](a)/dt] = = F[--dFs~([3)/dt + dFA~(/~)/dt] ~ dq(~)/dt =--dq((J)/dt
(30a)
218 is the non-faradaic c o m p o n e n t o f j and .._>
4__
jf = F[ktrCB+3((~) -- ktrCB~(~)]
(30b)
is the faradaic component• Under these circumstances and under the assumption that also the quantities FB+ contribute to the total charge in the electrical • . 3 . . , double layer to a neghglble degree the non-faradaxc c o n t r l b u h o n can be determined by measuring the current density j in the absence of BE. For the measurement of polarization curves an arrangement according to scheme (9) will again be used while the phases a and fi will be composed according to (18). The liquid junction potentials are assumed to be influenced by the presence of BE in a negligible extent only. The phases a and fi are in contact with auxiliary electrodes by means of which the current enters the system. Under these circumstances the dependence of the current I on AV coincides with the dependence I -- A ~ with the exception of a constant term which cannot be directly determined. However, this term is neither dependent a nor is varied if B + 3 is substituted by another ion on the concentration of B+ which again must influence the liquid junction potentials to a negligible degree only. -. +For ktr and ktr we assume the dependence ktr = k ° e x p ( - - ~ F [ A ~ - - A ~ ° ( B + 3 ) ] / R T ) = k ° exp(--aF[AV--
=
AV°(B+a)]/RT}
k~r = k ° exp((1 -- a ) r [ A ~
(31)
-- A ~ ° ( S ~ ) ] ) =
= k ° exp((1 -- a ) F [ A V - - A V ° ( B ~ ) ] / R T } where k ° is the standard rate constant of transfer of BE between the phases a and ~, a is the transfer coefficient and A ~ ° ( B ~ ) or AV°(B~), resp., are the values of A ~ or AV, resp., in the case that lim[cB~(a)/CB~(fl) ] = 1 cB~(~), CB~¢e)~ 0
(32)
A differential equation describing the transport of B~ is then specified by boundary conditions for x -~ 0
JB~(a)
.__> = ]~tr CB~((1)
--
4___ ]~tr CB~(fl)
JB~(a) = JB~(~)
(33)
(34)
If we assume for the terms in eqn. (33) that ._->
+-ktrCB~(a) > > IJB~(a)f
(35)
we can write -->
<--
ktr CB~(U) -- ktr CB~(fl) ~ 0
(36)
219
Thus, at the phase b o u n d a r y the N e r n s t - D o n n a n equilibrium is preserved even at current flow. In an analogous manner to polarography, this case can be classified as reversible. T h e n we have for x -+ 0 A~
-- A ~ ° ( B ~ )
= AV-- AV°(B~) =
(RT/F) ln[CB~(a)/CB~(fl)]
(37)
With respect to (4) and (6) we have further A~o = A V + const. -----z.~tJrt)'B ^ , - 0 ~ -~ ~ ,/ r~ +
(RT/F)ln[CB~(a)/CB~(~)]
(38)
It must be stressed that the constant term in eqn. (38) depends only on composition of the solutions of base electrolytes a and/3, on liquid junction potentials and on reference electrodes whereas it is independent of the nature of the ion B E. Under these circumstances we can base a relative scale of the values of A~0 ° on the values of standard Gibbs energies of transfer from the phase a to the phase/3, for example, as they were tabulated according to the assumption of Po.povych and Parker (see Table 1). In general, we write for an ion carrying
TABLE 1 Standard Gibbs energies of transfer f r o m water to n i t r o b e n z e n e [ 35,36 ] AG O'w~n and of lx,i n fl0 standard electrical potential differences b e t w e e n these phases (in part after ref. 19) Aw~ for various cations and anions Cations Li + Na + H+ NH~ K÷ Rb + Cs+ TMA+ TEA+ TBA+ TPhAs+
o w AGt]}, i ~n /kJ mo1-1
An~0 °
38.2 34.2 32.5 26.8 23.4 19.4
--0.395 --0.354 --0.337 --0.277 --0.242 --0.201
15.4 3.4 --5.7 --24.0 --35.9
--0.159 --0.035 0.059 0.248 0.372
--50.2 --39.4 --38.8 --35.9 --23.4 --4.6 8.0 18.8 28.4 31,4
--0.520 --0.407 --0.401 --0.372 --0.242 --0.047 0.083 0.195 0.295 0.324
Anions Dicarbollyl Co-Dipicrylaminate 15 TPB-13 Picrate C10 4 I-Br-C1--
220
z i elementary charges,
A ~ = --AV°;,~-~/ziF + (RT/ziF) ln[ ci(a )/ci(/3) ]
(39)
As an example we shall describe the transport to the electrolyte dropping electrode under polarographic conditions. The phase a is represented by the inside of the drop while the outer solution is the phase ft. If the ion which is capable of transfer from a to fl has originally been present only in the phase in a concentration c°(a) we have for the average current
== ~:i(a) [c°(a) -- el(a)] = = h:i(/3 ) Ci(/3)
(40)
where A is the area of the drop and ~i(a) and ~i(fi) are the coefficients of the Ilkovi~ equation modified for the media ~ and/3. When inserting from eqn. (40) into eqn. (39) we obtain ~
= --i('~O'a'-+fl ' ~ 1 ~
+ ( R T / 2 ziF ) ln(Di,~/Di.a)
+
(RT/ziF) ln[( -- /]
(41)
where is the average limiting diffusion current and Di, a and Di, ~ are diffusion coefficients of the ion i in the phases a or/3, respectively. Obviously, for the half-wave potential we have /~1/2
= --A('~O'o~-->fl ,~1--
+ ( R T / 2 ziF ) ln(Di.g/Di,a)
(42)
Analogous expressions could be deduced for an irreversible wave when the approximation (35) were not applicable. For a sufficiently large absolute value of A ~ a transfer of ions of the base electrolytes can take place. For the transfer of the ion B~, for example, we then have A ~ = --A ~-°,~-~ ~,t~,B~f + (RT/F) In KB;(/3) + (RT/F) ln[c°-~(~)/]
(43)
Let us also consider the case of electron transfer across the phase boundary of two immiscible electrolyte solutions
B~, Ay S~, A~B~, B3 B~, 84
(44)
The pairs B~, B 1 and B~, B 4 are components of two oxidation-reduction systems which, in the simplest case, cannot be transferred across the interface. The reaction taking place at the phase boundary, B~ + B 4 ~ B~ + B 3
(45)
can be split into two partial processes, B~+e~B 3 B~ + e ~ B 4
(46)
221
For the Faradaic current density we obtain, if the adsorption effects have been neglected, jffF
"-->
+
~e
=
- - ke,4eB4 (fl)
(47)
-~ JB~ = --JB 3 = JB~ = --JB4 The individual constants of electron transfer in eqn. (47) have the following meaning: k~,3 = ko,3 e x p [ ~ 3 F ( A ~ 0 - - A ~ o ° ) / R T ]
(48)
k~,3 = ko,3 exp[--(1 - - a 3 ) F ( A ~ 0 - - A ~ 0 ° ) ]
(49)
ke,4--> = ko,a e x p [ a 4 F ( A ~ v _ Aa~4)]~ 0
(50)
~-e,4 -- ko,4 exp[--(1 - - a 4 ) ( A { ~ - - A a~~ 4 )0 ]
(51)
In these expressions ko, 3 and ko, 4 a r e standard rate constants of electron transfer corresponding to eqn. (46), a3 and a 4 are the electron transfer coefficients and the standard electrical potential differences A~o ° and A ~ ° are defined for the couples BE, B3 and B~, B 4 in a manner analogous to eqn. (32). These quantities are connected by the relationship A~(~w3 ~o __ A~~W4 ~o . . . . . A G O / F
(52)
where AG O is the standard Gibbs energy change for the reaction (45). EXPERIMENTAL
The design of the electrolyte dropping electrode, the electrode assembly and the polarization and recording instrument were the same as described in the preliminary communication [29]. LiC1, NaBr, MgCle and t e t r a m e t h y l a m m o n i u m chloride were chemically pure substances supplied by Lachema, Brno. T e t r a m e t h y l a m m o n i u m bromide was a product of BDH. Tetrabutylaramonium tetraphenylborate (TBATPB) was prepared in this laboratory. Tetraphenylarsonium tetraphenylborate was prepared by Dr. M. Kyr~, Institute of Nuclear Research, Re~ near Prague and tetrabutylammonium dicarbollyl cobaltate(III) by Dr. M. Plegek, Institute of Inorganic Chemistry, Czechoslovak Academy of Sciences, l~e~ near Prague, to whom our thanks are due for the gift of these substances. The experiments at an initial stage were carried out with a two-electrode assembly and with an electrolyte dropping electrode of 0.1 M TBATPB dissolved in nitrobenzene (dropping, of course, downwards). For aqueous solutions of NaBr (0.2--2 M) a linear I - - A V dependence with oscillations following the regular frequency of dropping was only obtained (Fig. 1). The nitrobenzene drops had a diameter of about 12 mm. The completely prevailing
222
C) 0 =B-H • =C-H
Dicarbollyl c o b a l t a t e ( I I I )
factor was, in this case, the ohmic potential drop in the system. The resistance of the assembly was about 0.2 M ~2. In an alternative arrangement a 0.1 M and, later, a 0.05 M solution of TBATPB in nitrobenzene was placed in the bottom of the electrolytic cell. Aqueous solutions of NaBr in concentrations between 0.01 M and 2 M dropped upwards into the nitrobenzene solution. The originally linear I - - A V dependence changed to a non linear with an indistinct plateau at concentrations larger than 0.1 M NaBr. With 2 M NaBr the aqueous solution ceased dropping off the
I
30I/pA 20-
I~
A
~o°y
o L
i
-lO 0
0.'5
Ii
'
Fig. 1. Polarogram o f 10 m M NaBr in water, 0.1 M TBATPB in n i t r o b e n z e n e . I - - A V d e p e n dence recorded in a t w o - e l e c t r o d e s y s t e m is d e t e r m i n e d by the o h m i c drop o f potential. Fig. 2. Polarogram o f 0.5 M NaBr in water, 50 m M TBATPB in n i t r o b e n z e n e in a two-elect r o d e (B) and t h r e e - e l e c t r o d e (A) a r r a n g e m e n t . The current at A V < 0.4 V c o r r e s p o n d s to the t r a n s f e r o f TBA + f r o m n i t r o b e n e e n e to w a t e r while the current at A V > 0.7 V to the transfer o f Na + f r o m w a t e r t o n i t r o b e n z e n e .
223
capillary, since its density approached that of the nitrobenzene solution and assembled in the form of irregular clusters at the orifice of the capillary. With the three-electrode assembly, which was described in the preceding paper [29], the residual ohmic resistance of the system changed from 13.7 k ~2 for 1 M NaBr to 23.8 k ~2 for 0.1 M NaBr. The polarograms of 0.5 M NaBr for a two- and three-electrode system are shown in Fig. 2. A concentration dependence recorded in the three-electrode system is demonstrated in Fig. 3. Still better results were obtained with lithium chloride aqueous solutions of which 1 M LiC1 has shown as most suitable. When t e t r a e t h y l a m m o n i u m bromide (TEA) was added in concentrations between 0.05 mM and 1 mM to the aqueous phase the plateau of the I - - A V curve was raised as shown in Fig. 3, ref. 29. The supposedly faradaic limiting current of TEA measured at the inflection point of the I - - A V curve was directly proportional to the concentration of TEA. S-shaped polarographic waves were obtained with t e t r a m e t h y l a m m o n i u m bromide (TMA) present in the aqueous solutions of NaBr in concentrations
7_/ p A
3
0.2
O
0.2
~'v/v
0.4
~o.~v
J
2
1
Av
Fig. 3. P o l a r o g r a m s of a q u e o u s phases o f varying c o m p o s i t i o n a n d of 50 m M T B A T P B in n i t r o b e n z e n e . (1) 25 m M NaBr, (2) 50 m M NaBr, (3) 0.1 M NaBr, (4) 0.2 M NaBr, (5) 0.5 M NaBr. Fig. 4. P o l a r o g r a m s of t e t r a m e t h y l a m m o n i u m ion in water. C o m p o s i t i o n of base electrolytes: 1 M LiCl in water, 50 m M T B A T P B in n i t r o b e n z e n e . C o n c e n t r a t i o n s of T M A + : (1) 0, (2) 0.2 raM, (3) 1 raM, (4) 2 mM. T h e negative c u r r e n t c o r r e s p o n d s t o t h e t r a n s f e r o f T B A + f r o m n i t r o b e n z e n e t o water, t h e wave t o t h e t r a n s f e r o f T M A + f r o m w a t e r to n i t r o b e n z e n e a n d t h e s u b s e q u e n t positive rise o f c u r r e n t t o t h e t r a n s f e r of TPB-- f r o m n i t r o b e n z e n e t o water, and, f o r a smaller part, t o t h e t r a n s f e r o f Li + f r o m w a t e r t o n i t r o b e n zene. In t h e d i a g r a m e a c h curve is s h i f t e d b y 0.1 V t o w a r d s m o r e negative p o t e n t i a l w i t h respect t o t h e p r e c e d i n g one.
224
higher than 0.2 mM (Fig. 4). The limiting current determined in the inflexion point of the I - - A V curve was also directly proportional to the concentration of TMA. Analogous results were obtained with a LiC1 base electrolyte b u t the proportionality constant in the Id--C dependence was different (see Fig. 5). When 0.2 mM tetrabutylammonium iodide was added to the nitrobenzene phase the plateau of the I--A V curve was initially raised due to the transfer of iodide from the non-aqueous to the aqueous phase. As effect of the auxiliary polarization the nitrobenzene phase changed colour to pale b r o w n during 2 h and a new anodic wave was formed on the polarogram (see Fig. 6). In further experiments the composition of the base electrolyte solution was varied in order to increase the plateau of the I - - A V curve. For this purpose ions having more advantageous standard Gibbs transfer energies were used. Tetraphenylarsonium tetraphenylborate gave exceedingly drawn-out curves, an effect of high resistance due to low solubility of the substance. The most suitable was the combination of 2.2 M aqueous MgC12 with 10 mM t e t r a b u t y l a m m o n i u m dicarbollylcobaltate(III) in nitrobenzene (see Fig. 7). The small wave is probably an impurity effect. The extremely high value of standard Gibbs energy of transfer of the dicarbollylcobaltate(III) anion from nitrobenzene to water has been pointed out by Rais and coworkers [36]. Attempts were made to determine the dependence of the limiting current on the height of the electrolyte column and on the drop-time, which, unfortunately, could not be substantiated so far. The height of the electrolyte column is linked with the demand of regular dropping. Thus, with small increase of this height a jet of electrolyte is formed while with a small decrease
1.00
Z//uA
z/~A
8O
6O
4C
2O 0
2
4
6 c/lOT 4 M
8
10
0.4
0.6
0.8
1.0 ,J v/ v
1.2
Fig. 5. Dependence of the limiting current of tetramethylammonium ion on concentration in water. Base electrolytes: 1 M LiC1 in water, 50 mM TBATPB in nitrobenzene. Fig. 6. Polarogram of supposed polyiodide ion formed in the nitrobenzene phase.
//pA
T/j T
T
T
I/uA~
225
A
60
4o
40
IS.
o
20 0
-40 •
-20 -4
-80 -0:5
0.0
0.5
,#vl v
0.2
: 0
I _-----~ -0.2 -0.4
1
z/~,~+f~/v
Fig. 7. P o l a r o g r a m of 2.2 M MgC12 in w a t e r a n d 10 m M t e t r a b u t y l a m m o n i u m dicarbollylc o b a l t a t e in n i t r o b e n z e n e . T h e c u r r e n t at A V < - - 0 . 5 V c o r r e s p o n d s t o t h e t r a n s f e r o f TB/~ + f r o m n i t r o b e n z e n e t o w a t e r while t h e c u r r e n t at A V > 0.7 V possibly t o t h e transfer of Mg 2+ f r o m w a t e r t o n i t r o b e n z e n e . Fig. 8. P o l a r o g r a m o f t h e s y s t e m 1 M LiCI in water, 50 m M T B A T P B in n i t r o b e n z e n e . (A) T h e o r e t i c a l d e p e n d e n c e w i t h o u t r e s p e c t i n g t h e o h m i c p o t e n t i a l d r o p ; (B) t h e o r e t i c a l d e p e n d e n c e r e s p e c t i n g t h e o h m i c p o t e n t i a l d r o p ; (C) e x p e r i m e n t a l d e p e n d e n c e .
of the height the electrolyte stops dropping. The droptime could n o t be controlled mechanically. With sufficiently strong knocks the drop was torn from the orifice of the capillary b u t it was followed by an irregular sequence of small droplets. With very strong knocks the non-aqueous electrolyte was sucked for a m o m e n t into the capillary damaging thus the inner reference electrode. DISCUSSION
Resistance o f the electrode system In this series of resistances the main contribution arises from the resistances firstly between the reference electrode placed in the aqueous solution and the orifice of the capillary, secondly between the orifice arrd the expanding interface and thirdly between this interface and the non-polarizible electrode placed in the non-aqueous solution. When a capillary with a rather large diameter and with steeply narrowing conical orifice is used and when the aqueous electrolyte is sufficiently concentrated the latter two of the resistances contribute mainly to the total resistance. The distance of the platinum non-polarizable electrode from the interface seems not to be essential; we expect that the work with a four-electrode system including a reference electrode placed close to the orifice of the capillary in the non-aqueous solution will considerably decrease the
226
total resistance. This reference electrode must be, of course, of an ion-selective type with a liquid-liquid interface.
Numerical elimination o f the IR drop For this purpose the resistance of the electrode assembly was calculated from the slopes of the asymptotes of the I - - A V curves measured at higher current values. The theoretical I - - A V curve for the system 1 M LiC1 in water, 0.05 M TBATPB in nitrobenzene was calculated according to eqn. (43) using the tabulated standard Gibbs transfer energies (see Table 1), the values of the diffusion coefficients of both TBA ÷ and T P B - 5 × 10 - 6 cm 2 s-~ and the integral capacity of the interface 20 pF cm - 2 (Fig. 8, curve A) *. A distorted I - - A V curve was then calculated using this dependence and the value of total resistance R = 5.8 k ~2 (Fig. 8, curve B) and compared with the experimental I - - A V curve (Fig. 8, curve C). Obviously, the currents of the ions of the base electrolytes follow eqn. (43).
Standard Gibbs transfer energies and half-wave potentials According to Table 1 the ions giving sigmoid polarographic waves for the LiC1, TBATPB base electrolytes will include those ions the standard Gibbs transfer energies of which are in the interval 3 kJ mo1-1 < A~0'w-~n < 13 kJ ~tr,i mo1-1, which has been, indeed, the case of TMA ÷. A widening of the useful potential range can be expected from the MgC12, TBA dicarbollyl cobaltate base electrolytes. According to Rais [35] an increase (in absolute values) of standard Gibbs free energies is to be expected when using a non-aqueous solvent dissolving less water, like substituted nitrobenzenes (for example, 2-nitro-p-cymene [37]). In these circumstances, the transfer of the ions of the base electrolytes will be made more difficult and the useful potential range will be broader.
Limiting diffusion current For the given experimental conditions the limiting currents of 1 mM TMA÷ and TEA ÷, calculated according to the Ilkovi~ equation, have the values about 60 pA. However, the experimental values are by 20--90% higher. This discrepancy can be explained by taking into account h y d r o d y n a m i c effects. The flow rate of the aqueous solution in the orifice of the capillary is about 70 cm s- 1 . Thus, a flow to the top of the drop followed by tangential motion to the neck of the drop can be expected causing the same convective transport effects as in the case of polarographic maxima of the 2nd kind. The volume of the drop is about 20 m m 3. When the drop tears o f f the sta* T h e I - - A V curve is l i m i t e d b y t h e t r a n s f e r o f T B A + a n d T P B - - while Li + a n d C1-- h a v e e x c e e d i n g l y h i g h s t a n d a r d G i b b s t r a n s f e r energies.
227
tionary phase is markedly set in motion which may be another cause of convection. PERSPECTIVES
The polarography with EDE will, like "classical" polarography with DME, be used for analysis of ions which can be transferred across interfaces of immiscible electrolyte solution in a suitable range of electrical potential differences between these phases, making use of the direct proportionality of limiting current to concentration of that particular ion. Since the interface water-electrolyte solution immiscible with water is the basis of ion-selective electrodes with liquid membranes the analysis of I - - A V curves will give a direct kinetic evidence for the selectivity of the ions concerned, in a similar way as the current-potential curves at metallic electrodes show conditions for establishment of equilibrium and mixed potentials. Since biological membranes contain phase boundaries water/liquid or liquid-crystalline phase the study of only this phase boundary seems to deal with the simplest physical model of a biological membrane.
REFERENCES 1 H. Ti Tien, Bilayer Lipid Membranes (BLM), Theory and Practice, Marcel Dekker, New York, 1974, p. 217. 2 F. Braun, Wied. Ann , 42 (1891) 450. 3 F. Braun, Wied. Ann., 44 (1891) 473. 4 A. Bethe and T. Toropoff, Z. Phys. Chem., 88 (1914) 731. 5 A. Bethe and T. Toropoff, Z. Phys. Chem., 89 (1915) 597. 6 J. Janusevicience and V. Kaikaris, Chem. ir Chem. Technol. (Vilnyus), 6 (1965) 157. 7 E.S. Fetcher, R.S. Lillie and W.D. Harkins, J. Gen. Physiol., 20 (1937) 671. 8 P.S.B. Digby, Proc. Roy. Soc., 161B (1965) 504. 9 D.A. Haydon and S.B. Hladky, Quart. Rev. Biophysics, 5 (1972) 187. 10 P. L//uger, Science, 178 (1972) 24. 11 G. Szabo, G. Eisenman, R. Laprade, S.M. Ciani and S. Krasne in G. Eisenman (Ed.), Membranes -- a Series of Advances, Vol. 2, Marcel Dekker, New York, 1973, p. 179. 12 V.S. Markin and Yu.A. Chismadjev, Indutsirovannii ionii transport, Nauka, Moscow, 1974. 13 J.W. Woodbury, S.H. White, M.C. Mackey, W.L. Hardy and D.B. Chang in H. Eyring (Ed.), Physical Chemistry, An Advanced Treatment, Vol. IX B, Academic Press, New York, 1970, p. 104. 14 J. Guastalla, J. Chim. Phys., 53 (1956) 470. 15 C. Gavach, T. Mlodnicka and J. Guastatla, Compt. Rend., C 266 (1968) 1196. 16 J. Guastalla, Nature, 227 (1970) 485. 17 J.W. Ross, Science, 156 (1967) 1378. 18 C. Gavach, Compt. Rend., 273 (1971) 489. 19 C. Gavach and F. Henry, J. Electroanal. Chem., 54 (1974) 361. 20 C. Gavach and B. D'Epenoux, J. Electroanal. Chem., 55 (1974) 59. 21 M. Gainazzi, G. Silvestri and G. Suravalle, J. Chem. Soc. Chem. Commun., (1975) 200. 22 C.M. Starks, J. Amer. Chem. Soc., 93 (1971) 195.
228 23 C.M. Starks, J. Amer. Chem. Soc., 95 (1971) 3613. 24 M. Makosza and B. Serafinowa, Roczn. Chem., 39 (1965) 1223, 1401, 1595, 1799~ 1805. 25 M. Makosza and B. Serafinowa, Roczn. Chem., 40 (1966) 1647, 1839. 26 M. Makosza, Tetrahedron Lett., (1969) 673, 677. 27 A. Br~/ndstrbm and U. Jungren, Tetrahedron Lett., (1972) 473. 28 E.V. Dehmlow, Angew. Chem., 86 (1974) 187. 29 J. Koryta, P. Van:~sek and M. B~ezina, J. Electroanal. Chem., 67 (1976) 263. 30 A.J. Parker, Chem. Revs., 69 (1969) 1. 31 O. Popovych, Crit. Rev. Anal. Chem., 1 (1970) 73. 32 B. Case and R. Parsons, Trans. Faraday Soc., 63 (1967) 1224. 33 P. Delahay, J. Phys. Chem., 70 (1966) 2067. 34 R. Parsons in P. Delahay (Ed.), Advances in Electrochemistry and Electrochemical Engineering, Vol. 7, Interscience, New York, 1970, p. 177. 35 J. Rais, Collect. Czech. Chem. Commun., 36 (1971) 3253. 36 J. Rais, P. Seluck:~ and M. Kyr~, J. Inorg. Nucl. Chem., 38 (1976) 1376. 37 R.P. Scholler and W. Simon, Chimia, 24 (1970) 372.
211
ELECTROLYSIS WITH ELECTROLYTE DROPPING ELECTRODE II. B A S I C P R O P E R T I E S O F T H E S Y S T E M *
J. KORYTA, P. VANYSEK and M. BREZINA
Czechoslovak Academy of Sciences, J. Heyrovsk~ Institute of Physical Chemistry and Electrochemistry, Opletalova 25, 110 O0 Prague 1 (Czechoslovakia) (Received 17th May 1976)
ABSTRACT In a theoretical discussion the conditions have been pointed out where an interface of two immiscible electrolyte solution behaves as an equilibrium system metal ion-metallic electrode, as an ideally polarized electrode and as an electrode under faradaic current flow. The basic equations for current-electrical potential difference across the interface have been deduced for the cases of ion as well as electron transfer. Experimentally, various base electrolyte systems were studied, the most advantageous among these are LiC1 in water ÷ tetrabutylammonium tetraphenylborate in nitrobenzene and MgC12 in water + tetrabutylammonium dicarbollyl cobaltate in nitrobenzene. S-shaped polarographic curves were observed with the tetramethylammonium ion. The limiting current is directly proportional to concentration. The limiting currents are somewhat higher than those predicted by the Ilkovi6 equation which has been ascribed to the tangential movement of the interface.
INTRODUCTION T h e i n t e r e s t on p o l a r i z a t i o n p h e n o m e n a a t e l e c t r o c h e m i c a l m e m b r a n e s - - a r t i f i c i a l a n d n a t u r a l - - has d a t e d since t h e e n d o f t h e p a s t c e n t u r y . T h e eff e c t o f e l e c t r o s t e n o l y s i s ( f o r a r e v i e w , see ref. 1) b a s e d on m e t a l d e p o s i t i o n on glass [ 2 , 3 ] , c o l l o d i o n [ 4 - - 6 ] o r b i o l o g i c a l [ 7 , 8 ] m e m b r a n e s , t h o u g h perh a p s in s o m e cases c a u s e d b y s p u r i o u s i n f l u e n c e s , has d o u b t l e s s a r e a l e x i s t e n c e On t h e o t h e r h a n d t h e r e has b e e n a v a s t m a t e r i a l p u b l i s h e d on p o l a r i z a t i o n o f a r t i f i c i a l , p a r t i c u l a r l y b i l a y e r l i p i d ( f o r reviews, see e.g. refs. 9---12) a n d b i o l o g ical ( f o r a r e v i e w , see e.g. ref. 13) m e m b r a n e s . H o w e v e r , t h e s i m p l e s t s y s t e m of this k i n d , an i n t e r f a c e o f t w o i m m i s c i b l e e l e c t r o l y t e s o l u t i o n s , h a s b e e n i n v e s t i g a t e d u n d e r f l o w of e l e c t r i c a l c u r r e n t r a t h e r r a r e l y . I o n t r a n s f e r a c r o s s an i n t e r f a c e o f t h a t k i n d was first s t u d i e d b y G u a s t a l l a [14]. The c o n c e n t r a t i o n changes due to the ion transfer were indicated by
* In honour of Dr. G.C. Barker's 60th birthday.
212
changes of the interfacial tension. Steady state polarization curves [15] were obtained with an aqueous KC1 solution and nitrobenzene solutions of dodecyltrimethylammonium dodecylsulphate or picrates of dodecyltrimethylammonium, tetradecyltrimethylammonium or h e x y d e c y l t r i m e t h y l a m m o n i u m . A similar system was also studied by means of slow triangular potential pulses [16] (for analogous experiments with the system of the calcium ion-selective electrode [17] see ref. 18). Gavach and coworkers used c h r o n o p o t e n t i o m e t r y for investigation of the system NaBr containing low concentration of tetrab u t y l a m m o n i u m ion in water + t e t r a b u t y l a m m o n i u m tetraphenylborate in nitrobenzene [19] and of some other systems [20]. The E--t curves showed characteristics analogous to those found with the same m e t h o d using metallic electrodes. A metal deposition at a liquid-liquid interface was observed by Gainazzi and coworkers [21] who studied the polarization of the cell CuICuSO4, H20[JBu4NV(CO)6, C1CH2 • CH2CliPt The overall reaction taking place at the interface during current flow is V(CO)~- + 2 Cu 2+ -+ V aq 3+ + 6 CO + 2 Cu Similarly as a mixed potential reflects the characteristics of processes taking place at a metallic electrode, there are reactions occurring at an interface of two immiscible solvents which are termed as phase-transfer catalysis [22,23] (see also refs. 24--27, for a review see ref. 28). The basic step in these reactions is ion transfer across the interface, of course in the absence of an outer electrical current. In a preliminary communication [29] the experimental assembly for the electrolyte dropping electrode (EDE) was described together with some polarization characteristics of this system. In the present paper, after discussing the theoretical foundations for the static and dynamic behaviour of the interface of two immiscible electrolytes, it will be shown that the basic results obtained with EDE resemble those supplied by polarography with DME. THEORETICAL
A non-polarized interface of two immiscible electrolyte solutions Let us consider two immiscible solvents ~ and ~ in contact. In both solvents a uni-univalent electrolyte B]A 1 is dissolved consisting of the cation B~ and anion A~-, in a graphical representation
BIA 1 JJ B1A 1
(1)
In equilibrium the electrochemical potentials of chemically identical corn-
213 ponents are equal, =
(/3)
]~A~.(0~) = ]~Al(/3)
(2)
or p ° +(a) + R T In as+' (a) + F ~ ( a ) = pO ~(/3) + R T In as~(/3) + F~(/3) (3) p°-(a)
+ R T In aA~(a ) -- F ~ ( a ) = p°-l (fi) + R T In aA~(/3) -- F~(/3)
where the ai's are the ion activities in the appropriate phases, the ~'s are the inner potentials of individual phases and the pi's are the standard chemical potentials which include the terms describing the ion-solvent interaction so that the ai's are functions only of concentration of the i-th ion and of interionic interactions. The p°'s are, of course, quantities which are not accessible to direct measurement. At the interface a Galvani potential difference A ~ is formed A ~ = ~(/3) -- ~(a) = [p°+'(a) - p ° ~ ( / 3 ) ] / F + ( R T / F )
ln[aB+' (a)/aB+1 (/3)] =
(4)
. . . . [p° i (a) -- p ° i ( / 3 ) ] / F - ( R T / F ) ln[aAi(a)/aAi(/3) ] From eqn. (3) we have ln(labs(/3) • aAi(fi)]/[aB+l(a ) • aA](a)], } = = + /2A1 0 (0~) - - po (/3) -- p ' A ~ ( a ) ] / R T = In kB1Al(a, fi)
[u°~(~)
(5)
which is the distribution coefficient of B1A1 between the phases ~ and/3. The differences of the standard chemical potentials in eqns. (3) will be identified with the negative values of standard Gibbs energies of transfer of the cation i from the phase ~ into the phase/3,
~tr,i
:
__
(6)
The values of these quantities can be obtained using various extrathermodynamical assumptions. The most frequently used is that of Parker [30] and Popovych [31] supposing that the standard Gibbs energies of transfer of tetraphenylarsonium cation and tetraphenylborate anion between any pair of solvents are equal. With the help of this assumption a scale of standard transfer Gibbs energies can be calculated for any pair of solvents since the sum of standard transfer Gibbs energies for a cation and an anion (multiplied by corre sponding stoichiometric coefficients for the given electrolyte) is in a simple relationship (eqn. (5)) to the distribution coefficient which is an experimentally accessible quantity. For the present purpose this kind of representation by means of relative scales is quite satisfactory and it is not necessary to account here for the influence of surface potentials (cf. ref. 32). The quantity A ~ cannot be determined by a direct measurement based on
214 a thermodynamic approach. Let us consider the system (1) complemented by two electrodes reversible to the cation B~,
(7)
B11B1A1 [[B1 A1 ]B1 which is in equilibrium. The e.m.f, of this cell E is given by the sum E = /~1 ~ + a ~
+ /~1~
(8)
where
A~l~ = [po ( B 1 ) _ p o ( a ) ] / F _ (RT/F) In aB~(~) and = [p~(fl)
p°~(B1)]/F + (RT/F) In aB+(fl)
Here po~ (B1) denotes the standard potential of the ion B~ in the (metallic, for example) phase B1 and A ~ is given by eqn. (4). The quantity E is obviously equal to zero which also results directly when considering that a system which is in equilibrium cannot expend work. However, by means of a suitable non-thermodynamic procedure it is possible to determine indeed not directly A ~ but the changes of this quantity when the composition of the solutions is varied which is, for the present purpose, quite sufficient. For example, if with the help of suitable electrolyte bridges the reference electrodes are joined to the phases a and fl under conditions that (i) both the bridge and the solution of the reference electrode contain the same solvent as the phase ~ or fl, respectively, (ii) that, with its composition, the bridge minimizes the liquid junction potentials A~L in the scheme (9), then the changes of EMF of this cell are approximately equal to the changes of A ~ when varying the composition of
and ft. reference electro- electroelectrode lyte so- lyte 1 lution bridge 5 of reference electrode 1
AIB1
electro-I electro', lyte soA1 B1 1I I lyte bridge e [ lution of reference electrode 2
(v)
reference electrode 2
(9)
(D
/x~(6,v) Ideally polarized interface of two electrolyte solutions Let us again consider a system consisting of two immiscible solvents a and /3 in one of which an electrolyte BIA1 and in the other one an electrolyte
215
B2A 2 is dissolved, B1A1 IIB2A2
(10)
We shall assume that for the standard Gibbs energies of transfer of ionic components of the system (10) the relationship is valid o,~ >> 0 min~A~O,c~-~ _ A p 0 , ~ - ~ ~.~t__A~0,~-~ (11) "--, ~ t r , A 1 ' L'a~'~tr, B~ ' - - ' " ° ' ~ t "~tr, B~ ' A e t r , A ~ / 3 ) This inequality has two consequences: (i) The equilibrium of distribution of both electrolytes between the solvents a and fi is shifted in the case of the electrolyte AIB1 almost completely on the side of the solvent a while in the case of the electrolyte A2B2 almost completely on the side of the solvent ft. In fact, from the inequality (11) we obtain Ap0,a-+~ ~Jtr B + '. 1
+ A~o,~-+~ --~tr,A 1
>> 0
(12)
~tr, B~ + _ v t r , A~ < < 0 With respect to eqn. (6) these inequalities characterize the corresponding distribution equilibria. (ii) The exchange equilibria B~(a) + B~(fi) ~ BI(fl) + B~(a)
(13)
and
A~(~) + A~-(~)~ A~-(/~)+ A2(a)
(14)
axe shifted to the left-hand side, since from the inequality (11) the following relationships result A~O,c~-+~ __ A ~ O , c ~ - ~ U t r , B~ ~.a~-*tr,B ~ > >
0
Aco,~--~
0
~ t r , A1
-
>>
(15)
For the purpose of calculation of A ~ we shall assume that for one pair of ions of opposite sign i and j (e.g. A2 and B~ or A~ and B~) it holds +A~O,~-~ _+ AGtr o J, ~ ----~tr,i
< < ±AG°~'~ , -~ + A ~t~,l ~ °,a~
(16)
The upper sign applies in the case that the ion is predomirmntly present in the phase ~, the lower one in the opposite case and the indices k and 1 denote the remaining pair of ions. Under these circumstances the ions i and j determine the quantity A ~ according to the relationship, for example for the ion i (cf. eqns. (4) and (6))
A ~ = ~- A G ° ; , 7 ~ / F + ( R T / F ) ln[ai(a)/ai(fi)]
(17)
where the upper sign applies in the case that i is a cation and the lower one in the case that it is an anion.
216 If, for example, the ion i is identical with B~, then in the case of a large shift of the equilibrium for the electrolyte AIB1 in favour of the phase a, the determination of A ~ by the activity a.+(fl) is fictitious. When a certain amount DI of charge is transported to the phase boundary, only a small fraction of this charge is consumed for the transfer of B~ across the phase b o u n d a r y while, from a major part, it is used for charging the double layer at this interface. Thus, at a phase boundary characterized in this way the exchange of charge does not take place, at least in a certain range of A ~ ; the phase boundary has therefore the properties of an ideally polarized interface. A phase boundary defined above is an analogy of an ideally polarized electrode, e.g. of a mercury electrode in a KF solution. Among reactions occurring at the interface which have been mentioned in this paragraph only an analogy to eqns. (13) and (14) can be considered, i.e. the exchange reaction Hg(electrode) + K+ (solution) ~ K(electrode) + Hg+(solution) The equilibrium of this reaction is shifted to the left-hand side so that, in view of their only statistically characterized concentrations, neither potassium dissolved in the electrode nor mercurous ions can influence the e]ectrode potential. Let us consider a cell analogous to (9) b u t with phases a and fl according to (10). Since the phase boundary between the electrolyte solutions a and/3 is ideally polarized the difference of electrical potentials of leads connected to reference electrodes 1 and 2 can be arbitrarily (i.e. in the range where the interface is indeed ideally polarized) varied by means of an external source. This electrical potential difference AV is equal to the difference of inner electrical potentials A ~ with an additional constant independent of A V.
An interface o f two immiscible electrolyte solutions under flow o f current Let us consider a system
B~, A1, BElIB,, A~, BE
(18)
The ions B~ and AT, B~ and A2- are practically present only in one phase as shown in (18). The ion BE, present at a low concentration compared with the other ions, can be transferred between the phases a and/3. At the phase boundary an electrical double layer is formed with the charge density on the side of and fl
q(a) = --q(fi)
(19)
Obviously q(c~)/F= I~B; ( a ) - PA~(a)+ l~B~(0t)=
(20)
If electrical current flows through the system (18) from the left to the right
217 then for the current density j we have j / F = JB~((~) -- JA~(~) + JB+3(~) = JB~(~) -- JA~ (~) + JB~(~)
(21)
where the Ji(a) or Ji(fi) are material fluxes of the components of the phase a or fi, respectively. In view of the small concentration of B~ in comparison with BIA 1 and B2A2, which function as base electrolytes, the charge is transported by BIA1 and BeA2 outside the diffusion layer while inside the diffusion layer the current depends only on the transport of B~, i.e. (22)
f f F = JB~(~) = JB~(fJ)
At the interface we have to consider the balance of adsorption of the components of the system and the transfer reactions of BE characterized by rate constants ktr and ktr. For this balance for the phase a- side of the interface (x -~ 0) we have (a similar relationship for the interface metal ion in solutionmetal amalgam was deduced by Delahay [33], see also ref. 34) j / F = dPB~ ( a ) / d t - - dFA~ (a)/dt + dPB~(~)/dt + ktr CB~((~) -- ktr eBb(/3)
For the flux JB~(a) we have at the same time JB;(~) = dFB;(~)/dt + ~t, cB~(~) -- kt, Cs~(~)
(24)
so that in view of eqn. (20) we obtain j / F = ( l / F ) d q ( a ) / d t - - dFB~(a)/dt
+ JB~((~)
(25)
Similarly for the phase fi-side of the interface it holds __~
j / r = --dFB~(~)/dt + dFA~(~)/dt -- dFB~(~)/dt + ktr
<--
CB~(I~ ) -- ktr CB~(/~)
(26)
and JB~(~) = --dFB~(~)/dt + ktr c.~(a) -- ktr CB+3(~)
(27)
SOthat
j/F = (l/F) dq(a)/dt + dFB~(~)/dt+ JB~(fi)
(28)
Let us assume, for the sake of simplicity, that the absolute value of dFB+(a)/ dt as well as dPs+(fi)/dt is much smaller than the absolute values of the dif~eren rials of FB+ -- F A-1 or of--> FB+ -- FA:2 with respect to time and than the absolute 1 2 +value of the difference ktr cB~(~) -- ktrCB+3(~). Then we have 3
J = Jn~ + J~
.
.
(29)
where
Jn~ = F[dFB~(a)/dt -- dFA](a)/dt] = = F[--dFs~([3)/dt + dFA~(/~)/dt] ~ dq(~)/dt =--dq((J)/dt
(30a)
218 is the non-faradaic c o m p o n e n t o f j and .._>
4__
jf = F[ktrCB+3((~) -- ktrCB~(~)]
(30b)
is the faradaic component• Under these circumstances and under the assumption that also the quantities FB+ contribute to the total charge in the electrical • . 3 . . , double layer to a neghglble degree the non-faradaxc c o n t r l b u h o n can be determined by measuring the current density j in the absence of BE. For the measurement of polarization curves an arrangement according to scheme (9) will again be used while the phases a and fi will be composed according to (18). The liquid junction potentials are assumed to be influenced by the presence of BE in a negligible extent only. The phases a and fi are in contact with auxiliary electrodes by means of which the current enters the system. Under these circumstances the dependence of the current I on AV coincides with the dependence I -- A ~ with the exception of a constant term which cannot be directly determined. However, this term is neither dependent a nor is varied if B + 3 is substituted by another ion on the concentration of B+ which again must influence the liquid junction potentials to a negligible degree only. -. +For ktr and ktr we assume the dependence ktr = k ° e x p ( - - ~ F [ A ~ - - A ~ ° ( B + 3 ) ] / R T ) = k ° exp(--aF[AV--
=
AV°(B+a)]/RT}
k~r = k ° exp((1 -- a ) r [ A ~
(31)
-- A ~ ° ( S ~ ) ] ) =
= k ° exp((1 -- a ) F [ A V - - A V ° ( B ~ ) ] / R T } where k ° is the standard rate constant of transfer of BE between the phases a and ~, a is the transfer coefficient and A ~ ° ( B ~ ) or AV°(B~), resp., are the values of A ~ or AV, resp., in the case that lim[cB~(a)/CB~(fl) ] = 1 cB~(~), CB~¢e)~ 0
(32)
A differential equation describing the transport of B~ is then specified by boundary conditions for x -~ 0
JB~(a)
.__> = ]~tr CB~((1)
--
4___ ]~tr CB~(fl)
JB~(a) = JB~(~)
(33)
(34)
If we assume for the terms in eqn. (33) that ._->
+-ktrCB~(a) > > IJB~(a)f
(35)
we can write -->
<--
ktr CB~(U) -- ktr CB~(fl) ~ 0
(36)
219
Thus, at the phase b o u n d a r y the N e r n s t - D o n n a n equilibrium is preserved even at current flow. In an analogous manner to polarography, this case can be classified as reversible. T h e n we have for x -+ 0 A~
-- A ~ ° ( B ~ )
= AV-- AV°(B~) =
(RT/F) ln[CB~(a)/CB~(fl)]
(37)
With respect to (4) and (6) we have further A~o = A V + const. -----z.~tJrt)'B ^ , - 0 ~ -~ ~ ,/ r~ +
(RT/F)ln[CB~(a)/CB~(~)]
(38)
It must be stressed that the constant term in eqn. (38) depends only on composition of the solutions of base electrolytes a and/3, on liquid junction potentials and on reference electrodes whereas it is independent of the nature of the ion B E. Under these circumstances we can base a relative scale of the values of A~0 ° on the values of standard Gibbs energies of transfer from the phase a to the phase/3, for example, as they were tabulated according to the assumption of Po.povych and Parker (see Table 1). In general, we write for an ion carrying
TABLE 1 Standard Gibbs energies of transfer f r o m water to n i t r o b e n z e n e [ 35,36 ] AG O'w~n and of lx,i n fl0 standard electrical potential differences b e t w e e n these phases (in part after ref. 19) Aw~ for various cations and anions Cations Li + Na + H+ NH~ K÷ Rb + Cs+ TMA+ TEA+ TBA+ TPhAs+
o w AGt]}, i ~n /kJ mo1-1
An~0 °
38.2 34.2 32.5 26.8 23.4 19.4
--0.395 --0.354 --0.337 --0.277 --0.242 --0.201
15.4 3.4 --5.7 --24.0 --35.9
--0.159 --0.035 0.059 0.248 0.372
--50.2 --39.4 --38.8 --35.9 --23.4 --4.6 8.0 18.8 28.4 31,4
--0.520 --0.407 --0.401 --0.372 --0.242 --0.047 0.083 0.195 0.295 0.324
Anions Dicarbollyl Co-Dipicrylaminate 15 TPB-13 Picrate C10 4 I-Br-C1--
220
z i elementary charges,
A ~ = --AV°;,~-~/ziF + (RT/ziF) ln[ ci(a )/ci(/3) ]
(39)
As an example we shall describe the transport to the electrolyte dropping electrode under polarographic conditions. The phase a is represented by the inside of the drop while the outer solution is the phase ft. If the ion which is capable of transfer from a to fl has originally been present only in the phase in a concentration c°(a) we have for the average current
=
(40)
where A is the area of the drop and ~i(a) and ~i(fi) are the coefficients of the Ilkovi~ equation modified for the media ~ and/3. When inserting from eqn. (40) into eqn. (39) we obtain ~
= --i('~O'a'-+fl ' ~ 1 ~
+ ( R T / 2 ziF ) ln(Di,~/Di.a)
+
(RT/ziF) ln[( -- /]
(41)
where
= --A('~O'o~-->fl ,~1--
+ ( R T / 2 ziF ) ln(Di.g/Di,a)
(42)
Analogous expressions could be deduced for an irreversible wave when the approximation (35) were not applicable. For a sufficiently large absolute value of A ~ a transfer of ions of the base electrolytes can take place. For the transfer of the ion B~, for example, we then have A ~ = --A ~-°,~-~ ~,t~,B~f + (RT/F) In KB;(/3) + (RT/F) ln[c°-~(~)/]
(43)
Let us also consider the case of electron transfer across the phase boundary of two immiscible electrolyte solutions
B~, Ay S~, A~B~, B3 B~, 84
(44)
The pairs B~, B 1 and B~, B 4 are components of two oxidation-reduction systems which, in the simplest case, cannot be transferred across the interface. The reaction taking place at the phase boundary, B~ + B 4 ~ B~ + B 3
(45)
can be split into two partial processes, B~+e~B 3 B~ + e ~ B 4
(46)
221
For the Faradaic current density we obtain, if the adsorption effects have been neglected, jffF
"-->
+
~e
=
- - ke,4eB4 (fl)
(47)
-~ JB~ = --JB 3 = JB~ = --JB4 The individual constants of electron transfer in eqn. (47) have the following meaning: k~,3 = ko,3 e x p [ ~ 3 F ( A ~ 0 - - A ~ o ° ) / R T ]
(48)
k~,3 = ko,3 exp[--(1 - - a 3 ) F ( A ~ 0 - - A ~ 0 ° ) ]
(49)
ke,4--> = ko,a e x p [ a 4 F ( A ~ v _ Aa~4)]~ 0
(50)
~-e,4 -- ko,4 exp[--(1 - - a 4 ) ( A { ~ - - A a~~ 4 )0 ]
(51)
In these expressions ko, 3 and ko, 4 a r e standard rate constants of electron transfer corresponding to eqn. (46), a3 and a 4 are the electron transfer coefficients and the standard electrical potential differences A~o ° and A ~ ° are defined for the couples BE, B3 and B~, B 4 in a manner analogous to eqn. (32). These quantities are connected by the relationship A~(~w3 ~o __ A~~W4 ~o . . . . . A G O / F
(52)
where AG O is the standard Gibbs energy change for the reaction (45). EXPERIMENTAL
The design of the electrolyte dropping electrode, the electrode assembly and the polarization and recording instrument were the same as described in the preliminary communication [29]. LiC1, NaBr, MgCle and t e t r a m e t h y l a m m o n i u m chloride were chemically pure substances supplied by Lachema, Brno. T e t r a m e t h y l a m m o n i u m bromide was a product of BDH. Tetrabutylaramonium tetraphenylborate (TBATPB) was prepared in this laboratory. Tetraphenylarsonium tetraphenylborate was prepared by Dr. M. Kyr~, Institute of Nuclear Research, Re~ near Prague and tetrabutylammonium dicarbollyl cobaltate(III) by Dr. M. Plegek, Institute of Inorganic Chemistry, Czechoslovak Academy of Sciences, l~e~ near Prague, to whom our thanks are due for the gift of these substances. The experiments at an initial stage were carried out with a two-electrode assembly and with an electrolyte dropping electrode of 0.1 M TBATPB dissolved in nitrobenzene (dropping, of course, downwards). For aqueous solutions of NaBr (0.2--2 M) a linear I - - A V dependence with oscillations following the regular frequency of dropping was only obtained (Fig. 1). The nitrobenzene drops had a diameter of about 12 mm. The completely prevailing
222
C) 0 =B-H • =C-H
Dicarbollyl c o b a l t a t e ( I I I )
factor was, in this case, the ohmic potential drop in the system. The resistance of the assembly was about 0.2 M ~2. In an alternative arrangement a 0.1 M and, later, a 0.05 M solution of TBATPB in nitrobenzene was placed in the bottom of the electrolytic cell. Aqueous solutions of NaBr in concentrations between 0.01 M and 2 M dropped upwards into the nitrobenzene solution. The originally linear I - - A V dependence changed to a non linear with an indistinct plateau at concentrations larger than 0.1 M NaBr. With 2 M NaBr the aqueous solution ceased dropping off the
I
30I/pA 20-
I~
A
~o°y
o L
i
-lO 0
0.'5
Ii
'
Fig. 1. Polarogram o f 10 m M NaBr in water, 0.1 M TBATPB in n i t r o b e n z e n e . I - - A V d e p e n dence recorded in a t w o - e l e c t r o d e s y s t e m is d e t e r m i n e d by the o h m i c drop o f potential. Fig. 2. Polarogram o f 0.5 M NaBr in water, 50 m M TBATPB in n i t r o b e n z e n e in a two-elect r o d e (B) and t h r e e - e l e c t r o d e (A) a r r a n g e m e n t . The current at A V < 0.4 V c o r r e s p o n d s to the t r a n s f e r o f TBA + f r o m n i t r o b e n e e n e to w a t e r while the current at A V > 0.7 V to the transfer o f Na + f r o m w a t e r t o n i t r o b e n z e n e .
223
capillary, since its density approached that of the nitrobenzene solution and assembled in the form of irregular clusters at the orifice of the capillary. With the three-electrode assembly, which was described in the preceding paper [29], the residual ohmic resistance of the system changed from 13.7 k ~2 for 1 M NaBr to 23.8 k ~2 for 0.1 M NaBr. The polarograms of 0.5 M NaBr for a two- and three-electrode system are shown in Fig. 2. A concentration dependence recorded in the three-electrode system is demonstrated in Fig. 3. Still better results were obtained with lithium chloride aqueous solutions of which 1 M LiC1 has shown as most suitable. When t e t r a e t h y l a m m o n i u m bromide (TEA) was added in concentrations between 0.05 mM and 1 mM to the aqueous phase the plateau of the I - - A V curve was raised as shown in Fig. 3, ref. 29. The supposedly faradaic limiting current of TEA measured at the inflection point of the I - - A V curve was directly proportional to the concentration of TEA. S-shaped polarographic waves were obtained with t e t r a m e t h y l a m m o n i u m bromide (TMA) present in the aqueous solutions of NaBr in concentrations
7_/ p A
3
0.2
O
0.2
~'v/v
0.4
~o.~v
J
2
1
Av
Fig. 3. P o l a r o g r a m s of a q u e o u s phases o f varying c o m p o s i t i o n a n d of 50 m M T B A T P B in n i t r o b e n z e n e . (1) 25 m M NaBr, (2) 50 m M NaBr, (3) 0.1 M NaBr, (4) 0.2 M NaBr, (5) 0.5 M NaBr. Fig. 4. P o l a r o g r a m s of t e t r a m e t h y l a m m o n i u m ion in water. C o m p o s i t i o n of base electrolytes: 1 M LiCl in water, 50 m M T B A T P B in n i t r o b e n z e n e . C o n c e n t r a t i o n s of T M A + : (1) 0, (2) 0.2 raM, (3) 1 raM, (4) 2 mM. T h e negative c u r r e n t c o r r e s p o n d s t o t h e t r a n s f e r o f T B A + f r o m n i t r o b e n z e n e t o water, t h e wave t o t h e t r a n s f e r o f T M A + f r o m w a t e r to n i t r o b e n z e n e a n d t h e s u b s e q u e n t positive rise o f c u r r e n t t o t h e t r a n s f e r of TPB-- f r o m n i t r o b e n z e n e t o water, and, f o r a smaller part, t o t h e t r a n s f e r o f Li + f r o m w a t e r t o n i t r o b e n zene. In t h e d i a g r a m e a c h curve is s h i f t e d b y 0.1 V t o w a r d s m o r e negative p o t e n t i a l w i t h respect t o t h e p r e c e d i n g one.
224
higher than 0.2 mM (Fig. 4). The limiting current determined in the inflexion point of the I - - A V curve was also directly proportional to the concentration of TMA. Analogous results were obtained with a LiC1 base electrolyte b u t the proportionality constant in the Id--C dependence was different (see Fig. 5). When 0.2 mM tetrabutylammonium iodide was added to the nitrobenzene phase the plateau of the I--A V curve was initially raised due to the transfer of iodide from the non-aqueous to the aqueous phase. As effect of the auxiliary polarization the nitrobenzene phase changed colour to pale b r o w n during 2 h and a new anodic wave was formed on the polarogram (see Fig. 6). In further experiments the composition of the base electrolyte solution was varied in order to increase the plateau of the I - - A V curve. For this purpose ions having more advantageous standard Gibbs transfer energies were used. Tetraphenylarsonium tetraphenylborate gave exceedingly drawn-out curves, an effect of high resistance due to low solubility of the substance. The most suitable was the combination of 2.2 M aqueous MgC12 with 10 mM t e t r a b u t y l a m m o n i u m dicarbollylcobaltate(III) in nitrobenzene (see Fig. 7). The small wave is probably an impurity effect. The extremely high value of standard Gibbs energy of transfer of the dicarbollylcobaltate(III) anion from nitrobenzene to water has been pointed out by Rais and coworkers [36]. Attempts were made to determine the dependence of the limiting current on the height of the electrolyte column and on the drop-time, which, unfortunately, could not be substantiated so far. The height of the electrolyte column is linked with the demand of regular dropping. Thus, with small increase of this height a jet of electrolyte is formed while with a small decrease
1.00
Z//uA
z/~A
8O
6O
4C
2O 0
2
4
6 c/lOT 4 M
8
10
0.4
0.6
0.8
1.0 ,J v/ v
1.2
Fig. 5. Dependence of the limiting current of tetramethylammonium ion on concentration in water. Base electrolytes: 1 M LiC1 in water, 50 mM TBATPB in nitrobenzene. Fig. 6. Polarogram of supposed polyiodide ion formed in the nitrobenzene phase.
//pA
T/j T
T
T
I/uA~
225
A
60
4o
40
IS.
o
20 0
-40 •
-20 -4
-80 -0:5
0.0
0.5
,#vl v
0.2
: 0
I _-----~ -0.2 -0.4
1
z/~,~+f~/v
Fig. 7. P o l a r o g r a m of 2.2 M MgC12 in w a t e r a n d 10 m M t e t r a b u t y l a m m o n i u m dicarbollylc o b a l t a t e in n i t r o b e n z e n e . T h e c u r r e n t at A V < - - 0 . 5 V c o r r e s p o n d s t o t h e t r a n s f e r o f TB/~ + f r o m n i t r o b e n z e n e t o w a t e r while t h e c u r r e n t at A V > 0.7 V possibly t o t h e transfer of Mg 2+ f r o m w a t e r t o n i t r o b e n z e n e . Fig. 8. P o l a r o g r a m o f t h e s y s t e m 1 M LiCI in water, 50 m M T B A T P B in n i t r o b e n z e n e . (A) T h e o r e t i c a l d e p e n d e n c e w i t h o u t r e s p e c t i n g t h e o h m i c p o t e n t i a l d r o p ; (B) t h e o r e t i c a l d e p e n d e n c e r e s p e c t i n g t h e o h m i c p o t e n t i a l d r o p ; (C) e x p e r i m e n t a l d e p e n d e n c e .
of the height the electrolyte stops dropping. The droptime could n o t be controlled mechanically. With sufficiently strong knocks the drop was torn from the orifice of the capillary b u t it was followed by an irregular sequence of small droplets. With very strong knocks the non-aqueous electrolyte was sucked for a m o m e n t into the capillary damaging thus the inner reference electrode. DISCUSSION
Resistance o f the electrode system In this series of resistances the main contribution arises from the resistances firstly between the reference electrode placed in the aqueous solution and the orifice of the capillary, secondly between the orifice arrd the expanding interface and thirdly between this interface and the non-polarizible electrode placed in the non-aqueous solution. When a capillary with a rather large diameter and with steeply narrowing conical orifice is used and when the aqueous electrolyte is sufficiently concentrated the latter two of the resistances contribute mainly to the total resistance. The distance of the platinum non-polarizable electrode from the interface seems not to be essential; we expect that the work with a four-electrode system including a reference electrode placed close to the orifice of the capillary in the non-aqueous solution will considerably decrease the
226
total resistance. This reference electrode must be, of course, of an ion-selective type with a liquid-liquid interface.
Numerical elimination o f the IR drop For this purpose the resistance of the electrode assembly was calculated from the slopes of the asymptotes of the I - - A V curves measured at higher current values. The theoretical I - - A V curve for the system 1 M LiC1 in water, 0.05 M TBATPB in nitrobenzene was calculated according to eqn. (43) using the tabulated standard Gibbs transfer energies (see Table 1), the values of the diffusion coefficients of both TBA ÷ and T P B - 5 × 10 - 6 cm 2 s-~ and the integral capacity of the interface 20 pF cm - 2 (Fig. 8, curve A) *. A distorted I - - A V curve was then calculated using this dependence and the value of total resistance R = 5.8 k ~2 (Fig. 8, curve B) and compared with the experimental I - - A V curve (Fig. 8, curve C). Obviously, the currents of the ions of the base electrolytes follow eqn. (43).
Standard Gibbs transfer energies and half-wave potentials According to Table 1 the ions giving sigmoid polarographic waves for the LiC1, TBATPB base electrolytes will include those ions the standard Gibbs transfer energies of which are in the interval 3 kJ mo1-1 < A~0'w-~n < 13 kJ ~tr,i mo1-1, which has been, indeed, the case of TMA ÷. A widening of the useful potential range can be expected from the MgC12, TBA dicarbollyl cobaltate base electrolytes. According to Rais [35] an increase (in absolute values) of standard Gibbs free energies is to be expected when using a non-aqueous solvent dissolving less water, like substituted nitrobenzenes (for example, 2-nitro-p-cymene [37]). In these circumstances, the transfer of the ions of the base electrolytes will be made more difficult and the useful potential range will be broader.
Limiting diffusion current For the given experimental conditions the limiting currents of 1 mM TMA÷ and TEA ÷, calculated according to the Ilkovi~ equation, have the values about 60 pA. However, the experimental values are by 20--90% higher. This discrepancy can be explained by taking into account h y d r o d y n a m i c effects. The flow rate of the aqueous solution in the orifice of the capillary is about 70 cm s- 1 . Thus, a flow to the top of the drop followed by tangential motion to the neck of the drop can be expected causing the same convective transport effects as in the case of polarographic maxima of the 2nd kind. The volume of the drop is about 20 m m 3. When the drop tears o f f the sta* T h e I - - A V curve is l i m i t e d b y t h e t r a n s f e r o f T B A + a n d T P B - - while Li + a n d C1-- h a v e e x c e e d i n g l y h i g h s t a n d a r d G i b b s t r a n s f e r energies.
227
tionary phase is markedly set in motion which may be another cause of convection. PERSPECTIVES
The polarography with EDE will, like "classical" polarography with DME, be used for analysis of ions which can be transferred across interfaces of immiscible electrolyte solution in a suitable range of electrical potential differences between these phases, making use of the direct proportionality of limiting current to concentration of that particular ion. Since the interface water-electrolyte solution immiscible with water is the basis of ion-selective electrodes with liquid membranes the analysis of I - - A V curves will give a direct kinetic evidence for the selectivity of the ions concerned, in a similar way as the current-potential curves at metallic electrodes show conditions for establishment of equilibrium and mixed potentials. Since biological membranes contain phase boundaries water/liquid or liquid-crystalline phase the study of only this phase boundary seems to deal with the simplest physical model of a biological membrane.
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