Polarization phenomena at the water∣o-nitrophenyl octyl ether interface

ELSEVIER Journal of Electroanalytical Chemistry 426 (1997) 37-45

Jounl~u. o~

Polarization phenomena at the waterl o-nitrophenyl octyl ether interface Part ILl. Role of the solvent viscosity in the kinetics of the

tetraethylammonium ion transfer

Zden~,k Samec, Jan Langmaier, Antonin Trojfinek J. Heyrovsk~f Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Do!ej~kova 3, 182 23 Prague 8, Czech Republic

Received 2 September 1996; revised 1 November 1996

Abstract

The kinetics of the tetraethylammonium ion transfer from water to o-nitrophenyl octyl ether has been studied by impedance measurements at the equilibrium cell potential. Enhanced capacity of the interface points to a significant specific adsorption of the tetraethylammonium ion, probably via forming the interfacial ion pairs. In spite of the coupling between the ion transfer and the ion adsorption, a non-linear least squares fitting of impedance data to the Randles-type equivalent circuit or to an impedance model accounting for the specific ion adsorption yields similar values of the kinetic parameters. The most important finding is that the ratio of the rate constants of the tetraethylammonium ion transfer from water to nitrobenzene and to o-nitrophenyl octyl ether correlates with the inverse ratio of the organic solvent viscosities. The low viscosity of 1,2-dichloroethane can then be responsible for rather fast ion transfer kinetics at the waterll,2-dichloroethane interface. The viscosity effect is likely to be associated with the friction exerted by the organic solvent molecules on the hydrated ion penetrating the organic solvent to some depth prior to the ion transfer step. © 1997 Elsevier Science S.A.

Keywords: Kinetics; Ion transfer; Tetraethylammonium ion; So} . . . . . . osity; Impedance spectroscopy

1. Introduction

Theoretical and experimental aspects of ion transfer kinetics at liquidlliquid interfaces have been investigated intensively duOng the last two decades [1-4].

Most of the experimental work was done on the waterlnitrobenzene (WINB) system. While in the first kinetic measurements rather low values of the standard rate constant kg of ion transfer were obtained (10-3 to 10 -4 cm s-1) [5-7], more advanced kinetic studies yielded kg around 0.1 cm s-~ for a large number of ion transfer reactions [8-13]. Recently, two different experimental approaches have been used [14,15] to re-measul,, the standard rate constant of tetraethylammonium ion transfer, for which the values of 0.09 cm s- l [ 10], 0.11 cm s- ! [ 12] and 0.15 cm s - i [ 11] had been reported earlier. First, a careful analysis of the effect of the uncompensated resistance R u on the measured ion transfer admittance suggested that kg is probably greater than 0.5 cm s- l, but less than 1 cm s- [14]. However, an inspection of data in Ref. [14] reveals that in the absence of any additives, kg nears a value of 0 .2cms -~ as R u tends to zero, but systematically higher

values of kg towards approximately 0 .7cms -~ are obtained in the presence of various surfactants, sucrose, or when light water is replaced by heavy water. Second, the equilibrium impedance measurements of the tetraethylammonium ion transfer across a micro W INB interface yielded the value of 0.22 cm s - l [15]. Thus, kinetic data for this ion transfer reaction obtained by various electrochemical techniques seem to be in an excellent agreement.

Few kinetic measurements in other liquidlliquid systems have been reported [ 16-18]. A chronocoulometric study of acetylcholine ion transfer across the waterll,2-dichloroethane (WIDCE) interface indicated that the ion transfer rates could be of the same order of magnitude as in the WlNB system [16]. Later on, both simple and assisted ion transfer ~eactions at a micro liquidlliquid interface have been found to be unmeasurably fast, with the standard rate constant well above 1 cm s - l [ 17,18]. This might be an important result, which eventually does not contradict the kinetic data for the W INB interface, but rather points to a solvent effect.

In particular, the rate of ion transport can depend on the solvent viscosity r/. Theoretical approaches [ 19,20], which

0022-0728/97/$17.00 Copyright @ 1997 Elsevier Science S.A. All rights reserved. PII S0022-0728(96)05029-2

38 Z Samec et al. / Journal of Electroanalytical Chemistry 426 (1997) 37-45

are based on the Langevin equation of motion [21], imply that the rate of ion transfer across an ITIES should be inversely proportional to the friction coefficient of the solvent near the interface. Analogously, an integration of the Nemst-Planck equation assuming an activated [22] or non-activated [23] process shows that the ion transfer rate is p~portional to the ion diffusion coefficient, which in turn is inversely proportional to the solvent viscosity (Walden rule). A modification of the stochastic approach [21] postulates a fluctuating energetic [24] or geometric [25] barrier (fluctuating bottleneck). In the former case, the effective barrier is lower from what it would be if the barrier were static [24]. In the latter case, the transfer rate is proportional to the cross-sectional area of the bottleneck, which fluctuates because of thermal noise, and the fluctua- tion can decay in time. For small decay rates, an interest- ing effect is predicted that the transport rate is proportional to 71 -t /2 [25]. However, evidence for the presence or absence of a potential barrier at an ITIES is scarce. An analysis of the temperature effect on the ion transfer across the W lNB interface points to a relatively low potential barrier of about 5 kJ mol- ! [12]. Molecular dynamics simulations of transfer of small ions (Na ÷, K +, Cl-, F- ) across the WIDCE interface show that the transfer to the aqueous phase is an activated process, the activation energy being associated with the breakup of the interfacial water hydro- gen bonds [26]. Unfortunately, these conclusions concern the system, for which reliable kinetic data are difficult to acquire. Another effect of transport properties of the two adjacent phases on the apparent rate of ion transfer is associated with the rate of ion transport across the diffuse double layer (dynamic or Levich effect) [27,28]. Its magnitude depends on the ion mobilities (diffusion coefficients) in both phases, the potential differences across both space charge regions and on their thicknesses.

The effect of the solution viscosity on the rate of acetylcholine [16,29] and tetraethylammonium [14] ion transfer was studied by adding sucrose in the aqueous phase [14,16], replacing the aqueous phase with the corresponding heavy-water solution [14], or by replacing DCE [16] with dichloromethane or 1,2-dichlorobenzene or their mixtures [29]. However, while the rate constant of acetylcholine ion transfer seems to correlate with the viscosity of the aqueous or the organic phase [16,29], the effect of the viscosity of the aqueous phase on the TEA + ion transfer from water to NB is rather small and even opposite to what could be expected on the basis of diffusion models [14].

The main purpose of this work was to extend the kinetic analysis to ion transfer from water to o-nitrophenyl octyl ether (o-NPOE), the kinematic viscosity of which (13.8 cP) is considerably higher than that of NB (1.8cP) or DCE (0.78 cP). We intended to examine whether the ion transfer rates indeed follow the sequence, which is inverse to the sequence of solvent viscosities. The tetraethylammonium ion transfer reaction appears to be a convenient reference

for examining solvent effects on ion transfer kinetics, because the corresponding standard potential of transfer to NB, DCE or o-NPOE is close to zero [19], i.e. close to the potential of zero charge for the W INB, WlDCE [2,3] and probably also for W lo-NPOE. Consequently, the ion transfer kinetics should not be much affected by the static or dynamic effect of the electrical double layer.

2. Experimental

LiCI, tetrapentylammonium chloride (TPACI), tetraethylammonium chloride (TEACI), sodium tetraphenylborate (NaTPB) and sodium tetrakis[3,5-bis(trifluoromethyl)-phenyl]borate (NaTFPB) were purchased from Fluka as reagent-grade chemicals. Tetrapentylammonium tetrakis[3,5-bis(trifluoromethyl)-phenyl] borate (TPATFPB) or tetraethylammonium tetraphenylborate (TEATPB) were precipitated from the aqueous solutions of TPACI and NaTFPB or TEACI and NaTPB respectively. Doubly dis- tilled water and o-NPOE (Fluka, Selectophore ®) were used for preparation of solutions. Prior to use, the organic solvent was purified by passing slowly through a column of activated alumina.

Equilibrium impedance measurements of the TEA + ion transfer were carded out at ambient temperature, i.e. 295 + 2 K, in a four-electrode microcell, with a flat W Io-NPOE interface of geometric area 0.139 cm 2 [30]. The cell can be represented by the scheme:

I o.,MLic, ,,O.O, MT AT B I O.,MLiC, IA C,,A. + x mM TEACI ]I + y mM TEATPB + z mM TEACI

(w) 11 (o) (w' ) (1)

where x = 0.1, 0.2, 0.5, 1.0 or 2.0, y = 0.13, 0.26 or 0.52 and z = 2. The reference electrode connected to the organic solvent phase (o) is reversible to the TEA + ion, which is an arrangement necessary to prevent the extrac- tion of the TEA + ion from the phase (o) to (w') [31]. Capacitance measurements were carried out in the cell (1) in the absence of the TEA + ion (x = y = z = 0), with the organic reference electrode reversible to the TPA + ion, i.e. 0.1 M TPACI[AgCI[Ag'. The conversion of the cell potential E into the potential difference A'~o = ~o w - ¢o was based on a voltammetric determination of the reversible half-wave potential of the TEA + ion [32], which was added to the aqueous or the organic solvent phase after the capacitance measurements.

The W[o-NPOE interface was polarized by using a four-electrode potentiostat (1287 Electrochemical Interface Solartron, Solartron Instrument, UK). Impedance spectra were measured with the help of a frequency response analyser (1255 FRA Solartron, Solartron Instrument, UK). A 5mV peak-to-peak a.c. voltage from the FRA was applied via the potentiostat to the cell (1) sweeping the frequency range from 1 to 10 6 Hz at an equilibrium constant potential. In capacitance measurements, the potential was changed in a step-wise manner over the accessible

Z Samec et aL/Journal of Electroanalytical Chemistry 426 (1997) 37-45 39

potential range. The current and potential outputs of the potentiostat were connected to channels 1 and 2 of the FRA respectively, i.e. the impedance was measured by relating the actual potential difference between the reference electrodes to the current flowing between the counter electrodes. The system was equipped with software (ZPlot/ZView, Scribner Associates, Inc.) for computer control of impedance measurements and for the non-linear least squares fitting (NLLSF) of impedance data. The corrected impedance spectra were analysed with the help of another NLLSF software, EQUIVCRT [33], or the NLLSF routines provided by Mathcad Plus 6.0 (MathSoft Inc., USA). In all the fitting procedures, use was made of the weight factor represented by the inverse square of the modulus of measure t val:::,s, I/(Z~2-i - Z12) [33].

3. Results and discussion

El El

500k n

-4e+4

0e+0

0o+0 4e+4 8e+4

Z'/f~

Fig. 2. Impedance plot ( [ ] ) for the cell (1) in the frequency range 0. ! Hz to 500kHz for concentrations of the TEA + ion c w = 1 X 10 -4 moldm -3 and c ° = 2.6× 10-4moldm -3. Simulation ( ~ ) using Eq. (5) for the parameters: a I = 4.75 X 104, bm= 0.01, d I = 0, x= = 7.25 x 10 -6, r I = r' I = l, C m = lOpF and those given in Table 1, column B. Numbers give the frequency in hertz.

Fig. 1 shows the plot of the equilibrium potential E of the cell (1) at various concentrations of the TEA + ion in the aqueous (w) and the organic solvent (o) phase. Owing to a symmetry in the cell arrangement, the potential E should follow the relationship

E= (RT/F) In( aW'/a w ) (2)

where a w' and a w are the activities of the TEA + ion in the phases w' and w respectively. In agreement with Eq. (2), the potential E is independent of the TEA + ion concentration in the organic solvent phase, and the plot of E vs. log(c*'/c ~) is a straight line with a slope of 57mV passing through the origin. The potential difference Aw~p = ~o w - tp ° between the aqueous and the organic solvent phase corresponding to a potential E can be evaluated from the ratio of the TEA + ion concentrations in the organic and aqueous phase as A~tp = AWtp°+ (RT/F) ln(a°/aW), where the standard potential difference for the TEA + ion transfer w 0 A o ~p = 0.025 V [32].

100

80

60

• -.- 40 i i i

20

-20

r l

8

/

0.0 0.5 1.0 1.5

Iog(c*'lc*)

Fig. 1. Equilibrium potential E of the cell (1) vs. the logarithm of the ratio of the TEA + concentrations in the aqueous phases w and w'. Concentrations of TEA + in the organic solvent phase: 0.13 (C)), 0.26 ( [ ] ) or 0 . 5 2 m m o l d m - 3 (A) . Regression line: E = - 2 . 1 + 57. ! iog(cW'/ c w ),

A typical impedance plot of the cell ( l ) in the frequency range 0. l Hz to 500 kHz is displayed in Fig. 2. At frequencies lower than about 150 Hz, the cell seems to exhibit the behaviour of the Randles-type equivalent circuit, while in the intermediate (150 Hz to 100 kHz) or high (100 kHz to 500 MHz) frequency range an inductive or capacitive loop appears. A similar behaviour was observed when only the base electrolytes were present in the aqueous and the organic solvent phase [30]. The high frequency dispersion can be ascribed to the parasitic coupling impedances between the counter and reference electrodes. As they can also influence the impedance of the system in the low frequency range [30], we shall examine their effect first.

3.1. A correction of impedance data for parasitic elements

Provided that the ITIES can be represented by the Randles-type equivalent circuit, the real Z' and the imaginary Z ' components of the inteffacial impedance Z = Z' - jZ" (j = V'- 1 ) are given by

z ' = + (Rc, +

/ [ ( l + @toi/2Cd)2 + t02C~

×(Ro, + ] (3) z ' = [ + +

)2 /[(l + ,o C (Ro, + ,,,o-

where to is the angular frequency, R s is the solution resistance, Rct is the kinetic resistance of the charge transfer reaction, Cd is the differential capacitance of the ITIES. The coefficient of the Warburg impedance o" is related to the coefficient 110 of the Warburg admittance Y= Yo(jto) 1/2, o '= l/(2t/2Yo).

The role of the parasitic elements in the four-electrode cell used in impedance measurements was discussed in

40 Z. Samec et aL / Journal of Eieor,oana?ytical Chemistry 426 (1997) 37-45

detail elsewhere [30]. Parasitic effects were supposed to arise mainly from the coupling impedances between the reference electrodes (Z m) and between the reference and the counter electrode of the organic phase (Zst), and from the high impedances of the reference and counter electrode Zrl and Zet respectively. These impedances were supposed to be either purely capacitive, Z m = (j to C m)-l , or purely resistive, Zet = Rct, or series combinations of a resistance and a capacitance, Zsl = Rsl + (jtoCst)-I and Zrl = Rrt + (jcoCrl) -=. If SO, the apparent impedance Z a of the cell is given by [30]

Z a = ( EG "}" F H ) / ( G 2 Jr H 2 )

+ j( F G - E H ) / ( G 2 + H 2) (5)

where

E = Z ' + at(to2x~ + d t ) / ( l + to2x~) (6)

F = - Z " + a, toxt( l - d , ) / ( l + to2x~) (7)

G = 1 + ¢oCmZ"

+ {r,b,d, + bl f[rl- r ' ,(l- b , ) ( l - d,)]} / ( 1 + to2x~) ( 8 )

H - toCmZ'

+ { b t t o x t [ r l ( l - d r ) + r ' l ( l - b l ) ( d I + o~2x2)]}

/ ( 1 + to2x 2 ) (9)

are the functions of the angular frequency to with the parameters a t = R r t R ¢ t / R t t , b i = R r l / R t l ' dt = R . C . / R . I C r t , rt = Cm/Csl , r'! = Cm/C,I. xi = R . C , , .

Rtt = Rsl + Rrl + Rot and Ctl = (C~ 1 + C~] 1)- 1. When oJ 2x 2 << 1, and also Cm = C~t << Cd, Crl and dl << R~/a l << 1, Eq. (5) simplifies to [30]

Z a = (Z ' + a t to2x~) + j ( - Z " + a t t o x t ) (10)

which predicts that the Randles-type behaviour can be seen at low frequencies. However, as to increases, Eqs. (3) and (4) imply that Z'---> R s and Z"---> 0, and the inductive feature with a p,Jsitive imaginary component ( a l t o x t) starts to dominate. Therefore, Eq. (10) was used to infer the values of the parameters a t and x~ from the initial part of the inductive loop, see Fig. 2, yielding a t = (4.7-5.1) × 104 l'l and x t = (5.3-7.3) × 10 -6 s.

These estimates, together with those made previously [30], i.e. Cm'~Cst ~ 10pF, Crl --" 0.1 la, F, R~t = 5 k f l and R a ~- 7.5 k t l , confirm that the assumptions leading to Eq. (10) are fulfilled at frequencies lower than approximately 10kHz. Fig. 3 shows the components Z' and Z" of the interracial impedance Z, which were obtained by correct- ing the apparent impedance data for the terms a t toZx~ and at tox t respectively. At frequencies exceeding 1 kHz, Z" was a small difference of large numbers, and its evaluation was rather inaccurate.

Table 1 compares the parameters of the Randles-type equivalent circuit and their relative errors, as obtained by

le+5 Z |

o o °

10+4

KI le+3 i

r , i - Z "

le+2 [

le+1 o . . . . . . . . , . . . . . . . . . i . , . . . . . . . . . . . . . .

le-1 le+0 le+1 le+2 le+3

f l Hz

Fig. 3. Bode Z',Z' plot (O, O) based on the impedance data in Fig. 2 corrected for the parasitic effects, and the NLLSF to the Randles-type equivalent circuit ( ~ ) or to the impedance model accounting for the specific adsorption of the TEA + ion (---).

the non-linear least squares fit to impedance data before and after the correction for the parasitic elements. In addition to the transfer of the TEA + ion, we have taken into account also a contribution from the simultaneous transfer of the base electrolyte ions Yb = Y0b(Jto) nb. The parameters Y0b and n b, which have been evaluated previously [30], were fixed in the present analysE. As can be seen from Table 1, the solution resistance and the Warburg impedance remain practically unchanged. On the other hand, the correction leads to somewhat lower values of the kinetic resistance and the double layer capacity. Therefore, only the corrected data will be considered further.

The values of all parameters of the equivalent circuit were then used in Eq. (5) to simulate the behaviour of the cell (1) in the whole frequency range, see the full line in Fig. 2. As in the absence of the TEA + ion [30], the experimental impedance can be reproduced with an excellent precision up to the frequency 20kHz. At higher frequencies, just a qualitative description of the measured impedance could be attained.

Table 1 Parameters of the Randles-type equivalent circuit and their relative errors (in parentheses) obtained by the non-linear least squares fit to impedance data before (A) and after (B) the correction for the parasitic elements. Concentrations of the TEA + ion: c* = 1 X 10 -4 moldm -3, c ° = 2.6× l0 -4 moldm-3

A B

Range/Hz 0.3-150 0.3-1000 N a 29 39 1 0 - 4 R s / ~ 2.331 (0.1%) 2.315 (0.1%) e k / ~ 990 (23%) 582 (31%) 105Yo/f~- I s I/2 6.72 (0.7%) 6.67 (0.7%) n 0.51 (1.7%) 0.50 (1.4%) 105 Y0b / 1~- i s !/2 0.15 (rLxed) 0.15 (fixed) nb 0.50 (fixed) 0.50 (fixed) C d/p .F 5.8 (8.8%) 3.8 (l 1.5%)

a Number of impedance data points

Z. Samec et al. / Journal of Electroanalytical Chemistry 426 (1997) 37-45 41

6 0 • , • - . - • . - - , . , . ~ •

40 E o LI. ::L

0

2O

I ./

-200 0 200 400

a~q~ / mV

Fig. 4. Differential capacity C of the ITIES vs. the interfacial potential difference A'~tp in the absence (D) (taken from ref. [27]) and the presence (O, O) of TEA + in the aqueous and the organic solvent phase evaluated by using the Randles-type equivalent circuit (1"1, O) or the impedance model accounting for the specific adsorption of the TEA + ion (I) . Dashed line: the capacity of the diffuse double layer calculated by using the Gouy-Chapman theory from the surface charge density obtained by an integration of the C vs. A'~ tp plot starting at A'~ tp = 0.

3.2. Evidence for the specific adsorption o f the TEA ÷ ion

Fig. 4 shows the interfacial capacity of the ITIES in the absence [30] and in the presence of the TEA + ion. In the former case, the capacity exhibits a minimum at A'~ t¢ --- 0, which can be identified as the potential of zero charge A'~ tppz ~. A comparison with the theoretical capacity calculated by using the Gouy-Chapman theory, see the dotted line in Fig. 4, indicates the presence of a small surface dipole at low or negative surface charges on the aqueous side of the ITIES, and to a more significant surface dipole at positive surface charges.

The remarkable increase of the capacity in the presence of the TEA + ion points to a specific interaction of this ion with the interface, which gives rise to a contribution to the surface charge density at a given potential difference A'~ tp. Therefore, we shall consider the following overall scheme:

TEA +(w) TEA +(o) *1' *t

TEA a+d~ (w) ~ " + TEAads (0) (11)

which assumes that the TEA ÷ ion adsorbs specifically on both sides of the ITIES. A plausible mechanism of the specific adsorption is the formation of the interfacial ion pairs [34,35], i.e. the adsorbed species TEA a+d., (w) and TEAa+ds(O) are represented by TEA+TFPB~-a~ and TEA ÷CI ads respectively.

The coupling between the ion transfer and the ion specific adsorption as implied by Eq. (11) can complicate the impedance analysis. In particular, the interpretation of the impedance in terms of the Randles-type equivalent circuit may not be adequate [36]. It has been shown that the theoretical expression for the impedance simplifies

when the effect of either the interfacial potential difference or the bulk ion concentration on the amount of the specifically adsorbed ions Fi w and Fi ° is negligible [36]. Since the effect of the potential difference is likely to be well pronounced [37], we shall examine the latter simplification assuming a weak effect of the ion concentration on F~ w and Fi °, i.e. I(DW) -1/2 (al"iW/OcW)(jo~)l/2l= (DW)- l / 2 (OFiW/acW)a~ 1/2 << 1 and I (D°) - t / 2 (1)l"i°/OC°)(jo))l/2l=(O°)-l/2(OFi°/OC°)a) 1/2 << 1. The impedance Z of the ITIES is then given by [36]

1 Z = R s + . . . . . . . . . . . + [1 (12)

jcoC T r b + --p(jco)l/2]z=t

whct~ C T -= (0qW/~)A'~o), qW is the total surface charge dci~ity comprising the contribution of the specifically adsorbed ion, Zc, = Rot + y - I is the impedance of the TEA + ion transfer, Yb and Y are the Warburg admittances of the transfer of the base electrolyte ions and TEA + ion respectively, and the parameter p is defined by

( y~ yo )

p=(RT/F 2) cWDWl/2 + cODOl/-------- ~ (13) where yW=F(OFiw/aAwq~)and y ° = -F(aFi°/aAw~o) characterize the potential dependence of the specific ion adsorption. Note that Eq. (13) with p = 0 describes the behaviour of the Randles-type equivalent circuit used in the analysis above.

The parameters of the Randles-type equivalent circuit and the impedance model accounting for the specific ion adsorption, Eq. (12), are compared in Table 2. A similar analysis performed at various concentrations of the TEA + ion indicated that the parameter p was rather small. In- deed, the fitting of impedance data to these models yields only slightly different values of the capacity and of the transport or kinetic parameters, see Table 3 and Fig. 4.

In order to check whether the simplifying conditions leading to Eq. (12) are realistic, an attempt was made to estimate the magnitude of the charges of the specifically adsorbed ions, qW = FFi w and qi ° = - F F i ° by using a simple model of the ITIES [37]. The model assumes the existence of two space charge regions on each side of the ITIES separated by a sharp boundary, at which the ions

Table 2 Parameters of the Randles-type equivalent circuit and of the impedance model accounting for the specific adsorption of the TEA* ion (in parentheses) obtained by the non-linear least squares fit to impedance data corrected for the parasitic elements. Concentration of TEA + in the organic solvent phase c °= 1.3 × l0 -4 moldm -3

cW/ n 10s Yo mM /f~-I sl/2

0.1 0.52 (0.51) 3.70(3.76) 0.2 0.52 (0.51) 3.74 (3.73) 0.5 0.51(0.50) 3.96(4.03) 1.0 0.51 (0.51) 4.30 (4.28) 2.0 0.51(0.50) 4.62(4.57)

R~, /n CdI~F .... IO'pls '/"

908 (758) 4.2 (4.5) - (8.0) 674 (649) 4.2 (4.4) - (3.0) 609 (560) 4.2 (4.7) - (7.0) 524 (445) 4.6 (4.4) - (2.0) 275 (79) 4.1 (4.2) - (0.4)

42 Z Samec et aL / Journal of Electroanalytical Chemistry. 426 (1997) 37-45

Table 3 Components of the total charge density qW = q~, + qW + qO in the presence of TEA + evaluated for the ratio of its adsorption coefficients /3 ° / /3 w = 0.1.

Concentration of TEA + in the organic solvent phase c ° = 1.3 × 10 -4 tool dm -3. Data in parentheses: the surface charge density in the absence o f TEA +

cW/mM A w ~p/mV qW/ixC c m - 2 q~/l~C c m - 2 qW/p~C c m - 2 q°/p.C c m - 2 103p / s I/2

0.1 29 0.867 0.435 (0.337) 0.436 - 0.006 14

0.2 11 0.349 - 0 . 1 5 3 (0.120) 0.516 - 0 . 0 1 4 10

0.5 - 13 - 0 . 4 3 6 - 0 . 8 2 4 ( - 0 . 1 4 0 ) 0.418 - 0 . 0 3 0 6 1.0 - 30 - 0.951 - 1.188 ( -- 0.305) 0.274 - 0.037 5

2.0 - 48 - 1.564 - 1.684 ( - 0.490) 0.166 - 0.046 6

can adsorb specifically by forming the interfacial ion pairs, e.g. TEA+TFPB~ds and TEA+Clads. Their surface concentrations, Fi w and Fi ° respectively, are functions of the interfacial potential difference A w ~p:

Fi w =/3°Wc w exp[ FA w ~p/RT] (14)

o = a°Oc o e x p [ - F a w /RT] (15)

where fl0w and /3 °° are the adsoT.ption coefficients at AW~p = 0. The total charge qW splits into three contriba- tions:

q ' = q 7 +q~' +qO (16)

white q~' is the net charge present in the diffuse double layer. The capacity C a. and the parameter p can be then expressed by

C r = C d + 7 w + 7 ° = C d + ( F / R T ) ( q W _ qO) (17)

( qi w qO )

p = ( l / F ) cWOW,/2 + cOOO,/-.------- (18)

where C d is the differential capacity of the diffuse layer at constant ion concentrations and constant charges qW and qO. Note that Ca. is a function of the total charge qW, ~,w

and 7 ° are functions of the charges qW and qi ° respectively, and C a is a function of the charge in the diffuse double layer q ~ = q W _ q W _ q O = _q,~ [3.',5 Fqs. (16)- (18), together with a relationship between £~ and q~', e.g. expressed from the Gouy-Chapman theory, represent a suitable basis for the evaluation of q~', qW and qO from the experimental values of qW, Ca . and p.

However, the value of the parameter p determined in the analysis above was rather uncertain. Therefore, the surface charges q~', qW, qO were inferred for given values of qW and C T by a numerical fitting to Eqs. (16) and (17) only. The ratio qO/q~, was evaluated from Eqs. (14) and (15) for a selected ratio of the adsorption coefficients /3°°//3°w, which was then varied until the values of the parameter p calculated from Eq. (18) agreed reasonably with those estimated from the experiment, see Table 2. Since the capacity data in the presence of TEA r did not indicate a change in A w cpp~, the surface charge qW was evaluated by an integration of Ca. starting at A w ~p = 0 as in the absence of the TEA + ion.

Results of this analysis are summarized in Table 3, which also compares the surface charges in the diffuse

double layer q~' in the presence and absence of the TEA ÷ ion. Reasonable values of the parameter p were inferred for too~flow = 0.1, which indicates that the specific adsorption of the TEA+TPB - ion pairs is much stronger. Although the exponential dependence of the surface concentrations on the potential was not anticipated, the surface charges qW and qO vary in accordance with Eqs. (14) and (15) respectively. This can be seen from the almost constant value of the adsorption coefficient fl0w= 1.5 × 10 -5 cm, 1.7 x 10 -5 cm, 1.4 × 10 -5 cm, 0.9 × 10 -5 cm, and 0.6 × 10 -5 cm derived from qW at the concentrations c w = 0.1 mmol dm- 3, 0.2 mmol dm- 3, 0.5 mmol d m - 3, 1.0 mmol dm- 3 and 2.0 mmol dm- 3 respectively. The adsorption of TEA ÷ at a positive potential difference seems to have little effect on the surface charge in the diffuse double layer q~', which would imply a negligible change in the surface dipole, as if the orientation of the dominating adsorbed ion pairs (TEA+TFPB~s) is tilted by the electrical field to the direction parallel to the ITIES. On the contrary, at a negative potential difference, an increased potential drop in both space charge regions corresponding to an increased value of q~' apparently compensates for a positive surface dipole arising from the alignment of the dominating adsorbed ion pairs along the electrical field. Maximum surface charges qi "~ = 0.436 ~ C c m -2 and qi ° = - 0.046 IxC cm -~ correspond to the coefficients aFiW/ac w = FiW/c w = 4.5 × 10 -5 cm and aFi°/ac ° = FiO/cO = 3.7 x 10 - 6 c m . Then, for D w ---- 1.0 × 10 -5 cm 2 s- l and D ° = 4.2 × 10 - 7 c m 2 S-! (vide infra), the condi- t i ons ( D W ) - ~ / 2 ( a r i w / O c w ) ¢ o l / 2 << 1 a n d (D°)-l/2(OF~/Oc~a)¢o !/2 <<1 are fulfilled when co<< 4.9 × 10 3 S - 1 and 3.1 × 10 4 S - 1 respectively. Therefore, in most cases, Eq. (12) should be applicable at frequencies lower than approximately 1000Hz.

3.3. Ion transfer kinetics

Fig. 5 illustrates the effect of the concentrations c w and c ° of the TEA + ion on the coefficient Y0 of the Warburg admittance. The effect can be described theoretically by the equation

Yo' = ( R T / F 2 A cwOw,/2 + cODO,/-------- ~ (19)

Z. Samec et al. / Journal of Electroanalytical Chemistry 426 (1997) 37-45 43

0.04 ", . .

0.03 I f f l

( D

o 0.02 , ,¢..

"7, g

O.Ol

0 . 0 0 , i , i , 0 1 2 3 4 5 6

(cW)-l/106 cm 3 mo1-1

Fig. 5. Inverse coefficient of the Warburg admittance Yo ! vs. the inverse concentration of the TEA + ion in the aqueous phase (cW) -I at two different concentrations of the TEA + ion in the organic solvent phase c ° = 1.3X 10 -4 (O) and 5.2x 10 -4 moldm -3 (El).

where A is the interfacial area. The data yield the values of the diffusion coefficients D ° = (4.3 + 0.2) X 10 -7 cm 2 s- ! and D w = (0.8 + 0.5) × 10 -5 cm 2 s- i. Ow- ing to a relatively lower contribution of the first term in Eq. (19), see the low slope of the Yo I vs. (cW) -I plot, the latter value is less accurate. Nevertheless, the average value agrees well with that of 1.1 × 10 -5 cm 2 s-~ inferred previously from voltammetfic measurements [32]. It is also notable that the ratio of the diffusion coefficients D * / D ° = 18.6 is close to that predicted by the Walden rule based on the ratio of the solvent viscosities r / ° / r / * = 15.5 at

298 K. The apparent rate constant kf of the ion transfer from

the aqueous to the organic solvent phase was evaluated from the charge transfer resistance Rot according to

Rct --- RT/FEAkfc * (20)

Fig. 6 shews: the dependence of the rate constant kf on the potential difference A T ~p relative to the standard potential difference A'~tp ° (Tafel plot). It is seen that the kinetic data evaluated by using either the Randles-type equivalent circuit (empty points) or the impedance model accounting for the specific adsorption of the TEA + ion (solid points) coincide. Eq. (20) is based on the first-order rate equation, which appears to be adequate, as indicated by a negligible effect of the concentration of the TEA ÷ ion in the organic solvent phase, see Fig. 6. Linear regression of the data in Fig. 6 (solid line) yields the value of the apparent rate constant at A'~tp = Awq~ °, k ° = 1.8 × 10 -2 cms -I , and the value of the apparent charge transfer coefficient a = 0.69. It is remarkable that the ratio of the rate constants of the TEA + ion transfer to NB (ka°(NB)= 0 . 2 c m s -~ [10,11,14,15]) and to o-NPOE, k°(NB)/k°(o-NPOE) -" 10, is close to the inverse ratio of the viscosity coefficients, r / (o -NPOE)/7 / (NB)= 7.7. Provided that this rule is applicable to other organic solvents, we can predict the rate constant of the TEA + ion transfer to DCE as

k°(DCE) -- 0.5 cm s - t, which would correspond to the ratio 'r/(NB)/'r/(DCE) = 2.3. Although this estimate is still much lower than the rate constant k ° (DCE)= 32cm s - l [18] reported for the tetramethylammonium ion transfer, the reason that the ion transfer to DCE should be faster than to the other two solvents considered appears to be qualitatively acceptable. Besides, the impedance data [18] are largely distorted by contributions of parasitic elements, the interpretation of which may not be straightforward [30] and, hence, the confirmation of the high value of the rate constant quoted above by an independent kinetic study is needed.

The theoretical basis for the viscosity effect in the kinetics of ion transfer across the interface is provided for example by the stochastic approach [19], which assumes the existence of a sharp potential barrier located between a point x --- a near the aqueous phase and a point x = b near the organic solvent phase. In the present case, the effect of the electrical double layer can be supposed to be small and, hence, the ion concentrations at the points a and b are practically those in the solution bulk, i.e. c w and c ° respectively. Besides, when the potential differences across the space regions are small, the contributions of the aqueous or the organic phase to the dynamic double-layer effect depend on the ratio kf/D*K* or k b / D % °, respectively, where 1 / r w or I / K ° are the corresponding Debye reciprocal lengths (or the thicknesses of the space charge regions) and kb=kfexp[-F(AWtp-AWocp°) /RT] is the backward rate constant [28]. For kf ~- k b ~ 10 -2 cm s- i, D* = 0 . 8 × 10-Scm 2 s - I , D ° = 4 . 3 × 10-Tcm 2s - I , l / K W = 0 . 9 6 × 1 0 - 7 c m and l / r , ° = 1 . 7 × 1 0 - 7 c m , the ratios kf/D*K* = 10 -4 and kb/D°K ° = 4 × 10 -3, i.e. the dynamic effect is quite negligible. The rate constant kf is

then given by

k f = ko exp( otAe °) (21)

E ..---2

o

_ _ , . ~ . . . . ~ . . . . i

o /

-50 0 50

Awoq~ - A*oq~ ° I mV

Fig 6. Rate constant kf of the TEA + ion transfer from lhc aqueous t~,~ the organic solvem phase vs. A'~p- AWotp ° evaluated by using the Randles-type equivalent circuit (v , O, 1:3) or the impedance model accounting for the specific adsorption of the TEA + ion (O). Concentra- tions of the TEA + ion in the organic solvent phase c ° = 1.3 x 10- 4 ( v ), 2.6×10 -4 (O, 0 ) and 5.2xl0-4moidm -3 (El). Regression line: l o g kf = - 1.75 +0.0119(A'~ ~ - AWo ¢p°).

44 Z. Samec et al. / Journal of Electroanalytical Chemistry 426 (1997) 37-45

where

ko= [Mto*/~(a)](RT/27rM)'/2exp(-e * ) (22)

t~ = ¢ x o - a)d-' + RTAc°/(2Mto * 2d2) (23)

Ae°=e(b) - ¢ ( a ) = - F ( A t p - Aq~°)/RT (24)

M is the ion molar mass, to* is the angular frequency of ion motion near the top of the barrier (a harmonic approxi- marion), ~:(a) is the friction coefficient at x = a, d - b - a, e * = V * / R T is the dimensionless barrier height located at x - x o .

An obvious consequence of this approach is that the ion transfer rate is inversely proportional to the friction coefficient (or the viscosity) at the location x = a, the environ- ment of which is supposed to be formed mainly by water molecules. However, the present study points to a correla- tion of the rate constant with the inverse viscosity of the organic solvent. Such an effect could be associated with the friction exerted by the organic solvent molecules on the hydrated ion penetrating the organic solvent some depth prior to the ion transfer from a to b. Indeed, the existence of water capillaries (or water fingers) that play a dynamic role in the ion transfer from water to the organic solvent and vice versa, as well as the high probability that the first hydration shell of the ion remains nearly intact, has been indicated by molecular dynamics simulations [26]. The absence of the viscosity effect on the TEA + ion transfer from water to NB was ascribed to the depletion of sucrose, which was used to vary the viscosity of the aqueous phase, from the interfacial region [14]. However, this can also be a consequence of different roles of water and the organic solvent in the ion transfer dynamics.

4. Conclusions

Tetraethylammonium ion transfer from water to o- NPOE is accompanied by a significant specific adsorption of the ion probably via forming the ion pairs at the interface, among which the adsor~d TEA+TPB - species dominate. In spite of the coupling between the ion transfer and the ion adsorption, an NLLSF of impedance data to the Randles-type equivalent circuit and to an impedance model accounting for the specific ion adsorption yield similar values of kinetic parameters. The most important finding is that the ratio of the rate constants of the tetraethylammonium ion transfer from water to NB and to o-NPOE correlates with the inverse ratio of the organic solvent viscosities. The low viscosity of DCE can be then responsible for rather fast ion transfer kinetics at the W IDCE interface. The viscosity effect is likely to be associated with the friction exerted by the organic solvent molecules on the hydrated ion penetrating the organic solvent to some depth prior to the ion transfer step.

Acknowledgements

This work was supported by the Grant Agency of the Academy of Sciences of the Czech Republic (Grant No. 440411).

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Polarization phenomena at the water∣o-nitrophenyl octyl ether interface

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