Journal of Electroanalytical Chemistry 537 (2002) 77 /84 www.elsevier.com/locate/jelechem
Contact Galvani potential differences at liquid j liquid interfaces Part I: Experimental studies on single salt distribution at liquid j liquid interfaces using a streaming technique Henrik Jensen, Vale´rie Devaud, Jacques Josserand, Hubert H. Girault Laboratoire d’Electrochimie Physique et Analytique, Institut de Chimie Mole´culaire et Biomole´culaire, Ecole Polytechnique Fe´de´rale de Lausanne, CH-1015 Lausanne, Switzerland Received 6 June 2002; received in revised form 28 August 2002; accepted 30 September 2002
Abstract The distribution potential established when two liquids are placed in contact has been measured using a streaming technique. In particular the contributions from the diffusion potentials have been quantified. On the basis of the experimental results, the concept of distribution potentials upon the partition of a salt between two phases is revisited. We also compare Galvani potential differences for solutions in equilibrium and for situations where two liquids are placed in contact, as encountered in micro-TAS systems and micro-reactors. Finally, it is shown that in potentiometry we can define, as in traditional amperometry, a half-wave potential that takes into account the mass transfer of the salt to the interface. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Liquid j liquid interfaces; Diffusion; Potential; Ion flux; Conductivity
1. Introduction When two electrolyte solutions are placed in contact, the distribution of the ions between the two phases induces a polarisation of the interface that results in a Galvani potential difference being established between the two phases. This polarisation of the interface can be calculated at equilibrium, provided that the initial concentrations of the ions in the two phases prior to contact and the standard Gibbs energies of transfer of the different ionic species are known [1,2]. The equilibrium polarisation of the interface resulting from the distribution of a single salt has been known for a long time [3] and several theoretical accounts have appeared since the end of the 19th century [4,5]. By the early 70s, the interest in interfaces between immiscible electrolyte solutions had a revival following the pioneering work of Gavach and Davion [6]. In one of the more recent contributions Hung has presented a general
Corresponding author. Tel.: /41-21-693-3145; fax: /41-21-6933667 E-mail address:
[email protected] (H.H. Girault).
methodology to calculate the Galvani potential difference when more than two ions are present [2,7]. Unfortunately no general analytical solution exists and numerical methods are therefore required. In practice, the potential across the interface between two liquids (miscible as well as immiscible) is often far from equilibrium. In fact, during the establishment of equilibrium the diffusion of ions from one phase to the other will establish a diffusion potential depending on the ionic mobility differences. Although the concepts of distribution and diffusion potentials are well known only a few contributions have attempted to give a uniform description of the phenomena [8]. In the present paper the subject is addressed from an experimental point of view by using a streaming electrode to ensure that equilibrium is not established within the timescale of the potential measurements. A uniform theoretical treatment based on theoretical work by Hung [2,9] and Kakiuchi and Senda [8,10] is used to interpret the results. The theoretical development is extended to include a description of potentiometry and amperometry in the equilibrium case as well as in the non-equilibrium case.
0022-0728/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 7 2 8 ( 0 2 ) 0 1 2 5 0 - 0
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One of the key motivations for this work is to be able to predict the potential differences established when two laminar flows are brought in contact in m-TAS and micro-reactors. This has for instance implications for the optimisation of synthesis [11] and ion extraction [12,13] in microdevices.
2. Experimental The streaming electrode concept has been widely used to measure the potential of zero charge on mercury [14 / 16], but also that of liquid j liquid interfaces [17]. We adapt here this methodology to measure either diffusion potentials or contact potentials when using two immiscible electrolyte solutions. In fact, this experimental methodology dates even further back, since systems based on moving boundaries (albeit using a somewhat different set-up) have previously been used to measure liquid junction potentials [18 /22]. As shown in Fig. 1, the principle of the technique is to flow one solution (solution 1) through a fine capillary tip into another solution (solution 2). If the two solutions are of the same solvent, solution 1 streams into solution 2 whereas if the two solutions are immiscible, a spray of solution 1 in solution 2 can be observed. A syringe pump (Cole Palmer, 74900 series, USA.) is used to control the flow rate of solution 1 through the capillary. The potential of Cell I is measured using a high input impedance pH-meter/voltmeter (Tacussel, LPH 530T, Ion-meter, Fr). The reference electrodes are silver/silver halide electrodes prepared daily and crosschecked between each experiment.
3. Results and discussion 3.1. Experimental methodology and validation In order to validate the streaming technique, we have measured the diffusion potentials corresponding to hydrochloric acid, lithium chloride, sodium chloride, potassium chloride, tetramethylammonium chloride (TMACl), tetrapropylammonium chloride (TPrACl) and tetrabutylammonium chloride (TBACl). The resulting electrochemical cell was (Fig. 1): Ag ½ AgCl ½ MCl(1) (x mM)½½MCl(2) (10 mM) ½ AgCl ½ Ag Cell I Fig. 2 shows the results obtained for TPrACl and Table 1 reports the data for the other salts studied. The cell potential difference of cell I is simply a diffusion potential due to the different ionic mobilities of M and Cl . The slope of the variation of the measured potential can be compared with the equation describing diffusion potentials [23]. 1 RT c Dfdiff (tC tA ) ln F c2 1 RT c (2tC 1) ln (1) F c2 If we assume that the Ag/AgCl electrodes give a theoretical response of 60 mV per decade of chloride concentration, the potential difference of Cell I should be 1 RT c Ecell I (tC tA 1) ln F c2 1 RT c (2tC ) ln (2) F c2 A first observation when using a streaming technique is that the diffusion potentials are established quasiinstantaneously. The values of the variation of the diffusion potential measured upon changes of concentration corroborates quite well those predicted by Eq. (2). We can therefore conclude that the streaming
Fig. 1. Streaming electrolyte cell.
Fig. 2. Diffusion potentials for TPrACl measured using Cell I.
H. Jensen et al. / Journal of Electroanalytical Chemistry 537 (2002) 77 /84 Table 1 Diffusion potentials in mV measured using cell I at different flow rates c /mM
Flow rate/ml h 1 2.5
5
10
geometrical potential distribution using the streaming method, and will be discussed in part II of this series, by using a finite element simulation of the potential map. 3.2. Contact and equilibrium partition of a single salt, A C, between two immiscible phases
Potential for Cell I with HCl in 10 mM HCl 0.1 169.4 169.2 1 99.4 99.7 10 1.8 1.6 100 91.2 91.2
168.1 99.9 1.5 90.7
Potential for Cell I with LiCl in 10 mM LiCl 0.1 62.9 64.9 1 40.0 39.5 10 1.3 1.2 100 33.9 34.2
56.6 38.5 1.1 34.4
Potential for Cell I with NaCl in 10 mM NaCl 0.1 65.4 64.7 1 42.7 42.1 10 1.1 1.0 100 44.1 44.2
62.3 41.5 0.9 44.3
Potential for Cell I with KCl in 10 mM KCl 0.1 46.5 48.2 1 54.8 50.4 10 0.8 0.8 100 53.5 53.6
49.0 48.8 0.6 53.4
3.2.1. Equilibrium distribution potential and interface polarisability The Galvani potential difference, Dwo f; between two phases (o and w) in equilibrium can be expressed according to the Nernst equations for the ionic distributions of the respective ions. The Nernst equation for the cation C reads o RT a Dwo fDwo foC ln Cw (3) F aC and that for the anion Dwo fDwo foA
RT F
ln
o a A
(4)
awA
where Dwo fo is the standard transfer potential which is related to the Gibbs energy of transfer by
Potential for Cell I with TMACl in 10 mM TMACl 0.1 94.9 96.2 92.3 1 43.4 43.0 42.9 10 0.7 0.4 0.2 100 38.2 38.4 38.4 Potential for Cell I with TBACl in TBACl 0.1 44.4 46.5 1 22.8 22.7 10 0.7 0.4 100 20.3 20.4
79
o;w0o Dwo foi DGtr;i =zi F
(5)
Following the derivation by Hung [2], but taking into account a volume phase ratio, f/Vo/Vw, different from unity we arrive at the following equation:
42.8 22.1 0.1 20.4
1 f exp
ctot C F (Dwo fDwo fo? )=RT C
ctot A w
w
o?
1 f expF (Do fDo fA )=RT (6)
0 method provides a reasonable approach to measure contact potentials, which in the case of streaming water in water are simple diffusion potentials. To calculate the variations given in Table 2, we carried out a linear regression for the concentrations of solution 1 greater or equal to that of solution 2. As it happens, the diffusion potential values measured when the concentration of solution 1 was lower than that of solution 2 were often found to be lower than the theoretical values. This finding may be due to the
w o? w o where ctot is defined by ctot i ci fci and where Do f is the formal transfer potential taking into account the activity coefficients [1]. To evaluate the equilibrium Galvani potential difference by a graphical approach, we can draw the bulk aqueous charge qw defined by Eq. (7) as a function of the Galvani potential difference Df ,
qw cwC cwA
(7)
and then determine the Galvani potential value where the bulk aqueous charge is equal to zero. This condition
Table 2 Comparison of the variation of the experimental diffusion potential values as a function of concentration of solution 1 (in mV/decade) and the theoretical values provided by Eq. (2). The values given are average values Salt
Experimental values Theoretical values /tM/
HCl
LiCl
NaCl
KCl
TMACl
TPrACl
TBACl
95 98 0.821
37 40 0.336
43 47 0.396
52 58 0.490
42 44 0.370
26 28 0.235
21 24 0.203
The transport numbers are obtained from literature values of limiting equivalent conductivities of ions in water at 25 8C [33].
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represents the electroneutrality condition of the aqueous phase and equivalently that of the oil phase. In the case of a 1:1 electrolyte, the total concentration of the cation and the anion are equal. Fig. 3 illustrates the qw as a function of Df for different formal transfer potential values. At very negative potential values, qw corresponds to a hypothetical system where all the cations are in water and all the anions are in the nonaqueous phase. Inversely, at very positive potentials, qw corresponds to the hypothetical case where all the anions are in water and all the cations in the organic phase. When the formal potentials of the cation and the anion are separated by more than 180 mV, the formal potential values represents the two inflexion points on both sides of the graph. In any case, the equilibrium Galvani potential difference is obtained as the central inflexion point. Fig. 3 shows that when the standard transfer potentials are separated by more than 240 mV, the interface becomes polarisable around the equilibrium value as it becomes possible to vary the Galvani potential differences without altering significantly the chemical composition of the phases and therefore the electroneutrality of the adjacent phases. Inversely, if the standard transfer potentials are separated by less than 240 mV, the interface is non-polarisable as the condition of electroneutrality fixes the equilibrium Galvani potential difference. By definition, a non-polarisable interface is one where a small variation of the potential difference would result in a significant charge transfer and thereby break the electroneutrality rule. It is also interesting to make a comparison of the steady state amperometric response as a function of potential for a system comprising a single salt distributed between two adjacent phases. When a species i transfers from water to the organic phase under steady state conditions (for example using a micro-interface or a hydrodynamic method such as polarography) [24 /27], we can define a diffusion limited current
Idw zi FA Dwi cbw i =dw
(8)
Similarly, for a species transferring from the organic to the aqueous phase, we have Ido zi FA Doi cbo i =do
(9)
The current, I, is defined as the transfer of a positive charge from water to oil or of a negative charge from oil to water. In a steady state mode, the surface concentrations are related to the bulk concentrations by dw I dw (Idw I) w zi FADi zi FADwi
(10)
do I do (I Ido ) o zi FADi zi FADoi
(11)
bw csw i ci
and bo cso i ci
By substituting these surface concentrations into the Nernst equation for the species i, we can write w o RT Di d RT I Ido w w o? Do fDo fi ln o w ln (12) zi F zi F Di d Idw I and also define the half-wave potential by w o RT D d w w o? Do f1=2 Do fi ln io w zi F Di d
(13)
If we express the current as a function of potential, we have: I
1 exp
Idw zi F (Dwo fDwo f1=2 )=RT
1 exp
Ido zi F (Dwo fDwo f1=2 )=RT
(14)
To establish a comparison between the amperometric case and the equilibrium partition case, we can write Eq. (6) as ctot C 1 exp
F (Dwo fDwo f1=2;C )=RT
ctot A w
w
1 expF (Do fDo f1=2;A )=RT (15)
0 with Dwo f1=2 Dwo fo?
Fig. 3. qw as a function of the Df for a system comprising a cation having a formal transfer potential value DfoC 0:12 V and an anion A with the respective formal transfer potential values DfoA 0:06; 0:12; 0:18; 0:24 V: The phase ratio was assumed to be one.
RT zi F
ln f
(16)
We can therefore conclude that for both a potentiometric approach and an amperometric approach, it is possible to define a half-wave potential that corresponds to an apparent standard transfer potential. The concept of half-wave potential in potentiometry is interesting when dealing with the polarisability of an interface upon distribution of a single salt. For example, consider a salt such that the difference of the standard transfer potentials of the two ions is 120 mV. As seen
H. Jensen et al. / Journal of Electroanalytical Chemistry 537 (2002) 77 /84
above, when the phase ratio is unity the interface is nonpolarisable as the potential is unequivocally fixed. However, when the phase ratio is 1000 the half-wave potential shift according to Eq. (16) as shown in Fig. 4 and the interface becomes more polarisable. In terms of absolute value, the distribution potential does not depend on the phase ratio and the equilibrium distribution potential for this simple case of the distribution of a single salt can be calculated using Eqs. (3) and (4) which simply yields Dwo fdis
w o? Dwo fo? C Do fA 2
o w Dwo foC Dwo foA RT g g ln Cw Ao 2F 2 gC gA
(17)
The salt concentration ratio, also called the salt partition coefficient, is given by: KP
coC A w o? w o? expF (Do fCDo fA )=2RT w cC A
(18)
In conclusion, Fig. 4 shows that the distribution potential is independent of the phase ratio, whereas the polarisability is strongly dependent on it. 3.2.2. Contact distribution potential The streaming technique validated above for streaming water in water may be used for immiscible electrolyte solutions as well. Obviously, in this case the choice of salt is more restricted. We have measured the potential of the following cell: Ag ½ AgBr ½ TBABr(1) (streaming) (x mM)½½TBABr(2) (0:46 mM in DCE)½½14:53 mM TBABr(3)½AgBr ½ Ag Cell II At the right end of the cell, the Galvani potential difference between the organic and the aqueous side is governed by an equilibrium distribution potential (Eq.
81
(17)) whereas that on the left side is a contact potential difference (i.e. a non-equilibrium situation). To reach an equilibrium partition on the right side, 100 ml of 10 mM TBABr dissolved in 1,2-dichloroethane was equilibrated with 50 ml of 10 mM TBABr dissolved in water. The partition coefficient of this salt can be calculated from o Eq. (18) and found to be equal to 0.032 (/DGtr; TBA 1 o 22; DGtr; Br 39 kJ mol ); which gives the concentrations listed in the diagram of cell II assuming a complete equilibrium. When two electrolyte solutions are placed in contact, for example by flowing one phase into another (as in this work) or by contact of two laminar flows (as in a microTAS device), the surface concentrations adjust quasiinstantaneously according to a surface equilibrium. To make an analogy with chronoamperometry, we state that, considering that the ion transfer reaction is fast compared with mass transfer of the ions in the adjacent phases, we have a ‘reversible system’ where the interfacial Galvani potential difference is always given by the Nernst equation for the interfacial concentrations. To calculate the Galvani potential difference which results from this surface equilibrium, the equation corresponding to the conservation of the mass has to be replaced by a condition of zero current. The latter can also be written as an equality of the flux of the two species across the interface. JCw JCo JAw JAo I JCw JAw JCo JAo 0
(19) (20) (21)
In the absence of a current contribution from convection, the flux in the diffusion layers adjacent to the interface comprises diffusion and migration terms, which can be written as: Ji ci u˜i grad m˜ i Di grad ci zi Fci u˜i grad f
(22)
where u˜i is the electrochemical mobility of the species i. The zero current condition in the electrolyte means that in the diffusion layer both the anion and cation move at the same speed as a diffusion potential difference is established to slow the ion with the highest electrochemical mobility and speed up the ion with the lowest electrochemical mobility. Indeed, from the zero current condition which reads I F (DwC grad cwC FcwC u˜wC grad f) F (DwA grad cwA FcwA u˜wA grad f) 0
Fig. 4. qw as a function of the Df for a system comprising a cation having a formal transfer potential value DfoC 0:06 V and an anion A with the respective formal transfer potential value DfoA 0:06 V when the apparent phase ratio is equal to 1, 10, 100, 1000.
(23)
it is easy to show by rearranging Eqs. (21) and (22) that the system behaves as if the salt was diffusing with a mean diffusion coefficient defined by [28] JC JA DC A grad cC A with
(24)
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H. Jensen et al. / Journal of Electroanalytical Chemistry 537 (2002) 77 /84
DC A
DC u˜A DA u˜C u˜C u˜A
2RT
u˜C u˜A u˜C u˜A
(25)
For systems where a diffusion layer of thickness d is established on either side of the interface (e.g. microliquid j liquid interfaces or interfaces with hydrodynamic control) [24 /27], Eqs. (20), (21) and (24) yields DwC A w (cC A cws C A ) dw
DoC A o (cC A cos C A ) do
(26)
where csi is the surface concentration just outside the diffuse layer also called the Gou¨y/Chapman layer. To establish a correlation between the case of equilibrium partition and the case of contact partition, we can write the conservation of mass as [10] cws i fd
tot cos i ci
(27)
by defining a dynamic phase ratio, fd which depends on the thickness of the diffusion layers and the mean diffusion coefficient of the salt fd
dw DoC A
(28)
DwC A do
and with the apparent total concentration defined from the bulk concentrations by w o ctot i ci fd ci
(29)
In the contact mode, we can also write Dwo f1=2 Dwo fo?
RT
Dwo fo?
RT
zi F zi F
ln fd ln
dw DoC A DwC A do
(30)
To calculate the distribution potential in the contact mode, it is necessary to solve Eq. (15) by substituting the volume phase ratio by the dynamic phase ratio. Eq. (30) highlights as above that the absolute distribution potential will be independent of the mass transfer conditions (i.e. the dynamic phase ratio) and that the polarisability of the interface will vary as shown in Fig. 4. The diffusion potential for a 1:1 salt in the diffusion layer between the bulk solution (b) and the interface just outside the diffuse layer (s) can be written b RT u˜C u˜A c Dbs fd ln Cs A F u˜C u˜A c C A b RT c (tC tA )ln Cs A (31) F cC A In this equation tC/and tA represents the transport numbers of C and A, respectively. As previously
noted [8], the overall Galvani potential difference between the two bulk phases can be expressed as os ws wb Dwo fDwb ob fDob fd Dos fDws fd
(32)
The three terms in this equation are illustrated in Fig. 5. If we assume that the relative transport numbers are equal in the two phases, then we have os wb RT c c Dwo f (tC tA )ln Cob A Cws A Dws (33) os f F cC A cC A From an experimental viewpoint, only the bulk concentrations are known a priori; it is therefore advantageous to re-write Eq. (23): wb w o? (Do fC Dwo fo? RT c A ) Dwo f(tC tA ) ln Cob A 2 F c C A
w o? (Dwo fo? C Do fA ) 2
(34)
Eq. (34) follows from Eqs. (17) and (18) applied to the surface plane s, where a classical equilibrium partition exists. The first term of this equation represents the diffusion contribution to the total Galvani potential difference whereas the second represents the interfacial potential difference that is quasi-instantaneously established when the two solutions are placed in contact. The potential response of cell II, Ecell II, can be calculated according to the cell diagram, Eqs. (34) and (18). It is given by: 1;w RT cTBA Br Ecell II 2tTBA ln 2;o F cTBA Br w o? tTBA (Dwo fo? TBA Do fBr )
2tTBA
RT F
ln
1;w cTBA Br c2;o TBA Br
Kp
(35)
It may be noted that when Kp /1 the standard term vanishes and the expression corresponding to cell I is recovered. When the concentration ratio c1/c2 is Kp1 ; the cell potential is, as expected, zero, since the initial concentrations are already equal to the equilibrium values. The data obtained from cell II are shown in Fig. 6. The theoretical slope resulting from Eq. (35) is 23.6 mV/(dec. concentration of flowing electrolyte) assuming that the limiting molar ionic conductivities are 19.5 and 78.14 for TBA and Br , respectively. This value is lower than the experimental value of 38.5 mV/(dec. concentration of flowing electrolyte) obtained from the experimental data. The broken line in Fig. 6 corresponds to Eq. (35) and it appears that the agreement with Eq. (35) is rather good at high concentrations of electrolyte in the streaming solution. Apparently, the transport number of TBA is higher in DCE (or
H. Jensen et al. / Journal of Electroanalytical Chemistry 537 (2002) 77 /84
83
Fig. 5. Concentration profiles for an equilibrium partition and a contact partition.
Fig. 6. Diffusion potentials for TBABr measured using cell II. The broken line corresponds to Eq. (35).
equivalently the transport number of Br is lower). The hydration of TBA is expected to be rather modest both in DCE and water [29], but Br is known to be hydrated in nitrobenzene [30,31]. In the less polar DCE the hydration of Br might even be more significant. A larger effective radius of Br in DCE caused by a strong hydration would lead to a lower mobility and thereby a lower transport number of Br (i.e. a higher transport number of TBA ). One way to clarify this point would be to measure the diffusion potential of TBABr in DCE streaming in a DCE solution of TBABr. This proved, however, to be rather difficult due to the low conductivity of DCE and consequently no further experimental studies were carried out.
zero and Eq. (34) reduces to the classical Henderson equation for diffusion potentials. We shall present in Part II of this series, the potential distribution associated with diffusion potentials in the case of micro-devices with mixing of solutions as illustrated in ongoing work [32]. In the more general case of immiscible electrolyte solutions, the overall Galvani potential difference measured is composed of three contributions, namely the diffusion potential in phase 1, the interfacial Galvani potential difference and the diffusion potential in phase 2. It is worth pointing out that in the case of the distribution of a single salt between two phases, the interfacial potential difference is the distribution potential, which is independent of the phase ratio whereas the polarisability of the interface is dependent on the phase ratio. If more than two ions are involved, the interfacial Galvani potential difference is determined by the halfwave potential as given by Eq. (13). The latter point will be published later in Part III of this series which describes the case of systems with a potential determining ion.
Acknowledgements The authors wish to thank Professor T. Kakiuchi for helpful discussions. Methrom (CH) and the Swiss Commission for Technology and Innovation (CTI) are acknowledged for financial support.
4. Conclusion We have shown that when two liquids are placed in contact, the Galvani potential difference is quasi-instantaneously established according to Eq. (34). This process can be called ‘potentiometry of a reversible system’ by analogy with the expression ‘amperometry of a reversible system’. When the two solutions are from a common solvent (e.g. water), the standard transfer potentials are equal to
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