J. CHEM.SOC. FARADAY TRANS., 1994, 90(14), 2037-2041 Effect of Preferential Solvation on Gibbs Energies of Ionic Transfer Anna-Kaisa Kontturi, Kyosti Kontturi and Lasse Murtornaki Laboratory of Physical Chemistry and Electrochemistry, Helsinki University of Technology, Kemistintie 1, SF-02150,Espoo, Finland David J. Schiff rin Department of Chemistry, University of Liverpool, P.O. Box 147,Liverpool, UK L693BX It is shown that the transfer potential of the Rb+ ion between water and 1,2-dichloroethane is strongly influenced by ion pairing in the organic phase. A6 initio calculations of the energy of the Rb+-TPB- ion pair for different interionic distances leads to a contact ion-pair interionic distance of 0.36 nm. The very large differences in the transfer potential of Rb+ observed between organic solutions containing tetraphenylborate (TPB-) and tetrakis(4-chlorophenyl)borate (TPBCI-) are due to preferential solvation of the phenyl rings of the p-chloro derivative.These effects are likely to be present in systems where the size of the ionic components is greater than that of the solvent. There has been, recently, a renewed interest in the measure- ment of ionic Gibbs energies of transfer between immiscible electrolyte^.'-^ This has relevance both to problems of elec- troanalysis and separation science, and for the understanding of solvation effects. The electrochemical determination of these quantities presents many advantages over conventional methods based on solubility or partition measurements. However, the indiscriminate use of voltammetric techniques can lead to serious errors.The purpose of the present work is to clarify the limitations that can be encountered in their use and to highlight the effect that preferential solvation and ion pairing have on ionic transfer potentials. Voltammetry at Liquidbiquid Interfaces Linear sweep voltammetry has been extensively used for the determination of Gibbs energies of transfer. For singly charged ions (M+), the transfer reaction considered is M+(w)+M+(o) (1) where (w) and (0)refer to the aqueous and organic phases, respectively. Two experimental approaches have been used : (a) trace-ion transfer and (b) transfer in the absence of a base electrolyte. The difference between these is whether the poten- tial window is defined by the ion being investigated or by some other more hydrophobic base electrolyte ions.These techniques are straightforward transpositions of those generally used for reactions at metallic electrodes pro- vided that the relative permittivity of the organic phase is sufficiently large to avoid ion pairing of the transferred species with base electrolyte ions. However, this is not the case for the solvents commonly employed in ion-transfer studies at liquid/liquid interfaces. The effect of ion pairing in the low relative permittivity receiving phase has been taken into account in different ways. When analysing the transfer of associated electrolytes,6 the solution of the Nernst-Planck equation must be carried out considering all species present and the corresponding ionic association equilibria.For a cation-transfer process that can lead to ion pairing, the equilibrium condition M+(o)+ A-(o)sM+A-(o) (11) must be considered in solving the diffusion and migration equations. A-is the ion-pairing anion present in the organic phase. The current measured is due to ions crossing the inter- face;6 this appears as a boundary condition in the transport equation. In the organic side of the interface the current cor- responds to the total flux of the metal ion taken as the ion constituent [ref. 4, eqn. (6) and (711, as defined in ref. 7, instead of that of free ions. This is why the flux equations describing transport in the organic phase must always be written with respect to the metal ion constituent.Although the division of the flux in the organic phase into contribu- tions due to free and ion-paired species is possible, this is of little value. The Galvani potential difference across the inter- face is, however, determined by the interfacial thermodyna- mic activities of the free ions. The distinction is important for the calculation of standard ionic-transfer potentials. The solution of the diffusional problem in the case of trace-ion transport in the organic phase and binary aqueous electro- lytes has already been pre~ented.~ From the convolution inte- the current function x(ot) can be calculated, where 5 = a[Dy)/Dy)]1/2, = zFv/RT,D is the diffusion coefficient, v is the sweep rate, ciw) is the concentration in the aqueous phase of the transferred ion and the other symbols have their usual meaning.8 is given by : where y'+") and y$) are the activity coefficients of the cation corresponding to its surface concentration on the water and oil sides of the interface, respectively; a+ is the degree of dis- sociation of the Rb+ ion pair in the organic phase and A;Qi is the starting potential; it is assumed that there is no ion pairing in the aqueous phase. The current is given by: i = F~~~)J(naD~))x(at) (3) The standard ionic-transfer potential calculated from eqn. (1)-(3), A:@:, corresponds to the ionic equilibrium (I).Great care must be taken when calculating A:@,"+ from the half- wave potential (A:Q1,2) for associated electrolyte^.'*^ What is actually measured refers always to the ionic constituent being transferred and not to the free ion.The half-wave potential corresponds to a situation where the concentration of the constituent7 is equal on both sides of the interface. This condi- tion is not given by the equality of the ionic and ion-pair contributions to the total current.' For example, for the transfer of Rb+ ion from water to 1,2-DCE containing TPB- as the base electrolyte anion, the equilibrium condition : Rb+(o)+ TPB-(o)s Rb+TPB-(o) (111) when [Rb+(o)] + [Rb+TPB-(o)] 4 [TPB-(o)] results in the following relationship between free Rb+ and its total concen- tration as a constituent: (4) where C,(x) and CRb+(x)are the total and the free ion con- centrations at a distance x from the interface, Ka is the association constant for Rb+TPB- in 1,ZDCE and C;ppB-is the bulk concentration of TPB- in the organic phase.For the trace ion case, the concentration of the free ion is directly proportional to the total concentration, since the activity coefficients will be constant. In this case, the half wave poten- tial is given by: where is the standard transfer potential of the free ion. These considerations have been used by Samec et d.,' Wandlowski et d2and Sabela et aL3 for the calculation of for a series of ions based on an internal calibration using the transfer of the tetramethylammonium ion. Although medium effects were considered, the transfer poten- tial calculations were based on the assumption that the current crossing the interface could be divided into a free and an ion-paired component, with the half-wave potential being determined by the condition that these two currents should be equal.' This appears to contradict the conditions resulting from thermodynamic considerations.Eqn. (4) implies that in the trace-ion case, the ratio of free to total Rb+ ion concen- tration is constant and therefore, the only way by which the condition proposed in ref. 1 could apply is when either the electroneutrality condition is not fulfilled or the local activ- ities are strongly altered by the transferred species. The origin of this problem is that the contribution of the free ions to the current, as the authors in ref.1 defined it, is in fact the total (measured) current. Otherwise, the total current would be larger for a higher degree of association. This is probably one of the reasons for the difference in the measured value of A:@&+ between the results in ref. 1 and 4. Another approach to the measurement of transfer poten- tials makes use of the potential limit of polarisation when the aqueous base electrolyte consists only of a salt of the metal ion. The solution to this transport problem has already been pre~ented.~An alternative approach has been discussed by Shao et a/.,' who considered the integrated form of the cyclic voltammogram for the transfer of a trace ion. A calibration curve expressing the ratio of currents in the forward and return scans as a function of the difference in switching potential and half-wave potential was used.The value of Ar@ib+ obtained, 0.475 V, was significantly different from that previously determined (0.274 V)4 by convolution voltam- metry for the binary case?. There are several reasons that could account for this dis- crepancy. First, the integrated Nicholson and Shain current function used corresponds to the trace-ion case and cannot be used for a binary aqueous electrolyte, especially at the low t The value of A:@);;,,+ given in ref. 4 corresponded actually to the Galvani potential difference between the organic solvent and water; thus, the values for A;@);;,,+ are positive. J. CHEM. SOC. FARADAY TRANS., 1994, VOL.90 concentrations investigated, for which the migration terms are significant. Secondly, the calculation is based on the assumption that the double-layer capacitance has little dependence on potential at the limit of the polarisation window. This, however, is not the case' and different non- faradaic contributions at the end of the forward scan and the current peak in the return scan will introduce significant uncertainties. Thirdly, the high currents employed in ref. 5 result in very large uncompensated IR potential drops and, hence, the elementary calibration based on the idealised tracer case breaks down. The IR drop problem is inherent to transport reactions at high currents, when significant migra- tion effects result in changes in the value of the uncompen- sated resistance throughout the potential scan.Finally, no ionic association corrections appeared to have been made in the work of Shao et al.' Although in the previous work4 the currents measured were always sufficiently small to avoid the problems pre- viously discussed, the convolution analysis was carried out for the binary-ion transfer case and the aqlieous electrolyte concentrations used were always very high in order to avoid the simultaneous transfer of TPB-. The difference between the values of the transfer potentials measured by Shao and Girault' are too large to be due only to different experimen- tal approaches. The purpose of the present work was to understand the origin of the above discrepancies and to establish a reliable method for the analysis of ion-transfer potentials derived from voltammetric results.Experimental In order to distinguish between anion (TPB-) or cation (Rb+) transfers at the positive potential limit of the polarisa- tion window (A:@ > 0), a micropipette technique was used." This allows a distinction to be made between transfer of the anion from the organic to the aqueous phase from that of the aqueous cation in the opposite direction. Micropipettes were prepared from borosilicate glass capil- laries GC15OF-15 (Clark Electromedical Instruments) using a vertical pipette puller type L/M-3p-A (List-Medical, Germany). Settings in the pipette puller were adjusted to obtain tip diameters of ca.25 pm. The pipettes were used without polishing or other treatment. They were mounted in a pipette holder with a side tube (Clark Electromedical Instruments) and filled with the aqueous solution by suction through the side tube. The electrochemical cell consisted of a U-tube (3 mm id) inside which the organic solution was placed." The aqueous reference solution was placed on top of the organic phase in one branch of the U-tube and the micropipette was then immersed in the organic solution in the other. Linear voltage sweeps were applied to the aqueous reference electrode with a waveform generator (PPR1, Hi-Tek). The current was mea- sured with a current amplifier (Keithley, 428) connected to the electrode inside the micropipette and digitally recorded (Advantest R 921 1E Digital Spectrum Analyser).During the experiments, the interface was monitored with a microscope to ensure that this was located at the tip of the micropipette. The measured potentials corresponded to the cell: Ag I AgClIO.1 mol dm-3 RbCl(w), J 0.01 mol dm-3 TBATP(o) (or TBATPBCl) I mol dm-3 TBACl(w) I AgCl IAg (or LiCl(w)) The potentials were corrected to the absolute Galvani poten- tial scale as described el~ewhere.~ Tetrabutyl ammonium tetrakis(4-chloropheny1)borate (TBATPBCl) was prepared by mixing an excess of aqueous J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 15' 10; -20:-300 -200 -100 0 100 200 300 400 Ay@/mV Fig. 1 Voltammograms of (....) 0.1 mol dm-3 LiCl(w)-0.01 mol dmP3 TBATPB(o) and (-) 0.1 mol dm-3 LiCl(w)-0.01 mol dm-3 TBATPBCl(o).Sweep rate 100 mV s-'; micropipette 25 pm. (TBACl (Fluka) with an ethanol solution of KTPBCl (Lancaster Synthesis). The product was filtered and re-crystallised from acetone. Tetrabutyl ammonium tetra-phenylborate (TBATPB) was prepared as described earlier.4 RbCl, LiCl, (Merck pro analysis), TBACl (Fluka) and 1,2- DCE (Rathburn HPLC) were used without further purifi- cation. Water was purified with a millipore system (Milli-Q). The ab initio calculation of the structure of the Rb'-TPB- ion pair was carried out using Gaussian 92 (HF/STO-3G) in the Cray computer of the Centre for Scientific Computing, Helsinki. The calculation took 40 h of CPU time. The com- parison of relative sizes and orientations of 1,2-DCE and the TPBCl- anion were made with a desktop molecular model- ling package.' ' Results and Discussion In all the experiments, the aqueous phase was always present inside the micropipette.When the anion of the organic phase is transferred at the positive potential limit, spherical diffu- sion prevails in the forward sweep and linear diffusion is present during the return sweep. This results in a character- istic voltammogram showing a peak in the current on sweep reversal. If the species transferred is the aqueous cation, no such peak is observed during the return sweep. Thus, the shape of the voltammetric response is diagnostic of the nature of the ionic species being transferred. An example of the advantages of this technique can be seen in Fig.1, where the transfer of TPB- occurs in preference to that of Li+. The hemispherical diffusion due to Li+ transfer can be observed when the highly hydrophobic TPBCl- anion is employed in place of TPB -. Fig. 2 shows the voltammetric response for Rb+ transfer when TBATPB is used as the organic base electrolyte. It can be clearly seen that, contrary to reports in the literature,' the species transferred is the Rb+ ion and not the organic anion, as indicated by the absence of a peak during the reverse sweep at the positive end of the polarisation window. This is an important point that should be stressed, since it clearly shows that the convolution voltammetry technique pre-viously developed gave transfer data for Rb' and not for TPB-. In order to confirm these results, the same experiments were carried out using TPBCl- as the base electrolyte anion and the corresponding voltammograms are also shown in Fig.2. It is quite clear that in this case the species transferred is the Rb+ ion, in agreement with previous results by Shao and Gira~lt.~ The difference in A:@:,,+ in ref. 4 and 5 results /'/---20 1-400 -300 -200 -100 0 100 200 300 400 500 600 AyO/mV Fig. 2 As Fig. 1 but for RbCl(w) mainly from the different electrolytes used in the organic phase. However, the very large change in the transfer potential or Rb', ca. 210 mV, observed when the anion is changed from TPB- to TPBC1- is very unusual. If the difference were due to ion pairing of Rb+ in the organic phase, it would be very difficult to rationalise it in terms of distances of closest approach effects for a dielectric continuum model.The ion-pairing association constant is given by :' zlz2e2 K, = N, E,Eok, T Q(b)16x2 (-) with IZlZZ I e2b= 4ne, E~ k, Tr (7) where E, is the relative permittivity of the solvent, c0 is the permittivity of vacuum, z1 and z2 are the charge numbers of the cation and anion forming the ion pair, e is the electronic charge, N, is the Avogadro constant, k, is the Boltzmann constant, T is the absolute temperature and r is the sum of the ionic radii of the components of the contact ion-pair. Q(b) is an ion separation function, the values which are given in ref.12. Considering that the van der Waals radius (rVdw)of chlo- rine is ca. 0.175 nm,13 the change in the radius when TPB- is replaced by TPBCl- as the base electrolyte anion is of the order of 0.1 nm (taking rvdw for hydrogen as 0.12 nm). The hard-sphere diameter of TPB- is ca. 0.49 nm14 and, hence, the slight increase in molecular dimensions when a para-hydrogen in TPB- is replaced by chlorine cannot account for the large difference in association constant of the anion with Rb'. Certainly, there is no reason for assuming that the elec- trostatic contribution to the Gibbs energy of solvation should be altered significantly by the small change in ionic radius. The origin of this interesting effect can be understood when analysing in detail possible preferential solvation contribu- tions to the solvation energy of TPBCL-.Fig. 3 shows a molecular model of an Rb+-TPB- ion pair derived from the results of the ab initio calculation using Gaussian 92. This calculation gave a distance of closest approach between Rb' and the boron atom in TPB- of 0.36 nm. This is in reason- able agreement with crystallographic data of solid RbTPB, of 0.404 nm." The larger value in the latter case is expected due to ion-ion interactions in the crystal. As can be seen, in forming an ion pair, the Rb+ ion can approach the centre of positive charge in the molecule, the limitation being the n: Fig. 3 Minimum potential-energy configuration of the ion pair Rb+-TpB-from initiocalculations,showing the formation of the contact ion The atoms are drawn using their van der Waals radii.ring systems in the phenyl groups. This type of specific inter- action in ion-pair formation has been previously observed in solvents of low relative permittivity.' When the para-hydrogen atom in the phenyl rings of TPB- is replaced by chlorine, a large local dipole moment appears in each of the phenyl rings, of the order of 5.0 x lop3' C m.17 The C-Cl dipole moment contribution in 1,ZDCE is 4.90 x lop3' C m l8 and therefore, preferential solvation of the phenyl rings containing the dipolar C-Cl bond is expected to occur by dipoledipole interactions. Fig. 4 shows a simple visualisation of possible preferential solvation struc- tures." The configuration of the TPBCl- anion is favourable for strong short-range dipole-dipole interactions which results in the known increase of solvation energy observed when comparing TPB- with TPBCl-.From Fig. 1, it can be seen that this is at least 20 kJ mol-'. In fact, a larger differ- ence is expected since in this experiment, the positive limit is determined by Li+(w) transfer rather than by that of TPBCl-. The origin of this effect cannot be due simply to the small increase in ionic radius and the model show fn in Fig. 4 -Fig. 4 Molecular model showing a possible relative orientation of the 1,2-DCE molecules with respect to the TPBCl anion leading to large dipole-dipole interactions between the solvent and the C-Cl bond in the phenyl rings J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 clearly indicates that the increased solvation energy must be due mainly to preferential solvation of the phenyl rings by 1,2-DCE by dipole-dipole interactions. For Rb+-TPBCl- ion-pair formation to occur, the solvent molecules interacting with the C-C1 dipole in the phenyl ring must be displaced (cf:Fig. 4 and 3) and therefore the distance of closest approach will be strongly influenced by preferential solvation effects. These can be quantified by considering dis- tance effects on the ion-pairing constant. The association constant of Rb+-TPB- in 1,ZDCE has been estimated as 1700 considering E = 10.23;19 from eqn. (6) this value corre- sponds to a distance of closest approach of 0.794 nm.The radius of the Rb+ ion is 0.147 nm and from the molecular modelling results shown in Fig. 3, it is quite clear that the value of K, reported in the literature" must be wrong con- sidering the dimensions of the ion pair. The calculation of the ion-pair association constant cannot be carried out simply from the results of the ab initio calcu-lation, which is only applicable in vacuum. Although it is not feasible at present to Carry Out these CalCUlatiOnS including solvent molecules, the value obtained gives an indication of the expected distance range if electrostatic interactions over- ride anion solvation energy. Attempts to measure the associ- ation constant from the conductivity of saturated RbTPB solutions in 1,2-DCE were unsuccessful.The solubility of RbTPB in 1,ZDCE is 9.9 x mol dm-3 at 25"C,19 and with K, = 1700, this should have given a detectable conduc- tivity of K z 0.6 pS. However, K was less than the detection limit of 0.1 pS. Using eqn. (6) and (7) and r z 0.36 nm gives a value of ca. lo5 for K, ,and following the procedure described in ref. 4, A:@' = 0.360 V. However, the reason for observing the transfer of Rb+ and not that of TPB- is the very large association constant for the Rb+-TPB- ion pair. The above arguments are applicable to all cases where the size of the organic solvent is smaller than that of the ions; ion-pair association constants will be strongly influenced by local solvation effects. The authors thank Mr. Raimo Uusvuori, of the Centre for Scientific Computing, Helsinki, for carrying out the ab initio calculations.The support of the European Community, Human Capital and Mobility Programme (Contract Number ERB CHRXCT 920076) is gratefully acknowledged. References 1 Z. Samec, V. MareEek and M. P. Colombini, J. Electroanal. Chem., 1988,257, 147. 2 T. Wandlowski, V. MareEek and Z. Samec, Electrochim. Acta, 1990,35,1173. 3 A. Sabela, V. MaraEek, Z. Samec and R. Fuoco, Electrochim. Acta, 1992,37, 23 1. 4 A-K. Kontturi, K. Kontturi, L. Murtomaki and D. J. Schiffrin, J. Chem. SOC., Faraday Trans., 1990,86,819. 5 Y. Shao, A. A. 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