Double Transfer Voltammetry in Two-Polarizable Interface Systems

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Double Transfer Voltammetry in Two-Polarisable Interface Systems: Effects of the Lipophilicity and Charge of the Target and Compensating Ions Angela Molina, Eduardo Laborda, José Manuel Olmos, and Enrique Millan-Barrios Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b05051 • Publication Date (Web): 05 Feb 2018 Downloaded from http://pubs.acs.org on February 14, 2018

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Analytical Chemistry

Double Transfer Voltammetry in Two-Polarisable Interface Systems: Effects of the Lipophilicity and Charge of the Target and Compensating Ions Ángela Molina1*, Eduardo Laborda1, José Manuel Olmos1, Enrique Millán-Barrios2

1

Departamento de Química Física, Facultad de Química, Regional Campus of International Excellence “Campus Mare Nostrum”, Universidad de Murcia, 30100 Murcia, Spain 2

Laboratorio de Electroquímica, Departamento de Química, Facultad de Ciencias, Universidad de los Andes, 5101 Mérida, Venezuela

* Corresponding author: Tel: +34 868 88 7524 Fax: +34 868 88 4148 Email: [email protected]

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Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Analytical expressions are obtained for the study of the net current and individual fluxes across macro- and micro-liquid|liquid interfaces in series as those found in ion sensing with solvent polymeric membranes and in ion-transfer batteries. The mathematical solutions deduced are applicable to any voltammetric technique independently of the lipophilicity and charge number of the target and compensating ions. When supporting electrolytes of semihydrophilic ions are employed, the so-called double transfer voltammograms tend to merge into a single signal, which notably complicates the modelling and analysis of the electrochemical response. The present theoretical results point out that the appearance of one or two voltammetric waves is highly dependent on the interface size and on the viscosity of the organic solution. Hence, the two latter can be adjusted experimentally in order to ‘split’ the voltammogramns and extract information about the ions involved. This has been illustrated in this work with the experimental study in water|1,2dichloroethane|water cells of the transfer of the monovalent tetraethylammonium cation compensated by anions of different lipophilciity, and also of the divalent hexachloroplatinate anion.

Keywords: Analytical expressions; Two polarisable interfaces; Ion-transfer voltammetry; Compensating ion; Charge number


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INTRODUCTION In recent works, the analytical theory

1

and experimental study

1,2

of the transfer of a

+

monovalent ion ( X ) have been developed when it has access to both liquid|liquid interfaces in a two polarizable liquid|liquid interface system. In this kind of experiments, species X

+

can be

present either in both side phases of the electrochemical cell or in the central solution with different arrangements of immiscible solutions being possible. This type of measurements is useful for the simultaneous study of an analyte in two different medium conditions or of two analytes that cannot be present in the same phase, for the study of species poorly soluble in aqueous solution as well as for analysing the transport and distribution of ionic compounds across a lipophilic barrier. Typically, an organic solution is embedded between two aqueous phases

1–3

(see Scheme 1) though the

opposite situation (i.e, an aqueous solution between two organic phases) can also be found, for example, in ion-transfer batteries 4. In the former case, under most conventional conditions where the compensating ions of the aqueous supporting electrolytes are highly hydrophilic, so-called ‘double transfer voltammograms’ with two well-separated signals have been predicted and observed experimentally 1,2. The present work generalizes the theory (and also the experimental) of this kind of systems to situations where the compensating ion shows lower hydrophilic character, and also where the target and/or the compensating ions are not monovalent. Both factors affect significantly the theoretical treatment, the expressions of the voltammetric response and its features. A general analytical expression is derived for the calculation of the ion fluxes and the z

voltammetric response, valid regardless of the hydrophilicity and charge number of the target ( X X ) z

and compensating ( R R ) ions. As a function of the difference between the formal transfer potential of these two species, the separation between the two signals in cyclic voltammetry (CV) and cyclic square wave voltammetry (cSWV) varies significantly. Thus, as the target and/or compensating ions



in a water|organic|water arrangement are less hydrophilic, the two signals move closer together and they finally merge into a single voltammogram. In the transition, partially-overlapping signals are encountered that can be resolved more suitably with cSWV given its subtractive character that yields peak-shaped curves even when micro/nano-ITIES are employed 5. Also, it is demonstrated that the single signal can be ‘uncoupled’ by shrinking the liquid|liquid interface and/or increasing the viscosity of the organic phase, making it possible the determination of the standard Gibbs energy of ion transfer. The influence of the charge number of the target and compensating ions ( z X and z R , respectively) is also analysed, studying the effect on the features of the voltammograms, particularly on the CV peak-to-peak separation and on the cSWV half-peak width. These parameters offer simple criteria for the elucidation of the ion transfer processes involved. The influence of the lipophilicity of the compensating ion and of the charge number of the target species are tested experimentally in a water|1,2-dichloroethane|water cell. In the former case, the transfer of tetraethylammonium in presence of aqueous supporting electrolytes with anions of different hydrophilicity is studied in cSWV. Moreover, the response of the monovalent TEA+ is compared with that of the divalent chloroplatinate anion [PtCl6]2-, finding a satisfactory agreement between theoretical predictions and experimental data.


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THEORY Let us consider the mechanism of ion transfer showed in Scheme 1, where a target cation

X z X is present initially in the two aqueous phases ( W out and Winn ) of a two polarisable interface (1) (1) system such that under the application of a potential pulse between them, E1 = Eout , this − Einn

species can be transferred to the organic solution (phase M ) across either liquid|liquid interface. Since the current at both interfaces must be equal, the transfer of X z X is coupled to the transfer of another ionic species across the other interface; here, this is considered to be the anion of the aqueous supporting electrolyte (species R z R in Scheme 1), although the theoretical treatment would be similar in case of involving the cation of the organic supporting electrolyte. Thus, upon the application of a constant potential the net current at each interface ( I1out and I1inn ) is the sum of the contributions of X z X and R z R

  ∂c(1) M ( out ) I1out = I1,outX + I1,outR = − FA  z X DXM  X  ∂x  

  (1) M ( out ) M ∂c  + z R DR  R  x =0  ∂x

     x =0 

(1)

  ∂c(1) M ( inn ) I1inn = I1,innX + I1,innR = − FA  z X DXM  X  ∂x  

  ∂c(1) M ( inn ) + z R DRM  R   ∂x  x=d 

     x=d 

(2)

where A is the interfacial area ( Aout = Ainn = A has been considered for the sake of simplicity), D XM and DRM are the diffusion coefficients of species X z X and R z R in the organic solution, respectively, and other variables are defined in the Supporting Information (Section S1). The condition of equal currents at both liquid|liquid interfaces I1, X + I1, R = I1, X + I1, R = I1 , which applies regardless of the out

out

inn

inn

lipophilicities of species X z X and R z R , leads to the following non-explicit relationship between the (1)

(1)

potential at the outer and inner interfaces ( Eout and Einn )

 eηôut ,1   eηînn ,1  R R zR cR*Wout z c*Winn ηout inn ,1 ( t )  ηôutX ,1 + *Wout ξ R e  = I d ( t )  ηînnX ,1 + R R*Winn ξ R eηinn,1  z X cX z X cX  1+ e  1+ e  X

I

out d

X


(3)


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where 0 ≤ t ≤ τ , ci*Wout and ci*Winn are the bulk concentrations of species i ( i = X , R ) in phases out

W out and W inn , respectively, I d

( t ) and Idinn ( t ) are the diffusion-limited currents for the transfer

of species X z X from water to the organic solvent

Scheme 1. Ion transfer processes in a system of two polarisable interfaces when the target ion X z X is initially present in both aqueous phases. R z R is the compensating ion with charge number of opposite sign to X z X . ‘Bulk membrane’ refers to distances far away from the interface (compared to the diffusion layer in phase M ) where the concentration values are not perturbed.

I dout ( t ) =

z X FADXW c*XWout δ XW ( t )

I dinn ( t ) = −

;

z X FADXW c*XWinn δ XW ( t )

(4)

and

( (

)

z X F (1) ˆ X Eout − E1/2 RT z R F (1) R Eout − ∆WM φR0' ηout ,1 = RT

X ηôut ,1 =

ξi =

)

( (

)

z X F (1) ˆ X Einn − E1/ 2 RT z R F (1) R Einn − ∆WM φR0' ; ηinn ,1 = RT

X ; ηînn ,1 =

DiM δ XW ( t ) ; i = X,R DWX δ iM ( t )

)

    

(5)

(6)

In Eqs.(4)-(6), ∆WM φ R0 ' is the formal transfer potential of R z R between the water and organic solutions, δ iW and δ iM are the linear diffusion layer thickness in the aqueous and organic solutions that for macrointerfaces are given by 6


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δik ( t ) = π Dik t

; k = W, M

(7)

X M W (note that ξi = Di / DX for macrointerfaces) and Eˆ1/ 2 is the half-wave potential for the simple

transfer of species X z X in a system with only one polarisable interface 7

RT  1  X Eˆ1/2 = ∆WM φX0' + ln   F  ξX 

(8)

with ∆WM φ X0 ' being the formal transfer potential of X z X and ξ X being given by Eq.(6). From Eq.(3), (1)

(1)

the values of the potentials Eout and Einn can be calculated (for instance, by the Newton-Raphson method; see Section S4) and then the current flowing through the system is obtained. We consider now the application of an arbitrary sequence of potentials E1 , E2 ,...Em ,...E p of ( m)

( m)

the same duration τ . The current corresponding to the m-th potential pulse Em = Eout − Einn

is

given by (see Section S2) m

m

j =2

j=2

I m = I1out + ∑ I% jout = I1inn + ∑ I% jinn ; m = 2,3,... p

(9)

By following the procedure described in the Supporting Information (Section S2), the following general rigorous expression is obtained for I m as a function of the potential at the outer and inner interfaces m m   Z out Z out j, X j,R I m = FA  z X DWX c*XWout ∑ W  + z R DRM cR*Wout ∑ M j =1 δ X ( t jm ) j =1 δ R ( t jm )    m m   Z inn Z inn j, X j ,R  = − FA  z X DWX c*XWinn ∑ W + zR DRM cR*Winn ∑ M j =1 δ X ( t jm ) j =1 δ R ( t jm )   

(10)

where t jm = ( m − j + 1)τ and

Z out j,X = Z

inn j,X

=

1 X ηôut , j −1

1+ e 1

X ηînn , j −1

1+ e

− −

1 X ηôut ,j

1+ e 1

X ηînn ,j

1+ e

R ηôut ,j

Z out j ,R = e

; ;

Z

inn j,R

R ηînn ,j

=e

R ηôut , j −1 

−e

R ηînn , j −1

−e


   j = 1, 2...m  

(11)


X ηôut ,0

with e

X ηînn ,0

=e

R ηout ,0

=e

R ηinn ,0

=e

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X R = 0 and ηôut / inn and η out / inn being given by Eqs. (5) by replacing

() () ( ) ( ) Eout and Einn by Eout and Einn , respectively. 1

1

j

j

( j) ( j) The values of the interfacial potential E out and E inn can be determined by equalizing the

currents corresponding to the j-th potential pulse at the outer and inner interfaces ( out inn inn I out j , X + I j , R = I j , X + I j , R = I j ), leading to (see Section S2)

% out % inn % inn I% jout , X + I j,R = I j, X + I j,R

(12)

α where I% j ,i are given by Eq. (37) of the Supporting Information. Eqs.(9)- (10) can be used to analyse

the response in any voltammetric technique, such as cyclic voltammetry and cyclic square wave voltammetry, as well as for any charge number and lipophilic character of the ionic species (i.e., for any value of ∆WM φ X0 ' − ∆WM φR0' ). In addition, it is easily adaptable for the situation of very lipophilic ions dissolved in the organic phase. Microholes Eq. (10) is totally rigorous for macrointerfaces, since the interfacial concentrations are timeindependent in such a way that the superposition principle is applicable 8. This condition is also fulfilled for any interface geometry when equal diffusion coefficients for all species in water and in M M the organic solution can be assumed ( DW X = DX = DR = D ), Eq.(10) remaining valid with the

corresponding expression for the diffusion layer thickness. In the case of microholes δ is defined as follows 9

δ microhole =

(

(

)

π r0

(

(

4 0.7854 + 0.44315 r0 / Dt + 0.2146 exp −0.39115 r0 / Dt

)))

(13)

where r0 is the radius of the microhole. Under steady state conditions (ss), Eq. (13) becomes into

δ ssmicrohole =

π r0 4

(14)

and Eq.(10) holds regardless of the values of the diffusion coefficient with ξ imicrohole, ss = DiM / DW X . Also, in the case of microholes under transient conditions, accurate results are obtained even when the diffusion coefficients take very different values 1. Very different diffusivities are found when 8 ACS Paragon Plus Environment

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solvent polymeric membranes or room temperature ionic liquids are used as the organic phase. This can have a notable effect on the shape of the double transfer voltammograms, which is enhanced in the case of microinterfaces as will be discussed below.



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EXPERIMENTAL SECTION a) Reagents and solutions Lithium

chloride

(LiCl,

8M

solution),

tetraethylammonium

chloride

(TEACl),

tetradodecylammonium tetrakis-(4-chloro-phenyl)borate (TDDA-TClPB) and 1,2-dichloroetane (DCE) were purchased from Sigma. Potassium hexachloroplatinate (IV) (K2PtCl6), sodium perchlorate (NaClO4) and sodium tetrafluoroborate (NaBF4) were purchased from Aldrich, sodium nitrate (NaNO3) from Probus and hydrochloric acid (HCl 37%) from Panreac. Nanopure water (18 MΩ) from a Milli-Q (Millipore) system was used throughout.

b) Electrochemical measurements The electrochemical cell employed for the voltammetric studies (unless otherwise indicated) can be expressed as: Ag|5x10-2M LR, ymM X (Wout)║ 5x10-2M TDDA-TClPB (M) ║ 5x10-2M LiR, ymM X (Winn)Ag (Cell 1) with L = Na+, Li+ and R = Cl-, NO3-, ClO4-, BF4- and X = TEACl, K2PtCl6. Platinum wires were used as counter-electrodes and silver wires as (pseudo)reference electrodes. Description and photographies of this cell can be found in Section S6 of the Supporting Information.


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RESULTS AND DISCUSSION Influence of the lipophilicity of the compensating ion R z R The voltammetric response for the transfer of an ionic species X z X in a system of two polarisable interfaces W | O | W supported by electrolytes of very hydrophilic (phases W ) or lipophilic ( phase M ) character is highly affected by the initial distribution of X z X in the system. Thus, a single signal is obtained in conventional studies where the target ion is only added to the outer aqueous phase 3,10–12, while “double transfer voltammograms” with two separate waves 2 have been reported when the analyte X z X is added to both aqueous phases or to the organic solution 1 in such a way that it can be transferred across the two liquid|liquid interfaces. The separation between such two waves depends strongly on the lipophilic character of species X z X and of the compensating ion R z R , showing a variety of voltammetric responses ranging from two well-separated signals to a single one. Here, different situations determined by the lipophilicity of R z R will be studied in cyclic voltammetry (CV) and cyclic square wave voltammetry (cSWV) at macrointerfaces and also in steady state voltammetry (SSV) at microholes. The response in the single-pulse technique normal pulse voltammetry (NPV) at macrointerfaces compared to SSV is shown in Figure 1 for two different aqueous supporting electrolytes, differing in the hydrophilicity of the anion R z R . Note that the voltammograms are totally symetric, with the centre of symetry coinciding with the centre of the polarisation windows. This is a consequence of that the chemical compositions of the two aqueous phases are identical under the conditions of the figure ( c*XWout = c*XWinn and cR*Wout = cR*Winn )1. As can be seen, the shape of the voltammograms is clearly dependent on the diffusion coefficients of the ionic species and on the size of the interface, whereas the magnitude of the normalised limiting current ( I lim / I dout ) is identical in all cases. As observed in Figure 1, for a fixed value of ∆WM φ X0 ' − ∆WM φR0' , the separation between the waves is larger as the diffusivity in the organic M W M solution decreases with respect to the aqueous phase (i.e., when the ratios DW X / D X and D X / DR

increase). This effect is more apparent when the size of the interface shrinks and it is a consequence of the higher accumulation of the transferrable species at the organic side of the liquid|liquid interfaces 7. For quantitative analysis, the following expressions account for the differences between the half-wave potentials of the two well-separated signals 1



∆E

micro 1/ 2

∆E

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4  c*XWout ( DWX ) c*XWinn RT  = 2 ( ∆φ − ∆φ ) + ln F  4 c*Wout ( D M ) 2 ( D M )2 c*Winn X R R  R

macro 1/2

0' X

0' R

 *Wout W 2 *Winn RT  c X ( DX ) cX = 2 ( ∆φ − ∆φ ) + ln F  4 cR*Wout DXM DRM cR*Winn  0' X

0' R

   

   

(15)

(16)

from which it can be inferred that the separation between the responses recorded with microholes M W M and macrointerfaces increases with the values of DW X / DX and D X / DR

micro ∆E1/2 − ∆E1/macro 2

W 2  RT  ( DX ) = ln F  DXM DRM 

   

(17)

The behaviour shown in Figure 1 is also observed in other techniques such as cyclic voltammetry and square wave voltammetry (see Section S3 of the Supporting Information), and it clearly points out that, in Scheme 1, the use of smaller interfaces and/or solvents where diffusion is much slower than in water (such as solvent polymeric membranes 13 or room temperature ionic liquids) enables us to separate partially overlapped signals. The current-potential response can be better understood by analysing the individual contributions of the ions to the net current (calculated from Eqs.(9) and (12)), depicted in Figure 2 for cyclic voltammetry (CV) at macrointerfaces and microholes under steady state conditions. Equal diffusion coefficients for all the species have been considered in the two ‘limit’ situations: two wellseparated waves ( ∆WM φ X0' − ∆WM φR0' = 300 mV, figures 2a-b) and a single signal ( ∆WM φ X0' − ∆WM φR0' = 100 mV, figures 2c-d). In the case of separated waves, the transfer of species X z X at each interface takes place at very different potentials (from Wout when E >> 0 and from Winn when E 0 , whereas species R z R is only transferred across one of the interfaces (from phase Wout at

E > 0 ). This is a

consequence of the semi-lipophilicity of R z R and of its high concentration compared to that of X z X 12 ACS Paragon Plus Environment

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( cR* / c*X = 50 in Figure 2). Thus, the favourable transfer of R z R to the organic solution does not only trigger the full transfer of X z X across the opposite interface (see figures 2c-d), but also the partial transfer of X z X at the same interface. Note that a complex situation is found at the centre of the polarisation windows, with all the ions contributing to the signal (the contributions of R z R being larger than that of X z X ). This fact can be observed more easily in the steady state response obtained at microholes (Figure 3d).

Influence of the charge number of species X z X and R z R The charge number of ions X

zX

and

R z R also has a notable effect on the position,

magnitude and shape of the voltammetric response, which is analysed in Figure 3 for CV and cSWV when considering ∆WM φ X0' − ∆WM φR0' = 300 mV. In this figure, monovalent and divalent ions are considered, since ions of higher charge are not usually transferred within typical polarisation windows 14. When the anion of the supporting electrolyte is hydrophilic enough to provide two wellseparated signals, the peak-to-peak distance ( ∆E peak ) of each CV signal is around 90 mV when both ions are monovalent ( z X = zR = 1 ), coinciding with the data reported previously for conventional studies for two polarisable interface system (i.e., when the analyte is only added to the outer aqueous phase 15). This value is found to decrease to 41 mV when both X

zX

and R z R are divalent

(see Table S1 in Section S5), obtaining intermediate values when one of the ions ( X

zX

or R z R ) is

monovalent and the other one is divalent. The half-peak width ( W1/2 ) in cSWV follows the same trend as ∆E peak in CV, varying between 139 and 73 mV depending on the charge number of the transferrable species (see Table S1 in Section S5). The values of ∆E peak and W1/2 for a double and a single signal are gathered in Table S1 (see Section S5).

Experimental verification The influence of the lipophilicty of the ‘compensating ion’ ( R z R ) on the transfer of the target ion ( X z X ) and the impact on the double transfer voltammograms has been examined experimentally. Figure 4a shows the results obtained in cSWV for the transfer of tetraethylammonium (TEA+) across two water|DCE interfaces in the presence of different supporting electrolytes in the aqueous solutions with cSE ≈ 125cTEA (see Experimental Section). The key difference between them is related to the lipophilicity of the anion that compensates the transfer of TEA+ 16. 13 ACS Paragon Plus Environment


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When the electrolyte with the most hydrophilic anion is employed (i.e., Cl− ), two wellseparated pair of peaks are recorded related to the transfer of TEA+ across the outer interface (peaks at positive potentials) and across the inner interface (peaks at negative potentials) with exp W1/2 = 137 ± 2mV as corresponds to z X = zR = 1 (see Table S1 in Section S5). As predicted by

Eq.(16), the separation between the two signals decreases notably ( ≈ 220 mV) when the electrolyte anion employed is less hydrophilic ( NO 3− ), reflecting that the coupled transfer of R z R

is

thermodynamically more favourable and so the signals develop at lower potentials in absolute value. If the hydrophilicity of R z R is further decreased, then the two pair of peaks gradually overlap (see Figure 1 and Section S3) and they finally merged into one. This last situation is found when salts of ClO −4 or BF4− are employed as aqueous supporting electrolytes, with a single pair of peaks being

recorded around E = 0 . This reflects that the transfer of TEA+ compensated by ClO −4 / BF4− is very favourable, a situation of interest in the development of efficient ion-transfer batteries 4. These experimental results are in agreement with the theoretical predictions abovediscussed attending to the values reported in the literature for the transfer Gibbs energy between water and DCE of the anions assayed which increases in the order 16: BF4− < ClO −4

Double Transfer Voltammetry in Two-Polarizable Interface Systems

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