Facilitated proton transfer reactions via water autoprotolysis across oil|water interfaces. Half-wave potential

Electrochimica Acta 332 (2020) 135498

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Facilitated proton transfer reactions via water autoprotolysis across oil|water interfaces. Half-wave potential
ndez a, b, S.A. Dassie a, b, * F.M. Zanotto a, b, R.A. Ferna a b


rdoba, Ciudad Universitaria, X5000HUA, Co
rdoba, Argentina Departamento de Fisicoquímica, Facultad de Ciencias Químicas, Universidad Nacional de Co
rdoba (INFIQC), CONICET, Ciudad Universitaria, X5000HUA, Co
rdoba, Argentina Instituto de Investigaciones en Fisicoquímica de Co

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 November 2019 Received in revised form 10 December 2019 Accepted 11 December 2019 Available online 16 December 2019

The main purpose of this paper is to develop the equations for the half-wave potentials of facilitated proton transfer or protonated species transfer across liquid|liquid interfaces, explicitly considering the water autoprotolysis equilibrium. The main equation developed in this article allows simulating different chemical systems, which are compared to simulated results using a previously developed model (J. Electroanal. Chem. 578 (2005) 159e170). Both the effect of the initial concentration of the weak base and the volume ratio of the aqueous to organic phases on the half-wave potentials are presented. Finally, approximate equations are developed that allow not only to adequately justify the behaviour of the halfwave potentials with the volume ratio and the initial concentration of the weak base, but can also be used as a tool to explain or predict experimental results. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Facilitated proton transfer liquid|liquid interface Half-wave potential Protonated species transfer Water autoprotolysis

1. Introduction Facilitated proton transfer process across the interface between two immiscible electrolyte solutions (ITIES) has gained increasing importance due to the information it provides about the partition of different drugs with acid or base activity [1e10]. One of the main interests in these studies is the determination of partition coefficients, for both ionic and neutral species from the transfer of ionisable drugs across ITIES [6,11e13]. This information is essential in research areas such as Pharmacy and Pharmacology [4]. Many studies related to drug compounds have been dedicated to investigating their transfer across ITIES by electrochemical techniques. These reports have included not only experimental results, but also different theoretical models with different level of detail of the proton transfer processes [14e21]. In addition, analytical equations have been developed to calculate the half-wave potential for the transfer of weak bases [22] or acids [23] across liquid|liquid (L|L) interfaces, including ion pairing [22,23] and explicit activity coefficients [23]. Furthermore, a general model of a thick organic filmmodified electrode has been proposed to analyse the facilitated

* Corresponding author. Departamento de Fisicoquímica, Facultad de Ciencias
rdoba and Instituto de Investigaciones en Químicas, Universidad Nacional de Co
rdoba (INFIQC), CONICET, Ciudad Universitaria, X5000HUA, Fisicoquímica de Co
rdoba, Argentina. Co E-mail address: [email protected] (S.A. Dassie). https://doi.org/10.1016/j.electacta.2019.135498 0013-4686/© 2019 Elsevier Ltd. All rights reserved.

proton transfer-electron transfer coupled reactions (FPT-ET reactions) in different experimental conditions, such as pH and concentration ratios between the redox probe and the transferring protonated species [24,25]. Analytical equations to calculate the half-wave potential for the FPT-ET reactions at thick organic filmmodified electrodes (including ion pairing in the organic phase and considering a non-ideal electrolyte solution in both phases) have also been developed. This last model has been checked against experimental voltammetric responses [25]. In the last years, our research group has focused on an integrated theoretical-experimental approach to understand transfer processes of protonated species via water autoprotolysis [16e19,26]. These analyses were based on modelling the effect of water autoprotolysis on the proton transfer processes by comparing implicit or explicitly buffered to unbuffered solutions [16e19]. The proposed models were corroborated by experimental results measured for quinine or quinidine transfer across the H2O|1,2dichloroethane interface. The involved ion transfer mechanisms were analysed in terms of the current-potential profiles and theoretical concentration profiles [18,19,26]. Finally, an experimental analysis of the effect of forced hydrodynamic conditions (FHCs) on the current-potential profiles was performed. These FHCs studies applied to each phase confirmed the global mechanisms proposed previously [16,18], and they were expanded with a mass controlled transport [26]. Recently, we have introduced an experimental and theoretical study of the spectroelectrochemical response of the

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F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498

facilitated proton transfer processes via water autoprotolysis at the L|L interface. The aim of these studies was to confirm the generation of pH gradients at the L|L interface using coupled electrochemical and spectroscopic techniques. The spectroelectrochemical measurements were performed using a parallel beam configuration, in which a narrow light beam is passed at grazing incidence over the L|L interface. Experimental analysis was based on proton transfer assisted by Quinidine via water autoprotolysis and Thymol Blue was employed as a pH indicator. The colour change of Thymol Blue, in unbuffered aqueous solutions during the experiments indicated an increase in the pH adjacent to the L|L interface, generated as a consequence of the water dissociation reaction [21]. The main purpose of the present paper is to develop the equations for the half-wave potentials of facilitated proton transfer or protonated species transfer across L|L interfaces, explicitly including water autoprotolysis. The main equation developed in this research is capable of describing different chemical systems which are compared to simulated results according to a previously developed model [16]. The effect of the initial concentration of the weak base, and the volume ratio of the aqueous and organic phases on the half-wave potentials are presented. Finally, approximate equations are developed that allow not only to adequately justify the behaviours of the half-wave potentials with the volume ratio and the initial concentration of the weak base, but can also be used as a tool to explain or predict experimental results.

In this section, we present a summary of a general model, similar to one described in a previous paper [16] for the facilitated proton transfer across L|L interfaces in unbuffered aqueous solutions considering the water autoprotolysis. To derive the current-potential equation for these transfer processes by a neutral weak base present in single protonated form, HBþ , the complete list of the model assumptions are detailed in the Supplementary Material section. The acid-base equilibrium of the weak base is the following:

HB

base species, zk is the ionic charge, equal to þ1 in both of these cases, and Dw o f is the Galvani potential difference at the interface. The diffusion equation for the total weak base and the total charged species are defined by Fick’s laws:

vcaBtot ðx; tÞ v2 caBtot ðx; tÞ ¼ Da vt vx2 vcachargetot ðx; tÞ vt

¼ Da

(5)

v2 cachargetot ðx; tÞ

(6)

vx2

where the diffusion coefficients (Da ) are assumed (assumption (i)) to be the same for all species in each phase [27]. The total concentration of B is defined by the mass balance equation in each phase: w w cw Btot ðx; tÞ ¼ cB ðx; tÞ þ cHBþ ðx; tÞ

(7)

coBtot ðx; tÞ ¼ coB ðx; tÞ þ coHBþ ðx; tÞ

(8)

and the total charged species concentration is defined by the proton condition equation [28,29]:

caHþ ðx; tÞ ¼ caHO ðx; tÞ þ caB ðx; tÞ þ caa ðx; tÞ  cabþ ðx; tÞ

(9)

where cabþ ðx; tÞ and caa ðx; tÞ are the concentration of the strong al-

1.1. Theory

þ

0

o and Dw o fHBþ is the formal transfer potential of the protonated weak

þ

% H þB

considering activity coefficients equal to unity, the acid dissociation constant in the a-phase is defined by:

caB caHþ

K aa ¼ a cHBþ

kali and acid, respectively. These represent the initial amount of strong alkali or acid added to the mixture necessary to set the initial pH without a buffer solution. The protonated weak base and unionized water are taken as the zero level (reference level) species. Eq. (9) is rewritten as follows:

cachargetot ðx; tÞ ¼ caHþ ðx; tÞ  caB ðx; tÞ  caHO ðx; tÞ where

cachargetot ðx; tÞ ¼ caa ðx; tÞ  cabþ ðx; tÞ

Dw

Dw

vcw vco ð0; tÞ Btot ð0; tÞ ¼ Do Btot ¼ fBtot ðtÞ vx vx vcw ð0; tÞ chargetot vx

¼ Do

vcochargetot ð0; tÞ vx

Kw ¼ cw cw  Hþ HO

w; cw Btot ð0; tÞ ¼ cBtot  

(2)

The distribution of charged species at the interface is defined by the following Nernst equation:


cok ð0; tÞ z F ¼ exp k w RT ck ð0; tÞ

   w o0 Do f  Dw ; o fk

¼ fchargetot ðtÞ

(13)

pDw

coBtot ð0; tÞ ¼ co; Btot þ 

1

fBtot ðtÞdt

1

(14)

1

ðt  tÞ2

2

0

ðt 1

fBtot ðtÞdt

(15)

1

ðt  tÞ2

2

0

(4)

þ

H

ðt

1

pDo

for k ¼ H or HB , caHBþ ð0; tÞ the protonated weak base concentration and ca þ ð0; tÞ the proton concentration at the interface (x ¼ þ

(12)

The total interfacial concentrations are expressed as a function of the convolution integrals using Laplace transforms [30,31]:

H2 O % Hþ þ HO The water autoprotolysis constant is defined by:

(11)

According to the boundary conditions, the flux of species across the interface ðx ¼ 0Þ is expressed by:

(1)

for a ¼ organic phase (o) or aqueous phase (w), and water autoprotolysis is explicitly considered:

(10)

o0 0) at any time. Dw o 4Hþ is the formal transfer potential of the proton

w; cw chargetot ð0; tÞ ¼ cchargetot  

1

pDw

ðt 

1 2

fchargetot ðtÞdt 1

0

ðt  tÞ2

(16)

F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498

3

1.2. Half-wave potential as a function of pH

cochargetot ð0; tÞ ¼ co;* þ chargetot

1

pDo

ðt 1

fchargetot ðtÞdt 1

2

0

ðt  tÞ2

(17)

a; a; being cBtot and cchargetot the total weak base concentration and the

total charged concentration respectively, in the a-phase at t ¼ 0 and for all x values. These variables are independent of position and are defined as follows: w w cw; Btot ¼ cB ðx; 0Þ þ cHBþ ðx; 0Þ

(18)

o o co; Btot ¼ cB ðx; 0Þ þ cHBþ ðx; 0Þ

(19)

w cw; ¼ cw ðx; 0Þ  cw B ðx; 0Þ  cHO ðx; 0Þ Hþ chargetot

(20)

¼ coHþ ðx; 0Þ  coB ðx; 0Þ  coHO ðx; 0Þ co; chargetot

(21)

ðiÞ

þ rco; ¼ cw; chargetot chargetot

ðiÞ

(23)

(24)

    o cchargetot ¼ cw chargetot 0; t þ xcchargetot 0; t

(25)

Do Dw

12 .

By using Eqs. (24) and (25) it is possible to obtain all the concentration values at the interface at each simulation time. By numerical integration of the convolution integrals, according to Nicholson and Shain [33]:

ðt

fchargetot ðtÞdt 1 2

0

ðt  tÞ

i  1 h w ¼ pDw 2 cw;  c ð0; tÞ chargetot chargetot

(26)

it is possible to know the total current-potential response of the system:

IðtÞ ¼ FAfchargetot ðtÞ

a-phase side of the interface at this time. In unbuffered systems, more than one transfer process can be observed. Representing these in order, with a superindex i, at the half-wave potential value, where w ðiÞ Dw o f ¼ Do f1=2 , the Nernst equation for proton can be written as:

ðiÞ Dw o f1=2

    o cBtot ¼ cw Btot 0; t þ xcBtot 0; t



It can be asserted that during a voltammetry experiment, there exists a time for which the applied potential equals the half-wave potential. In order to simplify the notation, we define the concen  ðiÞ trations cak 0; Dw as the concentration of species k in the o f1=2

(22)

where r ¼ Vo V 1 w , is the ratio of organic phase volume to aqueous phase volume. The total interfacial concentration of weak base species and the total interfacial charge concentration in the system is obtained from Eqs. (14)e(17) by eliminating the convolution integrals:

where x ¼

where it represents the potential at half the limiting current from a sigmoidally shaped polarogram [35]. Considering that all the systems analysed in this work are electrochemically reversible and that the transfer of all charged species is a diffusion-controlled w process, Dw o fmid can be regarded as Do f1=2 [22].

of weak base (cinit B ) and the initial pH of the aqueous phase at the start of the experiment [14,16,17,32]. Considering that the weak base is dissolved in the aqueous phase, the following equations are obtained:

w o cinit chargetot ¼ cchargetot ðx; 0Þ þ rcchargetot ðx; 0Þ

in terms of the Galvani potential difference referred to an extra thermodynamic assumption. This assumption states that the ion transfer standard Gibbs free energies of the anions and cations of tetraphenylarsonium tetraphenylborate are the same for all pairs of immiscible liquids [34]. On the other hand, the term half-wave potential, Dw o f1=2 , has its origin in the polarography literature,

The total initial concentration of all species in each phase may be calculated for t ¼ 0 as a function of the total initial concentration

w; o; w o cinit B ¼ cBtot ðx; 0Þ þ rcBtot ðx; 0Þ ¼ cBtot þ rcBtot

The mid-peak potential, Dw o fmid , experimentally determined by cyclic voltammetry can be calculated by a simple relation between the peak potentials of the forward and reverse scans:   1 Dw fforward scan þ Dw freverse scan . These potentials are reported o peak o peak 2

(27)

According to the current-potential response the mid-peak potential can be obtained.

"  # ðiÞ aoHþ 0; Dw o f1=2 RT o0   ¼ Dw ln þ o f Hþ w ðiÞ F 0; D f aw o 1=2 Hþ "  # ðiÞ w coHþ 0; Do f1=2 RT   ln þ w ðiÞ F cw þ 0; Do f 1=2 H

o ¼ Dw o f Hþ

(28)

ðiÞ

According to Eq. (28), in order to determine Dw o f1=2 , the proton concentrations at the organic and aqueous sides of the L|L interface must be known. Moreover, aqueous side of the interface, the proton concentration evolves due to the formation of hydroxide anions, as a product of the facilitated proton transfer via water autoprotolysis [16e19,21,26]. Unlike other models developed by our research group [22,23,25], in this case the two proton transfer processes occur consecutively, involving the same neutral weak base, with a unique total concentration. Therefore, both proton transfer processes are controlled by the initial concentration of weak base (see Scheme 1). ðiÞ

Now, we will focus on the calculation of Dw o f1=2 for each process (i ¼ 1 or 2) for a single protonated species HBþ as a function of all other species present in the electrochemical system. The first process (i ¼ 1) involves the simple transfer of the protonated form HBþ and the transfer of Hþ facilitated by the presence of B near the interface, depending on the pH value. These reactions are limited by the amount of their corresponding reactant species near the interface. In the former case, HBþ is the reactant species, in the latter case, the limiting reactant must be considered, which is either Hþ or B. In order to take this into account, we define zmin ¼ o w min½cw B ð0; 0Þ þ xcB ð0; 0Þ; cHþ ð0; 0Þ, which represents the concentration of the limiting reactant for this latter reaction. Thus, the amount of reactants consumed only during the first process can be ð0; 0Þ þ zmin , and the rest of the weak base species, expressed as cw HBþ ð0; 0Þ þ zmin , is consumed during the second process c*Btot  ½cw HBþ

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F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498

(i ¼ 2), which involves the facilitated proton transfer via water autoprotolysis. This approach is illustrated in Scheme 1. The conditions necessary to find the half-wave potential for each process then can be found straightforwardly by setting the total concentration of products and the total concentration of reactants as those corresponding to the half point for each process in ð1Þ

w Scheme 1. Thus, for Dw o f ¼ Do f1=2 :

 8 *       2cBtot  cw ð0; 0Þ þ zmin w ð1Þ w ð1Þ w ð1Þ o w > HBþ > ¼ cw > B 0; Do f1=2 þ xcB 0; Do f1=2 þ cHBþ 0; Do f1=2 > 2 > > > < w   ð0; cHBþ 0Þ þ zmin ð1Þ ¼ zcoHBþ 0; Dw > o f1=2 > 2 > > > >             > : * ð1Þ w ð1Þ w ð1Þ w ð1Þ w ð1Þ w ð1Þ o w o w o 0; Dw cchargetot ¼ cw o f1=2 þ xcHþ 0; Do f1=2  cHO 0; Do f1=2  xcHO 0; Do f1=2  cB 0; Do f1=2  xcB 0; Do f1=2 Hþ

(29)

ð2Þ

w and for Dw o f ¼ Do f1=2 :

 8 c*  cw ð0; 0Þ þ z       min Btot w ð2Þ w ð2Þ w ð2Þ o w HBþ > > ¼ cw > B 0; Do f1=2 þ xcB 0; Do f1=2 þ cHBþ 0; Do f1=2 > 2 > > > < * w   cBtot þ cHBþ ð0; 0Þ þ zmin ð2Þ ¼ zcoHBþ 0; Dw > o f1=2 > > 2 > > >             > : * ð2Þ w ð2Þ w ð2Þ w ð2Þ w ð2Þ w ð2Þ o w o w o 0; Dw cchargetot ¼ cw o f1=2 þ xcHþ 0; Do f1=2  cHO 0; Do f1=2  xcHO 0; Do f1=2  cB 0; Do f1=2  xcB 0; Do f1=2 Hþ

cw Hþ

(30)

Rewriting equation systems (29) and (30), as a function of       ð1Þ w ð1Þ w ð1Þ o w 0; Dw o f1=2 , cHþ 0; Do f1=2 and cB 0; Do f1=2 , the following

equations are obtained for both of the half-wave potentials:

   

w  8 * w ð1Þ w ð1Þ w     cw 2c  c þ ð0; 0Þ þ zmin B 0; Do f1=2 cHþ 0; Do f1=2 > ð1Þ ð1Þ Btot w w w w HB > > ¼ cB 0; Do f1=2 þ xKD;B cB 0; Do f1=2 þ > > 2 Kaw > > > > > > > > >  < cw þ ð0; 0Þ þ z    xKD;B w  min ð1Þ w ð1Þ o HB ¼ cB 0; Dw o f1=2 cHþ 0; Do f1=2 o > 2 Ka > > > > > > > > >         > > Kw w ð1Þ w ð1Þ w ð1Þ w ð1Þ > * w o w >   cw 0;  0; D f x K c D f : cchargetot ¼ cHþ 0; Do f1=2 þ xcHþ 0; Do f1=2  w  D;B o o B B 1=2 1=2 ð1Þ cHþ 0; Dw o f1=2

(31)

F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498

5 ð1Þ

and,

w where, for Dw o f ¼ Do f1=2 :

    8 *

 w ð2Þ w ð2Þ w     cw cBtot  cw þ ð0; 0Þ þ zmin B 0; Do f1=2 cHþ 0; Do f1=2 > ð2Þ ð2Þ w w > w w HB > ¼ cB 0; Do f1=2 þ xKD;B cB 0; Do f1=2 þ > > 2 Kaw > > > > > > > > > >  * w >    > xKD;B w  < cBtot þ cHBþ ð0; 0Þ þ zmin ð2Þ w ð2Þ o ¼ cB 0; Dw o f1=2 cHþ 0; Do f1=2 o 2 Ka > > > > > > >         > > * ð2Þ w ð2Þ w ð2Þ w ð2Þ o w o > > 0; Dw cchargetot ¼ cw > o f1=2 þ xcHþ 0; Do f1=2  cHO 0; Do f1=2  xcHO 0; Do f1=2 Hþ > > > >     > : w ð2Þ w ð2Þ w cw B 0; Do f1=2  xKD;B cB 0; Do f1=2

Reordering Eqs. (31) and (32), according to the procedure detailed in the Supplementary Material section, the following cubic   ðiÞ 0; Dw is obtained: polynomial in cw o f1=2 Hþ

h   i3   i2 h ðiÞ ðiÞ cw 0; Dw 0; Dw þ a cw o f1=2 o f1=2 Hþ Hþ   ðiÞ 0; Dw þ bcw o f1=2 þ c ¼ 0 Hþ

(33)

a¼

b¼

Kw a

b¼

cw ð0; 0Þ þ zmin HBþ    cw ð0; 0Þ þ zmin HBþ

2c*Btot 2c*Btot

   cw ð0; 0Þ þ zmin HBþ 2

(35)

ð2Þ

w and for Dw o f ¼ Do f1=2 :

where:

Kw a

c¼

(32)

" (   1 þ xKD;B 1 þ 2c

K oa KD;B K w a

!# 

c*chargetot Kw a

)"

K oa 1þc KD;B K w a

!#1

!#1 "  2 Kw   K oa  K oa * 1 þ xKD;B  w  b þ cchargetot 1 þ xKD;B c 1þc KD;B Ka KD;B K w a




"   c ¼ Kw K w x K 1 þ D;B 1 þ c a

K oa KD;B K w a

(34)

!#1

Scheme 1. Representation of the total concentration of species available for reaction in absence of buffer solution. This amount is distributed between the two possible processes. In the most general case, both processes occur consecutively and consume different amounts of reactant, the first one consumes cw ð0; 0Þ þ zmin , and the second one the rest. The half HBþ ðiÞ point of the interval corresponding to each process defines the half-wave potentials Dw o f1=2 .

6

F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498

ðiÞ

w Fig. 1. Dependence of the half-wave potentials, Dw o f1=2 , on the initial pH of the aqueous phase for buffered and unbuffered aqueous solutions (panels (a), (b) and (c)). pK a ¼ 5.00 ð1Þ ð2Þ (a), 7.00 (b) and (d), and 9.00 (c). The red and blue solid lines correspond to the model presented herein: Dw and Dw . The solid black line represents Dw o f1=2 o f1=2 o f1=2 for ðiÞ aqueous buffer solutions according to Eq. (40). The full points represent Dw voltammograms using the model developed in Ref. [16]. First  o fmid obtained from the simulated ðiÞ proton transfer process (RI and II) and second process (RIII) . Dependence of the interfacial pH, pH 0; Dw o f1=2 , on the pH of the aqueous phase for unbuffered aqueous solutions w o w o o ¼ 1:0 mM, pKw ¼ 14:0, Dw (panel (d)). Other simulation parameters: cinit o fHþ ¼ 0:55 V [37,38] Do fHO ¼ 0:70 V (H2O|1,2-dichloroethane), Do fHBþ ¼  0:20 V, r ¼ 1:0, x ¼ 1:0 B and logðKD; B Þ ¼ 2:00. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

    ðiÞ w ðiÞ Fig. 2. Dependence of the interfacial distribution of species on the pH of the aqueous phase for unbuffered aqueous solution. , coHBþ 0; Dw , cw and o f1=2 B 0; Do f1=2   ðiÞ ð1Þ ð2Þ w w w . Panel (a): first proton transfer process (RI and II), at Do f1=2 , and panel (b): second process (RIII), at Do f1=2 . pK w ¼ 7:00. All other simulation parameters are the coB 0; Do f1=2 a same as in Fig. 1.

F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498

c¼

coHþ

c*Btot þ cw þ ð0; 0Þ þ zmin  HB  c*Btot  cw ð0; 0Þ þ zmin HBþ

ðiÞ 0; Dw o f1=2



¼

From the main equation, Eq. (33), we can calculate analytically ð2Þ

w the half-wave potentials, Dw o f1=2 and Do f1=2 , and the interfacial

concentration of all species, at these half-wave potentials, in all experimental conditions. To calculate the concentration of protons   ðiÞ 0; Dw in the aqueous side of the L|L interface, cw o f1=2 , first the Hþ 3b and G ¼ 9 G2 < Q 3 and cosðqÞ ¼ 2

following variables must be computed: Q ¼ a 2a 9abþ27c. It can be shown numerically that 54   ðiÞ pGffiffiffiffiffi, therefore, cwþ 0; Dw can be expressed o f1=2 H Q3 3

! h   Kaw 1 þ xKD;B w

xKD;B Ka

(38)

Finally, the expression for the pH dependence of the half-wave potentials can be found by replacing Eq. (37) in Eq. (38) and this result in Eq. (28), as following: ðiÞ w o0 Dw o f1=2 ¼ Do f1=2;HBþ

  2
pffiffiffiffi   3 p þ a  K w 1 þ xK 2 Q cos qþ2 c D;B a 3 3 7 RT 6 7  ln6 þ 4 5 p ffiffiffiffi F q þ2 p a þ3 2 Q cos 3 (39)

by the following

analytical equation [36]:

   pffiffiffiffi q þ 2p a ðiÞ  0; Dw ¼ 2 Q cos cw o f1=2 Hþ 3 3

cKao

 i ðiÞ 0; Dw þ cw o f1=2 Hþ

(36)

  c*Btot  cw ð0; 0Þ þ zmin HBþ b¼ 2 ð1Þ



7

2. Results and discussion

(37)

The concentration of protons in the organic side of the L|L   ðiÞ interface, coHþ 0; Dw o f1=2 , can be expressed by the following analytical equation, by following the procedure detailed in the Supplementary Material section:

In this section we present the results for representative chemical systems to demonstrate the usefulness of the main equation developed in Section 1.2. First, in Section 2.1, we analyse the dependence of the half-wave potential for both proton transfer ð1Þ

ð2Þ

w processes, Dw o f1=2 and Do f1=2 , on initial pH. The half-wave po-

tentials as a function of the pH obtained using Eq. (39), are compared to simulated results according to our previous model,

Fig. 3. Voltammogram (a), interfacial pH (b) and interfacial distribution of species in the organic (c) and aqueous (d) side of the L|L interface obtained for unbuffered aqueous solution using the model developed in Ref. [16]. The interfacial pH and the interfacial concentrations, (hollow points) obtained from the resolution of Eqs. (29), (30) and (39), to ð1Þ w ð2Þ w Dw o f1=2 and Do f1=2 are shown comparatively. pK a ¼ 7:00 and pH 5:00. All other simulation parameters are the same as in Fig. 1.

8

F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498

  ð2Þ w ðiÞ init Fig. 4. Dependence of the half-wave potential, Dw o f1=2 , (a); and interfacial pH (b) for the facilitated proton transfer via water autoprotolysis, pH 0; Do f1=2 , on logðcB Þ. pH 8:00: w ð2Þ r ¼ 1:00 and r ¼ 0:10 . pH 10:0: r ¼ 1:00 and r ¼ 0:10 . Panel (a): Do fmid obtained using the model developed in Ref. [16] for pH 10:0 and r ¼ 1:00 , and Dw o f1=2 ðiÞ for aqueous buffered solutions are shown comparatively (Eq. (40)). Panel (c): dependence of the half-wave potentials, Dw o f1=2 , on the pH of the aqueous phase for buffered and ð1Þ ð2Þ w w w unbuffered aqueous solutions at different cinit , Do f1=2 for all cinit and, Do f1=2 : cinit , 1:00 , 10:0 and B values. Do f1=2 for aqueous buffer solutions B values B ¼ 0:100 100 mM . pK w a ¼ 7:00. All other simulation parameters are the same as in Fig. 1.

which is solved by the Laplace transform method [16]. In Section 2.2, the effect of the initial concentration of the weak base and the volume ratio of the aqueous to organic phases on the half-wave potentials are presented. Sections 2.1 and 2.2 are essential for the validation of the main Eq. (39) and for understanding the charge transfer mechanisms that take place in the system. Finally, approximate equations are developed that allow not only to adequately justify the behaviours of

ðiÞ Dw o f1=2

with the volume ratio

and the initial concentration of the weak base, but can also be used as a tool to explain or predict experiments.

2.1. Comparison between simulated and theoretical results In this section, we will analyse the dependence of the half-wave potential for both proton transfer processes on initial pH. The behaviour of these systems under bufferized conditions is well known and widely reported in literature [2,22], thus, throughout the results and discussion section, our results for unbuffered aqueous solutions will be compared to the well-known behaviour of buffered aqueous solutions, which can be represented by the following equation [2,22]:

w o0 Dw o f1=2 ¼ Do f1=2;HBþ þ



RT  w  ln cHþ F

  RT w  ln Ka 1 þ xKD;B þ cw Hþ F

w o0 o0 being Dw o f1=2;HBþ ¼ Do fHþ 

(40) RT F

lnðxÞ 

 RT F

ln

KD;B Kaw Kao

.

ðiÞ

w Fig. 1 shows Dw o f1=2 for different pK a values for buffered and

unbuffered aqueous solutions. When aqueous buffered solutions are considered, the half-wave potential can be associated to only

Table 1 Free concentration of the neutral weak base in the organic phase for two pH values and different volume ratios. r

1 0.1 0.01 0.001 0.0001

1

coB ð0; 0Þ,ðcinit B Þ pH 5.0

pH 9.0

0.498 0.901 0.980 0.989 0.990

0.990 9.08 49.8 90.1 98.0

F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498

9

ð2Þ

for Dw o f1=2 (Fig. 2b), respectively. Clearly, these interfacial distributions can be used to identify the chemical species involved in each process. For pH < 4.0, the predominant species are HBþ in the aqueous phase and HBþ in the organic phase. For 4.0 < pH < 6.0, the predominant species are HBþ in the aqueous phase while in the organic phase B and HBþ coexist. Therefore, the global transfer ð1Þ

mechanism and Dw o f1=2 are defined by the following reactions: a simple transfer reaction (transfer of HBþ formed previously in the aqueous phase):

HBþ ðwÞ % HBþ ðoÞ

(RI)

and a facilitated proton transfer by interfacial protonation:

Hþ ðwÞ þ BðoÞ % HBþ ðoÞ

(RII) ð2Þ

On the other hand, for Dw o f1=2 and pH > 4.0, the predominant

and,

species are B and HBþ in organic phase. In this case, concomitantly with the proton transfer process, hydroxide ions are electrogenerated on the aqueous side of the L|L interface. Therefore, the

and 1:0

global transfer mechanism and Dw o f1=2 are defined by the facili-

ðiÞ

Fig. 5. Dependence of the half-wave potentials, Dw o f1=2 , on the pH of the aqueous phase for buffered and unbuffered aqueous solutions for different volume ratios. ð1Þ

Dw o f1=2 for aqueous buffer solutions ð2Þ Dw o f1=2 :

103

r ¼ 1:0 .

pK w a

 101

, 1:0 

, Dw o f1=2 for all volume ratio values

100

, 1:0  101

, 1:0  102

¼ 7:00. All other simulation parameters are the same as in Fig. 1.

one transfer process, which present a linear dependence on pH for pH[pK w a  logð1 þ xKD;B Þ, and a constant value, Df1=2 ¼ w o0 Dw o f1=2;HBþ , for pH≪pK a  logð1 þ xKD;B Þ. On the other hand, for

unbuffered aqueous solutions, the protonated weak base transfer occurs according to two different proton transfer processes. One of w o0 them occurs at low potentials, Dw o f1=2 ¼ Do f1=2;HBþ , related to the direct transfer of HBþ initially formed in the aqueous phase to the organic phase or related to the facilitated proton transfer. At high potential values, the transfer process occurs by facilitated proton transfer via water autoprotolysis. At extremely high initial pH values (pH > 11), the proton transfer process happens at the same half-wave potential value for buffered and unbuffered aqueous solution models. It occurs by facilitated proton transfer for the former model and by facilitated proton transfer via water autoprotolysis for the latter. In unbuffered aqueous solutions, the interfacial buffer capacity rises exponentially with increasing pH, due to water dissociation at the aqueous side of the L|L interface [16]. When the pK w a value increases, the pH range for which the direct transfer of HBþ prevails increases, therefore, the half-wave potentials obtained in buffered and unbuffered solutions are equal (Fig. 1 (a)e(c)). Clearly, the mid-peak potentials obtained directly from the simulated voltammograms (obtained from Eq. (27)) and the half-wave potentials obtained from Eq. (39) present a remarkable agreement. In this sense, Eq. ðiÞ

(39) allows to obtain Dw o f1=2 for different systems and with different experimental conditions. In particular, the evolution of the   ðiÞ interfacial pH, pH 0; Dw o f1=2 , for both half-wave potentials (Eq. (37)) is shown in Fig. 1 (d). It can be seen that the interfacial pH for the first process increases slightly at an initial pH greater than 4.0.   ð2Þ However, concomitantly, the pH 0; Dw corresponding to the o f1=2 second process changes drastically. It increases until it reaches a constant value (ca. 10.7) and at pH > 11, it is directly proportional to the initial pH. Additionally, from this model it is possible to determine the interfacial concentrations of the different species in the biphasic system at each half-wave potential. Fig. 2 shows the interfacial ð1Þ

distribution of species as a function of pH for Dw o f1=2 (Fig. 2a) and

ð2Þ

tated proton transfer via water autoprotolysis:

H2 OðwÞ þ BðoÞ % HBþ ðoÞ þ HO ðwÞ ð2Þ

Finally, for Dw o f1=2

(RIII)

  ð2Þ ¼ c*Btot and pH < 4.0, coHBþ 0; Dw o f1=2

because the first proton transfer process has occurred completely at lower potentials. At these low pH values the only species that can act as a reactant is the protonated base present in the aqueous phase.   ðiÞ Once the value of cw 0; Dw o f1=2 is calculated from Eq. (37), the Hþ interfacial pH, the half-wave potentials and the interfacial distribution of species can be easily determined. Fig. 3 (a) shows a voltammogram obtained from Eq. (27) at pH 5.0, where two perfectly defined charge transfer processes are observed. The first one is associated with reactions (RI) and (RII), and the second with reaction (RIII). With the aim of further comparison between the results of computer simulations and those obtained by Eq. (39), in Fig. 3 (b), the evolution of the interfacial pH is shown, including the interfacial pH and the values of the halfwave potentials obtained by Eqs. (37) and (39). As can be observed, the values calculated with the equation developed in this work, perfectly overlap with the simulated curve. In the same way, panels (c) and (d) show the interfacial concentrations of the predominant species, both in the aqueous phase and in the organic phase. The values of the interfacial concentrations of the different species obtained from solving Eqs. (29), (30) and (39) are included for comparison. Clearly, the results obtained from these equations provide a detailed description of the system under study for each ðiÞ Dw o f1=2 value.

2.2. Effect of initial neutral weak base concentration and volume ratio on the half-wave potential In this section, we focus our attention on the initial neutral weak base concentration and the volume ratio, which are the two main parameters that can straightforwardly be modified in the experimental setup. These can considerably affect the voltammetric response and thus the half-wave potential. Here, the effect of the initial neutral weak base concentration on the facilitated proton transfer process via water autoprotolysis is analysed. Fig. 4 (a)

10

F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498 ð2Þ

shows the variation of Dw o f1=2 for reaction (RIII) as a function of the initial weak base concentration, for two different volume ratio ð2Þ

values. For high total weak base concentration values, Dw o f1=2 presents a linear relation with respect to logðcinit B Þ, with a slope

1 at 25.0  C). This behaviour has equal to 2:303 RT F (59 mV dec already been found by our research group in experimental determinations [18] as well as computer simulations [16,18]. If the

cinit B

is increased in unbuffered solutions, the interfacial pH value of value reached is higher due to water autoprotolysis. Also, the extent of water autoprotolysis is repressed due to the increase in HO ð2Þ

concentration (RIII). Thus an increase in the Dw o f1=2 value is observed. At this point, it is important to remark that for buffered solutions, the half-wave potential does not depend on cinit B (see Eq. (40)) [8,16,18,22]. For comparison, at initial pH 10 and r ¼ 1, the ð2Þ

mid-peak potentials, Dw o fmid , obtained from the simulated voltammograms are shown in the same plot. These values overlap exactly with the

ð2Þ Dw o f1=2

value obtained with Eq. (39).

two orders of magnitude larger than at the lower pH value. ð2Þ

In this sense, the effect of decreasing r values, on Dw o f1=2 , is not similar to only increasing the weak base concentration. In Fig. 5, ðiÞ Dw o f1=2 as a function of initial pH for different r values are shown.

While the half-wave potential of the first proton transfer process (RI-RII) remains invariant with the different r values, similar to (see Fig. 4 (c)). The second process what was observed with cinit B shows a complete different behaviour. The half-wave potential ð2Þ

reaches the same Dw o f1=2 value for low initial pH (pH approx. 4e5) and for all values of r < 1. This behaviour can be interpreted considering the distribution of species at t ¼ 0. Without loss of generality, an acceptable assumption is to consider the free concentration of HBþ in the organic phase negligible. In this way, the coB ðx; 0Þ and in particular in the L|L interface (x ¼ 0), can be known [6]:





coB ð0; 0Þ ¼

aB KD;B cinit 1 þ r aB KD;B B

being aB ¼

Kw a . w Kw a þcHþ ð0;0Þ

(41)

For the same volume ratio but different initial pH, half-wave potentials match exactly at high initial weak base concentration values. This behaviour is due to the change in interfacial pH caused by the water autoprotolysis. The evolution of interfacial pH for two volume ratios and two different initial pH values is shown in Fig. 4 (b). For both volume ratio values, the interfacial pH values are equal   ð2Þ init values, because the interfacial (pH 0; Dw o f1=2 > 11) at high cB

According to Eq. (41), if r aB KD;B ≪1, then coB ð0; 0Þ ¼ aB KD;B cinit B . In this limiting case, coB ð0; 0Þ is independent of the value of r, therefore

buffer capacity rises exponentially with increasing pH. In Fig. 4 (c)

shown in Fig. 5 at pH 5.0, coB ð0; 0Þ,ðcinit B Þ

the

ðiÞ Dw o f1=2

values are shown as a function of the initial pH for

different cinit values. In general, two different effects can be B observed in this graph, first, that increases the pH range where both proton transfer processes (RI-RII and RIII) coexist and, second, that ð1Þ Dw o f1=2

cinit B

for the first process (RI-RII) remains invariant with different

ð2Þ Dw o f1=2 remains constant.

According to the chemical system used to obtain the results 1

pH > 7, when r decreases,

ð2Þ Dw o f1=2

1 (see Table 1). For ¼ 1þr

increases. However, coB ð0; 0Þ de1 ¼ aB KD;B . 1 o init cB ð0; 0Þ,ðcB Þ xKD;B (see

creases until it reaches a constant value, coB ð0; 0Þ,ðcinit B Þ For example, at pH 9.0, aB x1 and Table 1).

ð2Þ

values while Dw o f1=2 increases.

In general, for r < 1 and pH[pK w a  logðKD;B Þ, the free concentration of the neutral weak base (considering KD;B [ 1) in the organic phase increases with decreasing volume ratios. This is known as preconcentration effect [6]. Table 1 summarizes coB ð0; 0Þ,

2.3. Simplified equation to describe the half-wave potential for the reaction (RIII)

ðcinit as a function of r for two different pH values. As can be B Þ observed at the higher pH value, this concentrations ratio is almost

tool for the experimentalists. if pH[pK w a  logð1 þ xKD;B Þ, the cubic and quadratic terms (first and second terms) of Eq. (33) are negligible. In this conditions, Eq. (33) is reduced to:

1

ð2Þ

This section is devoted to simplifying Eq. (33) for Dw o f1=2, as a

ð2Þ

init Fig. 6. Dependence of the half-wave potential for the facilitated proton transfer via water autoprotolysis, Dw , 9:00 , o f1=2 , on the logðcB Þ. Panel (a): r ¼ 1:00. Initial pH 8:00 10:0 , 11:0 and 12:0 . Half-wave potential obtained using Eq. (49). Panel (b): pH 10:0. r ¼ 1:0  102 , 1:0  101 , 1:0  100 and 1:0 101 . Halfw wave potential obtained using Eq. (49) for different volume ratios. pK a ¼ 7:00. All other simulation parameters are the same as in Fig. 1.

F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498

bcw Hþ



ð2Þ 0; Dw o f1=2



11

init On the other hand, at pH > pK w a and high cB values, c ¼ 1, b þ

þc¼0

(42)

c*chargetot ¼ 

aB ð1þxKD;B Þcinit o B 2ð1þr aB KD;B Þ and K a ð1 þ xKD;B Þ≪1. In these conditions,

Eq. (45) can be rewritten as: where b and c are defined in Eq. (34). Therefore, the concentration of protons on both side of the interface is determined by the following equation:

  Kw Kaw KD;B 1 þ xKD;B   2    b þ c*chargetot 1 þ xKD;B KD;B Kaw  Kw KD;B D;B

  c ð2Þ 0; Dw ¼ ¼ cw o f1=2 Hþ b cK o K w 1 þ xK a

a

and

  ð2Þ ¼ coHþ 0; Dw o f1=2

cKao

! h

xKD;B Kaw

ð2Þ Dw o f1=2

 1 þ xKD;B Kaw

 i ð2Þ 0; Dw þ cw o f1=2 Hþ

(44)

Replacing Eqs. (43) and (44) in Eq. (28), the following simplified equation is obtained for

ð2Þ Dw o f1=2 :

 RT RT  lnðcÞ þ ln 1 þ xKD;B þ F F h  i    cKao 1 þ xKD;B  b þ c*chargetot KD;B

ð2Þ w o0 Dw o f1=2 ¼ Do f1=2;HBþ þ

RT Kaw ln F Kw KD;B

(43)

"   #  w aB 1 þ xKD;B 2 RT RT K   þ ln ln a ¼ þ F F Kw 2 1 þ r aB KD;B   2:303RT log cinit þ B F (49) o0 Dw o f1=2;HBþ

ð2Þ

init Consequently, the dependence of Dw o f1=2 on logðcB Þ values is a

1 at 25.0  C) and straight line with the slope of 2:303 RT F (59 mV dec the intercept is slightly dependent of the initial pH value (aB x1 for ð2Þ

w pH > pK w a ). To analyse this behaviour, the dependence of Do f1=2

with logðcinit B Þ, for different initial pH values, is shown in Fig. 6 (a). This figure compares the results obtained with Eqs. (44) and (48). ð2Þ

Clearly, the approximate Dw o f1=2

using Eq. (49) coincides

(45)

completely with the linear interval obtained with Eq. (45). In

Considering Eq. (41), it is possible to express c and bþ c*chargetot

addition, as the initial pH decreases, this interval of logðcinit B Þ increases in range. Additionally, in Fig. 6 (b) the effect of the volume

as follows:

    w 2  aB þ xaB KD;B cinit B þ 1 þ r aB KD;B cHþ ð0; 0Þ  c¼    w aB 1 þ xaB KD;B cinit B  1 þ r aB KD;B cHþ ð0; 0Þ

ð2Þ

ratio on Dw o f1=2 is shown by comparing the results obtained by

(46)

and

b þ c*chargetot ¼

cw ð0; 0Þ Hþ 2



  aB 1 þ xKD;B cinit Kw B   ð0; 0Þ cw 2 1 þ r aB KD;B Hþ

(47)

Eq. (45) allows to obtain the half-wave potential for reaction (RIII) in a wide range of experimental conditions. In particular, we will use Eq. (45) to demonstrate the slopes observed, at pH[ ð2Þ

w init pK w a  logð1 þxKD;B Þ for Do f1=2 vs. pH (see Fig. 1) and at high cB ð2Þ

init values for Dw o f1=2 vs. logðcB Þ (see Fig. 4 (a)).

At pH[pK w a  logð1 þ xKD;B Þ, it can be shown that c ¼ 1, bþ c*chargetot

w ¼ cw Kð0;0Þ and K oa ð1 þ xKD;B Þ≪1. In these conditions, Eq. Hþ

(45) can be rewritten as: ð2Þ w o0 Dw o f1=2 ¼ Do f1=2;HBþ þ

  2:303RT RT w  ln Ka 1 þ xKD;B þ pH F F (48) ð2Þ

Consequently, the dependence of Dw o f1=2 on pH values is a 1 at 25.0  C). This straight line with the slope of 2:303 RT F (59 mV dec equation can be directly compared with Eq. (40), obtained for o0 Df1=2 ¼ Dw buffer solutions, rewritten: o f1=2;HBþ þ

   RT ln K w 1 þ xK 2:303RT w pH [2,22]. D;B þ cHþ þ a F F

means of Eqs. (45) and (49). Eq. (49) adequately describes the slope of the straight lines and the dependence of the intercept with r. Intercept value decreases with increasing r and becomes independent when r/0 (data not shown). 3. Conclusion In this work, the equations describing the half-wave potentials, ðiÞ Dw o f1=2 ,

of facilitated proton transfer or protonated species transfer

across L|L interfaces, explicitly considering the water autoprotolysis equilibrium, were developed. The main equation (Eq. (39)) developed in this research allows to simulate different chemical systems, under different experimental conditions, in unbuffered aqueous solutions. The pH dependence of the half-wave potentials are compared for calculated results according to Eq. (39), and simulated results using a previous model developed in Ref. [16]. This comparison clearly confirms the validity of the half-wave potential equations developed in this work. Both the effect of the initial concentration of the neutral weak base, and the volume ratio of the aqueous to organic phases on the half-wave potentials were analysed. Furthermore, approximate equations that allow not only to adequately justify the behaviour of the half-wave potentials with the volume ratio and the initial concentration of the weak base, but can also be used as a tool to explain or predict experimental results were developed. Moreover, for a given experimental system under study, it is possible to know whether the processes of facilitated proton transfer via water

12

F.M. Zanotto et al. / Electrochimica Acta 332 (2020) 135498

autoprotolysis occur or not within the accessible potential window by the transfer of the charged species of supporting electrolytes. This last analysis is possible using the complete (Eq. (39)) or approximate (Eq. (45)) analytical equations.

[14]

Author Contributions Section

[15]

Franco M. Zanotto: Conceptualization, Calculation, Formal
ndez: Analysis, Writing-Review & Editing. Ricardo Ariel Ferna Formal Analysis, Writing-Original Draft, Writing-Review & Editing. Sergio Alberto Dassie: Funding Acquisition, Conceptualization, Validation and Data Curation, Writing-Original Draft, WritingReview & Editing, Supervision.

[16]

[17]

[18]

Acknowledgement R.A.F. and S.A.D. are researchers of Consejo Nacional de Inves
cnicas (CONICET). F.M.Z. thanks CONICET tigaciones Científicas y Te for the fellowships granted. Financial support from CONICET (PIP 00174) and Secretaría de Ciencia y Tecnología (SECyT-UNC) are gratefully acknowledged. The authors thank the anonymous reviewers for their useful comments.

[19]

[20]

[21]

Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.electacta.2019.135498.

[22]

[23]

References [1] D. Homolka, V. Mare cek, Z. Samec, K. Base, H. Wendt, The partition of amines between water and an organic solvent phase, J. Electroanal. Chem. Interfacial Electrochem. 163 (1984) 159e170, https://doi.org/10.1016/S0022-0728(84) 80049-2. [2] Y. Kubota, H. Katano, K. Maeda, M. Senda, Voltammetric study of the partition of amines between water and an organic solvent, Electrochim. Acta 44 (1998) 109e116, https://doi.org/10.1016/S0013-4686(98)00158-3. [3] F. Reymond, P.-A. Carrupt, B. Testa, H.H. Girault, Charge and delocalisation effects on the lipophilicity of protonable drugs, Chem. Eur J. 5 (1999) 39e47, https://doi.org/10.1002/(SICI)1521-3765(19990104)5:1<39::AIDCHEM39>3.3.CO;2-V. [4] H. Alemu, Voltammetry of drugs at the interface between two immiscible electrolyte solutions, Pure Appl. Chem. 76 (2004) 697e705, https://doi.org/ 10.1351/pac200476040697.
, H.H. Girault, Ion amperometry at the interface between [5] Z. Samec, E. Samcova two immiscible electrolyte solutions in view of realizing the amperometric ion-selective electrode, Talanta 63 (2004) 21e32, https://doi.org/10.1016/ j.talanta.2003.11.023. [6] J.I. Garcia, R.A. Fern
andez, A.J. Ruggeri, S.A. Dassie, Novel electrochemical approach to the determination of the partition coefficient of neutral weak bases, J. Electroanal. Chem. 594 (2006) 80e88, https://doi.org/10.1016/ j.jelechem.2006.05.034. [7] R.A. Fern
andez, M.I. Velasco, L.I. Rossi, S.A. Dassie, Transfer of tylosin across the H2O/1,2-dichloroethane interface. Analysis of degraded product in acid solutions, J. Electroanal. Chem. 650 (2010) 47e54, https://doi.org/10.1016/ j.jelechem.2010.09.008. [8] J.I. Garcia, M.B. Oviedo, S.A. Dassie, Effect of ligand protonation on the facilitated ion transfer reactions across oil/water interfaces. IV. Buffer solution effect, J. Electroanal. Chem. 645 (2010) 1e9, https://doi.org/10.1016/ j.jelechem.2010.02.035. [9] L. Poltorak, I. Eggink, M. Hoitink, M. De Puit, Electrified soft interface as a selective sensor for cocaine detection in street samples, Anal. Chem. 90 (2018) 7428e7433, https://doi.org/10.1021/acs.analchem.8b00916. [10] M. De Puit, L. Poltorak, E.J.R. Sudh, Electrochemical cocaine (bio)sensing. From solid electrodes to soft junctions, Trends Anal. Chem. 114 (2019) 48e55, https://doi.org/10.1016/j.trac.2019.02.025. €ki, Electrochemical determination of partition co[11] K. Kontturi, L. Murtoma efficients of drugs, J. Pharm. Sci. 81 (1992) 970e975, https://doi.org/10.1002/ jps.2600811003. €ki, K. Kontturi, Correction to “Electrochemical determination of [12] L. Murtoma partition coefficients of drugs”, J. Pharm. Sci. 81 (1992) 970e974, https:// doi.org/10.1002/jps.10139. J. Pharm. Sci. 91 (2002) 900e901. [13] F. Vega Mercado, J.M. Ovejero, F.M. Zanotto, M.R. Serial, M.I. Velasco, R.A. Fern
andez, R.H. Acosta, S.A. Dassie, Facilitated proton transfer across liquid|liquid interfaces under forced hydrodynamic conditions. Determination

[24]

[25]

[26]

[27]

[28] [29]

[30] [31] [32]

[33] [34] [35] [36]

[37]

[38]

of partition coefficient of neutral weak bases, J. Electroanal. Chem. 791 (2017) 64e74, https://doi.org/10.1016/j.jelechem.2017.03.005. F. Reymond, P.-F. Brevet, P.-A. Carrupt, H.H. Girault, Cyclic voltammetry for the transfer of multiple charged ions at large ITIES: general computational methodology and application to simple and facilitated ion transfer reactions, J. Electroanal. Chem. 424 (1997) 121e139, https://doi.org/10.1016/S00220728(96)04933-9. S. Sawada, T. Osakai, Hydrophobicity of oligopeptides: a voltammetric study of the transfer of dipeptides facilitated by dibenzo-18-crown-6 at the nitrobenzene/water interface, Phys. Chem. Chem. Phys. 1 (1999) 4819e4825, https://doi.org/10.1039/a905609b. S.A. Dassie, Effect of ligand protonation on the facilitated ion transfer reactions across oil|water interfaces. I. Water autoprotolysis, J. Electroanal. Chem. 578 (2005) 159e170, https://doi.org/10.1016/j.jelechem.2004.12.035. S.A. Dassie, Effect of ligand protonation on the facilitated ion transfer reactions across oil|water interfaces. II. Complex formation, J. Electroanal. Chem. 585 (2005) 256e268, https://doi.org/10.1016/j.jelechem.2005.09.001. J.I. Garcia, R.A. Iglesias, S.A. Dassie, Effect of ligand protonation on the facilitated ion transfer reactions across oil|water interfaces. III. Digital simulation and experimental approach, J. Electroanal. Chem. 586 (2006) 225e236, https://doi.org/10.1016/j.jelechem.2005.10.009. J.I. Garcia, M.B. Oviedo, S.A. Dassie, Effect of ligand protonation on the facilitated ion transfer reactions across oil/water interfaces. IV. Buffer solution effect, J. Electroanal. Chem. 645 (2010) 1e9, https://doi.org/10.1016/ j.jelechem.2010.02.035. ~ o, A. Molina, C. Serna, F. Karimian, Facilitated ion transfer E. Torralba, J. a Ortun of protonated primary organic amines studied by square wave voltammetry and chronoamperometry, Anal. Chim. Acta 826 (2014) 12e20, https://doi.org/ 10.1016/j.aca.2014.04.009.
ndez, R.A. Iglesias, S.A. Dassie, Facilitated proton F. Vega Mercado, R.A. Ferna transfer reactions via water autoprotolysis across oil|water interfaces, Spectroelectrochemical analysis, Electrochim. Acta. 299 (2019) 430e440, https:// doi.org/10.1016/j.electacta.2019.01.022. S.A. Dassie, Facilitated proton transfer or protonated species transfer reactions across oil|water interfaces, J. Electroanal. Chem. 728 (2014) 51e59, https:// doi.org/10.1016/j.jelechem.2014.06.020. F. Vega Mercado, F.M. Zanotto, R.A. Fern
andez, S.A. Dassie, Ion transfer of weak acids across liquid|liquid interfaces, J. Electroanal. Chem. 774 (2016) 111e121, https://doi.org/10.1016/j.jelechem.2016.05.012.
ndez, S.A. Dassie, Facilitated proton transfer-electron F.M. Zanotto, R.A. Ferna transfer coupled reactions at thick-film modified electrodes, Electrochim. Acta 258 (2017) 727e734, https://doi.org/10.1016/j.electacta.2017.11.119.
ndez, S.A. Dassie, An integrated F.M. Zanotto, T.A. Hern
andez, R.A. Ferna theoretical-experimental approach to understand facilitated proton transferelectron transfer coupled reactions at thick-film modified electrodes, Electrochim. Acta 283 (2018) 1719e1731, https://doi.org/10.1016/ j.electacta.2018.07.053.
ndez, S.A. Dassie, Effect of ligand F. Vega Mercado, J.M. Ovejero, R.A. Ferna protonation on the facilitated ion transfer reactions across oil|water interfaces. V. Applications of forced hydrodynamic conditions, J. Electroanal. Chem. 765 (2016) 100e104, https://doi.org/10.1016/j.jelechem.2015.08.001. H. Matsuda, Y. Yamada, K. Kanamori, Y. Kudo, Y. Takeda, On the facilitation effect of neutral macrocyclic ligands on the ion transfer across the interface between aqueous and organic solutions. I. Theoretical equation of ion-transfer polarographic current-potential curves and its experimental verification, Bull. Chem. Soc. Jpn. 64 (1991) 1497e1508, https://doi.org/10.1246/bcsj.64.1497. I.M. Kolthoff, E.B. Sandell, E.J. Meehan, S. Bruckenstein, Quantitative Chemical Analysis, 4th ed., Macmillan Publishers Limited, London, 1969. J. Kovac, Using the logarithmic concentration diagram, log C, to teach acidbase equilibrium, J. Chem. Educ. 89 (2012) 905e909, https://doi.org/ 10.1021/ed200675r. R. Greef, R. Peat, L.M. Peter, D. Pletcher, J. Robinson, Instrumental Methods in Electrochemistry, John Wiley & Sons, Southampton, 1985. A.J. Bard, C.R. Faulkner, Electrochemical Methods, Fundamentals and Applications, second ed., John Wiley & Sons, New York, 2001. F. Reymond, G. Steyaert, P.-A. Carrupt, B. Testa, H.H. Girault, Mechanism of transfer of a basic drug across the water/1,2-dichloroethane interface: the case of quinidine, Helv. Chim. Acta 79 (1996) 101e117, https://doi.org/ 10.1002/hlca.19960790111. R.S. Nicholson, I. Shain, Theory of stationary electrode polarography, Anal. Chem. 36 (1964) 706e723, https://doi.org/10.1021/ac60210a007. A.J. Parker, Protic-dipolar aprotic solvent effects on rates of bimolecular reactions, Chem. Rev. 69 (1969) 1e32, https://doi.org/10.1021/cr60257a001. F. Scholz (Ed.), Electroanalytical Methods: Guide to Experiments and Applications, 2nd ed., Springer-Verlag, 2010. W.H. Press, S.A. Teukolsky, I.T. Vetterling, B.P. Flannery, Numerical Recipes. The Art of Scientific Computing, third ed., Cambridge University Press, New York, 2007. A. Sabela, V. Mare cek, Z. Samec, R. Fuoco, Standard Gibbs energies of transfer of univalent ions from water to 1,2-dichloroethane, Electrochim. Acta 37 (1992) 231e235, https://doi.org/10.1016/0013-4686(92)85008-9.
ndez, F. Cortes-Salazar, H.H. Girault, Voltammetric deterA.J. Olaya, M.a. Me mination of extreme standard Gibbs ion transfer energy, J. Electroanal. Chem. 644 (2010) 60e66, https://doi.org/10.1016/j.jelechem.2010.03.030.