Introduction

Complex formation between cyclodextrin, CD [1] (cyclic oligosaccharides composed of seven d-glucose units) and viologens [2] can be electrochemically influenced through bringing changes in the oxidation states of viologen. Viologens have received much attention owing to their versatile redox system having three oxidation states: V2+, V+• and V∘.

$${\text{V}}^{2 + } + {\text{e}} \leftrightarrow {\text{V}}^{ + \bullet }$$
(1)
$${\text{V}}^{ + \cdot } + {\text{ e}} \leftrightarrow {\text{V}}^{ \circ }$$
(2)

Viologen cation radical may be soluble or can form a deposit on the electrode but the neutral form of viologen is almost insoluble in aqueous media. Complexation of reduced form of viologen with βCD resolves the problem of dimer formation and precipitation [3–5]. A number of studies [6–8] have been published exploring CD-viologen interactions, but these studies relied heavily on digital simulation and hardly any kinetics study has been explored.

Simulation, in general, is extensively used to obtain information about phenomena/processes studied. However, they may give ambiguous results in the case of chemically coupled electrochemical processes [9, 10]. At the same time, a most useful utilization of the cyclic voltammetry is in obtaining thermodynamic and kinetic parameters (such as equilibrium constant and rate constants, respectively) for chemically coupled electrochemical processes through the use of the theory of stationary electrode voltammetry. Once (thus) obtained, these parameters can be used in the simulation of experimentally recorded cyclic voltammograms for such chemically coupled electrochemical process as encountered in the present case. It may be noted that sound theoretical treatment and elegant equations are available in the literature for many chemically coupled electrochemical processes [11, 12].

So far, in the case of kinetics study on viologens, previous works [13, 14] relied on the measurement of peak current ratios—a method which becomes less reliable in aqueous medium due to dimerization and deposition problems associated with V+• and/or V∘.

Through such an electrochemical approach [11, 12] and simulation technique, as adopted in the present study, it is not only possible to obtain the formation constants and rate constants but also the number of βCD forming the complex with a V+• and/or V∘ molecule.

Thus, the objective of this investigation is to obtain the formation constants, the rate constants of formation and the association numbers of the complex formed between reduced species of Ev2+ and βCD.

Experimental

Chemicals

β-Cyclodextrin (Merck) and Ethyl Viologen dibromide (Merck) were used as received without any further purification. Buffer solution of pH 7 (Merck) and double deionized water were used. None of the reagents was found to show any spurious electrochemical signal in the voltage window of interest.

Electrochemical experiments

Electrochemical measurements were carried out on the Electrochemical Analyzer (Model CHI600C Series). For Cyclic voltammograms (CV), a glassy carbon electrode 3 mm in diameter, a platinum wire auxiliary electrode and a saturated calomel reference electrode (SCE) were used. Before taking each run, the glassy carbon electrode was polished with 0.05 μm alumina on a felt surface and rinsed with double deionized water.

The concentration of ethyl viologen dibromide solutions was typically in the range of 0.3–1.0 mM, to which varied concentration of βCD ranging from 0.31 to 12.0 mM was added. All solutions were prepared in buffer solution of pH 7 and before recording a cyclic voltammogram, were purged with nitrogen gas for 15 min to eliminate oxygen. Cyclic voltammograms were recorded for the buffer solution (pH 7). CV of blank buffer solution did not show presence of any electro-active species in the solution. The scan rates were 0.02, … 0.4 V/s. Simulation was carried out with DigiSim software (BAS E’CHEM Electrochemical Products Group).

Results and discussions

All viologens studied by various workers are known to exhibit two (reversible) reduction peaks corresponding to two single electron reductions. The two reduction waves of ethyl viologen dication (Ev2+) were observed by cyclic voltammetry in buffer of pH 7 versus the SCE (Fig. 1, solid line).

Fig. 1
figure 1

CVs of 0.602 mM ethyl viologen in the absence (solid line) and the presence (dotted line) of 11.89 mM βCD. Scan rate: 0.05 V/s, Temperature: 25 °C

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In the presence of a host (βCD), cathodic peak position of Ev2+ shifted in positive direction. The second reduction peak in particular shifted significantly, as shown in Fig. 1.

The complexation phenomena

Characterization of Electron transfer reaction coupled to chemical reaction

The coupling of chemical reactions to the electron transfer reactions can lead to changes in the peak potentials and peak currents. If the ratio of anodic to cathodic peak currents is unity and is not affected by switching potential, any coupled chemical reaction is ruled out [11]. It is a best diagnostic criterion for the investigation of the coupled chemical reactions. When βCD solutions of concentration between 0.3 and 12 mM are added to the ethyl viologen solution of concentration 0.60 mM, the Ipa/Ipc values for the corresponding Ev2+/Ev+• redox process, Eq. (1), remain close to unity even at 0.4 V/s scan rate (Table 1) indicating no significant effect of the addition of βCD on this electrochemical process.

Table 1 Effect of the addition of βCD host on peak current ratios measured for ethyl viologen solution at different scan rates
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It may thus be concluded that the reaction of βCD with Ev+•, if any, is slow and that Ev+• does not significantly bind with βCD. When Ev2+, in aqueous media, gets reduced to Ev∘, the later having poor solubility in water gets deposited on the electrode surface, giving rise to a corresponding oxidation peak which is sharp, symmetrical and much bigger in size. On the addition of βCD to Ev2+ solution, even when the ratio of βCD to Ev2+ is 2:1, no perceptible effect was found on either peak position or peak shape associated with the (two) reduction processes.

When the ratio (of βCD to Ev2+) is increased to five (times) or higher, the shape as well as the position of the peak associated with the second reduction process (Ev+• to Ev∘) gets affected (Figs. 2, 3).The huge, sharp and symmetrical second anodic peak changed into a regular cyclic voltammetric anodic wave, characteristic of a reversible process. The ratio of anodic to cathodic peak currents approaches unity, indicating the reversibility of the process as well as possibility of coupled (reversible) chemical reaction.

Fig. 2
figure 2

CVs of 0.602 mM Ethyl viologen (0.1 V/s) in the absence (a), and in the presence of various concentration (b–i) of βCD host, in phosphate buffer of pH 7; (b) = 0.313 mM, (c) = 0.626 mM, (d) = 0.938 mM, (e) = 1.25 mM, (f) = 3.13 mM, (g) = 6.26 mM, (h) = 9.07 mM, (i) = 11.89 mM

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Fig. 3
figure 3

CVs of 1.006 mM Ethyl viologen (0.1 V/s) in the absence (a) and in the presence of various concentration (b–e) of βCD host in phosphate buffer of pH 7: (b) = 0.5 mM, (c) = 1.01 mM, (d) = 5.03 mM, (e) = 10.06 mM

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Evaluation of equilibrium constants for the formation of Ev+•−nβCD and Ev∘−mβCD complex

It has been found experimentally that the interaction between Ev2+ and βCD, if any, is very weak as evidenced by the absence of any CE (a chemical reaction followed by a reversible electron transfer) effect on the Cyclic voltammogram of Ev2+ (Fig. 2).

From the observation on the shape and position of the two peaks, on the addition of βCD, a scheme (Scheme 1) may be proposed for the interaction of βCD with Ev2+/Ev+•/Ev∘.

The expression for the equilibrium constant for the complexation associated with the first reduction step can be written as Eq. (3) [15].

$$E_{\text{P1}} = \, E_{{_{\text{P1}} }}^{ \circ } + \frac{RT}{F} { \ln }\left( { 1+ K_{\text{eq}}^{(1)} \left[ \beta {{\text{CD}}} \right]^{n} } \right)$$
(3)

Where \(E_{{_{\text{P1}} }}^{ \circ }\) and E P1 are the peak potentials of Ev2+ in the absence and in the presence of βCD, respectively. \(K_{\text{eq}}^{(1)}\) is the formation constant for Ev+•−βCD complexation, n is the number of βCD associated with one Ev+•. If \(K_{\text{eq}}^{(1)} \left[ \beta{{\text{ CD}}} \right]^n \gg 1\), then Eq. (3) is reduced to

$$E_{\text{P1}} = E_{\text{P1}}^{ \circ } + \left( \frac{RT}{F} \right){ \ln }K_{\text{eq}}^{(1)} + \frac{nRT}{F} { \ln }\left[ \beta{{\text{ CD}}} \right]$$
(4)

A value of n could be obtained from approximate ln[βCD]—E p1 relationship at higher concentration range of βCD which gave a value of 0.54 for n.

One can obtain the equilibrium constant for the first reduction step by plotting the right hand side (RHS) of Eq. (5) against [βCD]0.54.

$${ \exp }^{\left[ {f\left( {E_{\text{p1}} - E_{\text{p1}}^\circ } \right)} \right]} = { 1} + \, K_{\text{eq}}^{(1)} {\left[ \beta{{\text{ CD}}} \right]}^{0. 5 4}$$
(5)

where f = F/RT. Such a plot is shown in Fig. (4).

Fig. 4
figure 4

Plot of the function \({ \exp }^{\left[ {f\left( {E_{{{\text{p}}1}} - E_{\text{p1}}^{ \circ } } \right)} \right]}\) for the first reduction step against βCD concentrations, f = F/RT

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The value of \(K_{\text{eq}}^{(1)}\) thus obtained is 13.6 M–n.

Gupta and Linshitz [16] have also reported n = 0.5 for the hydrogen bonding of the anion radical of dichlorobenzoquinone with tetrafluoroethanol. They neither elaborated the significance of n nor commented upon the numerical value n = 0.5.

This value of n = 0.54 may be coming from the participation of dimer of \({\text{Ev}}^{ + \bullet } - \, \left( {{\text{Ev}}^{ + \bullet } } \right)_{ 2}\)—in the association process with βCD. This dimerization of viologen cation radical is a known phenomenon [3–5, 17].

Second equilibrium constant \({\text{K}}_{\text{eq}}^{(2)}\) can be determined from Eq. (6) [15].

$${ \exp }\,\left[ {f\left( {E_{\text{p2}} - E_{\text{p2}}^\circ } \right)} \right] = \frac{{1 + K_{\text{eq}}^{ ( 2 )} [\beta{\text{ CD]}}^{\text{m}} }}{{1 + K_{\text{eq}}^{ ( 1 )} [\beta{\text{ CD]}}^{n} }}$$
(6)

Where m is the number of βCD associated with one neutral ethyl viologen Ev∘ and \(K_{\text{eq}}^{(2)}\) is the corresponding equilibrium constant. In case of strong association between host and guests, we may ignore 1 from numerator as well as denominator. The value of m–n can be determined from the plot of second cathodic peak potential (E P2) against ln[βCD]. This plot is shown in Fig. (5). The value of m–n thus obtained from slope is 0.71 which yields m = 1.25. However, if \({{1}} \gg K_{\text{eq}}^{(1)} [\beta{\text{ CD}}]^{n} ,\) then from Eq. (6) a plot of E P2 vs lnβCD will directly give the value of m. With n, m and \({\text{K}}_{\text{eq}}^{(1)}\) known, \(K_{\text{eq}}^{(2)}\) can be obtained from Eqs. (6) or (7).

Fig. 5
figure 5

Plot of the peak potential for the second reduction step against ln[βCD]

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$$\left\{ {{ \exp }^{\left[ {f\left( {E_{\text{p2}} - E_{\text{p2}}^{\text{o}} } \right)} \right]}} \right\}\left\{ { 1+ K_{\text{eq}}^{(1)} {\left[ \beta{{\text{ CD }}} \right]}^{n} } \right\} = 1+ K_{\text{eq}}^{(2)} {\left[ \beta{{\text{ CD}}} \right]}^{m}$$
(7)

A plot between the LHS of Eq. (7) against [βCD]m is shown in Fig. (6); a straight line is obtained. The slope of the plot yielded \(K_{\text{eq}}^{(2)} = { 2}. 1\times 10^{ 3} {\text{M}}^{ - m}\).

Fig. 6
figure 6

Plot of the function \(\left\{ {{ \exp }^{\left[ {f\left( {E_{\text{p2}} - E_{\text{p2}}^{ \circ } } \right)} \right]} \, } \right\}\left\{ { 1+ {\text{ K}}_{\text{eq}}^{(1)} {\left[ {\beta {\text{CD}}} \right]}^{n} } \right\}\) for the second reduction step against βCD concentrations, f = F/RT

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These values of \(K_{\text{eq}}^{(1)}\) and \(K_{\text{eq}}^{(2)}\) compare well with the values of formation constant reported for other CD-viologen inclusion complexes [6].

The values of equilibrium constant thus obtained get further support from the simulation of CVs (Fig. 7) (see below).

Fig. 7
figure 7

Overlays of experimental (solid line) and simulated (dotted line) Cvs of 0.602 mM ethyl viologen with 9.07 mM βCD

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The neutral ethyl viologen (Ev∘) has a formation constant with βCD which is at least 100 times that of the oxidized form, Ev+•. βCD has empty cone-like shape with non-polar interior and polar exterior of the cavity. Formation of the inclusion complex depends on the geometric compatibility between host cavity and the guest and also on the polarity and charge of the guest. Neutral molecules can easily be included in the βCD cavity as compared to its ionized counterpart Ev+•. This quantitative determination of equilibrium constant establishes that the neutral form of ethyl viologen dication forms much stronger complex with βCD as compared to its charged form (Ev+•).

Rate constants for the formation of viologen-βCD complex

When CVs of ethyl viologen dication were recorded in higher concentration range of βCD at various scan rates, it was observed that the ratio of peak currents corresponding to second reduction process (Ev+•/Ev∘) increased with the increasing scan rates (see Table 1). It showed that there was greater contribution of uncomplexed Ev∘ at higher scan rates. From this, it is inferred that at slow scan rate, more Ev∘ had complexed by the time the (Ep)a was reached. This indicates that the kinetics of formation of Ev∘−βCD complex is not quite as fast. Peak current ratio related to first reduction process was not found to be significantly affected. It is noted that the charged form of ethyl viologen (Ev+•) has low formation constant with βCD which also indicates that the rate of complex formation for Ev+• could be quite slow.

Rate constant for the reaction of Ev∘ with βCD could easily be obtained using the Nicholson-Shain theory [11] for the case in which a reversible chemical reaction follows a reversible charge transfer.

$${\text{O}} + {\text{e}} \leftrightarrow {\text{R}}$$
(8)
$${\text{R }} + \, \left[ {\text{A}} \right] \rightleftharpoons {\text{Z}},\,\, \ldots \,{\text{K}}$$
(9)

where O = Ev+•, R = Ev∘, A = βCD (which is in “large” excess), Z = Ev∘−βCD complex, \({{K_{\text{NS}} = k_{f}^{/} } \mathord{\left/ {\vphantom {{K_{\text{NS}} = k_{f}^{/} } {k_{\text{b}} }}} \right. \kern-0pt} {k_{\text{b}}, }}\)where K NS is equilibrium constant and \(k_{f}^{/}\)is pseudo-first order rate constant for forward reaction, whereas k b is first order reverse reaction. NS notates Nicholson-Shain.

By assuming a 1:1 interaction between Ev∘ and βCD and βCD is in large excess, a pseudo-first order rate constant \(\left( {k_{f}^{/} } \right)\) can be obtained from Eq. (10).

$$\begin{gathered} E_{{{\text{p}} }} = E_{ 1/ 2} - \left( \frac{RT}{nF} \right) [0. 7 8 { } + { \ln }K_{\text{NS}} \left( {{\text{a}}/l} \right)^{ 1/ 2} \hfill \\ - ln\left( { 1+ \, K_{\text{NS}} } \right)] \hfill \\ \end{gathered}$$
(10)

where \(l = k_{f}^{/} + {\text{k}}_{\text{b}} ,K_{\text{NS}} = K \times [\beta{\text{ CD}}],\) E p is the peak potential of viologen in the presence of βCD; E 1/2 is the half wave potential of viologen in absence of host and \({\text{a}} = {\text{nF}}\;\upsilon /{\text{RT}}\) (\(\upsilon\) is scan rate, Vs−1). From this pseudo-first order rate constant, second order rate constant k 2 could be obtained using Eq. (11).

$$k_{ 2} = {{k_{f}^{/} } \mathord{\left/ {\vphantom {{k_{f}^{/} } {\left[ \beta{{\text{ CD}}} \right]}}} \right. \kern-0pt} {\left[ \beta{{\text{ CD}}} \right]}}$$
(11)

The pseudo-first order condition was maintained using [βCD] about 10–20 times [Ev2+].

k 2 for the reaction

$${\text{EV}}^{ \circ } + \beta{\text{ CD}} \leftrightarrow \left[ {{\text{EV}}^{ \circ } - \beta{\text{ CD}}} \right]$$

was calculated to be 3.03 × 103 M−1s−1 and value of k b = 1.45 s−1.

These values of k 2 and k b were used in the simulation of the experimental CVs.

In the course of the investigation on the kinetics of Ev∘−βCD complex, it was found that in 1:9 (v/v) DMF/H2O solvent system, the second electron transfer step of Ev2+ followed an irreversible chemical reaction as,

$${\text{Ev}}^{ + \bullet } \;{\text{e}} \leftrightarrow \;\;{\text{EV}}^{^\circ }$$
(12)
$${\text{EV}}^{ \circ } + \left[\beta {{\text{ CD}}} \right] \to {\text{EV}}^{ \circ } - \beta{\text{ CD}}$$
(13)

On the other hand, in the same 1:9 DMF/H2O solvent system, no change was recorded in the peak current and/or in the peak position of first reduction step of Ev2+ on the addition of βCD as evident from Fig. 8.

Fig. 8
figure 8

Cvs of 0.396 mM ethyl viologen (0.05 V/s) in the absence (a) and in the presence (b = 1.24 mM), (c = 4.36 mM), (d = 25.5 mM) of βCD host in 1:9 (v/v) DMF/H2O solvent; (Temperature: 25 °C; 0.1 M KCl used as an electrolyte)

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If βCD is in large excess, a pseudo-first order rate constant \(\left( {k_{f}^{/} } \right)\) can be obtained from Eq. (14) [11].

$$E_{\text{p}} = E_{1/2} - \left( \frac{RT}{nF} \right)\left[ {0.78 - { \ln }\,\left( {{{k_{f}^{/} } \mathord{\left/ {\vphantom {{k_{f}^{/} } a}} \right. \kern-0pt} a}} \right)^{1/2} } \right]$$
(14)

From this pseudo-first order rate constant, the second order rate constant for the irreversible chemical reaction, (re Eq. (13))

$${\text{EV}}^{ \circ } + \beta{\text{ CD}} \rightarrow \left[ {{\text{EV}}^{ \circ } - \beta{\text{ CD}}} \right]$$

was calculated as 1.44 × 103 M−1s−1.

Digital simulation

For simulating the experimental cyclic voltammetric curves of Ev2+ in buffer of pH 7, the reaction scheme (scheme 1) that has been mentioned above was used for mechanistic probe. The experimentally determined values of n, m, equilibrium constants \(\left( {{\text{K}}_{\text{eq}}^{(1)} ,{\text{K}}_{\text{eq}}^{(2)} } \right)\) and rate constants (k 2, k b) were used for simulation of cyclic voltammograms(s). Values of electron transfer rate constants (k s) for first and second redox processes have been used as 0.05 and 0.1 cm/s, respectively, for simulation. α (electron transfer coefficient) was taken as 0.5 and D (diffusion coefficient) has been taken as 7.4 × 10−6 cm2/s. Rate constant for the formation of Ev+•−βCD has been taken as 1 M−1s−1. For other parameters see Table 2.

Scheme 1
scheme 1

Mechanism showing the electrochemical and chemical interactions of ethyl viologen guests in the presence of βCD

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Table 2 Electrochemical parameters: Reduction of ethyl viologen in the presence of βCD at 0.05 V/s sweep rate in phosphate buffer of pH 7
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Conclusion

Simulation, a powerful technique for investigating processes of interest, however, can be used as a good supporting technique in cases where there are chemically coupled electrochemical processes. Nevertheless, the present study presents a simple (electrochemical) approach for evaluating the equilibrium constant and rate constants for viologen- CD system which is based on sound stationary electrode voltammetric theory. This proposed simple electrochemical method gives equally reliable results. Furthermore, it is shown that through the use of the theory of stationary electrode voltammetry, the rate constants can also be evaluated for Viologen-CD system. This parameter—the rate constant—has not reported by earlier workers. The present method is, thus, superior to the peak current ratios method for the determination of rate constants, in particular, for viologens in aqueous medium.