The list of adsorbates and the electrode processes applied in the present study.
The investigation of organic adsorbate influence on electrode process was started in works of Loshkarev e.g. , Schmid and Reilley , with theoretical formulation of Weber and Koutecký [3,4]. The problem is described in the book by Heyrovský and Kůta ( and literature therein). Later investigations have led to formulation of the cup pair effect , systematically developed in a series of papers e.g. [7,8]. In our earlier paper  it has been shown that catalytic effect of electroinactive organic adsorbate on electrode process can be isolated from CV or NPP faradaic current responses in the form of Gaussian-shaped probabilistic curves (CPR -). It turned out that in presence of organic adsorbate showing electrocatalytic effect, the kinetic response can be split into two defined and well shaped responses: one, due to regular reduction of cation and the second one due to reduction catalyzed by an adsorption phenomenon. The latter was named, due to its shape, the current probabilistic response. It has been demonstrated that CPR effect can exemplify the visualization and the quantitative measure of organic substance catalytic effect on the electrode process and simultaneously become the picture of adsorption.
The electroinhibition phenomenon was analyzed by means of selected experiments with the use of typical electroinhibitors. As an example a quasi-reversible process of Zn2+ electroreduction in the presence of two adsorbates such as n-alkyl alcohols  and two cyclodextrins was chosen [11-13,14].
So far, the quantitative and qualitative comparison of two systems: without adsorbate (1) and with adsorbate (2) was realized by means of four manners: dividing the adsorption non-affected and affected faradaic currents (1)/(2) or (2)/(1) , Tafel plots [10,12], comparison of apparent or individual rate constants [7,8] and/or simple comparison of respective curves, recorded in the presence and absence of organic substance, performed on the same plot .
The task of resolution of enhanced or decreased faradaic current response to show the adsorption catalytic/inhibition effect alone has not been undertaken in literature.
The literature analysis indicates that both theoretical and experimental aspects of adsorption at metal solution interface are still developed for both macroscopic and microscopic inhomogeneites (e.g. [15,16] and literature therein). Owing to existing extensive data concerning influence of organic electroinactive substances on electrode process the visualization of adsorption process in an isolated “pure” form is needed. It can facilitate the data processing and be competitive or parallel to capacitance currents method. Therefore, in the present paper a number of experimental facts concerning CPR is analyzed. The questions which are answered include: if the CPR approach can be applied to electrode process inhibited by organic substances and if the CPR effect is observed at solid electrodes and/or in nonaqueous media. Moreover, successful attempt to generate CPR effect by numerical simulation with the use of EE model was done.
The CV, NPP and NPV experiments were carried out with the use of CV50W electrochemical analyzer (BAS, Inc.) and PGSTAT100 voltammetric analyzer (Autolab Eco-Chemie) for molecular oxygen reduction. The electrode system was CGME/SMDE type MF-9058 (BAS, Inc.). The mercury drop surface of working electrode was 0.0151 ± 0.0004 cm2 for CV experiment. The glassy carbon electrodes of working surface 0.0755 ± 0.001 cm2 (GCE3) as well as 0.0314 ± 0.001 cm2 (GCE2) were used. For NPP experiments, the drop time was 1.0 s with a pulse-width of 50 ms and sample width 10 ms. In contrary to previous paper data, since eq. (2) contains the element of subtracting of background current, the separate background files are not necessary. The reliability of such simplification was checked by the comparison of CPR curves obtained from residual current corrected and non-corrected data. Obtained differences were not significant for the μA current scale of CPR effect.
Coulometric experiments were carried out with the use of diaphragm electrolyzer on large Hg electrode (of about 12 cm2 surface), the volume of catholyte was 100 or 80 cm3. A Pt counter electrode was applied in separated anodic part.
The remaining experimental details concerning DMF solutions were identical with those described in previous paper .
In modeling of Zn2+ electroreduction process the following EE sequence with two one electron steps has been taken into account:
where: k1, k2, k-1, k-2 are the heterogeneous rate constants (cm s−1), α1, α2, and β1, β2 are elementary transfer coefficients of cathodic and anodic process, respectively. In the present paper the extended EE║Hg(Zn) mathematical model described in  was applied. For the considered sequence of elementary steps (1), the reversible electron transfer for both electrochemical steps was assumed. In the extended model the considered system consist of two parts: mercury drop area from r = 0 to r = R0 and the solution area r > R0. Additionally, it has been assumed that species Zn2+ and Zn+ dissolve only in electrolyte, whereas metallic zinc dissolve and diffuse only in the mercury phase. It is caused by the fact, that deposited metallic zinc is solution-phobic and has to be immediately pulled into Hg phase to form intermetallic compound (amalgam) spontaneously .
The problem formulated above was solved using the ESTYM_PDE software. The program was designed to solve and estimate parameters of partial differential equations (PDE) describing one-dimensional mass and heat transfer coupled with a chemical reaction. The validation and comparison with other software are described in . The examples of solving electrochemical problems by means of ESTYM_PDE software are described in previous papers [17-27]. The numerical basis of electrochemical simulation is described in references [28-33]. The two types of probabilistic fits with the use of Origin 7.5 program were applied: the simple Gaussian model y = y0 + (A/(w×(π/2)1/2))×exp(–2×((x-xc)/w)2); the asymmetric double sigmoidal model y = y0 + Am×(1/(1+exp(-(x-xc+w1/2)/w2)))×(1-1/(1+exp(-(x-xc-w1/2)/w3))), where y0, xc, A, Am and (w, w1, w2, w3) are baseline offset, center of the peak, area, amplitude and widths of peaks, respectively.
4. Results and discussion
4.1. The systems with electrode inactive organic adsorbate
where, i0(E) – faradaic current due to regular (i.e. in absence of adsorbate) electrochemical response, iads (E) – additional faradaic current due to adsorption effect. It is assumed that the adsorption process does not change the mechanism of the electrode process, which is in accordance with the literature quoted [1-8,10-13]. In other words, the both currents in eq. (2) represent the same reduction process and the same number of electrons exchanged, moreover their final product is the same as well. The condition should be complete for each considered case.
A representative example of the resolution of deformed by inactive organic adsorbate faradaic current response into components according to eq. (2) is presented in Fig. 1. The visualization of adsorption process in its isolated “pure” form is regular and well-designed (Fig.1). The observed adsorption effect is catalytic since the responses (2) and (3) are enhanced and passed in relation to (1) towards positive potential.
The subtraction of experimental currents (iobs(E) – i0(E) = iads(E)) according to eq. (2) is reasonable since both denote the same electrode process. The applied two-electron Zn2+ reduction is not naturally resolved into steps since k2 > k1  (cf. also the Fig. 10 caption). Therefore, an appearance of adsorption deformed responses (Fig. 1) cannot be explained in terms of resolution of coupled two-electron response. The only assumption is the additivity of currents, according to the rule commonly accepted in electrochemistry.
The two representative sets of the experimental data including five aliphatic alcohols and two cyclodextrins have been selected to establish whether the effect of inhibition can be described by current probabilistic response (CPR). In selection of inhibitors the compounds considered as simple adsorbates (a series of alcohols) as well as complex adsorbates (α,β-cyclodextrins) have been chosen. It has been shown  that α-cyclodextrin as inhibitor can form a condensed film. Both of the selected groups of compounds are known as electrode process inhibitors [7,10-13,35,36]. Moreover, the influence of eight additional organic adsorbates has also been investigated in connection with another electrode processes (see further).
The mechanism of Zn2+ electroreduction and the physical model of the inhibitors influence were proposed in quoted literature. It was shown that zinc electroreduction can be considered as successive two electron transfer steps (e.g., [37-40]). The results obtained by Fawcett and Lasia [34,41] in non-aqueous media in the presence of tetraalkylammonium perchlorates, especially in dimethylsulfooxide, revealed the complex, nonlinear potential dependence of experimental rate constant (c.f. also Fig. 1 in  for dimethylformamide). It indicates that the reaction consists of at least two steps. In dimethylsulfooxide the standard rate constant of the second step is greater than that of first one . It means that E0 potential of Zn2+/Zn+ couple should be more negative than that of hypothetical Zn+/Zn0 one. The similar conclusion is given in paper by Manzini and Lasia . Additionally, it was stated that “coulometric measurments indicate 100% yield and no metal was found in the solution after electrolysis” . It is not surprising since metallic zinc is solution-phobic and must be immediately pulled into Hg phase to form an intermetallic compound (amalgam).
Since the pure reversible EE process of Zn2+ reduction is not observed in practice, there must be a reason for quasi-reversibility in form of slow step. Fawcett and Lasia  suggested the model in which the two step reduction is complicated by slow adsorption process of substrate and its transfer to the electrode, similarly as it was proposed for reduction of Na+, Li+  and Ca2+, Sr2+, Ba2+ cations . In the case when the dehydration desolvatation of zinc cations were considered as chemical steps [37,40], another explanation of the quasi-reversibility is provided by the presence of such preceding slow elementary processes or the situation in which electron transfer is coupled with slow desolvation.
Our results obtained in 1.0 M NaClO4 solution revealed ip/v1/2 = f(v) dependence decreasing with scan rate v which suggests that the reduction process must be complicated by a slow step.
According to our assumption, the EE mechanism (1), i.e. the sequence of two consecutive steps , remains the same on both covered and uncovered electrode where intermediate Zn+ is stabilized by hydration, and undergoes fast electrochemical reduction. The analogical assumptions have been undertaken in relation to Cd2+ electroreduction . Since the CPR effect is based on comparison of the two reductions, namely in absence and presence of organic adsorbate, an extensive mechanistic analysis at the moment is not decisive for our purpose.
Our coulometric measurements were performed at sufficiently negative potentials diffusion region in order to avoid the participation of the anodic current, and gave the number of electrons exchanged 2.02 ± 0.05 for 1 mM Zn2+ and 1 M NaClO4 solution. In the presence of two representative adsorbates the obtained results were 2.00 ± 0.09 for n–pentanol (0.1 M) and 1.92 ± 0.05 for α-cyclodextrin (0.01 M).
The representative results of applying the CPR approach to inhibition are presented in Fig. 2A and 2B. It is striking that simple, according to eq. (2), subtraction of respective parent matrices recorded in presence and absence of inhibitor (or catalyst – Fig.1), provides the curves which are elegant and defined in shape. Very similar picture is observed once convoluted CV responses are considered. The Gaussian fit done for those curves is of good or even very good quality, which justifies the use of the adjective probabilistic. None of the experimental parent curves in this paper has been idealized by smoothing or other similar procedures.
Data presented in Fig. 3 indicate the increasing influence of aliphatic alcohols on the electrode process depending on the increasing, from n-propanol to n-hexanol, length of carbon chain, similarly as it was described in the literature .
The results indicate that the influence of cyclodextrins on the electroreduction process is not uniform and that α–CD is effective as an inhibitor, which remains in agreement with literature data . The data presented in Fig. 3 for alcohols and in Fig. 4 for cyclodextrins have shown, that it is possible to obtain the picture of inhibitory effect more pronounced than in case of applying the single value of kinetic parameter e.g. kapp or k1, k2 alone. The Gaussian fit is also included for data in Fig. 3 – 4. It is evident that fully shaped curves are obtained for relatively high concentration of the adsorbate. The quality of Gaussian fit decreases with the lowering of the adsorbate concentration as it could have been expected.
The detailed investigations with the use of cyclodextrins as adsorbates have shown that the adsorption process is complex with the possibility of compact layers or multi-layers, host-guest complexes formation . Our results with good quality Gaussian fit suggest that both complex (α, β-cyclodextrins) and simple adsorption (alcohols) undergo Gaussian distribution.
Application of CV method usually leads to a series of peaks corresponding to the different scan rates and so it is in our case. However, CV currents recorded at different scan rates are not comparable and should be normalized by v1/2 factor. The different scan rate data, performed in such a way, are presented in form of CPR curves in Fig. 5. In other words, instead of parent CV peaks for regular and inhibited process, the final CPR curves can be taken under consideration.
On the other hand, the Q = f(v) plot (Fig. 6A) makes it possible to express the inhibition effect quantitatively and normalization by v1/2 factor is not needed. In turn, the dependence of the relative inhibition effect (QCD – QZn)/QZn (where QZn, QCD are charges obtained from integrated cathodic parts of CV curves for electroreduction of Zn2+ 1 mM in 1 M NaClO4 in absence and presence of α,β-CD, respectively) at different concentrations and scan rates is presented in Fig. 6B.
Apart from better visualization and separation of adsorption effect from “mixed” current response, CPR approach gives the possibility of adsorption isotherm determination. A respective attempt is presented in Fig. 6B. An assumption was made that a charge QCD determined from CPR curve is proportional to the amount of adsorbed species. The similar assumption is commonly accepted when adsorption phenomena are investigated by differential capatitance method. A change ∂C is assumed to be proportional to ∂Q and to Γ. The results of Langmuir fit indicate that the obtained parameters are reasonable in the range of the published data .
The coincidence with the Gaussian function is expected not to be specific for studied system Zn2+/alcohols and Zn2+/cyclodextrin. It should be observed for at least other qusireversible-irreversible reduction/inert organic adsorbate systems in which pre-peaks or post-peaks do not appear.
It is very probable that numerous factual current responses (CR) and not only curves affected by the effects of inhibition, lead to similar CPR curves with almost identical shapes. Consequently, any change in electrochemical response caused by the influence of added adsorbate, complexing agent or other factors is manifested by, at least, the following influences: positive/negative shift of CR along potential axis and/or change of the CR slope and/or decrease/increase of its high. Above effects occur together, but usually one of them dominates. Therefore, the observed CPR effect, that is an output function, must be interpreted in frames of its parent experimental input.
Data of Fig. 8 A and B present the influence of added organic adsorbates as thiourea (part A, A’) and N,N-dimethylaniline (part B, B’) on molecular oxygen electroreduction in DMF and water, respectively. Fig. 9 presents the case in which the influence of substituent on adsorbate molecule on fixed electrode process is visible. The catalytic effect increases once the electron density on nitrogen atom in thiourea increases. The effect on substituent on thiourea molecule on apparent rate constant is described in paper by Ikeda and co-authors .
The results indicate that CPR effect is observed also on GCE and in nonaqueous medium (Fig. 8A).
4.2. CPR effect as a result of theoretical model
Since the presented results are only an experimental and fenomenological view of the problem, the respective theoretical background is needed. It turned out that the Gaussian-shaped curves of CPR type can be obtained also theoretically by numerical simulation. We used the theoretical kinetic EE║Hg(Zn) model and ESTYM_PDE software, both described in Kinetics section. The literature values of kinetic parameters determined for Zn2+ electroreduction in the 1 M sodium perchlorate solution  were applied. The EE mechanism provides the simple but reliable model among others proposed for Zn2+ electroreduction [38,39,46-49]. The results of simulation are presented in Fig. 10. It turned out that increase/decrease of electrochemical rate constant corresponds to a change of CV curve which is identical to Gaussian CPR experimental curve. For clarity, the results of Gaussian fit are shown separately in Fig. 10B. The obtained results of performed simulation provide an indirect evidence of assumption commonly applied in literature that electrocatalysis/electroinhibition effect can be described by increase/decrease of heterogeneous rate constant . The simulations confirm the literature adsorption model in which the effective observed current is the superposition of both currents on the free surface and on covered fraction i.e. “adsorption” current. It is assumed that the rate constants on covered and uncovered surface should be different (Fig. 10 – simulation). Moreover, the resolution of the experimental currents for two reductions gives possibility for calculation of individual rate constants. It has to be noticed, however, that the mathematical analysis described in reference  indicates that the effects of inhibition can be much more complex than a simple ks decrease analysis presented in Fig. 10.
Despite the fact that the results of modeling of the CPR effect have been presented (Fig. 10), this paper is based mainly on experimental facts. Deeper theoretical analysis of observed phenomena is not possible at the present state of knowledge.
4.3. The CPR effect obtained from processed literature data
In order to extend the scope of experimental data concerning CPR effect, the CPR effect obtained from processed literature data [5,14,51] is presented in Figs. 11-14. The influence of added organic adsorbate, namely polyvinyl alcohol, on VO2+ reduction is shown in Fig. 11 A and A' (source of data: [5b]).
Stochastic nature of adsorption phenomena is also visible on surface tension π vs. potential E dependences presented in monograph [15,16]. The CPR peaks involved in adsorption phenomena are similar to ones obtained by means of chromatography. The latter also undergo Gaussian statistics . Both facts confirm the probabilistic character of chemical dynamics .
4.4. CPR effects for auto-electrocatalysis processes (ACPR)
The hitherto presented data respected to the electroreduction of inorganic cations in the presence of non-electroactive organic adsorbate. Some experimental facts indicate that the idea of CPR can be extended on electroactive adsorbates. In paper  we have detected the autocatalytic effect caused by organic electroactive substance i.e. that which playes double role of organic adsorbate and electroactive substance. The autocatalytic effect was revealed by comparison of experimental and mathematical model responses as well as by comparison of results obtained on Hg (autocatalytic effect present) and GCE electrode (no autocatalytic effect).
In order to show more quantitative explanation of the influence of the autocatalytic effect on the enhancement the cathodic current observed on Hg electrode the difference between experimental and model curves will be shown in Fig. 15.
From the character of the difference curves of CPR kind one may conclude that observed effect is not random but rather systematic with the wave profile increasing with the decreased scan rate. The observed autocatalytic effect vanish at high scan rates, giving discrepancy low enough to permit the usage of these data for the estimation of kinetic parameters . If the effect is connected with adsorption of electrode reaction product, the adsorption process would be slow in comparison to the time window of the high scan rate experiment. Similar observations for inorganic reactant-organic substance/halide ion systems have been written down by the others, by whom catalytic effect was explained by bridging model  or surface reaction model (see  and the literature cited therein).
Interesting electrocatalysis/electroinhibition examples of CPR type effects can be provided by early published polarographic data. Maxima of first kind (sharp) and second kind (diffused) appearing on diffusion/convection controlled limiting currents generally are explained by adsorption of electroactive substance and/or a movement of the solution near the electrode surface. Polarographic maxima were recognized as a case of electrocatalysis [5c,55]. Since maxima hinder the precise evaluation of polarographic curves, they (maxima) are removed (damped) by introduction of strong surface active compounds as high-molecular organic compounds e.g. dyes (fuchsin). It means that a adsorption competition between electroactive adsorbate and nonelectroactive adsorbate takes place.
The adsorption of electroactive substance can be a source of its additional amount on electrode surface and consequently of limiting current excitation. Fig. 16 presents an example of such kind of auto-electrocatalysis, in which asymmetric curve, of autocatalytic CPR kind (ACPR), characteristic to first kind maximum, appears (source of data ).
The gradual passing from first kind maximum (a) to second kind maximum (f), presented in , can be interpreted as a change of adsorption mechanism visible as the change of shape of probabilistic curve (Fig. 18).
On the other side, electroinhibition examples can also be recognized as characteristic minima on limiting currents of anions electroreduction e.g. S2O82– (Figures XIV-17, XIV-21, XIV-22 in ). They also yield the difference curves of the symmetric probabilistic shape. Their precise explanation is much more complex and should be considered in frames of double layer structure changes.
The faradaic electrode process of electroreduction of inorganic cations creates a reference system on which the adsorption / inhibition effect can be observed.
The experimental catalysis/inhibition effect of electrode process affected by adsorption can be quantitatively separated from complex current response and displayed in the form of probabilistic type faradaic currents. The CPR curves can be considered as a quantitative adsorption characteristic of an electroinactive organic adsorbate. In many cases, the inhibition and catalysis processes are mutually coupled.
The results obtained by numerical simulation for EE process indicate that CPR effect is not accidental and that the assumption, that organic substance increases or decreases the apparent or individual rate constant of the electrode process, which is commonly accepted in literature is of value.
In the CPR presentation the effect of adsorption is separated and defined as well as can be processed and discussed quantitatively e.g. as a function of scan rate, a concentration of species in solution, etc. The shape of CPR curve (symmetrical or not symmetrical) may indicate the presence of possible interactions between molecules of adsorbate (Langumir or Frumkin model of isotherm).
The CPR effect is also observed for systems in which an organic or inorganic adsorbate is an electrode active reagent simultaneously (autocatalytic ACPR case).
Electrocatalysis/electroinhibition effect is a positive/negative difference between electrochemical response after and before introduction of a non-electroactive substance into solution and/or on electrode surface or a positive/negative difference between electrochemical response affected and non affected by substrate/product adsorption. The difference (eq. (2)) can be expressed quantitatively in the bell-shaped peak form of Current Probabilistic Response.
Abbreviations, symbols and acronyms
CPR – probabilistic type current response (“difference curves”) obtained from eq. (2)
ACPR – autocatalytic CPR effect
CV – cyclic voltammetry
NPP – normal pulse polarography
EE – set of two consecutive one electron steps
α-CD – α-cyclodextrin
β-CD – β-cyclodextrin
SCE – saturated calomel electrode
TBAP – tetrabuthyl ammonium perchlorate
DMF – dimethylformamide
Q – charge
1,4-BDF – 1,4-benzenedisulfonyldifluoride
1,4-NDF – 1,4-naphthalenedisulfonyldifluoride
|Adsorbate||Electrochemical. reaction,Electrode material||Figure||Observed effect||Literature|
|Zn2+ + 2e– = Zn,|
|Fig. 1||CPR||this paper|
|n-pentanol||Fig. 2A, B||CPR||this paper|
|Fig. 3A, B||CPR||this paper|
|α-cyclodextrin||Fig. 4A||CPR||this paper|
|β-cyclodextrin||Fig. 4B||CPR||this paper|
|α-cyclodextrin||Fig. 5||CPR||this paper|
|N,N’-dimethylthiourea||Fig. 7A||CPR||this paper|
|N,N,N’,N’-tetramethylthiourea||Fig. 7B||CPR||this paper|
|dextran||Fig. 7C||CPR||this paper|
|N,N-dimethylaniline||O2 + e– = O2 –. ,|
|Fig. 7D||CPR||this paper|
|dextran||Zn2+ + 2e– = Zn,|
|Fig. 7E||CPR||this paper|
|3,4-diaminotoluene||Fig. 7F||CPR||this paper|
|thiourea||Fig. 7G||CPR||this paper|
|N,N’-dimethylthiourea||Fig. 7H||CPR||this paper|
|N,N’-diethylthiourea||Fig. 7I||CPR||this paper|
|N,N,N',N'-tetramethylthiourea||Fig. 7J||CPR||this paper|
|thiourea||O2 + e– = O2 –. ,|
|Fig. 8A||CPR||this paper|
|N,N-dimetyloaniline||O2 + 2e– +2H+ = H2O2 , Hg||Fig. 8B||CPR||this paper|
|Bi3+ + 3e– = Bi,|
|Fig. 9||CPR||this paper|
|modeling via k variation||–||Fig. 10||CPR as a model effect||this paper|
|polyvinyl alcohol||V4+ + e– = V3+,|
|Modification of electrode surface||photocurrent,|
|Modification of electrode surface||photocurrent,|
p-Si and p-Si-Me electrodes
H2Q – 2e– = Q + 2H+,
|1,4-BDF||ArSO2F + 2e– = ArSO2 – + F–,|
|Pb2+ ions||Pb2+ +2e = Pb,|
|quinone||H+ + e = H||Fig. 17||ACPR|||
- Since PCR means Polymerase Chain Reaction and is well established in literature, in the present paper we use the abbreviation CPR.