Correspondence between the Frumkin and Alekseev-Popov-Kolotyrkin models at the adsorption of neutral organic molecules

ISSN 1023-1935, Russian Journal of Electrochemistry, 2007, Vol. 43, No. 1, pp. 9–16. © Pleiades Publishing, Ltd., 2007.Original Russian Text © B.B. Damaskin, 2007, published in Elektrokhimiya, 2007, Vol. 43, No. 1, pp. 11–18.

9

INTRODUCTION

In study [1], a method of the regression analysis ofdifferential capacitance curves was developed, whichassumes that the reversible adsorption of ions or neutralmolecules on the electrode obeys the Alekseev–Popov–Kolotyrkin model (APK model) supplemented with theFrumkin isotherm [2–8]. Application of this method tothe dependences of the differential capacitance (

ë

) onthe electrode potential (

Ö

) in a system

Hg/(H

2

O +

x

M NaF +

y

M

n

-BuOH) (A)

for

ı

= 0.1 led, however, to an unexpected result, whichcould not be explained straightforwardly. Namely, thestandard deviation of experimental

ë

vs.

Ö

curves fromthe Frumkin model [3, 9, 10] was

∆

= 9.3%, whereas forthe APK model, which is “physically more correct”,

∆

= 14.6%.In this study, we returned to this question based on

more complete and accurate experimental data in sys-tem (A).

EXPERIMENTAL RESULTS

The experimental results used in our calculationswere obtained by Yu.N. Kuryakov in his post-graduate

studies carried out at the Department of Electrochemis-try of the Moscow State University in 1975–1977. Thecapacitance vs. potential dependences were measuredfor four concentrations of the supporting electrolyte (insystem (A),

x

= 0.01, 0.03, 0.1, and 0.3). For each

ı

value, six differential-capacitance curves for differentadditions of

n

-butanol (

n

-BuOH) in the concentrationrange from 0.05 to 0.8 M were obtained. In thesecurves, the potential variation range changed in such away as to most clearly reveal the capacitance vs. poten-tial dependences in the vicinity of adsorption–desorp-tion peaks. Moreover, to check the theory of the diffuselayer,

ë

vs.

Ö

curves with the following additions ofsecondary butanol (2-BuOH) were measured: 0.1 and0.4 M for

x

= 0.1; 0.105 and 0.419 M for

ı

= 0.03; and0.107 and 0.425 M for

x

= 0.01. The changes in the2-BuOH concentration with

ı

compensated the salting-out effect and corresponded to the constant activity ofsecondary butanol at different supporting electrolyteconcentrations. All measurements were carried out at

20°ë

and an ac frequency of 420 Hz. The electrodepotential was measured related to a saturated calomelelectrode (SCE). In pure NaF solutions of different con-centrations, the zero-charge potential

E

q

=

0

= –0.44 V(SCE).

Correspondence between the Frumkin and Alekseev–Popov–Kolotyrkin Models

at the Adsorption of Neutral Organic Molecules

B. B. Damaskin

z

Moscow State University, Vorob’evy Gory 1, Moscow, 119992 Russia

Received May 16, 2006

Abstract

—By the example of a system

Hg/(H

2

O +

x

M NaF +

y

M

n

-C

4

H

9

OH)

for four

x

values (0.01, 0.03, 0.1,and 0.3) in combination with six different

y

values (in a range from 0.05 to 0.8), an assumption on the simulta-neous fulfillment of the classical model of the diffuse layer and the model of two parallel capacitors supple-mented by the Frumkin isotherm is analyzed. It is shown that the classical theory of the diffuse layer agreeswith experimental data on the capacitance in this system and also on the adsorption of secondary butanol notonly near the zero-charge potential but also in the vicinity of adsorption–desorption peaks where the electrodecharge reaches absolute values of 6–10

µ

C/cm

2

. At the same time, the experimental differential capacitancecurves in this system are well described by the model of two parallel capacitors supplemented by the Frumkinisotherm (the Frumkin model) for all supporting-electrolyte concentrations. However, this model is far lessaccurate in describing the calculated curves of the dense-layer differential capacitance, which contradicts thestraightforward physical basis of the Alekseev–Popov–Kolotyrkin model. To resolve this contradiction, furtherstudies with the use of molecular models are necessary.

DOI:

10.1134/S1023193507010028

Key words

: diffuse-layer model, model of two parallel capacitors, regression analysis, adsorption parameters

z

Author’s email: [email protected]

10

RUSSIAN JOURNAL OF ELECTROCHEMISTRY

Vol. 43

No. 1

2007

DAMASKIN

TESTING DIFFUSE LAYER THEORY

Virtually all of the numerous studies that tested theclassical theory of the diffuse layer (in the Grahameversion [11, 12]) in 1,1-electrolyte solutions used thefollowing equations:

(1)

(2)

Here,

C

2

is the diffuse layer capacitance which is afunction of the supporting electrolyte concentration

Ò

el

and the charge density on the electrode

q

;

C

02

is thedense layer capacitance which is assumed to be inde-pendent of

Ò

el

, while its dependence on

q

is found usingEqs. (1) and (2) based on the experimental differentialcapacitance

ë

values in a solution of a chosen concen-tration

Ò

el

. The quantities

F

,

R

, and

T

take their usual

meaning; the constant

A

=

, where

ε

is thepermittivity of this solvent and

ε

0

= 8.854

×

10

–12

F/m isthe permittivity of a vacuum.

Insofar as Eq. (2) can be applied at a given

q

value,then in the starting solution chosen, the electrodecharge is found by the numerical integration of theexperimental

C

vs.

E

curve from the zero-charge poten-

tial:

q

=

. To find the potentials at different

charges in all other solutions, numerical integration ofcalculated

(1/

ë

)

vs.

q

curves is used

(3)

C2F

2RT----------- 4A2cel q2+= ,

1/C 1/C02 1/C2.+=

2RTεε0

C EdEq 0=

E∫

E Eq 0=– 1/C( ) q.d

0

q

∫=

Analogously, the potential drop in the dense layer isfound. It this case, the

1/

ë

02

vs.

q

curves are integrated.However, when processing the data with the Origin

program, it is more convenient to use a formula of theGrahame theory for calculating the potential drop in thediffuse layer

(4)

At first, this formula is applied to all

q

values in thestarting solution, after which the potential drops in thedense layer are found

(5)

where

is the zero charge potential in the puresupporting electrolyte solution. This equation coupledwith Eqs. (1) and (2) and applied to the same

q

valuesin the starting solution affords a

ë

02

vs.

ϕ

02

dependence,i.e. a curve of the differential capacitance of the denselayer. Next, if we use Eqs. (1) and (4) to calculate thecapacitances

ë

02

and potentials

ϕ02 for all q values forwhich the values q, ë02, and ϕ02 are available and thenapply Eqs. (2) and

E = ϕ02 + + ϕ2 (5a)

we can find theoretical C vs. E curves in solutions of allconcentrations of the supporting electrolyte and com-pare them with the experimental curve.

It is evident that this method of testing the diffuselayer theory requires no additional curves to be plottedand no operations of numerical integration according toEq. (3) to be carried out.

First of all, we applied the proposed version of cal-culations to pure NaF solutions. Figure 1 demonstratesgood agreement between the experimental capacitancedata in 0.01 M NaF solution and the calculated dataobtained from the experimental C vs. E curve in 0.1 MNaF. This result is, in fact, a test for the reliability ofexperimental data in pure supporting electrolyte solu-tions.

As it follows from [13], a more rigorous conditionof the correctness of the diffuse-layer theory is the coin-cidence of the dense layer curves calculated based onexperimental C vs. E curves in solutions of differentconcentrations. Figure 2a confirms adequate agreementof ë02 vs. ϕ02 curves calculated based on experimentaldata in 0.3, 0.1, and 0.03 NaF solutions. However, asseen from Fig. 2b, a small peak appears in the vicinityof the zero charge potential in the ë02 vs. ϕ02curve mea-sured in 0.01 M NaF. A similar peak of ë02 was alsorevealed based on the experimental results obtained byGrahame [12, 13]. As it follows from Eq. (2), for closeë and ë2 values, such a peak can be caused by smallerrors in each of these values.

ϕ22RT

F----------- q

2A cel

----------------- 1q

2A cel

-----------------⎝ ⎠⎛ ⎞ 2

++ .ln=

ϕ02 E Eq 0=y = 0– ϕ2,–=

Eq 0=y = 0

Eq 0=y = 0

C, µF/cm2

0.5 0 –0.5 –1.0 –1.5ϕ0, V

1.010

20

30

40

12

Fig. 1. Differential capacitance curves of a mercury elec-trode in 0.01 NaF solution at 20°ë: (1) calculated based ondata in 0.1 M NaF, (2) experimental data.

RUSSIAN JOURNAL OF ELECTROCHEMISTRY Vol. 43 No. 1 2007

CORRESPONDENCE BETWEEN THE FRUMKIN 11

For the first time, the validity of the classical theoryof the diffuse layer for ë vs. E curves in system (A) wasdemonstrated in [14]. Figure 3 shows the results of theapplication of the aforementioned new calculationmethod to this system. As seen from this figure, theinterval of n-BuOH adsorption in calculated ë vs. Ecurves is somewhat longer as compared with experi-mental curves; moreover, this deviation increases withan increase in the supporting electrolyte concentrationin the starting curve. As was shown in [14], this effectcan be associated with salting-out effect. To take it intoaccount, it is necessary to compare the calculated ë vs.E curve with the experimental one for such a concentra-tion Ò2 of the organic substance that exceeds the startingconcentration Ò1 (i.e. in a solution with a higher sup-

porting electrolyte concentration) by a factor of .Here, k is the salting-out coefficient and ∆Òel is thechange in the supporting electrolyte concentrationwhen going from the starting (for this calculation) solu-tion to the final solution. In this study, we confirmedthis conclusion by the example of the adsorption of sec-ondary butanol (2-BuOH). In our calculations, solu-tions of 0.1 and 0.4 M BuOH by the background of

10k∆cel

0.1 M NaF were chosen as the starting, while the calcu-lations were carried out for the 0.01 M NaF supportingelectrolyte. Making allowance for the salting-out coef-ficient k = 0.32 l/mol [15], the results of calculationswere compared with experimental data in solutions of0.107 and 0.427 M 2-BuOH with 0.01 M NaF as thesupporting electrolyte. As seen from Fig. 4, under theseconditions, the complete coincidence between calcu-lated and experimental ë vs. E curves is observed.According to the data published earlier [14], the resultsobtained show that the classical theory of the diffuselayer agrees with the experimental capacitance data notonly near the zero charge potential but also in the vicin-ity of the adsorption–desorption peaks where the elec-trode charge reaches 6–10 µC/cm2 in the absolute mag-nitude. Thus, this theory can be used for the calculationof a series of dense-layer capacitance curves for differ-ent additions of the organic substance. Figure 5 showsthat in the first approximation these curves coincide

C02, µF/cm2

20

30

50

123

0.5 0 –0.5 –1.0 ϕ02, V

20

30

4012

(b)

(‡)

40

Fig. 2. Differential capacitance curves of the dense layer atthe Hg/(H2O + NaF) interface at 20°ë calculated based onthe data in NaF solutions of different concentrations, M:(a) (1) 0.3, (2) 0.1, (3) 0.03; (b) (1) 0.1, (2) 0.01.

C, µF/cm2

(‡)

0

40

80

120

12

0 –0.5 –1.0 –1.5 –2.0Ε, V (SCE)

0.50

40

80

120

34

(b)

Fig. 3. Differential capacitance curves in system (A) for(1, 2) ı = 0.01, Û = 0 and (3, 4) x = 0.01, y = 0.4. Curves 1and 3 correspond to experimental results, curves 2 and 4correspond to calculations for solutions with (a) 0.1 and(b) 0.3 M NaF as the supporting electrolyte.

12


DAMASKIN

when calculated for solutions with different NaF con-centrations and the same additions of n-BuOH. Next, aseries of such ë02 vs. ϕ02 curves with different n-BuOHadditions can be subjected to the regression analysiswithin the framework of the Frumkin model [16].

REGRESSION ANALYSIS OF DIFFERENTIAL CAPACITANCE CURVES IN SYSTEM (A)

AND OF CORRESPONDING DENSE-LAYER CAPACITANCE CURVES

First, the experimental ë vs. E curves in system (A)for different NaF supporting electrolyte concentrations,namely, 0.3, 0.1, 0.03, and 0.01 were subjected to theregression analysis. In the first stage, the following 5main adsorption parameters of the Frumkin model weredetermined using this analysis: (1) the maximum

adsorption potential ϕm measured from ; (2) theadsorption equilibrium constant at this potential βm; (3)the parameter of intermolecular interaction am at ϕ =ϕm; the parameter A = RTΓm, where Γm is the surfaceconcentration of adsorbate that corresponds to the totalsurface coverage by organic molecules θ = 1; and (5)the capacitance ë1 at θ = 1.

In addition, for optimum values of these five param-eters, the standard deviation ∆5 of the calculated capac-itance values from the experimental values was esti-mated. After this, we introduced the sixth variableparameter ‡m1, which expressed the possible lineardependence of the parameter of intermolecular interac-tion ‡ on the electrode potential. For the new combina-tion of six optimum parameters, a new standard devia-tion ∆6 was determined. If the quantity (∆5/∆6)2

Eq 0=y = 0

exceeded the theoretical Fischer criterion FT [18], thenthe parameter ‡m1 was considered as significant. In thiscase, the seventh variable parameter am2 was intro-duced, which determined the quadratic dependence of‡ on the electrode potential

(6)

The new combination of seven optimum adsorptionparameters gave the standard deviation ∆7. Now, it isthe ratio (∆6/∆7)2 which is compared with the Fischertheoretical criterion FT. If this value exceeds FT, thenthe seventh adsorption parameter am2 is also consideredsignificant. No more adsorption parameters were intro-duced to improve the agreement between the calcula-tions and experimental data.

Table 1 shows the standard deviations in system (A)for all supporting electrolyte concentrations, the ratios(∆5/∆6)2 and (∆6/∆7)2, the total number of points N, andthe theoretical Fischer criterion [18]. The equationsused in calculations of FT(N) are shown in [19].

As it follows from this table, 6 adsorption parame-ters are significant for describing the experimental ëvs. E curves in system (A) at 20°C within the frame-work of the Frumkin model [3, 9, 10]. Here, the values∆6 are even slightly lower than in system (A) at 25°ëwith 0.1 M NaF as the supporting electrolyte, accordingto the data of [20] after introduction of refining proce-dure [21]. This points to very high accuracy of theexperimental data obtained by Kuryakov.

In addition, Table 1 shows that the ratio (∆5/∆6)2 reg-ularly decreases with the decrease in the supportingelectrolyte concentration. Hence, the lower the NaFconcentration, the smaller the deviation of experimen-

a am am1 ϕ ϕm–( ) am2 ϕ ϕm–( )2.+ +=

C, µF/cm2

0 –0.5 –1.0 –1.5 –2.0Ε, V (SCE)

0.50

50

100

12345

Fig. 4. Differential capacitance curves of a mercury elec-trode in 0.01 M NaF + x M 2-BuOH solutions: (1) x = 0,experiment; (2) x = 0.1, calculation based on the results in0.1 M NaF + 0.1 M BuOH; (3) x = 0.107, experiment;(4) x = 0.4, calculation based on the results in 0.1 M NaF +0.4 M 2-BuOH; (5) x = 0.425, experiment.

C02, µF/cm2

0.5 0 –0.5 –1.00

200

400

123

ϕ02, V

Fig. 5. Differential capacitance curves of the dense layer atthe Hg.(Hg/(H2O + ıå NaF + 0.4 M n-BuOH) interface at20°ë calculated based on the data in system (A) for Û = 0.4and the following x: (1) 0.01, (2) 0.03, (3) 0.1



tal data from the classical model of Frumkin. Table 2shows these six parameters for all four concentrationsof the supporting electrolyte.

As seen from Table 2, with the increase in the sup-porting electrolyte concentration, the total surfaceactivity of n-BuOH, which is determined by the quan-tity (lnβm + am), increases. This can be explained qual-itatively by the salting-out effect, although the increasein (lnβm + am) proves to be smaller than it follows fromthe Sechenov law, viz., 2.303k∆cel.

To explain the decrease in the negative ϕm valuewith the increase in the NaF concentration, the follow-ing equation [10] should be taken into account:

(7)

which links the value ϕm with the shift of the zerocharge potential at the transition from θ = 0 to θ = 1 (ϕN)and with the electrode charge in a pure supporting elec-trolyte solution q0 at the maximum adsorption poten-tial. Indeed, with an increase in NaF concentration, thecapacitance in a pure supporting electrolyte solution ë0increases, while the value ϕN remains approximatelyconstant (ϕN = 0.2 V). Thus, the increase in the negative

ϕN –q0 ϕm( )/C1 ϕm,+=

charge q0(ϕm) = with an increase in the sup-

porting electrolyte concentration due to the increase inë0 should be compensated by the correspondingdecrease in the negative value of ϕm.

Finally, the decrease in parameter am1 with adecrease in NaF concentration reflects the above-men-tioned fact that the lower the NaF concentration the bet-ter the classical model of Frumkin describes the exper-imental ë vs. E curves. This result have not yet foundsimple physical substantiation, because the parametersshown in Table 2 effectively reflect the overlap of prop-erties of the diffuse layer and a monomolecular layerthat consists of a mixture of water and n-BuOH mole-cules.

According to above-mentioned results, the simplemodel of the diffuse layer [11, 12] is adequately appli-cable to system (A); hence, it was interesting to com-pare the curves of the dense-layer capacitance, whichwere obtained from experimental ë vs. E curves by theaforementioned method using Eqs. (1), (2), (4), and (5),with the Frumkin model [3, 9, 10]. It seemed that thethus obtained dependences of ë02 on ϕ02 should followthe Frumkin model more strictly than the starting ë vs.

C0 ϕd0

ϕm∫

Table 1. Quantities characterizing the regression analysis of experimental data on the capacitance in system (A)

cel, M ∆5,% ∆6,% ∆7,% (∆5/∆6)2 (∆6/∆7)2 N FT

0.01 8.02 7.03 7.00 1.301 1.007 340 1.207

0.03 7.07 5.55 5.56 1.623 1.004 348 1.205

0.1 8.23 6.11 6.07 1.814 1.013 342 1.207

0.3 9.93 7.30 7.31 1.865 1.003 351 1.205

Table 2. Adsorption parameters of the Frumkin model in system (A)

cel, M ϕm, V lnβm [l/mol] A, µJ/cm2 am am1, V–1 C1, µF/cm2

0.01 –0.119 ± 0.001 1.907 ± 0.022 1.319 ± 0.010 1.335 ± 0.011 0.133 ± 0.014 4.84 ± 0.05

0.03 –0.105 ± 0.001 1.908 ± 0.019 1.312 ± 0.009 1.341 ± 0.007 0.162 ± 0.011 5.14 ± 0.04

0.1 –0.097 ± 0.001 1.948 ± 0.018 1.320 ± 0.006 1.386 ± 0.009 0.202 ± 0.013 5.16 ± 0.05

0.3 –0.082 ± 0.001 1.955 ± 0.018 1.449 ± 0.010 1.409 ± 0.009 0.213 ± 0.013 4.99 ± 0.05

Table 3. Quantities characterizing the regression analysis of the dense-layer-capacitance curves calculated from C vs. Ecurves in system (A)

cel, M ∆5,% ∆6,% ∆7,% (∆5/∆6)2 (∆6/∆7)2 N FT

0.01 21.7 17.3 14.8 1.57 1.37 340 1.207

0.03 20.7 17.3 15.0 1.43 1.34 348 1.205

0.1 17.8 10.6 9.5 2.83 1.23 342 1.207

0.3 23.3 19.6 16.1 1.42 1.48 351 1.205

14


DAMASKIN

E curves. However, this conclusion is not confirmed bythe results of calculations, as follows from Table 3.

As seen from Table 3, in the regression analysis ofë02 vs. ϕ02 dependences all seven adsorption parame-ters shown in Table 4 proved to be significant. More-over, the standard deviations ∆7 which were found bytaking into account seven variable parameters turnedout to be greater than the standard deviations found bythe regression analysis of starting C vs. E curves whenfive variable parameters were taken into account (com-pare with Table 1).

As follows from Table 4, in agreement with the Ale-kseev–Popov–Kolotyrkin model, no definite depen-dence of the adsorption parameters on the NaF concen-tration is observed. This is why the last line in Table 4shows the averaged values of these parameters. How-ever, the dense layer properties substantially deviatefrom the model of two parallel capacitors coupled withthe Frumkin isotherm [3, 9, 10] if this model operates

with only five adsorption parameters. This is directlyindicated by the great values of adsorption parametersam1 and am2 that describe the parabolic dependence (6).

In turn, according to the generalized model of thesurface layer (GMSL) [22], the parabolic dependenceof the parameter of intermolecular interaction on thepotential reflects the deviation from the Frumkin modelto the Parsons model [23]. In the first approximation,when the equation of the Frumkin isotherm is used [3]1,parameter n in GMSL can be related to parameter am2by the equation

(8)

where the quantities and designate the denselayer capacitances at θ = 0 and θ = 1, respectively. Sub-stitution of the averaged parameters from Table 4 and

= 29.4 µF/cm2 into Eq. (4) gives the GMSL param-eter n = 1.115.

When the Parsons model [23] is fulfilled, this

parameter should be equal to / = 5.55, whereasn = 1 for the Frumkin model [22]. Obviously, thebehavior of an adsorption layer of n-butanol moleculesin the double-layer dense part suits the Frumkin modelfar better than the Parsons model. Nevertheless there isno doubt that this layer deviates more strongly from theFrumkin model as compared with the overall surfacelayer that includes its diffuse part. Now, we show thatthis unexpected result cannot be explained by the mis-takes in calculations according to the classical diffuselayer model [11].

Figure 6 shows the experimental capacitance in0.01 M NaF + 0.8 M n-BuOH and also the diffuse-layercapacitance in the same solution as a function of theelectrode charge. As seen from this figure, these depen-

1 The GMSL refinement, which is associated with the changeoverof the Frumkin isotherm for a more complex isotherm rigorouslyreflecting the GMSL [24], was considered in [25]. However, inthe concrete case of system (A), this refinement can be ignoreddue to its insignificance.

n n 1–( )n 1+( )3

--------------------am2A

4 C020 C02

1–( )------------------------------,=

C020 C02

1

C020

C020 C02

1

Table 4. Adsorption parameters of the Frumkin model calculated based on the data on system (A)

cel, M ϕm, B lnβm [l/mol] A, µJ/cm2 am am1, V–1 am2, V–2 C1, µF/cm2

0.01 –0.065 ± 0.001 1.956 ± 0.024 1.343 ± 0.008 1.321 ± 0.020 0.697 ± 0.021 1.161 ± 0.068 5.21 ± 0.09

0.03 –0.067 ± 0.001 1.851 ± 0.042 1.305 ± 0.002 1.405 ± 0.042 0.687 ± 0.027 0.997 ± 0.131 5.51 ± 0.08

0.1 –0.067 ± 0.001 1.885 ± 0.028 1.330 ± 0.006 1.414 ± 0.028 0.486 ± 0.021 0.692 ± 0.085 5.30 ± 0.07

0.3 –0.065 ± 0.001 1.928 ± 0.020 1.447 ± 0.003 1.387 ± 0.019 0.632 ± 0.022 0.973 ± 0.061 5.08 ± 0.06

Average –0.066 1.91 1.36 1.38 0.63 0.96 5.3

C, µF/cm2

10 0 –10 –20 –30q, µC/cm2

0

100

20012

20

Fig. 6. Dependences of the differential capacitance on thecharge in system (A) for ı = 0.01 and y = 0.8: (1) totalcapacitance, (2) diffuse-layer capacitance.



dences approach one another in the vicinity of theanodic adsorption–desorption peak, which, accordingto Eq. (2), leads to a stronger increase in the dense-layercapacitance in this peak as compared with experimentalë values. On the other hand, in the vicinity of thecathodic adsorption–desorption peak, the dependencesof C and ë2 on the charge are far from one another;hence, according to Eq. (2), ë02 should exceed ë by asmaller value. Figure 7 illustrates this conclusion as aresult of which the dense-layer capacitance curve turnsout to be much less symmetrical as compared with theexperimental ë vs. E curve. On the other hand, as fol-lows from the Frumkin model [10], the higher and morenarrow the adsorption–desorption peak in differentialcapacitance curves the more positive is the parameter ofintermolecular interaction ‡ in the Frumkin isotherm.Thus, the introduction of corrections for the diffuselayer capacitance should inevitably lead to the denselayer differential capacitance curves asymmetrical withrespect to ϕm as well as to the parabolic dependence‡(ϕ) described by Eq. (6). Note also that the possibledeviation of the diffuse layer capacitance from the cal-culations carried out according to Eq. (1), which iscaused by the approximate nature of the classical dif-fuse-layer theory in the vicinity of great |q|, cannotaffect the conclusion that the dependence of ‡ on thepotential changes when going from experimental ë vs.E curves to the curves of the dense-layer differentialcapacitance.

On the other hand, if assume that in the presence oforganic molecules, which adsorb with the positivedipole end to the electrode surface, the dense-layercapacitance strictly follows the Frumkin model withfive adsorption parameters (i.e. for ‡ = const), then thecombination of Eqs. (1) and (2) should inevitably lead

to the lower and wider anodic adsorption–desorptionpeaks as compared with the cathodic peaks in ë vs. Ecurves. However, this contradicts the experimental dataon the adsorption on a mercury electrode of simplemolecules of most aliphatic compounds in the presenceof which experimental electrocapillary and differential-capacitance curves are well described by the Frumkinmodel [10].

CONCLUSIONS

For the adsorption of organic molecules, we canstate the presence of a self-contradiction in the APKmodel that combines the model of two parallel capaci-tors for the double-layer dense part and the classicaltheory of the diffuse layer. Formally, the description ofthe dense layer within the framework of the GMSL[23–25] allows resolving this contradiction. However,from the physical viewpoint, the correct interpretationof the behavior of the electrical double layer at theadsorption of organic molecules on electrodes, whichwould explain why it is the total surface layer ratherthan its dense part that follows the Frumkin model,should be sought in the development of the correspond-ing molecular models. Note that the results of publica-tion [26], the authors of which proposed a generalapproach to the substantiation of GMSL on the molec-ular level, may prove to be useful.

ACKNOWLEDGMENTS

This work was supported by the Russian Foundationfor Basic Research, project no. 06-03-32 203.

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10. Damaskin, B.B., Petrii, O.A., and Batrakov, V.V.,Adsorption of Organic Compounds on Electrodes, NewYork: Plenum, 1971, ch. III and ch. IV.

11. Grahame, D.C., Chem. Rev., 1947, vol. 41, p. 441.12. Grahame, D.C., J. Am. Chem. Soc., 1954, vol. 76,

p. 4819.

C02, µF/cm2

0.5 0 –0.5 –1.0ϕ02, V

0

400

800

12

a

0

1

2

3

4

Fig. 7. (1) Differential capacitance curve of the dense layerat the Hg/(H2O + NaF + 0.8 M n-BuOH) interface and(2) the corresponding dependence of the parameter of inter-molecular interaction a on ϕ02.

16


DAMASKIN

13. Vorotyntsev, M.A., Itogi Nauki Tekh., Ser: Elektrokhim.,1984, vol. 21, p. 3.

14. Damaskin, B.B. and Kuryakov, Yu.N., Elektrokhimiya,1977, vol. 13, p. 533

15. Campbell, H.R., Shallal, A.K., and Bauer, H.H.,J. Chem. Eng. Data, 1970, vol. 15, p. 1207.

16. Damaskin, B.B., Safonov, V.A., and Baturina, O.A., Ele-ktrokhimiya, 1997, vol. 33, p. 117.

17. Damaskin, B.B., Baturina, O.A., Emets, V.V.,Vasil’ev, S.Yu., and Kazarinov, V.E., Elektrokhimiya,1999, vol. 35, p. 5.

18. Bol’shov, L.N. and Smirnov, N.V., Tablitsy matemat-icheskoi statistiki (Mathematical Statistics Tables), Mos-cow: Nauka, 1983.

19. Damaskin, B.B., Elektrokhimiya, 2005, vol. 41, p. 1301.20. Damaskin, B.B., Survila, A.A., and Rybalka, L.E., Elek-

trokhimiya, 1967, vol. 3, p. 146.21. Damaskin, B.B. and Safonov, V.A., Elektrokhimiya,

2006, vol. 42, p. 151.22. Damaskin, B., Frumkin, A., and Chizhov, A., J. Elec-

troanal. Chem., 1970, vol. 28, p. 93.23. Parsons, R., J. Electroanal. Chem., 1964, vol. 7, p. 136.24. Afanas’ev, B.N., Damaskin, B.B., Avilova, G.I., and

Borisova, N.A., Elektrokhimiya, 1975, vol. 11, p. 593.25. Damaskin, B.B. and Kuryakov, Yu.N., Elektrokhimiya,

1977, vol. 13, p. 98.26. Sangaranarayanan, M.M. and Rangarajan, S.K., Can.

J. Chem., 1981, vol. 59, p. 2072.

Documents

Correspondence between the Frumkin and Alekseev-Popov-Kolotyrkin models at the adsorption of neutral organic molecules