Bond formation in electrosorbates—I correlation between the electrosorption valency and pauling's electronegativity for aqueous solutions

Electrocfdmica *cm, 1976.Vol. 21, pp 327 336. Pergnmon Press. Printed in Great Britain

BOND

FORMATION

IN ELECTROSORBATES-J

CORRELATION BETWEEN THE ELECI’ROSORPTION VALENCY AND PAULING’S ELECTRON-EGATIWTY FOR AQUEOUS SOLUTIONS” J. W. Institut

and F. D.

%XKJLTZE

KOPP~TZ

fiir Physikalische Chemie der Freien Universitit, (Received

25 Octoher

1974;

in final form

Berlin, Germany

3 Decemhw

1974)

electrosorption valency, y, which can be determined experimentally, is discussed in dependence on system-specific parameters. For correlation purposes, values at the potential of zero charge, EN and small coverages, B z @l, only are used, and mixed adsorption and phase formation must be excluded. Experimental data for 50 ionic systems in aqueous solutions are summarized. For Abstract-The

homonucleus ions, a simple correlation between the ratio, y/z, and the electronegativity difference, txr%l, is established. This relationship can be described using a reasonable assumption on the geometric factor, 9, and Pauling’s formula for the charge transfer in diatomic molecules. It follows from

snnple model as well as from the experimental data that covalent adsorption (y/zz 1, - k/z z I), takes place in the range, IAxI < O-5, but ionic adsorption (y/z-C 0.2, J. z 0) occurs at iAx/> 1.0. For 05 < [AxI < 1.0 the partial charge transfer (0 < -J/z < 1) with the formation of polarized bonds is important. Heteronucleus ions are discussed qualitatively. The influence of the geometric factor seems to be dominant for these ions. this

I. THEORIES

ON BOND FORMATION ELECT3OSORBATES

coordination reaction. The formation of covalent bonds was also favoured by Lorenz[8,9], who used a MO-model to calculate the charge distribution in electrosorbates for different solvents. Lorenz[B] approached the problem experimentally, interpreting the charge flow, (8q,,,/8Qr obtained from experimental data as a partial charge transfer, 1. Some objections to this interpretation were raised by Parsons[iO] and Damaskin[li] who use the pure electrostatic concept for explanation of experimental data generally. Recently it was shown by Vetter and Schultze[12-141 that both concepts of electrostatic adsorption and covalent adsovtion can be combined in a general model of a partially discharged sorbate within the double layer. The correlation of this model to the electrosorption valency, y, which is defined thermodynamically and can be determined experimentally, allows some rough estimations of the charge transfer for several systems[14,15]. A detailed analysis of the y-values of various cations and anions demonstrated that systems with nearly complete discharge of the ions exist as well as systems with almost pure electrostatic adsorption of the ions without any transfer. Later, Kolb, Przasnyski and Gerischer[l6,17] correlated the underpotential shift of metal layer deposition with the difference of the work function, #J, of the adsorbent and the adsorbate. This correlation is applicable as long as the M-S-bond is only weakly polarized. Similar concepts were used for the description of bond formation in adsorption reactions from the gas phase. Eley[lX], for instance, applied Pauling’s electronegativityE19], r, to calculate bond energies. In accordance with Mulliken’s[ZO] approximation, I,,, = O-35 c$,, Stevensen[21] proposed the use of work

IN

In electrosorption reactions a substance, S’, from the electrolyte comes in direct contact with the electrode metal, M. Depending on the chemical nature of the adsorbent and the adsorbate, a charge transfer of i, electrons is possible. Including the desorption of v water molecules, the electrosorption reaction may be written vM-OH,

+ S”*aq$M-S””

+ ,&

+ vH,O.aq.

(1)

between M and S has been discussed by several authors using different approaches. Bockris, Devanathan and Miiller[ l] compared the adsorbability of halide ions at mercury with covalent bond energies. They concluded that covalent bond formation does not contribute to the adsorption. Andersen and Bockris[2] and later Bod&[3] came to the same conclusion. They only used electrostatic calculations in order to evaluate the free energy of adsorption for anionic adsorption systems. Andersen, Anderson and Eyring[4] compared the adsorbability of various ions with the standard free energy of the reaction M(g) + 3 X,(q)--r MXQ). They found no correlation and concluded that covalent bonds are negligible in the adsorption of anions. Barclay[5] found a better correlation between the adsorbability and the free energies of the reaction M+(g) -t X-@)+MX@). Further, Barclay tried to establish a correlation between work functiog electron affinity, and adsorbability. Barclay and Caja[6,7] applied Pearsons’ concept of hard and soft acids and bases to interpret the electrosorption’of anions as a soft

The

question

of bond

formation

*Presented in Extracts at the DECHEMA-Meeting, Frankfurt/Main, February 7th, 1974. 327 E.*. 21,5-*

J. W.

328

SCHULTZEAND

functions instead of electronegativities. Sachtler et a&22] correlated the surface potential, A&. with ‘the electronegativity of the adsorbate and the adsorbent. Finally, &good et a9231 correlated the ratio, A&j rionr with the electronegativity of the adsorbate and the hkl-surface of the metal. From this review the’question arises if in electrosorption there is a general correlation between bond formation and chemical data of the adsorbate and the adsorbent respectively. Therefore, a summary of electrosorption valencies of systems with anions and cations was compiled. The data for aqueous solution are analysed in this paper; nonaqueous solutions will be discussed in a paper to follow. The correlation made in these papers between the electrosorption valency, y. and the electronegativity difkrence, Ax, shows that in aqueous and nonaqueous solutions the charge transfer decreases continuously with increasing Ax. A simple model is described, yielding a reasonable correlation between r/t and lAxI.

F. D.

KOPPITZ

‘b)

I

I oi5tance

~istonce/A

/A

Schematic double layer model with non-adsorbed ions in the Helmholtz plane (outer layer), adsorbed water molecules and adsorbed ions in the inner layer. Effects of the diffuse layer are neglected (supporting electrolyte). (a) Anion adsorbed electrostatically and cation discharged Fig.

1.

partially. (b) Completely discharged cations.

2. THE FZECI’ROSORPTION VALENCY, y. AND THE CHARGE TRANSFER COEFFICIENT, A, IN DEPENDENCE ON SYSTEM-SPECIFIC PARAMETERS

2.1 De$nition

and interpretation

of y

The electrosorption valency, y, describes the potential dependence of the electrosorption equilibrium, (a~/&),, as well as the charge flow, (&Jar)_ during the electrosorption reaction. In case of an excess supporting electrolyte of large concentration, y is defined by the equation (2)[12,13]

where ps is the chemical potential of S’ in the electrolyte, E is the electrode potential, q,,, is the metal charge and r,, is the surface concentration of the specifically adsorbed substance. Equation (2) can be used at ideally polarizable electrodes and at reversible electrodes as well[24]. Only in the case of mixed adsorption[25] and in solutions without excess supporting electrolyte are further restrictions necessary[12,13]. The definition of y by the pure thermodynamic equation (2) permits the experimental determination of the electrosorption valency[l4]. The macroscopic value of y can be correlated with microscopic d+a of the system. At the potential of zero charge, cN’ equation (3) can be applied[14,15] YN

=

gz

-

w

-

9) +

&

-

VKW.

(3)

The geometric factor, g, describes the penetration of the adsorbate into the electric field of the double layer, which is shown schematically in Fig. 1. g is defined by the electric potential at the adsorption site, 4 *CL:

In Fig. 1 and in equation (4) it is assumed that the potential difference, +pe, between the outer Helmholtz layer and the electrolyte can be neglected (excess supporting electrolyte). The charge transfer coefficient, A, is defined by the difference between the

actual charge of the adsorbate, charge, z:

z,~, and the ionic

J. = z,* - z.

(5)

Because the probability of finding the electron in the adsorbate is not unity, R varies in the range between 0 and -z[9,26,27]. Generally, i is positive for anions and negative for cations. Tn equation (3), ~~ and ++, are dipole terms of the adsorbed substance and (of the v desorbed water molecules respectively. These terms are important for the electrosorption of neutral molecules. In the case of ionic electrosorption systems, however, rc, is zero and vlcw is small compared with the charge terms[15]. Therefore, equation (6) is used in this paper as a good approximation instead of equation (3) YN = 9 z - A(1 - g). 2.2 Influence of the adsorbent,

adsorbate

(6) and solvent

The experimental analysis of various electrosorption systems demonstrates the strong influence of the chemical nature of the adsorbent and the adsorbate on the value of y. According to equation (6) this influence is due to changes of the geometric factor, g, or the charge transfer coefficient, Iz. These effects are discussed in Section 4. The value of y is also affected by the nature of the solvent[8]. A detailed analysis of solvent effects, which are caused mainly by changes of the geometric factor, g, will be given in Part 2. 2.3 Injuence of electrode potential, coverage and temperature Since y may depend on the variables E, 0 and T, a standard state must be choosen for correlation purposes. According to the thermodynamic analysis, the potential dependence of y is given by the change of the double layer capacity, CD, with increasing surface concentration[ 12,131:

Y=YN-;. As long as small ions are electrosorbed,

(7) the double

Bond formation in electrosorbateeI layer thickness can be assumed to remain constant. A change of the double layer capacity may then be connected with the charge transfer. Hence, the experimental result, dy/& -z 0, points to a potential dependent charge transfer, ti/dE > 0. This was discussed recently using some selected systems as examples[l5]. In this paper, however, the potential dependence is eliminated as far as possible, and the discussion is limited to the potential of zero charge, Ed, without specific adsorption (0 = 0), according to the model proposed in ref.[12]. For the anionic adsorption systems, y,-values could be obtained for the majority of the investigated systems (see Table 1). Concerning the cationic systems, dy/& h 0 in many cases (see Table 2). Presumably this is valid for the other cationic systems as well, so that v(e) z Ye The dependence of y on the coverage, 0, or the surface concentration, Tad, has been measured and discussed for the Pt/Cu-system[28] and other cation systems[14]. It may be related to a charge transfer coefficient, depending on the coverage or on the crystallographic orientation of the substrate. Regarding the adsorption from the gas phase, it is generally known that the dipole moment of the adsorbate depends on the crystal plane[23,29,30,31]. For electrosorption reactions, a dependence of the electrosorption valency as well as of the adsorption isotherm may also be expected. Until now only a few measurements of adsorption isotherms have been carried out on definite single crystal planes. The results show a strong influence of the substrate in the systems Pt/ H+ [32] and Au/Pb’+ [ 1041, but a small influence only in the system Ag/Tl+[33]. In general, the electrostatic adsorption of ions without charge transfer (1 L O), eg that of alkali and chloride ions, does not exceed a coverage of ZOO/ In these systems, therefore, the evaluation of the electrosorption valency is limited to small coverages. Furthermore, different neighbours in adsorption layers may differ in their influence on the charge distribution of the adsorbate. This factor hinders a comparison. For these reasons, all y,-values in this paper refer to small coverages in the range of 10% where the influence of adsorbed ions in the neighbourhood is small and where the small dependence of yN on 0 can be neglected. This would not be justified at higher coverages up to a monolayer, which can be attained with almost completely discharged heavy metal ions[14]. The influence of the temperature on y or the equivalent “thickness ratio” was investigated by Parry and Parsons[34] as well as by Mint and Jurkiewicz-Herbichf35]. Generally, the temperature dependence seems to be negligible. This is reasonable because g and i are expected to be temperature independent. 2.4 Mixed

adsorption

and phase formation

The y-values of common

electrosorption systems are not dependent on the chemical composition of the supporting electrolyte. This indicates the absence

of any specific interaction between the electrosorbed substance and the ions in the outer Helmholtz layer. By contrast, characteristic changes of y can be observed in some special systems. Schmidt, Gygax and Biihlen[36], for instance, found for the system A&VPb‘* the electrosorption valency, y = 2, in common electrolytes,‘but much higher values in halide

329

solutions. This fact is explained by competitive adsorption[36,25]. Coadsorption has been discussed in the system H&Ed’+, N;[25] and Hg/Zn’+, SCN- [37] to explain negative y-values of the Cd’+ion and Zn2 ‘-ion respectively. Ion pair formation also seems to be important in the system Hg(Tl)/Tlf, NO;[38,39]. In principle, the analysis of mixed gdsorption systems yields a “mixed valency”, ymixr which requires a special analysis. This was discussed recently[25]. In the following correlations of single electrosorption processes yloiX-values have not been used. Further complications arise if place exchange reactions between the substrate and the adsorbate occur. With the start of phase formation, the measurement of the surface concentration and the evaluation of y becomes difficult or ambiguous. An example is the adsorption of cations in the systems Ag/Cd2+[40], Au/Cd’+ [41] or Ag/Sn’+[42], which is accompanied by alloy formation. Similarly, the adsorption of hydroxyl ions, even on noble metals, is followed by a rapid oxide formation which hinders the exact evaluation of adsorption data[14]. Phase formation has also been observed in the systems Hg,Tbz+ or HglTl+ in the presence of halides[43,44]. For all the special systems mentioned above electrosorption valencies are not reliable and cannot be used in the following correlations.

3. DmERMINATION

O”,,k&g

SUMMARY

OF

THE

During the last 20 yrs, many electrosorption systems have been investigated quantitatively by various authors. Thus the literature yields a considerable amount of data. In Section 3.1 the methods of determination are classified and described briefly. Further, a few comments on the special terminology of various authors are made. These comments refer b the column “method” of Tables 1 and 2. 3.1 Class$carion

of methods and special comments

According to equation (2), y can be evaluated from the charge flow or from the potential dependence of the clcctrosorption equilibrium. a. Determination from the charge flow. The determination from the charge flow requires the measurement of the surface concentration of the electrosorbed substance only. An elimination of diffuse double layer effects is necessary, usually by use of excess supporting electrolyte. The charge 4 must be measured or calculated for E = constant. al. During the anodic stripping of metallic adsorbate& coulometric and analytical measurements were carried out by Schmidt et al (eg ref.[45]). These measurements yielded the value “Aq/NMc-St&hiometrie” (= jAq/FAT),), which is an integral value calculated for the desorption of a monolayer. If y is independent of 8, which can be observed quite often for “‘metallic monolayers”, the results are identical with the electrosorption valency. In general, Schmidt corrected the potentiodynamic A q-values for the double layer charging in the pure supporting electrolyte. Therefore, the corrected values give the charge flow under potentiostatic conditions corresponding to equation (2).

J. W.

3.30

=HULTZE

F. D.

AN”

KOPPITZ

Table 1: Electrosorption valencies, yN, for anionic systems in aqueous solutions at small coverages, 0 r2:0.1. If necessary, the y-values were extrapolated to the potential of zero charge, + (t) = 0). Values marked by C) could not be evaluated for cN. For comments see Section 3 S’

M ClCl-

-0.2 - 1’

a8[l4]

Ag Pt Hg

clCl_

- 1’ - O-6’ - a.34

b3[55,61]

Ag Au Hg

BY BII-

- 1’

Hg

SCN-

-03

HB Hg 11

NY OHOH-

- 0.23 -0.65 -0-8

a5[8];a6,a8[102]

Sz-

- 1.4’

a3[72]

Hg

f&0:-

-0-7

a5, bl[73]

HB Hg Hg Hg Hg HI?

H,PO; c10; NO, PF,

-0.15

a6, aX[74] a8[75 J a8[76]; a6[77]

Hg Au

Br_

- 1’ -0.45

- 0.3 -00-X -0.5 --o-2 -0-52

Remarks

Method [ref.]

y,-Value

dy/de = -O.O7V-‘L-151 Monolayer (phase formation?)

; a6[35,59,60]

b3[55,61]

e =z 0.25, E” = 0.4 v dr/& = -@o-o8 v- ‘[15]

WQI

a8, b4[14];a6[63]; a8[64];a5, bl[8,65] b3[55] b4[56] a8[14];a6[51]; a5, bl C&65,663 a6, a8[67] ; a5, bl [S] a8[68,14] a5, bl[69] b2[70]

Monolayer dy/& = -O.l4V-‘[14]

;

Hg-S-bond[68]

Reversible at small R[70,71] Estimated from ysal” ate-+<0 Ion pairs in presence

a6, a8[78] a8[79] a8[14]; a6, b4[34]

of Zn 2+, Ni’+, Co” c731

.? = -2

* BS = Benzene-sulphonate. 7 BDS = Benzene-m-disulphonate.

a2. Analytical measurements using polarography or radiochemical methods have been carried out by Bowles[46], Sedlmaier[4~ and Schultze[28]. The combination of these with coulometric data, corrected for double layer charging, permits the determination of y. a3. Occasionally only potentiodynamic or galvanostatic charges are given corresponding to the thermodynamic quantity[ 131,

where Cn = (aq,/&)r is the double layer capacity at constant coverage, and C,, = F(ar.d/&)& is the adsorption capacity. If Cn G Cad, rough estimations of y are possible. Generally, IyI is smaller than IY&-131. For example, the ring disk measurements of Bruckenstein et a![481 allow the estimation of y from the “oxidation number” (= 2 - ysalv)given in Table 1 of reC[48]. a4. Salie and Lorenz[49] used rapid coulometric measurements of the desorption charge, Q!&, and of the reduction charge, Q$, to determine A. In reality, their measurements yield[14]

a5. From the frequency dependence of the double layer capacity, Lorenz et al (eg ref.[SO]) obtain a coef-

ficient, I, which is equivalent to y = -I[141 (and zl respectively). Since the change of double layer capacity with adsorption, i.dCu/dT, is given as well, the potential dependence of y can be eliminated according to equation (7). Since Lorenz[S] suggests I E ,i, the I-values given by Lorenz can be taken as y-values, too. a6. Parsons et al (eg ref.[51]) evaluated the capacity ratio K”“/K”, called “thickness ratio”, from capacity measurements. Actually, this value is equivalent to the electrosorption valency, Kozm = -$141. These “thickness ratios” measured at various values of E and 8 were extrapolated to low coverages and to the potential of zero charge in order to obtain Ye As far as earlier measurements are concerned, the absence of a supporting electrolyte does not interfere with the results, since the effects of the diffuse double layer were generally eliminated. a7. Values for the “thickness ratio” have also been published by Damaskin et al (eg ref.[SZ]); occasionally, however, no details on the potential dependence have been given. Therefore, an additional error of iO.05 may arise in the y,-values these not having been corrected for dy/de. a8 For a number of systems, the potential difference of the Helmholtz layer 4M_ z = f’(qm.r,,) is given in dependence on the metal charge and the surface concentration of the specifically adsorbed substance (eg ref.[53]). From these data we obtained q/r plots and finally yN according to the method described in ref.[14], eg Fig. 6.

Bond formation in electrosorbates--I

331

valencies, y. for cationic systems in aqueous solutions at B z O-1. y(e) can be taken as yN generally, since dy/& f; 0 for cations (see Section 2.3). Values for mixed adsorption systems are given in brackets. For further comments see Section 3

Table 2: Electrosorption

y,-Value

S’

M Pt Hg Hg Ga Hg Ga Bi Au Pt

H+ Kf

Pt

Tl+ (Cl-)

(0.6)

Tl+

1

Tl+ Q?+

CU Ag Au &) Pt

0.k 0.15 0.2 0.18 0.2 @I7 0.9 D85

Rb+ Rb+ cs+ CS+ CS+ Ag+ Tl+

c[14,58]

a5, bl[66] a5, bl[66]

aXW

a5, bl[66]; aS[66] a7[82] al, b3[83]; a2, b2[47]; a2[46]

a7[80,81]

[84] [14]

alC45.851

mixads (Cl-)?

(0.3)

a4[49]

1.8

a2, b2, c[28] a3[48]

ion pair formation C3&391 y = f(0); measurements in H,SO,[2S,48,86] ; dy/& = 0[28] mix ads in HCl[87,88]

( - 0.34)

a5[37]

Pt

(2 0.3)

b2[14,89]

(-0.3)

b2[25,9 l]

Cd’ + Pb*+ Pb’+

(x2) 2.05 1.95

1411 a1[85] al[93];

1.9 (2-6)

alC36.961 al[36] ; [97]

Au Ag Au Pt

Pb’+ PbZ+ (Cl_) Sb’+ Bi3 + Bi’+ Bi3+

J%* Hgf

PY+ Cl-py+

0.1 0.17

Au Cu Au Ag Ag

2

Cd2

’

small coverages are observed only dy/& x 0[66]

Ye=01 x om; Ye= 1 * 055[47] mix ads?

; b2[54]

Ag Au > J%

Hg

Remarks

Method [ref.]

;

al[45]

; a2, b2[47]

UK)

3 3 3 3

al[45,98] al[45] al[45,98]; a2[99]

b2[94]

mix ads; in ref.[37J 12 = Y/Z alloy formation? [41,89,90] mix ads, similar in SzO:- [92] alloy formation mix ads (Cl-)? alloy formation at E -z lpb only[95]

mix ads (CT, SCN-) ~25,361 mix ads (Cl-)?

b2[14,15]

b5[57] b5[57]

y -z 3 for 0 > @4[14,15] at B > 1 deposition of BiO+? 8 = 0.25 0 = 0.25; for further organic bases see ref.[57]

* py+ = pyridine+. i Cl-py+ = 2-Cl-pyridine+.

b. Derermination oJy from the potential dependence. The application of equation (2) allows the determination of y from the potential dependence of the electrosorption equilibrium. If the activity coefficients are constant, pcocan be substituted by the concentration, c,. At constant coverage, 13,, the derivative (aln c/k), yields y. bl. Lorenz (eg ref.[8]) obtained from (a&&),- a coefficient, J which is equivalent to y = -f[ 14] (and zf respectively). y,-values were obtained from these ,j’coctiicients after elimination of the potential dependence (equation (7)). b2. Coulometric measurements in dependence on E and @ were used by Schultze (Ed ref.[28]) for the evaluation of y in cationic electrosorption systems

using the reasonable assumption (&/Z+ = (a&Z&, where Q is the desorption charge corrected for double layer charging. The y-values obtained were independent of the potential E but dependent on the coverage 0. As was explained in Section 2.3, the values for small coverages were chosen as y,-values. The same comment is valid for the results of Bowles[54]. b3. The potential dependence of the electrosorption equilibrium was measured by Schmidt et al in a small concentration range. y-values can be taken from his F/(E-E,)-diagrams (eg ref[55], Fig. 2). b4. From adsorption isotherms, r = f(e,p,), given in the Iiterature (eg ref.[56]), &-diagrams were constructed and y,-values obtained. In solutions without supporting electrolyte, the potential dependence of

J. W. SCHULET, AND F. D. KOPPITZ

332

electrosorption valency ratio, y/z, us the absolute difference of electronegativitiea, IxM~ xSl. Data are taken from tables 1 and 2. 1 = Pt/H+, CujPb”, Cufll+, A@l+: 2 = Au/Cu2+, Au/Sb3+, Au/Bi3+: 3= Au/Tl+, Au/Cl- ; 4 = Pt/Cu’+. Fig. 2. Plot of the

the Helmholtz

layer, A& must be u&d instead of

l[12]. With this modification, y-values were obtained

by Schultze and Vetter (ref_[14], Fig. 5, 7). This method was also used by Parry and Parsons[34], who again call the result the “thickness ratio”. Values were taken for small coverages and Ad = 0. b5. Barradas and Conway (eg ref.[57]1 calculated the standard electrochemical free energy 0AC of the adsorbate in dependence on E, but for constant 0. The slope of these curves at Ed yields yN directly. c. Determination ffom kinetic measurements. The electrosorption vahncy can also be obtained from the sum of the transfer coe&ients[14]. This method was used by Lorenz and SaliC[49], by Schultze[28] and by Vetter and Klein[SX].

3.2 Summary of the data Using these methods, y,-values were evaluated as far as possible. The results for ionic electrosorption systems in aqueous solution are summarized in Tables 1 and 2. Some electrosorption systems were measured by several authors using different methods. In spite of these differences, the y,-values coincide sufficiently, even in systems with and without excess supporting electrolyte. This was discussed for the system Hg/I- as example[14]. Average values are given in Tables 1 and 2 taking into account the experimental reliability of the differing methods. For many systems, y,-values are given with two decimals. The limits of error, however, are not better than kO.1 generally. y(cjvalues, which could not be corrected for the unknown potential dependence, dy/&, may have an additional error smaller than &0,05. Further comments on the systems are given in the last COlUtI-llI.

4. DISCUSSION

4.1 The correlation between y and the electronegativity, x The summary of experimental electrosorption valencies shows a wide scattering from negative to positive values. In general, the valencies of the cations are positive and those of the anions negative. To compare these different values, it is convenient to divide *The following discussion refers only to the y,-values of Tables 1 and 2. Hence, the subscript N can be omitted for reasons of simplicity.

7 by the ionic charge, z. Then the ratio y/z* is in the range, 0 < y/z < 1. A rough inspection of Tables 1 and 2 shows that there are two types of systems, one with y/z 2 1 and the other with y/z -+ 1. Espe cially those electrosorption systems with heavy metal ions have ratios y/z z 1 and obey the Nernst equation and Faraday’s Law. On the other hand, strong electronegative or electropositive ions, eg the alkali metal ions and the halide ions show ratios r/z 4 1. It was shown recently[14,15] that these differences in behaviour can be explained by the formation of a covalent bond, 3, z -.z, on the one hand, and by a mainly electrostatic adsorption without charge transfer, ,I zz 0, on the other. Of course, there may be an intermediate range with a more or less polarized bond between the electrode and the adsorbate[8,27]. Generally, the analysis of electrosorption valencies is easier for mononuclear than for polynuclear ions. Hence, in the following sections only the mononuclear ions are discussed. Polynuclear ions will be discussed in Section 4.4. According to Pauling[19], the polarity of a chemical bond increases with increasing diffcrcncc in the electronegativities, [Ax], of the two atoms involved in the bond formation. Since the ratio, y/q is a rough measure for the bond formation, these values of the mononuclear ions were plotted in Fig. 2 us the absolute difference of the electronegativities, /AxI= lxhl - xsl of the electrode, xM, and of the adsorbate, xs. Figure 2 demonstrates that this correlation is reasonable for cations as well as anions. A similar correlation can be obtained for methanol and other solvents (Part 2). For small differences lAx[ < 05, the ratio, y/z, is nearly 1 but decreases with increasing IAx/. At /AxI > 1-O an almost constant value, y/z = 0.16, is reached. In general, the experimental values are scattered around the solid line, which will be calculated in Section 4.3. The deviations are smaller than 02 for most systems. Only the systems Ag/B- and A&‘show completely different behaviour, the reason for which is not clear. It may be that phase exchange reactions cannot be excluded in these systems, similar to the oxide forming systems (see Section 2.4). The summary of data in Fig. 2 establishes a (y/z)/ lAxI-correlation experimentally. In the following two sections it will be attempted to derive a model describing the charge transfer in electrosorbates. Because of various limitations, however, the model allows qualitative estimations only. 4.2 Estimation

of the yeometric factor,

g

The analysis of the y/z-values must start with the simplified equation (6). The division by z yields

+g-+gg).

(10)

As was pointed out earlier[14], the analysis is impeded by the fact that both g and 1 are unknown. However, the constant region of y/z beyond IAxl z I.0 indicates a lower limit of charge transfer: obviously A z 0. This means that all ions in this region are electrosorbed electrostatically, ie as ions without charge transfer, as is assumed by many authors[52,53,63]. With A z 0, a minimum geometric factor, gmin z 0.16, follows from the data of Fig. 2. This means that in

333

Bond formation in electrosorbat-I

the electron gas of the metal[14,15]. Partially discharged ions (Fig. la) represent an intermediate case. Because of the partial dipping .into the electron gas, the electrical potential, #ad. may he nearer to 4, than in the case of electrostatically adsorbed ions. Hence, a geometric factor that increases with increasing charge transfer would be a better approximation, especially in the range, 1Axl c 03. The assumption (13)

IO \

\

o-a (x20.6

o-4

(13)

02 I cl

I

I

I

,

2

3

,

B

Fig. 3. The “thickness ra:o” (la - X,)/Q, calculated as a function of the inner layer ‘distance, xi, for a constant

value of x2 = 4%1, and the ratio y/z (experimental data IX the radius Y,of ions adsorbed electrostatically (Kf, Rb*, Cs+, CI-) and discharged partially (Br C, I-).

the case of electrostatic

adsorption the electric potential at the adsorption site, &, is not so different from the potential of the Helmholtz layer, &, (see equation (4)). The question arises whether this geometric factor, g, and the minimum value of y/z, can be interpreted in terms of a “thickness ratio”,

The thickness of the double layer, x2, will be about 4 A. Let us take the radius of the electrosorbed ion, rs, as distance from the surface, x,. Since rs < 2 8, for most ions, a “thickness ratio”, (x2 - x1)/x2 > 05, would be generally obtained. According to equation (ll), y,,Jz should also exceed 0.5, which is not observed. Further, the geometric factor, g, should increase with decreasing ionic radius. It follows that y/z should increase also. Figure 3 shows a plot of y/z us r, for alkali metal ions and the halide ions. The experimental y/z- values are much smaller than the values calculated for the common assumption (11) which is shown by the dotted line. Further, there is not the expected influence of r, on y/z. Hence, it must be concluded that assumption (11) based on the linear field approximation is invalid, possibly because the field is not linear. If the potential difference, & - I&, is generally small compared with +,,, - $Q,, it can be taken that the influence of rs on y/z is small. The same effects are observed in nonaqueous solvents (Part 2). The increase of y/z from chloride to iodide is not due to the increasing radius but to the beginning charge transfer, which cannot be neglected for bromide and iodide[ 141. In the following discussion the geometric factor g z gminE 0.16

(b = 0.84 = l-g,,,_) takes this dependence into account. According to (13), g is in the range, gmin< g < 1, since L/z is negative generally.* The somewhat arbitrary assumption (13) will be justified quabtatively by the discussion in the next section for the region, -d/z > 0.6, but may he questionable in the range of smaller charge transfer. 4.3 Estimation of A applying Pading’s formula According to Pauling[t9], the covalent bond formation and, consequently, the charge transfer can be estimated from Ax using the empirical relation - i = exp[-a(Ax)*]. This formula describes the charge transfer in a diatomic molecule in the gas phase. Of course, it will not be valid with the same constant, a, in aqueous solution where the hydration of the electrosorbate has a strong influence on the charge distribution in the adsorbate[S]. Because of its large dielectric constant, water supports the ionization. Therefore, a larger “a” must be expected for the aqueous medium. To obtain the best fit of experimental values, ie a smah charge transfer, -L/z < @05, in the range of electrostatic adsorption, IAxj > 1.0, a = 3 was assumed instead of a = 0.25, suggested by Pauling for the gas phase. The corresponding curve for the charge transfer, -L./z, qd for the actual charge of the adsorbate, z&d/z (equation (5)), is shown in Fig. 4. For small Ax-values, IAxl -C 0.3, the charge transfer is nearly complete, and the true charge, z&z, is almost zero. On the other hand, the charge transfer is small or negligible for large AX-value& lAxl > 1.0. The formation of polarized bonds with a partial charge transfer is important in the range, 0.3 c 1AxI -C 1-O.

(12)

is used for the aqueous solution as a first approximation. It should be pointed out, however, that this approximation is invalid for metallic monolayers with VIZ = 1 (see Fig. lb). In these systems g approaches unity, as electrosorbed ions penetrate completely into *Theoretically, g-factors, 9 > 1 or 9 -=z0, are possible according to equation (41 if #*., is not in the range between Q,,, and 45,[1031, The experimental values of Y/Z however, are always in the range g,in c y/z -C 1. Hence, hypothetical values n > 1 or g < 0 are irrelevant in real systems.

Fig. 4. The expressions, 9, --A/z, y/z and z.&, according to equations (13-161, as a function of the absolute difference of electronegativities I xu - xs/

J. W.

334

SCHULTZE

AND

To calculate y and y/z respectively, the first approx(12), is used. Combining equation (10) and (14), equation (15) is obtained:

imation

Y/Z= gmj, + (l_g,,,S-expC-

a(A#l.

(151

The corresponding curve is shown in Fig. 2 in dependence on IAx\ by the dotted line. In the range, /AxI < 0*7, the calculated curve does not fit the experimental points sufficiently because of an underestirnation of the gcomctric factor, g. Hence g was calculated according to the second assumption. equation (131, which was combined with equation (14). Of course a large increase of g is obtained for small values of lAxI_ The corresponding curve is plotted in Fig. 4, too. The combination of equation (13) with equations (10) and (14) yields instead of equation (15) the better approximation (16): Y/Z= s,~,,+

2bexdL-4Wl

- bewC-24&X)21, (16)

where b = 084. Using equation (16), the full line plotted in Figs. 2 and 4 for y/z was calculated. This line fits the experimental values better than the dotted curve which seems to be a qualitative justification of assumption (13). However, in spite of the large differences in the geometric factor between the first and the second assumption (see Fig. 4), the differences in the resulting equations (15) and (16) are smaller as can be seen by the relatively small shift from the dotted to the solid line in Fig. 2. For this reason. a further discussion of better approximations than (13) is not reasonable since it does not have such a large influence on the results. In principle, the description of the experimental data of Fig. 2 by a general model of bond formation at the interface metal/aqueous solution, equation (16), can give only a rough idea of the real distribution of charge. Of course, differences in the hydration of. anions and cations, in bond length, in the crystallographic orientation and in the band structure of the substrate and further effects may be reasons for deviations of the experimental points from a generally assumed model. On the other hand, the qualitative agreement is reasonable, and this justifies the qualitative application of the model. These considerations indicate that covalent adsorption with almost complete charge transfer, L z -2, can be expected in the range [AxI -=x0.5, which is schematically represented in Fig. lb. The electron gas of the metal thus extends over the adsorbate and a strong increase of the geometric factor is the consequence. Because of the small or negligible charge of the adsorbate electrostatic repulsion within the adsorbate is small and monolayers can be built up. The whole double layer is unchanged but has shifted to the electrolyte side. The ‘partial charge transfer”, 0 < -a/z < 1, favoured by Lorenz[S] and discussed hy Plieth and Vetter[26,27] must be expected in the range 0.3 < IAxl < 1.0. For small values of [AxI, PLJ 0.3 < IAxl < 0.5, however, the inlluence of the partial charge transfer on the electrosorption valency is smaller than expected from the @-curve of Fig. 4, since in this range the electronic interaction with the electrode metal may be so strong that g is not greatly different from 1. For instance, systems with y/z z 1 exist even [or /AxI< @6, and metallic monolayers

F. D.

KOPPITZ

with small polarization of the adsorption bonds may also exist[14,16,28]. A hrther increase of lAxI. however, usually yields strong polarized bonds. The adsorbate retains some charge, from which strong electrostatic repulsions follow. The adsorption is thus restricted to small coverages, and the adsorbate remains in the inner layer (Fig. la). The system Hg/- is a typical example. The coverage of I- is generally smaller than 02. From the comparison of the electrosorption valencies of the halide ions, a value of A L 0.3 was deduced using geometric arguments[l4]. This result seems to be justified by the model curve in Fig. 4, which yields a partial charge transfer of about 0.34 for IAxl = 0*6, corresponding to an actual charge of about -057 or less instead of z = - 1. The increase of the double layer capacity, (XJFarI~), = -dy/& = 0-14-V-l gives a further support for the conclusion that the iodide ion is partially discharged[14,15]. It should be emphasized once more, however, that the assumptions regarding the geometric factor according to equation (12) and (13) respectively are arbitrary. The arguments for equation (13) are strong in the range of small lAxIvalues but weak in the range of partial charge transfer. Hence, it cannot be decided which equation is better for the system Hg/I-. In regard to the halide ions at mercury, the correlation between -A/z and IAxl is paralleled by the colour and the solubility of the corresponding mercury halide compounds, both of which indicate an increasing charge transfer in the order Cl- < Br- < I-[14,15]. Instead of the electronegativity, the work function could also be used for correlations[17]. Such a correlation, however, is possible only for metal ions, but not for anions. Furthermore, the work function is approximately proportional to the electronegativity[20,100]. Hence, a plot of y/z vs A4 is similar to Fig. 2 and gives the same information, but only for cations. The corresponding range for covalent adsorption is 0 -C A4 < 1.2V and for electrostatic adsorption A$ > 2V respectively. According to Barclay and Caja[7], the adsorption of anions increases with the softness of the adsorbed base (anion). The degree of softness is given by Pearson’s classificationrl011. This classification. however. is similar to the Londept of electronega&ity. Sofi (hard) bases show small (high) eiectroneg@vities. Thus, the qualitative concept of Barclay and Caja[7], restricted to anions, is supported by the more general correlation carried out in this work. 4.4 Pvlynuclrar ivns After the extended discussion of mononucleus ions, a short comment should be made on the polynuclear ions. As in case of the simple ions, the ratio y/z should be discussed only. As can be seen from the systems Hg/benzen*sulphonate and m-disulphonate respectively, the electrosorption valency increases parallel to the increase in charge (Table 1). In general the ratio y/z is very small for the polynuclear ions, eg NO;, HIPO; (Table l), or the pyridinum ions (Table 2). This indicates that y/z is determined in these systems mainly by gmi, z 0.16. Of course, y may be even smaller for the ions which are much larger than potassium or chloride ions. The PF; represents an exceptional case, because two or three F--ions of the

Bond formation

in electrosorbates-I

complex may be attached to the mercury surface. The effective charge of - 2 or - 3 in the inner layer could c\plain the large value, y = -05. In the ions containing sulphur,

SCN-[8]

and

S,O$-[73],

on the other

hand, a small charge transfer may also take place, similar to the bromide or iodide system. This explana$ion is consistent with the concept of Barclay and Caja[7J since these ions are soft bases. Finally, a charge transfer also seems to be important for the OH--ion[69,70]. However, place exchange reactions are rapid in the systems containing oxygen, so that one should be cautious regarding these values. Acknowledgements-We are obliged to Prof. Dr. H. Gerischer and Dr. D. M. Kolb for stimulating discussions. The financial support of the Deutsche Forschungsgememschaft is gratefully acknowledged. REFERENCES 1. J. O’M. Bockris, M. A. V. Devanathan and K. Miiller, Proc. R. Sot. A274, 55 (1963). 2. T. N. Andersen and J. O’M. Bockris, Electrochim ACfU 9, 347 (1964). 3. D. D. Bodir, Jr., J. phys. Chem. 76, 2915 (1972). 4. T. N. Andersen, J. L. Anderson and H. Eyring, J. ahvs. C&m. 73. 3562 (19691. Chem. 28, 443 (1970). 5. b.- J. Barclay, ‘J. &c&a&l. d. ele@rounul. Chem. 19, 318 (1968). 6. D. J. Barclay, 7. D. J. Barclay and J. Caja, Grout. &em. Acta 43, 221 (19711 , __ _, 8. W. Lorenz. 2. ohms. Chem. 232, 176, (1966). 9. W. Lorenz, Z. bh&s. Chem. 244, 65 (1970). 10. R. Parsons, A& Hectrochem. 7. 188 (19701. 11. B. B. Damaskin, Elektrokhimiyu’ 5, 77i (19k9). 12. K. J. Vetter and J. W. Schultze, Ber. Bunsenges. phys. Chem. 76, 920 (1972). 13. K. J. Vetter and J. W. Schultze, Ber. Bunsenges. phy.~. Chem. 76, 927 (19721. 14. J. W. Schultze and i. J. Vetter, J. elecrrocmal. Chem. 44, 63 (1973). 15. J. W. Schultze, Proc. of the II Int. Summer School of EfectroMechanical Aspects Quantwn $&&try, Ohrid, Yugoslavija 1972. 16. D. M. Kolb,. Przasnyski and H. Gerischer, J. electroanal. Chem. 54, 25 (1974). 17. H. Gerischer, D. M. Kolb and M. Przasnyski, Surface Sci. 43, 662 (1974). 18. D. D. Eley, Discuss. Farodav Sac. 8. 34 I1950). 19. L. Paul&, J. Am. them. Sdc. 54, 3570 i1932j; “The Nature of the Chemical BonR, 3rd ed. Cornell Univ. Press, Ithaca, N.Y. 1960. 20. R. S. Mulliken, J. them Phys. 2, 7X2 (1934), 3, 573 (1935). 21. D. P. Stevenson, J. them. Phys. 23, 203 (1955). 22. J. J. Broeder, L. L. van Reijen, W. M. H. Sachtler and G. C. A. Schuif 2. Elrktrochem. 60, 838 (1956). 23. A. J. Sargood, C. W. Jowett and B. I. Hopkins, Surface sci. 22, 343 (1970). 24. K. J. Vetter and J. W. Schultze, J. e[ectroanal Chem. 53, 67 (1974). 25. J. W. Schultze and K. 5. Vetter, Electrochim. Acta, 19, 913 (1974). 26. W. I. Plieth and K. J. Vetter, Z. phys. Chem. NF 61, 282 (1968). 27. W. J. Plieth and K. J. Vetter, Colln. Czech. them. Commun. 36, 816 (1971). 28. J. W. Schultze, Ber. Bunsenges. phys. Chem. 74, 705 (1970). 29. E. P. Gyftopoulos and J. D. Levine, J. appl. Phys. 33, 67 (1962). 30.: T. A. Delchar and G. Ehrlich, J. them. Phys. 42, 2686 (1965).

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