voltammetric study of humic and fulvic substances: part iv. behaviour of fulvic substances at the...

J. Electroanal. Chem., 121 (1981) 273--299 273 Elsevier Sequoia S.A., Lausanne - - Printed in The Nether lands

VOLTAMMETRIC STUDY OF HUMIC AND FULVIC SUBSTANCES

PART IV. BEHAVIOUR OF FULVIC SUBSTANCES AT THE MERCURY--WATER INTERFACE

J. B U F F L E * and A. COMINOLI

Department of lnorgamc and Analytical Chemistry, University of Geneva, Sciences II, 30 quai Ernest Ansermet, CH-'1211 Geneva 4 (Switzerland)

(Received 2nd October 1979; in final form 29th Sep tember 1980)

A B S T R A C T

The adsorpt ion and reduc t ion propert ies of FA are studied at the dropping mercury elec- t rode by means of electrocapil lary measurements and ch ronoamperome t r i c techniques. An es t imat ion of the adsorpt ion parameters is obta ined. These results tend to show that the interact ions o f F A at the e lect rode surface play a role in the adsorpt ion process. Further- more, a faradaic irreversible reduc t ion current is observed, even for E > --1.0 V. The usefulness of the parameters obtaine-d in this work for the in terpre ta t ion of vo l tammet r ic studies in the presence of F A has been discussed.

(I) I N T R O D U C T I O N

In our previous papers on humic (HA) and fulvic (FA) substances, we showed that their adsorption on the mercury electrode [1] influenced strongly the redox properties of lead [2,3]. In water chemistry such effects may have important consequences regarding the interpretation of the results obtained for speciation studies by voltammetric techniques, as well as on the determination of concentrations of heavy metals by anodic stripping vol tammetry [4,5]. It is well known that FA and HA are adsorbed at other interfaces, e.g. water synthetic resin [6], air--water [7] and water--silicates [8--10]. Thus, a bet ter knowledge of the adsorption properties of FA and HA would be useful in understanding a wide range of chemical and biochemical aquatic reactions. In this paper we have a t tempted to determine the nature and the magnitude of the main factors which are responsible for the behaviour of FA at the mercury elec- t rode reported in ref. 1. A quantitative evaluation of the corresponding parameters is necessary in order to conduct physiochemical studies either with model compounds or by computer simulation, as well as to interpret correctly the analytical voltammetric data, to take into account any secondary effects occur- ring due to the presence of FA.

* To w h o m correspondence should be addressed.

0022-0728 /81 /0000- -0000 /$02 .50 , @) 1981, Elsevier Sequoia S.A.

274

(II) GENERAL CONSIDERATIONS

Fulvic and humic substances are organic compounds resulting from the decomposi t ion of living organisms by very complex microbiological and chemical processes [8]. Although their nature itself is little known, they are present in natural waters as a group of compounds showing properties of considerable importance. The predominant characteristics of their structure is the presence of large numbers of phenolic and aromatic carboxylic groups. However, they cover a wide range of molecular weights (Mw) (several hundreds to millions): the low molecular weight fraction (some hundreds to tens of thousands) are called fulvic acids (FA), whereas the high molecular weight fraction is refered as humic acids (HA). Hence, these compounds exhibit gradual changes in their properties: HA may be considered as polyelectrolytes, whereas the low molecular weight FA behave rather as "simple" dissolved compounds. However, they may form aggregates with each other [8,11,12], which may make their properties very dependent on their concentration. Their hydrophobic i ty also seems to depend on their molecular weight as well as the proport ion of their oxidizable or reducible groups (particularly phenolic and quinonic groups) in the molecule. Although FA and HA may be roughly fractionated, e.g. by membrane ultrafiltration or gel filtration, the gradual change in their properties as well as the very large number of components in the mixture prevent their separation into pure fractions. It is difficult even to remove completely the inorganic components (particularly the complexed metal ions such as Fe(III): see section VI) wi thout losing an important proport ion of organic matter [13].

The results of ref. 14 showed that, even for benzoic acid, which may be considered as the simplest component of the FA mixture, the adsorption process on the mercury electrode is relatively complex. Hence, one may expect a very complicated situation for the behaviour of FA at the electrode. Some of the possible important factors which must be considered, when comparing their behaviour with that of a pure "simple" adsorbable compound, are the following:

(1) Competitive adsorption: due to the fact that the adsorbability of the components may be expected to be dependent on their molecular weight, the adsorption increasing with increase in molecular weight.

(2) Diffusion process: the diffusion coefficient o f the components will decrease with increase in molecular weight, resulting in a slower rate of transport of the high-Mw components compared to that of the compounds having low Mw.

(3) Aggregate formation: aggregates may be formed bo th in the bulk of the solution and at the electrode surface. This will result in an increased adsorbability with the degree of coverage. It will be shown later (Section V.5) that these three factors may affect adsorption rates at the electrode.

(4) Redox process: FA and HA may be reduced or oxidized [15] and this process may depend on the degree of coverage of the electrode as well as on the size of the molecule.

(5) Polyelectrolytic nature of FA and HA: this factor may play a role on the dependence of the adsorption on pH and potential. Furthermore, a possible rearrangement of the macromolecular structure at the electrode surface may

275

also alter the rates of desorpt ion/adsorpt ion process. Because of these difficulties, to make studies on synthetic model compounds

or on mixtures of model compounds instead of the FA system itself, might seem to be a bet ter approach. For instance, it has been reported that the acid-- base and complexat ion properties of FA could be simulated reasonably well with a mixture of three simple aromatic compounds [16]. However, the choice of these compounds implies that the predominant characteristics of FA are known. It is true for the acid-base properties [16,17] and complexation with at least certain metals (e.g. refs. 18 and 19). But at present very little is known as to what are the most important factors which affect the behaviour of FA at the mercury electrode. Therefore, the objective of the present work is to t ry to point ou t these factors in order to facilitate further detailed investigations on realistically chosen model compounds.

In such preliminary studies, it must be realized that, because of the complex nature of the FA system, the variability of the measured signals is relatively high (often about 10%), irrespective of the method used. Consequently, relatively large errors are incurred in the measured parameters representative of the properties under consideration. Furthermore, their magnitude increases with the number of adjustable parameters used for interpreting the data. For the FA system, it was observed in other investigations [18,20] that a detailed investigation of their properties is mainly limited by the fact that the use of too many parameters makes them lose their significance. Thus, only the factors which predominantly affect the behaviour of FA can be investigated. Hereafter they will be called the predominant phenomena. Obviously, the relative importance of the predominant phenomena may depend on the methods and experimental conditions used. Hence, for practical usefulness, the measured parameters should be checked by widely different methods and under a wide range of experimental conditions. In this respect the results given here and those reported in Part III [1] are closely linked together.

Owing to the relatively large variability in the measured signal, not only the predominant phenomena are observed but also the measured parameters are averaged parameters. They are overall parameters because firstly they include, in addition to the predominant processes, secondary processes which are more or less important bu t cannot be detected separately. Secondly, they represent the mean behaviour of a range of compounds treated together. Thus, these parameters should not be considered as representative of the behaviour of each of the components of the system. However, the use of overall parameters enables us to evaluate qualitatively the factors which are important and those that can be neglected. Furthermore, from an analytical viewpoint, the description of a complex system by means of overall parameters may be very useful, as long as their conditions of applicability are clearly stated. In the field of water chemistry, hardness, alkalinity and total organic carbon may be cited as examples of useful overall parameters. In the case of the electrochemical behaviour of FA, the overall parameters can be used to predict semi-quantitatively and simply, the occurrence of a secondary reaction resulting from the presence of FA in the water sample during electroanalysis of trace metals of the sample. They will also enable us to make the appropriate corrections for their inter- ference while interpreting the data.

276

Their usefulness also depends on the representativeness of the FA sample used for their determination. The results o f ref. 1 indicate that FA from freshwater samples other than those used here behave similarly. Furthermore, other properties {molecular weight, complexat ion [6,8,11] ) of FA of fresh waters seem to be little dependent on the nature of the source. Hence, although this aspect has ye t to be studied in more detail, it is reasonable to expect the general conclusion drawn from this work to be applicable to FA of other freshwater samples.

(III) EXPERIMENTAL

A P.A.R. polarograph Model 170, was used for recording the electrocapillary curves and the current--t ime curves. The drop time and flow rate of the capillary tubes were respectively 27 s and 0.179 mg s -1. All potentials were measured with respect to the Ag/AgC1/sat. KC1/0.1 M KNOa reference electrode.

The air--water surface tension measurements were made by means of a Lecomte de Nouy apparatus, KRUSS.

All the solutions were prepared from pro analysis Merck products. Bertholet S.A. (Geneva) nitrogen, certified with a puri ty of 99.995%, was used for prepa- ration of the solutions.

Studies were made using water samples Nos. 50a, 50b and 22, the composi- t ion and t reatment of which are described elsewhere [ 11 ]. The concentrations of FA are expressed in M 1-* using 1000 for the molecular weight of FA (see Parts I--III, refs. 1--3). Unless otherwise stated all the measurements were car- ried out at 25 + 0.5°C and in 0.1 M KNO3 medium. The errors reported for the values of the parameters are only statistical.

(IV) PARAMETERS OBTAINED FROM THE DC CURRENT--TIME CURVES

(IV.l) Nature o f the model to fi t the experimental data

Current--time curves were recorded for a series of concentrations of FA in the range --0.3 to --0.8 V, in steps of 0.1 V, at pH 3.8, 5.0 and 7.0. These curves were used to derive quantitatively the overall parameters representative of the most important properties of FA at the electrodes by fitting them to the model described below. In view of the discussion of Section II, this model was based on the following considerations:

(1) It takes into account qualitatively all the phenomena observed with regard to the behaviour of FA at the mercury electrode using the various voltammetric techniques (Parts I--IV). These observations were the followi.ng:

(a) FA are slowly adsorbed on the electrode (Parts I and II, Sections IV.2, IV.3) and this produces changes in the capacitive current, ic (Part III), particularly in the range --0.2 to - 0 . 7 V, and in the electroreduction process of the complexed trace metal ions if they are present (Part II).

(b) The current measured by dc polarography (Part III and this work) is composed, at least partly, of a faradaic component , i~, and it is probable that the increase in the slope of the baseline with increase in [FA], observed in normal pulse polarography [21] could also be interpreted as due to the appearance

277

of a slow faradaic process. However, the experimental results do not enable us to assess the relative importance of the capacitive and faradaic components , therefore both of them have to be taken into account in the model used to interpret the data.

(c) Here, if may be assumed to arise from a slow irreversible reduction process for E > --1~1 V, since a faradaic peak was not observed in fast (ACP, Kalousek, DPP: see Part III) or even moderately fast techniques (cyclic voltam- merry) in the above potential range. Also, no wave was observed in dc polarography in this range (Part III).

(2) It represents the simplest model possible, i.e. that for which the results of the i - - t curve measurements can be interpreted quantitatively by means of the least number of adjustable parameters and the simplest mathematical equa- tions.

(3) It permits us to obtain physically reasonable values for the corresponding parameters.

The simplest hypothetical system which could represent the experimental observations described under (1) and in Section IV.2, is a system composed of two components: an adsorbable component A for which the adsorption process is the slow step, and a slowly and.irreversibly reducible substance D, the reduction rate of which may be influenced by the adsorption of A. Such systems have been considered by several authors (e.g. see ref. 22). In the Appendix, equa- tions are derived which give the influence of the experimental parameters (time, potential, [D], [A]) on the total measured current, i, for such an hypothetical system. The applicabilities of the assumption made in the hypothetical system, to interpret the overall behaviour of the real experimental FA system are discussed in Section V.

In Section IV.2, eqns. (A7), (A9) and (A10), derived in the Appendix, will be used to fit the experimental data after making the following modifications to take into account the complex nature of the FA system: the nature of A and D cannot be specified in the FA system, but the following relationships may be used:

[D] = K D [ F A ] 0 < K D ~ < 1

and

[A] = K A [ F A ] 0 < K A y < l

where KD and K A are constants. As the fitting of eqn. (A10) to the results of the complex FA mixture may give only overall parameters (as defined above) and not rigorous constants, they will be differentiated from the true constants by using superscripts ~ on the corresponding symbols.

With these modifications, eqns. (A10) and (A9) will be applied to the FA system, in the form:

i - - r t - 1 / 3 = p t 2 / 3 _ p t 2 / 3 A F m F(~') (1)

where r is defined as in eqn. (A3) and is a constant at a given potential. It is determined experimentally by recording the current--t ime curves in pure 0.1 M KNO3 solution.

~= (k~ [FA] + k b ) t (2)

278

where kf a n d kb are the overall parameters corresponding respectively to k a / F m

and kd/ I" m in eqn. (A9).

P = 0.85m 2/3 [Cehf - - CF] [FA] = p ' [ F A ] (3)

where

b e = K A [•C(E - - E•) - - C0/kE m] (4)

and

CF = 10-3 n F K D k o (5)

1 + 0 ~ ( 1 - - h,/k0) (6 )

' ~ F m - 1 - -CFIO~k f 1 - - Cekf lC F

(IV. 2) Exper imen ta l results

To evaluate qualitatively whether or not the phenomena assumed in deriving eqn. (1) are reasonable for the FA system, one may (a) compare the numerical values of the overall parameters obtained with reasonable values of the corresponding constants, and (b) test these parameters under widely different experimental conditions. The corresponding results are given below.

( IV .2 .1 ) Relat ive impor tance of the capacitive and [aradaic c o m p o n e n t s Typical i = f(t) curves are shown in Fig. 1. From these curves, p may be

determined experimentally by plotting (i - - rt -u3) as a funct ion of t 2/3. Indeed F(~) -~ 0 when t -~ 0, so that p is given by the slope of the tangent at the curve for t -~ 0, in the above plot (see eqn. 1). Here, p vs. [FA] plots are given in Fig. 2, for pH = 3.8. It can be seen that good straight lines are obtained which are in agreement with eqn. (3). Similar results were obtained at pH 5.0 and 7.0. ' According to eqn. (3), the slopes, p', of these straight lines should be proportional to Ce and CF, which themselves depend on the potential in two completely different ways. Hence, from the dependence of p' on the potential, an

15~ -,/nA

5 '

,

i-~InA 3 0 '

i s b " |

| I i L i i 1 ! ii

0 5 10 15 2 0 2 5 t / S

Fig. 1. Typical exper imenta l cur ren t - -brae curves; KNO3 0.1 M; T = 25°C; pH 3.8. ( . . . . . . ) [PAl =0,( ) [ F A I = 7 O m g l - I , E = ( a ) - - o . a v ; ( b ) - - O . 6 V .

30

20

10

- p / h A s -2/3

¢ ) ,

J,

Y

/ • A •

~ A A " ~ ° " ' " ~

~ , ~ . . . . . [ FA]//M

2.0 &O 6.0 8.0 10.0 1210 14.0 x10-5

Fig. 2. Change in p (see eqn 3) with [FA]. For experimental conditions see Fig. 1. E = (c]) --0.3 V; (A) --0.4; (O) --0.5 V; (A) --0.6 V, (~,) --0.7 V

279

estimation of the relative importance of the capacitive and faradaic components of the current may be obtained. A plot of log Ip't as a function of E is shown in Fig. 3 for pH 3.8. From the definition of Cc (eqn. 4) such an almost linear dependence on E is unlikely for this parameter. On the other hand, CF is proportional to k0 (eqn. 5), an overall measured parameter which is assumed to be predominantly due to the rate constant of charge transfer, k0. Now, accord-

log I P'I

373I° °' 3533 IL

3.0 5.0 7.0

-3J,

- 3 . 6 '

- 3 . 8 •

-4.0 •

-4.2 .

/ f

-4.&- E//V

-o~ -o~ -o.~ -o.s -o6 -o~ -o~

Fig. 3. Change in p ' (see eqn. 3) with potential. For experimental conditions see Fig. 1. Insert: influence of pH on the reduction process, E = --0.7 V.

280

ing to eqn. (A6), In k0 depends on the applied potential, E, and on the potential in the plane of closest approach, ~. Relationships between E and ~ were computed theoretically (see ref. 22, p. 233 and ref. 23) and checked experimentally [23], for simple electrolyte solutions. These results show that, in our experimental conditions, (0.1 M KNO3 and IE - - E ° i < 0.35 V) one has, approx- imately, ~ = f . (E -- E~), where f is a constant. From the results of ref. 23, it may be seen that f = 0.17 f o r E < E~ and f = 0.1 f o r E > E ~ . As it may also be expected that the distance of closest approach of FA will be larger than that of the ions used in ref. 23, we can use here the condition f ~< 0.15. The above conditions may be combined with eqn. (A6) and eqn. (5), to obtain a relationship between In CF and E:

In CF = C t e - - [~n(1 - - f ) + zf] ( F / R T ) E = C t e - - ( b F / R T ) E (7)

where the constant includes all the parameters independent of potential. Figure 3 shows that a straight line is obtained when one plots loglp'l as a

function of E, at pH = 3.8, in the potential range --0.3 to --0.8 V. Similar linear plots are obtained for pH 5.0 and 7.0. Comparison of these results with eqns. (3) and (7) suggests that, in the total measured current, the contr ibut ion of the faradaic component represented by the term CF in P', is more important than the change in the capac i t ivecomponent due to the adsorption process represented by the term Cck~. If this term is neglected then b can be evaluated from the slope of the curve in Fig. 3. The average value of b thus obtained was found to be 0.08 -+ 0.015 for the three pH values. This figure seems to be reasonable, since it could correspond to the combination of the following values of the four parameters of eqn. (7): a = 0.5, n = 2, f = 0.15 and z = --5, which are all realistic. In particular, for pH < 7, z is mainly fixed by the number of dissociated carboxylic groups which was found to lie between 4 and 9 per mole (Mw = 1000) for HA and FA [8].

Finally, from eqn. (3), using CF as defined in eqn. (5) and putting CckF = 0, one obtains: log{nKDk0) = loglp'] -- log(0.85 × 10-3m2J3F)

The values of the left-hand-side term, measured at E = - 0 . 7 V, are plot ted in the inside figure of Fig. 3 as a function of pH. The mean slope of the curve was found to be - 0 . 2 . Considering the values generally reported for the change in log k0 with pH, for organic compounds (see ref. 22, p. 258), and considering the complexi ty of the system, the above value seems to be reasonable.

Hence, all these results confirm the important part played by the faradaic current .compared to the capacitive component . In other words:

Cck f /C F << 1 (8)

Moreover, these results also seem to indicate that the measured overall parameter k0 is really predominantly representative of the rate of reduction of the reducible component of FA.

( I V . 2 . 2 ) Overal l k i n e t i c p a r a m e t e r s o f t h e a d s o r p t i o n p r o c e s s Since p is known, eqn. (1) can be written as

A F = 1 - - (i - - r t-1/3)/pt2/3 = AFro" F(~) (9)

281

~F

0.5 x / x /

0.4 A~

/ / , L /

o.3 / ' / , / ~

0.1

t/s w i i i i I i I i I i •

0 4.0 8.0 12,0 16.0 20.0 24~

Fig, 4. Change in AF (eqn 9) with time. (X, A, e) Points computed from the experimental i--t curves, full line curves: curves adjusted using the theoretical F(T) function [ 24 ]. KNO3 0.1M;pH 5.0, T= 25°C,E =--0 7 V. [FA] = (e) 2 X 10 -s M;(A)5.7 × 10 -s M,(×) 1 05 × 10 -4 M.

Typical plots of AF = f(t) are shown in Fig. 4. Two parameters, AFm and Cr can be determined by fitting experimental curves to the theoretical ones [24]. C~ is defined as

C T = kf [FA] + kb = ~/t (10)

By inspecting the theoretical curve it can be seen that AFm and Cr can be determined quite accurately, simply by choosing two values of times t, and t2, such that t2/tl = 2 and for which the corresponding values of AF (AF1 and AF2) are such that A F 2 / A F , = 1.5. In this case, Cr = 1 / t , and AFro = AF, / 0.425. From Fig. 4, it can be seen that the experimental curves fit well the theoretical F(T) function. Analogous results were obtained for potentials in the range --0.3 to --0.8 V at pH values of 3.8, 5.0 and 7.0.

Plots of Cr vs. [FA] at constant potentials and for pH = 5.0 are shown in Fig. 5. Within the experimental errors, a linear dependency of Cr with [FA] was found, in agreement with eqn. (10). Within experimental errors Cr was also found to be independent of potential between --0.3 and - 0 . 7 V. The mean values of log(kf/M -1 s -1) and 1og(~b/S -1 ) measured in this potential range were 2.85 + 0.1 and --1.4 + 0.1 respectively.

Analogous results were obtained at pH 3.8. Mean values of 2.95 + 0.05 and 1.35 + 0.1 were obtained for log kf and log/eb respectively, in the same potential range. For both pH, 3.8 and 5.0, the values of kf and kb were found to be respectively slightly lower and higher at E = --0.8 V than at other potentials.

The measurements at pH = 7.0 were made over a smaller concentration range. Because of this, l a~er dispersions in the Cr values were observed, and as a result, values of lef and k b could not be computed. However, it must be noted that the order of magnitude of the values of Cr obtained at pH 7.0 was very similar to that of pH 3.8 and 5.0.

All these results show that in the experimental conditions tested, the overall

282

C~r / s -I

0.20

11 0.15 ~ " A

o " - / i

o.1o 1 1 ~ "" ~ "" '~

i _ . . j l " a 0.05

[FA] / M

i io . . . . . 0 20 410 6 8.0 10.0 12.0 14.0 16.0 x l

Fig. 5 Change in C T (see eqn. 10) with FA. For experimental conditions see Fig. 4. E = (5) --0 3 V; (A) --0 4 V, (o) --0.5 V, (A) --0.6 V; (),) --0.7 V.

kinetics of adsorption of the FA system may be described by using the theory of Weber and Kouteck~r developed for the adsorption of a simple compound for which the adsorption reaction is the rate-limiting step. However, this find- ing does not imply that this model can be considered as directly applicable to each component of the FA mixture separately. Interestingly, the overall kinetic parameters kf and kb do not seem to be much affected either by the electrode potential or the pH, in the potential and pH ranges studied.

By analogy with the true equilibrium constant for the adsorption of A (see Appendix) defined ~ K a f f ka/kd, an overall pseudo-equilibrium parameter may be computed using Kt = kf/kb, where the subscript t is used to recall that this parameter was measured from the data obtained under non-equilibrium conditions. Log/~t was found to be 4.3 + 0.1 for both pH values 3.8 and 5.0 (see also Section V.3.2). The limits of significance of/~t are similar to those of / ~ which are discussed in Section IV.2.4.

(IV.2.3) Influence of the adsorption process on the reduction of FA It was observed experimentally that AFm is strongly dependent on [FA] and

that the curves AFro = f ( [FA] ) resembles adsorption isotherms, reaching a limiting value, AF~ ax, for [FA] > 1.2 × 10 -4 M. This behaviour is as expected from eqn. (6), and confirms the validity of the condition (8). Thus, putting Cckf /CF = 0, eqn. (6) becomes:

AR m = 0 ~ (1 -- k l/k0) (11)

and, for [FA] -~ ~ (i.e. 0~ -* 1):

ARm max = 1 - - k l / k 0 (12)

Here, k 1/ko was computed from the values of AF~aXdetermined experimentally, for all the potentials and pH values. Values of k 1/ko were found to increase gradually from 0.07 to 0.14 when the potential changed from --0.3 to --0.8 V, for both pH 3.8 and 5.0. ~ Owing to the statistical and systematic errors incurred in the computat ion of k Jko, it is difficult to say whether or not the variation observed in this parameter with E is significant. Anyway, a low value for it seems to indicate that the

283

main effect of the adsorption of FA is to inhibit the reduction process strongly, irrespective of the potential or pH. This observation seems to be very reasonable [22] particularly because the FA components are all negatively charged and consequently this may cause an electrostatic repulsion between the adsorbed component and the reducible ion at the electrode surface.

(IV.2.4) The adsorption parameters at "infinite" time By using the value of k 1/ko obtained above, the values of the overall degree

of coverage at " infini te" time, 0~, may be computed from eqns. (6) and (11) as a function of [FA]. It must be remembered, however, that 0~ is computed from the values of AFm which correspond to the extrapolation, to t -~ oo, of the por- tion of the AF = f(t) curve corresponding to the first 25 s. Hence, 0~ is only representative of the conditions at infinite t ime provided that the adsorption process for a large time scale (t > 25 s) is not modified with respect to the short one (t < 25 s).

Nevertheless, 0~ is useful to test the applicability of the model to the FA system, and to obtain an insight on the reactivity of FA at the interface. Indeed, an overall pseudo-equilibrium p a r a m e t e r , / ~ , may be computed from 0~ by analogy with the true equilibrium constant which may be obtained from the degree of coverage at equilibrium. Similarly, by using the concept of the Frumkin isotherm [25], the change, p, of log/~oo with 0~ is related to the interactions of the adsorbed FA at the interface:

I( 0~ ]] = 1 ° g ~ ° - 0 " 4 3 X p X ~ (13) log K~ = log 1 -- ~-~)[FA

where/~o is the value o f / ~ extrapolated to [FA] -~ 0, i.e. the value of the constant in the absence of interactions.

Experimental results for pH = 5.0 are shown in Fig. 6. The points corresponding to 0~ > 0.93 must be taken with caution because, in these cases, the errors i n / ~ may be fairly high. Despite the dispersion of the points in the plot of Fig. 6, a slight increase in log g ~ is observed. From the mean straight line drawn through these points, the values of log K ° and p were found to be 4.2 +

5.S

5.0

/*.5

([FA]: M ) II

°o A° -

o o.1 o z o.s o.4 0.s o.6 0.? o.e 0. t0

Fig. 6. Influence of the degree o f coverage o n log K~ ( eqn . 1 3 ) . For experimental conditions and symbols see Fig. 5. ( ) Regression straight line computed for 0 < 0oo < 0.93. ( ...... ) limits of the experimental errors.

285

(4) Influence of the adsorption on the faradaic current. Equation (A.5) for it is valid for cases where an unadsorbed electroactive compound is influenced by the adsorption of an electroinactive compound. This could be likely in our case provided that the observed current is due to the reduction of some non- adsorbed component of the FA sample. Otherwise, eqn. (A.5) is valid only if both the reduced and oxidized forms exhibit similar adsorption properties. This is not unlikely: since the mean size of FA molecules is relatively large, only a small part of the molecule may be modified as a result of the reduction process.

(5) Influence of the potential gradient at the interface and the polyelectrolytic nature of FA. These effects might affect either the reduction or the adsorption processes. However, they were not specifically taken into account because of the reasons discussed in Section II: including them in the model would have resulted in too many adjustable parameters. Hence, these effects as well as other "secondary" phenomena are included in the overall reduction or adsorption parameters. It must be added, however, that the very small dependence observed for the adsorption parameters on the potential of the electrode, and even on pH, seems to indicate that the above-mentioned effects do not play an important role.

(V.2) Applicability of the Kouteck:~--Weber theory

The application of this theory to the FA system, may be considered from two points of view:

(1) Its usefulness to obtain empirical kinetic parameters representative of the overall adsorption process. This usefulness was tested by comparing the fittings of the AF = f(t) curves based on the Kouteck~--Weber theory on the one hand, and on the theory developed for a diffusion-controlled rate~letermining step on the other [27,28]. The value of log Ka [28] was taken as equal to log K t = 4.3 (see Section V.3.2), and that of Ka/ro as equal to zero. In fact, in our case the value o f gt/ro lies between 0.1 and 0.2, but the shape of the corresponding curves F/Feq = 0 = f(T) [28] are not drastically modified compared with the curves for which Ka/ro = O. In the above equation, T is defined as

T= 2 2 t D/FmK a (14)

where D is the diffusion coefficient of the adsorbable compound and Fm is its maximum sttrface concentration. The best possible fit of the experimental AF = f(t) curve to the theoretical 0 = f(T) curve may be found by making the parameter tl (Section IV.2.2) of the experimental curve to be equal to the value of T1, found on the theoretical curve and corresponding to the conditions T2/T1 = t2/t~ = 2, and 02/01 = 1.5. This best possible fit is shown in Fig. 7.

It can be seen that the correlation is not good. In the neighbourhood of zero time, the theoretical curve tends asymptotically to 0 = 0. This is due to the fact that, in the diffusion-controlled process, 0 is proportional to t ~/2 at short times. Conversely, the experimental curves tend to zero in a rather linear way, as is the case for the theoretical curve of the Kouteck:~--Weber theory. Moreover, when the values of T~ are measured, as described above, on the theoretical curves of ref. 28, and 1/TI is plot ted as a function of Kac (where c is the bulk

286

0 (b)

0.12

0.10

0.08

0 O6

0.04

0,02 -

000

AF (a )

0.5

0.4

-0.3 d i

-0.2 / ~ / i

/ ii # / /

/ /~"

7' 8.0 i i

g 2'0 ,:0

b

/ i f /

16.0 24D 32D ~).0 t / s , , , , , , , ~ ( a )

6:0 6"0 d0 12:0 1~:0 16:0 ,705 ;(b)

Fig. 7. C o m p a r i s o n o f e x p e r i m e n t a l resul ts ( i , a) wi th theor i e s o f d i f fus ion-con t ro l l ed ( . . . . . . , b) and reac t ion rate con t ro l l ed ( , a) a d s o r p t i o n processes. F o r e x p e r i m e n t a l cond i t i ons see Fig. 4; [ F A ] = 5.7 x 10 -s M. ( ~ ) F u n c t i o n F(T) [24 ] ad jus ted on experi- m e n t a l po in t s by using t he bes t values of t he pa rame te r s AFro and Cr (eqns. (9) and (10)) ( A F m = 0 .664, C r = 0 .093 s - l ) ; ( . . . . . . ) bes t a d j u s t m e n t o f e x p e r i m e n t a l da ta by means o f the t heo re t i ca l f u n c t i o n derived for d i f fus ion-con t ro l l ed processes [ 28 ] wi th Ka/ro = O.

concentration of adsorbate), a curve is obtained, whereas our experimental results, as well as the Kouteck~--Weber model, show a linear dependency.

Hence, all these results indicate that the theory corresponding to a diffusion- controlled adsorption process is inadequate to describe the overall adsorption behaviour of FA, even from a purely empirical viewpoint. In this respect, the Kouteck:~--Weber theory is much better, not only because it enables us to get very good curve fittings but because it is mathematically simple and makes use of fewer parameters to explain the overall adsorption process.

(2) Its ability to represent the real physical process o f adsorption. In the case of the adsorption of a simple compound in a pure solution, the Kouteck:~-- Weber theory implies that (a) there is no interactions between the adsorbable molecules on the surface, and (b) the rate of the adsorption reaction is the slow step. It was seen (Section IV.2.4) that condit ion (a) is not fulfilled. However, the parameter p is relatively low, so that the change in the adsorption properties during the t ime scale of the experiment may be neglected, since the error incurred by doing this is of the same order of magnitude as the variability of the measurements. As far as condit ion (b) is concerned, until now the adsorption of most surface active agents on a mercury electrode was reported as diffusion controlled. However, evidence for kinetic control in the adsorption-- desorption step was reported [29,30]. Moreover, it is also known that, when a mixture of surface active agents is present, as is the case for FA, a behaviour similar to that of a slow adsorption process may be observed (ref. 22, p. 332).

The only experimental results actually available, and which are in favour of the representativity of the Kouteck:~--Weber model, are the facts that the experimental curves fit well with the theoretical ones, the resulting adsorption

287

parameters have reasonable values, and , particularly, that the values of the pseudo-equilibrium parameters,/~t or K~ found by this method are close to those obtained by other methods (see Section V.3) and seem to be in accor- dance with the equilibrium constants found for the adsorption of FA at other interfaces (Section V.4). It might be pointed out that a maximum in the i--t curve is predicted by the work of Weber and Kouteck:~ [24], whereas in our case a maximum is observed only in a few cases corresponding to the strongest adsorption conditions. This is related to the fact that the results of ref. 24 are valid for the condition a = 0~(1 -- kl/ko) = 1. Now it may be shown, by recom- puting the g(a,r) function in ref. 24, that no maximum is observed for a < 0.9, and that a maximum is noticeable, in practice, only for a > 0.95, which was almost never the case with our experimental conditions.

In the case of the diffusion-controlled theory of adsorption, a good fitting of the experimental data could not be obtained, even under the best conditions (Fig. 7). Nevertheless, by means of eqn. (14), one may evaluate the term

2 2 D / F m K a from the ratio of T~ and t, found in these best conditions. A value of 3.7 X 10 -4 s -1 was found. By substituting D = 2 X 10 -6 cm 2 s- ' [2] and log Ka = log ~:t = 4.3, Fm was found to be 4 X 10 -9 mol cm- : , which is a very unrealistic value, since this would imply a surface area of 0.03 nm 2 molecule -1. It may be pointed out that adsorption curves in ref. 28 were computed for a stationary sphere, whereas the DME, i.e. an expanding sphere, was used here. However, it may be estimated from ref. 31 that this expansion effect will only increase the time for the at tainment of equilibrium by a factor of ~2, which is not suffi- cient to modify the above result. Finally, if a value of Ka/ro > 0 is chosen for the curve fitting, values of T1 still shorter (or Fm still higher) would be obtained.

Thus, these considerations suggest that the model based on Kouteck~-- Weber theory is more suitable than the diffusion-controlled one for the descrip- t ion of the overall adsorption of FA, both from the empirical standpoint and because the parameters obtained from it have more realistic physical significance. However, this does not necessarily imply that it is representative of the adsorption process of each of the components of FA (see Section V.5).

(V. 3) Physical significance of the adsorption parameters obtained

An idea of the physical significance of the adsorption parameters, particularly /~t a n d / ~ evaluated in Section IV.2, may be obtained by comparing them with analogous parameters obtained by different methods. The methods making use of different time scales are particularly useful for obtaining an idea as to the at tainment of a true equilibrium.

( V. 3.1) E lectrocapillary measurements Examples of electrocapillary curves obtained by the dynamic method of

Ku6era [22] are given in Figs. 8 and 9. Although the Lippman apparatus is a better method for ensuring the at tainment of thermodynamic equilibrium, it was found to be inapplicable in our case. Indeed, sufficiently accurate results were obtained only with capillary tubes having a very small bore diameter. But in solutions containing FA, the results were irreproducible due to the clogging

288 l

430 . Y E ~420

410

400

390 a, #

i

380

370 /

:! 360, "/A

/

350 •

340.

, / .~.A ~ - ~ = \ : . / ' / " "~-.= \~ ~00

/ / \'\4. / 3 9 0 "

3 8 0

37O

3 6 0

$ 3 5 0

E/v 34o

0.0 -0 .2 -0.4 - 0 . 6 - 0 . 8 -1.0 -1.2

/ \

? /

E/ V I I I I I I I

0.0 -02 , -0 .4 -0,6 -0.8 -1.0 -1,2

Fig. 8. I n f l u e n c e o f t h e c o n c e n t r a t i o n o f F A o n t h e e l e c t r o c a p i l l a r y curves ; pH 3.8; KNO3 0.1 M; T = 25°C. FA = (e) 0; (×) 28; (©) 70;(A) 123 mg 1-1.

Fig. 9. I n f l u e n c e o f p H o n t h e e l e c t r o c a p i l l a r y c u r v e s in t h e p r e s e n c e o f FA; KNO3 0.1 M; T = 25°C, [FA] = 70 mg1-1, pH = (×) 3 .8 ; ( e ) 6.9.

of the bore, arising probably from adsorption of FA on the glass walls of the tube. The advantage of using KuSera's method is that a renewed surface is obtained by the falling drops.

The 7 = f(E) curves for various concentrations of FA were obtained by recording drop time (td) as a function of potential (E) and computing 7 using the equation (see ref. 22, p. 23):

~/ = m t d g / 2 u re

where g is the gravitational constant, m the f low rate of mercury and rc the internal radius of the capillary tube. It was found experimentally that m is almost independent of E and [ FA] ; re was computed from td in the absence of FA and using the value of 7 reported in the literature [32] , the resulting value of re being checked experimentally.

The fol lowing remarks can be made from the observation of Figs. 8 and 9: (1) There is a lowering of 7 in the presence of FA, which confirms the

adsorption of FA at the mercury electrode. The lowering in 7 is more marked as [FA] increases and the pH decreases. Moreover, this effect is more pronounced on the positive side of the electrocapillary maximum, as expected for the adsorption of negatively charged compounds.

(2) The electrocapillary maximum shifts gradually towards negative poten-

289

tials, as we go from pure solutions of KNO3 (--0.450 V) to solutions containing 150 mg 1-1 of FA (--0.550 V). This shift is independent of pH.

(3) No breaks in the curves are observed indicating that there is no sharp boundary potential for the adsorption. This is confirmed by the absence of a tensammetric peak in ac polarography on the DME [1] or HMDE. Similarly, no sharp symmetrical peak is obtained in cyclic vol tammetry on the HMDE.

(4) The slowness of the overall adsorption process was tested by measuring 7 in the same solutions, bu t using two capillary tubes having different diameters. Changes in 3, were smaller for shorter td (4.5 s) than for longer ones (25 s).

Examples of the change in 3, with logarithm of [FA] are shown in Fig. 10 for pH = 3.8 and three different potentials. A rigorous interpretation of these curves is not possible in the present case for several reasons: firstly from the results of Section IV.2 it was seen that equilibrium is not reached up to 25 s. These results as well as others [11,12] also showed that interactions be tween FA molecules have to be taken into account. The decrease in the slope of the 7 -- 3'0 = f ( ln[FA]) curves observed for high values of [FA] could be an addi- tional indication for such interactions in the bulk of the solution, bu t it must be noted that, according to the work of Guidelli [33], this effect may also be observed with diffusion-controlled adsorption processes for which equilibrium is not reached at the end of the drop time. Finally, the results of Section IV .2 show that for rigorous interpretation of the electrocapillary curves the occurrence of a faradaic current has to be taken into account. Although these phenomena may be treated quantitatively for simple systems [33,34], an un- ambiguous rigorous interpretation of the electrocapillary data is not possible here (see discussions of Section II).

However, it would be useful qualitatively to compare the changes in the elec-

~0

-10

-20

-30

T I -11;0 -10.5 -100 9.5 [n( [FA]/M) 9,0 ~ , ~ l" - i - i I1

~ t t

Fig. 10. Change in the surface tension with natural logar i thm of the F A concent ra t ion . For exper imenta l condi t ions see Fig. 8; 7o ~ surface tension for [ F A ] = 0. E -- (J~) --0.7 V; (e) - -0 .5 V; ([]) - -0 .3 V; $ errors on the exper imenta l values o f ~' computed f rom the repro- ducibi l i ty of 10 dif ferent measurements .

290

trocapillary curves with pH, E and Temperature to show the t rend in the behaviour of FA, and for this purpose two parameters of these curves have been used: (a) the ratio of the maximum value of the slope of the tangent at the curve, to RT, and (b) the intercept of this tangent on the abscissa of the curve. Because these parameters have the same dimensions as for maximum surface concentrat ion and equilibrium adsorption constants respectively, they will be denoted by l~m and Kec (ec referring to electrocapillary curve), to keep uniform- ity with the terminology used for the interpretation of the dc i--t curves.

Here, I~m and Kec were measured at 25°C for pH 2.85, 3.8, 5.0 and 7.0, and, for each pH, these parameters were measured at potentials over the range --0.1 to --0.8 V by steps of 0.05 V. The values of log/~ec and Fm were found to be statistically constant irrespective of the pH or potential, with mean values of 4.65 -+ 0.15 and (6 + 1) × 10 - '° mol cm -2 (which corresponds to 0.28 nm 2 molecule) respectively for these parameters. It is interesting to note that the values of log/~e~, log/~t and l o g / ~ are close to each other, and that in the three cases their dependence on pH and E, if any, were found to be very small. As mentioned above, the relatively low value found for Fm might be related to the occurrence of association of molecules at the interface (Section IV.2.4), but it could also be an artefact due to the fact that equilibrium is not reached at the end of the drop time.

The measurements of log/~e~ and Fm were repeated by keeping pH constant (2.85) and varying the temperature. The temperatures used were 3.5, 10.0, 17.8, 27.5, 37.7, 48.7 and 60 ° C. In each case, these parameters were determined at potentials --0.1, --0.3 and --0.5 V. With the exception of the last two values of the temperatures where l o g / ~ c increased slightly, fairly constant values of l o g / ~ and l~m were observed. Their mean values were found to be 4.6 + 0.1 and (5.5 + 1) × 10 -1° mol cm -2. It may be noted here that, because of the observed independence of the two parameters, particularly I~m, f rom temperature, the possibility of an artefact, such as that ment ioned in ref. 33, is less likely. Indeed, in such a case it would be expected that the rate of transport by diffusion would increase with temperature so that the parameter l~m should increase and tend to the true value of the maximum surface concentration. On the other hand, the constancy of the equilibrium parameters with temperature is consistent with the results obtained at other interfaces (Sections V.4 and V.5).

(V.3.2) Influence of the time scale of the experiments The overall adsorption parameters/~ measured here do not correspond to

true equilibrium conditions. Therefore, for practical purposes, the t ime scale for which they are applicable should be specified. From a more fundamental standpoint it is also interesting to t ry to estimate how much these parameters differ from the true equilibrium constants. Two kinds of t ime scales may influence the values of t he /~ parameters, namely the duration, tads, during which adsorption may occur and the relaxation time, tr, characteristic of the technique used and corresponding to the duration of the perturbation produced during the measurement of the desired signal (e.g. pulse duration in pulse polarographic techniques).

To test how these two factors may affect the values of/~, the ac current

I i ~ 1o o 20.0

- 10 ~ •~'~ -20

-30.

-40,

lo 6[FA] / M i 0

30.0 40.0

\ ' - ' - L b

291

Fig. 11. Change in the capacitive ac current Ai_ measured on the HMDE, with concentration of FA (Ai~ = i~ -- z~, where in and i°are the ac current in the presence and absence of FA). KNO3 0.1 M; pH 7.0; T = 25°C;co = 400 Hz, phase angle 90° ;amplitude 10 mV, E = ---0.430 V; scan rate 20 mV s -1. (a) ac polarograms recorded immediately after the formation of the drop (adsorption time <~5 s), (b) ac polarograms recorded 5 rain after the formation of the drop

(90 ° out of phase) as a function of [FA] was measured on the HMDE at high frequency (¢o = 400 Hz). Owing to the low value of the rate constant of the redox process, the high value of the frequency and the chosen phase angle, mainly the capacitive component of the current is measured (Part III). This current i~ was measured "immediately" after the formation of the drop, i.e. at tads = 5 S and at tads = 5 min after the drop was formed (Fig. 11). It is seen that one obtains the same kind of curves, having a profile of an adsorption isotherm, as those which were obtained with the same technique, but on the DME [1] . Although the curvature of the profile corresponding to tads = 5 S Was very similar to that obtained on the DME, the curvature corzesponding to tad~ = 5 min was much more pronounced, indicating a stronger adsorption of FA. As the observed curves bore resemblance with the Langmuir adsorption isotherm,

TABLE 1

Influence of the time scale of the experimental technique on the values o f the measured overall pseudo-equilibrium adsorption parameters. Arrows indicate that the log K values were obtained by extrapolating adsorption time to infinity (-+~) or [FA] to 0 (-->0)

Method Parameter tads/S tr/s 104 [FA]/mol 1-1 log

Chronoamperometry K7 0--25 0--25 0.2--1.5 4.3 Chronoamperometry ~:~ (0.2--1.5) 0 4.2 (0-25) -~ ~ 0 - 2 5 -~ Chronoamperometry K~ (0--25) -* ~ 0--25 1.0 4 9 Electrocapillary Kec 25 25 0.1--1.4 4.6

curves Ac polarography ~ac 5 0.0025 0.03--0.5 4.5 Ac polarography Kac 300 0.0025 0.01--().5 5.7

292

the appropriate equation was used to measure overall adsorption parameters, /~c, characteristic of these curves. Good linear relationships between [ FA]/ Ai_ and [FA] were observed and the values of/~,c calculated from these lines are given in Table 1, along with the other overall adsorption parameters measured in this work.

Table 1 seems to indicate that the nature of the measuring technique does not greatly influence the operational parameter/~, as far as the value of t~ is concerned. The duration of the adsorption time also does not seem to be very important for the time scale 1--30 s. On the other hand, the adsorption process for large time scales (several minutes) seems to be very different from that at a short time scale (several seconds). The actual influence of FA concentration is difficult to tell, but the large value of log/~,c measured for t~ds = 300 S, together with the fact that its order of magnitude is similar to that obtained for l o g / ~ for 0~ -+ 1 (Fig. 6) seem to confirm the general trend observed in Fig. 6 which seems to indicate that the adsorption process is positively influenced by association of FA molecules at the surface.

( V. 4 ) Comparison of adsorption at various interfaces

The variation of surface tension of aqueous solution of FA, with FA concentrations as well as temperature, were measured in 0.1 M KNO3 at pH = 2.85, using Lecomte de Nouy apparatus. The results are shown in Figs. 12 and 13 and summarized in Table 2. In this case, the constants reported may be considered as true equilibrium constants.

It can be seen from the results in Table 2 that log K, is independent of temperature. The entropy of adsorption, AS,, was found to be 104.2 J K "~ mol -~, the concentration of FA being expressed in molar fraction. Chen and Schnitzer [7] have also investigated the adsorption of FA (pH = 3.2) and HA (pH = 7) at the air--water interface. They report specific surface areas of 0.965 nm 2 molecule -1 and 0.404 nm 2 molecule -1 for FA and HA respectively. Their value, for FA, agrees quite well with the values found here.

Mantoura and Riley [6], on the other hand, studied the adsorption of FA on an Amberlite XAD-2 resin. They report log Ka = 4.8. They also found that Ka is only slightly dependent on temperature, the values of AHa and ~-~a for the adsorption process be ing--5 .4 kJ mo1-1 and 106.8 J K-~ mol -~ respectively.

T A B L E 2

Change in equ i l ib r ium c o n s t a n t K a and m a x i m u m surface c o n c e n t r a t i o n , I 'm, as a f u n c t i o n of t e m p e r a t u r e for the adso rp t ion of F A at a i r - -wa te r in te r face (pH 2.85; 0.1 M KNOa)

T e m p e r a t u r e / log K a 101° r m / Surface area per molecu le / °C mol cm -2 n m -2 molecu le -1

12.0 3 .66 2.2 0 .74 20,0 3 .69 2.0 0 .85 26,0 3 .70 1.8 0 .93 32.0 3.71 1.7 0 .96 38.0 3 .69 1.6 1 .01

293

74

E72 z E

7O

68

66

\ \

-10.0 -9.0 ' -8'.0 l°([rA]/M)-a:.0 Fig. 12. Inf luence o f concentra t ion o f F A on the surface t ens ion o f the air--water interface; KNO3 0.1 M; pH 2 85; T-- 25°C.

When one compares these results with those obtained at the mercury--wa~r interface, it can be seen that (a) the order of magnitude of the values of log K for the mercury--water interface and of log Ka for the air--water and resin-- water interfaces are similar, and (b) the effect o f temperature is very similar in all cases. In particular, the value of l o g / ~ when extrapolated to 0~ -+ 0, tends to a value relatively close to that of log Ka obtained at the air--water interface. This seems to indicate that the association reactions of FA at the air--water interface are smaller than at the mercury--water interface, and it seems to be supported by the fact that the value of Fm found for the water--mercury interface is larger than that of Fm corresponding to the air--water interface.

76

E

72

70

68

~o

+~

x~

66

64

T//°C , ; ' .

10 0 0 ~0

Fig. 13. Inf luence o f temperature on the surface t ens ion o f the air--water interface o f aqueous so lut ion o f FA, KNO3 0.1 M; pH 2.85. [FA] = (a) 0; (b) 3.0 X 10 -4 M, (c) 7.0 X 10 -4 M.

294

(V.5) Phenomena involved in the adsorption process

The fact that Ka and/~ are independent or almost independent of temperature at the three interfaces considered here means that the chief contr ibut ion to adsorption energy comes from the entropy factor. Furthermore, similar ASa values obtained for the various interfaces seem to suggest that a change in entropy is caused by a phenomenon common to these systems, such as reor- ganization or replacement of water by the FA molecules at the interface. How- ever, this does not explain two important results obtained in the present s tudy at the mercury--water interface, namely, the slowness of the adsorption process, and the tendency o f / ~ to increase with coverage. In addition the interpretation of the nature of the adsorption process should take into account the fact that, although the duration of adsorption plays an important role on the results, the time scale tr of the technique of measurement is not very important (Section V.3.2).

These observations might be explained in several ways, two of which are mentioned here, only to give an idea of the factors which, in our opinion, may influence the overall nature of the adsorption parameters obtained in this study:

(1) FA is a mixture of compounds having different molecular weights, those with the largest Mw having the lowest values of diffusion coefficients and these may be expected to have the largest values of adsorption equilibrium constants. Even if the adsorption reaction of each component is fast, the slowly diffusing substances, which are more strongly adsorbed, will replace the quickly diffusing, but slightly adsorbed ones. This global behaviour might result in an apparently slow global adsorption process, even though the overall diffusion process of the various components is the real limiting process.

(2) In the above scheme, the limiting step could also be the replacement reaction of a slightly adsorbed molecule by a more strongly adsorbed one. For instance the dissolved molecule may undergo sterical rearrangement before being adsorbed at the electrode. It is also known that in the adsorption process of polymer, and even simpler molecules [30] desorption may be the slow step. Thus, the global slow adsorption reaction observed may be at tr ibuted to the slow desorption of the FA molecules. A true slow adsorption reaction could also occur if association reactions of FA molecules at the interface are involved in the global adsorption or desorption process[35]. This last phenomenon has been postulated to occur in the bulk of the FA solution [8,12] and seems to be supported by fluorescence results [ 11 ], at least for [ FA] > 100 mg 1-1. Attractive interactions between the adsorbed molecules have been also postulated to explain the observed slow desorption of simple molecules [30], and it may b e n o t e d that, as observed in the present work, these authors also observed only a very weak dependence of the rate constant o f desorption on the potential.

The real occurrence of a global slow adsorption reaction is favoured by the consistency in the results observed for the parameters obtained from kinetic data on the one hand, and pseudo-equilibrium methods (at mercury--water interface) or equilibrium methods (at other interfaces) on the other. Further- more, the important role played by chemical factors in the adsorption process

295

is shown by the fact that none of the adsorption parameters (k~, k b , / ~ , / ~ e c and Fro) are hardly dependent on "electrical" factors such as pH (which influ- ences the charge of FA) and potential. It follows that the electrical component of the free energy of adsorption [36], as well as that of the activation energy of the reaction [34], are not the dominant factors. As observed for the complexation properties, the polyelectrolytic nature of FA does not seem to play an important role in the adsorption process.

(VI) PRACTICAL IMPLICATIONS OF THE PRESENT RESULTS

(VI. 1) Adsorption parameters

Despite the global and conditional nature of the above adsorption parameters, they may be very useful in practical applications, as they enable one to predict and even allow one to correct for [ 3] the secondary reactions due to the adsorption of FA when voltammetric techniques are used for studies of metal ions in water samples. The fact that the overall adsorption process may be described by means of an overall kinetic parameter and the equation for a slow adsorption reaction, irrespective of whether or not it is truly representative, enables one to make necessary corrections for the secondary effects, whereas a much more complicated mathematical procedure, difficult to deal with, would be needed if the diffusion and adsorption constants of each of the component of the mixture are considered. Moreover, owing to the relatively large errors incurred in each of these parameters and to the propagation of errors, even the usefulness of such a procedure would be doubtful .

The discussions of Section V (particularly Section V.3.2) give an idea of the limits of applicability of the reported kinetic or pseudo-equilibrium parameters: they may be used in the range 1 < (FA~ < 100 mg 1-1 and they do not seem to be much affected by the nature of the potential--t ime function used for the recording of the voltammetric curve. On the other hand, Fig. 11 and Table 1 show that the adsorption time may strongly influence the value of/~. In this respect, it is reasonable to expect for a given concentrat ion of FA, ASV techniques to be much more sensitive to the adsorption of FA than the direct reduction methods on the DME since not only tads but also/~, will be larger for the former. One might expect a worse situation with the techniques using electrodes with non-renewable surfaces, since complete desorption of FA from the electrode by electrical means does not seem to be possible. Figure 11 shows that, as soon as the t ime of contact between the electrode and the solu- t ion exceeds a few minutes, significant adsorption may occur even for a concentration of FA as low as 10 -6 M (~1 mg 1-1).

(VI.2) Reduction of FA

The nature of the compounds of the FA mixture which give rise to the reduction current observed is not known. However, the only inorganic reducible compound which might be present in sufficiently high concentrat ion is Fe(III), as its complete removal from an FA sample is not possible wi thout relatively large loss in FA. In Table 3 the dc current measured at E = --0.7 V

296

TABLE 3

Value of the dc current, i, at --0.7 V, the TOC and the samples

iron content of the various water

Sample No Porosity of the membrane i/nA TOC/mg 1-1 106 [Fe ]/M (see ref. 12) used for filtration

50d 0.2/~m 174 68.4 11.0 50d PM-10 156 60.4 6.4 22 0.2 gm 134 51.4 3.0 50d 0.2 pm 96 29.9 5.4 50d PM-10 75 30.2 2.6 22 0.2 pm 60 25.4 1.7

for water samples having different ratios of concentrat ion of iron to total organic compounds {represented by their total organic carbon (TOC) value) are given. This ratio was varied by using two water samples of different origins [11], one of which was filtered through two membranes having different porosi- ties (for PM-10 the molecular weight cut-off limit is about 10,000).

Table 3 shows that the reduction current is well correlated with the organic content bu t not with iron, confirming that the reduct ion current is indeed due to some organic component . This is likely as the existence of reducible groups such as quinones, ketones as well as phenoxy radicals have been reported to be present in FA [8,12]. The results also showed that the shape of the i = f(E) curves are the same for all the samples, indicating that the reduction and adsorption processes are mainly due to compounds with molecular weights less than 10,000, and that these processes are not very dependent on the origin of the water sample.

The reduction of FA is generally unimportant for the analytical interpretation of the polarograms obtained in trace metal analysis of natural water, as most of the techniques used for these analysis are fast ones which are insensi- tive to irreversible processes. However, faradaic processes are of ten quite specific, so that a detailed investigation of the reducible compound would be useful for the analysis of FA itself. Furthermore, a bet ter knowledge of the redox properties of FA would be very useful as these may be important in the understanding of the reaction of FA with some inorganic ions, such as iron, in water masses.

(VII) CONCLUSION

The results presented here give an order of magnitude of the adsorption parameters of FA at a mercury electrode and the influence of the most important experimental conditions on the values of these parameters. Owing to the similarity in the behaviour of the various water samples studied, with regard to either their adsorption properties [1] or other properties [11,13,15], it is likely that the most important features of the results obtained here would be applicable to other freshwater samples of the same type. Despite the conditional nature of these parameters, their usefulness has been examplified by their

297

successful application in the correction of complexation data of Pb(II) by FA, as measured by differential pulse polarography [3].

These results also show the most important problems which should be dealt with while studying model compounds in order to obtain a better insight into the behaviour of the fulvic and humic substances of natural waters at the mer- cu ry -wa te r interface. Although the electrical factors do not seem to play a very important role, the most important aspects are as follows:

(1) The nature of the reducible compounds. (2) The nature of the factors controlling the rate of adsorption, i.e. diffu-

sion or surface reaction. (3) The behaviour of the mixture of adsorbable compounds. (4) The effect of the association of these compounds on the global adsorp-

tion process.

APPENDIX

According to Section IV.I., the description of the hypothetical system should take into account both the capacitive and faradaic components of the current. It will be assumed here that the total current can be computed from a linear combination of the two components:

i = is + ic (A1)

Although Delahay [26] showed that this equation is not rigorously valid, his work indicates that the smaller the current exchange density of the redox system of interest, the more reasonable is this approximation.

If an adsorbable compound, A, is present, the capacitive current is given by

dQ_ d[OQ1 + ( 1 - - 0)Q0] ic - dt d t

_ dQ0 + (Q1 - - Q0) + 0 ( A 2 ) dt dt

Here, 0 is the degree of coverage and Q, Q0 and Q1 are the charges of the electrode for 0 < 0 < 1, 0 = 0 and 0 = 1 respectively; Q1 and Q0 are given in ref. 22 (p. 54): Q0 = 0.85m 2/3t2/3 Co(E - - E ~ ) and Q1 = 0.85m 2/3t2/3 C I ( E - - E ~ ) , where Co and C1 are the specific capacities for 0 = 0 and 0 = 1 respectively, and E~ and E~ are the corresponding values of the potentials of zero charge. Hence:

dQo/dt = 0.567m ~/3 Co(E ~ E ~ ) t -113 = rt -113 (A3)

where r is a constant at constant potential, and

i~ = rt -113 + 0.85m 2/3 Cot 213 dO +-3

where C~ = AC(E -- E~) -- Co Z ~ m = constant, 2~C = C1 -- Co and z ~ TM = ET -- Ep .

Simultaneously the slow and irreversible reduction of a depolarizer D gives rise to a negative faradaic current, is, given by [22, p. 308] :

if = --0.85 m 2/3 CF[D] t 2~3 [(1 - -0 ) + klO/ko] (A5)

298

where CF = 10 -3 nFko is a constant for a given potential, k0 and kl are the rate constants for the reduction process, when 0 = 0 and 0 = 1 respectively and n is the number of electrons involved in the reduction process. In k0 depends on the applied potential E and on the potential in the plane of closest approach of the electrode, ~, by the relationship [22, p. 233]:

anF anF E + (an -- z) ~ ~ (A6) Inko = In k ° + -R-~Eo R T

where k ° is the rate constant at the normal potential (E = E0), a the charge transfer coefficient and z the algebraic number of charge of the reducible species.

If the rate-limiting factor in the adsorption process of A is the adsorption reaction itself, then the theory of Weber and Kouteck:~ [24] may be used for the computat ion of the 0 = f(t) function. From ref. 24 one has:

0 = 0~o F(r) (A7)

and it can be shown that:

d 0 + 2 0 ka[A] dt 3 t = - - F m [ 1 - - F ( r ) ] (AS)

where

ka[A] + kd (A9) T - t

I~m

where F(T) is a tabulated function [24], 0 ~ is the coverage at r -* oo (or at t -~ oo) and corresponds to the coverage at equilibrium when kd ¢ 0, P m is the maximum surface concentration of A and ka and kd the rate constants of adsorption and desorption respectively. They are assumed to be independent of the degree of coverage.

By combining eqns. (A4), (A5), (A7) and (A8), one obtains:

i - - r t -lj3 = 0.85m 2/3 (Cc[A] -~mm--CF[Dl)t2/3 1 . . . .

with R = C F [D]/(Cc [A]ka/Fm ). (A10)

ACKNOWLEDGEMENTS

This work was partly supported by the Swiss National Foundat ion (Project No. 2587-0.76). We are grateful to Professors W. Stumm, J. Kuta and Z. Galus and Dr. P. Valenta and H. Van Leeuwen for their very valuable comments. Professor R. Parsons is also gratefully acknowledged for his comments and sug- gestions.

R E F E R E N C E S

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