Environ. Sci. Technol. 1994, 28, 21 12-21 19
Kinetics of Adsorption of Humic Matter on Mercury Jose P. Plnhelro,' Ana M. Mota, and Maria S. Gongaives Centro de Quimica Estrutural, Instituto Superior Thcnico, Av. Rovisco Pais, 1096, Lisboa Codex, Portugal
Herman P. van Leeuwen Laboratory for Physical and Colloid Chemistry, Agricultural University, De Dreijen 6 6703BC Wageningen, The Netherlands
Simulations of 0 vs t1i2curves for an unstirred medium and an electrode of constant area were set assuming that the global adsorption process of humic matter on mercury is controlled by both steps, diffusion and adsorption kinetics at the interface. Experimental 0 vs N 2 results obtained by alternating current voltammetry for different concentrations of humic matter at pH 2.5 and pH 5.0 were successfully fitted to theoretical curves if an association reaction of humic matter a t the surface of the electrode and repulsive interactions that strongly affect high 0 values were considered after a certain degree of surface coverage.
Introduction Humic matter (HM) present in natural waters is generally strongly adsorbed on the surface of the mercury electrode at the potential of zero charge due to its hydrophobic properties or to the gain in entropy (especially important in adsorption of macromolecules which displace a large number of ordered water molecules adjacent to the interface). It should be emphasized that, although HM has a large number of charged groups with no affinity for uncharged mercury, it also has aromatic rings (mainly in pedogenic matter) and/or linear carbon chains (mainly in aquagenic matter), both being easily adsorbed at the mercury surface around the potential of zero charge with the charged groups oriented toward the solution. In this context, adsorption studies of HM at the mercury/water interface might be used as a model for its adsorption on hydrophobic particles in natural waters, since mercury behaves as a hydrophobic surface in the range of the potential of zero charge. On the other hand, adsorption of organics on the electrode influences the voltammetric signal obtained in speciation studies of heavy metals in natural samples. Therefore, the time dependence of adsorption and the adsorption kinetic parameters should be known in order to extrapolate to the electrode conditions during the voltammetric measurements, in particular in environmental analysis. Adsorption studies of natural dissolved organic matter by alternating current voltammetry have been presented in the literature in order to (a) check the influence of the potential, concentration of HM, contact time solution/ electrode, pH and/or ionic strength on the adsorption process (1-3); (b) characterize surface-active substances from the comparison of their electrochemicalresponse with that observed for a standard surfactant (4-6);(c)determine adsorption-equilibrium parameters (7-9); and (d) study the kinetics of adsorption (10, 11). In ref 10, it was shown that the diffusion mechanism is inadequate to describe the overall adsorption process of HMin the whole Orange and for the concentrations studied, due probably to the influence of the kinetics of adsorption 2112 Environ. Sci. Technol., Vol. 28, No. 12, 1994
at the interface. On the other hand, in ref 11, the adsorption of a fulvic acid was better interpreted when the adsorption rate was considered as the rate-limiting step instead of diffusion. A review on the time dependence of adsorption was presented by I. Ruzic for both mass transport and intrinsic kinetic control at the interface (12). A mathematical model that considers the Frumkin isotherm at equilibrium and the global adsorption process controlled by both steps, diffusion and adsorption kinetics a t the interface, was successfully applied to strongly adsorbable organics such as Triton X-100 (13) and poly(ethy1ene glycols) ( 1 4 ) . In this work, the same type of model was applied to the adsorption of HM at pH 2.5 and 5.0, the applied potential being near the potential of zero charge [E = -0.5 V (SCE)]. It was found that, although both steps should be considered in the global adsorption process, other isotherm processes rather than Frumkin should be used, which includes an association mechanism of adsorbed molecules. The value of pH 5.0 was chosen since a t this pH the solution was naturally buffered. The adsorption of HM is similar for the pH range of 5-8 (IO),values usually found in natural waters. Adsorption was also studied at pH 2.5 to check the influence of the charge on the adsorption process, since a t pH 2.5 the HM is almost neutral and at pH 5.0 a large number of carboxylic groups are deprotonated.
Mathematical Treatment In the global adsorption process of organics on the mercury electrode, there are two processes that should be taken into account: the mass transport and the adsorption kinetics at the interface. The boundary conditions are
t=O
XLO
t>O
x-m
cc=c c, = c
(1)
where C", C,, and C are the concentrations, respectively, at the electrode surface, a t the distance x from the electrode, and in the bulk solution; x is the distance to the electrode; and t is the contact time solution/electrode during the adsorption process. To obtain CO vs t , the first Fick's diffusion law, represented by eq 2 for electrodes of constant area, should
be solved according to the model considered for the global adsorption mechanism where D stands for diffusion coefficient, rm is the maximum number of adsorbed molecules per area unit, and 0 is the degree of coverage of the electrode. 0013-936X/94/0928-2112$04.50/0
0 1994 American Chemical Soclety
Since CO is not a constant value, eq 2 cannot be solved analytically but by using finite differences
Table 1. Values of ( x 2 ) X l o 4 for Different Fittings between Theoretical and Experimental Curves.
C (mol m4 X
where C1is the concentration at the distance Ax from the electrode, A0 is the increment of 0 during two consecutive instants tl and t2, and At = t2 - tl. In eq 3, the value of C1 used is determined from the finite differential approach applied to the diffusion process (1.9,and A0 is replaced by its expression in the function of Coaccording to the model considered as described below. Some considerations about the values of Ax and At to be used are presented in Appendix 1. Pure Diffusion Control. If the diffusion is the only controlling step, Le., if the adsorption kinetic a t the interface is very fast compared to the diffusion, then Co is an equilibrium value, related to 0 through an isotherm (eq 4,if the Frumkin isotherm is assumed)
(4) where b is the interaction parameter (>O for attractive forces) and PO is the intrinsic adsorption constant. The value of Cois then determined in each instant from eq 3 replacing A0 by 0 - 01, where 0 is related to Cothrough eq 4 and el is the value found in the previous instant tl. I t should be noted that for low 0 values, in the range where CO Oi
(7)
0i is the 0 value from where the increase of the slope is observed, and p is the order of the association reaction. The value of p = 1 was first considered. If k, only affects the adsorption reaction, eq 6 becomes
1
0.8
0.6
0 0.4
0.2
0
1
0.8
0.6
8 0.4
0.2
0 0
2
4
8
6
10
12
14
tA1/2 /sAl/2 Flgure 3. Fitting obtained considering diffusion and adsorption kinetics as limiting steps at the interface, without association of the molecules, for the adsorption parameters in Table 2. (A) pH 2.5, concentrations as in Figure 2. (B)pH 5.0, concentrations as in Figure 1.
AO/At = k,k,Co(l - @eAbs - k,Oe-'l-A'bs
(8)
It should be noted that the modification introduced corresponds to a new isotherm for p
> 0, represented
by
Table 3. Values of 01, Obtained for Best Fitting
C (mol m-3 X lo2) 1.18 2.36 3.54 4.72 5.83 8.83 11.7 14.7 29.0 pH 2.5 pH5.0 a
It can be seen from the experimental curves that, with the increase of the bulk concentration, Oi is reached a t shorter times and increases. This suggests that the association reaction begins for a certain degree of coverage but takes some time to become detectable due to slow kinetics, which increases Bi values obtained at shorter times for higher concentrations. The fitting is clearly improved for pH 2.5 using the association reaction with Oi dependent on the concentration and p = 1 (Table 3), as observed from the comparison of Figures 3A and 4. The other parameters have the same values as in Figure 3A. However, the fitting is not
a 0.11 0.19 a 0.225 a 0.375 a 0.725 0.12 0.26 0.375 0.46 0.50 0.60 a 0.64 a
Experiment not performed.
acceptable yet for C > 11.7 X mol m-3, with ( ~ 2 much higher than ( x ~ ) ~ . ,(Table , 1). To improve the fitting a repulsive interaction was included with b = -1.15 and X = 0.5, which suggests that, although the molecule as a whole is almost neutral a t pH 2.5, repulsive forces might be present due to the polarities of the groups in the molecule at the interface. This last fitting (Figure 5A) presents (x2) values within the experimental errors for all the concentrations. The same model was tried for the experimental results a t pH 5.0 with a good fitting for C I8.83 X 10-2 mol m-3 (Figure 5B). For higher concentrations, (x2)is slightly ~ , ,to some discrepancies between higher than ( x ~ ) ~due Environ. Scl. Technol., Vol. 28, No. 12, 1994 2115
)
1
0.8
0.6
e 0.4
0.2
0 0
2
4
6
tA (1/2)
8 /SA
10
12
14
(1/2)
Flgure 4. Fitting obtained at pH 2.5 considering diffusion and adsorption kinetlcs as limiting steps at the interface, with association of the molecules using eq 9, for the adsorption parameters presented in Table 2 (Langmuir isotherm) and 6,in Table 3. The same concentrations as in Figure 2.
theoretical and experimental values for 6 > 0.85. However, with this model, no other set of parameters improves the fitting of the complete set of experimental curves. This behavior might be due to a variation of PO with 6, due to a change of electrostatic and chemical interactions, more detectable a t pH 5.0 than at pH 2.5. In spite of this slight discrepancy, it can be concluded that the global adsorption process for pH 2.5 and pH 5.0 can be interpreted as controlled by diffusion and the adsorption reaction rate at the interface if an association reaction of adsorbed molecules is also considered. This last phenomenon has been postulated to occur for fulvic acids in the bulk solution (17,18)and seems to besupported by fluorescence results (19). It should be noted that the association reaction produces a well-defined sigmoidal shape for pH 2.5 and not for pH 5.0 because at the first pH the kinetics of adsorption a t the interface is slower (higher k, value at pH 5.0, as can be seen from Table 2). Comparison of Adsorption Parameters. The lower rm value obtained a t pH 5.0 compared with pH 2.5 might be due to the increase of the effective area of the adsorbed molecule at this pH, caused by repulsive forces between adjacent groups. The value obtained a t pH 2.5 in grams per unit area is almost half the value for a fulvic acids mixture at pH 2.85 in 0.1 M KN03 ( I l ) ,which might be due to the much higher molar mass of the humic matter, leading to different configurations of the humic substances adsorbed. The rate constant of adsorption, k,, is higher a t pH 5.0 probably due to an easier defolding of the molecule a t the electrode surface facilitated by the repulsion of negative groups in the Helmholtz inner layer, where the cations of the electrolyte do not penetrate easily, although in the bulk solution HM should present a similar configuration at both pH values since the presence of an excess of supporting electrolyte neutralizes the negative charges a t pH 5.0. The value obtained for the rate constant of adsorption of the fulvic acid at pH 2.85 (11) is between these two values, which indicates a similar kinetics for both substances at the interface. Since the diffusion of HM is slower than that of fulvics, due to its higher molar 2116
Environ. Sci. Technol., Vol. 28, No. 12, 1994
mass, the global adsorption process should be faster for fulvic compounds at the same pH value. A slightly higher value of PO was obtained a t pH 2.5, which was expected since HM is more hydrophobic than at pH 5.0. This parameter is almost 300 times higher than the value presented for the fulvic acid ( l l ) ,which implies a much lower value for the desorption constant rate of humic matter. Apart from the possible different configuration of both substances, this might be due to the higher molar mass of HM that gives rise to a higher number of contacts with the surface (per mole of HM) and to a higher hydrophobicity of HM. The parameters b and p are only slightly different between pH 2.5 and 5.0, but the difference observed is consistent from a chemical point of view. In fact, b is more negative a t pH 5.0, where the carboxylic groups are more deprotonated, and p is lower at pH 5.0, where the association reaction should be more difficult due to a charge effect. In this work, several other isotherms have been tried. One of them (Figure 6 and Table 1)produces an equivalent fitting to that presented in Figure 5. This isotherm leads to A6lAt = k,k,Co(l - 0)' - k,O
(10)
In this equation, q is a repulsive interaction parameter that affect the equation only for high 6 values. The models represented by eqs 9 and 10 cannot be distinguished from a statistical point of view considering the experimental results. In chemical terms, they both consider a slow kinetic step, an association reaction after a certain degree of coverage, and some kind of repulsive interaction that influences high 0 values. It is worthwhile to emphasize that, although the models considered in Figures 5 and 6 fit quite well the experimental values with a coherent set of parameters that are chemically acceptable, no other experimental evidence is presented to support them, and it may be possible that other models also can fit the same set of experimental results.
1
0.8
0.6
0 0.4
0.2
0
0
2
4
8
6
tA (1/2)
/SA
10
12
10
12
14
(1/2)
1
0.8
0.6
0 0.4
0.2
0
0
2
4
6
8
14
t”1/2 /sA1/2 Flgure 5. Fitting obtained considering diffusion and adsorption kinetics as the limiting steps at the Interface, with association of the molecules using eq 9, for the adsorption parameters presented in Table 2 (Frumkin isotherm), and 8, in Table 3. (A) pH 2.5, concentrations as in Figure 2. (B)pH 5.0, concentrations as in Figure 1.
Conclusions
The adsorption of humic matter at PH 2.5 and 5.0 on the interface mercury electrode/electro1fle solution and near the potential of zero charge can be interpreted with the same model for both pH values. This model includes diffusion and kinetics of adsorption a t the electrode surface as the controlling steps in the global mechanism. With the increase of the number of adsorbed molecules, an association reaction takes place that further increases B values. For higher B values, a repulsion between adsorbed molecules becomes detectable for both pH values due either to the polarity and/or the charge of the groups near the interface. The influence of the charge a t each pH is responsible for the lower rm and higher k a values observed for pH 5.0 as well as for the more negative value of b and lower p value a t this pH. The agreement obtained in the adsorption parameters rm and k a for different samples of humic substances obtained by different authors (II,19-21)seems to indicate that these compounds have similar adsorption properties.
It should be emphasized that in the conditions of this work for humic concentrations higher than 5.83 X mol m-3 (pH 5) and 29.0 10-2 mol m-3 (pH 2.5) at a potential of -o,5 (near the potential of the HMDE would become saturated during the deposition step if ASV is being used for typical values of deposition time (1 or 2 min) with stirring. This has to be kept in mind, in particular when ASV is used in environmental Of
Appendix 1
Simulation Program. The theoretical curves 0 vs t1I2 were built from t = 0 up to t , increasing the time by increments of At. This increment should be small enough so that by decreasing its value the same curve is obtained. However, smaller At intervals imply longer computation times, and so a compromise should be attained. In this work, At = 10” s was used since lower values lead to the same curves within an error lower than 2% in B values. Envlron. Sci. Technol., Vol. 28, No. 12, 1994
2117
1
0.8
0.6
C3 0.4
0.2
0 0
2
4
6
8
10
12
14
t" (1/2) /aA (1/2) Flgure 6. Fitting obtained considering diffusion and adsorption kinetics as the limiting steps at the interface, with association of the molecules using eq 10, for the adsorption parameters presented in Table 2 and 6, in Table 3. The same concentrations as in Figure 2.
To determine Co, from eq 3, the increment Ax should also be a known value. This increment is related to At through a dimensionless parameter DM ( = D A t / ( A x ) 2 )the ; value 1/6 was used for D M since it allows a meaningful decrease in the error of the calculation (22). The simulation program is developed based on eq 3 and on the equation that relates C" with 8 (eq 4 for diffusion mechanism and eq 8 for diffusion and kinetics at the interface), as explained in mathematical treatment. In the program, the determination of CO for the instant t , from eq 3, uses C'determined in the previous instant. The simulation program is available upon request. Appendix 2
concentration in the bulk solution concentration in solution at the interface diffusion coefficient adsorption rate constant desorption rate constant kinetic parameter of the proposed association reaction at the electrode surface order of the association reaction repulsion parameter Greek Symbols adsorption equilibrium parameter, equal to &ebo P for Frumkin isotherm kinetic parameter of Frumkin isotherm x maximum number of adsorbed moles per area of rm electrode degree of surface coverage of the electrode 0 degree of surface coverage where the increase of 0i slope 6 vs t begins
Estimated Value of k,. There are two considerations for ka value: The first is about the controlling step: if k , is so small that the adsorption flux is much smaller than the then the diffusional flux, ( k , C r , > 7r-112D1/2t-1/2/At, Literature Cited then the controlling step will be the diffusion. In either Greter, F. L.; Buffle, J.; Haerdi, W. J . Electroanal. Chem. case, the mathematical treatment is simpler than the one 1979,101, 211-229. used in this work. Greter, F. L.; Buffle, J. J. Electroanal. Chem. 1979, 101, The second consideration states that the surface cannot 231-251. be covered in just one time period: Cominoli, A,; Buffle, J.; Greter, F. L. J . Electroanal. Chem. 1980,110, 259-275. k,CAt 0: attractive forces) 2118
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(14) Mota, A. M.; Farinha, J. P.; Gonqalves, M. L. S. Colloids Surf., in press. (15) Bard, A. J.;Faulkner, L. R. Electrochemical methods; John Wiley & Sons: New York, 1980; Appendix B, pp 675-697. (16) Pinheiro, J. P.; Mota, A. M.; Gonqalves, M. L. S.Ana1. Chim. Acta 1994,284,525-537. (17) Schnitzer, M.; Khan, S. U. Humic substances in the environment; Marcel Dekker: New York, 1972. (18) Wershaw, R. L.; Pinckley, D. J.; Booker, S. E. J . Res. U.S. Geol. Surv. 1978,5, 565-569. (19) Buffle, J.; Delahay, P.; Haerdi, W. Etude de caractbrisation et de comparaison des propribtbs des matibres humiques et fulviques de diffbrentes eaux. Report of Project 2587-0.76
of the Swiss National Foundation, 1976. (20) Buffle, J.; Delahay, P.; Haerdi, W. Anal. Chim. Acta 1978, 101, 339-357. (21) Wilson, S. A.; Weber, J. H. Chem. Geol. 1979,26,345-352. (22) Holub, K., The J. Heyrovsk$Institute of Physical Chemistry and Electrochemistry, Praha, Czech Republic, personal communication, 1992.
Received for review February 10, 1994. Revised manuscript received July 18, 1994. Accepted July 21, 1994.' ~
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Abstract published in Advance ACS Abstracts, August 15,1994.
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