Environ. Sci. Technol. 1996, 30, 3216-3222
Diffusion and Binding of Protons in Sediments PIERRE BRASSARD,* EVADNE MACEDO, AND SUSAN FISH Department of Chemistry, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S-4M1
The exchange of metal and protons with natural particles requires long equilibration time due to their porous and heterogeneous structure. Apparent exchange measured in the bulk solution results from binding to the available sites as well as from diffusion inside the particle. We reduced diffusion to a predictable component of the system by fixing the time interval between successive titrant additions and ensuring that the same pH increment occurs each time. We assume that local equilibrium prevails and the apparent delays in equilibration are entirely caused by diffusion. Under these assumptions, it is possible to explain apparent proton binding to a divinylbenzene macroporous sphere as diffusion into a Donnan domain where mobile ions are kept inside the particle by the opposite charge of strong sulfonate sites. Similar analysis of Hamilton Harbour sediments shows that one-third to one-half of the binding capacity resembles diffusion into a Donnan domain.The remaining binding occurs on ampholyte sites such as iron oxide or silicate surfaces.
fragments bound together with an organic “glue” (4, 5) that could mask the charge on the original surface (6) and alter exchange equilibrium. Although metal adsorption to particulate surfaces has been modeled after simple mineral oxides (7), Davis (8) has shown that alumina surfaces coated with natural organic extracts acquire a complexation constant similar to the organic ligands in solution. Rates of binding for a variety of surfaces are rapid with relaxation times less than 1 s (9, 10), but the overall exchange of contaminants with particles is slow (11), suggesting slow migration through the organic layer. Understanding proton or metal binding is complicated further because the surface of each embedded mineral fragment is probably not equally available to the ion in solution. Metal and proton binding on sediments is measured by a titration done at equilibrium to justify calculations based on thermodynamics. Equilibrium is operationally defined, usually as a threshold level of stability that must be reached before adding the next amount, but few studies report the actual reaction time, especially when using automatic titrators. In natural conditions however, the exposure of suspensions is usually transient and depends on sporadic events such as wind. The actual contact time of a particle with the solution is therefore finite, and exchange becomes limited in time. In the end, contact time may significantly determine the amount and type of contaminant exchanged. We thus expect the proton binding of aggregates to be diffusion dependent as was shown for porous alumina particles (12). Once captured on the surface, the metal ion can either travel inward or be released again depending on its affinity to the inner volume of the particle. In this paper, we propose to use a model based on simple diffusion to examine proton binding titrations of two Hamilton Harbour sediments and to compare it to the properties of a porous macroreticular polymer bead (13).
Approach Introduction Hamilton Harbour is a closed embayment at the western end of Lake Ontario. It is about 2150 ha in area with mean/ maximum depths of 13/26 m. It is a major shipping harbor and borders the industrial city of Hamilton (1). The bottom sediments are a composite of natural deposition and 100 years of municipal and industrial loadings. They are considered heavily polluted, and Hamilton Harbour has been designated an “area of concern” by the International Joint Commission (2). Surficial sediments in Hamilton Harbour have been extensively studied as part of remediation. There is concern that the release of contaminants would occur as a result of resuspension events caused by wind and dredging. We have shown recently that resuspended surficial sediments are in equilibrium with the water column at ambient pH (3). The transport and exchange of metals in natural waters depends mostly on properties of natural particulates brought in the water column by settling and resuspension of sediments. Electron microscope pictures of natural aggregates invariably show an assemblage of mineral * Corresponding author fax:
[email protected].
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905-522-2509; e-mail address:
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Two considerations arise during the acid/base titration of porous particles. First, the free proton is only partly accessible from measurements taken in the bulk solution, as some free proton can still remain inside the particle. Second, transfer of the titrant to binding sites inside the particle takes time. From the bulk solution, an observer would thus see a binding site with an apparent equilibrium constant that is, in fact, a composite of binding and diffusion. The object of this approach is to distinguish between the two. To do so, we consider that diffusion is the only process causing a significant delay between titrant addition. We thus state that reaction rates are at local equilibrium and transfer is diffusion limited. To account for diffusion, we control the time interval for each titrant addition so that its cumulative effect can be predicted by a simple model. The method of timecontrolled titration restricts particle volume accessible to the titrant by imposing three constraints: (1) the time interval between successive additions is fixed; (2) the titrant is added to cause a pH increment fixed at 0.1 pH unit during the interval; (3) the variation of solution pH at the end of the delay period is less than 0.01 pH unit over 4 s. The end result of this control is to “chop” the titration in equal welldefined increments so that the total integration of mass
S0013-936X(95)00920-5 CCC: $12.00
1996 American Chemical Society
transferred inside the particle can be conveniently approximated by a simple summation. We first test the model on synthetic macroporous polymer spheres known to have a uniform charged domain and then examine real suspended surficial sediments from Hamilton Harbour. Titration. Consider an acid/base titration. At any time during the titration there is an ion balance between the bulk solution and the apparent charges inside the particle. The titration with acid, A, of a particle suspension containing an attached ligand after an initial addition of base, Bi, is written as
Bi+ - AA- ) OH- - H+ + [OH*- - H*+ + tSO- - tSOH2+] (1) where the asterisk denotes species inside the particle. We do not consider contributions of the strong ions arising from the addition of titrants because the system was kept at an ionic strength of 0.05 with KCl as the inert salt. Concentrations of Cl- and K+ are therefore deemed at equilibrium at the start of titration and constant thereafter. A blank titration run with pure water and containing the same amount of inert salts will occur as
Bi+ - A0- ) OH- - H+
(2)
We define as M as the charge excess concentration (equiv/ L), obtained from the difference of eqs 1 and 2:
A0+ - AA- ) [H*+ - OH*- - tSO- + tSOH2+] ) M (3) We define M* as the concentration of charge (equiv/L) due to the mobile species H and OH in the particle, at a given pH:
M* ) M - [tSOH2+ - tSO-] ) [H*+ - OH*-] (4) Weak sites attached inside the particle can be expressed according to equilibrium constants K1* and K2*. Following the convention of Schindler and Stumm (14), we do not include an electrostatic term and assume its contribution to be constant and lumped into K1* and K2*, which then become conditional stability constants
K1* )
{tSOH2+} {tSOH}[H*+] -
K2* )
(K1H 2 - K2) m w - LT (7) 2 vapp v (K H + K + H) app 1
2
where w is the total particle weight (g), vapp is the apparent volume of particles (L), and m is the charge excess (equiv). Finally, the charge concentration of the mobile species in the bulk solution is accessible by measurement of pH:
M0 ) H+ - OH-
(8)
Model. We consider a simple two-compartment model to represent the particles and the solution, separated by a diffusion boundary of fixed properties. Although we cannot account for the transport of individual species across the boundary, we can measure the transfer of charge due to mobile species H+ and OH- from one domain to the other. If we assume diffusivities of H+ and OH- to be equal, then the transfer of charge due to these two species should follow the same rule of diffusion as would the individual species. We thus assume this transfer to be a Fickian diffusion relation, proportional to the charge concentration of H+ and OH- between the two domains. The difference in charge is brought about by strong and weak sites attached within the particle that set a Donnan potential. We do not assume a particular shape for the particles, only that all solutes and binding sites inside are deemed evenly distributed. The total charge transferred inside the particle due to H+ and OH- is written as
dm ) R(M0 - M*) dt
(9)
where R is a transfer coefficient (L/s). Replacing M* from eq 7, we have
(
(K1H 2 - K2) dm m w ) R M0 + L T dt (K1H 2 + K2 + H) vapp vapp
)
(10)
We define the ratio R/vapp as β and solve:
m ) Re-βt
∫
t
0
(
(5)
)
(K1H 2 - K2) w βλ M0 + L T e dλ (K1H 2 + K2 + H) vapp (11)
The integral can be replaced by its summation equivalent. Time is expressed as the cumulation of the n equal time intervals of the titration:
+
{tSO }[H* ] {tSOH}
An expression for the total weak sites derived from above is
(K1*H 2 - K2*) tSOH2+ - tSO- ) LT (K1*H 2 + K2* + H)
M* ) M - [tSOH2+ - tSO-] )
(6)
where brackets have been removed for clarity and LT is total site concentration per gram of suspension. Since we do not know the actual proton concentration inside the particle, [H*+] is expressed instead as H, the bulk solution proton concentration that is directly measurable. Equilibrium constants therefore become apparent conditional constants K1 and K2 relative to the bulk solution
N
-βN∆t
m ) Re
(
∑M
n)1
0
(K1H 2 - K2)
)
w βn∆t + LT e ∆t (K1H 2 + K2 + H) vapp (12)
Adjustment of Parameters. The model requires five parameters to be optimized by error minimization: LT, R, vapp, K1, and K2. Each parameter is given a starting value and then adjusted for best fit. The diffusion transfer coefficient, R, in unit of flow (L/s) represents the average equivalent volume that would have to flow into the particle in order to transfer the required charge excess. Expressed as a fraction of the total particle volume, R indicates the extent of solute penetration. The
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TABLE 1
Properties of D6 Macroporous Spheresa size (µm) CVa (%) porosity (mL/g) density (g/mL) surface area BET (m2/g) elemental analysis (%) H C S a
4-8 40 1.8 1.05 257 67.2 7.2 7.5
CV, coefficient of variation.
term also includes effects of tortuosity arising from the macroporous structure, which would lengthen the diffusion path. Apparent volume, vapp, is the equivalent particle volume inside the particle expressed in terms of bulk solution properties. Its value is adjusted to ensure that there is no mass (charge) transfer between the two domains at equilibrium. There are two cases. For porous particles without ligand, simple diffusion occurs, and vapp equals true interstitial particle volume because concentrations at zero transfer are the same inside the particle and in the bulk solution. For particles with internal ligands, a Donnan equilibrium arises and sets a concentration gradient between the two domains even if there is no transfer. The model accounts for this unequal concentration by increasing vapp until calculated transfer is zero. Values for apparent volume are therefore indicative of Donnan equilibrium. Weight and densities for DVB spheres (Table 1) were used to generate initial values. For sediments, a density of 1.165 was assumed from the settling of flocs by Burban et al. (15). Total ligand concentration, LT, is the total concentration of weak sites in the particle and is constant throughout the titration (eq 6). Its value is given a first approximation by measuring the apparent site concentration, Lapp, being the difference in charge excess between the start and the end point of the longest titration in a given set (Table 2). Apparent equilibrium constants, K1 and K2, are given initial values for hydrous ferric oxide (HFO) surfaces (log K1 ) 7.3; pK2 ) -8.3) and adjusted thereafter. HFO surfaces have been chosen because of their ubiquitous presence in natural waters (16). Although it is possible to adjust all profiles independently, the heuristic value of the model would suffer if too many parameters were left free. We consequently adjust the model with the restriction that LT, K1, K2, and vapp are the same for all profiles done on the same sample. Only R is allowed to compensate for the longer exposure. This requirement recognizes that binding properties are independent of exposure time (rigid sphere assumption). Since the model does not take into consideration the shape of particles, we expect R to decrease with longer titrations as solutes would diffuse through a thicker portion of the particle. Thus, a set of titrations done at different time intervals on particles with uniform domains should all be predictable by changing the value of only the R parameter.
Experimental Section Sediment Samples. Surficial sediments from Coote’s Paradise (Coote’s sediments) were collected with a square dredge from the deck of a scow in the western part of Hamilton Harbour at a depth of less than 3 m. The shallow depth of the embayment and strong winds maintain oxic
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conditions year round. Previous work on these sediments and at other locations in the harbor are given in Brassard et al. (17). Coote’s sediments consist of erosion debris, mostly clays, coated with a small layer of organic matter arising from the very active algal and bacterial populations. Loadings in Coote’s Paradise come mainly from creek erosion (47050 Kg/day in 1987) and farming operations. Stelco sediments were sampled at a depth of 5 m, well below wave turbulence, near Randle’s Reef, an area known for its large organic and metal contaminant mainly due to the past 75 years of industrial activity. Oil and grease were loaded at a rate of 4579 Kg/day in 1977 (1). Surficial sediments were stored in polyethylene bottles at 4 °C until decanted. We used a settling procedure designed to remove the coarse particulates, a necessary step to prevent grinding in the reactor and wear of electrode surfaces. Sediments were mixed with equal amounts of tap water, stirred for 5 min with a magnetic bar, then allowed to settle for exactly 5 min. The first 5 cm was decanted. Calculations from Stokes law predict a size distribution of the remaining suspended particles to be less than 17 µm. A suspension stock of about 2 L was prepared by pooling several decantation steps. The final concentration of the stock was determined by filtering an aliquot on 0.45 µm (Millipore) and weighing the dried filter until constant weight. Beads. Macroporous divinylbenzene resins were synthesized by Li et al. (13) as follows: commercial divinylbenzene-55 (DVB-55) was polymerized by a conventional suspension method using (1) 2,2′-azobis(2-methylpropionitrile) (AIBN) as the initiator, (2) a 60/40% dodecanol/ toluene mixture as the porogen, and (3) methocel E50 as the water phase stabilizer. The principle rests on vigorous mixing during 2 h of the combined DVB monomers, initiator, and porogen to ensure a fine dispersion in the water phase, followed by polymerization at 70 °C for 25 h. Porosity is determined by the porogen ratio. The beads used here are 4-8 µm in diameter and roughly spherical (Figure 1). Sulfonation of the beads followed the method of Round et al. (18) in which prepared beads were added to dichloromethane in a round-bottom flask. The mixture was sonicated, evacuated for 2 min, and stirred for 1 h at room temperature. A chlorosulfonic acid in dichloromethane mixture was then slowly added. Sulfonation was complete after 8 h. Table 1 shows elemental analysis and surface area of the finished product. Titration. All titration was done under CO2-free air, obtained by filtering incoming instrument air through an ascarite column and followed by a water wash bottle. The reactor consisted of a 50-mL polyethylene conical centrifuge tube. The cap of the tube was modified to accept a delrin nylon insert to hold reference and pH electrodes. It also contained small holes for titrant addition and air tubes. This method allowed rapid insertion and removal of electrodes to the reactor tube and thus minimized exposure to ambient CO2. The following procedure was followed for all titrations. The electrode assembly was first calibrated against standard buffers immediately before the titration. Electrodes were rinsed with a 0.05 M KCl solution to minimize disturbances to the liquid junction of the reference. The reactor tube was then filled with 19.50 mL of analyte followed by 0.5 mL of 2.0 M KCl to bring the ionic strength to 0.05 M. The
TABLE 2
Optimization Parameters for Best Fit of Modela sample DVB spheres Stelco Coote’s
interval (min)
w (g)
LT (µequiv/g)
10 5 0.5 5 1 5 1
0.02 0.02 0.02 0.022 0.026 0.023 0.023
0 0 0 1100 1100 600 600
(2) (6) (13) (27) (14) (45) (10)
log K1
8.2 8.2 10.0 10.0
(-) (-) (-) (0.07) (0.02) (0.05) (0.3)
log K2
-7.2 -7.2 -10.25 -10.25
(-) (-) (-) (0.07) (0.02) (0.05) (0.3)
vapp (mL) 12.5 12.5 13 63 62.5 29 29
(0.1) (0.9) (2.1) (3.8) (0.6) (6) (2)
R (µL/s) 0.88 0.88 6.7 7.2 20.8 1.36 9.7
(0.03) (0.04) (0.3) (0.4) (0.1) (0.01) (0.2)
Lapp (µequiv/g) 382 436 375 3030 2000 1430 998
a Values in parentheses denote absolute variation required to increase error of fit by 5%. Interval, time elapsed during two successive titrant addition; w, mass of particle added to 20 mL reactor volume; LT, binding site concentration of weak sites; K1, equilibrium constant for protonated site (tSH2+); K2, equilibrium constant for deprotonated site (tSO-); vapp, apparent particle volume; R, transfer coefficient; Lapp, apparent total site concentration taken from titration extremes.
and normalized start values at zero for all titrations. A direct consequence of this operation was to set the proton condition at zero, thereby removing contributions by strong ligands, acids, and bases. Variations in relative charge excess were therefore due only to exchange between mobile species and weak sites inside the particles. Optimization. Parameter adjustment was optimized using the Levenberg-Marquardt method. In a first pass, we optimized all five parameters for each profile done on the same sample and chose the set of LT, K1, K2, and vapp, yielding the best fit. We then ran each profile again to obtain R, holding the other four parameters to the chosen values.
Results and Discussion FIGURE 1. Photomicrograph of DVB sulfonated spheres.
pH of the reactor was brought up to about pH ) 11 by adding 200 µL of 0.100 M KOH followed by prompt capping of the reactor with the electrode assembly and flushing with air. The assembly was lowered in a constant temperature jacket held over a magnetic stirrer and left to equilibrate at 25 °C for 30 min. Titration with 0.100 M HCl then proceeded and was always accompanied by recalibration of the electrodes followed by a blank titration of 0.05 M KCl water. Because titration profiles for the blanks did not necessarily fall on the same pH points as the analyte, blank titration data were interpolated to the corresponding pH value of the analyte using the cubic spline method. The difference between analyte and interpolated blank titrant addition at the same pH values yielded charge excess in the suspension. The titration profile was controlled by a computer-driven titrimeter (Tanager Scientific Systems Model 8901) and done at equal 0.1 pH intervals, based on estimates of the buffer capacity obtained from the previous titration point. Titrations at set time intervals ranging from 30 s to 10 min between titrant addition were done to show the effect of exposure time on equilibrium. The effect of diffusion is time dependent and must be evaluated against some reference point where all solutes are in equilibrium both inside the particle and in solution. At the start, the suspension was held for 30 min to ensure equilibrium, and the charge excess at that point was taken as the zero reference for the titration. The model was adjusted with this relative charge excess as the dependent variable and M0, the independent variable, similarly adjusted at zero. This operation offset eq 12 by a constant
DVB Spheres. Adjustments of the model for the DVB spheres are shown in Figure 2 and Table 2. The model was forced to fit all profiles with total weak ligand, LT set to zero, consistent with a single type of strong site, a polymertoluene sulfonic acid uniformly distributed in the sphere. Reported values of pK for sulfonate groups based on several toluene sulfonate compounds lie between 0 and 1 (19). No weak ligands should therefore be present in the DVB spheres. The fact that it is possible to adjust the model only by changing the value of R attests to the validity of our simple assumptions regarding the role of diffusion. An apparent volume of 13 mL (Table 2) indicates Donnan effect, since the real volume of DVB spheres added is close to 0.02 mL. The value for apparent site concentration, Lapp, indicates the total concentration of strong sulfonate sites in the particle. Although there is no binding of protons to the sites, the spheres appear to trap mobile species in the high negative environment of the domain in the same manner as polyelectrolytes. Miyajima et al. (20) recognize two types of binding: a “territorial” binding where ions are held by attraction to strong sites in the domain and a “site” binding where actual binding takes place with concomitant alteration of the charge density. The DVB spheres therefore represent territorial binding. The ratio vapp/R indicates the time scale to penetrate the whole apparent volume of the particle and is 4 h for the 10- and 5-min interval runs. Consider that it would take less than 1 s for a solute to diffuse into a sphere of 5-µm radius (21) assuming only unhindered molecular diffusion in water (D ) 1 × 10-9 m2 s-1). Since the spheres have only strong sites, we conclude that the increase in penetration time is due to tortuosity, which would lengthen the effec-
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Dapp ) R
FIGURE 2. Proton binding of DVB spheres for three time intervals: (a) 0.5 min; (b) 5 min; (c) 10 min. Data points are shown as squares; solid line is the model. Adjustment parameters are shown in Table 2.
tive path of diffusion, and due to a decrease in the diffusion of mobile ions because of the polyelectrolyte effect (22, 23). Similar values for R between the 5- and 10-min runs indicate that the time interval of 10 min is close to complete penetration of the sphere. From total element analysis (Table 1) and assuming complete conversion of all sulfur into sulfonate groups, only about 18% of the sulfonate groups are reached by the solute in the 10-min run. We can calculate the equivalent apparent diffusion coefficient, Dapp (m2/s), for the DVB spheres because their shape is known. The conversion between apparent diffusion coefficient and R is
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a A
(13)
where A is the total surface of particle suspension and a is the radius of the sphere. For A ) 0.036 m2 at an average radius of 3 µm, we calculate that Dapp is 1.32 × 10-13, much lower than free diffusion. Papelis et al. (12) report even smaller values for Cd and selenite binding on porous alumina particles and attribute the lower values only to tortuosity. A discrepancy occurs at the start of the 30-s and to a lesser extent in the 5-min run, which we attribute to inhomogeneities near the surface as shown by the mottled texture of the spheres (Figure 1). We think it represents the transition zone between bulk solution and a point inside where the domain becomes uniform. Hamilton Harbour Sediments. Both sediments share similar features. Although Stelco sediments have a greater binding capacity per unit weight than Coote’s sediments (LT and Lapp, Table 2), profiles for both Coote’s (Figure 3) and Stelco (Figure 4) sediments show inflections different from DVB spheres (Figure 2) due to significant surface site binding (LT, K1, and K2 in Table 2). Penetration times taken at the 5-min runs (ratio vapp/R) are 2.5 and 6.0 h for Stelco and Coote’s sediments, respectively. We expect these values to be lower estimates due to the short time interval used. Weak sites in Hamilton Harbour particle behave like ampholytes. Contrary to simple surface oxides (14), values for K1 are higher in magnitude than K2 (Table 2), indicating that the transition between deprotonated and protonated surface sites is very sharp, leaving almost no room for the neutral tSOH site. We attribute this difference to interaction between surfaces and other sites from natural organic matter on the particle. The total concentration of weak sites, LT, is furthermore consistently lower than the apparent site concentration, Lapp, so that nearly one-half to two-thirds of measured binding is due to a Donnan-type domain as shown by the large apparent volumes (Table 2). The surprisingly large contribution of this domain shows that two types of binding occur on particles: an ampholytic surface site (14) and a polyelectrolyte domain. This view is consistent with the structure of resuspended flocs consisting of mineral and biological debris entrapped in an organic matrix (4, 5). We can propose a functional identity for the polyelectrolyte and deprotonated sites in this model by comparing with two humic acid models that consider only negative sites. Proton binding for humic and fulvic materials has been condensed for a wide range of experimental titration into a unifying model (24). The model is based on binding properties of humic matter (25). A low, carboxylic type site at pK ) 3.3 and a phenolic type site at pK ) 9.6 are taken as basic values. Four other sites are postulated to exist at fixed distances from each basic value for a total of eight operational sites. The average concentration of carboxylic sites in their model (4.7 mequiv/g) is twice the phenolic site. The ratio is therefore one-third phenolic and twothirds carboxilic, nearly equal to our ratio between LT and Lapp. We therefore propose a concordance between their phenolic site and our deprotonated surface site (K2) and assign their carboxylic site as the attached polyelectrolyte site. A similar comparison can be made with the discrete log K approach derived from several approaches in the
FIGURE 3. Proton binding of Coote’s sediments: (a) 1 min; (b) 5 min. Conventions are the same as in Figure 2.
FIGURE 4. Proton binding of Stelco sediments: (a) 1 min; (b) 5 min. Conventions are the same as in Figure 2.
literature (26). As previously, total ligand concentrations were highest for the pK ) 4 site and about half for the others. Although the sediments analyzed were only from Hamilton Harbour, we believe that the range of conditions between the Coote’s and Stelco sites is sufficiently broad for generalization to other waters. The dual properties exposed here appear inherent to particle structure. The model presented here emphasizes the contribution of polyelectrolye sites and is surely simplistic. We assume that all detrital material embedded in the particle keep their surface properties without bias from the surrounding organic matrix and, further, that the resulting binding is a linear combination of surface plus polyelectrolyte terms. The importance of the surface term should however be re-examined. Recent work (27) shows HFO to be three dimensional because its binding characteristics, predictable by classic surface models, can also be obtained by using the simpler polyelectrolyte approach. If this is general, then binding on natural particles formed from porous mineral surfaces could instead be described as a combination of the two polyelectrolyte domains. The relative importance of surfaces sites and polyelectrolyte domains to explain binding in both the organic matrix and the embedded materials is an important question in modeling chemical exchanges with natural particles. We think it is possible to test each domain by creating artificial suspensions using calibrated artificial surfaces of varying porosity exposed to natural organic matter. Experiments run at different ionic strength would show the contribution of the Donnan term (28).
Conclusion Suspended particles in natural waters exchange protons according to two important mechanisms that can be related to their visible structure. Binding on surfaces imprisoned in the organic matrix accounts for one-third to one-half of the total binding capacity while the rest is caused by a polyelectrolyte sorption in the interior of the particle. Based on humic acid binding models, we assign carboxylic groups as the polyelectrolyte domain binding site and a nonporous ampholytic surface site to account for binding on mineral debris aggregated into the particle. We believe that the large polyelectrolyte domain of the particle causes the solute to diffuse slowly inside and retards the establishment of equilibrium. Artificial macroporous spheres show residence times of at least 4 h for complete permeation. Natural and contaminated sediments in the harbor require between 2 and 6 h. Estimated diffusion coefficients are lower than free diffusion in water by several orders of magnitude and probably result from the combined effect of increases in tortuosity and charge density of polyions. Since natural sediments exchange bound metals with protons, the conclusion can be extended to metal exchange. We see two exchange modes associated with the two mechanisms for binding: a fast exchange associated with surfaces present in the agglomerate and a slower exchange governed by penetration of metals inside the particle. Although previous emphasis on surface exchanges implied a dominant role for the smaller particles due to their relative large surface area, diffusion in a polyelectrolyte domain
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inside the particle indicates that exchange with large particles would become important on longer time scales.
Acknowledgments We benefited from discussions with Dr. R. Dumont on the calculus of diffusion and with Dr. W.-H. Li and Dr. H. D. Stover, who also graciously provided the DVB polymer spheres and Figure 1. The discussion section of this paper benefited from comments by an anonymous reviewer.
Literature Cited (1) OME, Ontario Ministry of the Environment. Remedial Action Plan. Stage 1 report. Environmental conditions and problem definitions. March 1989. (2) IJC, International Joint Commission Great Lakes Water Quality Board. 1985 Report on Great Lakes Water Quality. Windsor, Ontario, 1985. (3) Brassard, P.; Kramer, J. R.; Collins, P. The control of dissolved metal by resuspended sediments in Hamilton Harbour. Submitted to J. Great Lakes Res. (4) Leppard, G. Analyst 1992, 117, 595-603. (5) Filella, M.; Buffle, J.; Leppard, G. G. Water Sci. Technol. 1993, 27 (11), 91-102. (6) Hunter, K. A. Limnol. Oceanogr. 1980, 25 (5), 807-822. (7) Balistrieri, L. S.; Murray J. W. Geochim. Cosmochim. Acta 1982, 46, 1253-1267. (8) Davis, J. A. Geochim. Cosmochim. Acta 1984, 48, 679-691. (9) Hayes K. F.; Leckie, J. O. In Geochemical Processes at Mineral Surfaces; Davis, J. A., Hayes, K. F., Eds.; ACS Symposium Series 323; American Chemical Society: Washington, DC, 1986; pp 114141. (10) Hachiya, K.; Sasaki, M.; Ikeda, T.; Mikami, N.; Yasunaga, T. J. Phys. Chem. 1984, 88, 27-31. (11) Ball, W. P.; Roberts, P. V. Environ. Sci. Technol. 1991, 25, 12371249. (12) Papelis, C.; Roberts, P. V.; Leckie, J. O. Environ. Sci. Technol. 1995, 29, 1099-1108.
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Received for review December 6, 1995. Revised manuscript received May 25, 1996. Accepted June 14, 1996.X ES950920V X
Abstract published in Advance ACS Abstracts, September 15, 1996.
