Metals in aquatic systems Predicting their scavenging residence times JLom laboratory data remains a challenge Bruce D. Honeyman Swiss Federal Institutefor Water Resources and Water Pollution Control (EAWAG) CH-8600Diibendo~, Switzerland Peter H. Santschi Texas A & M University Galveston, Ix 77550 The biogeochemical cycling of ma.., elements on this planet is strongly influenced by human activities. With increasing frequency, waste products generated by industrialized societies have not been disposed of according to scientific reasoning, but rather in response to economic pressures or merely by the most convenient method. As a result, many waste products have been dispersed at elevated concentrations over wide areas, through aunospheric and aquatic reservoirs. To choose the best disposal options and to assess the “self-cleaning” capacities of aquatic reservoirs, we need to develop the ability to predict the residence times of trace substances in flowing and standing water bodies. One of the main objectives of environmental chemistry has been to describe the behavior of elements in tural systems based on knowledge of their fundamental physical-chemical properties. In many natural systems, the behavior of metals is profoundly affected by the presence of particle surfaces. During the last decade, significant advances have been made in applying the concepts and mathematical formalisms of coordination chemistry to metal-particle interactions (1-3). Current knowledge about aqueous surface chemistry has come primarily from studies of equilibrium metal adsorption in model laboratory systems. As a result, a large amount of thermo dynamic data have been generated concerning metal ion adsorption onto wellcharacterized model particles (predominately metal oxides). In addi862 Environ. Sci. TeChnOl., Val. 22, No. 8, 1988
4
tion, models that require the use of highly detailed information have been developed for the oxide-solution interface. Such models are useful heuristic devices for probing our understanding of the basic physical-chemical nature of metal-particle interactions; however, these models also are being used increasingly to predict the transport of toxic and radioactive metal species in ground and surface waters (4)and to assess human and animal health risks.
In spite of the successes of surface complexation models (SCMs) as tools for understanding the basic interactions that take place at the oxide-solution interface, several observations of metal sorption cannot currently be accounted for in such deterministic models. These effects include surface site heterogeneity (3, anomalous effects of particle concentration ( 6 I I ) , nonadditivity in multiple-adsorbent systems (12), and slow sorption kinetics (&I@.
0013936x18810922-0862$01.5010 @ 1988 American Chemical Sociely
complexation model* Eauilibrlurnexonu(on
In this article we address the general question of whether we can yet predict metal-scavenging residence times in natural systems based on current knowledge about metal behavior as derived from laboratory studies. Although we will show that our ability to predict metal behavior is still relatively limited, such a conclusion should not be construed as a criticism of the reductionist approach. Rather, it should be seen that a number of challenges remain for surface chemists interested in the natural environment.
Metal residence times The residence time of a metal in the dissolved phase in oceanic, estuarine, or lacustrine (lake) water columns may be defined as the ratio of the total dissolved concentration of the metal to its rate of removal from the dissolved phase to particle surfaces 7 ~= . [Me&, (1) where r, is the net rate of transfer of a metal, Me, from the dissolved [Me,,] to the particulate phase (mol L-'day-'). For cases in which the primary removal process of a metal from a specified volume of water is by its association with sinking particles, the total metal residence time, sr, may be defined as 7T - [Me],. - 7e (2)
r,em
f,
where r, is the removal rate of Me (mol L-'day-') from the reference volume of water; rp represents the average residence time of particles; and& is the fraction of all Me species associated
with the particulate phase. In writing Fquations 1 and 2, no assumption is required about the existence of sorptive equilibrium. If the characteristic partitioning time of a metal between the solution and particle phases is short compared with the time of solution-particle contact, then equilibrium or steady-state descriptions
An aqueous solute may react with a preexisting solid phase by three main processes: adsorption (the accumulation of matter at an interface without the development of a three dimensional molecular arrangement), absorption (the diffusionof an aqueous chemical species into a solid phase), and surface precipitation. The generic term used here to describe the general removal of a solute from the solution phase to a contiguous solid phase is sorption (79). Detailed discussions of these processes may be found elsewhere in the literature (79-22).In addition, we distinguish between equilibrium and nonequilibrium descriptions of metal sorption. The symbol K is reserved for the equilibrium value of a relation among concentrations or activities (because we do not relate K to state functions such as AGO and A@, we are not attempting a thermodynamic description per se) and Q is reserved for nonequilibrium descriptions.
may be used to estimatef,, and consequently 7T.Schindler (23) has used this approach in his zero-order model for oceanic scavenging. Balistrieri, Brewer, and Murray (24) used it to evaluate the relative sorptive efficiency of differentparticle types. It is becoming increasingly clear, however, that many systems, even those at steady state, apparently are not at sorptive equilibrium and that metal residence time models must explicitly take into account the rate of approach to equilibrium (15-18, 25). To describe trace-metal residence times, one must recognize either thatf, = f(time) or that f , f f(time) because of steady-state conditions or local equilibrium. In the following sections we will discuss the estimation off, and, therefore, of 71;Equilibrium descriptions of metal sorption will first be emphasized, and discussions of kinetic considerations will follow. Equilibrium metal ion adsorption Surface complexation theory evolved from the observation that the tendency of metal ions to interact with oxide surfaces is related to the tendency to form solution-phase complexes (I, 26, 27). The analogy of solution-phase complexes to surface complexation is exact. The objective in using SCMs is to describe experimental observations using a minimum set of reactions with specific thermodynamic properties. For example, such a set of self-consistent equations may be similar to those presented in Table I. Such reactions are Environ. Sci. Technal.. Val. 22. No. 8. 1988 863
postulated because it is currently very difficult to determine unambiguously the speciation of metals at oxide surfaces, except in a few cases (29). Because SCMs differ in the way in which the free energy of adsorption is resolved into electrostatic and chemical components, the specific values of the association constants are strictly mcdeldependent. A powerful attribute of the surface complexation approach is that surfaceand solution-phase reactions may be considered together as a series of linked, linear, and nonlinear equations ( 3 9 . Moreover, SCMs can describe the extent of metal ion adsorption in terms of the specific nature of the adsorbent (site density and acidity) or the adsorbate (in terms of the metal-surface site association constant); the effect of a m plexing ligands, which may either enhance or reduce the extent of metal ion adsorption (31-34); general ionic strength effects (35-37); and, to a certain extent, the competition of solutes for surface sites (38-39). ’ h o important aspects of the application of surface complexation theory to estimating metal residence times are illustrated in Figure l. For a given metal, the tendency to form surface complexes varies depending on the nature of the particle surface. Also, particle surface sites form complexes with different metals to varying extents. For example, for values o f f , < 0.1, a 1 order of magnitude change in the tendency of metals to associate with partcle surfaces will affect metal residence time by approximately 1 order of magnitude. Figure 1 shows that the type and concentration of particle (sorbent) used as a basis for scavenging calculations will have a significant effect on estimates of metal-scavenging residence. times. The work of Balistrieri and colleagues (24) and of Schindler (23) approaches the question of metal residence times solely from the perspective of hydrolytic scavenging or surface complexation. Although the work of Morel and Hudson ( 4 9 and of Whitfield and ’hrner (41) has raised some questions about the general applicability of such an a p proach, particularly with regard to the role played by biota, the concept of surface complexation remains a useful starting point for predicting the fate of the group of metals that are predominately influenced by chemical interactions with particle surfaces (41). Semi-empirical descriptions of metal inn adsorption. The success of SCMs as heuristic devices for exploring the details of solute-particle surface interactions has made them the reigning aquatic chemistry paradigm. In practice, however, SCMs often have been 864 Environ. Si.Technol., MI.22, No. 8, 1988
supplanted by semiempirical descrip tions of adsorption that retain the generic relationships among master variables expected from SCMs. This tendency is ascribable, in part, to the amount of detailed information required for the implementation of SCMs (Table 1). The net change in state for a metal ion (solution -t particle phases), undoubtedly the consequence of several reactions, can be written in terms of an overall reaction >XOH, Me., = >XOMe XH (3) with the corresponding conditional partitioning coefficient
+
+
where >XOH, represents all “free sites,” or particle surface sites not associated with any species of the metal (Me); >XOMerepresents the sum of all Me-containing surface species; Me,, denotes the sum of all solution species of the metal; x is the overall HlMe exchange coefficient;and [ ] and { ] indicate concentration and activity, respectivelp The fraction of the total metal
associated with particle surfaces is
This is the general relationship needed to relate the intensity of metal-particle surface site interactions to scavenging residence times (seeEquation 2). The parameters x and Kp are empirical and vary with pH, ionic strength, and type and concentration of complexing ligands. These parameters are conditional because they represent the contribution of several species at once. In this discussion, however, we are considering a system containing one metal ion only. Equation 3 may be considered to represent, in a single mass action expression, all appropriate reactions yielding a net change of state for the metal. Although the stoichiometric ccefficientsfor the postulated (SCM) reactions have integer values (such as those in Table I), x may have any real value: positive for cationic and negative for anionic adsorbates. With certain exceptions (42), x has a noninteger value because it represents the net of all reactions (Table 1 in addition to solutionphase reactions) involved in proton
transfer. The apparent net proton coefficient may be determined graphically from adsorption data by two different methods: Kurbatov plots (43),in which Equation 4 is linearized to solve for x and Kp, or analysis of adsorption isotherms, log r vs. log [Me,,] (44). The net proton coefficient, x, depends on both adsorption density r and pH, where (T = pXOMe]/([>XOMe] pXOH,]) the fraction of total available surface sites associated with species of Me) (44,4.9. Because x is a measurable quantity, users of SCMs employ the overall proton coefficient determined from experiments to adjust association constants of the postulated surface reactions (the intrinsic constants in Table 1). Conversely, through the choice of a thermodynamically valid set of species and stoichiometric reactions, the overall partition and proton coefficients can be expressed in terms of thermodynamic equilibrium constants and species (28). Although the conditional nature of the partitioning coefficients makes them inappropriate for predicting s o p tion behavior outside the set of conditions for which they were calibrated (Le., the suite of complexing ligands and the ionic strength), these coefficients have been used in a wide range of applications to extract important information about interactions at the solution-mineral interface (5, 42, 46, 47). In the discussions that follow, partitioning coefficients will serve as useful surrogate parameters for exploring behavior that is nondeterministic in the context of current SCMs. Further remarks on the conditional nature of such coefficients can be found elsewhere (28, 42, 45-46).
+
species, [>XOH,],, is constant and that the total metal concentration, [Me],, is varied. At low adsorption densities (r < 1 W mol Melmol particle surface sites), sorption isotherm data initially will fall on line A of Figure 2a. At adsorption densities greater than some critical value (designated r*),however, the data will deviate from Langmuirian behavior and follow a path similar to line B; in other words, the calculated Kp (Equation 4) will decrease with increasing adsorption density. This be-
havior generally has been interpreted as evidence of heterogeneity in surface although other explanations sites (3, (such as surface precipitation) have been considered (48).Critics of the surface heterogeneity hypothesis may argue that the effect is at least partially an artifact of using conditional constants to describe metal ion sorption (the observation that x is also a function of P may tempt one to invalidate the concepts of Benjamin and Leckie [I); however, recent kinetics studies of the
Anomalous metal behavior
In this section we will describe characteristics of metal sorption that apparently cannot be explained by straightforward application of SCMs. Surface site heterogeneity. Qpically, the specified, postulated (SCM) reactions and their associated equilibrium constants are considered to be the m e for all sites present on the adsorbent. This is the equivalent of a Langmuirian surface. When sorption data gathered over a range in total metalltotal available surface sites ([Me]r/pXOH,],) is plotted as log r vs. log [Me.& metal adsorption, which behaves in a Langmuirian fashion, will fall on a line of slope equal to 1 (line A, Figure 2a). For the same set of data, Kp will be independent of adsorption density (lie A, Figure 2b). In reality, experimental systems may behave differently Assume that the tw tal number of surface sites in the system available to form complexes with metal
r*
I
Envimn. Sci. Technol.. W. 22.No. 8,lSSS SS5
-1.0
opinion is that the effect of C, is the consequence of physical-chemical processes such as particle-particle interactions that affect the equilibrium distribution of solutes (8, 52). For example, light-scattering experiments by Chang and cc-workers (53)suggest that the C, effect they observed for Zn(II) adsorption onto titania was not attributable to the presence of colloids but rather to the degree of particle aggregation. On the other hand, Anderson and colleagues (54) have suggested that phosphate may form a bridge between particles, thereby affecting particle aggregation in a manner that depends on the solid-liquid ratio. Higgo and R e s (52)and Morel and Gschwend (50)approach the problem in essentially the same way: The soption of metals on colloids and filterable or settleable particles may be described by characteristic association coefficients for each particle size group. The dependency of the measured, overall K, on C, arises from the relative effect of adsorbates associated with colloids but still operationally considered to be in the “dissolved” fraction. Both groups of authors suggest that log K, a n . log C’; the exact relationship depends on whether colloids and particles are in a fixed ratio (n -1) (50,51) or are covariant (n -2) (52). Sorption data in which n = - 1 has been observed for hydrophobic organic material studied by Gschwend and Wu (IO) and for the adsorption of various metals such as Ni and Co-montmorillonite (a, Ni on quartz, and Sn (17) and Am (51)on red clay. Other metals, however, show log Kpllog C, relationships by which slopes distinctly differ from -1.0. For example, log Kd vs. log C, data for Be (17, 55-58), Ce
-
(27),Sn(27),andTh(28,59),inwhich
metal ion bonding mechanism (49) have provided further, more direct evidence in support of the site heterogeneity hypothesis. When adsorption densities are in the region where metal adsorption behaves in a non-Langmuirian fashion (r > r*, Figure Zb), values for Alog KpI Alog r have been observed in the range of -0.5 to - 1.0 (5,22,45,46). These values depend on the nature of the components and the way in which x depends on r. Particle concentration and Kp. According to our current phenomenological model of interactions at surfaces, Kp should be solely a function of the relative magnitude of system components-for example, the surface siteadsorbate ratio. Consequently, curves A and B of Figure 2a should be inde866 Environ. Sci. Technol., Vol. 22, No. 8, 1988
pendent of the path taken: a constant [>X0HlTand variable [MeIr, and the converse, should produce the same isotherm. Recently, however, numerous reports ( 6 1 1 ) have indicated an anomalous effect of the absolute particle concentration, not just the total available surface site-total metal ratio ([’XHxld [MeIT)on Kv This relationship is indicated by curve C of Figure 2 and manifests itself when K, is determined at constant [MelTand variable [>XOH,]r (or particle concentration, C)., ’ h oscbools of thought have evolved over the interpretation of the so-called particle concentration effect. One holds that it is essentially an experimental artifact caused by colloids that are operationally defined as part of the dissolved fraction but that are nevertheless adsorbing solutes (50, 51). The other
these elements interact with a variety of adsorbents, are linear functions with slopes in the range of -0.4 to -0.5. Th shows a C, effect over nearly 7 orders of magnimdde in particle concentration (Figure 3a). It also is clear that the origin of these observations cannot be resolved solely through the rigorous application of SCMs. When this was attempted, it became necessary to make arbitrary changes in intrinsic surface complexation constants to fit model curves to metal sorption data over a range in Cp values (Figure 3b)(44, 53). Sediment models and particle-partide interactions. The development of surface complexation theory and laboratory studies of metal ion adsorption onto model mineral colloids have established complexation hierarchies for the same solute interacting with different mineral types. Thus the idea has developed that the overall adsorptive behav-
ior of sediments is analogous to a suite for each constituent adsorbent (61). In of ligands competing for complexation this context n of the metal ions ( M 6 2 ) . A metal ion will be distributed among a suite of par- &,,3ys = C [-XOMeli/[MelT (8) ticles falling through a water column i= 1 according to the number of surface sites Accordingly, the partitioning coeffipresent for each particle type and its cients for the entire system (Kp,rysand characteristic Me-particle surface site x,) should be aggregates of the relative contributions for metal interaction association coefficient (Kpi). This approach is based on an under- with each mineral constituent in the lying assumption that when the sedi- suite of particles. For example, ment or soil consists of a group of dis(9) tinct adsorbent types, particles affect x, , = ElXl + E2x2 + + E”X. each other only to the extent that they are in competition for the adsorbate (i.e, there are no manifest interactive 1% Kp,ryr = El ’ 1% Kp.1 + E2 ’ effects on adsorption). Had there been such effects, they would have included logKp.2 + ‘ ’ ’ E. ’ log K,,,, (10) particle bridging by sorbates (54); sur- where n face “regulation” phenomena (63);or the loss of available surface sites Ei = [ -XOMe]J .’ [ >XOMeIi r=l througb particle aggregation, particle Particle-particle interactions that dissolution, and reprecipitation of solubilized material on other particle sur- have manifest interactive effects on adsorption will produce overall partitionfaces. The competition of particles for a ing coefficients that are different in magnitude relative to the ideal, “addisorbate may be expressed as (6) tive” value (Equations 7-10). Thus n [Me]= =[Me,] [l + C [-XOMe]J log K$& = log Kp,rys + log I (11) i=l (7) where I is an empirical interaction term. Observed values of log I range from about -2 to +5 (12). The effect of adsorptive nonadditivity in mixed adsorbent systems on metal Kp,” . [-XOH,]n + 1 scavenging estimations is shown in FigWIxn ure 4. Observed Cr(V1) adsorption in a where terms 2 through n 1 represent binary mixture of Ti02 and (am) the solution-particle partitioning of Me Fe203.H20 is compared with ideal
...
... +
+
mixed-sorbent behavior. The topmost and bottommost lines represent Cr(V1) adsorption onto a single, model adsorbent. The line labeled “expected” is the composite behavior according to a combination of Equations 2 and 7, with TP equal to 1 day. In the experimental system (12), the fraction of Cr(V1) on all particles in the binary mixture of Ti02 and (am) Fe203.H20is greater than anticipated from a summation of the individual properties of the sorbents. Estimated from these laboratory studies, rr (Equation 2) is shorter than would be expected from individual component behavior because& for the mixed system is enhanced. This enhancement may be caused either by modification of the iron oxide surface by titanium or by creation of a more favorable binding environment in the interfacial region between coagulated particles. The result is a system that is more effective at scavenging metals than would be expected from component properties. Other multiple adsorbent systems have been observed to decrease the fractional metal removal relative to “ideal” behavior, most likely as a consequence of decrease in available surface sites through coagulation (12). These results point up the need to investigate metal ion sorption in assemblages of materials and to evaluate our ability to describe sorption in natural systems from model system analogues. Kinetic considerations Until recently, laboratory studies of metal sorption have focused on equilibrium descriptions of metal-particle interactions. Now, however, there is a growing body of literature describing kinetics studies of metal ion adsorption (49, 64, 65).These studies have indicated likely surface complexation mechanisms and have shown that surface complex formation is rapid with characteristic times on the order of milliseconds. By contrast, observed characteristic times for metal sorption in natural systems range from less than a day to weeks (15, 16, 18, 25, 59). Whether a kinetic description for tracemetal scavenging is required generally depends on two factors: the rate of a p proach to sorptive equilibrium and the length of time that a tluid containing sorbates is in contact with particles (rp). A kinetic approach to scavenging was outlined by Nyffeler and colleagues (16). With the solution phase as the reference point, one can write the following general rate expression:
Environ. Sci. Technol., Vol. 22, NO. 8, 1988 867
where 4 and k, represent apparent removal (adsorption) and production (desorption) rate constants. At steady state, d[Me,,]/dt = 0, and the system is at sorptive equilibrium. The kinetic shucture of Equation 12 is not written to imply a specific s o p tion process, but rather t o q r e s e n t an empirical relationship among master variables and a change of state for the metal from the ocerationaJlv defined dissolved phase -to the particulate phase. The general solution to Equation 12, in terms of Q,is (13)
Because equilibrium is a balance between opposing rates (production and removal), rprb = &/Q(r). and e(?)+ &as r, 0. The equilibrium distribution coefficient (in volume/mass) corresponding to Equation 13 is
-
The distribution coefficientis related to Kp by the factor Mx/N,.where N, is the number of surface sites per mass of particles. Three alternative processes have been suggested as explanations for the slow sorption Idnetics: slow chemical 808 Envimn. Sci. Technol.. Vol. 22. No. 8. Igse
-
Ilu---iF-i
reaction (21, 22). mass transport control (63,#), and aggregation of colloids with larger filterable particles (those particles removed by filtration) (70-72). Although the number of available surface sites should, in principle, affect surface complexation kinetics (49, 64,65). in many natural systems the number of available surface sites should be far in excess of the total metal ion concentration. For example, total Th concentrations range from lW4to 1VZoM, depending on the isotope, whereas particle site concentrations may range from le9M in the deep sea to >lm4 M in estuaries or coastal zones. This suggests that another process is responsible for the dependency of sorption rate on Cr Unfortunately. little direct evidence indicates which F m s s controls the rate of s o p tion in natural svstems: most likelv. one or more proms& opeAte under gfferent conditions. Differentiating between the processes experimentally may be problematical; for example, metal solubility control by reversible chemical reaction or by diffusion has been shown
to be mathematically equivalent with respect to derived breakthrough curves for flow through a porous medium (73). More work needs to be done to examine metal behavior when the sorbates are in the presence of disordered, metastable solid phases rather than crystalline solids and to develop methods that will distinguish between reaction rate and mass transport control. A promising avenue of research with respect to mass transport control is the extension of the Damkohler numbers (dimensionless ratios of the average transit time to reaction time) (74) to the analysis of sorption processes. Most of the work with such dimensionless groups, however, has been in terms of groundwater transport (68)or sediment mixing (7.9, with few applications to settling particles (67). An emerging and very active area of research concerns the role of colloids and particle aggregation, especially subfilterablewith filterable particles, in the production of slow-sorption kinetics (70-72), the dependence of sorption
rate on particle concentration (59, 66, n),the determination of the particle concentration effect (50, 51, 59), and the transport of sorbing substances through porous media (79. Thus far, colloids have been implicated largely hy inference. Major problems are the identification of the colloidal fraction, such as particle size distribution and composition, and the development of models linking the chemical and physical characteristics of colloids. We have described observations of metal sorption kinetics as a consequence of variations in particle concentration. Figure 5 shows k, (day-') and k,C(day-') for a number of different metals in the presence of a single sorbent type at constant C,. The relationships in Figure 5 are purely observational; however, because K d (or K,) represents a ratio of rate constants, such a general relationship is m n able. From Equation 14, (d log k,)/(d log Kd) 1, which is approximately the slope of the data in Figure 5a. The correlations shown in Figure 5 still require a strong theoretical explanation, although one possibility rests in linear freeenergy relationships (LFER) (77). Such correlations between rate and equilibrium distribution coefficients may be useful in predicting the fate of a variety of metals for which specific rate data do not exist. The relationships shown in Figure 5 have interesting implications for system dynamics. Consider the idealized scenario shown in Figure 6 for a system that is initially at sorptive equilibrium. Following a step increase in the particle concentration (Figure 6a), the system will progress toward a new equilihrium state. The rate at which the new equilibrium state is reached. may be described in terms of the system response
time, f c s p . For a reversible, first-order reaction, the rate of approach to equilibrium is the reciprocal of the sum of the forward and reverse reaction rate constants: fXOMeI + [’XOHx]) such that the equilibrium adsorption density r is at r*(the adsorption density indicating the limit of Langmuirian behavior). At constant C, increasing [Me]* by a factor of lo2 increases r by somewhat less than 2 orders of magnitude; also produced is a commensurate decrease in K,, as generalized in Figure 2. The exact relationship between AK, and A[M~]Tis system-dependent. From E, decreasing C, (or [>XOH,IT)also will increase I?, provided [MeIT remains the same (for the moment, ignoring the C, effect). If l? > r*,K and& will decrease and the system wi& move in the direction of point 4. x = f(pH, r).The Me/H overall exabout 0.2to 0.3 and cause a decrease in
k),
fv).
870
Environ. Sci. Technol., Vol. 22, No. 8, 1988
Kp of 1-2 orders of magnitude. For cation adsorption, the proton coefficient is a positive function of I? (44, 45). At constant MeT, for example, decreasing Cp will, in the absence of significant particle concentration effect, increase F; therefore, x will increase. An increase in x causes a relative decrease in K,. From E the system will move in the direction of point 5 . This illustrates the danger of using conditional coefficients that have not been “calibrated” specifically for the system (for example, with Kp as a function of pH and r). Interactions in mixed-adsorbent systems. At a fixed total particle concentration, particle interactions that have manifest effects on overall metal adsorption (such that K,“Yy,f Kp.sys [Equation 111) will displace the actual T T , relative to the calculated rT, along the rT axis. The direction of the displacement will depend on whether the interactions enhance or reduce overall adsorption. Although a broad base of knowledge exists about the effect of solution composition on particle interactions, little is known about the extent to which particle-particle interactions affect metal adsorption. Consequently, our ability to calculate metal residence times from a knowledge of their behavior in model (and mostly single adsorbent) systems is limited. Kinetic effects. When particle-solution contact times are short relative to the characteristic time for adsorption, nonequilibrium (kinetic) descriptions of metal-particle interactions must be used. Kinetic parameters are complex and, as yet, incompletely known functions of C, and K,. In general, however, low C, systems have longer characteristic adsorption response times than do higher C, systems. If r,, is less than the time required to reach equilibrium, fp and Q will be less than the equilibrium value and the observed rT will be longer. For example, if the equilibrium K is lo-’ at any particular C,, kinetic ekects will produce a displacement of the log TT/log C, relationship in a direction away from the K, = line toward a longer TT.
Modeling natural systems The nondeterministic and interactive effects described above generally influence the estimation of an apparent partitioning coefficient by 1 to 3 orders of magnitude in either direction. This, in turn, has a similar effect on rT. At extreme particle concentrations, for instance, in the deep ocean or in soils and sediments, our ability to observe small changes of a metal in the solute or particulate fraction, respectively, is restricted. Even in environments of moderate particle concentrachange coefficient, x, is a sensitive
function of both pH and adsorption density. For example, a pH decrease of 0.25 may yield an increase in x of tion such as those found in lakes, streams, estuaries, and continental shelves, our ability to model metal behavior from known, thermodynamic constants is severely limited. Given these uncertainties, one must conclude that the reductionist approach alone has failed thus far to provide a sound basis for the prediction of trace-element behavior in aquatic systems. Even though more holistic and therefore more empirical approaches such as whole ecosystem experimentation (15, 80-82) often result in better understanding of the overall consequence of interactive process, these approaches fail to provide an understanding of what occurs at the molecular level. Consequently, only through a combination of the two complementary approaches can we hope to improve our capacity to predict traceelement behavior in aquatic systems. Interactive effects limit our ability to model ion transport in natural waters, most likely because we assume that the chemical composition of the natural particle surface (such as coatings and gel layers) is given by the bulk composition of the particle interior and that larger (filterable or centrifugable) particles are dominant in controlling the fate of trace elements. In the future, the most promising approaches to understanding metal behavior most likely will incorporate a detailed knowledge of the chemical composition of the interfacial region of natural particles, the particle size distributions over the entire range of particle sizes, the physical relationships among particles (e.g., particle agglomeration and aggregate composition), and the role of organisms and nonliving organic material in the coupling of metal cycles (81).
Acknowledgments The authors dedicate this article to Paul Schindler of the University of Bern, in celebration of his 60th birthday. Many of the authors cited herein have benefited from his pioneering work in aquatic chemistry and from his ideas on applying thermodynamic information to the description of metal behavior in natural systems. The authors also are thankful to Laurie Balistrieri, Laurent Charlet, Rob N. J. Comans, Bruce Faust, James J. Morgan, Peter Reichert, R. Scott Summers, and ES&T reviewers for their thoughtful comments on the manuscript. The writing of this paper was supported by the Swiss National Science Foundation. This article has been reviewed for suit-
ability as an ES&T feature by James W. Murray, University of Washington, Seattle, WA 98915; by James A. Davis, U.S. Geological Survey, Menlo Park, CA 94025; and by Kevin Farley, Clemson University, Clemson, SC 29634-0919.
1981.42. 191.
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( 5 ) Benjamin. M. M.; Leckie. I . 0. J. Colloidlnterfar~Sri. 1981, 79. 209-21. (6) Atkinson. R. J.; Posner. A. M.: Quirk. 1. P 1. Inorg. Nucl. C h m . 1972, 34. 2201. (7) O'Connor. D. I.: Connolly. 1 . P Woter Res. 1980. 14. 1517. (8) Di Tom. D. M. et al. Environ. Sci. Techno/. 1986,20. 55-61. (9) Voice. T. C.: Rice, C. P; Weber. W. 1. Environ. Sri. Technol. 1983,17. 513-18. (IO) Gschwend. P M.; Wu. S. Ennviron. Sci. Technol. 1985.47, 131 1-23. (11) Enfield. C. E.; Harlin, C. C.. Jr.; Bledsoe, B. E. Soil Sri. SOC. Am. J . 1976,40. 243. 1121 Honevman. B. D. Ph.D. Thesis, Stanford Univ;rsity. 1984. (13) Kurbalov. M. H.; Wood, G. B. J. Phys. Chem. 1952,56. 698-701. (14) Hingston, F. 1 . In Adsorption oflnorgon-
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Bmce D. Honeyman (I) is a research associare in rhr Deparrmenr of Radiology and lsorope Geodrrmisrp ar the Sivi.ss Fedrral Institute for Wafer Re.source.s and Wafer Pollution Conrml (EAWAG). He holds a B. S. in applied earth science and M.S. nnd Ph.D. degrees in environtnenral engineering and science from Sranford Unirersin. Before coming lo EAWAG, Honewnari was a visiring srienrisr in rhe School of Oceanography at rhe Universiv of Washingron. Peter H. Santschi (rJ was head of rhe radiology and isotope geochemisrp section of EAWAG and senior lecturer in geochemical oceanography and isotope geochemisrn at the Swiss Federal lnsrirure of Trchnology (ETH) in Zurich. He is now professor of oceanography in the Deparrment of Marine Science. Texas A & M Oniverrit?. at Galveston. His currrnr researchfocuse.s on radionuclide and rrace-elemenr rycliq in the environment. especially in oceans. lakes, atmosphere. and groundwflrers. Enviran. Sci. Technol., Vol. 22.No. 8. 1988 871
