Fresenius J Anal Chem (1995) 351:54-61

Fresenius' Journal of

© Springer-Verlag 1995

Characterization of NOM-colloid aggregates in surface waters: Coupling transmission electron microscopy staining techniques and mathematical modelling K.J. Wilkinson, S. Stoll, J. Buffle D@artement de chimie min~rale, analytique et appliqu~e, Universit6 de Gen~ve, CH-1211 Gen~ve4, Switzerland Received: 24 May 1994/Revised: 30 August 1994/Accepted: 2 September 1994

Abstract. The role of inorganic colloids and natural organic macromolecules in aquatic and soil systems is essential for our understanding of contaminant and nutrient transport. The submicron organic fraction, although important in terms of total surface area, is poorly electron-dense and thus not susceptible to observation by transmission electron microscopy. Several staining techniques were therefore developed to enable the observation of the submicron aggregate fraction in natural waters. Lead and silver based stains were especially successful in increasing the contrast of previously unobservable organic macromolecules. Computer simulations were developed for the interpretation of observed aggregate structures in natural waters. Based on the TEM observations, modelling was employed to examine the formation kinetics and structural characteristics of aggregates under different physicochemical conditions. The modelling results offered insight into the underlying mechanisms and important factors influencing the aggregation processes.

Introduction The transport and bioavailability of both nutrients and toxic compounds are primarily regulated by the extent to which they are partitioned among the soluble, colloidal or particulate fractions of the water column [e.g. 1]. Sorption of trace compounds occurs on several phases [2] including (i) inorganic solids such as clays, silicas or iron and maganese oxy-hydroxides; (ii) organic macromolecules such as humic substances, polysaccharides or proteinaceous compounds and (iii) biological organisms, debris of exudates. The fate of associated pollutants/nutrients will thus be largely influenced by the interaction of the particulate, colloidal and dissolved matter. The recyDedicated to Professor Dr. Dieter Klockowon the occasion of his 60th birthday Correspondence to: J. Buffle

cling, transport and elimination of the resulting aggregates will largely depend upon their size, density and sedimentation rate [3]. The role of particles larger than 1 gm is well documented [e.g. 2, 4, 5]: their rapid sedimentation, following or without coagulation, results in the burial of micropollutants in the sediments. On the other hand, experimental limitations have often restricted study on the submicrometric particles. In a recent study [6, 7], it was demonstrated that even though the submicrometric fraction comprised only 1 - 1 0 % of the total particulate mass in the Rhine River, their surface area and thus their capacity to sorb pollutants was estimated to be 5 0 - 80% of the total particulate and colloidal surface. In the same study, it was demonstrated that these particles are often associated with organic matter matrices in the water column. Despite these results, the role of the associated organic matter remains unclear. Depending on the suspension composition, the physicochemical conditions and the nature of the organic macromolecules, organic matter could be expected to either stabilize the inorganic colloids, leading to their elimination by the outflowing river, or facilitate the aggregation processes and their subsequent removal from the water column. The available results indicate that further characterization of the natural organic matter (NOM) and of the NOM-colloid associations is necessary; however, given the complexity of the natural aquatic colloids, it will likely be a difficult task. Presently, few techniques exist which allow the nonevasive detailed examination of the aggregates in the water column [3]. Photon correlation spectroscopy permits an overview of size distributions, but an aggregate is often "seen" as one large particle; the fine structure of the aggregates plays an important role in their behaviour but can only be estimated through their fractal dimensions. Transmission electron microscopy (TEM) [3, 7 - 9] has allowed the morphological examination of very small colloids (down to 1 - 2 nm) but difficulties still persist in the observation of the less electron-dense organic matrix. The few available TEM observations using high contrast conditions have revealed the existence of large, often fila-

55 mentous matrices which interact with small, spheroidal inorganic particles. Filamentous, polysaccharide-conraining microbial exudates appear to bridge rather than coat particles [10], suggesting that microbial processes may play a predominant role in the flocculation process. Smaller fulvic compounds might also play a role in colloid stability by coating the particles [3]. One of the goals of this work was thus to develop staining techniques to enhance the observation of natural organic matter. Classical staining techniques, developed over the past 30 years for the staining of cellular components, were modified to take into account the unique characteristics of the NOM. Quantitative information must also be obtained with respect to aggregate conformation and concentration as a function of the physicochemical conditions and/or time. It has been shown that computer simulations are a powerful tool for the systematic investigation of some of the physicochemical factors influencing the morphology of colloidal structures such as aggregates, gels and sedimenting flocs [11-13]. For complex problems that are difficult to solve analytically, computer simulation acts as a useful bridge between the microscopic details and the macroscopic behaviour. Tight coupling between simulations and TEM observations is essential since observations are the only way to incorporate valid initial conditions into the models (e.g. size and shape of colloids and macromolecules) and simulation is required to get a quantitative estimate of the parameters which relate the interparticulate forces and aggregation rates. Mathematical modelling of bridging flocculation using computer simulations has generally been directed towards studies where the sizes of the polymer chains are approximately equal to or smaller than those of the colloidal particles [14-16]. Under these conditions, the kinetics of adsorption and reconformation of the chains on the particle surface play a predominant role in the stability of colloidal suspensions. In such situations, polymer chains favour aggregation by acting as a polymeric glue between the surfaces of the comparatively large particles. Very few simulation studies have been performed [17] for systems in which the polymer chains are much larger than the interacting particles, a situation which seems to occur frequently in natural aquatic systems (see discussion on TEM observations). In this case, the kinetics of adsorption and reconformation of the polymers are less important while the relative size of colloids and macromolecules and the conformation of the latter are key factors. In this paper, we report the results of a three-dimensional model developed to simulate a bridging flocculation process between small colloidal particles and large polymer chains. The particles may not only be bridged by the macromolecules but may also facilitate the formation of larger aggregates due to the adsorption of several macromolecules on the same particle. In summary, the goal of this study was to increase our understanding of the structure and behaviour of the submicron particulate fraction by coupling two complementary approaches. Staining technology was developed to enable the observation of NOM and NOM-colloid aggregates in whole mounts of hydrophilic resins with little or no effect on the conformation of the colloid system of in-

terest. The influence of (i) the reactivity of small aggregating particles with large polymer chains, (ii) the relative polymer/particle concentration ratio and (iii) the conformation of the chains, on the evolution of aggregate size distribution was studied using computer simulations.

Experimental Sample collection and preparation Water samples were collected from lake Bret (Vaud, Switzerland), a small eutrophic lake with a maximum depth of about ~8 m, from October to December, i.e. during a period of rather low biological productivity. Water was sampled in a 20 L cuve at a depth of 5 m, insulated to prevent warming, and returned immediately to a cold room which had the same temperature as the lake (_+ 1 °C). Particulate matter was allowed to sediment for 2 h, water was then centrifuged 2 h at 4000 rpm (3700 g) to remove the largest particles (primarily > 1 ~tm, [6]). Four copper (200 mesh, collodion and carbon coated) TEM grids were covered by 8 ~tL of a hydrophilic resin (nanoplast) on a ceramic plaque in a four milliliter ultracentrifuge tube. Particle concentration dependent sample volumes (1.4 to 3.0 mL) were added to the tubes just prior to centrifugation onto the grids (24 h, 30000 rpm, 124000 g), resulting in the embedding of the particles in the thin layer of resin. This method allows formation of a highly reproducible, very thin nanoplast layer which requires only minimal handling.

Sample staining In the histochemical literature, high concentrations of stains (often metal ions) are often employed to ensure diffusion through cell walls and across membranes and cytoplasm [e.g. 18]. In comparison, in our experiments, it was necessary to reduce stain concentrations by several orders of magnitude so as to avoid conformational changes in the easily deformable organic matrix. Experiments were performed to determine the image enhancing ability of the following stains: AgNO 3, Pb-citrate, Pb-acetate, CuSO4, La(NO3)3, VOSO4, ruthenium red, uranyl acetate, toluidine blue, alcian blue, ammonium molybdate and colloidal gold and iron. Two staining regimes were employed in order to minimize possible artefacts due to the stain itself. In the first series (staining), a small volume (approx. 0.5°70 total sample volume) of buffered (pH 7.4, 10-2mol/L HEPES) stain was added directly to the water sample prior to centrifugation to give a final stain concentration of l - t 0 ~ t m o l / L . Colloidal gold (total Au concentration = 50nmol/L, colloid dimensions: 5 nm) and iron (total Fe concentration = 1 ~tmol/L colloid dimensions (hematite): 70 nm) were also added directly to the water sample. In poststaining experiments, embedded samples obtained after centrifugation but before complete polymerization of the resin were immersed in 1 mmol/L stain for 15 s - 4 min. In this case, addition of stain would not be expected to modify the morphology of the organic matrix, already largely fixed by the embedding resin. Morphological features which were observed

56 with one staining combination were verified with different stains and/or the opposite staining regime.

Electron microscopy High-resolution transmission electron microscopy observations were made with a JEOL JEM-1200EXII Temscan. The chemical composition of individual particles was determined with energy dispersive spectroscopy (Princeton Gamma Tech IMIX system).

Simulation model

Colloidal particles and polymer chains are confined to a cubic cell with normal periodic boundary conditions allowing them to pass freely through the periodic walls of the cell. The chains consist of several jointed spherical segments, like a pearl necklace, where the size of the segments is not that of the chemical monomer, but rather of a group of successive monomers whose size is of the order of a Kuhn step length ([19], characteristic length along the chain over which the directional correlation between the segments disappears). The relative sizes of chains and particles are controlled by adjusting the diameter of the colloidal particles and the length of the polymer chains through the number and size of the spherical segments. The configurations of the chains, therefore their Kuhn lengths, are influenced by the solvent "quality". The pH, ionic strength and density of charged sites on the polymers give macromolecules diverse structural properties in solution and thus influence the colloid-polymer in, teractions. For example, large changes in overall polymer dimensions and conformations are observed by increasing the degree of ionization of the chains [20]. In order to take into account a wide range of structural configurations from coils (fractal dimension close to 2) to rigid rods (fractal dimension close to 1), a method for generating polymer chains has been used in which their fractal dimension Df is adjusted by imposing angular constraints between the unconnected segments based on their repulsive energy. The interaction energy u(r) between two unconnected segments is given by:

ur,:{0

where r is the distance between the two segment centres, 2 a range parameter and d the segment radius. The number evolution of aggregates has been computed using a cluster-cluster aggregation (CCA) model (where cluster and aggregate are used as synonyms) [211. The particles and chains, as well as the aggregates, are allowed to move in space according to their diffusion coefficient, which is fixed by their size and conformation. In this paper, the sticking probability is assumed to be one for particle-chain contacts (leading to the formation of an irreversible bond), and to be zero for particle-particle and polymer-polymer contacts (the model does however allow modifications of these values). Aggregates are thus formed only by polymer-particle contacts; particles may

bind to several segments of various chains and then act as ligands bridging the chains - behaving as a colloidal glue. The diffusional motion of the particles, polymers and clusters is represented by random walks in the cell, the number of steps of these walks during one unit of relative time being proportional to the diffusion coefficients of the moving entities. For clusters, the latter is calculated by taking into account the elementary number of segments and the fractal dimension (Df) of the chain-forming aggregates which can be computed from their spatial configuration. The values of the diffusion coefficients were calculated to be 8.1 x 10 -12 m2/s for the free colloidal particles (60 nm) and 6.94x 10 -13 m2/s for a polymer chain of total length of 1000 nm with a fractal dimension equal to 1.05. The diffusion coefficient of a cluster composed of 10 polymer chains (Df = 1.05) of total length of 1000nm was 7.56× 10-I4m2/s. The factors influencing the determination of these values will be presented in a future paper, which will be exclusively dedicated to the computer simulations and mathematical modelling of bridging flocculation processes. After each particle, chain and cluster has been randomly moved, the relative time is increased by one unit. The link between the relative and physical times is made by correlating the mean deplacement of a reference particle or cluster in the cell and their diffusion coefficients. Results and discussion

Visualization of natural samples by TEM Several stains were effective in enhancing the resolution of the natural organic matter. This result is not unexpected: although lacustrine organic matter is highly heterogeneous [2], each specific class of organic matter (e.g. humic substances, polysaccharides, proteinaceous matter) has a variety of functional groups able to bind several different stains which may include metals or complex substances. Although a given stain may be more or less specific to one kind of functional group, it is unlikely to be specific to a given class of organic matter. Comparison of various stains is therefore not straightforward, even when similar stain concentrations are used. In addition, image enhancement is affected by various physicochemical properties of the stain including its electron density, its capacity to diffuse through the nanoplast (post-staining) and its relative affinity (with respect to the NOM) for the nanoplast resin itself. Clearly, the improvement of the microscopic image is due not only to the physicochemical properties of the stain vis-a-vis the NOM but to a combination of all the above factors. Despite these limitations, TEM images were greatly enhanced by low concentrations of lead and silver based stains (1 gmol/L staining; i mmol/L post-staining), however, in some cases, precipitates were observed along the backbone of the NOM matrix. Although lead carbonate formation is well documented in the presence of atmospheric CO2 [18], the similarity of occurrance of the two precipitates and the fact that Ag precipitates were also observed along the edges of the copper grids, suggests that

57 the metals may have been reduced by the Cu grids or by the organic matter itself. In fact, in some of the poststaining experiments with 10 ~tmol/L- 1 m m o l / L lead or silver, increases in electron density were observed inside a same grid due both to adsorbed and precipitated metal, caused seemingly by an irregular diffusion across the nanoplast. Clearly, further study is needed to elucidate the mechanism of formation for these precipitates. Although Cu addition was less effective than Ag or Pb, it imparted an increased electron density to the images without precipitate formation. Similar results were obtained for the addition of uranyl acetate. Colloidal gold was highly effective for highlighting organic structures, and was thus generally used in accordance with a second stain which could be adsorbed to the NOM rather than simply deposited along the chain lengths. In addition, some general observations could be made: (i) Despite a large proportion of carboxylic functional groups in NOM, micromolar concentrations of ionic lanthanum stains were largely ineffective in staining the NOM. (ii) Generally stains reacted synergistically (i.e. the use of 1 m m o l / L each of three stains was more efficient than 3 m m o l / L of any of the three stains employed individually). (iii) Although ruthenium red was highly useful in the absence of nanoplast, the contrast was highly reduced in its presence. (iv) For equivalent total stain concentrations, Cu based alcian blue was not as effective as the CuSO 4 salt. Several morphologically different types of NOM were observed (Figs. 1 - 4 ) . In Fig. 1 particles containing a high Si (and Ag) concentration are visible after staining with silver nitrate. The organic matter matrix partly resembles the results of Leppard et al. [9], in which they used TEM to study the aggregation properties of aquatic pedogenic fulvic acids. A similar overall morphology is observed in Fig. 2, where colloidal gold is employed to stain the organic matter. EDS analysis once again indicated Si as a major component of the central particle. In Fig. 2 only the outline of the organic matter is seen clearly, although the existence of the particle-NOM interaction is apparent. Note that the organic matter behind the colloidal gold is too close to the contrast limits of the apparatus to be ascribed to NOM without confirmation by the gold stain. In Fig. 3 two large Si-containing particles appear to be joined by an extremely long fibrous material. Although the EDS determined particle composition is similar in Figs. 1 - 3 , the organic matter morphology is clearly different. Note that the predominance of silicate particles is likely due to the sampling regime (oxidic waters from the epilimnion selected to maximize organic matter concentration and diversity) and in no way reflects the general particle composition in this lake. In Fig. 4 particles are observed to be incorporated directly into the organic fibrils. Based on the above images and a number of others, two important observations can be made: (i) the staining procedures allowed observation of NOM structures which could not be seen prior to staining; (ii) although many types of aggregate structures are observed, those

Fig. 1. TEM image of centrifuged natural water sample following 30 s of silver nitrate staining (1 ttmol/L). The visible particles contain Si as a major element (EDS)

Fig. 2. TEM image of centrifuged natural water sample following colloidal gold pre-staining (50 nmol/L) followed by 1 min silver nitrate post-staining (1 mmol/L). The particle in the centercontains Si as a major element (EDS)

58

Fig. 3. TEM image of centrifuged natural water sample following 1 min of lead acetate post-staining (1 mmol/L). The visible particles contain Si as a major element (EDS)

Fig. 4. TEM image of centrifuged natural water sample folIowing 30 s of lead acetate post-staining followed by 30 s of uranyl acetate poststaining. Given the size of the particles (below the detection limit of the EDS), the nature of the particles is unknown

formed with fibrous or filamentous material are frequent. Interactions between small spherical colloids and large linear polymers have thus been studied below by computer simulation.

Computer simulation of bridging floceulation Figures 5 and 6 show examples of aggregates obtained by mathematical simulation using stiff and collapsed polymers. Both of these aggregate types can be observed in nature. Typical evolution curves of colloid, polymer and aggregate number are shown in Fig. 7 for a three-dimensional simulation comprising 100 rigid polymer chains (Df = 1.05) and 100 colloidal particles. Three distinct successive modes of cluster growth are displayed. In the first mode (Fig. 7, region a), aggregates (subsequently referred to as type II) are formed rapidly. They consist of a simple chain associated with one or more colloidal particles. Free particles disappear quickly due to their high diffusion coefficients, concurrent with a simultaneous rapid decrease in the number of naked chains. The number of type II aggregates attains a maximum when all the particles are bound to the chain while the number of naked chains decreased slowly with time. Due to the assumption that the sticking probability is zero for colloidal particle contacts, no aggregates of type I, i.e. composed solely of particles, are formed. It is worthwhile

Fig. 5. Three-dimensional aggregate consisting of 45 colloidal particles (60 nm, 3.2× 1015 particles/L) and 10 chains, each of a total length of 840 nm. The fractal dimension of each chain is 1.05, leading to the formation of a very loose matrix. The size of the cell is equal to 2413 nm

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Fig. 6. Three-dimensional aggregate consisting of 45 colloidal particles (60 nm, 3.2x 10 a5 particles/L) and 10 chains, each of a total length of 840 nm. The fractal dimension of each chain is equal to 1.8, leading to the formation of a very compact structure

to note that type II aggregates are similar to the structure observed in Fig. 3. In the second mode (Fig. 7, region b) of cluster growth, aggregates of type II collide with each other or with naked chains to form large structures via particle bridges. Aggregates of more than one chain are denoted by type III clusters (similar to that observed in Fig. 4). In the first mode, the rate of cluster formation is controlled by the diffusional motion of the elementary particles and chains. In the second mode, the probability of two clusters approaching one another and sticking together depends on the nature of the contact, regardless of the presence or absence of a bridging particle. Every walk does

0

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i

,

Physical time (min) 5.3 11.7

,

D

i

20.8

32.3

i

D

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0

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2000 3;00 Relative time

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Fig. 7 a - c . Colloid, macromolecule and aggregate n u m b e r evolutions in a system containing 100 chains of total lengths of 1000 n m and 100 particles o f a diameter of 60 nm. The initial particle and macromolecule concentrations are equal to 2.7x 1015 particles/L, a - c See text

not lead to a contact between particles and each contact does not systematically lead to sticking. Hence, the sticking probability between clusters is less than one and aggregation between clusters can be described as a reactionlimited (RLA) aggregation process. Moreover, with time, the decrease in number of type II aggregates is much faster than the corresponding decrease in naked chains. This reflects the larger reactivity of chains covered with particles at this concentration ratio. In the third mode (region c) of cluster growth, i.e. for longer time scales, the number of type III aggregates declines. Type III clusters associate to form larger aggregates and adsorb the few remaining naked chains. Finally, type III clusters combine to form one single large aggregate which is observed at the end of the simulation (note that this situation arises owing to the assumption made that the system is finite; no particles or chains are added to the cell during a simulation run). These results suggest that the formation of large aggregates is a slow process, controlled by the reactivity of the clusters, despite the fact that microcolloids react very quickly with the macrochains. In addition, there was a strong dependence of aggregation kinetics on the particle/chain concentration ratio and on the configurational properties of the chains. The simulation of the effect of the relative concentration ratio on aggregation processes demonstrated that at colloid/chain concentration ratio lower than that of Fig. 7, the aggregate number curves are quite different; the number of naked chains does not decrease to zero but rapidly reaches a plateau value, type II clusters disappear slowly and the number of type III aggregates reaches a quasi plateau value. Such a behaviour is due to the lack of colloidal particles required for linking polymer segments. After a long period of time, the system seems to be frozen; there are no remaining free particles but many naked chains and type II aggregates and a few type III aggregates. At a high colloid/chain concentration ratio, the polymer chains are quickly saturated with particles as shown in Fig. 8. The system becomes frozen with aggregates and free particles in the absence of naked chains (note that this situation arises due to the assumption that the contact between two colloidal particles does not lead to sticking). The rate of saturation is dependent on the initial particle concentration. A very high initial particle concentration leads only to the formation of single coated chains, whereas at lower particle concentrations, chain saturation is slow enough to allow some type III aggregates to be formed. Simulations using more collapsed chains, with a fractal dimension close to 1.8, reveal the formation of more compact clusters as shown in Fig. 6. The salient point of the study of evolution curves for the simulation using collapsed chains is that the optimal conditions for bridging flocculation are reached for a lower particle/polymer concentration ratio. Hence, with more collapsed chains, the aggregates formed at a high initial concentration ratio are less reactive for cluster/cluster formations than those formed at lower concentration ratios. This observed decrease in reactivity at a high initial concentration ratio can be explained by the fact that the number of particle

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Fig. 8. Three-dimensional simulation consisting of 200 particles and 10 rigid chains performed in a cubic cell of the size of 2413 nm. The chains are saturated with free particles. In this case, formation of type III aggregates is much slower than that of type II aggregates, so that the polymer chains are saturated before type III aggregates can be formed

adsorption sites on collapsed chains is lower, due to the entrapment of a non-negligible fraction of segments into the polymer coil, effectively rendering the corresponding sites inaccessible for the particles. It should be noted that the negative effect of the structural configuration of the chains on the reactivity of the clusters is nonetheless attenuated because the diffusion coefficients are higher for a more compact structure.

water treatment flocculation step. As well, there is particular relevance for analytical/environmental chemists: sampling, fractionation and characterization of natural colloids and organic matter is one of the most important challenges posed to analytical chemists, not only because of the complexity of such mixtures, but also because the colloidal systems are not thermodynamically stable systems [3]. Due to continuous exchanges such as soil leaching, water productivity or sedimentation, water bodies are at steady state with respect to colloids. In the instant when the sample is collected, the open water body is transformed into a closed system and many of the internal processes are stopped until the colloidal system attains a new steady state, often by coagulation. Understanding the nature and rate of these changes is imperative to improving sampling and fractionation techniques, with the goal of more closely relating experimental observations to the natural system of interest. In conclusion, the coupling of TEM with staining and mathematical modelling is extremely promising. In the future, instead of only considering contacts between particles and chains, additional sets of interactive forces, such as attractive interactions between particles, will be introduced to account for homocoagulation. The use of polydispersed particle and polymer systems will also be investigated. Future work will also be focused on the development of stains which are more specific to particular types of macromolecules. Glossary Chain: polymer Cluster: aggregate Colloid (or colloidal particle): inorganic particle ___1 pm Macromolecule, polymer: organic component of NOM NOM: natural organic matter Particle: inorganic particle > 1 pm TEM: transmission electron microscopy

Acknowledgements. Financial support from the Fonds National Suisse Conclusions

Staining procedures greatly improve our capacity to observe the submicron fraction of aggregates in natural waters, and as such should much increase our knowledge as to the importance of organic matter in natural aggregation processes and the structure of aggregates. The simulation studies demonstrate that the bridging flocculation model developed here can be used as the starting point for the interpretation of experimental observations both for quantitative description of structures and aggregation kinetics. While both modelling and direct observations can be used independently to increase our knowledge of natural systems, the combination of experimental observations and simulation results can considerably enhance our understanding of the underlying mechanisms of real aggregation processes in natural waters. In addition to increasing our understanding of the behaviour of inorganic colloids and natural organic macromolecules in aquatic and soil systems, applications are foreseen with respect to industrial processes involving flocculation steps in order to obtain a better control of

is gratefully acknowledged (project no. 2000-037598.93/1). Partial postdoctoral funding (KJW) was provided by FCAR (Fonds pour la formation de chercheurs et l'aide 5 la recherche, Qu6bec). We thank D. Flannigan, G. G. Leppard and J. Lott for their assistance with the TEM facilities at McMaster University (Canada) and J. C. N6gre for his assistance in the field work. The calculations reported here were performed on an Indy SiliconGraphics computer.

References 1. Sigg L (1987) In: Stumm W (ed) Aquatic surface chemistry, Chap 12. Wiley, New York 2. Buffle J (1988) Complexation Reactions in Aquatic Systems. Ellis Horwood, Chichester 3. Buffle J, Leppard GG (1994) Environ Sci Technol (in press) 4. Lerman A (1979) Geochemical processes. Wiley, New York 5. Lerman A (1978) Lakes: chemistry, geology, physics. Springer, Berlin 6. Perret D, Newman M, Negre JC, Chen Y, Buffle J (1994) Water Res 28:91 - 106 7. Newman M, Filella M, Perret D, Negre JC, Chen Y, Buffie J (1994) Water Res 28:107-118 8. Filella M, Buffle J (1993) Colloids and surfaces. Physicochemical and Engineering Aspects [A] 73:255-273 9. Leppard GG, Buffle J, Baudat R (1986) Water Res 20:185-196

61 i0. Alldredge AL, Passow U, Logan BE (1993) Deep Sea Research I. 40:1131 11. Stoll S, Pefferkorn E (1993) J Colloid Interface Sci. 160:149-157 12. Meakin P, Jullien R (•988) J Chem Phys 89:246-251 13. Ziff RM (•984) Kinetics of aggregation and gelation. Elsevier, Amsterdam 14. Dickinson E (1984) J Colloid Interface Sci 132:274-282 15. Dickinson E, Euston S (1991) J Chem Soc Faraday Trans 87:2193 -2199

16. Dickinson E, Euston S (1992) Colloids and Surfaces 62:231-241 17. Jullien R, Botet R, Mors PM (•987) Faraday Discus Chem Soc 83:134-136 18. Hayat MA (1986) Basic techniques for transmission electron microscopy. Chap 4, Academic Press, San Diego 19. Kuhn W (•934) Kolloid Z 68:2 20. Takashima J, Takasu M, Hiwatari Y (•989) Phys Rev [A] 40:2706- 2711 21. Family F, Meakin P, Vicsek T (1985) J Chem Phys 83:4144-4150