Environ. Sci. Technol. 2009, 43, 7265–7269
Modeling the Adsorption and Coagulation of Fulvic Acids on Colloids by Brownian Dynamics Simulations MARIANNE SEIJO,† SERGE ULRICH,‡ MONTSERRAT FILELLA,§ J A C Q U E S B U F F L E , † A N D S E R G E S T O L L * ,‡ Analytical and Biophysical Environmental Chemistry (CABE), Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, Sciences II, 30 quai E. Ansermet, CH-1211 Geneva 4, Switzerland, Institute F.A. Forel, Environmental Physical Chemistry, University of Geneva, 10 route de Suisse, Case Postale 416, CH-1290 Versoix, Switzerland, and Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, Sciences II, 30 quai E. Ansermet, CH-1211 Geneva 4, Switzerland
Received January 23, 2009. Revised manuscript received March 31, 2009. Accepted April 6, 2009.
Humic substances (HS) play an important role in the reactivity and transport of colloids in natural environments. In particular, the presence of fulvic acids (FA) in natural waters modifies the interactions between inorganic particles and biopolymers and makes difficult to predict their stability with regard to aggregation processes. In this study, Brownian dynamics (BD) modeling is applied to quantify the interactions between negatively charged FA and (i) a positively charged inorganic particle and (ii) a rigid neutral polysaccharide in aqueous solutions. Hematite and schizophyllan are respectively used as model colloids. Modeling the adsorption of FA at the hematite particle surface and on the polysaccharide is based on van der Waals attractive forces and electrostatic interactions. Possible applications of the model, however, are not restricted to this system and any interaction potential or colloidal particle can be considered. The competition between FA adsorption and FA homocoagulation in solution is studied as function of the solution ionic strength. Results show that, under the conditions used, the amount of adsorbed FA is largely controlled by the solution ionic strength. At low ionic strength the amount of adsorbed FA is limited by the electrostatic repulsion between FA at the colloid surfaces and FA monolayers are formed. By increasing the ionic strength the number of adsorbed FA is found to increase. At a sufficiently large ionic strength, however, FA coagulation in solution may strongly compete with FA adsorption at the hematite and polysaccharide surfaces. FA aggregates then adsorb at the colloid surfaces to form extended and porous structures. Results also suggest that FA adsorption and structure of the adsorbed layers are mainly driven by the complex interplay between electrostatic attractive and repulsive interactions.
* Corresponding author phone: (+41) 22 379 6427; fax: (+41) 22 379 0329; e-mail:
[email protected]. † Analytical and Biophysical Environmental Chemistry (CABE). ‡ Institute F.A. Forel, Environmental Physical Chemistry. § Analytical and Applied Chemistry (CABE). 10.1021/es9002394 CCC: $40.75
Published on Web 06/05/2009
2009 American Chemical Society
Introduction Humic substances (HS) represent an important and active fraction of natural organic matter (NOM) in aquatic environments and play an important role in water quality due to their strong sorbent properties for many pollutants such as trace metals, radionuclides, and organic compounds. For this reason, they have a significant impact on the chemical speciation, bioavailability, and transport of trace metals and trace organic pollutants (1). However, HS also adsorb on mineral surfaces (2, 3) and biopolymers (4) and the resulting adsorption layers and subsequent surface modification have a significant impact on the final reactivity of the suspended colloidal fraction. For instance adsorbed HS facilitate the adsorption of organic contaminants on colloid surfaces (5) and modify the surface charge of colloids, which largely controls their stability and mobility via electrostatic interactions. For example, it has been shown that inorganic colloids in contact with HS exhibit similar negative surface charges (6-9), irrespective of their intrinsic chemical nature. Therefore, HS are important for the fate and circulation of inorganic colloids since stable colloids may be transported over long distances whereas unstable colloids are eliminated through aggregation and sedimentation processes (10). Hence, a better understanding of HS adsorption at the surface of colloids and of the structure of the adsorbed layer is essential for understanding the role and fate of colloids in natural waters. This paper is focused on fulvic acids (FA) which is the major component of HS (11) and also play an important role in the binding and bioavailability of trace pollutants (12). Brownian dynamics (BD) simulations are here used to study the interactions of FA with two important colloidal components of aquatic systems: inorganic particles and large biopolymer chains. A spherical hematite particle serves as a model of natural inorganic particles covered with iron oxyhydroxide, and the schizophyllan, a neutral rigid polysaccharide is used as a model of long chain aquatic biopolymer. The number of adsorbed FA at the hematite surface and on the schizophyllan is investigated as a function of time to get an insight into the effect of the electrostatic repulsive and attractive interactions on the amount of adsorbed FA and structure of the adsorbed layer. Since the ionic strength is expected to profoundly affect FA interactions, a systematic investigation of this factor on FA adsorption and homocoagulation is also considered.
Methodology Model Description and Interaction Forces. FA, hematite particles, and polysaccharides are represented at a coarse grained (mesoscopic) level to simulate much larger time scales than in molecular dynamics simulations. Offlattice 3-dimensional computations are performed with periodic boundary conditions to represent bulk simulations. FA are represented at the coarse grained level as rigid, uniformly charged spheres with a radius of 1 nm. This is in agreement with experimental observations which have shown that FA may be considered as rigid, branched, spherical small polyelectrolytes bearing a large negative charge density (10-20 mol kg-1) at pH 6-9 (13) and that their radius ranges between 0.75 and 1.25 nm (14-16). An arbitrary radius of 10 nm is used for the spherical, impenetrable, and uniformly charged hematite particle. The polysaccharide is represented as a succession of connected monomers (pear-necklace model) with a radius of 1.5 nm and a monomer number equal to 50 to give a contour length of 150 nm. These dimensions correspond to those of the schizophyllan (17, 18) VOL. 43, NO. 19, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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which is a neutral polysaccharide dispersed in water as a rigid triple helix with a mean persistence length of 160 nm and a diameter of 1.5 nm (18). The polysaccharide is represented in our model as a rigid neutral rod. The solvent (water) is treated as a dielectric continuum medium with a relative dielectric permittivity εw of 78.54 at 298 K. The DLVO approach is used to calculate the forces and total interaction energy between colloids (FA, hematite, schizophyllan) and forces which are required in the Brownian dynamics computer-based simulation technique (see next section). Attractive van der Waals interaction energies uvdW between two colloids, n°1 and 2, are calculated in kBT units by making the assumption of pairwise additivity using the classical Hamaker nonretarded sphere-sphere interactions (19): uvdW(h) ) -
(
( ))
A1w2 2R1R2 2R1R2 B + + ln 6kBT B C C
(1)
where B ) h2 + 2R1h + 2R2h and C ) B + 4R1R2. R1 and R2 represent the radius of spherical colloids 1 and 2, kB the Boltzmann constant, T the temperature, h the surface-tosurface separation between the spheres, and A1w2 the effective Hamaker constant between the colloids 1 and 2 separated by water. A1w2 is defined as (20): A1w2 ) √A1w1A2w2
(2)
The effective Hamaker constant for hematite-hematite interactions is calculated with the final form of the nonretarded Hamaker constant obtained by Russel et al. (21): A1w1
(
3kBT ε1(0) - εw(0) ) 4 ε1(0) + εw(0)
)
2
+
2 2 3hpω1UV (n21 - nw ) 2 2 2 32π √2 (n1 + nw)
4πε0εw R1R2ψ1ψ2 exp(-κh) kBT (h + R1 + R2)
2.2936pH3 - 0.070631pH4 + (2.903pH - 3.356) log I (5) where I represents the ionic strength. This equation is valid within the limits 4.0 e pH e 10.7 and 0.005 e I e 0.15 mol · L-1. The values obtained with eq 5 are in good agreement with other data of the literature (28, 29). Values of -47, -53, -67, -87, -93 mV are obtained at pH ) 8 and I ) 1.0 × 10-2, 5.0 × 10-2, 1.0 × 10-2, 1.0 × 10-3, 5 × 10-4 mol L-1, respectively. The validity of the linearized form of the PB equation was verified by comparison with the non linearized form using a finite difference method (UHBD software) to solve the nonlinearized PB equation (30, 31). Based on the experimental hematite potential values found in the literature and their variations as a function of pH (32-34), in particular close to the point of zero charge, the surface potential of hematite at pH ) 8 was fixed to 25 mV and assumed to a first approximation to be independent of the ionic strength. Brownian Dynamics Simulations. Brownian dynamics is a computer based simulation technique. The components of the system are allowed to respond to the instantaneous forces present in a given configuration, and to adopt a new configuration, with possible aggregation. The forces in this new configuration are then calculated again, and another configuration is computed. This sequence of steps simulates the evolution of the true system in time and space. In BD new positions of particles (i.e., the colloids or their aggregates) are calculated at time t + ∆t, based on the positions at time t according to (35, 36): r(t + ∆t) ) r(t) +
(3)
where ε1(0) represents the static dielectric constant(ε1(0) ) 12.0), n1 is the refractive index (n12 ) 9.3025), and ω1UV is the UV absorption frequencies of hematite (ω1UV) 0.346 × 1016 rad.s-1) (22). εw(0) corresponds to the static dielectric constant (εw(0) ) 78.54) and nw is the refractive index (n2w ) 1.755) of water (23), hp is the Planck constant (6.63 × 10-34 J · s). Values of Hamaker constants for FA-FA interactions and interactions between monomers of the biopolymer are taken from the literature. Values (and the corresponding references) of A1w1 and A1w2 are given in Table 1. The long-range electrostatic double layer interaction energies are calculated using the linearized PoissonBoltzmann (PB) equation (26): uDH(h) )
ψsurface ) -205.4 + 119.63pH - 25.999pH2 +
D DLVO (t)∆t + ∆rG F kBT
where D is the diffusion coefficient of the particle considered and ∆r G the random term that takes into account the effect of water collisions on the motion of the particle (Brownian motion). Each component of ∆r G is chosen from a Gaussian distribution with 0 mean and a variance equal to 〈(∆r G)2〉 ) 2D∆t. F DLVO(t) corresponds to the interparticle DLVO force vector. The force between two particles, separated by a distance h, due to the electrostatic (uDH) and the van der Waals (uvdW) interaction energies, is given by F DLVO(h) ) -
d (u (h) + uvdW(h)) dh DH
(7)
uDH and uvdW are given in eqs 4 and 1. The diffusion coefficient of spherical particles (FA and hematite) are given by the Stokes-Einstein equation:
(4) Dsphere ) -12
where ε0 represents the vacuum permittivity (8.85 × 10 C · V-1 · m-1), εw is the relative dielectric constant of water at 298 K (78.54), ψ1 and ψ2 are the surface potentials (mV) of the spherical colloids 1 and 2, respectively, and κ is the Debye-Hu ¨ ckel parameter in m-1 units. The schizophyllan is uncharged (ψ ) 0). The surface potential of FA has been calculated with the following equation (13, 27):
(6)
kBT 6πηR
(8)
where η represents the viscosity of the medium and R the radius of the particle. The diffusion coefficient of the mass center of the rod like polymer is expressed as (37) DRL )
kBT(ln(L/b) - γ) 3πηL
(9)
TABLE 1. Values of the Hamaker constants used in the calculations of interactions between Fulvic acids, Hematite particles and Schizophyllan.
fulvic acid hematite particle rigid polymer (schizophyllan)
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fulvic acid
hematite particle
5.0 × 10-21, refs (26,27) 1.58 × 10-20 eq 2 6.32 × 10-21 eq 2
1.58 × 10-20 eq 2 5.0 × 10-20 eq 3 and ref (23)
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rigid polymer (schizophyllan) 6.32 × 10-21, eq 2 8.0 × 10-21 refs (24,25)
FIGURE 1. Stability ratio W of FA as a function of the ionic strength assuming a total volume fraction O equal to 0.002. The decrease of W is due to the salt screening of the electrostatic forces between the FA. A value W ) 1 is achieved above the critical coagulation concentration (CCC) corresponding to I ) 0.3 mol · L-1. Above this value, FA aggregates are formed at a maximum rate controlled by diffusion. r ) 1/W is the collision efficiency parameter. where L represents the rod length, b the rod diameter and γ a constant which is the result of end effects due to the rod geometry. The value of γ was experimentally determined in ref 38 and found to be equal to 0.3. In the following, the adsorption of FA on hematite and schizophyllan, and the possible coagulation of FA are studied as function of the ionic strength. The pH (8) and temperature (T ) 25 °C) were maintained constant, as well as the concentration of FA, expressed in volume ratio φ ) 0.002. φ is the ratio of the total volume of FA over the volume of solution. By using a density of 1 kg/L for the FA, φ ) 0.002 corresponds to a concentration of fulvics of 2 g/L. This is very large compared to their typical concentrations in natural waters (2-20 mg/L). However, using values of φ < 0.002 for simulations results in exceedingly long computer times. Extrapolation of the present values to lower FA concentrations is discussed in the Discussion section.
FIGURE 2. Variation of the number of FA adsorbed at the surface of the hematite particle in the first adsorption layer as a function of the ionic strength I : O, 5 × 10-4 mol · .L-1; 9, 1 × 10-3 mol · L-1; 3, 1 × 10-2 mol · L-1; b, 5 × 10-2 mol · L-1; 4, 1 × 10-1 mol · L-1; 2, only with vdW interactions. O ) 0.002, pH 8, T ) 25 °C. A rapid saturation of the hematite surface is observed in all cases. The amount of FA adsorption at the hematite surface is controlled by the ionic strength in solution. Note that it reaches a maximum value at intermediate ionic strength value (1 × 10-2 mol · L-1). The right axis gives NFA, the number of FA/nm2.
Results Homocoagulation of Fulvic Acids. Figure 1 shows the predicted evolution of the stability ratio W as a function of the ionic strength I. In the presence of an energy barrier, only a certain fraction of collisions between fulvics leads effectively to coagulation. This fraction is known as the collision efficiency R and its reciprocal value is known as the stability ratio W ) 1/R. Figure 1 shows that log(W) decreases linearly when log(I) increases. When I g 0.3 mol · L-1, log(W) becomes constant and equal to 1. This value of I corresponds to the critical coagulation concentration (CCC ) 0.3 mol · L-1). For I g CCC, the potential energy barrier disappears and FA aggregation can occur at a maximum rate, determined by the transport rate and the collision frequency between FA. For I < CCC, FA homocoagulation is expected to be controlled by the collision efficiency factor R. Under such conditions FA aggregates are formed via slow and reaction limited aggregation. Adsorption of Fulvic Acids on Hematite. Brownian Dynamics simulations were performed by considering one hematite particle surrounded by 103 explicit FA. To get an insight into the structure of the FA adsorption layer, successive layers, with a thickness equal to 2 nm, around the particle were defined. Simulations were stopped when the first layer reached saturation, i.e., when the number of adsorbed FA was found to be independent of time. Figure 2 shows the variation of the number of FA adsorbed in the first layer (in direct contact with the hematite surface) as a function of time, for different ionic strengths. A rapid increase
FIGURE 3. FA-hematite structures obtained at different ionic strengths: (a) 5 × 10-4 mol · L-1, (b) 1 × 10-3 mol · L-1, (c) 1 × 10-2 mol · L-1, (d) 5 × 10-2 mol · L-1, (e) 1 × 10-1 mol · L-1. O ) 0.002, pH 8, T ) 25 °C. The hematite particle is the central particle and fulvic acids are the small ones. At low ionic strength (5 × 10-4 mol · L-1), only a monolayer of FA is observed at the hematite surface. By increasing the ionic strength, not only the number of adsorbed FA, but also the thickness of adsorbed FA increases. in the number of adsorbed FA in the first layer followed by a plateau (saturation) is observed. Saturation is controlled by the electrostatic repulsive interactions between FA at the hematite surface. The total number of FA adsorbed in the first layer increases with the ionic strength from I ) 5 × 10-4 to 1 × 10-2 mol · L-1. This increase is due to salt screening effect which results in a decrease of the electrostatic repulsion between FA at the hematite surface. FA adsorption is thus promoted, even though, simultaneously, the strong attractive electrostatic interactions between the positively charged hematite and the negatively charged FA are also reduced. When the ionic strength increases further (up to 5 × 10-2 and 1 × 10-1 mol · L-1) the number of adsorbed FA in the first layer is found to decrease. To help understanding such a behavior one should refer to Figure 3 which shows the FA-hematite structures obtained at different ionic strengths. It is clearly observed that the complex structures obtained at high ionic strengths (5 × 10-2 and 1 × 10-1 mol · L-1) are VOL. 43, NO. 19, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Variation of the number of FA adsorbed at the surface of the biopolymer as a function of time for different ionic strengths I : O, 5 × 10-4 mol · L-1; 9, 1 × 10-3 mol · L-1; 4, 1 × 10-2 mol · L-1; b, 5 × 10-2 mol · L-1; 4, 1 × 10-1 mol · L-1; 2, only with vdW interactions. O ) 0.002, pH 8, T ) 25 °C. A rapid saturation of the schizophyllan surface is observed in all cases. The amount of adsorption at the biopolymer is controlled by the ionic strength in the solution. It should be noted that it reaches a maximum value at I ) 5 × 10-2 mol · L-1. The right axis gives NFA, the number of FA/nm2. significantly different from those obtained at lower ionic strengths. Two mechanisms are here involved. At high ionic strength the FA adsorbed on the hematite surface forms a very porous and heterogeneous layer. Such a structure is mainly attributed to the direct adsorption of FA and to the simultaneous formation of FA aggregates in solution which are adsorbed at the hematite surface in a second step. Direct coagulation of FA on the hematite surface may also occur. The adsorption of large FA aggregates significantly hinders further adsorption of isolated FA at the hematite surface. The number of adsorbed FA in the first layer has also been calculated under conditions where only van der Waals interactions were operative (no electrostatic interactions). In all cases, this number was found to be smaller than that obtained in presence of electrostatic interactions, thus showing that the net effect of electrostatic forces (FA-hematite attractions and FA-FA repulsions) significantly promote the adsorption of FA. Adsorption of Fulvic Acids on Schizophyllan. It is important to keep in mind that no electrostatic interaction is involved between the neutral schizophyllan and the FA. From an electrostatic point of view only FA-FA interactions play a role. Simulations were performed with a schizophyllan chain (rigid rod) in presence of 103 explicit FA, with a volume concentration ratio, φ, equal to 0.002. Figure 4 shows the increase of the number of FA adsorbed in the first layer as a function of time and for different ionic strengths. The number of FA adsorbed in the first layer increases with the ionic strength until I ∼5 × 10-2 mol · L-1, where the number of adsorbed FA reaches a maximum value. Then, any further increase of I causes the amount of FA adsorbed in the first layer to decrease, due to both the formation of FA aggregates in solution and the adsorption of those aggregates on the schizophyllan. It is worth noting that the ionic strengths corresponding to the maximum amount of FA adsorption in the first layer is different from that absorbed on hematite: I is equal to ∼1 × 10-2 mol · L-1 for the hematite and ∼5 × 10-2 mol · L-1 for the polymer. This difference is attributed to the fact that the hematite is positively charged and, therefore, that the electro-attractive interactions between the FA and the hematite counterbalance the electro-repulsive interactions between FA. This effect does not exist on the polysaccharide chain. 7268
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FIGURE 5. Aggregates obtained at different ionic strengths (a) 5 × 10-4 mol · L-1, (b) 1 × 10-3 mol · L-1, (c) 1 × 10-2 mol · L-1, (d) 5 × 10-2 mol · L-1, (e) 1 × 10-1 mol · L-1. The biopolymer appears in green, fulvic acids in yellow. For each case two views are given (longitudinal and perpendicular to the biopolymer axis). At a low ionic strength (5 × 10-4 mol · L-1), only a monolayer of FA on the hematite is observed. By increasing the ionic strength, the layer thickness of adsorbed FA increases due to the adsorption of FA aggregates formed in the solution.
Discussion Computer modeling using BD is an important tool for the analysis and quantification of interaction processes between colloids, including adsorption, homocoagulation, and heterocoagulation of colloid mixtures. The novelty of this approach is 3-fold. Very few studies have been undertaken to date to understand the combined and systematic role of key parameters such as the colloid architecture, colloid physicochemical properties, solution properties, combined role of coagulation, and adsorption, on the behavior of colloid mixtures which are representative of environmental conditions. To the best of our knowledge, the BD numerical scheme has not been developed and systematically applied to linear biopolymers and mixtures of small and large size colloids. This being an unexplored area, and may lead to entirely new findings for the understanding of colloidal compounds in natural systems. Finally, as shown in this study, the BD simulations/DLVO theory are applicable to FA adsorption and coagulation processes. The results reported here should be considered as a first step for a few reasons. In particular, the exact values of Hamaker constants for FA and biopolymers are difficult to extract. We believe, however, that they do not have a major impact on the final results, because the results show that adsorption is largely controlled by electrostatic interactions between FA. The effect of FA concentration [FA] should also been studied in more details, in particular in the range of natural concentrations. It can be expected that the time required to reach saturation of hematite or schizophyllan will be inversely proportional to [FA], i.e., these times will be of the order of a fraction of second for [FA] of about 2 mg/L. On the other hand, we have observed (data not shown) that coagulation rates of FA are higher than first order with respect to [FA]; coagulation rates of FA will then decrease faster than its adsorption on hematite and schizophyllan when [FA] decreases. Thus, it can be expected that by increasing dilution, monolayer formation of adsorbed FA will be favored compared to FA coagulation. Moreover, the fraction of a second, needed to reach saturation of the monolayer, is a much shorter time that those typically encountered in coagulation or flocculation of typical inorganic colloids and biopolymers. Thus the present results strongly suggest that, when studying such coagulation processes in presence of FA, the interaction of FA with colloids and biopolymers can be considered as instantaneous compared to the coagulation process. In other words, the interacting colloids can be considered as covered with FA from the beginning of the coagulation process. Another interesting result of this study is the fact that the adsorption of large quantities of FA at the surface of inorganic colloids or large biopolymers does not necessary lead to the formation of an homogeneous compact adsorbed layer. On
the contrary, the present results suggest that this layer can be very porous and extended in solution. This may have a significant impact on the binding of metals or organic pollutants by inorganic particles covered by fulvics or humics in soil and water. Obviously, BD modeling is a tool which ideally should be combined with experimental methods (electrophoretic measurements, light scattering, fluorescence correlation spectroscopy, etc) to enable intervalidation of adsorption and coagulation kinetics and aggregate structures. It should be emphasized that the BD method exemplified here with interactions of FA, hematite, and schizophyllan is not restricted to this case and can probe the behavior of different colloidal materials (including nanomaterials and the possible interactions between nanoparticles and environmental compounds) by adjusting their sizes, relative concentration ratio, and physicochemical properties.
Acknowledgments We gratefully acknowledge the financial support received from the Swiss National Science Foundation (Research Project 200020-101974).
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