ARTICLE pubs.acs.org/Langmuir
Dynamics and Heterogeneity of Pb(II) Binding by SiO2 Nanoparticles in an Aqueous Dispersion Danielle Goveia,†,‡ Jose Paulo Pinheiro,*,§,|| Viktoria Milkova,§ Andre Henrique Rosa,† and Herman P. van Leeuwen§ †
Departamento de Engenharia Ambiental—UNESP, Sorocaba-SP, ‡Instituto de Química de Araraquara—UNESP, Araraquara-SP, and Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Wageningen, The Netherlands
§
bS Supporting Information ABSTRACT: Pb(II) binding by SiO2 nanoparticles in an aqueous dispersion was investigated under conditions where the concentrations of Pb2þ ions and nanoparticles are of similar magnitude. Conditional stability constants (log K) obtained at different values of pH and ionic strength varied from 4.4 at pH 5.5 and I = 0.1 M to 6.4 at pH 6.5 and I = 0.0015 M. In the range of metal to nanoparticle ratios from 1.6 to 0.3, log K strongly increases, which is shown to be due to heterogeneity in Pb(II) binding. For an ionic strength of 0.1 M the Pb2þ/SiO2 nanoparticle system is labile, whereas for lower ionic strengths there is loss of lability with increasing pH and decreasing ionic strength. Theoretical calculations on the basis of Eigen-type complex formation kinetics seem to support the loss of lability. This is related to the nanoparticulate nature of the system, where complexation rate constants become increasingly diffusion controlled. The ion binding heterogeneity and chemodynamics of oxidic nanoparticles clearly need further detailed research.
’ INTRODUCTION Nanoparticles are currently emerging as intriguing research objects in all fields of chemistry. Their special properties, which make them so valuable in many applications, are a cause of concern in ecosystem analysis. As a considerable portion of nanoparticles will eventually be disposed in the environment, their chemical interactions and cycling/fate are evolving into an important subject of discussion and research.1 One key point of such discussion is how the nanoparticles will interact with the other components of the natural waters, in particular metal ions, dissolved organic matter, and microorganisms. Here, our focus will be on the interaction of nanoparticles with metal ions in environmental systems. To understand the behavior of trace metals in the environment, it is fundamental to understand their speciation, i.e., the relationships between the different physicochemical forms of the metals and their ensuing reactivity, mobility, and bioavailability. Due to the inherent complexity and the dynamic nature of environmental systems, they practically never reach chemical equilibrium. Thus, a quantitative understanding of trace metal speciation generally requires characterization of dynamic aspects, i.e., kinetic features of the interconversion of metal complex species.2 Among the most relevant processes in natural systems are the reactions of metal species at an interface, as occurring, e.g., in the bioaccumulation of metal ions. Such processes require transport of metal species from the medium to the consuming interface, often followed by conversion to some surface-active r 2011 American Chemical Society
chemical form. Bioavailability of metal species therefore is of a dynamic nature and generally requires consideration of the overall flux of different species toward the surface of the organism. Chemodynamic principles for metal ions in colloidal ligand dispersions have recently been described for hard spheres3 and soft coreshell particles,4 taking into account the impact of some electrostatic factors.5 Among the analytical techniques for trace metal speciation analysis, several are based on dynamic processes, thus allowing the determination of dynamic parameters. A relatively new electroanalytical technique is stripping chronopotentiometry at scanned deposition potential, SSCP.6 The characteristic parameters of the SSCP wave (the limiting wave height, actually representing a metal flux, and the half-wave deposition potential) provide information on the association/dissociation rate parameters of metal complex systems.7 Considering its sensitivity and the availability of a solid theoretical background, SSCP seems to be particularly suited for measuring metal speciation dynamics in nanoparticulate complex dispersions. Due to their abundance in nature and their physical characteristics, silica-based materials are among the most interesting nanoparticulate systems. The Ludox silica nanoparticle family has been studied since the 1950s and is known for stability and Received: March 3, 2011 Revised: May 6, 2011 Published: May 25, 2011 7877
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monodispersity. As a matter of fact, these particles are used in many laboratories to calibrate dynamic light scattering instruments, given that the Ludox particles are commercially available spherical nanoparticles with radii varying from ca. 5 to 50 nm. Already in the 1950s, Bolt8 performed the first protolytic titrations, which have been detailed by other authors.915 Electrophoretic mobilities and ζ potentials have been investigated and profusely discussed,13,1618 while other studies describe the extraordinary stability of these nanoparticles.12,19,20 Additionally, several metal interaction studies with macroscopic silica surfaces have been described.21,22 There are a plethora of studies on trace metal interaction with particles, but these were performed with bulk materials (>450 nm), especially for naturally occurring oxides23,24 or oxides with adsorbed organic layers.25 In these experiments, the particles used have radii ranging from a few hundred nanometers to a few micrometers and the metal concentrations cover a range from trace level to surface site saturation level. The nanoparticles have radii below those of colloidal particles; thus, their number concentrations are generally much higher. The situation where nanoparticle and target metal ion concentrations are of the same order of magnitude is a common one. Thus, we can easily investigate the binding of one or just a few metal ions per individual nanoparticle. In this work we shall study the dynamics of trace metal ion binding in nanoparticulate silica dispersions with special attention to the regime where the metal to nanoparticle ratio is of order unity.
’ THEORY Fundamental Features of Dynamic Trace Metal Speciation. Let us consider the scheme of a metal ion Mnþ (M for
short) which can (i) associate with a ligand L to form an electroinactive complex ML and (ii) be reduced to the metal atom, M0, at an electrode surface:
where ka and kd are the rate constants of ML formation and dissociation, respectively. Generally, the rate constant for complex formation (ka) is consistent with a mechanism in which formation of an outersphere ion pair complex between a metal ion and a ligand is followed by a rate-limiting removal of water from the inner coordination sphere with a metal rate constant kw. The scheme is commonly known as the Eigen mechanism.26 The values of kw are intrinsic for each type of metal ion, and the most relevant values were compiled by Margerum et al.27 The electrostatically determined outer-sphere stability constant Kos is K os ¼
4πNAv a3 expð U os Þ 3
ð2Þ
where a is the charge center-to-center distance of closest approach between M (with its intact inner coordination shell) and L and Uos is the electrostatic energy normalized by KT, determined by the primary Coulombic energy and screening by the electrolyte.
Understanding the dynamics of metal species under conditions of an interfacial process requires consideration of the overall flux (J) toward the electrode. Generally, J is defined through the coupled diffusion and the rates of association/ dissociation reactions between various metal species in the medium. The system is dynamic or static if the rates for these volume reactions are fast or slow, respectively, on the effective time scale of interest, t: kd t, ka 0 t . 1 kd t, ka 0 t , 1
ðdynamicÞ
ð3aÞ
ðstaticÞ
ð3bÞ
ka0 is defined for conditions of sufficient excess of ligand over metal: ka 0 ¼ ka cL, T
and
K 0 ¼ ka 0 =kd ¼ KcL, T
ð4Þ
where K is the stability constant of ML and cL,T is the effective ligand concentration. In the rather usual case where only the free metal ion is undergoing an interfacial electron transfer reaction, the contribution of complexes to the overall metal flux depends on the relative magnitudes of their diffusive and dissociation kinetic fluxes, * and Jkin * , respectively. Well-known limits for dynamic systems Jdif are labile (diffusion control) and nonlabile (kinetic control). The lability criterion parameter, L, is defined as the ratio * /Jdif * :28 Jkin ( labile Jkin .1 L¼ ð5Þ ,1 nonlabile Jdif Dynamic Speciation in Colloidal Dispersions. Nanoparticulate ligands are intrinsically different from small ligands due to some or all of the following features: (i) the binding sites are nonhomogeneously distributed over the dispersion volume, i.e., confined to particle bodies, (ii) the charge distribution within the particle bodies may be nonhomogeneous, (iii) if the nanoparticles are not constant in size and/or shape, there are variations in their mobility, (iv) often the reactive sites display chemical heterogeneity, which may be both intraparticulate and extraparticulate in nature. In the situation where a solution of metal ions and a dispersion of particulate ligands are mixed, the metal ions react with the binding sites and a metal ion concentration gradient develops at the particle/medium interface. The overall complexation process is composed of two successive steps: (i) the diffusion of M toward the particle and (ii) the complexation formation reaction of M with the ligand site. For the general case of a coreshell particle, including the limiting cases of hard and soft spheres, Duval et al.4 obtained an apparent association rate constant, keff a by solving the set of differential equations in space and time with the appropriate initial and boundary conditions for the dispersion: !1 ka expðzM eψ=kTÞNS eff ka ¼ ka expðzM eψ=kTÞ 1 þ 4πrp DM NAv
ð6Þ where NS is the number of reactive sites per particle and ψh is the average potential at the nanoparticle surface. The equivalent smeared-out site concentration over the entire dispersion volume 7878
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number (cS) is related to NS and the number concentration of colloids (cp) by cS ¼
NS cp NAv
ð7Þ
Equation 6 shows that when diffusion is very fast with respect to the chemical reaction, i.e., kaNS/4πrpDMNAv f 0, keff a reduces to ka exp(zMeψh/kT) (and keff d f kd). In the opposite case, when diffusion is the slow step, the quotient is much larger than unity; thus, keff a = (4πrpDMNAv)/NS, which is much smaller than ka (and kdeff , kd). As long as the electric potential remains constant, the stability constant K is not affected by the diffusion step; hence, eff the ratio keff d /kd is the same as ka /ka. These expressions are valid for sufficiently dilute colloidal dispersions with the particles so far apart that their electric double layers do not interact.29 For further details see a recent review30 on the progress in understanding the formation/dissociation kinetics of aquatic metal complexes with complexants in different size ranges and the paper by Duval5 on the detailed role of electrostatics. Evaluation of Chemical Heterogeneity. The presence of chemical heterogeneity gives rise to a spread out along the Ed axis as compared to a homogeneous system (Supporting Information). The extent is independent of the deposition time, td, and electrode size.6 Each point in the SSCP curve is an independent experiment for a given deposition potential. In the limiting flux region the free metal at the surface is zero (at potentials ,E°), whereas in the intermediate region the free metal concentration at the surface of the electrode is controlled by the applied potential, following a Nernstian relation for a reversible electron transfer reaction. Since the ligand concentration is in excess over the metal, thus effectively constant, the metal to ligand ratio at the surface is highest at the foot of the wave and lowest at the top of the wave. For a chemically homogeneous system a Nernstian slope will be recovered, whereas in a chemically heterogeneous system the weakest sites are the first to release the bound metal; thus, the strength of the metal binding will increase from the foot to the top of the wave, producing a drawn-out curve. This effect was well studied for the case of metal binding by humic matter; a first-order approximation, based on a Freundlich isotherm, was proposed to quantify the degree of chemical heterogeneity.31,32 For heterogeneous complexes in nonlabile situations, the lability decreases from the foot to the plateau of the SSCP wave as the contribution of progressively more stable complexes to the deposition current becomes increasingly significant. This effect is more pronounced for larger degrees of heterogeneity; i.e., as the degree of heterogeneity increases, the onset of loss of lability occurs closer to the foot of the wave.33 Thus, in contrast to the homogeneous case, kinetic currents will impact the shape of the SSCP wave for heterogeneous metal complexes, enhancing the flattening effect of the heterogeneity.
’ EXPERIMENTAL SECTION Reagents. All solutions were prepared in ultrapure water from a Barnstead EasyPure UV system (resistivity >18 MΩ 3 cm). Cd(II) solutions were prepared from solid Cd(NO3)2 (Merck, p.a.) and those with Pb(II) from dilution of a certified standard (0.100 M Pb(NO3)2, Metrohm). NaNO3 was from solid NaNO3 (Merck, Suprapur). Stock solutions of MES (2-(N-morpholino)ethanesulfonic acid) and MOPS (3-(N-morpholino)propanesulfonic acid) buffers were prepared from the solids (Fluka, Microselect, >99.5%). Solutions prepared from HNO3
(Merck, Suprapur) and NaOH (0.1 M standard, Merck) were used to adjust the pH. Ludox LS30 was obtained from Sigma-Aldrich (4208081L) as a 30% (w/w) dispersion with a surface area of 215 m2/g, a density of 1210 kg 3 m3, and a pH of 8.2 (manufacturer information). The density of the dry material was 2200 kg 3 m3. The ionic strength of nanoparticle suspensions used for potentiometric titration was varied by adding NaCl (Merck, p.a.). Using dynamic light scattering (DLS), we measured a Stokes diffusion coefficient of (2.7 ( 0.3) 1011 m2 s1 for the SiO2 nanoparticles (Ludox LS30), consistent with the reported radius of 7.5 nm. DLS measurements showed no particle aggregation or intensity variation in the dispersion aliquots taken before and immediately after the voltammetric experiments. There was a slight increase of the radius when LS30 was placed at the lower pH and higher ionic strength of the experiments, although no change was observed in the measurements before and after the SSCP experiment. Apparatus. An EcoChemie Autolab PGSTAT10 potentiostat (controlled by GPES 4.9 software from EcoChemie, The Netherlands) was used in conjunction with a Methrohm 663 VA stand (Metrohm, Switzerland). The working electrode was a thin mercury film electrode plated onto a rotating glassy carbon (GC) disk (1.9 mm diameter, Metrohm), a GC rod counter electrode, and a double-junction Hg| Hg2Cl2|KCl (3 M) encased in a 0.1 M NaNO3 solution. The titration was performed in a glass-jacketed Duran vessel that was kept at constant temperature (25 °C) using a circulating water bath. The vessel was continuously purged with nitrogen gas. The titration vessel was sealed with a polypropylene screw cap which was equipped with sockets that provided access to the electrodes, burets, and gas lines. The addition of a volume of titrant (acid or base) and electrode measurements were computer controlled.34 To obtain the dependence of the surface charged density on the pH of the colloid particles, a suspension containing the colloid of known electrolyte concentration and volume was titrated. The concentration of nanoparticles was 3 wt % (∼6 1018 particles/dm3) to ensure a high enough total surface area in solution. The charge density of the colloid at a given pH value was obtained as the difference between the amount of Hþ or OH ions added to the suspension and the amount added to a blank solution with volume and electrolyte concentration equivalent to those of the colloid suspension. The amount of titrant used to produce a given pH value in the suspension was then diminished with the amount necessary to produce this given pH value in the blank solution. The difference then constituted the proton consummation at a given pH and corresponding to the surface charge density of the colloid particles. The electrophoretic mobility (and respective ζ potential) of the nanoparticles at different pH values and ionic strengths of the solution was measured using a Malvern Zetasizer 2000. Dynamic light scattering measurements were performed using an ALV apparatus with an Ar ion laser (514.5 nm). All data were taken at 90°, and the intensity fluctuations were analyzed automatically and in a single run by means of an ALV-7000 digital correlator. Preparation of the Thin Mercury Film Electrode. Prior to coating, the GC electrode was conditioned following a reported polishing/cleaning procedure.35 These polishing and electrochemical pretreatments were repeated daily. The thin mercury film was then prepared ex situ with 0.12 mM mercury(II) nitrate in thiocyanate media (5 mM, pH 3.4) by electrodeposition at 1.3 V for 240 s and a rotation rate of 1000 rpm. Full details of the electrode preparation were previously published.36 Potentiometric Titrations. To convert the values of K0 into the stability constant K, we need the total concentration of deprotonated silanol groups for each condition (pH and ionic strength); thus, potentiometric titrations were carried out to obtain these parameters. The dependence of ng as a function of pH in the presence of 0.010 and 0.100 M NaCl is presented in Figure 1. The inset indicates the surface 7879
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Figure 1. Number of deprotonated groups (ng) per nanoparticle as a function of the pH at different salt concentrations: 0.010 M NaCl (2) and 0.100 M NaCl (4). charge density of Ludox LS30 nanoparticles at different conditions determined by potentiometric titration. The results show that the negatively charged density of the particles increases with increasing pH and the amount of salt in the suspension. Since our results agree with those published by Bolt8 within experimental error, we decided to use for the lower ionic strength (0.015 M) the values reported therein. Chronopotentiometric Procedures. Stripping chronopotentiometric measurements were carried out in 23 mL NaNO3 solutions (0.0015, 0.01, and 0.1 M) spiked with Pb(II) or Cd(II) as the reference metal ion. All solutions were purged for 60 min in the beginning of every stripping chronopotentiometry (SCP) experiment. An oxidizing current, Is, of 7.5 108 A was applied in quiescent solution until the potential reached a value sufficiently beyond the transition plateau. The SSCP waves were constructed from a series of individual SCP peak areas, plotted as a function of the deposition potential. For each point the potential was held at Ed for the duration of the deposition time, td, after which the oxidizing current was applied (0.69 V for Cd(II) and 0.51 V for Pb(II)). The SSCP waves were obtained for Pb(II) and Cd(II) in the absence and in the presence of silica nanoparticles. Previous to the addition of the ligand, the solution was set at the desired pH using MES buffer or MOPS (3-(N-morpholino)propanesulfonic acid). pH and Ionic Strength Impact Experiments. After some preliminary tests, we chose a Pb2þ concentration of 5 107 M and an LS30 concentration of 0.125% (w/w), which translates to a number of particles of 3.4 1017 per dm3, yielding a metal/particle ratio of 0.85. Measurements comprise a total of nine sets of conditions covering a matrix of three pH values (5.5, 6.0, and 6.5) and three ionic strengths (0.0015, 0.010, and 0.100 M). Ligand Titration Experiments. The ligand titrations in the presence of lead were carried out in a medium containing a Pb2þ concentration of 5 107 M at I = 0.010 M and pH 6.0. The metal/nanoparticle number ratio was varied from 1.7 to 0.3. The ligand titrations in the presence of cadmium were carried out in a medium containing a Cd2þ concentration of 5 107 M at I = 0.010 M and pH 7.2. The nanoparticles were added so that the metal/nanoparticle number ratio varied from 1.0 to 0.2. These are sufficiently diluted particle dispersions, with the average separation between particles being 45 nm or higher (k1 ≈ 10 nm for I = 0.0015 M) so that electric interactions between the particles are negligible.29
’ RESULTS AND DISCUSSION Impact of the pH and Ionic Strength. The first step of our study was to determine the stability parameter (K0 = KcL,T) for
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the Pb2þ/SiO2 complexes in a situation where the number of Pb2þ ions and dispersed nanoparticles are of the same order of magnitude. Table 1 shows the number of deprotonated groups per particle (ng) as obtained from the protolytic titrations, the equivalent volume concentration of deprotonated binding groups (cL,T), and the values of the stability parameter K for a metal to nanoparticle (np) ratio (RPb/np = cPb,T/cnp,T) of 0.85 and different values of the pH and ionic strength. The table shows that K increases with pH while decreasing with increasing ionic strength, as generally expected. For pH 6.5, however, the lower ionic strength results are higher than expected. The experimental SSCP curves that yielded these values showed a slope lower than the theoretical slope for homogeneous systems. To check the electrostatic contribution to the Pb2þ binding by the negatively charged nanoparticles, a first estimation can be made by separating the intrinsic chemical binding, Kint, from the electrostatic Boltzmann coefficient: ! zM eψ int K ¼ K exp ð8Þ =fPb 2þ kT where Kint is the intrinsic binding constant and fPb2þ is the activity coefficient of the lead ion. A more detailed expression is given in ref 5 (eq 32), but the electrostatic data necessary to apply it are not available presently. Recent reports16 suggest that the LS30 silica nanoparticles are not completely hard spheres but have a thin permeable surface layer; thus, the surface potential as obtained from the total interfacial charge might provide inadequate results. Therefore, we also measured the electrokinetic ζ potential that yielded values of 25, 20, and 12 mV for pH 6.0 and 0.0015, 0.010, and 0.100 M ionic strength, respectively. Note that these ζ potentials underestimate the real effective ψh and thus are just a first-order approximation. Using these values in applying the electrostatic correction (eq 8) to the log K values obtained at pH 6.0 yields log Kint of 4.65, 4.6, and 4.9 (as compared with the apparent values of 4.6, 5.1, and 5.7) for the ionic strengths of 0.100, 0.010, and 0.0015 M, respectively. The trend in intrinsic stability constant values suggests that this is not a purely electrostatic phenomenon; hence, some kind of binding heterogeneity should be playing a role. Impact of the Particle Concentration. To further explore the heterogeneity issue, a titration of Pb2þ ions with LS30 nanoparticles was performed at constant pH and ionic strength to maintain the same electrostatic conditions throughout the experiment. Figure 2 shows the variation of log K with the metal/ nanoparticle ratio (RM/np). It is found that for Pb(II) the values of log K strongly increase with decreasing metal to particle ratio, providing evidence for a substantial heterogeneity in the Pb(II) binding. For comparison a similar experiment was performed with Cd2þ ions. Due to the lower binding strength for cadmium, the measurements were done at higher pH and higher particle concentrations. Figure 2 shows the Cd2þ results obtained for pH 7.2 (ng = 125) and RCd/np between 0.8 and 0.2. In spite of the low values of RCd/np, the variation of log K for Cd2þ with the metal to particle ratio is much weaker than that for Pb2þ. The SSCP wave shapes for Cd2þ do not show evidence of heterogeneity. Evidence of Heterogeneity from the SSCP Curves. The heterogeneity of metal ion binding is also manifest in the slopes of the SSCP curves. Figure 3 shows the normalized SSCP data for the Pb(II)-only (]) and two different RPb/np values. The full squares and open triangles represent RPb/np of roughly 7880
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Table 1. log K Values Obtained by Application of Eq S7 (Supporting Information) for the Interaction of 5 107 M Pb2þ Ions with 0.125% LS30 (RPb/np = 0.85) for Different Ionic Strengths and pH Valuesa I = 0.100 M
a
5
I = 0.010 M
I = 0.0015 M K0
ng
cL,T /105 M
log K
5.0
2.2
18
0.8
5.4
5.1
5.7
25
1.1
5.7
38
1.7
6.4
pH
K0
ng
5.5
0.5
49
2.2
4.4
1.4
32.5
1.4
6.0
1.4
77
3.4
4.6
2.9
52
2.3
6.5
2.8
111
4.9
4.8
75
3.3
5.6
cL,T /10
M
log K
K0
5
12b
ng
cL,T /10
M
log K
42b
The average estimated error in log K when using eq S7 (Supporting Information) is (0.1 log unit. b Irregular SSCP waves.
Figure 2. log K values obtained from eq S7 (Supporting Information) for metal ion in the presence of increasing amounts of LS30 for an ionic strength of 0.01 M and pH 6.0 for Pb(II) (b) and pH 7.2 for Cd(II) (9).
Figure 3. Normalized SSCP experimental points and simulated curves for 4.3 107 M lead ions (]) and in the presence of LS30 (I = 0.01 M, pH 6.0) for ligand concentrations of 2.35 105 M (RPb/np = 0.95) (Γ = 0.9) (9) and 4.7 105 M (RPb/np = 0.47) (Γ = 0.7) (Δ).
1/1 (0.95) and 1/2 (0.47). Their fit to the SSCP curves computed for Freundlich-type heterogeneity (full lines)22 is of good quality and yields values for the heterogeneity parameter (Γ) of 0.9 and 0.7, respectively. For the highest RPb/np (not shown) it is possible that there is some loss of lability which may affect the shape of the curve.33 The issue is discussed in some detail in the section below. The meaning of these results can be understood by comparison with the metal binding with humic matter, a prototypical chemically heterogeneous system, for which the Cd2þ binding generally presents very weak heterogeneity (Γ = 0.91.0), Pb2þ presents a moderate heterogeneity (Γ = 0.60.8), and Cu2þ presents a strong heterogeneity (Γ = 0.20.4).33 Thus, the Pb(II)/silica nanoparticle shows moderate heterogeneity, with an apparent increase in heterogeneity with a decrease of the metal to ligand ratio. It is timely to recalculate the log K values pertaining to the experiments where heterogeneity was detected using eq S13 (Supporting _ Information). The following values were obtained for log K *: 5.5 (instead of 5.6) for pH 6.5 and I = 0.01 M and 6.2 (6.4) for pH 6.5 and I = 0.0015 M for values in Table 1 and 5.4 (5.6) for RPb/np = 0.29, 5.3 (5.4) for RPb/np = 0.40, and finally 5.1 (5.2) for RPb/np = 0.47. Dynamic Behavior of the Pb(II)/LS30 System. With increasing stability, the degree of lability of a metal/np complex generally decreases. We applied the in-built lability diagnosis of SSCP7 to the Pb2þ/SiO2 np system. It is based upon comparison between the K0 values as obtained from the half-wave potential shift (K0 (ΔE), eq S7, Supporting Information) and those obtained from the decrease in the limiting wave height, τ*, for the supposed labile situation (K0 (τ), eq S9, Supporting Information). In the case of reduced lability K0 (τ) becomes significantly larger than K0 (ΔE). Heterogeneity will affect the two types of computation in a different manner. To take it into
account is cumbersome but not always necessary since loss of lability is also manifest in extremely large differences between K0 (ΔE) and K0 (τ). Table 1 shows that most cases are labile except I = 0.0015 M at pH 6.0 (K0 (ΔE) = 5.7, K0 (τ) = 19) and 6.5 (K0 (ΔE) = 42, K0 (τ) = 180), where the differences observed suggest the onset of loss of lability. In the case of Figure 2 the two lowest RPb/np values show some loss of lability which is modest for RPb/np = 0.40 (K0 (ΔE) = 12, K0 (τ) = 50) but quite significant for RPb/np = 0.29 (K0 (ΔE) = 30, K0 (τ) = 10 000). These results show that for higher particle concentrations, lower salt levels, and higher pH there is an indication of loss of lability. To further investigate this issue, we can compute the theoretical value of the effective association rate constant operational in colloidal dispersions, i.e., ka* as defined by eq 6. The rate of elimination of a water molecule from the inner hydration shell (kw) is 7 109 s1 for [Pb(H2O)62þ].27 Estimation of the stability of the precursor outer-sphere complex, Kos, requires that the surface charge and screening effects be taken into account.37 For this silica material (LS30A), an exact calculation of Kos is not yet possible, but an estimate on the basis of the measured ζ potential indicates that this value should be on the order of 1 M1, thus yielding a ka exp(zMeψ h/kT) of order of magnitude 1010 M1 s1. The values of exp(zMeψ h/kT) range from 7 at I = 0.0015 M to 2.5 at I = 0.1 M. To elucidate the kinetics, the key comparison is the ratio ka exp(zMeψh/kT)NS/4πrpDMNAv in eq 6. For the present Pb2þ/SiO2 nanoparticulate system referred to in Table 1, the nanoparticle number concentration, cp, is 3.3 1020 m3 (RPb/np = 0.85), with the smeared-out metal binding site concentrations varying with the pH and ionic strength between 0.8 and 4.9 105 M, corresponding to values of NS (eq 7) ranging between 18 and 111. Considering the silica nanoparticle as a hard sphere of radius 7.5 109 m and taking 7881
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’ ASSOCIATED CONTENT
bS
Supporting Information. SSCP theoretical background. This material is available free of charge via the Internet at http:// pubs.acs.org/.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Phone: þ351-289-800905. Fax: þ351289-819403. Notes
)
the diffusion coefficient of lead ions in solution as 9.85 1010 m2 s1, the corresponding values for ka exp(zMeψ h/kT)NS/4πrpDMNAv range from 12 to 62. This shows that the diffusion of Pb2þ to the nanoparticle surface is an important rate-limiting step in the complex formation process. From eq 6 we obtain keff a values between 1.5 109 and 2 1010 M1 s1. These keff a values can be converted to the corresponding kd values by using the most appropriate K0 , that is, K0 (ΔE). The resulting kd represents the average kd for the actual bound Pb2þ/np ratio. In our experiments, this ratio is restricted to values around unity, while the total number of binding sites per particle is much larger than unity. For the present purposes of estimation of possible loss of lability of the Pb2þ/np complex, we have to consider the lowest kd values in this occupied lower end, i.e., the strongest complexes at the very bottom of the kd distribution. If we arbitrarily set this lowest kd at 0.1kd, then we find that the lability parameter L (eq 5) varies from 105 for 0.1 M ionic strength to less than 10 for I = 0.0015 M and pH 6.5. A similar exercise for the case of Figure 2 shows that the points of RPb/np = 0.40 and 0.29 give L values around 50 and 10, respectively. This result indicates that for the latter set of conditions one may expect to see the first signs of loss of lability and the corresponding decrease of the flux of the Pb2þ/np complex. In future work we plan to use the shape of the SSCP curve as an indicator for loss of lability in heterogeneous systems.33 The results obtained here do not allow the discrimination between heterogeneity and lability within experimental error. This is probably due to the fact that even for the conditions of weakest lability (high pH/low I) we are only approaching the onset of loss of lability. Chemodynamics of the Nanoparticulate Metal Complexes. For metal to nanoparticles number ratios around unity, the SiO2 nanoparticles display a strongly heterogeneous Pb2þ ion binding behavior. This feature is accompanied by loss of lability for higher pH and lower ionic strengths. These findings are remarkable and raise several key questions on the chemodynamics of the nanoparticulate complexes. The heterogeneity might be chemical in nature since it is likely that some surface groups of orthosilicic acid might act as monodentate and as bidentate ligands. Impurities in the silica, of which aluminum is a known possibility, might also impact the chemical properties of the surface sites. The actual state of the SiO2 surface is uncertain in itself. Allison16 and other authors could not interpret their electrophoretic mobility results in terms of a hard-sphere electrostatic model and thus had to divert to a permeable soft layer of a few nanometer thickness. Such a thin soft permeable layer at the surface of a nanoparticle is likely to be nonuniform, with inherent spatial heterogeneity thus generating a heterogeneous electrostatic field distribution. Lowering the ionic strength and increasing the pH have been shown to cause heterogeneous expansion of the interphasial layer in soft particles,38 and this should provoke an increase in K as shown in Figure 9 of ref 5. At this stage it seems likely that the heterogeneity stems from both electrostatic and chemical spacial heterogeneity. The loss of lability of the Pb2þ/SiO2 complex seems to be due to the nanoparticulate nature of the system, where diffusion-controlled reactivity and electrostatic effects from the highly charged surface start to play crucial roles in the ion site association process.39
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Currently on leave from CMQE/IBB, Departamento de Química e Farmacia/Faculdade de Ci^encias e Tecnologia Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal.
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