Modeling the kinetics of silica nanocolloid formation and precipitation in geologically relevant aqueous solutions
Introduction
In soils and natural waters, the solid–water interfaces of colloids can regulate the concentrations of most reactive elements and of many pollutants. Colloid surfaces control aggregation reactions, act as redox catalysts and play an important role in the uptake and transport of nutrients and contaminant materials (Brown et al., 1999). The size, shape and composition of colloids can also have a profound effect on their function as a catalyst or sol–gel in industrial applications. The growth and nucleation of silica nanocolloids is especially interesting as they are ubiquitous in nature and the mechanism by which they grow and precipitate is essential to understanding a variety of geologic processes. Silica reaction kinetics play a critical role in thermally enhanced oil recovery and subsurface contamination remediation, disposal of reactive waste by burial and geothermal waste-waters by injection into the subsurface (Carroll et al., 1998).
Despite the extensive characterization of the silica system, few studies have examined the formation of silica in fluids of geologic significance with relatively low silica concentrations, varying ionic strengths and the full natural pH range. Even fewer studies have characterized the kinetics of the formation and growth of the nanocolloidal phase. Most research investigating the formation of silica nanocolloids has been directed at the production of materials for industrial applications. Methods for synthesizing monodisperse colloidal silica through techniques such as the Stöber method are well established (Bogush and Zukoski, 1991, Van Blaaderen et al., 1992, Arriagada and Osseo-Asare, 1999, Pontoni et al., 2002) and sophisticated models have been derived to describe the growth of these particles over time (for example, Lee et al., 1998). Additionally, characterization techniques such as small angle X-ray scattering (SAXS) have provided detailed information as to the growth mechanism and changes in the physical and chemical properties of these Stöber particles over time (Boukari et al., 1997, Pontoni et al., 2002). Conversely, silica colloids formed at low degrees of supersaturation from aqueous solutions are often amorphous particles of such low density that traditional characterization techniques are unable to provide reliable information as to changes in particle size, shape and porosity. Therefore, the application of more sophisticated aggregation models is hindered in these systems.
In this study, we extend our previous work (Icopini et al., 2005) by applying kinetic models to determine both rate constants for the conversion of monomeric to nanocolloidal silica (k1) and the subsequent conversion of nanocolloidal silica to the precipitated form (k2). The overall reaction of the silica precipitation process can be defined as:where silica follows the general behavior observed for precipitation in closed systems; the supersaturation in solution declines as monomeric silica (SiO2(mono)) nucleates and grows to a critical nucleus (SiO2(cn)) whose size may vary depending on the experimental conditions (Rajasekaran et al., 2003, Izumi et al., 2005, Madras and McCoy, 2005). The critical nucleus is defined as the smallest cluster of molecules or atoms needed for growth to continue spontaneously. Once the critical nucleus is formed, oligomerization rapidly continues to form a nanocolloidal phase (SiO2(nano)). Primary nanocolloidal silica particles have been shown to be 3 nm in diameter and consist of approximately 300 silica monomer units under the conditions of our experiments (Icopini et al., 2005). Continued growth of the nanocolloidal phase through some mechanism such as coalescence or aggregation results in precipitation (SiO2(ppt)). In this study, precipitated silica is defined as particles that do not pass through a 0.1 μm filter. The rates of these processes can be described by the rate constants k1 (oligomerization) and k2 (precipitation) as shown in Eq. (1).
Icopini et al. (2005) investigated the initial stages of silica oligomerization and nanocolloid formation (i.e., k1) in solutions from pH 3 to 11 in a low ionic strength solution (0.01 molal) and a geothermal brine (0.24 molal). The work presented in this paper builds upon the previous results by (1) extending the model employed by Icopini et al. (2005) to fit silica precipitation (i.e., k2), and (2) to fit silica oligomerization and precipitation using a modified kinetic model based on Goto (1956). Whereas the focus of Icopini et al. (2005) was to characterize the formation of the nanocolloidal silica fraction by investigating the disappearance of monomeric silica, the primary focus of this work is to determine not only what factors affect the rate of nanocolloidal silica formation, but also to examine nanocolloid conversion to precipitated silica. Understanding the conditions under which nanocolloidal silica forms and persists will allow for a more complete understanding of the environments in which these particles should be considered important in geochemical studies.
The first model we tested is taken directly from Icopini et al. (2005) and assumes that the rate of polymerization of silica is directly proportional to the concentration of monomeric SiO2 in solution. This model will be termed the “concentration model” for the purpose of this study. The rate of decrease in molybdate-reactive (or “monomeric”) silica with time was observed to be fourth-order leading to the following rate equationwhere k1 is the reaction rate constant for the formation of the critical nucleus. Details of the derivation of this model and its fourth-order dependence can be found in Icopini et al. (2005). Note that Icopini et al. (2005) used the initial rate method to determine rate constants for the conversion of SiO2(mono) to SiO2(nano) and only utilized a subset of the entire dataset. Because we are interested in the long term behavior of the nanocolloidal fraction, we have utilized the entire data set for fitting resulting in slightly different rate constants reported here.
To develop this model so as to incorporate precipitation, we assume that the growth of the critical nucleus to the nanocolloid phase is fast, but that the reaction from the nanocolloid to the precipitate (rate constant k2) is slow. Thus, the change in nanocolloidal silica concentrations with time may be described as in Eq. (3) as the difference between the growth of SiO2(nano) from critical nuclei formed by SiO2(mono) (assumed to be fourth-order as shown by Icopini et al., 2005) and the loss of SiO2(nano) through the formation of SiO2(ppt):where k1 is the reaction rate constant for the formation of critical nuclei, k2 is the reaction rate constant for the conversion of SiO2(nano) to SiO2(ppt), and m is the reaction order with respect to SiO2(nano).
The second model we tested was originally formulated by Goto (1956) to describe the loss of monomeric silica from aqueous solution by incorporating a term for the solubility of amorphous silica at a given temperature. For the fourth-order reaction observed by Icopini et al. (2005), the rate equation for the change in SiO2(mono) over time using the supersaturation model is expressed in Eq. (4). Substituting this expression into Eq. (3) gives the rate equation for SiO2(nano) Eq. (5).The reaction rate constants k1 and k2 describe the formation of the critical nucleus and the rate of precipitation, respectively, and m is the reaction order with respect to SiO2(nano). SiO2(eq) is the equilibrium solution concentration of amorphous silica at a given temperature and is generally reported to be approximately 2.0 mmolal at 25 °C (Weres et al., 1981, Icenhower and Dove, 2000). However, the solubility of amorphous silica can vary as a function of pH with a higher solubility at acidic pHs (∼2.5 mmolal at pH 3) and lower solubility at neutral pH (∼1.7 mmolal at pH 7) (Alexander, 1954, Iler, 1979). In this model, the rate of reaction is dependent not only on the initial concentration of SiO2(mono), but also on the degree of supersaturation with respect to amorphous SiO2. It is assumed that conversion to critical nuclei will occur as long as the concentration of monomeric SiO2 is greater than the equilibrium concentration of amorphous SiO2.
Section snippets
Batch experiments
The silica oligomerization and precipitation data fit in this work are the result of experiments reported in Icopini et al. (2005). Briefly, stock solutions of aqueous SiO2 were prepared by dissolving 10.593 g Na2SiO2·5H2O in 500 mL distilled, deionized water. Sodium was removed with a cation exchange resin (Dowex 50W-X8, 20–50 mesh, H-form) reducing the pH to <3. The solution was then filtered and the pH raised to >10.85 with 1 M NaOH. Oligomerization of silica was studied at a low ionic strength
Silica concentrations
Two distinct trends were observed in the concentrations of the individual silica fractions in these experiments. At low pH (3–4) at both high and low ionic strengths for initial SiO2 concentrations of 20.8 and 12.5 mmolal, a fast initial decrease in SiO2(mono) was followed by the establishment of an apparent steady state between SiO2(mono) and SiO2(nano) with little SiO2(ppt) forming (representative data shown in Fig. 1). Under these conditions, the concentration of the SiO2(mono) fraction
Discussion
In supersaturated solutions, oligomerization of monomeric silica to form stable nuclei of a critical size is the first step in the precipitation process. Once critical nuclei form they spontaneously grow to form spherical particles (Iler, 1979, Perry and Keeling-Tucker, 2000). The focus of this work was to predict the evolution of the concentrations of monomeric and, for the first time, nanocolloidal and precipitated silica over time as a function of pH, ionic strength, and initial SiO2
Summary and conclusions
This work provides the first kinetic models for the appearance and evolution of nanocolloidal silica over time under environmentally relevant conditions. Changes in the rate of formation of silica nanocolloids depended on the degree of supersaturation, ionic strength and pH of the experimental solutions while the stability of the nanocolloidal fraction is largely controlled by the pH of the solution. Both the concentration model and the supersaturation model predict similar rate constants for
Acknowledgments
The authors thank three anonymous reviewers whose efforts greatly improved this manuscript. This project was funded by the U.S. Department of Energy (DE-FG07-00ID13954), and The Pennsylvania State University Center for Environmental Kinetics Analysis (NSF EMSI Grant No. CHE-0431382).
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- 1
Present address: Montana Bureau of Mines and Geology, Montana Tech of the University of Montana, Butte, Montana, 59701-8997, USA.
- 2
Present address: Ehime University, Department of Civil and Environmental Engineering, Matsuyama 790-8577, Japan.