Correlating inter-particle forces and particle shape to shear-induced aggregation/fragmentation and rheology for dilute anisotropic particle suspensions: A complementary study via capillary rheometry and in-situ small and ultra-small angle X-ray scattering
Graphical abstract
Introduction
Predicting the stability and aggregation behavior of nanoparticles, especially under flow, is important to several fields in engineering, materials science, and chemistry including water treatment [1], polymer latex manufacturing [2], paper manufacturing [3], protein stability/folding [4], and transport of monoclonal antibodies [5]. However, shear-induced aggregation and fragmentation of colloidal dispersions is complex and heavily influenced by the physical parameters [6], [7] and surface/solution chemistry of the system [8], [9], [10] through their coupling to flow characteristics. These are directly correlated to particle interactions that are often understood through a delicate balance between van der Waals () and electrostatic () interactions in the context of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. More complex interactions such as hydration and steric repulsive forces have been addressed using adjustments to DLVO theory, but are often system specific [11], [12], [13], [14]. For example, ion-specific adsorption can lead to variations in particle surface charges manifesting as ion-specific effects [15]. Additional complications arise in concentrated ionic systems, where significant deviations from Debye screening lengths are expected in the dilute limit, leading to long-range electrostatic forces, and have been reported in concentrated aqueous salt solutions and ionic liquids [16], [17]. These affect the stability of colloidal particles, creating challenges in predicting and controlling particle aggregation [18], which have been addressed using kinetic approaches (typically 2nd order kinetics [19]). Such aggregation kinetics can be characterized by a rate coefficient () that depends on particle interactions as well as external “driving” forces such as Brownian, shear, and differential gravitational forces. The importance of particle interactions to aggregation kinetics has been represented as a stability ratio (), given as the ratio of the rate coefficients () [20], where denotes an “ideal” rate coefficient without inter-particle forces.
Aggregation under flow has been studied extensively [20]. The interplay of shear and colloidal forces has been fairly well established [21], and the basic rheological properties of colloidal dispersions at a wide range of volume fractions have been described on the basis of inter-particle forces [22], especially using a hard sphere assumption [23]. However, connecting aggregate properties, such as size and shape (i.e. fractal dimensions (), to rheological properties remains an active field of research, being studied using a variety of scattering techniques [24], [25], [26], [27], [28]. For example, thixotropy, and other non-reversible processes are still not well understood, especially for complex (e.g. inhomogeneous) aggregates [29]. For systems with broad, inhomogeneous size distributions, small angle X-ray scattering (SAXS) and small angle neutron scattering (SANS) have been especially useful for correlating rheological properties to aggregate properties [30], [31], [32]. Particle shape can greatly affect the stability of aggregates (and thus rheology), but is difficult to quantify and predict [33], and fragmentation and aggregate restructuring under flow are also poorly understood because of the complexity of the process [34]. While models have been developed for predicting fragmentation events by estimating hydrodynamic, van der Waals, and repulsive interactions using Stokesian dynamics for monodisperse systems [35], [36], quantifying and predicting the rheological responses for non-spherical polydisperse materials is challenging.
The physical and chemical complexities described above exist in virtually all practical applications of slurry flow. One important example is treatment of the wastes stored in tanks at the Hanford Site in Washington state, United States [37]. The rheology of these materials involves a number of complicating factors, including high levels of radioactivity, elevated pH (>12), high ionic strength, and non-spherical particle shapes, which combine to influence the aggregation and rheological behavior of the slurries and sludges in the waste tanks. The mineralogy of these materials also adds to the complexity. While many solid phases are present, the most common are aluminum (oxy)hydroxides. Of these, boehmite (γ-AlO(OH)) is of particular concern as it forms complex aggregates that affect solutions rheology, complicating waste recovery and treatment [38], [39]. Furthermore, like many other minerals, boehmite nanoparticles have a platelet-like particle geometry composed of sharp-edges and significant three-dimensional anisotropy (see TEM image in Fig. S1). It is not well understood how non-spherical geometry, coupled with the complex solution structure around boehmite nanoparticles, affects macroscopic properties such as aggregation, precipitation, and response to flow, especially in the aforementioned complex environments [40], [41].
A number of explorations into how particle forces influence aggregation and the resultant boehmite nanoparticle morphology at elevated ionic strengths and pH have been performed [42], [43]. Using small- and ultra-small-angle neutron and X-ray scattering, the discrete size distributions and fractal dimensions () of the aggregates were found to be highly dependent on solution conditions. For instance, approximately 100 times less Ca(NO3)2 than NaNO3 was needed to produce similar changes to aggregate structures [42]. Analysis of Brownian aggregation of boehmite nanoparticles using dynamic light scattering [43] demonstrated that particle shape anisotropy strongly influenced boehmite particle aggregation. Significant deviations were observed between calculated stability ratios based on spherical particles () and those observed experimentally (). Interestingly, a very large () stability ratio was reported at pH = 9 without additional salt, close to point of zero charge (PZC) of boehmite [44], [45]. Under these conditions attractive van der Waals forces should dominate repulsive electrostatic forces, leading to a low stability ratio. The large stability was attributed to orientation-dependent colloidal and hydrodynamic interactions that do not exist for spherical particles. Despite these studies, however, how changes in boehmite nanoparticle aggregation emerge from the unique physicochemical nature of boehmite forces, and their impact on rheology, have not been clearly understood.
In this study, the effects of flow on the aggregation and fragmentation of boehmite nanoparticles were investigated as a function of cumulative shear stress, as was the question of whether the effects of shape anisotropy on aggregation structures and kinetics manifests under shear in a manner that contrasts with the behavior of typical spherical particles. An experimental method was developed that allows monitoring the time evolution of boehmite aggregation and fragmentation resulting from the interplay of flow and particle interactions using in-situ measurements of hierarchal aggregate structures and slurry rheology. This combined capillary rheometry with in-situ small-angle X-ray scattering (SAXS), ultra-small-angle X-ray scattering (USAXS), and wide-angle X-ray scattering (WAXS) to quantify boehmite particle behavior at scales from 6 to 10,000 Å with a time delay of a few minutes per analysis over several hours. Additionally, computational fluid dynamics (CFD) was used to more rigorously describe the flow and calculate the shear dissipation energy to explain aggregate property changes in terms of the total and rate of energy input.
Section snippets
Boehmite synthesis
Boehmite nanoparticles were prepared using a method detailed elsewhere [46] and briefly summarized here. Aluminum nitrate nonahydrate (250 mmol, Al(NO3)3·9H2O, purity ≥98%, Sigma-Aldrich) was dissolved in 1000 mL of deionized water followed by sufficient additions of 3 mol dm−3 sodium hydroxide (NaOH, purity ≥98%, Sigma-Aldrich) to achieve a final pH of 10. The mixture was stirred for 1 h at room temperature and the resulting gel-like precipitates were collected by centrifugation and washed
Slurry viscosity and rheology
The values of the initial suspension viscosity (), , , and measured after the pre-shearing cycle calculated using Eqs. (1), (2), (3), and (4), respectively, are shown in Table 1. values indicate the flow was laminar, assuming the contribution from the quartz tube was negligible. In order to calculate Pe, which assumes that the particles are spheres, a value of 200 nm was chosen as the representative hydrodynamic particle radius (). This was calculated from the average size
Discussion
The experiments in this study were designed to evaluate the effects of increasing shear rate on the structure of boehmite aggregate suspensions. The Peclet number (Eq. (4)) provides an estimate of the relative importance of hydrodynamic shear on the boehmite particles. This was calculated as a function of for the 200 nm aggregate (Table 1). The values for a 9 nm particle (i.e., unified fit level 1) were less than or on the order of 1 for all cases. This indicates that Brownian forces
Summary and Conclusions
Using a combination of USAXS, SAXS, WAXS and in-situ capillary rheometry at different flow conditions, the rheological responses of relatively dilute boehmite suspensions (2.5 wt% solid and pH 9) and their correlations with aggregation/fragmentation under flow were studied. A relatively wide range of flow conditions, characterized by Peclet numbers ranging from 1.9 to 480, enabled determination of both boehmite aggregation and rheological response under conditions ranging from little to
CRediT authorship contribution statement
Anthony J. Krzysko: Methodology, Formal analysis, Investigation, Writing - original draft, Writing - review & editing. Elias Nakouzi: Formal analysis, Writing - review & editing. Xin Zhang: Resources. Trent R. Graham: Resources. Kevin M. Rosso: Writing - review & editing. Gregory K. Schenter: Formal analysis, Writing - review & editing. Jan Ilavsky: Methodology, Formal analysis. Ivan Kuzmenko: Methodology, Resources. Matthew G. Frith: Methodology, Resources. Cornelius F. Ivory: Writing -
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research was supported by the Interfacial Dynamics in Radioactive Environments and Materials (IDREAM), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences. PNNL is a multiprogram national laboratory operated for DOE by Battelle Memorial Institute under Contract No. DE-AC05-76RL0-1830. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the
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