Extending the diffuse layer model of surface acidity behavior: I. Model development

Savage

2008

Water Air Soil Pollut

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Developing procedures for assessing the potential environmental fate and transport of nanomaterials is an active endeavor of the environmental technical research community. Insufficient information exists for estimating the likelihood of nanomaterial deposition on natural surfaces in aquatic environments. This work develops a framework for estimating potential metal oxide nanomaterial selfaggregation through the combined application of recent developments in diffuse layer model surface complexation theory with historical Derjaguin-Landau-Verwey-Overbeek (DLVO) procedures. Findings from the work include: 1) the surface, diffuse layer, and/or zeta potentials of nanomaterials in environmental aqueous systems are likely to have an absolute value less than 25 mV, 2) only nanomaterials with a Hamaker constant as large as 1E-19 J (and an absolute surface potential < 25 mV) will likely aggregate in most environmental aquatic media, 3) natural organic matter coatings may render metal oxide nanomaterials less likely to aggregate in aquatic systems, 4) nanomaterials in aqueous suspension will likely have an absolute surface potential less than their micron-sized counterparts of the same composition, and 5) robust diffuse layer model databases of intrinsic surface site reactivity constants with multivalent aqueous environmental ions will need to be developed in order to provide accurate mechanistic estimates of the surface potential of nanoparticles suspended in aqueous environmental systems.

Section: Aqueous Acidity Of Metal Oxide Nanomaterialsmentioning

confidence: 99%

An Assessment of the Fate of Metal Oxide Nanomaterials in Porous Media

Savage

2008

Water Air Soil Pollut

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“…At very low ionic strengths, the hydronium ion activity coefficient can be estimated using the Debye -Huckel Limiting Law (DHLL). Because the derivation of the DHLL displays analogies with that of the charging energies discussed in earlier papers in this series (Loux, 2006(Loux, , 2008b, its derivation will be discussed in detail later in this section.…”

Section: Historical Metal Oxide Acidity Reaction Formulationsmentioning

confidence: 95%

“…As in Loux (2006), the degree of counterion condensation for spherical particles was estimated using the expression:…”

Section: Methodsmentioning

confidence: 99%

“…In historical applications the bound site activity coefficients in equations (5a) and (5b) are either ignored or assumed to equal one and the excess free energy term contained in the exponential in these expressions is assigned a value of: Loux (1999Loux ( , 2000Loux ( , 2003Loux ( , 2006Loux ( , 2008b examined the role of counterion condensation (Oosawa, 1971;Manning, 1972Manning, , 1981Manning, , 2007aManning, , 2007bZimm and Lebret, 1983;Ramanathan, 1988) in these phenomena and suggested that rather than estimating a charging energy value of FC, a more correct highcharge-density bound site charging energy term can be described by ð1 À tÞFC where t is the degree of counterion condensation associated with imparting to the surface a potential-determining-ion surface charge of + e (t ranges in value between 0 and 1). Within the context of this interpretation, the reaction becomes more of an ion exchange reaction when t approaches a value of one.…”

Section: Historical Metal Oxide Acidity Reaction Formulationsmentioning

confidence: 99%

“…Lastly, within the context of this discussion, these charging energy terms are assumed to be the principal excess free energy terms contributing to dissolved ion and bound site non-ideality. Loux (2006) examined the effects of a potentially variable value of t (more likely to occur under conditions of extremely low charge densities) and integrated expression (10a) [ð1 À tÞð+2Qe þ e 2 Þ y8per pcl ] from t 1 to t 2 (again assuming that the integration constant equals 0) and arrived at:…”

Section: Historical Metal Oxide Acidity Reaction Formulationsmentioning

confidence: 99%

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Extending the diffuse layer model of surface acidity behaviour: III. Estimating bound site activity coefficients

Chemical Speciation & Bioavailability

2009

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Although detailed thermodynamic analyses of the 2-pK diffuse layer surface complexation model generally specify bound site activity coefficients for the purpose of accounting for those non-ideal excess free energies contributing to bound site electrochemical potentials, in application these terms are ignored based on one or more of the following assumptions: (1) bound site activity coefficients cancel out in the mass action quotients; (2) bound sites display ideal behaviour; andyor (3) these energies are already included in the exponential Boltzmann terms. In this work it is demonstrated that the bound site charging energy terms discussed in the two previous papers in this series have both conceptual and computational analogies to the charging energy contribution to the activity coefficients obtained from the Debye -Huckel Limiting Law. On high charge density colloidal particles at constant counterion condensation (t), these charging energies can be related to the surface potential (C) by: DG charging ¼ ð1 À tÞFC (where F is the Faraday constant). If one assumes a maximum practical accuracy of AE 10% in experimental estimates of C, then it is suggested that charging energies are likely to be experimentally indiscernible under conditions where t ! 0:9. These findings support the historical practice of ignoring bound site activity coefficients with the 2-pK diffuse layer surface complexation model in the following situations: for spherical particles with a radius ! 0.1 mm at ionic strengths ! 0.001 M (1 : 1), and for spherical particles with a radius 40.01 mm at an ionic strength 40.1 M (1 : 1). In contrast, charging energies (and non-ideal behaviour) are predicted to be significant at all charge densities and ionic strengths for spherical particles with a radius of 0.001 mm.

Simulating the Stability of Colloidal Amorphous Iron Oxide in Natural Water

2010

Water Air Soil Pollut

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Considerable uncertainty exists as to whether existing thermodynamic equilibrium solid/ water partitioning paradigms can be used to assess the mobility of insoluble manufactured nanomaterials in the aquatic environment. In this work, the traditional Derjaguin-Landau-Verwey-Overbeek theory of colloidal particle stability was examined by using three published expressions for estimating critical coagulation concentrations (CCCs; i.e., the minimum ionic strength needed to induce rapid self-aggregation) via incorporation of diffuse-layer potential estimates obtained from MINTEQA2 geochemical model implementations of an enhanced version of the MIT diffuse-layer model (DLM) and the historical triple-layer model (TLM). Amorphous iron oxide was selected as a test colloid in this assessment and its electrostatic properties were simulated over a pH range of 4 to 10 in 0.7 M seawater, 0.1 M diluted seawater, world average river water, US continental average groundwater and Midwestern US 50th percentile rainwater. Findings from the study included: (1) sources of variation in predictions of the onset of rapid colloidal particle self-aggregation were observed to occur in the following order: aquatic chemistry>selection of DLM vs. TLM diffuse-layer potentials>uncertainties in the Hamaker constant> selection of CCC equation≈ the distance to the plane of shear (with the DLM), (2) the magnitude of the DLM diffuse-layer potential estimates exceeded that of the TLM estimates, (3) TLM diffuse-layer potential estimates were consistent with a conjecture by Loux and Anderson, Colloids and Surfaces A, 177, 123-131, (2001) that the magnitude of environmental interfacial potentials were likely to be less than RT/F (~25 mV) and DLM estimates were not, and (4) TLM estimates predict that amorphous iron oxide suspensions are likely to be relatively stable only in high pH rainwater; DLM estimates predict relative colloidal iron oxide suspension stability in rainwater and extreme pH river waters. These predictions of rapid aggregation are at least qualitatively in accord with data published in the literature.