Abstract
Purpose
Triple-layer model (TLM) is distinct from other surface complexation models (SCMs) with the charged β-layer between solid surface and diffuse layer. However, its structure of electrical double layer, i.e., three capacitors connected in series, produced an uncharged β-layer according to the rule of capacitors in the electrical circuit theory. The objective of this study was to modify TLM with the development of a new structure of electrical double layer and mathematical models for the charge-potential relationships.
Methods
The rule of capacitors in the electrical circuit theory was used to modify the electrical double layer in TLM. Published acid-based titration experiments on goethite in KNO3 solution by Yates and Healy (J Colloid Interface Sci 52:222–228, 1975) was used to demonstrate the modified TLM. Simulation study of the modified TLM for goethite was carried out by changing pH from 4.0 to 10.0 and ionic strength of KNO3 solution from 0.001 to 0.100 mol l−1.
Results
The finite size of ions in aqueous solution determined the parallel connection of the two capacitors, which were described by the constant capacitance model (CCM) and the diffuse layer model (DLM). A new concept termed as ion size factor δ, which was governed by the radius r of hydrated ion, was proposed to quantify the percentages of surface area occupied by the CCM and DLM capacitors. A new characteristic relationship of the modified TLM was derived to be a linear relationship between net surface charge and square root of ionic strength when the surface potential was small. The experimental results verified the characteristic relationship, and the ion size factor was validated by the success in estimating the dielectric constant of the CCM capacitor and the radii of hydrated ions (K+ and NO3−). The CCM capacitor occupied 33.8% of the area of goethite surface. Simulation results showed that substantial amount of charge was at the compact layer, and it contributed 14.6% to 74.4% of the net surface charge.
Conclusion
New electrical double layer with structure of connection of the two capacitors in parallel eliminated the internal flaw of the classical TLM, modified the classical TLM into a general model which unified CCM and DLM, and supported the core of the classical TLM (i.e., the charged compact layer and the diffuse layer).
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References
Atkinson RJ, Posner AM, Quirk JP (1972) Kinetics of isotopic exchange of phosphate at the α-FeOOH-aqueous solution interface. J Inorg Nucl Chem 34:2201–2211
Bard AJ, Faulkner LR (2001) Electrochemical methods: fundamentals and applications. Wiley, New York
Bird J (2014) Electrical circuit theory and technology. Routledge NY. 60–61
Catalano JG, Fenter P, Park C (2007) Interfacial water structure on the (012) surface of hematite: ordering and reactivity in comparison with corundum. Geochim Cosmochim Acta 71:5313–5324
Catalano JG (2011) Weak interfacial water ordering on isostructural hematite and corundum (001) surfaces. Geochim Cosmochim Acta 75:2062–2071
Davies CW (1962) Ion Association. Butterworths, London
Davis JA, James RO, Leckie JO (1978) Surface ionization and complexation at the oxide/water interface: I. Computation of electrical double layer properties in simple electrolytes. J Colloid Interface Sci 63:480–499
Dzombak DA, Morel FMM (1987) Adsorption of inorganic pollutants in aquatic systems. J Hydraulic Engineering ASCE 113:430–475
Dzombak DA, Morel FMM (1990) Surface complexation modeling. Wiley, New York
Goldberg S (2005) Inconsistency in the triple layer model description of ionic strength dependent boron adsorption. J Colloid Interface Sci 285:509–517
Goldberg S (2013) Surface complexation modeling Reference Module in: Earth Systems and Environmental Sciences Elsevier Reference Module in Earth Systems and Environmental Sciences 1-14. https://doi.org/10.1016/B978-0-12-409548-9.05311-2
Goldberg S, Sposito G (1984a) A chemical model of phosphate adsorption by soils: I. Reference oxide minerals. Soil Sci Soc Am J 48:772–778
Goldberg S, Sposito G (1984b) A chemical model of phosphate adsorption by soils. II. Noncalcareous soils. Soil Sci Soc Am J 48:779–783
Hayes KF, Leckie JO (1987) Modeling ionic-strength effects on cation adsorption at hydrous oxide-solution interfaces. J Colloid Interface Sci 115:564–572
Hayes KF, Papelis C, Leckie JO (1988) Modeling ionic strength effects on anion adsorption at hydrous oxide/solution interfaces. J Colloid Interface Sci 125:717–726
Hayes KF, Redden G, Ela W, Leckie JO (1991) Surface complexation models: an evaluation of model parameter estimation using FITEQL and oxide mineral titration data. J Colloid Interface Sci 142:448–469
Healy TW, Yates DE, White LR, Chan D (1977) Nernstian and non-Nernstian potential differences at aqueous interfaces. J Electroanal Chem 80:57–66
Hohl H, Stumm W (1976) Interaction of Pb2+ with hydrous γ-Al2O3. J Colloid Interface Sci 55:281–288
Huang CP, Stumm W (1973) Specific adsorption of cations onto hydrous γ-Al2O3 surface. J Colloid Interface Sci 43:409–420
Israelachvili JN (2011) Intermolecular and surfaces forces. Academic Press, New York
James RO, Healy TW (1972) Adsorption of hydrolysable metal ions at the oxide-water interface III. A thermodynamic model of adsorption. J Colloid Interface Sci 40:65–81
James RO, Parks GA (1982) Characterization of aqueous colloids by their electrical double layer and intrinsic surface chemical properties. Surf Colloid Sci 12:119–216
Kerisit S, Ilton ES, Parker SC (2006) Molecular dynamics simulations of electrolyte solutions at the (100) goethite surface. J Phys Chem B 110:20491–20501
Motta A, Gaigeot MP, Costa D (2012) Ab initio molecular dynamics study of the AlOOH boehmite/water interface: role of steps in interfacial Grotthus proton transfers. J Phys Chem 116:12514–12524
Peak D, Ford RG, Sparks DL (1999) An in-situ ATR-FTIR investigation of sulfate bonding mechanisms on goethite. J Colloid Interface Sci 218:289–299
Sahai N, Sverjensky DA (1997) Evaluation of internally consistent parameters for the triple-layer model by the systematic analysis of oxide surface titration data. Geochim Cosmochim Acta 61:2801–2826
SAS Institute (2012) SAS 9.3 language reference: concepts. 2nd ed. SAS Inst., Cary, NC
Seber GAF, Wild CJ (1989) Nonlinear regression. John Wiley & Sons, New York
Shuai X (2018) Surface reactions of phosphorus extracted by the modified Truog method to predict soil intrinsic pools. Soil Sci Soc Am J 82:1140–1146
Smit W (1986) Surface complexation constants of the site binding model. J Colloid Interface Sci 113:288–291
Sparks DL (2002) Environmental soil chemistry, 2nd edn. Academic Press, San Diego, CA
Sposito G (1984) The surface chemistry of soils. Oxford Univ. Press, New York
Sposito G (2004) The surface chemistry of natural particles. Oxford Univ. Press, New York
Sverjensky D (2001) Interpretation and prediction of triple-layer model capacitances and the structure of the oxide-electrolyte-interface. Geochim Cosmochim Acta 65:3643–3655
Uehara G, Gillman G (1981) The mineralogy, chemistry, and physics of tropical soils with variable charge clays. Westview Press, Boulder CO
Van Riemsdijk WH, Bolt GH, Koopal LK, Blaakmeer J (1986) Electrolyte adsorption on heterogeneous surfaces: adsorption models. J Colloid Interface Sci 109:219–228
Wei SY, Tan WF, Liu F, Zhao W, Weng LP (2014) Surface properties and phosphate adsorption of binary systems containing goethite and kaolinite. Geoderma 213:478–484
Weng LP, Van Riemsdijk WH, Hiemstra T (2012) Factors controlling phosphate interaction with iron oxides. J Envrion Quality 41:528–635
Westall JC (1986) Reactions at the oxide-solution interface: chemical and electrostatic models. ACS Symp Ser 323:54–78
Westall J, Hohl H (1980) A comparison of electrostatic models for the oxide/solution interface. Adv Colloid Interface Sci 12:265–294
Yates DE, Healy TW (1975) Mechanism of anion adsorption at the ferric and chromic oxide/water interfaces. J Colloid Interface Sci 52:222–228
Yates DE, Levine S, Healy TW (1974) Site-binding model of the electrical double layer at the oxide/water interface. J Chem Sot Faraday Trans 170:1807–1818
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Shuai, X. New structure of electrical double layer to modify triple-layer model at oxide–water interface. J Soils Sediments 23, 880–890 (2023). https://doi.org/10.1007/s11368-022-03353-2
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DOI: https://doi.org/10.1007/s11368-022-03353-2