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Finite ion size effect on the stability ratio of colloidal dispersions

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Abstract

An algorithm is presented for calculating the stability ratio of a dispersion of spherical colloidal particles on the basis of the Derjaguin–Landau–Verwey–Overbeek theory. The finite ion size effect is taken into account by using the approximate form of ionic activity coefficients given by Carnahan and Starling. A simple approximate analytic expression for the stability ratio without involving numerical integration is also derived.

Finite ion size effect on the stability ratio of colloidal dispersions.

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References

  1. Fuchs N (1934) Über die Stabilität und Aufladung der Aerosole. Z Phys 89:736–743

    Google Scholar 

  2. Reerink H, Overbeek JTG (1954) The rate of coagulation as a measure of the stability of silver iodide sols. Disc Faraday Soc 18:74–84

    CAS  Google Scholar 

  3. McGown DNL, Parfitt GD (1967) Improved theoretical calculation of the stability ratio for colloidal systems. J Phys Chem 71:449–450

    CAS  Google Scholar 

  4. Spielman LA (1970) Viscous interactions in Brownian coagulation. J Colloid Interface Sci 33:562–571

    CAS  Google Scholar 

  5. Honig EP, Roebersen GJ, Wiersema PH (1971) Effect of hydrodynamic interaction on the coagulation rate of hydrophobic colloids. J Colloid Interface Sci 36:97–109

    CAS  Google Scholar 

  6. Ruckenstein E (1978) Reversible rate of adsorption or coagulation of Brownian particles - effect of the shape of the interaction potential. J Colloid Interface Sci 66:531–543

    CAS  Google Scholar 

  7. Marmur A (1979) A kinetic theory approach to primary and secondary minimum coagulations and their combination. J Colloid Interface Sci 72:41–48

    CAS  Google Scholar 

  8. Prieve DC, Ruckenstein E (1980) Role of surface chemistry in primary and secondary coagulation and heterocoagulation. J Colloid Interface Sci 73:539–555

    CAS  Google Scholar 

  9. Kostoglou M, Karabelas AJ (1991) Procedures for rapid calculation of the stability ratio of colloidal dispersions. J Colloid Interface Sci 142:297–301

    CAS  Google Scholar 

  10. Gisler T, Borkovec M (1993) Stability ratios for doublet formation and for deposition of colloidal particles with arbitrary interaction potentials: an analytical approximation. Langmuir 9:2247–2249

    CAS  Google Scholar 

  11. Dukhin SS (1995) Electrochemical characterization of the surface of a small particle and nonequilibrium electric surface phenomena. Adv Colloid Interf Sci 61:17–49

    CAS  Google Scholar 

  12. Behrens AH, Borkovec M (2000) Influence of the secondary interaction energy minimum on the early stages of colloidal aggregation. J Colloid Interface Sci 225:460–465

    CAS  PubMed  Google Scholar 

  13. Snoswell DRE, Duan J, Fornasiero D, Ralston J (2003) Colloid stability and the influence of dissolved gas. J Phys Chem B 107:2986–2994

    CAS  Google Scholar 

  14. Dukhin SS, Mishchuk NA, Loglio G, Liggieri L, Miller R (2003) Coalescence coupling with flocculation in dilute emulsions within the primary and/or secondary minimum. Adv Colloid Interf Sci 100-102:47–81

    CAS  Google Scholar 

  15. Wu KL, Lai SK (2005) Theoretical studies of the early stage coagulation kinetics for a charged colloidal dispersion. Langmuir 21:3238–3246

    CAS  PubMed  Google Scholar 

  16. Urbina-Villalba G, García-Sucre M (2005) Role of the secondary minimum on the flocculation rate of nondeformable droplets. Langmuir 21:6675–6687

    CAS  PubMed  Google Scholar 

  17. Guaregua MJA, Squitieri E, Mujica V (2006) A computational study of the stability ratios of spherical colloidal particles. J Mol Struct THEOCHEM 76:165–170

    Google Scholar 

  18. Guaregua MJA, Squitieri E, Mujica V (2009) A general algorithm using Mathematica 2.0 for calculting dlvo potential interactions and stability ratios in spherical colloidal particle systems. J Comput Meth in Science and Engineering 9:223–240

    CAS  Google Scholar 

  19. Guaregua MJA, Squitieri E, Mujica V (2009) Correlations between the maximum parameters of DLVO interaction energy curves and the electrolyte concentration. J Comput Meth in Science and Engineering 9:241–256

    CAS  Google Scholar 

  20. Chen KL, Smith BA, Ball WP, Fairbrother DH (2010) Assessing the colloidal properties of engineered nanoparticles in water: case studies from fullerene C60 nanoparticles and carbon nanotubes. Environ Chem 7:10–27

    CAS  Google Scholar 

  21. Rahn-Chique K, Puertas AM, Romero-Cano MS, Rojas C, Urbina-Villalba G (2012) Nanoemulsion stability: experimental evaluation of the flocculation rate from turbidity measurements. Adv Colloid Interf Sci 178:1–20

    CAS  Google Scholar 

  22. Ohshima H (2013) Simple analytic solution of the rate equations for the early-stage aggregation kinetics of colloidal particles. Colloid Polym Sci 291:3013–3016

    CAS  Google Scholar 

  23. Ohshima H (2014) Approximate analytic expression for the stability ratio of colloidal dispersions. Colloid Polym Sci 292:2269–2274

    CAS  Google Scholar 

  24. Urbina-Villalba G, García-Valera N, Rahn-Chique K (2015) Theoretical prediction and experimental measurement of the mixed flocculation/coalescence rate of ionic hexadecane-in-water nano-emulsions. RCEIF 4:1–17

    Google Scholar 

  25. Kobayashi M, Yuki S, Adachi Y (2016) Effect of anionic surfactants on the stability ratio and electrophoretic mobility of colloidal hematite particles. Colloids Surf A Physicochem Eng Asp 510:190–197

    CAS  Google Scholar 

  26. Lachin K, Le Sauze N, Raimondi NDM, Aubin J, Cabassud M, Gourdon C (2019) Estimation of characteristic coagulation time based on Brownian coagulation theory and stability ratio modeling using electrokinetic measurements. Chem Eng J 369:919–827

    Google Scholar 

  27. Derjaguin BV, Landau DL (1941) Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochim USSR 14:633–662

    Google Scholar 

  28. Verwey EJW, Overbeek JTG (1948) Theory of the stability of lyophobic colloids. Elsevier/Academic Press, Amsterdam

    Google Scholar 

  29. Ohshima H (1995) Effective surface potential and double-layer interaction of colloidal particles. J Colloid Interface Sci 174:45–52

    CAS  Google Scholar 

  30. Delgado AV (ed) (2000) Electrokinetics and electrophoresis. Dekker, New York

    Google Scholar 

  31. Lyklema J (2005) Fundamentals of interface and colloid science, Volume IV, Chapter 3, Elsevier/Academic Press, Amsterdam

  32. Spasic A, Hsu J-P (eds) (2005) Finely dispersed particles: Micro-, nano-, and atto-engineering. CRC Press, Boca Raton

  33. Ohshima H (2006) Theory of colloid and interfacial electric phenomena. Elsevier, Amsterdam

    Google Scholar 

  34. Adamczyk Z, Warszyński P (1996) Role of electrostatic interactions in particle adsorption. Adv Colloid Interf Sci 63:41–149

    CAS  Google Scholar 

  35. Das S, Chakraborty S (2011) Steric-effect-induced enhancement of electrical-double-layer overlapping phenomena. Phys Rev E 84:012501

    Google Scholar 

  36. Das S (2012) Electric-double-layer potential distribution in multiple-layer immiscible electrolytes: effect of finite ion sizes. Phys Rev E 85:012502

    Google Scholar 

  37. Andrews J, Das S (2015) Effect of finite ion sizes in electric double layer mediated interaction force between two soft charged plates. RSC Adv 5:46873–46880

    CAS  Google Scholar 

  38. Ohshima H (2016) An approximate analytic solution to the modified Poisson-Boltzmann equation: effects of ionic size. Colloid Polym Sci 294:2121–2125

    CAS  Google Scholar 

  39. Ohshima H (2017) Approximate analytic expressions for the electrostatic interaction energy between two colloidal particles based on the modified Poisson-Boltzmann equation. Colloid Polym Sci 295:289–296

    CAS  Google Scholar 

  40. Ohshima H (2018) Approximate expressions for the surface charge density/surface potential relationship and double-layer potential distribution for a spherical or cylindrical colloidal particle based on the modified Poisson-Boltzmann equation. Colloid Polym Sci 296:647–652

    CAS  Google Scholar 

  41. Ohshima H (2019) Finite ion size effect on the force and energy of the double-layer interaction between two parallel similar plates at arbitrary separations in an electrolyte solution. Colloid Polym Sci 297:35–43

    CAS  Google Scholar 

  42. Carnahan NF, Starling KE (1969) Equation of state for nonattracting rigid spheres. J Chem Phys 51:635–636

    CAS  Google Scholar 

  43. Attard P (1993) Simulation of the chemical potential and the cavity free energy of dense hard sphere fluids. J Chem Phys 98:2225–2231

    CAS  Google Scholar 

  44. Isralachvili JN (2011) Intermolecular and surface forcesThird edn. Academic/Elsevier, Amsterdam, p 79

    Google Scholar 

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  1. Faculty of Pharmaceutical Sciences, Tokyo University of Science, 2641 Yamazaki Noda, Chiba, 278-8510, Japan

    Hiroyuki Ohshima

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  1. Hiroyuki Ohshima
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Ohshima, H. Finite ion size effect on the stability ratio of colloidal dispersions. Colloid Polym Sci 298, 1113–1117 (2020). https://doi.org/10.1007/s00396-020-04687-4

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  • DOI: https://doi.org/10.1007/s00396-020-04687-4

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