Korean Chemical Engineering Research

The Korean Institute of Chemical Engineers (한국화학공학회)
권호 표지

A Statistical-Mechanical Model for Solutions of Monodisperse Micelles

단분산 마이셀 용액의 통계 역학적 모델

  • Kang, Kye-Hong (Department of Chemical Engineering, Chung-Ang Uiversity) ;
  • Lim, Kyung-Hee (Department of Chemical Engineering, Chung-Ang Uiversity)
  • Received : 2008.05.19
  • Accepted : 2008.06.09
  • Published : 2008.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

micellar solution which is comprised of surfactant monomers, monodisperse micelles, and solvent(water) is studied from a statistical-mechanical point of view. The model examined in this article is for the ideal mixture of monomers, micelles, and solvent with the dielectric constant identical to that of solvent, which is an assumption common to continuum models. The model also reflects interactions between monomer and solvent molecule, and also between micelle and solvent molecule. The statistical-mechanical model under consideration yields ln $X_{CMC}=A+BT+C/T+D{\ln}T$ with $X_{CMC}$ being critical mcielle concentration (in mole fraction), being temperature, and A, B, C, D being constants which depend on the properties of the surfactant molecules. The statistical-mechanical model discussed in this article provides a theoretical basis on the thermal dependence of critical micelle concentration

용매인 물과 마이셀을 이루지 않고 있는 계면활성제 단분자를 포함한 단분산 마이셀 용액을 통계 역학적으로 고찰하였다. 본 논문에서 논의된 모델은 물, 계면활성제 단분자와 마이셀로 이루어진 계에 대한 것이며, 계면활성제 단분자의 분배 함수와 마이셀의 분배 함수는 용매인 물과의 서로 작용을 포함하고 있다. 이 모델에서 계는 용매의 유전 상수를 갖는 이상 기체로 가정하였는데 이것은 보통 유체를 연속체로 보는 관점과 일치한다. 이 모델은 임계 마이셀 농도(CMC)가 온도에 대해 ln CMC = A+BT+C/T+DlnT와 같이 변하는 결과를 제공하여 임계 마이셀 농도의 온도 의존성을 이론적으로 해석할 수 있는 기반을 구축하였다. 이 식에서 T는 온도이고 A, V, C, D는 마이셀을 이루는 계면활성제 분자의 성질에 의존하는 상수이다.

Keywords

References

  1. Muller, N., "Temperature Dependence of Critical Micelle Concentrations and Heat Capacities of Micellization for Ionic Surfactants," Lagmuir, 9, 96-100(1993) https://doi.org/10.1021/la00025a022
  2. Kim, H.-U. and Lim, K.-H., "A Model on the Temperature Dependence of Critical Micelle Concentration," Colloids Surf. A, 235, 121-128.(2004) https://doi.org/10.1016/j.colsurfa.2003.12.019
  3. Kang, K.-H., Kim, H.-U. and Lim, K.-H., "Effect of Temperature on Critical Micelle Concentration and Thermodynamic Potentials of Micellization of Anionic Ammonium Dodecyl Sulfate and Cationic Octadecyl Trimethyl Ammonium Chloride," Colloids Surf. A, 189, 113-121(2001) https://doi.org/10.1016/S0927-7757(01)00577-5
  4. Shinoda, K, in Shinoda., Nakagawa, T., Tamamushi, B. I. and Isemura, T., (Eds.), Colloidal Surfactants: Some Physicochemical Properties, Academic Press, New York(1963)
  5. Tanford, C., The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed., Krieger, Malabar(1980)
  6. Israelachvili, J. N., Mitchel, D. J. l. and Ninham, B. N., "Theory of Self-assembly of Hydrocarbon Amphiphiles into Micelles and Bilayers," J. Chem. Soc. Faraday Trans. 2, 72, 1525-1568(1976)
  7. Gunnarsson, G., Jnsson, B. and Wennerstrm, H., "Surfactant Association into Micelles. An Electrostatic Approach," J. Phys. Chem., 84(23), 3114-3121(1980) https://doi.org/10.1021/j100460a029
  8. Jnsson, B. and Wennerstrm, H., "Phase Equilibria in a Threecomponent Water-soap-alcohol System. A Thermodynamic Model," J. Phys. Chem., 91(2), 338-352(1987) https://doi.org/10.1021/j100286a021
  9. Wennerstrm, H., in Friberg, S. E. and B. Lindman, (Ed.), Organized Solutions, Surfactant Science Series Vol. 44, Marcel Dekker, New York(1992)
  10. Hoeve, C. A. J. and Benson, G. C., "On the Statistical Mechanical Theory of Micelle Formation in Detergent Solutions," J. Phys. Chem., 61(9), 1149-1158(1957) https://doi.org/10.1021/j150555a005
  11. Poland, D. C. and Scheraga, H. A., "Hydrophobic Bonding and Micelle Stability," J. Phys. Chem., 69(7), 2431-2442(1965) https://doi.org/10.1021/j100891a055
  12. Poland, D. C. and Scheraga, H. A., "Hydrophobic Bonding and Micelle Stability - Correction," J. Phys. Chem., 69(12), 4425-4426(1965)
  13. Poland, D. C. and Scheraga, H. A., "Hydrophobic Bonding and Micelle Stability; the Influence of Ionic Head Groups," J. Colloid Interface Sci., 21(3), 273-283(1966) https://doi.org/10.1016/0095-8522(66)90012-2
  14. Nemethy, G. and Scheraga, H. A., "The Structure of Water and Hydrophobic Bonding in Proteins. III. The Thermodynamic Properties of Hydrophobic Bonds in proteins," J. Phys. Chem., 66(10), 1773-1789(1962) https://doi.org/10.1021/j100816a004
  15. Ruckenstein, E. and Nagarajan, R., "Critical Micelle Concentration, Transition Point for Micellar Size Distribution," J. Phys. Chem., 79(24), 2622-2626(1975) https://doi.org/10.1021/j100591a010
  16. Ruckenstein, E. and Nagarajan, R., "On Critical Concentrations in Micellar Solutions," J. Colloid Interface Sci., 57(2), 388-390(1976) https://doi.org/10.1016/0021-9797(76)90213-7
  17. Ruckenstein, E. and Nagarajan, R., "Critical Micelle Concentration: A Transition Point for Micellar Size Distribution: A Statistical Thermodynamical Approach," J. Colloid Interface Sci., 60(2), 221-231(1977) https://doi.org/10.1016/0021-9797(77)90282-X
  18. Lim, K.-H., Kang, K.-H. and Lee, M.-J., "A Statistical-Mechanical Model on the Temperature Dependence of Critical Micelle Concentration," J. Korean Ind. Eng. Chem., 17(6), 625-632(2006)
  19. Lim, K.-H., Statistical Thermodynamics, Hantee Media, Seoul(2008)
  20. Nemethy, G. and Scheraga, H. A., "Structure of Water and Hydrophobic Bonding in Proteins. I. A Model for the Thermodynamic Properties of Liquid Water," J. Chem. Phys., 36(12), 3382-3400(1962) https://doi.org/10.1063/1.1732472