단분산 마이셀 용액의 통계 역학적 모델

강계홍; 임경희; Kye-Hong Kang; Kyung-Hee Lim

Korean Chemical Engineering Research, Vol.46, No.4, 824-832, August, 2008

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단분산 마이셀 용액의 통계 역학적 모델

A Statistical-Mechanical Model for Solutions of Monodisperse Micelles

강계홍^{1, 2}, 임경희 ^{1, †}

¹중앙대학교 화학공학과, 156-756 서울시 동작구 흑석동 221
²(주) 아모레퍼시픽 기술연구원, 449-729 경기도 용인시 기흥구 보라동 314-1

Kye-Hong Kang^{1, 2}, and Kyung-Hee Lim^{1, †}

¹Department of Chemical Engineering, Chung-Ang Uiversity, 221 Huksuk-dong Dongjak-gu, Seoul 156-756, Korea
²R&D Center, Amorepacific Corporation, 314-1 Bora-dong Giheung-gu, Yongin-si Gyeonggi-do 449-729, Korea

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초록

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.

A 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 XCMC= A+BT+C/T+DlnT with XCMC 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.

Keywords:Statistical-Mechanical Model;Micellization;Critical Micelle Concentration(CMC);Temperature Dependence;Monodisperse Micelle

[References]

Muller N, Langmuir, 9, 96 (1993)
Kim HU, Lim KH, Colloids Surf. A: Physicochem. Eng. Asp., 235, 121 (2004)
Kang KH, Kim HU, Lim KH, Colloids Surf. A: Physicochem. Eng. Asp., 189, 113 (2001)
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Israelachvili JN, Mitchel DJl, Ninham BN, J. Chem. Soc.-Faraday Trans., 72, 1525 (1976)
Gunnarsson G, Jnsson B, Wennerstrm H, J. Phys. Chem., 84(23), 3114 (1980)
Jnsson B, Wennerstrm H, J. Phys. Chem., 91(2), 338 (1987)
Wennerstrm H, in Friberg, S. E. and B. Lindman, (Ed.), Organized Solutions, Surfactant Science Series Vol. 44, Marcel Dekker, New York (1992)
Hoeve CAJ, Benson GC, J. Phys. Chem., 61(9), 1149 (1957)
Poland DC, Scheraga HA, J. Phys. Chem., 69(7), 2431 (1965)
Poland DC, Scheraga HA, J. Phys. Chem., 69(12), 4425 (1965)
Poland DC, Scheraga HA, J. Colloid Interface Sci., 21, 273 (1966)
Nemethy G, Scheraga HA, J. Phys. Chem., 66(10), 1773 (1962)
Ruckenstein E, Nagarajan R, J. Phys. Chem., 79(24), 2622 (1975)
Ruckenstein E, Nagarajan R, J. Colloid Interface Sci., 57(2), 388 (1976)
Ruckenstein E, Nagarajan R, J. Colloid Interface Sci., 60(2), 221 (1977)
Lim KH, Kang KH, Lee MJ, J. Korean Ind. Eng. Chem., 17(6), 625 (2006)
Nemethy G, Scheraga HA, J. Chem. Phys., 36(12), 3382 (1962)

[Related Articles]

[1] Muller N, Langmuir, 9, 96 (1993)

[2] Kim HU, Lim KH, Colloids Surf. A: Physicochem. Eng. Asp., 235, 121 (2004)

[3] Kang KH, Kim HU, Lim KH, Colloids Surf. A: Physicochem. Eng. Asp., 189, 113 (2001)

[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 JN, Mitchel DJl, Ninham BN, J. Chem. Soc.-Faraday Trans., 72, 1525 (1976)

[7] Gunnarsson G, Jnsson B, Wennerstrm H, J. Phys. Chem., 84(23), 3114 (1980)

[8] Jnsson B, Wennerstrm H, J. Phys. Chem., 91(2), 338 (1987)

[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 CAJ, Benson GC, J. Phys. Chem., 61(9), 1149 (1957)

[11] Poland DC, Scheraga HA, J. Phys. Chem., 69(7), 2431 (1965)

[12] Poland DC, Scheraga HA, J. Phys. Chem., 69(12), 4425 (1965)

[13] Poland DC, Scheraga HA, J. Colloid Interface Sci., 21, 273 (1966)

[14] Nemethy G, Scheraga HA, J. Phys. Chem., 66(10), 1773 (1962)

[15] Ruckenstein E, Nagarajan R, J. Phys. Chem., 79(24), 2622 (1975)

[16] Ruckenstein E, Nagarajan R, J. Colloid Interface Sci., 57(2), 388 (1976)

[17] Ruckenstein E, Nagarajan R, J. Colloid Interface Sci., 60(2), 221 (1977)

[18] Lim KH, Kang KH, Lee MJ, J. Korean Ind. Eng. Chem., 17(6), 625 (2006)

[19] Nemethy G, Scheraga HA, J. Chem. Phys., 36(12), 3382 (1962)