An Asymptotic Theory for the Re-Equilibration of a Micellar Surfactant Solution
Abstract
Micellar surfactant solutions are characterized by a distribution of aggregates made up predominantly of premicellar aggregates (monomers, dimers, trimers, etc.) and a region of proper micelles close to the peak aggregation number, connected by an intermediate region containing a very low concentration of aggregates. Such a distribution gives rise to a distinct two-timescale re-equilibration following a system dilution, known as the $\tau_1$ and $\tau_2$ processes, whose dynamics may be described by the Becker–Döring equations. We use a continuum version of these equations to develop a reduced asymptotic description that elucidates the behavior during each of these processes.
MSC codes
Keywords
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
E. A. G. Aniansson and S. N. Wall, On the kinetics of step-wise micelle association, J. Phys. Chem., 78 (1974), pp. 1024–1030.
2.
E. A. G. Aniansson and S. N. Wall, Kinetics of step-wise micelle association and dissociation. Correction and improvement, J. Phys. Chem., 79 (1975), pp. 857–858.
3.
E. A. G. Aniansson, S. N. Wall, M. Almgren, H. Hoffmann, I. Kielmann, W. Ulbricht, R. Zana, J. Lang, and C. Tondre, Theory of the kinetics of micellar equilibria and quantitative interpretation of chemical relaxation studies of micellar solutions of ionic surfactants, J. Phys. Chem., 80 (1976), pp. 905–922.
4.
R. Becker and W. Döring, Kinetische behandlung der Keimbildung in ubersattigten dampfern, Ann. Phys., 24 (1935), pp. 719–752.
5.
D. M. Colegate, Structure-Kinetics Relationships in Micellar Solutions of Nonionic Surfactants, Ph.D. thesis, Durham University, Durham, UK, 2009.
6.
J. N. B. de Moraes and W. Figueiredo, Dynamical study of a micellar system, Phys. Status Solidi, 187 (2001), pp. 57–62.
7.
I. M. Griffiths, C. D. Bain, C. J. W. Breward, D. M. Colegate, P. D. Howell, and S. L. Waters, On the predictions and limitations of the model for reaction kinetics in micellar surfactant solutions, J. Coll. Int. Sci., 360 (2011), pp. 662–671.
8.
M. Jorge, Molecular dynamics simulation of self-assembly of n-Decyltrimethylammonium Bromide micelles, Langmuir, 24 (2008), pp. 5714–5725.
9.
J. Lang, C. Tondre, R. Zana, R. Bauer, H. Hoffmann, and W. Ulbricht, Chemical relaxation studies of micellar equilibriums, J. Phys. Chem., 79 (1975), pp. 276–283.
10.
G. Mohan and D. I. Kopelevich, A multiscale model for kinetics of formation and disintegration of spherical micelles, J. Chem. Phys., 128 (2008), 044905.
11.
M. J. Rosen, Surfactants and Interfacial Phenomena, John Wiley, New York, 2004.
12.
R. Nagarajan and E. Ruckenstein, Aggregation of amphiphiles as micelles or vesicles in aqueous media, J. Colloid Int. Sci., 71 (1979), pp. 580–604.
13.
R. Nagarajan and E. Ruckenstein, Theory of surfactant self-assembly: A predictive molecular thermodynamic approach, Langmuir, 7 (1991), pp. 2934–2969.
14.
S. Puvvada and D. Blankschtein, Molecular-thermodynamic approach to predict micellization, phase behavior and phase separation of micellar solutions. I. Application to nonionic surfactants, J. Chem. Phys., 92 (1990), pp. 3710–3724.
15.
M. Teubner, Theory of ultrasonic-adsorption in micellar solutions, J. Phys. Chem., 83 (1979), pp. 2917–2920.
16.
T. Yasunaga, K. Takeda, and S. Harada, Kinetic study of Sodium Dodecyl Sulfate micelle dissociation by a stopped-flow method, J. Colloid Int. Sci., 42 (1973), pp. 457–463.
Information & Authors
Information
Published In
Copyright
Copyright © 2012 Society for Industrial and Applied Mathematics.
History
Submitted: 22 July 2011
Accepted: 17 November 2011
Published online: 24 January 2012
MSC codes
Keywords
Authors
Metrics & Citations
Metrics
Citations
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited By
- Dynamics of particle chopping in blenders and food processorsJournal of Engineering Mathematics, Vol. 112, No. 1 | 6 August 2018
- Molecular modeling of ionic aggregates at several concentrations of SDS in aqueous solutionJournal of Molecular Liquids, Vol. 236 | 1 Jun 2017
- Full-time kinetics of self-assembly and disassembly in micellar solution via the generalized Smoluchowski equation with fusion and fission of surfactant aggregatesThe Journal of Chemical Physics, Vol. 145, No. 17 | 2 November 2016
- Molecular dynamics study of salt influence on transport and structural properties of SDS micellar solutionsFluid Phase Equilibria, Vol. 424 | 1 Sep 2016
- Diffusivities of species in ionic micellar solutions: Molecular dynamic simulationColloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 480 | 1 Sep 2015
- Multi-scale times and modes of fast and slow relaxation in solutions with coexisting spherical and cylindrical micelles according to the difference Becker-Döring kinetic equationsThe Journal of Chemical Physics, Vol. 141, No. 6 | 8 August 2014
- Kinetic modeling of self-aggregation in solutions with coexisting spherical and cylindrical micelles at arbitrary initial conditionsRSC Adv., Vol. 4, No. 93 | 1 January 2014
- Direct Observation of the Formation of Surfactant Micelles under Nonisothermal Conditions by Synchrotron SAXSJournal of the American Chemical Society, Vol. 135, No. 19 | 2 May 2013
- Adsorption kinetics of non-ionic surfactants in micellar solutions: effects of added chargeFaraday Discuss., Vol. 160 | 1 January 2013
- A new pathway for the re-equilibration of micellar surfactant solutionsSoft Matter, Vol. 9, No. 3 | 1 January 2013