Stochastic simulations of micellization kinetics

Journal of Chemical Physics

Volumn 111, Issue 9, 1999, Pages 4310-4318

  Mavelli, F ^a   Maestro, M ^b  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF BARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011285741     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.479729     Document Type: Article

References (42)

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3. On the autopoietic micelles see for instance (a) Y. A. Chizmadzhew, M. Maestro, and F. Mavelli, Chem. Phys. Lett. 2267, 56 (1994);
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9. It has been shown that a maximum in the slow micellar relaxation time (which is related to the micellar stability) correlates to reduced formability, a minimum in fabric wetting rate and a maximum in oil solubilization rates in solutions of micelles, see S. G. Oh, P. D. T. Huibers, and D. O. Shah, in Dynamic Properties of Interfaces and Association Structures, edited by V. Pillai and D. O. Shah (AOCS Press, New York, 1996).
10. The mechanism in scheme 1 is valid for nonionic surfactants, but it can be used for charged amphiphiles if counterions adjust almost instantaneously to the formation of ennamers.
11. R. Ginnel, Association Theory (Elsevier, Amsterdam, 1979).
12. Throughout this paper the backslash "\" will be used to symbolize the integer quotient of a division between integer numbers, for instance "i\2" means "i/2" if i is even or "(i-1)/2" if i is odd.
13. Exact analytical solutions exist only for the Smoluchowsky equation used for an irreversible coagulation. These solutions hold only for particular dependence of the kinetic constants on the aggregation number and very simple starting conditions; see for instance: K. K. Sabelfeld, S. V. Rogasinsky, A. A. Kolodko, A. I. Levykin, Monte Carlo Methods and Appl. 2, 41 (1996).
14. One of the main problems Is that the maximum size of ennamers are in principle unknown and consequently the differential equation set must remain open.
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22. j will be used in equations valid only for micelles (see next section).
23. μ-dt as the average probability, to first order in dt, that a particular combination of reactant molecules in the considered system will react according to the stoichiometry of the μ reaction.
24. The relationship between macroscopic kinetic constants and the stochastic rate is a very complex matter. In this paper we consider that both the deterministic and the stochastic approach are valid to describe the time evolution of self-assembly chemical systems and that they must give the same outcomes in the thermodynamic limits, i.e., when the molecular populations of the species increase to high values. So, relation (5) can be easily obtained assuming that the average of the product of all the concentrations involved in a certain reaction equals the product of the concentration averages.
25. It has been shown that assuming a reversible stepwise association model the linearity of the kinetic constants on the ennamer size is a necessary condition to predict an exponential relaxation of the monomer after a sudden displacement from equilibrium: M. Almgren, E. A. G. Aniansson, K. Holmaker, Chem. Phys. 19, 1 (1977).
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29. It should be clear that the ennamer size distribution is proportional to the ratio between the surfactant size distribution φ and the aggregation number i.
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