Improved kinetic description of fast relaxation of cylindrical micelles

• Published in: Physica A 2019-03, Vol.518, p.299-311
• Main Authors: Adzhemyan, L.Ts, Eroshkin, Yu.A., Shchekin, A.K., Babintsev, I.A.
• Format: Article
• Language: English
• Subjects: Aggregation; Becker–Döring equation; Cylindrical micelles; Kinetics; Relaxation; Self-assembly and disassembly
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2018.11.057

On the basis of the linearized analytical and numerical kinetic description of stepwise aggregation of surfactant aggregates, the hierarchical relaxation times have been found for a polydisperse micellar system close and above the critical micellar concentration. The description was based on the difference and differential Becker–Döring kinetic equations with using a specific boundary condition and improved models for the attachment rates of surfactant monomers to cylindrical aggregates. Two models have been considered: the linear model for cylindrical aggregates and the attachment rate to elongated spheroidal aggregates. The rate of attachment of monomers to an elongated spheroidal aggregate was found explicitly as a function of the aggregation number. With applying the truncation techniques, the analytical solution of differential kinetic equations for fast relaxation of polydisperse micellar systems has been obtained for a linear model of the aggregation rate. In the case of the attachment rate for an elongated spheroidal aggregate, the semi-analytical solution has been found. •New approach to relaxation kinetics of cylindrical micelles is formulated.•The concentration dependence of fast relaxation times is described.•Models of the attachment rate to a cylindrical aggregate are analyzed.