Evidence for diffusion-controlled recombination kinetics in model wormlike micelles

J. T. Padding; E. S. Boek

doi:doi:10.1209/epl/i2003-10246-4

Europhys. Lett., 66 (5) , pp. 756-762 (2004)
DOI: 10.1209/epl/i2003-10246-4

Evidence for diffusion-controlled recombination kinetics in model wormlike micelles

J. T. Padding^{1, 2} and E. S. Boek¹

¹ Schlumberger Cambridge Research, High Cross Madingley Road, Cambridge CB3 0EL, UK
² Department of Chemistry, University of Cambridge Lensfield Road, Cambridge CB2 1EW, UK

(Received 19 December 2003; accepted in final form 24 March 2004)

Abstract
We study the recombination kinetics and stress relaxation in a generic reversible polymer model, which is believed to resemble a wormlike micellar system. We find evidence that, at high concentrations, the recombination kinetics in this model cannot be described by a mean-field approach, but is diffusion-controlled and dominated by self-recombination events. We observe that the long-time stress relaxation of unentangled chains is proportional to $\sqrt{1/t}\exp[-t/\tau_{\ab{relax}}]$ , with a relaxation time given by $\tau_{\ab{relax}}= (t_h^{2/3}\tau_{\langle L\rangle}^{1/3})$ , where t_h is the average diffusion time to a different chain end, and $\tau_{\langle L\rangle}$ is the characteristic relaxation time of a system of "dead" polymers of length equal to the average micellar length. A recombination activation barrier is needed to drive the system towards mean-field behaviour. This, in its turn, is often required in order to realistically model the rheology and dynamics of wormlike micelles.

PACS
82.20.Wt - Computational modeling; simulation.
83.80.Qr - Surfactant and micellar systems, associated polymers.

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