Linear viscoelasticity of wormlike micelles: a comparison of micellar reaction kinetics

Stress relaxation in worm-like micelles and other “living polymers” is governed by an interplay between simple reptation and intermicelle reactions. A simple model of stress relaxation is used in which the linear viscoelastic functions can be written as averages over a certain one-dimensional stochastic process. A detailed numerical study was recently made for the case when scission and end to end recombination reactions are present (Turner M. S. and Cates M. E., Langmuir 7 (1991) 1590). In the present work we use the same approach to study other reaction mechanisms. We consider both end-interchange, where the end of one chain “bites” into the sequence of another, and bond-interchange, where chains exchange material by formation of a fourfold-coordinated intermediate. We find that end-interchange results in quantitatively similar viscoelastic behaviour to the reversible scission case: for τbreak τᵣₑₚ the terminal time τ is much reduced from the reptation value and the spectrum becomes monoexponential with . Here τrep is the reptation time of a hypothetical unbreakable chain of the average length, and τbreak a suitably defined micellar scission time. For the case of bond-interchange we predict qualitatively similar behaviour, although the terminal time τ is less strongly affected than for the other two reaction schemes; in the regime τbreak≪τrep we predict τ∼τbreak1/3τrep2/3. This result is also confirmed in the numerical study. Finally we include an idealised treatment of constraint release which suggests that the effect of tube renewal on stress relaxation is relatively weak in these systems. We use the Cole-Cole representation of the frequency-dependent modulus G*(ω), which provides a sensitive method of probing the relaxation. Comparison of our calculated plots with experimental viscoelastic data may provide, in principle, a method for determining the reaction mechanisms present in any given system.