Living Polymers & Wormlike Micellar Kinetics

Living polymers (wormlike micelles) are supramolecular assemblies that break and reform continuously. At equilibrium (Cates 1987), the length distribution is exponential: n(L) ∝ exp(−L/⟨L⟩), with mean length ⟨L⟩ ~ φ^{1/2} (κ₊/κ₋)^{1/2}. The viscoelastic response is described by the reptation-reaction model: a Maxwell fluid with single relaxation time τ = √(τ_rep · τ_break) where τ_break = 1/(κ₋⟨L⟩). Above the overlap concentration φ*, micelles become entangled. The storage modulus G' ~ φ² at high frequency reveals the plateau modulus. Remarkably, the loss tangent tan δ = G''/G' has a minimum value (Granek-Cates 1992), giving a semicircle in the Cole-Cole plot.