Stress relaxation in model transient networks: percolation and rearrangement of the crosslinks

We investigate model transient networks consisting of oil in water droplet microemulsions into which we add various proportions of a telechelic polymer. The time resolved stress response to moderate step shear strains is almost Maxwellian: so the instantaneous shear modulus G(0) and the terminal relaxation time τR are characterized accurately as function of the concentration of the polymer. Both G(0) and τR vanish below a finite concentration of polymer: this is the signature of a percolation threshold. We show that, if we keep in the frame of the mean field interpretation of the kinetics of transient networks, there is a contradiction between the notion of percolation on the one side and the smooth stress relaxation on the other side. We argue that this contradiction arises from two simplifying assumptions of the classical description: (i) the network homogeneously deforms affinely at all scales; and (ii) broken links no longer participate to the stress history. To illustrate our views, we perform simple numerical simulations where these assumptions are removed: they produce relaxations which compare well to the experiments.