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 polyme r. The time resolved stress response to moderate step shear strains is almo st Maxwellian: so the instantaneous shear modulus G(0) and the terminal rel axation time tau (R) are characterized accurately as function of the concen tration of the polymer. Both G(0) and tau (R) vanish below a finite concent ration of polymer: this is the signature of a percolation threshold. We sho w that, if we keep in the frame of the mean field interpretation of the kin etics 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 assumpti ons of the classical description: (i) the network homogeneously deforms aff inely at all scales; and (ii) broken links no longer participate to the str ess history. To illustrate our views, we perform simple numerical simulatio ns where these assumptions are removed: they produce relaxations which comp are well to the experiments. (C) 2001 Elsevier Science B.V. All rights rese rved.