Colloids and Surfaces A: Physicochemical and Engineering Aspects 183 – 185 (2001) 203 – 212 Stress relaxation in model transient networks: percolation and rearrangement of the crosslinks Mohammed Filali a , Eric Michel b , Serge Mora b , Franc ¸ois Molino b , Gre ´goire Porte b, * a Laboratoire de Physique des Solides, Faculte ´ des Sciences Dhar Mehraz, BP 1796 Atlas, Fes, Morocco b Groupe de Dynamique des Phases Condense ´es, UMR 5581 du CNRS, Case 026, Uniersite ´ Montpellier II, 34095, Montpellier Cedex 05, France Abstract 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  R are characterized accurately as function of the concentration of the polymer. Both G (0) and  R 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. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Model transient networks; Stress relaxation; Numerical simulations www.elsevier.nl/locate/colsurfa 1. Introduction The notion of temporary network is at the basis of some of the earliest attempts to understand the rheological behaviour of strongly viscoelastic ma- terials [1]. In such models, the immediate elastic response to an applied strain arises from the existence of crosslinks capable of sustaining tem- porarily shear stresses; while the liquid-like be- haviour at long times is determined by the finite life time of the cross links. Appropriate realiza- tions of such model structures are provided by semidilute solutions of telechelic polymers [2 – 7]. As an example, water soluble polymers with hy- drophobic end blocks (or conversely a liposoluble polymer with hydrophilic end stickers) indeed ex- hibit viscoelastic behaviour at moderate concen- tration in water (respectively in oil). The spontaneous tendency of the end caps to self * Corresponding author. E-mail address: porte@gdpc.univ-montp2.fr (G. Porte). 0927-7757/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII:S0927-7757(01)00548-9