Elastic properties at the sol-gel transition

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Abstract
We study the elasticity behaviour at the sol-gel transition with a percolation dynamic model via computer simulations on a square lattice. From the fluctuations in the center-of-mass motion of the percolating cluster we determine the critical behaviour of the macroscopic elastic constant of the gel phase, growing above the gel point with a critical exponent ' 2:7 0:1. We also study time autocorrelation functions and nd that the relaxation times diverge, as the percolation threshold is approached from below, with a critical exponent s' 1:9 0:1. In a polymeric solution the bond formation among dierent molecules can be induced leading to the constitution of a macroscopic polymeric structure, the gel phase. This phenomenon, which is called the sol-gel transition, produces a change in the viscoelastic properties of the system: it is characterized by the rapidly increasing viscosity in the sol and by the onset of the elastic behaviour of the gel phase (1, 2). This transition is typical of polymer phenomenology and can be observed in many dierent materials of great interest. It represents an aspect of the viscoelastic behaviour of polymer systems which is not fully understood. Thus, in the frame of the actual interest in the polymeric materials and their phenomenology, from non-Newtonian behaviours to gelation and glass transition, the study of sol-gel transition is the subject of many recent works which investigate dierent aspects and study its main features from the experimental and theoretical point of view (3). We here consider the sol-gel transition in the case of strong gelation, where bonds are permanent and the transition threshold is sharply dened. In the experiments the viscosity coecient in the sol is a function of the extent of the polymerization process diverging at the gel point with an exponent s, whereas the elastic modulus of the gel phase starts growing at the gel point with a critical exponent t .T he experimental value of these exponents is still unclear as the results are quite scattered and a coherent picture of the critical dynamic properties has not been obtained yet (3-5).