A unifying approach to relaxation properties of chemical and colloidal gels

Abstract

We study the viscoelastic properties and the relaxation process in a gelling system by means of a minimal statistical mechanics model. The model is based on percolation and bond-fluctuation dynamics. By opportunely varying some model parameter we are able to describe a crossover from the chemical gelation behaviour to dynamics more typical of colloidal systems. The results suggest a novel connection linking classical gelation, as originally described by Flory, to more recent results on colloidal systems. I IntroductionThe gelation transition transforms a solution of polymeric molecules, the sol, which is essentially a viscous fluid, into an elastic solid. This happens when the bond formation between different molecules is induced and it is phenomenologically characterized by the divergence of the viscosity coefficient in the sol and by the appearence of an elastic response in the gel phase. This corresponds to the constitution inside the sol of a macroscopic polymeric structure [1], which characterizes the gel phase. This polymerization process leading to the formation of an interconnected stress-bearing network in the system is then responsible on one hand for the divergence of the viscosity coefficient η and on the other hand for the growing of a non-zero elastic modulus Y . The critical growth of the connectivity can be straightforwardly interpreted by means of a percolation transition, which starting from the work of Flory and Stockmayer [1,2,3] is practically considered as the basic model for gelation transition. Depending on the particular system the gelation can be observed by lowering the temperature, or as function of time or else of the monomer concentration in the sol. In any case close to the gelation transition the viscosity coefficient grows with a power law behaviour characterized by a critical exponent k. The onset of the elastic response in the system corresponds to a power law increasing of the elastic modulus described by a critical exponent f .Approaching the gelation threshold complex polymeric structures are formed, characterized by different relaxation processes over many different lenght scales. Infact the relaxation functions in most of the experiments display a long time stretched exponential decay ∼ e −( t τ 0 ) β in the critical solution approaching the gelation threshold [4,5,6,7]. The relaxation process becomes critically slow at the gel point, where the onset of a power law decay is typically observed.This complex relaxation somehow resembles what is typically observed in a supercooled liquid approaching the glass transition [8] and in general this form is interpreted in terms of many decay processes, occurring over different time scales. One has to recognize that here the relaxation process is actually controlled by the growth of the connectivity. At the gelation threshold τ 0 → ∞ and the relaxation functions decay as a power law [4,5]. In the gel phase the relaxation behaviour displays a variety of complex behaviours depending on the system. These features are actually common to ...