Evolution of rheology during chemical gelation

Abstract

Rheology is a sensitive measure of the evolving molecular structure in a crosslinking polymer. Dynamic mechanical experiments in small amplitude oscillatory shear give the storage modulus G′(ω, p) and the loss modulus G″(ω, p) as a function of frequency ω. The extent of crosslinking, p(t), changes with reaction time. Dynamic mechanical experiments allow detection of the gel point (GP) and give a macroscopic description of the critical gel state (network polymer at GP). This critical gel state is used as a reference for describing the entire evolution of rheology. The most surprising discovery of these experiments was that critical gels exhibit stress relaxation in a power law, i. e. the relaxation modulus is given as G()=St ⁻ⁿ. The relaxation exponent, n, depends on network structure. The power law behavior is an expression of mechanical self similarity (fractal behavior). The range of self similarity is defined between an upper and a lower frequency limit. The lower frequency limit (reciprocal of characteristic relaxation time) corresponds to an upper scaling length, the correlation length, which is of the order of the linear size of the largest molecular cluster (of pre-gel) or of the largest remaining percolation cluster (of post-gel). High frequencies probe relaxation within single chains. The upper frequency limit corresponds to a lower scaling length, the glass length, which is given by the dimension of the molecular network units responsible for glassy behavior. The correlation length and, hence, the characteristic relaxation time increase in the approach of the gel point, diverge to infinity at the gel point, and then decrease again with increasing extent of crosslinking. The critical gel has no characteristic length or time scale. All observations are restricted to polymers at a temperature above the glass transition temperature and at frequencies much below the glass frequency.