Testing percolation theory in the laboratory: Measuring the critical exponents and fractal dimension during gelation

Abstract

Real-time fluorescence measurements have been developed for measuring the fractal dimension d_{f} and critical exponents gamma and beta simultaneously during the sol-gel transition of acrylamide bisacrylamide cross-linking copolymerization. We observed that d_{f} passes through a minimum value of approximately 2.5 at a critical time t_{c} and crossover to 3 above it. The exponents gamma and beta , measured at t_{c} , were found to be around 1.8 and 0.45, respectively. All parameters d_{f} , beta , and gamma measured at the critical point t_{c} agree with three-dimensional percolation results.