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

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