Critical Dynamics of Cross-Linked Polymer Chains near the Gelation Threshold

The dynamics of cross-linked polymer chains in solution near the gelation threshold has been investigated by dynamic light scattering. The time−intensity correlation function (ICF) was obtained as a function of initial monomer concentration, C NIPA, and cross-linker concentration, C BIS, where NIPA and BIS denote N -isopropylacrylamide and N, N ‘-methylenebis(acrylamide), respectively. The ICF exhibited a distinct change at a unique set of ( C NIPA, C BIS ) for a given R BIS (≡2 C BIS /( C NIPA + 2 C BIS )), i.e., (1) from a stretched exponential to a clear power-law behavior and (2) depression of the initial amplitude of ICF. According to the previous work [Norisuye et al. Macromolecules 1998, 31, 5316], this point was determined to be the gelation threshold, ( C NIPA th, C BIS th ). The locus of ( C NIPA th, C BIS th ) was a decreasing function of C NIPA th with the lower cutoff at C NIPA th ≈ C NIPA * and was in good agreement with the prediction of the site-bond percolation theory, where C NIPA * is the so-called chain overlap concentration. Several characteristic features at this connectivity transition point, such as anomaly in the scattered intensity and the power-law exponent, are discussed as critical dynamics.