Small-angle x-ray scattering study of kinetics of spinodal decomposition in N-isopropylacrylamide gels

We present synchrotron-based time-resolved small-angle x-ray scattering (SAXS) measurements of spinodal decomposition in a covalently cross-linked N-isopropylacrylamide gel. The range of wave numbers examined is well beyond the position of the maximum in the structure factor S(q,t). The equilibrium structure factor is described by the sum of a Lorentzian and a Gaussian. Following a temperature jump into the two phase region, the scattered intensity increases with time and eventually saturates. For early times the linear Cahn-Hilliard-Cook (CHC) theory can be used to describe the time evolution of the scattered intensity. From this analysis we found that the growth rate R(q) is linearly dependent on q(2), in agreement with mean-field theoretical predictions. However the Onsager transport coefficient Lambda(q) approximately q(-4), which is stronger than the q dependence predicted by the mean-field theory. We found that the growth rate R(q)>0, even though the wave numbers q probed by SAXS are greater than sqrt[2]q(m) where q(m) is the position of the peak of S(q,t), also in agreement with the mean-field predictions for a deep quench. We have also examined the range of validity of the linear CHC theory, and found that its breakdown occurs earlier at higher wave numbers. At later times, a pinning of the structure was observed. The relaxation to a final, microphase-separated morphology is faster and occurs earlier at the highest wave numbers, which probe length scales comparable to the average distance between crosslinks.