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.
Synchrotron-based time-resolved small-angle X-ray scattering was used to measure the early-stage spinodal decomposition kinetics in a highly viscous semidilute solution of polystyrene in dioctyl phthalate. Although strong nonlinearities in the kinetics were observed, a linear theory analysis could fit the evolution of the structure factor at short times and low wavenumbers. Nonlinearities become significant earlier at higher wavenumbers, which is consistent with recent computer simulation studies. From the linear theory analysis, the exponential relaxation rate of the structure factor R(q) was found to be linear in q 2 in the low-wavenumber region of the experiments, in agreement with mean-field theory for spinodal decomposition in polymer solutions. The wavenumber-dependent Onsager transport coefficient Λ(q), which is the Fourier transform of the nonlocal mobility in a polymer system, was determined to scale as q -4 . This q dependence, which is stronger than that predicted by existing theory, may be related to entanglement effects.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.