A NONLINEAR-THEORY OF TRANSIENTS FOLLOWING STEP TEMPERATURE-CHANGES IN POLYMER BLENDS

A nonlinear theory for the scattering intensity I(q,t) during spinodal decomposition, dissolution (reverse quench), and transients following step temperature changes within the one-phase region is developed including coupling among density modes. It is shown analytically that the peak position q(m)(t) of I(q,t) behaves as q(m)(t) approximately t-1/3 asymptotically during spinodal decomposition, and I(q,t) scales approximately as I(q,t) approximately q(m)(t)-3y2/(2 + y6), where y = q/q(m)(t), with a calculable temperature-dependent proportionality constant. The possibility of a power law q(m)(t) approximately t-1/2 during dissolution after a reverse quench within an intermediate time interval is demonstrated. An asymptotic power law q(m)(t) approximately t1/3 during transients following step temperature changes within the one-phase region is obtained. A discussion of various interpretations of the fluctuation-dissipation relation in nonlinear systems is also included.