Growth and decay of concentration fluctuations in polymer–polymer mixtures

Abstract

AbstractA computer simulation based on the Cahn–Hilliard nonlinear diffusion equation, developed in the field of metallurgy, is applied to the demixing behavior of a polymer–polymer mixture. The simulation is a one‐dimensional version. Spatially periodic concentration fluctuations appear at a very early stage and evolve with the wave number almost constant. Later some waves are absorbed into neighboring ones, resulting in a decrease in the average wave number of the concentration fluctuation. Thus, characteristic phenomena in the demixing are successfully described by the computer simulation. Furthermore, the simulated time variation of wave number agrees with experimental results in the literature. The analysis is extended to two‐step quenching: after a homogeneous mixture undergoes the first temperature‐jump from the single‐phase region to the two‐phase region of the phase diagram, the system is allowed to demix isothermally for a time, and then the demixed system undergoes the second jump to deeper or shallower quench. When the quench depth of the second jump (ΔT2) is smaller than half the first depth (ΔT1), the concentration fluctuation as developed under ΔT1 decays with time after the second jump. When ΔT2 is between ΔT1 and (ΔT1/2), the fluctuation decays slightly after the second jump and then increases. When the second jump is to a deeper quench (ΔT2 > ΔT1), a new fluctuation of short wavelength is superimposed on the previously developed one.