Phase separation with interfacial sliding in polymer systems

The phase separation of polymer blends with very large molecular weight far from the critical point is discussed, applying the stability problem of a thread. Far from the critical point the interfacial thickness is very narrow. Then different sorts of polymer molecules are not as entangled at the interface as like polymer molecules in the bulk. Thus the effective viscosity at the interfacial region is much smaller than in the bulk. Therefore the interface may easily slide against the shear stress. The instability of a liquid thread with interfacial sliding or interfacial friction is discussed. Then the most unstable mode is extracted to identify the growth rate of interconnected droplets under phase separation. The droplet radius R obeys the well-known growth law: R{∝}t for small R and large R, whereas it obeys a slower growth law R{∝}tᶜ with values of the effective kinetic exponent c=0.7--0.8 in the intermediate droplet size. This is qualitatively in agreement with experimental observations by Hashimoto and co-workers. On the other hand, the wave number kₘ for which the thread is most unstable obeys the decay law kₘ{∝}t^-3/4 for small R, whereas it obeys the decay law kₘ{∝}t^-1 for large R. This means that there are two length scales showing the invalidity of the dynamical scaling within the framework of the present theory for small R.