Real space observation of dynamic scaling in a critical polymer mixture

Abstract

We have studied the growth of the wetting layer formed at the surface of a critical mixture of poly (ethylene propylene) and perdeuterated poly (ethylene propylene) during spinodal decomposition. The wavelength of the surface spinodal wave is found to grow as t 1/3 over the entire range of times accessible in the experiment. The composition profiles exhibit universal scaling behavior in the near-surface region. These results are in excellent agreement with a recent numerical study on surface-directed spinodal decomposition.PACS numbers: 61.25.Hq, 05.70.Fh, 64.60.Ht, When a binary mixture is quenched from a single homogeneous phase to a point inside the spinodal curve, spontaneous phase separation takes place. For bulk systems, this process has been extensively studied in the past both by theory and experiment [1][2][3][4][5][6]. Several distinguishable time regimes during the evolution of bulk spinodal decomposition are now well established. The initial stage is described by the linear theory of Cahn, Hillard, and Cook, while at later times nonlinear effects become dominant and a scaling description is applicable, where the average size of the domains R(t) is the only relevant length scale in the system. In this regime, R(t) is found to grow like R(t) -t ,/3 . For fluid mixtures, however, hydrodynamic effects become important at later times and the growth law is found to change to R(t)~~t in the socalled final stage of spinodal decomposition.Only recently, it has been recognized that in the vicinity of a symmetry breaking surface the process of spinodal decomposition may be severely altered as compared to the bulk behavior [7], If one of the two components of the mixture is preferentially attracted to the surface, a quite anisotropic evolution of the phase separation is expected to occur in the near-surface region. This was first observed experimentally by Jones et al. [8] who found an oscillatory composition profile near the surface of an isotopic polymer mixture after a quench into the two-phase region. Meanwhile, different theoretical studies have focused on this effect [9-11], aiming toward a detailed understanding of the time dependence of the spinodal decomposition close to an attractive wall. For sufficiently deep quenches, both simple scaling arguments [10] and coarse-grained order parameter simulations [10,11] predict a / 1/3 growth of the wetting layer thickness at later times, closely resembling the bulk behavior. In addition, the composition profiles perpendicular to the wall are expected to show scaling behavior; i.e., they should collapse onto a unique master curve when rescaled with the actual wetting layer thickness. In contrast to these clear and unanimous theoretical results, the experimental data on surface-directed spinodal decomposition are still rare and an unambiguous analysis of the time dependence of the "surface spinodal wave" is still lacking. In this Letter, we present the first experimental evidence for both a power law growth of the wetting layer thickness /(/) during spinodal decomp...

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