We study the percolation problem in a binary phaseseparating polymer mixture. By well-designed experiments, we can delineate the percolation line on the phase diagram with sufficient accuracy. Our experiments show that the percolation thresholds start from the random percolation limit (Φ ∼ 0.15) located near spinodal point at T → T c and then converge toward the geometric coalescence limit (Φ ∼ 0.36) with an increase in the quench depth. This apparent percolation difficulty comes about largely from the Rayleigh instability accompanied by large-amplitude, short-wavelength fluctuations during the spinodal decomposition at deeper quench depth. As a result, the broken "rigid" domains tend to pack closely, and the so-called droplet spinodal decomposition occurs. On the other hand, we observe that, between the selectively attractive walls, the surfacedrying percolating phase will break up into droplets prematurely, thereby shifting its percolation line rather considerably. To our knowledge, such an effect is not yet predicted by theory or simulation.T he coexistence curve provides us with basic information on the equilibrium composition and the relative proportion of the two coexisting phases under a given set of conditions. However, materials scientists are interested in how to quantitatively relate the phase diagram to the developing domain structure. Certainly, this involves the kinetic aspects of the phase separation, so that many experiments have been carried out to determine the spinodal curve, which subdivides the miscibility gap into the thermodynamically metastable (nucleationgrowth, NG) and unstable (spinodal decomposition, SD) regions. 1 As is well-known, the NG usually implies the formation of isolated droplets in a metastable background, whereas the most striking feature of the SD is the interconnected domains caused by coherent composition fluctuations. This difference is also reflected in their coarsening kinetics. For the isolated droplets, the growth is diffusioncontrolled R ∼ t 1/3 , where the R is the droplet size. 2−7 For the interconnected domains, or rather interpenetrating fluid tubes (Siggia's phrase), the hydrodynamic effects result in a much faster coarsening ξ ∼ (γ/η)t, where ξ is the correlation length of the domains, γ is the interfacial tension, and η is the viscosity. 8 However, as examined later on, that the factors controlling the SD structure depend not only on how it came into being, but also on the volume fraction of the minority phase Φ. 9 So even in the SD case, the connectivity of the domains must disappear at Φ p . This is just the typical percolation problem, 10 and Φ p is the so-called percolation threshold.Inasmuch as whether or not the percolation occurs is so crucial for the SD, where is its precise location? The random percolation limit (Φ ∼ 0.15) has in the past been postulated as a possible boundary. 8 However, the experimental evidence has shown that the percolation region is much narrower. 11,12 Accordingly, a geometric coalescence limit (Φ ∼ 0.36), 13 which the percol...
