Surface-directed phase separation

As a final illustrative application of the LB method, we consider an example of blend phase separation where one boundary is solid and the other interface is fluid (Figs. 18-21). Figure 18 shows the initial fluid composition at a quench depth of $\tau _G=0.7$_G = 0.7. The dark liquid phase has a preferential interaction [111] with both the solid substrate (bottom boundary) and a third fluid ("air"). This image illustrates the well known phenomena of "surface-directed spinodal decomposition," in which the compositional waves of phase separation are brought into registry with the symmetry breaking walls [95,112,113,114,115,116]. The coarsening of the layer structure at early and intermediate times occurs much like a bulk blend (see Fig. 12), but the continued coarsening at long times requires the intermittent loss of fluid layers. At some point, the undulations within the layers grow sufficiently large (perhaps associated with the rupture of inner layers as required by coarsening) to induce perforations in the outer surface of the blend film at the polymer air-boundary (Fig. 20). This undulation phenomenon then causes the layered structure to break up into a structure that superficially resembles a spinodal decomposition pattern when seen from above (Fig. 21). A number of studies have indicated the presence of a "fast mode" [117] in layered blend films, corresponding to a rapidly growing length scale consistent with a hydrodynamic instability. The instability shown in Figs. 18-21 provides a possible explanation for the geometrical nature of this transition. Further computational and experimental studies of the late stage coarsening instabilities in layered blends would clearly be interesting to check this novel picture of phase separation in thin quiescent films in which the surface exerts a strong perturbing influence on the phase separating blend film structure.

  

Figure 18: Initial density of three phase systems to undergo surface driven phase separation. The blue and green regions correspond to the location of the two-phase mixture. A third phase, lying above, is rendered as the translucent red region. The quench depth $\tau _G=0.7$_G = 0.7.

  

Figure 19: "Surface-directed" phase separation. Phase separation of a fluid mixture between interacting solid and air boundaries. The layered morphology corresponds to "surface-directed spinodal decomposition". This stage of the phase separation corresponds to $\bar{t}=1.0$ = 1.0.

  

Figure 20: Phase separation of a fluid mixture between interacting solid and air boundaries. This image indicates the development of an instability which disrupts the layers in late stage phase separation. The reduced time equals $\bar{t}=1.6$ = 1.6.

  

Figure 21: "Disrupted" surface-directed phase separation. The disruption effect of "pinching" of the layers allows for further coarsening and leads to a collapse of the layered structure shown in Figs. (19-20). The reduced time equals $\bar{t}=4.0$ = 4.0.