Spatial modulation in cross-linked binary polymer blends

Spatial modulation means that the free energy of the composite mixture is minimized at a finite wavenumber, which defines the primary length scale, the maximum size possible, of the evolving phases. Although spatial modulation may appear in different systems in different ways and is not necessarily a thermodynamic precept, here it is expressed as a thermodynamic consequence of short-range interfacial forces pitted against long-range elastic forces. Cross-linked chains bring about new thermodynamic interactions based on their conformations and the fractal dimensions of the chain networks to which they tether and belong. Interplay among these different interactions during phase ordering brings about the spatial modulation and the spatial pattern. Here, the underlying processes are only succinctly outlined.