Wool [57] has considered the fractal nature of polymer-metal and polymer-polymer interfaces. He argues that diffusion processes often lead to fractal interfaces. Although the concentration profile varies smoothly with the dimension of depth, the interface, considered in two or three dimensions is extremely rough [75]. Theoretical predictions, supported by practical measurements, suggest that the two-dimensional profile through such an interface is a self-similar fractal—that is one which appears similar at all scales of magnification. Interfaces of this kind can occur in polymer-polymer and polymer-metal systems.
Polymer-polymer fractal interfaces may result from the interdiffusion of monomers or of polymers themselves. Hashimoto et al. [56,57] annealed the interface between polystyrene and a styrene-isoprene diblock polymer at 150° C and showed extensive roughening of the interface by mutual interdiffusion on a micrometer scale (Fig. 6).
Metal-polymer fractal interfaces may result from processes such as vacuum deposition and chemical vapor deposition where metal atoms can diffuse considerable distances into the polymer. Mazur et al. [76,77] electrodeposited silver within a polyimide film. The Silver [I] solution was able to diffuse into the polymer film where it
Annealing at 150 C
(SI:Mn= 1.7×10 5) / (PS:Mn=6.0xl0 4)
PS Homopolymer Phase
Interface
Figure 6 Electron micrographs showing the interface between (top) polystyrene and (bottom) a styrene-isoprene diblock polymer annealed at 150° C for the times shown. (Isoprene units are stained and appear black.) (Reproduced from Ref. 56, copyright 1990 American Chemical Society.)
was subsequently reduced to the metal. The adhesion was excellent: the only way that Mazur could remove the silver was by abrasion. Examination of a section through the interface by transmission electron microscopy showed an extremely rough interfacial region on the submicrometer scale. Wool [57] analysed the profile and showed the interface to be fractal with a dimension of around 1.6.
Wool [57,78] suggests that these principles could be used to develop pretreatments which give a highly ramified, fractal surface to which high adhesion by mechanical interlocking would be expected. Consider a blend of polyethylene with a second phase, perhaps starch, amenable to removal by selective attack or dissolution. Above a critical concentration some of the second phase particles will be connected, forming a fractal structure. Treatment of the polyethylene surface, then, will leave fractal voids, receptive to an adhesive, such as a liquid epoxy resin.