FRACTAL STRUCTURE OF POLYMER INTERFACES

When diffusion occurs at an interface, the concentration profile p(x, t) varies smoothly as a function of the one-dimensional depth x. Howev er, when the diffusion process is viewed in two or three dimensions, t he interface is not smooth and is very rough. The random nature of dif fusion permits the formation of complex structures with fractal charac teristics. In this paper, we use gradient percolation theory developed by Sapoval et al. to examine the structure and properties of diffuse interfaces formed by metallization of polymer substrates and welding o f symmetric amorphous polymer interfaces. Gradient percolation separat es the connected from the nonconnected region of the diffusion field. The edge of the connected region is the (fractal) diffusion front. We examine the ramified diffuse interface structure in terms of the diffu sion front's width sigma(f), length N(f), position X(f), breadth B(f), fractal dimension D, and ''noise'' in these properties, deltasigma(f) 2, deltaN(f)2, deltaX(f)2, and deltaB(f)2, respectively, as a function of the diffusion length L(d). We obtained the following computer simu lation and theoretical results: width, sigma(f) approximately L(d)1/D, deltasimga(f)2 approximately L(d)3/D; front length, N(f) approximatel y L(d)1-1/D, deltaN(f)2 approximately L(d)2-1/D, deltaN(f)2 approximat ely L(d)2-1/D; position, X(f) approximately L(d), deltaX(f)2 approxima tely L(d)2-1/D, breadth B(f) almost-equal-to 6sigma(f), deltaB(f)2 app roximately L(d)2-1/D, where D = 7/4. The simulation results compared v ery favorably with an experimental analysis of diffuse silver-polyimid e interfaces. For welding of polymer-polymer interfaces, we examined t he diffusion front for reptating chains of molecular weight M and foun d that the interface became fractal at diffusion distances L(d), great er than the radius of gyration R(g) approximately M1/2, and at times t , longer than the reptation time T(r). At t < T(r) and L(d) < R(g), se lf-similarity was lost due to the correlated motion of the chains crea ting ''gaps'' in the interface. However, the interface was very rough and the diffusion front was determined by N(f) approximately L(d)d/M, where d is the dimensionality (d = 2 or 3). When L(d) much greater tha n R(g), the polymer diffusion front behaved as the monomer case with N (f) approximately L(d)1-1/D. The fractal nature of diffuse interfaces plays an important role in controlling the physical properties of poly mer-polymer and polymer-metal interfaces.