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.