POWER-LAW RELAXATION OF PERIMETER LENGTH OF FRACTAL AGGREGATES

For a realistic aggregate grown under the diffusion control, the fract al scaling holds between two cutoff lengths. These cutoff lengths ofte n control the dynamics of aggregation and relaxation. During thermal a nnealing, coarsening of the aggregate structure takes place, and the l ower cutoff length increases. When the relaxation is limited by kineti cs, we show by a simple dimensional argument that the perimeter length (or area) A of the aggregate shrinks in a power law with time t as A( t) similar to t((d-1-D)/2) in a d-dimensional space, where D is the fr actal dimension of the aggregate. This prediction is tested by Monte C arlo simulation of the thermal relaxation of a two-dimensional diffusi on-limited aggregation.