Influence of the chain mobility on the dynamic scaling of chain-chain aggregation in three dimensions

The dynamical scaling of the chain-chain aggregation model is investigated in three dimensions. Monte Carlo simulations are performed on a cubic lattice with a diffusion coefficient proportional to $k^{\gamma }$ for a chain of mass $k$. At large times the mean chain mass grows like $t^z$ and the meansquare radius of gyration like $t^{\frac{2z}{D}}$, where $D$ is the fractal dimension of the chains. The relation $z={(1-\frac{1}{D}+\varphi -\gamma )}^{-1\mathrm{}}$, obtained when one assumes that the sticking probability between two chains of mass $k$ is proportional to $k^{-\varphi }$, is checked numerically with $\varphi \mathrm{}\left(3D\right)\mathrm{}\approx 0.72$.