Role of Diffusion in Scaling of Polymer Chain Aggregates Found in Vapor Deposition Polymerization

Linear polymer chain aggregates grown by 1+1D Monte Carlo simulations of vapor deposition polymerization (VDP) were studied. The behavior of chain length distribution $n_{s}(t)$ as a function of chain length (s) and deposition time (t) was examined for relevant model parameters. The scaling of $n_{s}(t)$ was found to be sensitive to the ratio $G = D/F$ of deposition rate (F) and free monomer diffusion (D). A systematic approach is presented to isolate the dependence of $n_{s}(t)$ on $t$, $s$, and $G$. We found power law dependence of $n_{s}(t)$ on $t$ with exponent $\omega=1.01 \pm 0.02$ that was invariant with changes in $G$. For small $s$ and deposition time of $t$ = $1 \times10^3$, $5 \times 10^3$, and $10 \times10^3$, $n_{s}(t)$ showed a power-law decrease with $s$ and exponent $\tau=-0.58 \pm 0.02$. We observed a strong influence of $G$ on the rescaled $n_{s}(t)$ data that prevented the manifestation of unique scaling function for varying $G$. The dependence of scaling function of $n_{s}(t)$ on $G$ was found to be a characteristic of VDP and elucidates the sensitivity of polymer chain aggregates to $G$.