Role of diffusion in scaling of polymer chain aggregates found in vapor deposition polymerization

Polymer chain aggregates grown by (1+1)-dimensional Monte Carlo simulations of vapor deposition polymerization (VDP) were studied. The dynamic scaling behavior of polymer chain length distribution n(s)(t) was studied as a function of chain length (s), deposition time (t), and the ratio G=D/F of deposition rate (F) and free monomer diffusion (D). The dynamic scaling approach was employed to highlight the dependence of n(s)(t) on t, s, and G. With an increase in t, we found a power law increase in n(s)(t) and total number of polymer chains N(total)(t), given by N(total)(t)~t(ω) and n(s)(t)~t(ω) with exponent ω=1.01(2) that was invariant for a range of G=10 to 10^{4}. For small s and t=10^{3}, 5×10^{3}, and 10^{4}, n_{s}(t) decreased according to n(s)(t)~s(-τ) with τ=0.58(2). As G was increased from 10 to 10(4), we observed a systematic influence of G on the rescaled n(s)(t) data that prevented the manifestation of unique scaling function for polymer chain aggregates. The dependence of scaling functions of n(s)(t) on G elucidates the sensitivity of polymer chain aggregates to G and is thought to be a characteristic of VDP.