Reversible island nucleation and growth with anomalous diffusion

Motivated by recent experiments on submonolayer organic film growth with anomalous diffusion, a general rate-equation (RE) theory of submonolayer island nucleation and growth was developed [J.G. Amar and M. Semaan, Phys. Rev. E {\bf 93}, 062805 (2016)] which takes into account the critical island-size $i$, island fractal dimension $d_f$, substrate dimension $d$, and diffusion exponent $\mu$,and good agreement with simulations was found for the case of irreversible growth corresponding to a critical island-size $i = 1$ with $d = 2$.However, since many experiments correspond to a critical island-size larger than $1$, it is of interest to determine if the RE predictions also hold in the case of reversible island nucleation with anomalous diffusion.Here we present the results of simulations of submonolayer growth with $i = 2$ ($d = 2$)which were carried out for both the case of superdiffusion ($\mu > 1$) and subdiffusion ($\mu < 1$) as well as for both ramified islands ($d_f \simeq 2$) and point-islands ($d_f = \infty)$. In the case of superdiffusion,excellent agreement is obtained with the RE theory for the exponents $\chi(\mu)$ and $\chi_1(\mu)$ .In the case of subdiffusion we find only partial agreement with the RE theory for the case $i = d = 2$.