Film Growth and Surface Roughness with Fluctuating Covalent Bonds in   Evaporating Aqueous Solution of Reactive Hydrophobic and Polar Groups: A   Computer Simulation Model
  A computer simulation model is proposed to study film growth and surface roughness in aqueous ($A$) solution of hydrophobic ($H$) and hydrophilic ($P$) groups on a simple three dimensional lattice of size $L_x \times L_y \times L_z$ with an adsorbing substrate. Each group is represented by a particle with appropriate characteristics occupying a unit cube (i.e., eight sites). The Metropolis algorithm is used to move each particle stochastically. The aqueous constituents are allowed to evaporate while the concentration of $H$ and $P$ is constant. Reactions proceed from the substrate and bonded particles can hop within a fluctuating bond length. The film thickness ($h$) and its interface width ($W$) are examined for hard-core and interacting particles for a range of temperature ($T$). Simulation data show a rapid increase in $h$ and $W$ is followed by its non-monotonic growth and decay before reaching steady-state equilibrium ($h_s, W_s$) in asymptotic time step limit. The growth can be described by power-laws, e.g., $h \propto t^{\gamma}, W \propto t^{\beta}$ with a typical value of $\gamma \approx 2, \beta \approx 1$ in initial time regime followed by $\gamma \approx 1.5, \beta \approx 0.8$ at $T = 0.5$. For hard-core system, the equilibrium film thickness ($h_s$) and surface roughness ($w_s$) seem to scale linearly with the temperature, i.e., $h_s = 6.206 + 0.302 T, W_s = 1,255 + 0.425 T$ at low $T$ and $h_s = 6.54 + 0.198 T, W_s = 1.808 + 0.202 T$ at higher $T$. For interacting functional groups in contrast, $h_s$ and $W_s$ decay rapidly followed by a slow increase on raising the temperature. 
Shihai Yang, Adam Seyfarth, Sam Bateman, Ras B. Pandey