Statics and dynamics of a polymer chain adsorbed on a surface: Monte Carlo simulation using the bond-fluctuation model

A polymer chain under good solvent condition near a short-range attractive impenetrable wall (xy plane) is investigated by dynamic Monte Carlo simulation using the bond-fluctuation model. For the statics, the adsorption transition is clearly observed and the adsorption transition temperature, ${\mathit{T}}_{\mathit{a}}$ for this model is determined. Chain conformation, segment orientation, fraction of segment adsorbed, chain dimensions, and layer thickness as a function of temperature and distance away from the wall are studied and discussed. Our results for the scaling behavior of the radii of gyration and fraction of segment adsorbed confirm previous analytical theories and static simulation results. We also obtain an estimate for the critical exponent which is consistent with previous static simulations of self-avoiding walks. Furthermore, our data on specific heat show another peak, apart from the one at ${\mathit{T}}_{\mathit{a}}$, at a temperature ${\mathit{T}}_{2}$ distinctively below ${\mathit{T}}_{\mathit{a}}$, suggesting a second transition. As for the dynamics, both the time autocorrelation function and the time dependence of the mean square displacement of the center of mass of the chain are studied. We find that the time autocorrelation function in the adsorbed state can be fitted to a stretched exponential form and the relaxation time starts to diverge for temperatures below ${\mathit{T}}_{2}$. The diffusion coefficients for motions parallel (${\mathit{D}}_{\mathit{z}}$) and perpendicular (${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$) to the z axis are also extracted. ${\mathit{D}}_{\mathit{z}}$ shows a sharp drop as the temperature is lowered below the adsorption transition temperature while ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$ remains constant until around ${\mathit{T}}_{2}$ at which it decreases abruptly. Furthermore we also observe that the lateral diffusion (${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$) crosses over from a Rouse behavior (${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\sim}${\mathit{N}}^{\mathrm{\ensuremath{-}}1}$) to a ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\sim}${\mathit{N}}^{\mathrm{\ensuremath{-}}2}$ behavior for temperatures below ${\mathit{T}}_{2}$. These results are discussed in terms of the appropriate scaling theories.