Abstract:
In this thesis we investigate the problem of a single polymer chain one-end grafted
to a surface of adjustable attraction strength. Particularly we introduce
a locally defined adsorption order parameter and analyze its spatial and
temporal correlations to check the consistency of the "blob" picture. We first
check the accuracy of our molecular dynamics simulations by reproducing known
results pertaining to mean number of adsorbed monomers M, mean height
of the chain's free end Z_end, and mean parallel-to-surface component of the
chain's gyration radius R_Gpar. We then characterize the scaling of the system in
the adsorption regime, finding dynamic dependencies such as t_Zend ~ Zend^3.67,
t_RGpar ~ Zend^-0.5, and t_Zend / t_M to hold very well against predictions of scaling
theory in conjunction with Rouse model dynamics. The relation between Zend
taken as a measure of the adsorption blob size, and the correlation length measured
along the chain contour did not take the expected form. Finally, the ratio
of the adsorption relaxation time of individual monomers to the global relaxation
time, t_mi=t_M was analyzed as a function of the adsorption strength. For large
enough N, it shows a sharp drop at the transition point, but both relaxation
times scale with N in the same way irrespective of the adsorption regime.
