Collapse transition of a chain in the bulk and next to adsorbing surfaces

We performed lattice MC simulations of single, flexible, self-avoiding chains in bulk solution$^{\ast }$, or adsorbed onto a surface, under poor solvent conditions. Our simulations spanned a wide range of chain lengths (N=20-10000) and cohesive energies. The chain length dependence of the chain size in poor solvents was characterized by a wide plateau of almost null growth. This plateau was related with the development of the incipient constant density core. The ``volume approximation'' regime and genuine power law dependence (1/3) was not reached even for the longest chains and poorest solvents studied. Sufficiently long chains became more but not fully spherical and underwent a 2$^{nd}$ order phase transition. Conformations of the adsorbed chains onto attractive surfaces are not controlled by the bulk $\Theta $- temperature, but by a new temperature $\Theta $' which depends strongly on the interactions with the surface. The adsorption-desorption transition width is determined by the N-dependence of the bulk radius of gyration, for every solvent quality. In poor solvents and strongly attractive surfaces, the coil-to-globule transition turns into a coil to ``pancake'' transition. $^{\ast}$ Rissanou \textit{et al. J. Polymer Sci.~:Part B~: Polymer Phys}., \textbf{44}, p.3651 (2006)