Adsorption of Polymer Molecules at Low Surface Coverage

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Abstract
A statistical‐mechanical treatment of a polymer molecule adsorbed on a solid surface is given. The surface coverage by adsorbed molecules is assumed to be sufficiently low that the interactions of the adsorbed polymer molecules with each other may be neglected. The partition function is derived for a polymer molecule with sequences of repeating units adsorbed at an interface and with other sequences (loops) held at the surface only at their ends. The assumption of Gaussian statistics for the loops leads to a formulation equivalent to that used for the helix‐coil region in DNA molecules. A broad distribution of loop sizes is found, in contrast to Silberberg's theory in which a sharply peaked distribution is assumed. The latter theory predicts also small loops for all values of the adsorptionfree energy. In contrast, our theory predicts large loops and few units adsorbed for small adsorptionfree energies and small loops and more units adsorbed for larger adsorptionfree energies when the chains are sufficiently flexible. This result is also in partial disagreement with earlier theories that predict large loops, even for relatively large adsorptionfree energies. On the other hand, for stiff chains our theory predicts only a small number of loops with most units at the surface. A relationship between the initial slope of an adsorption isotherm and the molecular weight of the polymer is presented.