Adsorption of Flexible Macromolecules. III. Generalized Treatment of the Isolated Macromolecule; The Effect of Self-Exclusion

Abstract

A generalized treatment of adsorption at an interface of an isolated flexible macromolecule from solution is presented. Adsorption is assumed to involve the arrangement of the segments of the chain into conformations in which loops of segments and trains of segments attached to the surface alternate each other. Adsorption will occur only if the free‐energy change ΔF_s per segment in going from loop to train is less than a critical value. For a very long chain (no end effects) the distribution functions of loop and train sizes do not depend on the length of the chain. The arrangment possibilities of the loops and trains are represented by functions of the type ω(i) = γi^−auⁱ which have been used to allow for nonintersection effects (volume exclusion effects) in random walks. If in the above, the exponent a characterizes loops and the exponent ā trains, it is conjectured that the proper choice of (a, ā) is ($\frac{4}{3}$ , —⅓) rather than ($\frac{3}{2}$ , 0). With this choice, self‐exclusion within the loops and trains is allowed for. It is shown that a reduction in the a priori probability of leaving the surface and returning to it $[\mathrm{small}\mathrm{\hspace{0.17em}(\gamma \gamma ̄)]}$ favors large loops. The ratio (ū/u) is shown to equal 0.4 independent of lattice type.