The adsorption of flexible macromolecules. Part I. The isolated macromolecule at a plane interface

Abstract

The adsorption of an isolated, flexible linear polymer molecule of high molecular weight is treated at an infinite plane surface. The question of a possible equilibrium configuration is examined when it is required that some at least of the segments of the polymer molecule are in contact with the surface, and it is assumed that for each segment so placed the internal energy of the system is reduced by an adsorption energy xkT. It is shown that the polymer molecule will split up into sequences of segments; alternate stretches of PS segments all in the surface and loops of PB segments all out of the surface, whose size is not a function of molecular weight. The length, PB, of the loops will decrease and the fraction, p, of segments in the surface will increase as the absorption energy x increases. Several models are considered. For an all adsorbable polymer molecule on an all adsorbing surface, the loops PB are small and p is large even at small values of x. Such polymer molecules stay close to the surface with practically all their segments, and behave essentially as two-dimensional structures. In cases where not all surface sites are adsorbing, or not all polymer segments are adsorbable, or both, the size of loop is considerably increased and much higher adsorption energies are required. Restrictions limiting the re-entry of an adsorption loop into the surface, as well as any increase in specificity, have a similar effect. It is shown that structural principles affect polymer adsorption in sensitive fashion. The methods described can easily be adapted to discuss a variety of cases and are useful for this reason. It is one of the consequences of this model that the ends of the polymer molecule are on the surface. A discussion of previous theories, which predicted rather different results, is given.