Adsorption of Flexible Macromolecules. IV. Effect of Solvent–Solute Interactions, Solute Concentration, and Molecular Weight

Abstract

The adsorption of a linear flexible macromolecule to a plane interface brings about a change in its conformational topology. Instead of an isotropic random coil (single three-dimensional random walk) the molecule becomes a cooperative structure of adsorbed segment trains (two-dimensional random walks; average length PS) alternating with free standing loops (barrier restricted three-dimensional random walks; average length PB). These adsorbed macromolecules generate a surface-attached phase of a thickness proportional to PB in which the segment concentration φB is considerably different from the concentration φ* in the bulk equilibrium phase and from the concentration θ in the surface proper. An approach is developed for deriving the configurational factor and the configurational energy in the partition function of such a composite system in the Bragg–Williams approximation using a lattice model. The parameters of the adsorbed phase (θ, φB) and the adsorbed macromolecules [PB, PS, p = PS / (PB+ PS)] are determined as functions of the bulk equilibrium phase concentration (φ*), the molecular weight (P), the polymer flexibility (adaptibility to the surface) parameter (γBγS), and the polymer–solvent (χ) and the polymer–surface energy interaction parameter (χS). Two cases are discussed, an athermal polymer solvent mixture (χ = 0) and a θ-solvent mixture (χ = 0.5). It is shown that concentration and solvent effects considerably alter the results obtained for the isolated macromolecule. Whereas in the case of the isolated macromolecule, a molecular-weight dependence of the conformation arose only as a result of end effects at the point of desorption, considerable changes in configuration are introduced due to the concentration, solvent, and molecular-weight dependence of the segment activity parameter α. The experimentally observed concentration and molecular-weight dependence of the amount adsorbed (θ / p) and the loop size (PB) are found to be qualitatively and quantitatively predicted by the model. It turns out that the concentration θ in the surface phase in immediate contact with the adsorbent is (for given P and χ) primarily determined by χS, while the concentration φB and the loop size PB, characterizing the diffuse surface-attached bulk phase, are primarily a function of φ*. The change in surface tension Δσ in the case of a free-solvent-air interface, i.e., the equation of state of the surface layer, is also computed.