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

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 $P_S$ ) alternating with free standing loops (barrier restricted three‐dimensional random walks; average length $P_B$ ). These adsorbed macromolecules generate a surface‐attached phase of a thickness proportional to $P_B$ in which the segment concentration ${\phi }_B$ is considerably different from the concentration $\mathrm{\phi *}$ in the bulk equilibrium phase and from the concentration $\theta$ 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 ${\mathrm{(\theta ,\; \phi }}_B)$ and the adsorbed macromolecules ${\mathrm{[P}}_B{\mathrm{,\; P}}_S{\mathrm{,\; p\hspace{0.17em}=\hspace{0.17em}P}}_S{\mathrm{\hspace{0.17em}/\hspace{0.17em}(P}}_B{\mathrm{+\hspace{0.17em}P}}_S\mathrm{)]}$ are determined as functions of the bulk equilibrium phase concentration $\mathrm{(\phi *)}$ , the molecular weight $\mathrm{(P)}$ , the polymer flexibility (adaptibility to the surface) parameter ${\mathrm{(\gamma }}_B{\gamma }_S)$ , and the polymer–solvent $\mathrm{(\chi )}$ and the polymer–surface energy interaction parameter ${\mathrm{(\chi }}_S)$ . Two cases are discussed, an athermal polymer solvent mixture $\text{(χ\hspace{0.17em}=\hspace{0.17em}0)}$ and a θ‐solvent mixture $\text{(χ\hspace{0.17em}=\hspace{0.17em}0.5)}$ . 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 $\alpha$ . The experimentally observed concentration and molecular‐weight dependence of the amount adsorbed $\mathrm{(\theta \hspace{0.17em}/\hspace{0.17em}p)}$ and the loop size ${\mathrm{(P}}_B)$ are found to be qualitatively and quantitatively predicted by the model. It turns out that the concentration $\theta$ in the surface phase in immediate contact with the adsorbent is (for given $P$ and $\chi$ ) primarily determined by ${\chi }_S$ , while the concentration ${\phi }_B$ and the loop size $P_B$ , characterizing the diffuse surface‐attached bulk phase, are primarily a function of $\mathrm{\phi *}$ . The change in surface tension $\mathrm{\Delta \sigma }$ in the case of a free‐solvent‐air interface, i.e., the equation of state of the surface layer, is also computed.