Grafted Adsorbing Polymers: Scaling Behavior and Phase Transitions

Abstract

Grafted adsorbing polymers are investigated with the Scheutjens−Fleer self-consistent field model. The surface pressure of such systems is calculated numerically and semiquantitative agreement is found with experimental surface pressure isotherms of PS−PEO diblock copolymers at the air/water interface. Scaling relationships of mean-field models predict the surface pressure π and the height H of neutral brushes to scale as π ∼ σ5/3 and H ∼ σ1/3, respectively, as a function of the grafting density σ. These scaling relationships for the surface pressure and the thickness are corroborated experimentally for long PEO chains, provided contributions to π due to adsorption to the air−water interface are taken into account. In the SCF model the pancake−brush transition in a good solvent is found to be continuous for all chain lengths and adsorption energies. At high adsorption energies the transition is abrupt and resembles a continuous phase transition close to a critical point, a so-called λ-transition.