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 ∼ σ 5/3 and H ∼ σ 1/3 , 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.

Stuffed brushes: theory and experiment

“…7 the surface pressure isotherms of PS-PEO block copolymers at the air/water interface are shown. The interpretation of these isotherms is discussed elsewhere [16]. Here, we merely note that for surface pressures above 10 mN/m dense PEO-brushes are formed at the air/water interface.…”

“…In the most simple model for a brush the monomer density is assumed uniform throughout the grafted layer, the so-called Alexander-de Gennes model [11,12]. Although several more refined models based on nonuniform density distributions normal to the grafting surface have been presented [13][14][15], the simple Alexander-de Gennes model has been surprisingly successful in predicting scaling relationships for the brush height and surface pressure as a function of the grafting density and chain length [16]. We refer the reader to the mentioned reviews and references therein for more details [9,10].…”

Dynamic Properties of Poly(styrene)–Poly(ethylene oxide) Diblock Copolymer Films at the Air–Water Interface

“…From a fundamental point of view the interest to surface films of diblock copolymers is mainly determined by their ability to form polymer brushes at high surface concentrations (4)(5)(6)(7)(8)(9). Since the pioneering works by Alexander (10) and de Gennes (11), many authors studied the equilibrium properties of polymer brushes theoretically using the scaling approach (12,13) or the mean field theory (7,9,(14)(15)(16)(17). The obtained conclusions were examined in a number of experimental studies at the solid-liquid (4,5) or liquid-gas interfaces (7)(8)(9)(17)(18)(19)(20)(21)(22).…”

First-order phase transition during displacement of amphiphilic biomacromolecules from interfaces by surfactant molecules

“…However, as with the mushroom-brush case, detailed numerical SCF calculations by Currie et al [50] have shown that the transition remains a continuous one for finite size chains, at finite segment adsorption energies. Only as the strength of attractive segment-surface interaction,  s , becomes infinite does a discontinuous transition result [50]. It is interesting to point out that, in this sense, the pancake-brush transition, exhibited in these systems, can be considered as a zero temperature phase transition (since  s ~ 1/T), much in the same way as those predicted in certain models of spin-glasses and other magnetic systems [51].…”

“…It has been speculated that this pancake-brush transition might be a first-order transition [49]. However, as with the mushroom-brush case, detailed numerical SCF calculations by Currie et al [50] have shown that the transition remains a continuous one for finite size chains, at finite segment adsorption energies. Only as the strength of attractive segment-surface interaction,  s , becomes infinite does a discontinuous transition result [50].…”