Mean-Field Lattice Calculations of Ethylene Oxide and Propylene Oxide Containing Homopolymers and Triblock Copolymers at the Air/Water Interface

Abstract

The adsorption of poly(ethylene oxide), poly(propylene oxide), and triblock copolymers containing ethylene oxide (EO) and propylene oxide (PO) at the air/water interface was modeled on the basis of a mean-field lattice theory for multicomponent mixtures of copolymers with internal degrees of freedom occurring in heterogeneous systems. The surface tension, the surface excess, and the volume fraction profiles across the interface were examined for PEO and PPO homopolymers and for a number of PEO−PPO−PEO triblock copolymers. The effects of the self-assembly of the copolymers in the solution, of depletion of the copolymers in the solution at small volume-to-surface ratios, and of a mass distribution of the copolymers on the adsorption were also considered. Interaction parameters obtained for PEO and PPO in simpler systems were used. Density profiles of PEO homopolymers across the air/water interface are compared with recent neutron reflectivity measurements. The shape and extension of the EO profiles into the water subphase agree well with the results extracted from the experiments, but the predicted surface excess is too large. On the basis of the results from the triblock copolymer systems, the low-concentration break, often experimentally observed when the surface tension is viewed as a function of the logarithm of the concentration, is proposed to be an effect of a depletion of the copolymers in the solution. This new proposal (i) clarifies the unreasonably small surface areas per molecule previously obtained and (ii) brings the predicted reduction of the surface tension made by the copolymers into agreement with experimental data. Finally, the model calculations predict correctly the dependence of the surface tension on the composition of the triblock copolymers. For the polydisperse model systems, the calculations demonstrate that below the cmc the longest and most surface active component dominates the adsorbed amount. Above the cmc, the long components self-assemble preferentially, making the solution depleted of these components and hence reducing the adsorbed amount of the long polymer components at the interface.