Free surfaces of polymer blends. I. Theoretical framework and application to symmetric polymer blends

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Abstract
In this paper we develop a general mean‐field lattice model, in the spirit of the Scheutjens and Fleer theory of polymer solutions [J. M. H. M. Scheutjens and G. J. Fleer, J. Phys. Chem. 83, 1619 (1979); Macromolecules18, 1882 (1985)], of an N‐component polymer blend in the vicinity of an impenetrable surface. We consider the special case of N=3, model one component as noninteracting holes and obtain the bulk density of this system by using the Sanchez–Lacombe equation of state. The free surface of a polymer blend is then modeled by considering the interphase which forms when this ternary mixture is phase separated. One sample case corresponding to the free surface of a symmetric isotopic polystyrenelike blend is probed and we find that the deuterated component is partitioned to the air surface in agreement with experiment. The application of the concept of the Gibbs dividing surface relative to the polymer density profile at the free surface is then examined, and we show that all comparisons to experiment must be conducted relative to this hypothetical plane. Finally, comparisons of the concentration profiles predicted by this theory to existing square gradient theories of binary polymer blends, as well as Monte Carlo simulations, are performed to highlight the usefulness of these calculations to realistic systems.