Surface segregation in conformationally asymmetric polymer blends: Incompressibility and boundary conditions

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Abstract
Recent experiments, analytical theory, and simulations have raised and examined the possibility of entropically driven segregation effects in conformationally asymmetric polymer blends. We consider herein a model of surface segregation in a molten blend of two polymers with different flexibilities as characterized by the pure-component parameter β2=R2g/Vmol, where Rg is the radius of gyration and Vmol is the molecular volume of a polymer chain. Analytic solutions to the self-consistent field equations are presented for small deviations of the conformational asymmetry parameter ε=(βA/βB)2 from unity. Even in the absence of enthalpic interactions with the wall, we find an effective exchange surface potential of entropic origin, which can be understood in terms of an imperfect screening of the wall by the self-consistent potential. We find that the more flexible component segregates to the surface, in qualitative agreement with an earlier density functional calculation, but with a different parameterization of the surface potential. For weak conformational asymmetry, the magnitude of the segregation is found to be proportional to (ε−1), and inversely proportional to the bulk screening length of the total monomer density. Our analysis indicates that unlike single-component melts, where reflecting boundary conditions are appropriate, molten blends near a surface are described by an effective mixed boundary condition on the polymer Green’s function G(z,z′;s,s′) of the form ∂zG∝UG, where U is the strength of the surface potential. In the perturbative limit, ‖ε−1‖≪1, this proves equivalent to effective constant flux boundary conditions.