SURFACE SEGREGATION IN CONFORMATIONALLY ASYMMETRIC POLYMER BLENDS - INCOMPRESSIBILITY AND BOUNDARY-CONDITIONS

Recent experiments, analytical theory, and simulations have raised and examined the possibility of entropically driven segregation effects i n conformationally asymmetric polymer blends. We consider herein a mod el of surface segregation in a molten blend of two polymers with diffe rent flexibilities as characterized by the pure-component parameter be ta(2)=R(g)(2)/V-mol, where R(g) is the radius of gyration and V-mol is the molecular volume of a polymer chain. Analytic solutions to the se lf-consistent field equations are presented for small deviations of th e conformational asymmetry parameter epsilon=(beta(A)/beta(B))(2) from unity. Even in the absence of enthalpic interactions with the wall, w e find an effective exchange surface potential of entropic origin, whi ch can be understood in terms of an imperfect screening of the wall by the self-consistent potential. We find that the more flexible compone nt 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 magn itude of the segregation is found to be proportional to (epsilon-1), a nd inversely proportional to the bulk screening length of the total mo nomer density. Our analysis indicates that unlike single-component mel ts, where reflecting boundary conditions are appropriate, molten blend s near a surface are described by an effective mixed boundary conditio n on the polymer Green's function G(z,z';s,s') of the form partial der ivative(z)G proportional to UG, where U is the strength of the surface potential. In the perturbative limit, \epsilon-1\much less than 1, th is proves equivalent to effective constant flux boundary conditions. ( C) 1996 American Institute of Physics.