Self-consistent mean-field calculation of surface segregation in a binary polymer blend

In this Brief Report we use a self-consistent mean-field (SCF) method to predict the surface excess (${\mathit{z}}^{\mathrm{*}}$) and surface volume fraction (${\mathrm{\phi }}_1$) of the surface active component in a binary polymer blend. The SCF results are in excellent agreement with the measured ${\mathit{z}}^{\mathrm{*}}$ and ${\mathrm{\phi }}_1$ values of deuterated polystyrene (dPS) in a blend of dPS and PS. However, the approach proposed by Schmidt and Binder (SB) [J. Phys. (Paris) 46, 1631 (1985)] fails to predict simultaneously ${\mathit{z}}^{\mathrm{*}}$ and ${\mathrm{\phi }}_1$ for the same value of the excess surface free energy. A comparison of the dPS volume fraction profiles calculated by the SCF and SB models illustrates the limitations of the SB theory as applied to the dPS-PS experiments. Using the SCF model, the excess surface free energy is shown to have a complex dependence on ${\mathrm{\phi }}_1$, in contrast to the linear behavior proposed by SB.