Anomalous $\chi $ for Polydisperse Polystyrene-$b$-Poly(octyl acrylate)

We have performed small-angle neutron scattering (SANS) measurements on a disordered block copolymer from deuterated polystyrene (dPS) and self-adhesive poly(octyl acrylate) (POA) in order to elicit the effective Flory-Huggins $\chi $, which carries the essence of the copolymer phase behavior. The sample for the measurement was prepared by blending two polydisperse dPS-$b$-POAs of different molecular weights for the purpose of adjusting the average size to a proper value. The SANS profiles for the copolymer were fitted to Leibler's scattering function for a polydisperse copolymer system described by Schulz-Zimm distribution. It was shown that the resultant $\chi $ as a function of inverse temperature has a strong entropic contribution and a weak enthalpic contribution. By adopting a simple analysis for specific interactions, it was found that the entropically dominated $\chi $ for dPS-$b$-POA arises from the steric hindrance of long alkyl side groups of POA.