Effects of Fluctuations and Compressibility on the Phase Behavior of Loop-Forming Diblock Copolymers

Phase Behaviors in Compressible Polymer Blends

We study phase behaviors in compressible polymer blends by using an equation of state in the framework of classical density-functional theory. The phase behaviors are explored by decomposing the compressible mixing of polymers into two steps: incompressible mixing as holding the volume and density relaxation at the given pressure. There exists both upper consolute pressure (UCP) and lower consolute pressure (LCP). LCP-type behaviors are driven by the entropy effect of asymmetric size of molecules, while UCP-type behaviors are driven by energetic interactions. The value of LCP follows a scaling of O(N^-2), which can be improved to O(N^-1.8) by taking into account the effects of random chain conformation. The volume of LCP-type polymers expands upon mixing, while that of UCP-type polymers contracts. A closed-loop phase coexisting curve may appear because of the interplay between UCP- and LCP-type behaviors. At the UCP/LCP boundary, the mixing free energy of density relaxation is much smaller than that of both UCP- and LCP-type behaviors. The contribution from incompressible mixing step always dominates the phase behaviors, while that from density relaxation step could distinguish UCP-type between LCP-type behaviors.

Two-Dimensional Heterospectral Correlation Analysis of Wide-Angle X-ray Scattering and Infrared Spectroscopy for Specific Chemical Interactions in Weakly Interacting Block Copolymers

We investigated, via two-dimensional heterospectral correlation analysis of wide-angle X-ray scattering (WAXS) and infrared (IR) spectroscopy, the specific chemical interactions existing in weakly interacting polystyrene-block-poly(n-pentyl methacrylate) copolymers (PS-PnPMA). PS-PnPMA was shown to exhibit a closed-loop-type phase behavior, where, upon heating, a lower disorder-to-order transition (LDOT) was found at lower temperatures, and an upper order-to-disorder transition (UODT) was observed at higher temperatures. The specific interaction between the PS and PnPMA blocks mainly arises from the dipole in the benzene ring of PS and the induced dipole in the PnPMA due to cluster formation with a size of 1 approximately 2 nm. We found that the synchronous 2D WAXS-IR heterospectral correlation spectrum of the ordered state was completely different from that in the two disordered states. The CH group of the main chains of PS and PnPMA did not contribute to the cluster formation in the two disordered states, indicating that the main chains of PS and PnPMA blocks were randomly distributed in the two disordered states. However, only the C=C group in the PS block contributed to the cluster at a disordered state below the LDOT, whereas both the C-C-O group in PnPMA and the entire phenyl ring and C=C group in PS contributed to cluster formation at another disordered state above the UODT. Thus, the probability that PS (and PnPMA) chains were located at their own neighboring chains at one disordered state above the UODT is larger than that at another disordered state below the LDOT.