Lower and Upper Critical Ordering Temperatures in Compressible Diblock Copolymer Melts from a Perturbed Hard-Sphere-Chain Equation of State

Solubilization Behavior of Homopolymer in Its Blend with the Block Copolymer Displaying the Feature of Lower Critical Ordering Transition

Blending with homopolymer offers a facile approach for tuning the microdomain morphology of block copolymer, provided that the homopolymer chains are uniformly solubilized in the corresponding microdomain to swell the junction point separation. Here we studied the solubilization behavior of poly(4-vinyl pyridine) homopolymer (h-P4VP) in the lamellar microdomain formed by its blends with a poly(ethylene oxide)-block-poly(4-vinyl pyridine) (PEO-b-P4VP) showing the feature of lower critical ordering transition (LCOT) in terms of weaker segregation strength at lower temperature. We revealed that, while the conventional criterion of homopolymer-to-block molecular weight ratio for attaining uniform solubilization was applicable to LCOT blend, there was an excess swelling of junction point separation upon the addition of homopolymer, leading to a decrease of interdomain distance with increasing homopolymer composition. This anomalous phenomenon was attributed to the reduction of interfacial free energy due to the incorporation of P4VP homopolymer into the microdomain interface.

Superposition in Flory-Huggins χ and Interfacial Tension for Compressible Polymer Blends

We investigate theoretically the response of interfacial tension γ for compressible polymer blends to thermodynamic variables. Helfand's self-consistent field theory is first extended to be combined with an off-lattice equation-of-state model to describe compressibility. Typical incompatible blends reveal that the effects of temperature and pressure (T-P) on γ are superposed into a single curve by a dimensionless pressure variable through the superposition in Flory-Huggins χ and density. In the case of polymer blends with strong compressibility difference, γ shows an anomaly upon pressurization with no T-P superposition, even though χ still follows the superposition.

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.

Concentration fluctuation effects on the phase behavior of compressible diblock copolymers

A Hartree analysis has been performed for compressible diblock copolymers of incompatible pairs to investigate the concentration fluctuation effects on their microphase separation behavior. The free energy in the Hartree analysis is obtained from the self-consistent correction to its mean-field cousin, which was recently formulated for such copolymer systems. The mean-field phase diagram is shown to be significantly affected by the fluctuation effects as the copolymer chain size N is lowered. An effective interaction chi(cRPA), which carries not only the change in contact interactions but also the compressibility difference between block components, plays a key role in understanding of the phase behavior and the pressure responses of various thermodynamic transitions for the copolymers with finite sizes. In particular, a symmetric copolymer at disorder-to-lamella transition is found to satisfy Nchi(cRPA)(q*)=10.495+41.022N(-1/3) when evaluated at a characteristic wave number q* for ordered microphases.

Effect of hydrostatic pressure on closed-loop phase behavior of block copolymers

The effect of hydrostatic pressure (P) on closed-loop phase behavior of deuterated polystyrene-block-poly(n-pentyl methacrylate) copolymers [dPS-PnPMA] was investigated by using small-angle neutron scattering and birefringence. For P<20.7 bar, dPS-PnPMA exhibited a lower disorder-to-order transition temperature (T(LDOT)) at 175 degrees C, and then an upper order-to-disorder transition temperature (T(UODT)) at 255 degrees C. With increasing pressure both T(LDOT) and T(UODT) were markedly changed, where dT(LDOT)/dP was 725 degrees C/kbar and dT(UODT)/dP was -725 degrees C/kbar. These are consistent with predictions by the Clausius-Clapeyron equation using measured values of the volume and enthalpy changes of both transitions. The large pressure coefficients imply that the closed-loop phase behavior observed for PS-PnPMA is an entropic-driven phase transition.

Closed-loop phase behaviour in block copolymers

Closed-loop phase diagrams are known in systems with specific intermolecular interactions. In weakly interacting systems, however, such behaviour has never been observed. Here, diblock copolymers formed from polystyrene covalently linked to poly (n-pentylmethacrylate), P(S-b-nPMA), which have only weak segmental interactions, are shown to exhibit a closed-loop phase behaviour over a narrow range of molecular weight. The endothermic transitions from the disordered to ordered and back to the disordered state, as a function of increasing temperature, are dominantly entropic in origin. The morphology and rheological properties of P(S-b-nPMA) undergo characteristic changes at the transitions. Whereas the disorder-to-order transition temperature increases with decreasing molecular weight, the order-to-disorder transition temperature decreases. At a limiting molecular weight, the closed-loop vanishes and no ordering occurs. These findings provide quantitative insight into an elusive transition in weakly interacting multicomponent systems.