Lower and upper critical ordering temperatures in compressible diblock copolymer melts from a perturbed hard-sphere-chain equation of state

The random-phase approximation is combined with the perturbed hard-sphere-chain (PHSC) equation of state for copolymer systems to represent the microphase separation transition in compressible diblock copolymer melts. The PHSC equation of state takes into account the equation-of-state effect that results from differences in compressibility between pairs of segments comprising a diblock copolymer; these differences favor demixing. Upon increasing the temperature of a microphase-separated diblock copolymer melt, theory first predicts an order-to-disorder transition that corresponds to the upper-critical-solution-temperature behavior in the binary blend of parent homopolymers. At conditions where the equation-of-state effect is significant, theory also predicts a disorder-to-order transition at further elevated temperature that follows closely the lower-critical-solution-temperature behavior in the binary blend containing the parent homopolymers. To compare theory with experiment, we obtain the binary interaction parameter between copolymer segments from the coexistence curve for the binary blend of parent homopolymers. Predicted microphase-separation-transition temperatures of diblock copolymer melts are compared with experiment for styrene-based diblock copolymer melts including poly(styrene-bloch-n-butyl methacrylate) melts that show both order-to-disorder and disorder-to-order transitions. We also discuss the pressure dependence of order-to-disorder transition temperatures of styrene-based diblock copolymer melts. Theory and experiment show semiquantitative agreement.