An Analytical Free Energy and the Temperature−Pressure Superposition Principle for Pure Polymeric Liquids

Pressure Effects on Self-Assembly in Mixtures Containing Zwitterionic Amphiphiles

To understand the responses of self-assembly in mixtures containing zwitterionic amphiphilic chains to high pressure, we introduce a self-consistent field theory in combination with a molecular equation-of-state model for them in a primitive way. The free energy density for those in the bulk state is first formulated. Its locally equilibrated excess part is then incorporated into Edwards Hamiltonian along with the electrostatic energy contributions to elicit the saddle point approximation to the partition function with proper self-consistent field equations. It is shown that charge-charge correlations enhance self-assembling tendency for the amphiphiles with the opposite charges on one component side, as the medium dielectric constant ε_r decreases. Those with the opposite charges at the two chain ends respond in a more complicated way to ε_r. Densification by applied pressure strengthens the self-assembly for both at a moderate ε_r, similar to typical phospholipids, but pressure effects are strongly dependent on the position of charges along the chains at a lower ε_r. It is argued that the manipulation of the dielectric environment and disparity in component dispersion interactions can yield useful materials exhibiting various types of baroresponsivity or thermoresponsivity with re-entrant self-assembly.

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.

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.

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.