Layer hopping by chains in polymeric smectics?

Theory of microphase separation on side-chain liquid-crystalline polymers with flexible spacers

We model a melt of monodisperse side-chain liquid-crystalline polymers as a melt of comb copolymers in which the side groups are rod-coil diblock copolymers. We consider both excluded-volume and Maier-Saupe interactions. The first acts among any pair of segments while the latter acts only between rods. Using a free-energy functional calculated from this microscopic model, we study the spinodal stability of the isotropic phase against density and orientational fluctuations. The phase diagram obtained in this way predicts nematic and smectic instabilities as well as the existence of microphases or phases with modulated wave vector but without nematic ordering. Such microphases are the result of the competition between the incompatibility among the blocks and the connectivity constraints imposed by the spacer and the backbone. Also the effects of the polymerization degree and structural conformation of the monomeric units on the phase behavior of the side-chain liquid-crystalline polymers are studied.

The frozen state in the liquid phase of side-chain liquid-crystal polymers

Quenched isotropic melts of side-chain liquid-crystal polymers reveal surprisingly an anisotropic polymer conformation. This small-angle neutron-scattering (SANS) result is consistent with the identification of a macroscopic, solidlike response in the isotropic phase. Both experiments (rheology and SANS) indicate that the polymer system appears frozen on millimeter length scales and at the time scales of the observation. This result implies that the flow behavior is not the terminal behavior and that cross-links or entanglements are not a necessary condition to provide elasticity in melts.

Entropy-induced microphase separation in hard diblock copolymers

Whereas entropy can induce phase behavior that is as rich as seen in energetic systems, microphase separation remains a very rare phenomenon in entropic systems. In this paper, we present a density functional approach to study the possibility of entropy-driven microphase separation in diblock copolymers. Our model system consists of copolymers composed of freely jointed slender hard rods. The two types of monomeric segments have comparable lengths, but a significantly different diameter, the latter difference providing the driving force for the phase separation. At the same time this system can also exhibit liquid crystalline phases. We treat this system in the appropriate generalization of the Onsager approximation to chain-like particles. Using a linear stability (bifurcation) analysis, we analytically determine the onset of the microseparated and the nematic phases for long chains. We find that for very long chains the microseparated phase always pre-empts the nematic. In the limit of infinitely long chains, the correlations within the chain become Gaussian and the approach becomes exact. This allows us to define a Gaussian limit in which the theory strongly simplifies and the competition between microphase separation and liquid crystal formation can be studied essentially analytically. Our main results are phase diagrams as a function of the remaining model parameters: i.e., the diameter ratio, the length ratio, and the number ratio of the two types of segments. We also determine the amplitude of the inhomogeneous order as a function of position along the chain at the onset of the microphase separation instability. Finally, we give suggestions as to how this type of entropy-induced microphase separation could be observed experimentally.

The theory of competing nematic phases of comb polymers

Comb polymers have been proposed to exhibit a variety of nematic states according to the relative nematic tendencies of the backbone and teeth, and the molecular attachment of the two. The equilibria of such nematic phases with each other and with the isotropic state can be described by a mean field model, which combines a Maier‒Saupe theory of con­ventional liquid crystals and the worm concept of semiflexible polymers. Here the model is solved analytically in terms of universal functions. Graphical constructions on the free energy reminiscent of the Maxwell area rules are derived. The method allows both qualitative and quantitative conclusions to be made of the shape and gradients of phase diagrams. Triple points and a critical point inside one of the nematic phases are predicted. The stability of equilibria is examined. The occurrence of re-entrant nematic phases is identified as a consequence of the main-chain flexibility.