Geometrical aspects of the frustration in the cubic phases of lyotropic liquid crystals.

Abstract

Bicontinuous cubic phases, composed of bilayers arranged in the geometries of periodic minimal surfaces, are found in a variety of different lipid/water systems.It has been suggested recently that these cubic structures arrive as the result of competition between two free-energy terms: the curvature energy of each monolayer and the stretching energy of the lipid chains. This scenario, closely analogous to the one that explains the origin of the hexagonal phases, is investigated here by means of simple geometrical calculations. It is first assumed that the lipid bilayer is of constant thickness and the distribution of the (local) mean curvature of the phospholipid-water interfaces is calculated. Then, assuming the mean curvature of these interfaces is constant, the distribution of the bilayer's thickness is calculated. Both calculations quantify the fact that the two energy terms are frustrated and cannot be satisfied simultaneously. However, the amount of the frustration can be smaller for the cubic phase than for the lamellar and hexagonal structures. Therefore, this phase can appear in the phase diagram between the other two, as observed in many recent experiments.

A Re-Evaluation of the Morphology of a Bicontinuous Block Copolymer−Ceramic Material

“…periodic minimal surface (IPMS) 9,13,20 where the thickness of the membrane determines its volume fraction. These "constantthickness" models are a good approximation for water-rich, surfactant bilayer network structures and have also been applied to the structure of block copolymers.…”

“…For the intermediate, liquid crystalline state, constant curvature 31 (G CC ) and constant thickness 9,13,20 (G CT ) structural models with the topology of the double gyroid structure were used to model the deformation of the PI and PEO/aluminosilicate domains. As illustrated in Figures 4c and 4d, contraction during these two stages of the solvent casting process should lead to different types of deformation.…”

“…To determine if a distorted double gyroid (distorted-G) structure was consistent with the experimental data, the structural deformations caused by lattice contraction were calculated for models of the double gyroid structure with elastic (G el ), constantthickness 20 (G CT ), and constant-curvature 20 (G CC ) material properties. Structure factors for these three distorted double The green IPMS divides space between the gold and blue skeletal frames, each of which forms a continuous network in all three spatial directions.…”

Photoinduced Fusion of Liposomes

“…The formation of QlI phases is also governed by the competition between curvature energy and the stretching energy of lipid chains (Anderson et al, 1988). As is the case in the hexagonal phase, the two terms are frustrated and cannot be simultaneously minimized.…”

“…Gruner and coworkers (Anderson et al, 1988) The largest factor contributing to their different phase behavior is the ability of PE to form hydrogen bonds between adjacent lipid head groups in the same membrane . The zwitterionic PC head group cannot form hydrogen bonds with its neighbors.…”