The effects of pressure and temperature on the energetics and pivotal surface in a monoacylglycerol/water gyroid inverse bicontinuous cubic phase

We have studied the effect of pressure and temperature on the location of the pivotal surface in a lipid inverse bicontinuous gyroid cubic phase (Q(II)(G)), described by the area at the pivotal surface (An), the volume between the pivotal surface and the bilayer midplane (V-n), and the molecular volume of the lipid (V). Small angle X-ray scattering (SAXS) was used to measure the swelling behaviour of the lipid, monolinolein, as a function of pressure and temperature, and the data were fitted to two different geometric models: the parallel interface model (PIM), and the constant mean curvature model (CMCM). The results show that an increase in temperature leads to a shift in the location of the pivotal surface towards the bilayer midplane, whilst an increase in pressure causes the pivotal surface to move towards the interfacial region. In addition, we describe the relevance of An, Vn and V for modeling the energetics of curved mesophases with specific reference to the mean curvature at the pivotal surface and discuss the significance of this parameter for modelling the energetics of curved mesophases.