1) Condensed matter physics 
In physics, a mesophase is a state of matter intermediate between liquid and solid. Gelatin is a common example of a partially ordered structure in a mesophase. Further, biological structures such as the lipid bilayers of cell membranes exemplify the mesophase state. Georges Friedel (1922) called attention to the `mesomorphic states of matter` i.....
The phase of a liquid crystalline compound between the crystalline and the isotropic liquid phase.
a phase intermediate between liquid and solid. May also be a smectic phase.
<biochemistry> Arrangement of phospholipids in water where the liquid crystalline phospholipids form multi layered parallel plate structures, each layer being a bilayer, the layers separated by aqueous medium. ... (18 Nov 1997) ... 
(= smectic mesophase) Arrangement of phospholipids in water where the liquid-crystalline phospholipids form multi-layered parallel-plate structures, each layer being a bilayer, the layers separated by aqueous medium.