Microscopic measurement of the linear compressibilities of two-dimensional fatty acid mesophases

The linear compressibility of two-dimensional fatty acid mesophases has been determined by grazing incidence X-ray diffraction. The unit cell parameters of the \(\), \(\), \(\), S and \(\) phases of behenic acid \(\) and of the \(\) phase of myristic acid \(\) were determined as a function of surface pressure and temperature. Surface pressure versus molecular area isotherms were reconstructed from these measurements, and the linear compressibility (relative distortion along a given direction for a two-dimensional isotropic applied stress) was determined both in the sample plane and in a plane normal to the aliphatic chain director (transverse plane). The linear compressibilities range over two orders of magnitude from 0.1 to 10 m/N and are distributed depending on their magnitude in 4 different sets which we are able to associate with different molecular mechanisms. The largest compressibilities (10 m/N) are observed in the tilted phases. They are apparently independent on the chain length and could be related to the reorganization of the headgroup hydrogen-bounded network, whose role should be revalued. Intermediate compressibilities are observed in phases with quasi long-range order (directions normal to the molecular tilt in the \(\) or \(\)phases, S phase, and could be related to the ordering of these phases. The lowest compressibilities are observed in the solid untilted \(\) phase and for one direction of the S and \(\) phases. They are similar to the compressibility of crystalline polymers and correspond to the interactions between methyl groups in the crystal. Finally, negative compressibilities are observed in the transverse plane for the \(\) and \(\) phases and can be traced to subtle reorganizations upon untilting.