  The linear compressibility of two-dimensional fatty acid mesophases has
determined by grazing incidence x-ray diffraction. Surface pressure vs
molecular area isotherms were reconstructed from these measurements, and the
linear compressibility (relative distortion along a given direction for
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
(10m/N) are observed in the tilted phases. They are apparently independent of
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 L_2 or L_2' phases, S phase), and
could be related to the ordering of these phases. The lowest compressibilities
are observed in the solid untilted CS phase and for 1 direction of the S and
L_2'' 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
L_2' and L_2'' phases and can be traced to subtle reorganizations upon
untilting.
