Phases hexagonales colonnaires thermotrope et lyotrope : défauts observés par cryofracture et caractère anomal du thermotrope

Electron microscopy observations of replicas of freeze-fractured samples of two columnar hexagonal phases of different nature (a lyotropic one, the inverse AOT in water; a thermotropic one, ) yield very different results: most defects at microscopic scales are screw dislocations in the lyotropic phase, longitudinal edge dislocations in the thermotropic phase. A possible way to interpret these differences is as follows: in the lyotropic the Lamé coefficients and μ and the bend modulus K₃ would not display any anomaly compared to expected values; in the thermotropic the shear modulus μ would be ten times smaller than the compressibility modulus , while K₃ would still be comparable to (but larger than) the bend modulus of a small molecules liquid crystal. We present an elementary theoretical model of the latter case which could explain the anomalous measurements of K₃ and of the longitudinal compressibility (Ref. [#!ref10!#]) without contradicting more recent measurements of (Refs. [#!ref17!#,#!ref22!#]). Essentially, the hexagonal phase would be a phase with defects (longitudinal dislocations) akin to an hexatic phase but with some differences. Re?u : 26 mai 1997 / Révisé : 20 Janvier 1998 / Accepté : 27 avril 1998