A number of experimental data on hexatic liquid crystal phases, namely the smectic I and F phases of various members of the TBnA family, are presented. They allow a better understanding of the respective structures and information of the smectic I and F phases.

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We present a study of the range molecular interactions inside layers in smectic phases Α and I of PBnA (phenyl-4 benzylidene 4'-alkylaniline) liquid crystals family. The purpose of this work is to determine the correlation length of the molecules, gravity centers in existing domain of smectic phases and at the transition between them. We used X-rays in-plane peaks of the pattern diffraction of aligned sample by a magnetic field.PACS numbers: 61.30. 64.70.Md, 61.30.Gd 1. General The notion of correlation length [1-4] is easy to understand if we take into consideration the fluidity of liquid crystals. It is clear that this property is incompatible with infinite range of translation order. If we are placed on a specific point of smectic plane, the position of neighboring molecules will be entirely determined by the basic transition of smectic order. However this translation order is lost if w consider further molecules. The length at which this disorder becomes predominant is called correlation length. This correlation length can be taken in a simple way as the particle's ray having two-dimensional crystalline order that constitutes the smectic plan. This order was previously understood in the framework of the Nelson-Halperin theory [5] based itself upon the Kosterlitz-Thouless theory [6]. For these authors the melting of two-dimensional solid is assisted by continued dissociation of dislocation pairs. But recent results of high-resolution heat-capacity study and electron diffraction measurements performed on a number of liquid crystalline series in the vicinity of the smectic A-smectic I (SA-SI) phase transition have shown [7][8][9][10] an important disagreement with the predictions of Nelson-Halperin theory.To participate to this debate, we have studied and determined, by X-rays, the correlation length of the position order of molecules inside layers in smectic phases Α and I of family PBnA of liquid crystals (phenyl-4 benzylidene 4'-alkylaniline).

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