Long-range positional three-dimensional order

The mesomorphic state refers to anisotropic liquids (LCs) that are intermediate between a true liquid and a pure crystalline phase. More explicitly, it refers to the degree of molecular order that lies in-between the ideal three-dimensional, long-range positional and orientational order found in crystals and the random arrangement found in isotropic liquids, gases, and amorphous phases. Anisotropic liquids that exhibit the mesomorphic state are usually elongated, aromatic organic molecules. The mesomorphic state can be divided into the smectic and the nematic states. 

Long-range positional order in three dimensional is maintained only for structural features which are not point-centered (e.g., for the chain axes, for which two periodicities only are sufficient to define a three-dimensional repetition) iii) Long-range positional order of some feature is maintained only in two or in one dimension (e.g., only along each chain axis). 

Soft crystals that exhibit long-range positional molecular order, with three-dimensional stacks of layers correlated with each other. 

In liquid crystals or LC-glasses one looks for orientational order and an absence of three-dimensional, long-range, positional order. In liquid crystals, large scale molecular motion is possible. In LC-glasses the molecules are fixed in position. The orientational order can be molecular or supermolecular. If the order rests with a supermolecular structure, as in soap micelles and certain microphase separated block copolymers, the molecular motion and geometry have only an indirect influence on the overall structure of the material. 

Within the family of untilted smectics, there is a hierarchy of phases with order ranging from that of smectic A, in which there is no positional order within each layer, to the crystalline smectics B and E, which have long-range positional order within each layer, namely hexagonal and orthorhombic for the B and E phases, respectively. This inplane order, represented by the dots within circles or ellipses of Fig. 10-27, propagates from layer to layer, producing fully three-dimensional crystalhne order. The family of tilted smectics includes similar ordered phases J, G, K, and H. 

Liquid crystal is a term that is now commonly used to describe materials that exhibit partially ordered fluid phases that are intermediate between the three dimensionally ordered crystalline state and the disordered or isotropic fluid state. Phases with positional and/or orientational long-range order in one or two dimensions are termed mesophases. As a consequence of the molecular order, liquid crystal phases are anisotropic, i.e., their properties are a function of direction. 

The crystalline form of PAN may be classified as a solid mesophase of type ii) the PAN crystals or paracrystals have long-range positional order only for not-point-centered structural feature, that is the chain axes, for which the two a = b periodicities are sufficient to define a three-dimensional repetition of the position of the chain axes [97]. 

SmBhex Deh X T(l) A stack of interacting hexatic layers with three-dimensional, long-range, sixfold, bond orientational order and liquid-like positional correlations within the layers... 

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