Short-range orientational correlations

Strong short-range orientational correlations can be conveniently taken into account in the cluster approximation. The simplest version of the cluster approximation in the theory of liquid crystals was proposed by Ypma et al. [26] who used the general approach of Callen and Strieb developed in the theory of ferromagnetism. 

The orientational order generated in a polymer network by an uniaxial stress is probed with deuterium NMR. The experiments are performed either on polydimethylsiloxane (PDMS) network chains or on PDMS probe chains dissolved in the network. The stress-induced orientation observed on both kind of chains is explained by short-range, orientational correlations between chain segments. 

A system exhibiting short-range orientational correlations among interacting species requires to modify the usual pair interaction parameters Xij (i = network chain segment, j = free chain segment or... 

There exist pre-transition effects in the isotropic phase heralding the I-N phase transition. Such pre-transition effects, which are consistent with the weakly first-order nature of the I-N transition, can be attributed to the development of short-range orientational order, which can be characterized by a position-dependent local orientational order parameter Q(r), where all component indices have been omitted [2]. In the Landau approximation, the spatial correlation function < G(0)G(r) > has the Omstein-Zemike form < G(0)G(r) exp(—r/ )/r, where is the coherence length or the second-rank orientational correlation length. The coherence length is temperature-dependent and the Landau-de Gennes theory predicts... 

Stack of interacting hexatic layers with in-plane short-range positional correlation and long-range 3D six-fold bond-orientational order... 

Similar to the positional pair correlation fnnction, the Gg function would possess a short-range orientation order for liqnid phases and long-range orientation order for crystal layers. Hence, analysis of the in-plane two-dimensional pair correlation function and orientation correlation function jointly can provide the transition between liquid and solid. Nevertheless, precise calculation of coexistence liqnid-solid phases can be done only by evaluating the chemical potential of the individual phases, or equality, of the grand potential Q = F - pAf (Fortini and Dijkstra 2006). 

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

Polymer Liquid and Glass. II. Short Range Order and Orientation Correlation. 

On the other hand, WAXS measurements of PE melt clearly indicate a range of intermolecular distance correlations of about 25 A [3]. Together with the relatively high density of polymer melts, the fact that the first interchain halo in WAXS patterns of oriented amorphous polymers tends to lie in the equatorial direction and the relatively high WAXS intensity of the interchain halo support the idea of parallel chain segments on the short range scale. 

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