Orientationally disordered state

Molecular orientational order in adsorbed monolayers can be inferred indirectly from elastic neutron diffraction experiments if it results in a structural phase transition which alters the translational symmetry of the 2D lattice. In such cases, Bragg reflections appear which are not present in the orientationally disordered state. Experiments of this type have inferred orientational order in monolayers of oxygen (41) and nitrogen (42) adsorbed on graphite. However, these experiments have not observed a sufficient number of Bragg reflections to determine the molecular orientation by comparing relative Bragg peak intensities with a model structure factor. 

Figure 2. The structure of the chromonic N and M phases The basic structural unit of both phases is the untilted stack of molecules. The N phase is a nematic array in which these stacks lie in a more or less parallel pattern, but where there is no positional ordering. Tlie M phase is a hexagonal array of these columns. The six-fold symmetry is a result of orientational (but not positional) disorder. A schematic diagram of a localized region, as shown in (a) has only orthorhombic symmetry, but, averaged over the whole structure, each column actually lies in a site with sixfold symmetry (b). The restrictions to the possible orientations of the columns are shown in (c). Because of packing considerations, for any particular orientation of a column, as shown on the left, an adjacent column (right) can take up only two of the three possible orientations (i) and (ii). A representation of the orientationally disordered state of the M phase is given in Fig. 9. Note that the molecular columns are shown here in a highly stylized way. They are not necessarily such simple one-molecule-wide stacks.

Orientational disorder and packing irregularities in terms of a modified Anderson-Hubbard Hamiltonian [63,64] will lead to a distribution of the on-site Coulomb interaction as well as of the interaction of electrons on different (at least neighboring) sites as it was explicitly pointed out by Cuevas et al. [65]. Compared to the Coulomb-gap model of Efros and Sklovskii [66], they took into account three different states of charge of the mesoscopic particles, i.e. neutral, positively and negatively charged. The VRH behavior, which dominates the electrical properties at low temperatures, can conclusively be explained with this model. 

Durham polyacetylene occurs in a highly disordered state on conversion from the precursor polymer [90], but using stretch orientation techniques during the conversion reaction, a high degree of order with long conjugated sequences can be achieved [91-93],... 

McCullough, J.P., Finke, H.L., Gross, M.E., Messerly, J.F., and Waddington, G. Low temperature calorimetric studies of seven 1-olefins effect of orientational disorder in the solid state, / Phys. Chem., 61(3) 289-301, 1957. 

Order-disorder transitions are generally associated with (i) positional disordering, (ii) orientational disordering or (iii) disordering of electronic (or nuclear) spin states. The configurational entropy due to disordering is given by... 

Consider a disordered crystal of monodeuteriomethane in which each tetrahedral CH3D molecule is oriented randomly in one of four possible ways. Use Boltzmann s formula to calculate the entropy of the disordered state of the crystal if the crystal contains ... 

Another most interesting phenomenon has been observed by Mikami et al.31> The ethanol molecules exhibit orientational disorder over three different sites in the high-spin phase, but orient themselves more and more in one of the three sites with decreasing temperature. The variation with temperature of the orientational ground state population seems to be strongly correlated with the temperature dependent spin transition. The authors therefore suggest that the disorder-order transition of the ethanol molecule triggers the spin state transition. 

Fig. 5. Snapshots of C60 in (a) the high temperature disordered state and (b) the orientational glassy state (from Chakrabarti et al. [15]).

An appropriate analysis of the dynamics of the orientational disorder of the cations can be performed by means of proton NMR second-moment studies [53-55]. Such studies have established in the case of TEA(TCNQ)2 that the cation disorder is dynamic above 270 K while it is static below 205 K, with some transitional regime in between [53,54]. The wide transition of TEA(TCNQ)2 at about 210 K may then be considered to be a continuous structural transition from a state of dynamic disorder at high T to a state... 

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