Monodomains

An aligned monodomain of a nematic liquid crystal is characterized by a single director n. However, in imperfectly aligned or unaligned samples the director varies tlirough space. The appropriate tensor order parameter to describe the director field is then... 

Zhang SM, Greenfield MA, Mata A et al (2010) A self-assembly pathway to aligned monodomain gels. Nat Mater 9 594—601... 

Since the walls between heterochiral domains are unacceptable defects in an LC display, enantiomericafly enriched dopants are added to the LC to favor one sign of twist over the other in actual devices, providing a monodomain in the TN cell. It should be noted, however, that the chirality of the structure derives from the interaction of the LC director with the surfaces the molecular chirality serving simply to break the degeneracy between mirror image domains to favor one over the other. 

When analyzing the experiments, one normally assumes that ferromagnetic clusters are monodomain particles that is, all magnetic moments of the... 

Note 2 For a smectic mesophase, the term monodomain also implies a uniform arrangement of the smectic layers. 

Instabilities caused by the anisotropy of conductivity and corresponding to a periodic deformation of the alignment of the director in a nematic monodomain under the action of a direct current or low-frequency alternating current. 

Fig. 4.9 Crystal healing of goethite polydomainic serrated goethite crystals formed at 4 °C transformed to monodomainic smooth crystals after hydrothermal treatment at 180°C (Schwert-mann et al., 1985, with permission).

Fig. 4.14 Synthetic lepidocrocite produced by oxidation of a FeCl2 solution, a) Monodomainic, lath-shaped crystals, produced by oxidation with 100 ml air min " at 50°C and pH 7.5 shadowed with 5 nm chromium at 45° (Courtesy R.Ciova-noli). b) Multidomainic crystals obtained at pH 7-7.5 and room temperature (see Schwertmann Taylor, 1972a). c) Crystal aggregates produced in the presence of urotropin (courtesy R. Ciova-noli). d) Very small crystals showing (010) lattice fringes of 1 nm (Schwertmann. Taylor, 1979, with permission), e) Cubic crystals formed after ageing multidomainic crystals shown in (b) in M KOH containing 3.32 10 M Si at 80°C for 1749 h (Schwertmann Taylor, 1972, with per-...

Fig. 12.17 Dissolution morphology of synthetic 210 faces, c) Monodomainic Al-goethite (Al/ goethite crystals after partial dissolution in 6 M (Fe-tAI) = 0.097 mol mol" ) with cavernous dis-HCI at 25 °C. a) Pure goethite with dissolution solution at crystal edges (Schwertmann, 1984 a, along domain boundaries, b) Pure goethite with with permission), diamond-shaped dissolution holes bounded by...

Monodomains by Introducing Three-Point Coordination Statistics.66... 

The partition of molecular distance correlations into intra- and intermolecular contributions allows us to interpret these correlations in terms of a simple geometrical model. By this means, we are able to elicit structural units as for example segment-clusters that include intermolecular interference phenomena. These clusters are the primary structure units which we call monodomains . These natural units characterize the basic symmetry of the whole structure. If we keep in mind this basic symmetry, we can construct our structure model from a molecular level up to the level of the monodomain treating intra- and intermolecular correlations independently. If we do so, every X-ray pattern can be represented by accounting for the orientation distribution of these monodomains. 

The calculation of the monodomain structure factor requires several averaging procedures to account for all possible molecular conformations and orientation configurations. For reasons of clarity we have labelled each of these averaging procedures according to Table 2. 

The concept of defining monodomains in the way shown above includes (with the exception of pathologic cases) that, in the assembly of monodomains, each orientation occurs with the same probability. So it should be possible to construct a rotationally averaged representative monodomain. 

The first term on the right hand side gives the intramolecular contribution in the laboratory system which depends on conformation and orientation of the relevant single segments that means it depends on the mean intramolecular structure. The second term requires knowledge about the intermolecular structure within the monodomains. 

Now we must look at the consequences of the averaging procedures (1)—(5) with regard to the monodomain structure factor (see Table 2). First we calculate the intermolecular part Iimer.D °f the structure factor of a single domain and apply the averaging procedures (1)—(4) to it... 

To carry out the last averaging procedure (5), we have to integrate the monodomain structure factor Iin(er>D in system D with regard to the laboratory system L given in polar coordinates formulated as... 

Now we are able to express the whole monodomain structure factor in terms of the intra and intermolecular structure factors already calculated ... 

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