Deformation twist

We shall now extend the theory of the Freedericksz effect to study the dynamical behaviour when the magnetic field is switched on or off suddenly. The analysis is particularly simple for a twist deformation (fig. 3.4.1 b)) because the torsion exerted on the director does not result in a translational motion of the centres of gravity of the molecules. Neglecting director inertia in (3.3.2) we obtain the following equation of motion for this geometry  

The most general solution satisfying the boundary conditions 0 = 0 at z = +rf/2 is 

Neglecting higher harmonics and remembering that 0 has a maximum value at z = 0, we take 

Thus OmixU) attains the value d(oo) with a time constant t(H) given by 

If the field is now reduced to a value less than the decay rate is still given 

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Fig. 10 Co-operative twist deformation of a bundle with three chains. Reproduced with permission from [13]. Copyright 1998 Am Chem Soc... 

The rotational relaxation of DNA from 1 to 150 ns is due mainly to Brownian torsional (twisting) deformations of the elastic filament. Partial relaxation of the FPA on a 30-ns time scale was observed and qualitatively attributed to torsional deformations already in 1970.(15) However, our quantitative understanding of DNA motions in the 0- to 150-ns time range has come from more accurate time-resolved measurements of the FPA in conjunction with new theory and has developed entirely since 1979. In that year, the first theoretical treatments of FPA relaxation by spontaneous torsional deformations appeared. 16 171 and the first commercial synch-pump dye laser systems were delivered. Experimental confirmation of the predicted FPA decay function and determination of the torsional rigidity of DNA were first reported in 1980.(18) Other labs 19 21" subsequently reported similar results, although their anisotropy formulas were not entirely correct, and they did not so rigorously test the predicted decay function or attempt to fit likely alternatives. The development of new instrumentation, new data analysis techniques, and new theory and their application to different DNAs in various circumstances have continued to advance this field up to the present time. 

Fig. 30. Schematic representation of the twist deformation (a) changes in the components of the director w, defining the orientation change (b) twist deformation of an oriented layer of a nematic liquid crystal.

Backbone fractal dimension 54 Bending-twisting deformation 55 BET-surface area 13-14, 20 Brake system, frictional 145 Breakdown, filler cluster 64, 76... 

Fig. 5, 0°, structure on the left) which in FET results in a metastable product radical cation, and and one derived from a twisted (deformed) state where the electron density is shifted more to the hetero-atom (Fig. 5, 90°, right hand side) which in the prompt ionization should result in an extremely unstable and dissociative radical cation with high charge density at the hetero-atom. 

The desymmetrization of an achiral figure to transform it into a high-symmetry chiral one can also be achieved by a twist deformation around the C axis, and the direction of the twist determines the chirality of the figures generated... 

Figure 7). Osawa s recent force-field calculation study (21) of cage-shaped molecules with ethano bridges affords an excellent demonstration of this twist deformation at the molecular level. In six achiral cage-shaped molecules so far studied, his calculations showed that each molecule assumed a twisted, chiral conformation to minimize torsional and nonbonding strain. Tricyclo[4.2.2.2.2,s]dodecane (5) was shown to be 1.1 kcal/mol more stable in a twisted D2 than in the eclipsed D2h conformation, and his calculation also suggests that perhydrotriquinacene and C16-hexaquinane should assume C3 rather than conformations, contrary to naive pictures obtained by a casual observation of molecular models. 

The three kinds of deformations are associated with the variation of n, i.e. Vn. For the splay deformation, the divergence of the n vectors, V n, is not zero for the twist deformation, n V x n 0, and for the bend deformation, n x V x n 0. In order to describe the meaning of the three formulae, it is supposed that in the undeformed sample, n points along the z direction. These three deformations can hence be written in the form of components as follows... 

It is noted that there is no twisted deformation in liquid crystals, thus the K22 term does not appear in Fs. If the deformation is not so great, the splay deformation is dominant. When the deformation becomes greater, the bend deformation becomes more important. 

Concerning the twist deformation, shown in Figure 6.1(b), the parallel molecules are arranged in parallel planes but are twisted in these successive... 

If a magnetic field H is applied along the Y axis, the cholesteric liquid crystal has only the twist deformation. 

Here nd are elastic constants. The first, is associated with a splay deformation, K2 is associated with a twist deformation and with bend (figure C2.2.11). These three elastic constants are termed the Frank elastic constants of a nematic phase. Since they control the variation of the director orientation, they influence the scattering of light by a nematic and so can be determined from light-scattering experiments. Other techniques exploit electric or magnetic field-induced transitions in well-defined geometries (Freedericksz transitions, see section (C2.2.4.1I [20, M]. 

All physical parameters mentioned above are material specific and temperature dependent (for a detailed discussion of the material properties of nematics, see for instance [4]). Nevertheless, some general trends are characteristic for most nematics. With the increase of temperature the absolute values of the anisotropies usually decrease, until they drop to zero at the nematic-isotropic phase transition. The viscosity coefficients decrease with increasing temperature as well, while the electrical conductivities increase. If the substance has a smectic phase at lower temperatures, some pre-transitional effects may be expected already in the nematic phase. One example has already been mentioned when discussing the sign of Ua- Another example is the divergence of the elastic modulus K2 close to the nematic-smecticA transition since the incipient smectic structure with an orientation of the layers perpendicular to n impedes twist deformations. 

However, the threshold for a twist deformation cannot be detected optically when viewed along the twist axis. This is because of the large birefringence dri) of the medium for this direction of propagation (the case... 

Fig. 3.4.3. (a) The usual experimental configuration for the optical observation of the Freedericksz effect. Li t is incident normal to the film. However, for reasons discussed in the text, this arrangement is unsuitable for observing a twist deformation, b) Oblique configuration which enables the optical detection of a twist deformation. The magnetic field is perjjendicular to the plane of the paper... 

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