Twist fluctuations

The study of a dilute solution of a polymer allows one to find the structure of an isolated chain. Therefore, it provides the unique opportunity to relate the conformational disorder, curvature of the chain and twist between monomer units, to the electronic properties of the conjugated backbone. From that viewpoint, several theoretical works paid special attention to the effects of twist fluctuations, emphasizing their influence on the n electron delocalization [25—29]. Besides, as some of these solutions exhibit spectacular colour changes as a function of the temperature or solvent quality, they were considered as the relevant systems to characterise the relationship between the n electron delocalization and the local structure of the chain. 

As possible explanations, several ideas have been proposed a hand-waving argument based on destabilization of twist fluctuations" [52], a possibility of an isotropic mechanism based on the non-uniform space charge distribution along the field [53] and the flexoelectric effect [55-57]. 

Fig. 4.7. Relaxation time r for the fundamental twist fluctuation mode dots) as a function of sample thickness d. The aligning layer was rubbed Nylon, the liquid crystal was 4-n-pentyl-4 -cyanobiphenyl (5CB) in the nematic phase (T = 32° C). Comparison between the best fit of the theoretically derived equation (solid line) and the best fit assuming infinite anchoring strength (dashed line) is made [32].

Fig. 4.10. Relaxation time t of the twist fluctuation mode circles) as a function of sample thickness d. For thicknesses below 3 (im a parabolic behaviour is observed solid line) and in this range the anchoring coefficient can be determined. For larger thicknesses the influence of higher fluctuation modes becomes apparent and the relaxation time decreases and approaches its bulk value [32].

Flow which fluctuates with time, such as pulsating flow in arteries, is more difficult to experimentally quantify than steady-state motion because phase encoding of spatial coordinate(s) and/or velocity requires the acquisition of a series of transients. Then a different velocity is detected in each transient. Hence the phase-twist caused by the motion in the presence of magnetic field gradients varies from transient to transient. However if the motion is periodic, e.g., v(r,t)=VQsin (n t +( )q] with a spatially varying amplitude Vq=Vq(/-), a pulsation frequency co =co (r) and an arbitrary phase ( )q, the phase modulation of the acquired data set is described as follows ... 

Here, the second term describes the change of the hopping amplitudes due to the displacement of the atoms parallel to the chain [cf. Eq. (3.5)] and the third term is a random contribution resulting from the conformational disorder (chain twists). While the lattice displacements u are dynamic variables, the fluctuations dl +t due to disorder are assumed to be frozen ( quenched disorder). 

Note that, while the random chain twists always decrease the hopping amplitudes (all ()/ , + are negative), // (a) can be both positive and negative, as it is the alternating part of the fluctuations. As in the FCM, we consider white noise disorder with a correlation function given by Eq. (3.22). This corresponds to independent random variations of the hopping amplitudes <5/ on different bonds. 

A very different model of tubules with tilt variations was developed by Selinger et al.132,186 Instead of thermal fluctuations, these authors consider the possibility of systematic modulations in the molecular tilt direction. The concept of systematic modulations in tubules is motivated by modulated structures in chiral liquid crystals. Bulk chiral liquid crystals form cholesteric phases, with a helical twist in the molecular director, and thin films of chiral smectic-C liquid crystals form striped phases, with periodic arrays of defect lines.176 To determine whether tubules can form analogous structures, these authors generalize the free-energy of Eq. (5) to consider the expression... 

Recently, the effects of static and dynamic structural fluctuations on the electron hole mobility in DNA were studied using a time-dependent self-consistent field method [33]. The motion of holes was coupled to fluctuations of two step parameters of a duplex, rise and twist (Fig. 1), namely the distances and the dihedral angles between base pairs, respectively. The hole mobility in an ideally ordered poly(G)-poly(C) duplex was found to be decreased by two orders of magnitude due to twisting of base pairs and static energy disorder. A hole mobility of 0.1 cm V s was predicted for a homogeneous system the mobility of natural duplexes is expected to be much lower [33]. In this context, one can mention several theoretical studies, based on band structure approaches, to estimate the electrical conductivity of DNA [85-87]. 

Although L-dopa can increase dopamine levels in the brain, its effectiveness decreases across time, such that larger and more frequent doses are required for it to be effective. In addition, after only 2-5 years of L-dopa treatment, its duration of effect is reduced. Chronic administration of L-dopa has been reported to produce psychiatric symptoms, such as paranoia, mania, anxiety, depression, hallucinations as well as increased incidence of insomnia and nightmares (92). It is not clear whether these symptoms are associated with chronic L-dopa therapy or disease course, since the two are temporally related (94). Chronic L-dopa therapy may also produce a state where patients response to administration fluctuates, such that they experience an on/off phenomena of L-dopa s effects. Additional symptoms of dyskinesias, e.g., involuntary twisting and writhing, are associated with this on/off phenomenon. Consequently, treatment with L-dopa is typically delayed until other treatments are no longer effective. 

Fluctuation relations for the shear viscosities and the twist viscosities were originally derived by Forster [28] using projection operator formalism and by Sarman and Evans analysing the linear response of the SLLOD equations [24]. They were very complicated, i. e. rational functions of TCFI s. The reason for this is that the conventional canonical ensemble was used. In this ensemble one... 

Note that these TCFl s are equal to the twist viscosity only in an ensemble where Q is constrained to be zero. Physically Eq. (4.6) expresses that the twist viscosity is high when there are large fluctuations in the torque needed to constrain the director. In the conventional canonical ensemble these integrals are zero, so that one must use other expressions for the twist viscosity. One such expression is... 

The twist viscosity is consequently inversely proportional to the TCFI of the director angular velocity correlation function. The physical interpretation of this relation is, that the twist viscosity is low when there are large fluctuations in the director orientation. This is usually the case when the order parameter is low. When the order parameter increases it becomes harder for the director to reorient, so that the twist viscosity increases. 

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