Viscosity anisotropy

The first viscosity measurements of nematic liquid crystals were performed with classical shear flow viscometers flow induces a change in orientation of the director, see EQN (4), so the effective viscosity measured is r o [54,55]. Since r o can be considered a relatively good approximation to the Miesowicz r i, conventional viscometers are still in use in conjunction with yi measurements [44,56,82,86]. However, for the purpose of measuring the viscosity anisotropy oldo instruments had to be modified and new ones developed. 

Multidimensionality may also manifest itself in the rate coefficient as a consequence of anisotropy of the friction coefficient [M]- Weak friction transverse to the minimum energy reaction path causes a significant reduction of the effective friction and leads to a much weaker dependence of the rate constant on solvent viscosity. These conclusions based on two-dimensional models also have been shown to hold for the general multidimensional case [M, 59, and 61]. 

Small molecules in low viscosity solutions have, typically, rotational correlation times of a few tens of picoseconds, which means that the extreme narrowing conditions usually prevail. As a consequence, the interpretation of certain relaxation parameters, such as carbon-13 and NOE for proton-bearing carbons, is very simple. Basically, tlie DCC for a directly bonded CH pair can be assumed to be known and the experiments yield a value of the correlation time, t. One interesting application of the measurement of is to follow its variation with the site in the molecule (motional anisotropy), with temperature (the correlation... 

Einstein coefficient b, in (5) for viscosity 2.5 by a value dependent on the ratio between the lengths of the axes of ellipsoids. However, for the flows of different geometry (for example, uniaxial extension) the situation is rather complicated. Due to different orientation of ellipsoids upon shear and other geometrical schemes of flow, the correspondence between the viscosity changed at shear and behavior of dispersions at stressed states of other types is completely lost. Indeed, due to anisotropy of dispersion properties of anisodiametrical particles, the viscosity ceases to be a scalar property of the material and must be treated as a tensor quantity. 

The flow velocity, pressure and dynamic viscosity are denoted u, p and fj and the symbol (...) represents an average over the fluid phase. Kim et al. used an extended Darcy equation to model the flow distribution in a micro channel cooling device [118]. In general, the permeability K has to be regarded as a tensor quantity accounting for the anisotropy of the medium. Furthermore, the description can be generalized to include heat transfer effects in porous media. More details on transport processes in porous media will be presented in Section 2.9. 

Rotational dynamics of a fluorescent dye adsorbed at the interface provides useful information concerning the rigidity of the microenvironment of liquid-liquid interfaee in terms of the interfacial viscosity. The rotational relaxation time of the rhodamine B dye was studied by time-resolved total internal reflection fluorescent anisotropy. In-plane... 

When anisotropy increases due to increase of local viscosity producing higher friction on rotating unit. This can happen, for instance, in micelles or lipid... 

Situation with H-bonding also demands to take into account the fact that alcohols have ability to form various associates or even clusters at normal conditions. The most efficient method for determination of inhomogeneity in the excited states is fluorescence polarization measurements. These methods also frequently applied for studying of solvent viscosity, they may be provided in two variants steady state and time-resolved. Relations for time-resolved and steady state fluorescence anisotropy may be given as [1, 2, 75] ... 

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

Borst JW, Flink MA, van Hoek A, Visser AJWG (2005) Effects of refractive index and viscosity on fluorescence and anisotropy decays of enhanced cyan and yellow fluorescent proteins. JFluoresc 15 153-160... 

If the g- and hyperfine anisotropies are known from analysis of a solid-state spectrum, the line-width parameters (1, and yt can be used to compute the rotational correlation time, tr, a useful measure of freedom of motion. Line widths in ESR spectra of nitroxide spin labels, for example, have been used to probe the motional freedom of biological macromolecules.14 Since tr is related to the molecular hydrodynamic volume, Ft, and the solution viscosity, r, by a relationship introduced by Debye 15... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

It is quite common to observe that the lines in a nitroxide spectrum show variations in width. One feature which contributes to this is the anisotropy of the nitroxide grouping, as a consequence of which the high field component of the nitrogen triplet may be perceptibly broadened. This effect is particularly noticeable when free tumbling of the nitroxide molecule is restricted either by the viscosity of the solvent or when the radical is incorporated into a very large (e.g. polymer) molecule. This selective line broadening is, of course, one of the principal sources of information in spin-labelling experiments (Berliner, 1976). 

It is worth pointing out that many artifacts can alter the measurements of emission anisotropy. It is necessary to control the instrument with a scattering non-fluorescent solution (r close to 1) and with a solution of a fluorophore with a long lifetime in a solvent of low viscosity (r x 0). It is also recommended that the probe concentration is kept low enough to avoid interaction between probes. 

Such is the newness of appreciation of near-IR fluorescence techniques that there is a dearth of examples in the literature of implementations of many of the classic fluorescence methods in the IR. Anisotropy is one striking example of this. However, in a comprehensive study of the anisotropy decay of dyes, including oxazine fluorescence at 720 nm, in mixed isotropic solvents Dutt et al.( T7 TS) have investigated the effects of viscosity on molecular rotation. 

As discussed, there are various methods of cation-radical generation. Every individual case needs its own appropriate method. A set of these methods is continuously being supplemented. For example, it was very difficult to prepare the cation-radicals of benzene derivatives with strong acceptor groups. However, some progress has been achieved, thanks to the use of fluorosulfonic acid, sometimes with addition of antimony pentafluoride, and lead dioxide (Rudenko 1994). As known, superacids stabilize cationic intermediates (including cation-radicals) and activate inorganic oxidants. The method mentioned is effective at -78°C. Meanwhile, -78°C is the boundary low temperature because the solution viscosity increases abruptly. This leads to the anisotropy of a sample and a sharp deterioration in the ESR spectrum quality. 

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