Anisotropy total

If there is a crystal anisotropy, with the easy axis parallel to the shape-anisotropy axis of the particle, the total anisotropy is = shape + crystal and the total switchHig field is = (A — Aj,)Af + 2Aj = crystal anisotropy constant). In the case of practical... 

Fluorescence depolarization by excitation transfer between intercalated ethidium dyes was originally studied in attempts to determine their unwinding angle/65, 156l5S i The total anisotropy was assumed to be given by a simple... 

The chemical shift 5, defined by Equation (22), was measured at 40.0 and 15.6 Mc./sec. and was found to be —3 2 relative to water for both SA and SG. The derivatives of the resonance absorptions were recorded in the measurements. If the total anisotropy of the chemical shift of protons in the solid is somewhat less than the line width, the cross-over point of the derivative will correspond to the average value of S as for liquids, and will be directly comparable with the shifts for protons in the liquid state. Comparison of the shift value with those of H3O+ (aqueous) (1 1), S = -1-11, OH (aqueous) (121), S = -1-10 dilute solutions of alcoholic-type protons... 

A value of 0 corresponds to the total isotropy, whereas a value of 1 indicates the total anisotropy. 

Bonet et al. (1999) performed the first three dimensional switching field measurements on individual magnetic nanoparticles of barium ferrite in the size range 10-20 nm. They showed conclusively that the total anisotropy energies of such particles of hexagonal symmetry could not be modelled as uniaxial but that a hexagonal anisotropy... 

Fluorescence anisotropy is an additive quantity when weighted by the fraction of total intensity emitted, i.e. if several different fluorophores are present in a sample, or if a single fluorophore is present in several different environments, the total anisotropy measured at a given wavelength will be given by [26]... 

London s method 31> for the calculation of 7r-electron anisotropies was an improvement on the Pauling approach but when applied to the higher benzenoid hydrocarbons still gave values which were somewhat too large. Subsequently, the more refined ah initio calculations si.33) on benzene have indicated the probable reason for this deviation. These calculations which were designed to obviate the need of an empirical value for the carbon-carbon resonance integral ( 3), indicated that only a part of the total anisotropy arises from the ir-electron ring current... 

The total anisotropy, AA = + AAjj, is derived by summing the aniso-... 

Anisotropy constants vary considerably with temperature. In most cases, anisotropy decreases steeply from a high value at low temperature and then slowly decreases down to zero at 7. The temperature dependence of the anisotropy constant for Zn,jNii Fe204 ferrites is shown in Fig. 4.27, for various compositions. At low temperatures, total anisotropy can be described in terms of anisotropy contributions from each cation (Kanamori, 1963). The anisotropy of Ni-Zn ferrites at 4 K, for example, can be obtained from contributions of Fe in octahedral and tetrahedral sites (Broese van Groenou, Schulkes Annis, 1967). The contribution from some cations, in particular Co and Fe, is positive above a given concentration of any of these cations, the anisotropy constant at low... 

In this expression r(/) is the time-dependent anisotropy, 0 the correlation times and g, the fraction of the total anisotropy (r ) which decays with this correlation time. In general we expect one component (tf,) due to rotational diffusion of the protein, and one due to torsional motions of the tryptophan residue, if such motions are significant. In proteins which contain more than a single fluorescent residue there can be energy transfer among the residues, which can appear as a component in the anisotropy decay. The timescale of energy transfer depends upon the distance and orientation between the residues, but there is little information on the timescale of energy transfer between intrinsic fluorophores in proteins. 

Suppose that a fraction a of the total anisotropy is lost due to the segmental motion, with a fast correlation time 6/r, and the remainder decays by overall rotational diffusion of the protein (6 ). For independent segmental motions and rotational diffiision, the anisotropy is given as the product of the depolarization frctOR (Section 10.10), and... 

Altem vely, the total anisotropy can be a variable parameter. In this case. 

An anisotropy decay more typical of proteins is shown by phospholipase A2. This enzyme catalyzes the hydrolysis of phospholipids and is active mostly when located at a lipid-water interface. Phospholipase Ai has a single tryptophan resichie (trp-3), which serves as the intrinsic probe. The anisotropy decay is clearly more complex than a single exponential. At long times, the correlation time is 6.5 ns, consistent with overall rotational diffusion. However, in comparison with LADH, there is a dramatic decrease in anisotropy at short times (Figure 11.14), The correlation time of the fast component is less than 50 ps, and this motion accounts for one-(hird of the total anisotropy. Independent tryptophan motions have been observed in a large number of proteins " and have been predicted by molecular dynamics calculations. Fast components in the anisotropy decay are also observed for labeled pro teins. Hence, segmental motions of intrinsic and extrinsic fluorophores appear to be a common feature of proteins. 

The cone angle for trypu ian rotational ffeedom can be calculated from the ratio of the anisotrq>y amplitude associated with the long correlation time to the total anisotropy. The fractional conliihed of die Imig cocida-tim time (r is ghrra by... 

The ThMni2 tetragonal structure (axial) causes anisotropy in the reported compounds. The anisotropy, particularly at low temperature, results predominantly from the lanthanide (R) sublattice however, as mentioned above it has recently been acknowledged that there is also a substantial contribution from the transition-metal sublattice (Thuy 1994, private communication). The interplay of anisotropy of both sublattices gives the final shape of the total anisotropy and causes the interesting phenomenon of the spin-reorientation transition to be discussed in sect. 3.3.3. 

Nevertheless, the total anisotropy of the ThMni2-type compounds result from the contributions of both magnetic-rare-earth and 3d-transition-metal sublattices. The anisotropy of the R sublattice is mostly determined by the crystal-field (CEF) interactions whereas the anisotropy of the transition-metal sublattice is due to anisotropy of exchange interactions. The Hamiltonian for the 4f-3d compounds (see e.g. Stefans and Wrzeciono 1989)is... 

---