Crossover region

The first report [11] of a spin transition in a synthetic iron(II) system seems to be the result of a well-planned, deliberate strategy to identify the singlet/ quintet crossover region by the systematic variation of the field strength of the anionic groups in the six-coordinate species [Fe(phen)2X2] [7]. One... 

Modification of the field of 2,2/-bipyridine by replacement of one or both of the pyridine rings with five-membered heterocycles is a much more effective means of generating the crossover situation than replacement by six-membered rings. This has resulted in the crossover region being attained in a relatively large number of instances. The incorporation of thiazole moieties il-... 

The two principal strategies detailed above for reducing the field strength of diimine systems have also been effectively adapted to bring the field strength of tridentate terimine systems into the crossover region. 

In contrast to 6-substituted-bipyridine systems such as 49, attachment of a five-membered heterocycle to the 2-position of 1,10-phenanthroline, which is a structural modification similar to the replacement of one of the terminal rings of terpyridine, does generally bring the ligand field into the crossover region and spin transitions have been observed for such systems when the heterocycle is thiazole 51 [74], imidazoline [75], triazole [76], pyrazole [77] and oxadiazole [78]. 

The exponents in Eqs. (10) and (12) agree in the crossover region which, therefore, should correspond to Consequently, the concentrated solu-... 

For concentrations between the Rouse and reptation regimes, D can depend more sensitively on N due to the entropic barrier mechanism [6, 64]. In this crossover region, D can be written as... 

Fig. 4. Countour plot, with gray-scale shading ofthe effective exponent a,ffas a function ofthe common logarithms of the dimensionless ratios R/Rst and Rsu Rst- The large regions of gray, light gray, and white represent a = 1,2, and 3, indicative ofEC, TD, and PD, respectively. The crossover regions are relatively narrow. FromKhareandEinstein (1996). with permission.

The extreme nonidealities characteristic of electrolyte solutions warn of the dangers inherent in approximations commonly employed in general chemistry. Except in the crossover region of intermediate m where y + 1, blithe replacement of activity by molarity is seldom justified for strong electrolytes. Elementary treatments of acid dissociation, solubility products, and the like may therefore be subject to considerable error unless the realistic variations of chemical potential with concentration are properly considered. 

Phase separations could also be observed for Bu4NPic in alkanediols and glycerol, but the latter solvents possess a high cohesive energy density, and the phase transition seems to be of solvophobic nature [72]. In fact, Narayanan and Pitzer [108-110] showed that addition of 1,4-butanediol to 1-dodecanol shifts the crossover region away from Tc. For pure 1,4-butanediol, plain Ising behavior is observed. 

This crossover theory has been repeatedly tested with regard to MC simulations of the 3D lattice gas with variable interaction range. For example, a recently developed MC algorithm [318] allows the ratio of t/Na to be varied over eight orders of magnitude to cover the full crossover region [319]. The crossover theory gives an excellent representation of these data [320]. 

Fig. 128 Temperature dependence of the loss modulus, in the fi-a crossover region for PMMA and various CMIMx copolymers (from [79])...

Whereas for PMMA (Fig. 113) the two p peaks are quite well superposed, except in the p - a crossover region, in the case of the CMIM20 copolymer, the dielectric loss is weaker than the mechanical loss in the high-temperature part of the P transition. In contrast, in the p - a crossover region, the same behaviour is observed for the mechanical and dielectric responses, showing that, in CMIM20, the CMI units lead to a complete decoupling between the P and a transitions, which is not the case for PMMA. 

In the ft-a crossover region, typically above 50 °C, the intramolecular co-operativity of the ft motions is such that they can be considered as precursors of the a motions. A direct consequence is that yielding and plastic flow can occur under almost identical stresses, as shown in the strain softening amplitude (Fig. 23). 

The magnetic moments rise only slightly at elevated temperatures (see Table 5), which led the authors to conclude that some population of the higher sT2(Oh) state is possible. No clear distinction can be made as to which of the influencing factors, viz. electronic effects, steric hindrance, and crystal solvent effects, plays the dominant role here, because all of these are operative to some extent. Data from the UV-vis spectra of the nickel(II) complexes indicate that the ligands have field strengths in the iron(II) crossover region. 

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