Stepwise transitions

In summary, the fragmentary evidence at hand suggests that sulfur was the primordial iron complexing material and that this ligand system was selectively modified by stepwise transition to a mixed sulfur-nitrogen and sulfur-oxygen and, finally, to an all-oxygen type of coordination. 

Monte Carlo calculations have been carried out to simulate the spin transition behaviour in both mono- and dinuclear systems [197]. The stepwise transition in [Fe(2-pic)3]Cl2-EtOH as well as its modification by metal dilution and application of pressure have been similarly modelled by considering short- and long-range interactions [52, 198, 199]. An additional study of the effect of metal dilution was successfully simulated with the Monte Carlo treatment considering direct and indirect inter-molecular interactions [200]. A very recent report deals with the application of the Monte Carlo method to mimic short- and long-range interactions in cooperative photo-induced LS—>HS conversion phenomena in two- and three-dimensional systems [201],... 

Fig. 2. Degree of conversion n as a function of reduced time k,t. Initial equilibrium corresponds to K0 = Ki = 1, for example, to kt = k2 = k3 = kt = k2 = k3. Stepwise transition to...

The simplest situation occurs if X is highly stereoselective regarding the formation of R and if it shows an overwhelming preference to form the XR over the XS dimer. In this case, the competition between k 6 and k ]0 alone gives rise to the enantioselectivity reversal. Here, R is inhibited by the process X + R-o-XR but promoted by A + Z + X R + X. In this particular case, a stepwise transition between the two optically active states can be obtained by simulation within a certain range of the involved rate parameters when the concentration of the additive is gradually increased. A more general case where all the realistic processes are operative is shown in Fig. 7. 

Fig. 8 Early time evolution of the R and S Soai reaction products on both sides of the stepwise transition as shown in Fig. 7. a R-trapping is dominant giving rise to enantioselectivity reversal (pro-R catalyst [X]0 = 1.55 x 10 3 M) b R-catalysis is dominant resulting in the preservation of enantioselectivity (pro-R catalyst [X]o = 1.95 x 10-3). Same initial conditions and rate parameters as in Fig. 7...

We now turn from the single, possibly first-order like nature of the LDA-HDA transition to the multiple amorphous-amorphous transitions in water. When pressurizing LDA at slow rates at 125 K, a stepwise transition LDA—>HDA—>VHDA is observed [173], The piston displacement and density data as obtained from a piston-cylinder experiment that shows the stepwise nature are depicted in Fig. 11. The upstroke HDA >VHDA densification of 5% takes place in the pressure range 0.80-0.95 GPa and is somewhat less sharp when comparing with the upstroke LDA > HDA densification of 20% at 0.40-0.50 GPa. During fast compression, the LDA — HDA transition is still sharp, whereas the HDA—>VHDA transition is smeared out over a broad pressure range [173]. These findings support the possibility of an LDA-HDA first-order like transition but leave the question open whether a first-order like transition underlies the HDA—>VHDA transition and/or whether the observed second step... 

As already mentioned, stepwise transitions in foam films are observed, as a rule, at thicknesses less then 60 - 70 nm. The number of transitions increases with the increase in surfactant concentration. Manev et al. [351] have observed up to 10 transitions when the NaDoS concentration in the initial aqueous solution was raised to 0.5 mol dm 3 (in the absence of additional electrolyte). Upon increasing the ionic strength (addition of electrolyte or ionic surfactants) the differences in the transition thicknesses decrease. In some cases [351-353] electrolyte inhibits stratification. 

For AOS without electrolyte, again there were two thickness transitions although the stepwise transitions seemed somewhat greater than those for the foam film. The final thickness of the emulsion film was also greater than that of the foam film (about 20nm). 

We have seen evidence of a similar structuring of micelles in thin foam and emulsion films containing C AOS, in the form of stepwise transitions or stratification phenomena (see Figure 5). 

Wasan et al. (27-28) explained the process of stratification on the basis of a micelle-latticing structure model. In Figure 8 a schematic of the latticing model for film thinning is provided. By fluctuations in the structure of the micellar lamellae (i.e. the individual rows of micelles in Figure 8), the film can change its thickness by stepwise transitions, each of which are equal to the micellar-lamellae thickness. According to this model the number of transitions will depend upon the micelle concentration. 

Goulet T, Pepin C, Houde D, Jay-Gerin J-P. (1999) On the relaxation kinetics following the absorption of light by solvated electrons in polar liquids Roles of the continuous spectral shifts and of the stepwise transition. Radiat Phys Chem 54 441 48. 

In the beginning of the 20th century, Johnnott and Perrin observed that soap hhns decrease their thickness by several stepwise transitions. The phenomenon was called stratification. Bruil and Lyklema and Friberg et al. studied systematically the effect of ionic surfactants and electrolytes on the occurrence of the stepwise transitions. Keuskamp and Lyklema anticipated that some oscillatory interaction between the Him surfaces must be responsible for the observed phenomenon. Kruglyakov and Kruglyakov and Rovin reported the existence of stradficaHon with emulsion films. 

The experimental observations show that stratification is always observed when spherical colloidal particles are present in the film at a sufficiently high volume fraction therefore, a realistic explanation can be that the stepwise transitions are manifestations of the oscillatory structural forces. The role of the hard spheres this time is played by the colloidal particles rather than by the solvent molecules. The mechanism of stratification was studied theoretically in Reference 346, where the appearance and expansion of black spots in the stratifying films were described as being a process of condensation of vacancies in a colloid crystal of ordered micelles within the film. 

They indicated [211] that, while this equation reflects the state-of-the-art, its major limitations prevent one from obtaining quantitative structure-property relationships based on it. It does not involve the structural parameters of the material it takes no account of the relaxation (prefracture) state and it provides no way to describe any stepwise transitions, discontinuities, and abrupt qualitative changes upon the interaction of a material with its environment. They then devised a new method based on their autooscillation model of the solid state, and showed the promise of this method by using a heat-resistant polyimide as their example. 

Direct (instead of stepwise) transition metal catalyzed dicarboration is achieved by a modification of the palladium-catalyzed Heck reaction 2 4-85,86 116 if the final dehydropal-ladation step is suppressed. This step usually occurs after alkene insertion into an aryl - or a vinyl-palladium bond formed from the corresponding halide or triflate. 

Fig. 11.5 The tensile stress-strain curves of the two-phase PC/PMMA blends, obtained at room temperature. The plots illustrate a stepwise transition of yielding by crazing characteristic of PMMA, to shear banding, characteristic of PC (From Kyu et al. (1991) reprinted with permission of Hanser Verlag)...

In Fig. 11.5, the stress-strain plots are depicted for a series of two-phase PC/PMMA blends with various concentrations. The phase-separated morphology was obtained by melt mixing. The position of the yield point on the stress-strain curves illustrates the stepwise transition of micromechanism of tensile deformation, characteristic of PMMA, which is crazing, to the mechanism of deformation, characteristic of PC - shear 5delding. 

Fig. 13. Time-dependent electronic populations of the X, B and C states of Bz+ obtained from wavepacket dynamical calculations. The ab initio parameters of Ref. 148 and the MGTDH wavepacket propagation method have been employed in the study. The initial wavepacket is defined by a FC transition to the C state potential energy surface it is seen to undergo a stepwise transition to the B and then to the X state of the cation. The respective time constants are approximately 20fs and 200fs. (a) Calculation with degenerate vibrational modes and electronic states, (b) Analogous calculation, but suppressing these degeneracies. Apparently, this simpler calculation reproduces the full result of panel (a) quite well. For more details see text.

In addition, further thinning can cause an additional transformation into a thinner stable region (stepwise transitions). This usually occurs at high electrolyte concentrations and leads to a second, very stable, thin black film, known as Newton, Perrin or secondary black films 4 nm thickness). In these circumstances, short-range steric/hydration forces control the stability, and the disjoining pressure versus film thickness isotherms can be defined by the following relationship ... 

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