Sharp transitions

Seven isotopes of helium are known Liquid helium (He4) exists in two forms He41 and He411, with a sharp transition point at 2.174K. He41 (above this temperature) is a normal liquid, but He411 (below it) is unlike any other known substance. It expands on cooling its conductivity for heat is enormous and neither its heat conduction nor viscosity obeys normal rules. 

It is somewhat disconcerting that the MYD analysis seems to present a sharp transition between the JKR and DMT regimes. Specifieally, in light of the vastly different response predicted by these two theories, one must ponder if there would be a sharp demarcation around /x = 1. This topic was recently explored by Maugis and Gauthier-Manuel [46-48]. Basing their analysis on the Dugdale fracture mechanics model [49], they concluded that the JKR-DMT transition is smooth and continuous. 

Multiblock process Firestone has a trade secret process that produces rubbers with a multiblock structure, tapering of the blocks (i.e. there is not a sharp transition between the styrene and mid-block monomer composition), a broader molecular weight distribution (typically Mvj/M 2 versus 1.05-1.1 for the other processes). 

The sharpness of the transition in pure lipid preparations shows that the phase change is a cooperative behavior. This is to say that the behavior of one or a few molecules affects the behavior of many other molecules in the vicinity. The sharpness of the transition then reflects the number of molecules that are acting in concert. Sharp transitions involve large numbers of molecules all melting together. 

In order to predict Lhe transition point from stable streamline to stable turbulent flow, it is necessary to define a modified Reynolds number, though it is not clear that the same sharp transition in flow regime always occurs. Particular attention will be paid to flow in pipes of circular cross-section, but the methods are applicable to other geometries (annuli, between flat plates, and so on) as in the case of Newtonian fluids, and the methods described earlier for flow between plates, through an annulus or down a surface can be adapted to take account of non-Newtonian characteristics of the fluid. 

It appears from Fig. 3.2 that the experimental curve has been rounded off at Fdecomp.. as there is no such sharp transition between Cl2 gas at 1 atm diffusing... 

Overall mass-transfer rates at a sphere in forced flow, and mass-transfer rate distribution over a sphere as a function of the polar angle have been measured by Gibert, Angelino, and co-workers (G2, G4a) for a wide range of Reynolds numbers. The overall rate dependence on Re exhibited two distinct regimes with a sharp transition at Re = 1250. Local mass-transfer rates were deduced from measurements in which the sphere was progressively coated by an insulator, starting from the rear. 

Attempts to measure a critical flocculation volume of nonsolvent by titration with non-solvent as used by Napper (4) were not successful. A sharp transition between a relatively stable dispersion and a sudden loss of all colloidal stability was never observed and no unambiguous end-points could be detected. 

In the micellar region the trend to decreasing colloid stability is arrested and a partial improvement, in line with the enhanced level of polymer adsorption, is noted until the conditions for gross phase separation are reached. Only the intermediate block copolymer BC 42 shows indications of discontinuities in behavior at the solvent composition for micelle formation. The results presented here do not show the sharp transition from stability to instability found experimentally (4,8,17) by Napper and generally expected on theoretical grounds. However, there are important differences in experimental methodology that must be emphasised. 

Salicylaldimine ligands often give stable Fe(III) complexes, so it is uncommon to meet Fe(II) complexes with such ligands. The dark blue-green complex [Fe 17] (17) shows an unusual thermally-induced, two-step spin-state conversion where two sharp transitions are separated by a plateau extending over 35 K in which 50% high-spin and 50% low-spin molecules coexist [41]. 

Another class of red dopants, tetraphenylporphyrins (63), offer a direct energy transfer from blue to red [151], The absorption bands comprise the sharp porphyrin Soret band at 418 nm and the weaker Q bands at 512 and 550 nm. The photoluminescence shows two sharp transitions at 653 and 714 nm and can be induced from a blue emitting host by Forster transfer to the Soret band and internal conversion to the Q bands. 

In the early 1970s, Brigham and Tozer were the first to make a systematic study, using temperature as the variable, of the connection between potential, temperature, and pitting corrosion (Fig. 12). They argued that in principle a critical pitting temperature should exist, but the data obtained showed a transition over a range of temperatures. The sharp transition was demonstrated experimentally by Quarfort in 1989. 

The primary evidence for the conversion of gaseous monolayers at the air-water interface to other intermediate states lies in the abrupt changes found on the n-A isotherms of many film-forming compounds. So many of these isotherms have been reproduced in fine detail in a number of laboratories under a variety of conditions that they cannot possibly be rejected wholesale as artifacts. The sharp transitions from curves to plateaus, where the molecular area varies readily at constant surface pressure, may be related... 

Figure 4.2 Plot of the variable (emf — she) against the volume of ceric ion soiution during a potentiometric determination of [Fe ]. The end point is clearly shown by a sharp transition from the standard electrode potential of the analyte couple, p 2+. to that of the titrant couple, 3 (cf. equation (4.1)).

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