Sharpness of transition

Fig. 3. Effect of varied crosslink density on swelling of HPMC-E gels. Increased crosslinking decreases swelling below the transition temperature but has little effect on gel transition temperature, sharpness of transition, or degree of swelling above the transition. Lines added are to guide the eye. Reprinted from the Journal of Controlled Release (1991) 17 175 by permission of the publishers, Elsevier Science Publishers BV [52]...

For equilibrium polymerizations, the sharpness of transition has a well-defined physical meaning and may be defined mathematically by,... 

Table 27. Effect of polymer type on transition temperature and sharpness of transition of gels crosslinked with divinylsulfone [163]...

Derivative M LCST1 PQ Crosslinking density x 105 (mol cm-3) Sharpness of transition (%/° Q... 

The Kabalnov-Wennerstrom theory predicts that the sharpness of the transition from unstable to stable emulsions is controlled by the value of When the surfactants are compared in a homologous series, k increases and ao decreases with the surfactant chain length. Accordingly, the sharpness of transition from unstable to stable systems is expected to increase with the surfactant chain length. 

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. 

The distinction between the first member of the group and the two heavier members, which was seen to be so sharp in the early groups of transition metals, is much less obvious here. The only unsubstituted, discrete oxoanions of the heavier pair of metals are the tetrahedral [Ru 04] and [Ru 04]. This behaviour is akin to that of iron or, even more, to that of manganese, whereas in the osmium analogues the metal always increases its coordination number by the attachment of extra OH ions. If RUO4 is dissolved in cold dilute KOH, or aqueous K2RUO4 is oxidized by chlorine, virtually black crystals of K[Ru 04] ( permthenate ) are deposited. These are unstable unless dried and are reduced by water, especially if alkaline, to the orange... 

Numerical simulations of the k = oo case reveal a sharp phase transition at Ac = 0.27 [wootters]. Simulations also suggest that the spread in values of entropy decreases with increasing k, and that the width of the transition region probably goes as k f [woot90]. 

The transition from laminar to turbulent flow in micro-channels with diameters ranging from 50 to 247 pm was studied by Sharp and Adrian (2004). The transition to turbulent flow was studied for liquids of different polarities in glass micro-tubes having diameters between 50 and 247 pm. The onset of transition occurred at the Reynolds number of about 1,800-2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. 

In the laminar region the rms of streamwise velocity fluctuations was expected to be zero (Sharp et al. 2001). Figure 3.10 shows that the first evidence of transition, in the form of an abrupt increase in the rms, occurs at 1,800 < Re < 2,200, in full agreement with the flow resistance data. There was no evidence of transition below these values. Thus, the behavior of the flow in micro-tubes, at least down to a 50 pm diameter, shows no perceptible differences with the macro-scale flow. 

The number and sharpness of fluid layers depend sensitively on the porewldth as Is Illustrated by the theoretical results (which agree qualitatively with simulations) plotted In Figure 2. As porewldth Is Increased from say h = a, there appear one, two, three, etc. density peaks. A transition from N to N -h 1 peaks occurs as the porewldth varies from a value at which N layers are favored to a value at which N -f 1 are favored. A... 

McPhail (1989) gives a detailed account of the experimental approach to depth profiling of semiconductors, including the quantification of the data. He illustrates the analysis of a silicon epilayer grown by molecular beam epitaxy (MBE) in which 11 boron-rich layers were incorporated by co-evaporation of boron. The intended structure is shown in Figure 4.8, and it was desirable to establish the concentration of boron in the layers, the inter-peak concentration and the sharpness of the doping transitions. 

The reduction of N reduces considerably the increase in Qred(Q, t) and smears out the sharpness of the transition ... 

The electronic absorption can be attributed to the lowest polaron and/or bipolaron states in the gap (see Figure 3.72). It is clear from the above discussion that some form of transition in the carrier behaviour occurs near c. —0.2 V this is reinforced by a consideration of the IRAV absorptions in Figure 3.83(b). The IRAV bands are reasonably sharp up until —0.2 V after which they broaden and appear less well-defined. 

The width of the peaks in LETS depends upon the sharpness of the onset of the inelastic process, which in turn depends upon the thermal distribution of electron energies about EP. Thus, the IETS line width depends strongly on temperature and as shown by (3) [75]. Because of this, vibrational IETS provides infrared-quality resolution only when performed below 5 K. Electronic transitions are usually much broader than vibrational transitions therefore, electronic IETS is usually performed at liquid nitrogen temperature and slightly above (>77 K). An example of a system showing both vibrational and electronic IETS is presented in Fig. 5 [19]. 

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