Compressibility, transition region

According to Ehrenfest, a second-order transition occurs when p and its first derivatives are continuous across the transition region, but the second derivatives, Cp and compressibility, k are discontinuous. This behavior is illustrated in the second column of Figure 13.1. For these transitions, the enthalpy, in addition to the entropy and volume, is continuous across the transition. 

Before use, all the polymer pellets were dried at Ta +20 K for at least 48 h. Then, sheets of controlled thickness B were firstly compression molded under vacuum at Ta + 50 K and then cooled down slowly through the glass transition region. Next, samples of dimensions suitable for the SENB tests were cut from the sheets with a diamond saw, machined to produce the notch, and annealed once more at Ta +20 K for 72 h. The purpose of this thermal treatment is double first, it allows the elimination of the residual stresses induced by sample pressing and machining and secondly, it permits removal of eventual moisture which is known to affect dramatically the SAPA mechanical properties [12]. The pre-crack was produced in the samples just before testing. 

Upon further compression of the monolayer, a pronounced break, or discontinuity in the Isotherm marks a region of co-existence of the LE and the LC states. In most research papers it is stated that x(A) still increases upon compression beyond the beginning of the LE-LC transition region. Breaks may be indicative of higher-order phase transitions. The order of such a transition depends on the extent of co-operatlvity between the aliphatic chains. However, the presence of such transitions is not always well established. Pallas and Pethica found that... 

Figure 10. Fluorescence microscope images of PDA. The probe was NBD-hexadecylamine and the probe concentration was 1 mol%. (a) Isotherm at 20°C. The monolayer is prepared in the G-LE transition region (iii) bar = 100/tm. Expansion produces a foam structure (ii) that grows with time (i). With compression, (iii) is converted to an all-white phase and small dark islands appear at the LE-LC two-phase boundary (i v). The islands grow with further compression (v) and eventually deform and coalesce (viy The granular appearance of the LE phase in (vi) is the result of demixing of the dye at low dye concentrations this effect is not seen, (b) Measurements as a function of time after a quench from 20°C to 14°C at a fixed molecular area of 52 A. Circular bubbles of the gas phase nucleate around the LC domains and grow with time.

As already noted, when the LE phase is expanded, bubbles of gas grow and thin lamellae of fluid are left between them, forming a two-dimensional foam structure (Fig. 10a) in which the size of the cells and the distribution of the number of sides changes with time. Dendritic structures (Fig. 21) are observed in the LE-LC transition region when the monolayer is compressed, or in temperature quenches from the LE one-phase region into the two-phase region. In the case of fatty acids,only circular islands are observed at low temperature, even with rapid compression. The temperature threshold for the appearance of dendritic patterns is quite sharp. Such structures are also found in phospholipid monolayers. ... 

Actually, in both cases the interval of monomers concentrations in which reaction systems keep their homogeneity is practically coincides (of course with definite correction by temperature course of investigated processes since polymerization kinetics as it was mentioned earlier was measured at 60°C, and viscosimetry studies were carried out at 30°C). Moreover, undoubtedly the correspondence of "transition region" of monomer concentrations values was also traced at which compression of macroradicals balls and their turning obtained by mentioned independent methods (dilatometer and viscosimetry) was observed. 

A transitional region of relatively high compressibility may exist between L] and L2 films. This region corresponds to the so-called intermediate films (see region / of the curves shown in Fig. 11-22), the nature of which is not yet fully understood. 

TA Instruments dynamic mechanical analyzers are used over a temperature range from -150 to 600°C (-238 to 1112°F) to measure deformations for shear, tension, compression, three-point bending, and dual/single cantilever [3]. They include an optical encoder. DMA instrumentation is more sensitive than differential scanning calorimetry for measuring smaller transition regions. The company s DSC instruments measure heat... 

Heat transfer results are uncertain in the transition region because of the large number of parameters which determine when and how transition occurs (wall roughness, cross-sectional geometry, compressibility, Reynolds number and so on). Experimental results indicate that in smooth microchannels below Reynolds numbers of 1800-2000 the heat transfer results will be laminar and above 10 000 the results will be normally turbulent. The results in between are difficult to predict (see pressure-driven single-phase flow) unfortunately, this region is largely used... 

We now examine more closely the details of the volume contraction as portrayed in Fig. 11-7. The isotherms at different temperatures are closely superposable by horizontal translations just as are those for shear deformation in Fig. 11-1. Moreover, if one particular temperature in the transition region is arbitrarily designated as Tg. the translations of logarithmic time expressed as log Qt follow equation 21 closely. This result, obtained by Kovacs for several polymers, indicates that the temperature dependences of the molecular processes in bulk compression and in shear deformation are identical. Moreover, it permits calculation of the effect... 

The lipid monolayer is compressed into the phase transition region. This leads to the fonnation of solid-analogous lipid domains in a liquid-analogous matrix (Fig. 4 A). Injection of the labeled phospholipase A2 into the subphase (Fig. 4 B) is followed by specific recognition between the... 

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191]. 

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