Phase transition region

In the case of Gaussian and uniform distributions of the adsorption energy, the smearing of the phase transition region in the the first as well as higher layers was observed. Thus, insead of vertical jumps, the adsorption isotherms exhibited only finite slope even at quite low temperatures. This result is consistent with the predictions of Dash and Puff [32]. 

Fig. 68 Comparison of temperature-dependent intensity of first-order Bragg peak for bare matrix copolymer (A) containing 0.5 wt% nanocomposites with plate-like (V), spherical (o) and rod-like ( ) geometry. Data are vertically shifted for clarity. Inset dependence of ODT temperature on dimensionality of fillers (spherical 0, rod-like 1, plate-like 2). Vertical bars width of phase transition region. Pure block copolymer is denoted matrix . From [215]. Copyright 2003 American Chemical Society...

Figure 1. Comparison of the considered nuclear EoS. The hybrid EoS (dashed curve) has a phase transition region (1.8po < p < 3.5/9o) where adiabatic indices are substantially lower, followed by a quark phase which is has a similar stiffness as the nuclear matter at those densities.

A quark-hadron mixed phase between 5 x 1014g/cm3 and 1015g/cm3 3.5po where both quark and hadrons are present. In this phase transition region, the EoS substantially softens with T 1 — 1.5. 

A substantial simplification of the systematics in nuclear phase transition regions is obtained if the data are plotted against the product, Np Nn, of the number of valence protons and neutrons instead of against N, Z, or A as is usually done. Such a scheme leads to a unified view of nuclear transition regions and to a simplified scheme for collective model calculations. 

In Figure 7 a comparison is made of the frequency of the CHj antisymmetric stretching vibration as a function of molecular area for DPPC monolayer films at the A/W and A/Ge interfaces. As described above, the frequency of (his vibration is related to the overall macromolecular conformation of the lipid hydrocarbon chains. For the condensed phase monolayer (-40-45 A2 molecule 1), the measured frequency of the transferred monolayer film is virtually the same as that of the in-situ monolayer at the same molecular area, indicating a highly ordered acyl chain, predominately all-trans in character. For LE films as well as films transferred in the LE-LC phase transition region, however, the measured frequency appears independent (within experimental uncertainty) of the surface pressure, or molecular area, at which the film was transferred. The hydrocarbon chains of these films are more disordered than those of the condensed phase transferred films. However, no such easy comparison can be made to the in-situ monolayers at comparable molecular areas. For the LE monolayers (> ca. 70 A2 molecule 1), the transferred monolayers are more ordered than the in-situ film. In the LE-LC phase transition region ( 55-70 A2 molecule 1), the opposite behavior occurs. 

The results for the calculation of the orientation distribution for the hydrocarbon chains in the transferred monolayer films are presented in Figure 8. As is the case with the orientation distribution of the in-situ monolayers, the transferred films have a similar tilt angle in the expanded and phase transition regions. For the transferred monolayer, however, the tilt angle is in the range 35-40° from the surface normal, a much more oriented monolayer than the calculations indicate for the in-situ film (Figure 5). Figure 8 also shows that the condensed phase transferred monolayers are more oriented than those films transferred in the LE and LE-LC... 

The temperature dependences of optical properties of organic conductors beyond the phase-transition region have not been investigated sufficiently so far. The quantitative temperature studies of the e-mv coupling are very difficult and possible only for some selected low-dimensional salts. It was shown [94,95] that an analysis of T dependence of the IR spectra of the salts composed of isolated dimers (TCNQ)2- makes it possible to pinpoint the main mechanisms responsible for thermal evolution of the IR spectra and changes in the absorption coefficients. Among other things it was... 

The reaction rate sharply increases (up to several orders of magnitude) in the phase transition region [135, 136]. 

The normal component of the volume force, that is non-zero only within the phase transition regions, can then be expressed in terms of the volume fraction gradient [25] ... 

As could be expected, it follows from the results of this model that the phase transition region broadens with increasing temperature and disappears at high temperatures. The same picture was obtained for 2D structures in the paper (26) in the Weiss molecular field approximation. 

Magnetic Susceptibility of TTF-TCNQ Single Crystals in the Phase Transition Region 481... 

MAGNETIC SUSCEPTIBILITY OF TTF-TCNQ SINGLE CRYSTALS IN THE PHASE TRANSITION REGION ... 

The main limitation of ADSA as a film beilance is caused by the accuracy of the spread amount. To spread a big amount of surfactants will either make the drop fall down or make the isotherm enter the phase transition region too early. Considering the restricted surface area, a small amount of surfactant has to be spread which may cause relatively large errors in the calculation of the absolute molecular area of the surfactant onto the drop surface. This will lead to a shift of the isotherm along the x-axis and its stretching. So it is necessary to take particular care in delivering the substance onto the pendent drop. 

T his chapter presents a new formulation of the equation of state for - -fluids at subcritical and critical temperatures, T < 1. Unlike many other equations of state, this equation of state is defined as a differential equation, and is designed to describe not only the behavior of isotherms on their stable vapor and liquid branches, but also in the two-phase transition region. Interesting insights concerning the nature of metastable and absolutely instable phases are obtained also. 

Condition 2, a very strong constraint, ensures the proper behavior of the slope dP/dp on the phase boundary. Note that when P = Pa, then dP/dp = 0 for all regular points of Equation 1, i.e. Equation 1 yields the correct isothermal behavior in the two-phase transition region of a fluid (see Figures 1 and 2). 

The Differential Equation of State 1 provides not only a good qualitative description of isothermal behavior at subcritical temperatures T < 1, but also yields accurate quantitative representations of experimentally measured data. It describes not only the stable vapor and liquid branches, but also the two-phase transition region, additionally yielding information on the nature of metastable and absolutely unstable phases. A complete and simple description of the vapor-liquid-phase transition and the critical point also is provided by the differential equation of state. 

Fig, 5. The equation of state of 870 hard discs in the phase transition region.. i4, is the area of the system at close packing. The triangles refer to points for 72 particles. 

A copolymer of vinylidene fluoride-trifluoroethylene (VDF/TrFE) copolymer is well known as the polymer for which a clear Curie point was found for the first time in an organic material. At this Curie point, the polymer undergoes a solid-to-solid phase transition from paraelectric to ferroelectric phases with decreasing temperature. Therefore, the changes in the physical properties such as crystal structure, electrical and thermal properties upon the ferroelectric phase transition have drawn many researchers interest. Here, the results concerning the ultrasomc spectroscopic mvestigation on acoustic and viscoelastic behaviour around the ferroelectric phase transition region of this copolymer are described [15]... 

Fig. 16. Temperature and frequency dependence of absorption in P(VDF/TrFE) copolymer at the ferroelectric phase transition region...

Fig. 17. Temperature dependence of absorption at several frequencies at the ferroelectnc phase transition region of P(VDF/TrFE) copolymer...

In the a a phase transition at temperatures and hydrogen pressures below 293°C and 2 MPa, respectively, the lattice expands at the phase transition point increasing in volume by about 10% [22]. This unit cell volume change can result in mechanical strains, physical distortions, and possibly failure of the palladium if cycled through the palladium hydride phase transition region. 

ON THE INFLUENCE OF A DC FIELD ON THE THERMAL CONDUCTIVITY OF BARIUM TITANATE BASE CERAMIC SPECIMENS AND TRIGLYCINE SULFATE SINGLE CRYSTALS IN THE PHASE TRANSITION REGION. //ENGLISH TRANSLATION OF IZV. AKAD. NAUK SSSR, SER. FIZ. 31 /11/1842-4,... 

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