Strong First-Order Transitions

For a strong first order transition, as suggested in [21], a new branch in the mass-radius diagram could exist, see Figure 9. 

Figure 9. For a strong first order transition, a new stable branch can exist in the mass-radius relation (Figure from [17]).

In summary, we showed that near a FQCP, spin fluctuation exchange gives rise to a strong first order transition into a triplet superconducting state. As a result, Tc saturates at a nonzero value at criticality. The first order transition persists up to a finite distance from the FQCP, where it becomes second order. 

Figure 1(a) gives the temperature dependence of H near a strongly first-order transition with a large latent A//l at 7,r. The variation of H with T is nearly linear above and below Ttr resulting in almost temperature independent Cp values in the low and high temperature phases. Figure 1(b) represents the case of a weakly first-order transition with only a small latent heat but H... 

FIG. 16 Phase diagram of fluid vesicles as a function of pressure increment p and bending rigidity A. Solid lines denote first-order transitions, dotted lines compressibility maxima. The transition between the prolate vesicles and the stomatocytes shows strong hysteresis efifects, as indicated by the error bars. Dashed line (squares) indicates a transition from metastable prolate to metastable disk-shaped vesicles. (From Gompper and KroU 1995 [243]. Copyright 1995 APS.)... 

The curvature correction can be important when K is small, R is small, and/or a is large. With regard to this aspect, Hirotsu has recently found strong size-dependence of the first-order transition temperature and proposed that a can be much larger in ionized gels than in neutral gels due to the presence of an electric double layer at the interface [31]. 

Another unique feature of ionized NIPA gel has been found recently both of the equilibrium swelling ratio a and the first-order transition temperature T0 depend strongly on the shape of samples [31]. The measurement of equilibrium a has been made on ionized NIPA gel rods of various diameters, and also on plates and cubes. The gel contained 680 mM NIPA, 20 mM acrylic acid (AA), and 8.6 mM BIS. All samples were prepared from the same pregel solution at the same time so as to guarantee that the composition and the structure of all samples were the same. 

The phase coexistence observed around the first-order transition in NIPA gels cannot be interpreted by the Flory-Rehner theory because this theory tacitly assumes that the equilibrium state of a gel is always a homogeneous one. Heterogeneous structures such as two-phase coexistence are ruled out from the outset in this theory. Of course, if the observed phase coexistence is a transient phenomenon, it is beyond the thermodynamical theory. However, as will be described below, the result of the detailed experiment strongly indicates that the coexistence of phases is not a transient but rather a stable or metastable equilibrium phenomenon. At any rate, we will focus our attention in this article only on static equilibrium phenomena. 

It is characterized by double-bifurcation reactions with three directly connected first-order transition states. These are two transition states 570 and transition state 562. The chemical behavior of cation 560 is determined by the stereocomposition of a cyclo-propylcarbynyl cation moiety in conjugation with two vinyl group. The 9-barbaralyl cation 560 is characterized by four weak C—C single bonds (bond orders = 0.54 and 0.84) and one strong nonbonded interaction that can be easily broken and closed. 

Raman spectra for the sample were conducted in a compression-decompression cycle. In this experiment, the crystalline diffraction began to disappear above 7-8 GPa during compression, and pressure-induced amorphization was indicated by the Raman spectra above 13 GPa (Fig. 14). The resultant HDA Si exhibits the Raman spectrum that differs from the spectrum of normal -Si (LDA Si). Rather, the characteristics of the spectrum for HDA Si resemble those of the (3-tin crystal, which indicates that HDA Si has a (locally) analogous structure to the (3-tin structure. The synthesis of the HDA form of Si by Deb et al. [263] has a strong resemblance to that of water (ice) by Mishima et al. [149, 196]. Whereas compression induced amorphization that was almost completed at 13-15 GPa, decompression induced an HDA-LDA transition below 10 GPa, which is clearly shown in the Raman spectra (Fig. 14). This is the first direct observation of an amorphous-amorphous transition in Si. The spectrum at 0 GPa after the pressure release exhibits the characteristic bands of tetrahedrally coordinated -Si (LDA Si). Based on their experimental findings Deb et al. [263] discussed the possible existence of liquid-liquid transition in Si by invoking a bond-excitation model [258, 259]. They have predicted a first-order transition between high-density liquid (HDL) and low-density liquid... 

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