Unstable critical point

Fig. 3.2. Profiles of the charge density along the C2 symmetry axis for the dissociation of the water molecule. In (a) p decreases monotonically from a maximum value at the oxygen nucleus. As Ro is increased, an abrupt change occurs in the form of the curve when a point of inflexion appears (b). This unstable critical point exists only for this single configuration X, of the nuclei and a further increase in Rq results in Its bifurcation to yield a maximum, corresponding to the formation of a bond critical point and a minimum, corresponding to the formation of a ring critical point a.s typified by (c). The system has entered the region of the ring structure.

III) the point x = 0 is a structurally unstable critical point (degenerate critical point) ... 

The double critical point is formed if stable and unstable critical points merge. 

CPl and CP2 diminishes and finally vanishes for Ve = 1.4364, Fig. 6. Then, the stable critical point CPl and the unstable critical point CP2 merge, forming a double critical point. The cloud-point curves 1 and 2 and the shadow curves I and 2 reduce to a double critical point. If increases further, there appear only the critical point CP3 as well as the stable cloud-point curve 3 and the shadow curve 3. 

Depending on the MWD features, the critical point may be located on the continu ation of one of the two branches of the CPC drawn inside the phase separation region (metastable critical point) or on the line connecting two cusp points with which the continuations of the CPC branches end (unstable critical point). 

The reason for this s-shaped form of the spinodal is an unstable liquid— liquid critical point. Below the triple temperature, there exists a polymer-rich liquid and a solvent-rich liquid. Both binodal and spinodal of the polymer-rich phase become richer in solvent upon increasing temperature. This tendency of the polymer-rich spinodal persists also above the triple temperature, the spinodal runs towards the (unstable) critical point of the liquid—liquid phase coexistence, which would terminate the liquid— liquid phase coexistence if it was not pre-emptied by liquid-vapor coexistence. The unstable critical points are marked by a square in Figs. 19 and 20 (a-c). The influence of the unstable liquid—liquid critical point is also detectable in the combination c of densities which becomes unstable at the spinodal. Initially, spinodal decomposition leads to a liquid-liquid phase separation. This effect also matches the observation slightly above the triple temperature that the critical bubble is not filled with solvent-vapor - the thermodynamically stable phase - but rather with liquid solvent. Only at temperatures farther above the triple temperature, the spinodal adopts the normal behavior and approaches the liquid-vapor critical point. In this region the unstable mode also changes from liquid-liquid to liquid-vapor. 

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