Limit of metastability

The ultimate limit of metastability is reached in reality when AF /kaTc is of order unity. Thus the width over which the spinodal singularities are rounded can be estimated from AF /kaTc oc 1 as... 

Note 1 The divergence temperature is the lowest limit of metastable supercooling of the isotropic phase. 

Figure 16.5. Supersaturation behavior, (a) Schematic plot of the Gibbs energy of a solid solute and solvent mixture at a fixed temperature. The true equilibrium compositions are given by points b and e, the limits of metastability by the inflection points c and d. For a salt-water system, point d virtually coincides with the 100% salt point e, with water contents of the order of 10-6 mol fraction with common salts, (b) Effects of supersaturation and temperature on the linear growth rate of sucrose crystals [data of Smythe (1967) analyzed by Ohara and Reid, 1973],...

Lynden-Bell RM (1995) Landau free energy, Landau entropy, phase transitions and limits of metastability in an analytical model with a variable number of degrees of freedom. Mol. Phys. 86 1353-1374... 

On the basis of the Saam-Cole-Findenegg approach, we are now able to revise the ideal isotherm for capillary condensation. A more realistic isotherm for the physisorption of a vapour in an assemblage of uniform cylindrical mesopores is shown in Figure 7.5. Here, C represents the limit of metastability of the multilayer (of thickness fc) and M the point at which the three phases (multilayer, condensate and gas) all coexist. Along MC the multilayer and gas are in metastable equilibrium. 

Because of the complexity of the processes involved and the various methods of measuring them, phase diagrams of organogels can be envisioned by different theoretical approaches. In one option, network formation can be considered according to a spinodal decomposition mechanism. Briefly, the spinodal curve in a phase diagram represents the limit of metastability defined by the second derivative of the free energy with respect to concentration Important features of such a mechanism are (1) the phase separation in solute-rich and solute-poor... 

ESTIMATION OF THE EXPLOSIVE BOILING LIMIT OF METASTABLE LIQUIDS... 

Figure 1. Pure water phase diagram in (P,T) coordinates calculatedfrom the IAPWS-95 equation of state, extrapolated at negative liquid pressures in the superheat domain. The outer lines starting from the critical point are the thermodynamic limits of metastability (spinodal). The dotted line is one of the proposed kinetic metastability limii (see text). Three isochoric lines (950, 900 and 850 kg m ) are also calculated by extrapolation of the IAPWS-95 equation.

Notice, that the critical point (Vr = 1, Pr = 1) is the upper limit of metastability (i.e., Pr < as the limit of single phase stability. 

Hence the Leibler theory [43] indeed predicts a second order transition for f = 1/2, while for f + 1/2 where the third order term is present, a first order transition is predicted, S-1(q ) = 0 then only yields the limit of metastability of the disordered phase ( spinodal curve ). Thus using the higher order terms in Eq. (184) to actually compute the free energies of various candidates for the ordered structure, one finds which phase has the lowest free energy, and in this way the phase diagram shown in Fig. 42 (left part) has resulted [43]. 

Fig. 47a-d. Hartree approximation for the free energy density fH(A) of a symmetrical diblock copolymer melt plotted vs the amplitude A of a concentration wave with q = q. For high temperatures (X < Xo) only the disordered phase (A = 0) existsfa). Aty0 N the limit of metastability of the lamellar ordering in the disordered phase appears (b), two metastable minima at A 0 develop, which become stable for % = %t- (c). Forx > X, the disordered state(A = 0) is only metastable (d), the lamellar phase being in stable thermal equilibrium. From Fredrickson and Binder [61]... 

The line oti the temperature vs. composition phase diagram for a mixture of two components, which separates the region from the two-phase regions. Hence, with binodal, it represents the limits of metastability of a two-phase system, viz., in polymer solutions or polymer blends. See also Binodal. ... 

F. Caupin, S. Balibar, and H. J. Maris, Limits of metastability of liquid helium, Phys. B-Condens. Matter ZZa, 356-359 (2003). 

The minimum and maximum of the isotherm in Fig. 3 indicate the limit of metastability of HDL and LDL, respectively. In other words, the system can remain in a metastable, homogeneous LDL state at < F < Fldl and in metastable, homogeneous HDL state at Fhdl < F < F ql- The maxima of all isotherms at T < Tc define the LDL spinodal line, (T). Similarly, the minima... 

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