Liquid-solid spinodal

For the better understanding of blend morphologies, the fundamental mechanisms of morphology development are discussed, viz. the liquid-solid phase transition (crystallization), the liquid-liquid phase separation e.g., spinodal decomposition under non-isoquench depth), as well as the complex mechanism of the morphology generation that results from the competition between these two transitions. The effects of chemical reactions and flow fields on morphology development have also been discussed. Finally, several evidences of a local structure in single-phase polymer-polymer mixtures are presented. 

FigureZ. PhasedlagramofwaterproposedbySpeedy [18] plotted using the lAPWSEoS [25,26]. The solid curves are equilibrium lines, the dotted curve is the liquid-vapor spinodal, and the dashed curve the LDM. The circles show the experimental determination of the LDM at negative pressure [27]. When the spinodal and the LDM meet, the spinodal pressure reaches a minimum, and (for this EoS) retraces to positive pressure at low temperature. However, note that this would imply an improbable crossing between the spinodal and the metastable liquid-vapor equilibrium (see text for details).

Figure 4. Cavitation pressure as a fimction of temperature for two scenarios for water reentrant spinodal scenario (a) and liquid-liquid critical point scenario (b). These scenarios predict a different temperature behavior for the liquid-vapor spinodal (dotted curve), eitha- with a minimum (a. based on extrapolation of positive pressure data [40]), or monotonic (b. based on molecular dynamics simulations with theTIPSP potential [41]). The solid curve shows the prediction of CNT based on the bulk surface tension of water it becomes unphysical when it goes beyond the liquid-vapor spinodal. The dashed curve is the DPT prediction [40] that correctly remains above the spinodal, and reflects its temperature dependence.

Figure 23. The ph ase diagram of supercooled silicon in pressure temperature (P, T) plane obtained from simulations using the SW potential. The phase diagram shows the location of (i) the liquid-crystal phase boundary [115]—thick solid line, (ii) the liquid-gas phase boundary and critical point—line and a star, (iii) the liquid-liquid phase boundaiy and critical point—filled diamond and a thick circle, (iv) the liquid splnodal—filled circle (v) the tensile limit—open circle (vi) the density maximum (TMD) and minimum (TMinD) lines— filled and open squares, and (vii) the compressibility maximum (TMC) and minimum (TMinC) line—filled and open circle. Lines joining TMD and TMinD (dot-dashed), TMC and TMinC (solid), Spinodal (black dotted line) are guides to the eye.

In Fig. 1.14, the dotted lines for each curve show the activity of the coexisting phases at chemical equilibrium. Similarly in Fig. 1.16 the dotted line BDF shows the activity of the coexisting phases (5 = 0.185 and 0.815). The coexisting phases, which have the same structure, differ in the concentration of vacancies. This phenomenon is generally called phase separation or spinodal decomposition (it is observed not only in the solid phases but also in the liquid phases), and originates from the sign of the interaction energy... 

Figure 7.4 Phase diagram for adhesive hard spheres as a function of Baxter temperature rg. The solid line is the spinodal line for liquid-liquid phase separation (the dense liquid phase is probably metastable), the dot-dashed line is the freezing line for appearance of an ordered packing of spheres, and the dashed line is the percolation transition. (Adapted from Grant and Russel 1993, reprinted with permission from the American Physical Society.)...

Fig. 16. Calculated phase diagram of the soft-sphere plus mean-field model, showing the vapor-liquid (VLB), solid-liquid (SI.E ), and solid-vapor (SVE) coexistence loci, the superheated liquid spinodal (s), and the Kauzmann locus (K) in the pressure-temperature plane (P = Pa /e-,T =k T/ ). The Kauzmann locus gives the pressure-dependent temperature at which the entropies of the supercooled lit]uid and the stable crystal are equal. Note the convergence of the Kauzmann and spinodal loci at T = 0. See Debenedetti et al. (1999) for details of this calculation.

Figure 7. Spinodal of superheated liquid water solid line - by the empirical equation of state 1 - by Filrth equation , 2 -by Gimpan equation , - saturation line, C - critical point.

Figure 2. Schematic diagram showing the extent of the isotherm pressure jump following the vaporisation of a metastable (overheated) liquid with different levels of metastability (a

Figure 1. Pressure-temperature diagram illustrating the different perturbation processes of liquid water, and their relations with the stable, metastable and unstable fields of Hf). Solid line the saturation curve (LG). Dotted lines the mechanical liquid spinodal curve Sp(L) and the mechanical gas spinodal curve Sp(G).

Figures. Stability fields, calculated by the Anderko andPitzer equation of state of the HzO-NaCl system in a pressure-temperature diagram. Solid lines the saturation curve (LG) of pure water and the spinodal isopleths of p[fD-NaCl fluids (numbers refer to the mole fractions of NaCl). Dotted lines the liquid spinodal curve Sp(L, Hfd) and gas. spinodal curve Sp(G, HfJ) of pure water.

Figure 10. a) Conceptual sketch of hydrothermal systems, b) P-T diagram illustrating potentially explosive processes for the HfD-NaCl in an hydrothermal environment (see text). Thick solid lines the saturation curve for pure water (Sat) and the three-phase halite-liquid-vapour curve (HLG). Dotted line the critical curve (CC). Thin solid lines the spinodal curves forxj uCl 0.01 (3.2 wt% NaCl), 0.05 (14.6 wt % NaCl) and O.l (26.5 wt % NaCl) with their corresponding critical points (filled circles). The gray zones along liquid spinodal curves Sp(L) indicate the onset of the instability field of superheated NaCl... 

Figure 8.20 Txx diagram for liquid-liquid or solid-solid equilibria in binary mixtures that obey the Porter equation (8.4.32) with parameter A given by (8.4.38). Filled square is the critical point filled circles lie on the isotherm at 30°C. The inner envelope, with labels C and D, is the spinodal and satisfies (8.4.37). The outer envelope is the equilibrium curve, which satisfies the equilibrium conditions (8.4.35).

Spinodal decomposition of liquids or solids gives a distribution of the phases that has scale symmetry and these composites are fractals within a range of sizes. 

There are two fundamentally different ways that a solid can precipitate from a homogeneous fluid (gas or liquid) or in a homogeneous bulk solid by spinodal decomposition or as a nucleation and growth process. The morphologies of the products of these two processes are very different, as described in Section 4.2. 

Figure 1.13. State dicigram of a binary system with liquid-liquid amorphous separation a presents the bin-odal (solid curve) and spinodal (da.shed curve). The temperature dependences of the correlation length of the concentration fluctuation (at T > 1 ) and of the order parameter Aa 2 (at 7 < Tc) are described by power functions b shows the average molar Gibbs potential at T = 7) [bi,. sp are points on the binodal and spinodal, respectively)...

Binder, K., Billotet, C., and Mirold, P. (1978) On the theory of spinodal decomposition in solid and liquid binary Mixtures, Z. Physik B. 30, 183. 

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