Phase diagram spinodal line

FIG. 4 Theoretical NaPSS/LaCl3 phase diagram. The lines represent the spinodal lines for a degree of polymerization N of 106 (solid), 5 X 103 (long dash) and 5 X 102 (short dash). 

Figure A2.5.10. Phase diagram for the van der Waals fluid, shown as reduced temperature versus reduced density p. . The region under the smooth coexistence curve is a two-phase liquid-gas region as indicated by the horizontal tie-lines. The critical point at the top of the curve has the coordinates (1,1). The dashed line is the diameter, and the dotted curve is the spinodal curve.

FIG. 4 Qualitative phase diagram close to a first-order irreversible phase transition. The solid line shows the dependence of the coverage of A species ( a) on the partial pressure (Ta). Just at the critical point F2a one has a discontinuity in (dashed line) which indicates coexistence between a reactive state with no large A clusters and an A rich phase (hkely a large A cluster). The dotted fine shows a metastability loop where Fas and F s are the upper and lower spinodal points, respectively. Between F2A and Fas the reactive state is unstable and is displaced by the A rich phase. In contrast, between F s and F2A the reactive state displaces the A rich phase. 

Fig. 1. Equilibrium phase diagram T, c)=iT/Tc,c) for the alloy model used in Ref.. Solid lines boundaries of the disordered (a) and homogeneously ordered (6) fields areas c, d and e corre.spond to the two-phase region. Dashed line i.s the ordering spinodal separating the metastable disordered area c from the. spinodal decompo.sition area d. Dot-dashed line is the conditional spinodal that separate.s the area d from the ordered metastable area e.

Fig. 8 Phase diagram for PI-fc-PEO system. Only equilibrium phases are shown, which are obtained on cooling from high temperatures. ODT and OOT temperatures were identified by SAXS and rheology. Values of /AT were obtained using /AT = 65/T + 0.125. Dashed line spinodal line in mean-field prediction. Note the pronounced asymmetry of phase diagram with ordered phases shifted parallel to composition axis. Asymmetric appearance can be accounted for by conformational asymmetry of segments. Adopted from [53]...

Fig. 1. Phase diagram of a polymer solution. The upper curve shows LOST and the lower curve UCST behavior. Solid lines binodal, dotted lines spinodal T. temperature, x polymer concentration...

Fig. 40 Schematic phase diagram of the disordered phases for particles interacting with isotropic potentials (upper panel) and limited valence potentials (lower panel). In the first, standard case, the glass line hits the gas-liquid spinodal at large densities. In the limited valence case, the shrunk gas-liquid coexistence region leaves a new region in which a stable network with saturated bonding can develop. Reproduced with permission from [167]...

Figure 111 4 3. The phase diagrams obtained by computing the spinodal lines from Eq. 1. We can observe the occurrence of four phase separations indicated by the four spinodal lines in panel a). In the panel b), c), d), e) and f) we show the effect of the strength of the directional bonds (see text)...

We have reproduced the experimental pseudo-gap temperature using the thermodynamic model above discussed. The phase diagram has been obtained calculating the spinodal line from Eq.l. We have imposed Yo=a/Z>=19.5 meV, b= 2.00-K)-4 m3/mol, lyil=44meV, VyI= 9.25-Kr4 m3/mol, (j =Vy 16.25, ly2l=14 meV, Vy2= 4.8M04 m3/mol, a2-Vy 8.33,... 

The phase diagrams, obtained by calculating the spinodal line from Eq. 1, depend on the thermodynamic parameters described above. In Fig. 3 we report same... 

Figure 111 4 3. The phase diagrams obtained by computing the spinodal lines from Eq. 1.

Figure 11.22 shows that for compositions for which d2G/dc2 > 0, such spin-odal decomposition is not possible and nucleation of aq and 002 is required. Hence, spinodal reactions are possible only for composition/temperature combinations for which d2G/dc2 is negative. Sometimes this region is shown by dotted lines on phase diagrams, as in Figure 11.23. 

In contrast to the critical temperature Tc, the spinodal temperature Tsp is well below the binodal temperature for off-critical mixtures and can hardly be reached due to prior phase separation. The diffusion coefficients in the upper left part of Fig. 8 have been fitted by (23) with a fixed activation temperature determined from Dj. The binodal points in Fig. 8 mark the boundary of the homogeneous phase at the binodal. The spinodal temperatures Tsp are obtained as a fit parameter for every concentration and together define the (pseudo)spinodal line plotted in the phase diagram in Fig. 7. The Soret coefficient is obtained from (11) and (23) as... 

Fig. 17 Phase diagram of a PDMS/PEMS (16.4/48.1) blend. The dashed lines are the binodal and the spinodal. The phase contrast micrographs show typical demixing patterns for spinodal decomposition and nucleation and growth in the respective regions. The bullets mark the initial sample positions. See text for details. Figure from [112]. Copyright (2007) by the American Chemical Society...

In Figure 3.13 the precipitation pathway enters the two-phase region of the phase diagram above the critical point at which the binodal and spinodal lines intersect. This is important because it means that precipitation will occur as a liquid droplet in a continuous polymer-rich phase. If dilute casting solutions are used, in which the precipitation pathway enters the two-phase region of the phase diagram below the critical point, precipitation produces polymer gel particles in a continuous liquid phase. The membrane that forms is then weak and powdery. 

Figure 28 shows the spinodal lines for all the systems under discussion. At a low 0 (< 0.1), no noticeable differences are observed. This region of the phase diagram (including the critical point) corresponds to macrophase sep-... 

Fig. 1.9 Calculated polymer-solvent phase diagram. The bimodal (continuous line) is the coexistence curve the points below it correspond to thermodynamically unstable states, which undergo phase separation. However, the pints between the bimodal and the spinodal (dashed line) are ki-netically stable, since there is a free-energy barrier to phase separation. C indicates the critical point the collapse temperature. The deviation of the low-concentration branch of the spinodal from the vertical axis below T is an artifact of the mean-field approximation. (From ref. [62])...

Figure 13.11. A sehematic phase diagram of a binary mixture. Broken line spinodal. The metastable phase is hatched.

The resultant phase diagram is shown in Fig. 1. The line connecting points at various temperatures at composition satisfying Eq. (7) is the binodal. The line connecting points at composition satisfying Eq. (9) is the spinodal. 

Figure 5.13 Predicted phase diagrams for physical gels made from low-molecular-weight molecules with junctions of unrestricted functionality 4> is the total volume fraction of polymer, and Tr is here the reduced distance from the theta temperature, Tr = — Q/T. The parameter Aq controls the equilibrium constant among aggregates of various sizes. The outer solid lines are binodals, the inner solid lines are spinodals, and the dashed lines are gelation transitions. CP is a critical solution point, CEP is a critical end point, and TCP is a tricriti-cal point. (Reprinted with permission from Tanaka and Stockmayer, Macromolecules 27 3943. Copyright 1994 American Chemical Society.)...

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.)...

In a UCST system, when the temperature is reduced to a final value 7/ that is below the critical temperature Tc, a mixture with a concentration 0 not too far from the critical composition phase separate into two phases whose compositions lie on the opposite sides of the binodal envelope line of Fig. 9-1. The dynamics of the separation process of a single phase into these two phases is controlled by Tf, the composition , the rate of the quench dT/dt, the viscous (or viscoelastic) properties of the phases formed, and the interfacial tension F between the two phases. Although a variety of different kinds of behavior can occur, there are two generic types of phase separation, namely, spinodal decomposition (SD) and nucleation and growth (NG). SD occurs when the mixture is quenched into a part of the phase diagram where the mixture is unstable to small variations in composition, leading to immediate growth of phase-separated domains. When the quenched... 

Figure 9-1 Schematic phase diagram of a binary fluid mixture of small molecules. The two-phase region lies under the binodal line, the apex of which defines the critical temperature Tc and critical composition Between the binodal and the spinodal lines, phase separation is by nucleation and growth (NG), while under the spinodal line it is by spinodal decomposition (SD). Within the region of spinodal decomposition, near the compositional symmetry line, there is a region where the morphology is initially bicontinu-ous. Outside of this region, one of the phases is a discontinuous droplet phase. Eventually,...

The schematic phase diagram in Fig. 141 shows the miscibility gap marked by the full line 1. The intersections of horizontal lines with the full line boundary specify the composition of both phases being separated. The dashed line and the hatched area show the region of spinodal decomposition. 

Fig.6. Phase diagram of PS/PVME blend [23] where the line represents the calculated results using the simulated equation-of-state parameters with (,= 1.00066 and filled circles represent experimental spinodal data [37]...

Herein, we expand on the discussion of our recently observed isothermal amorphous-amorphous-amorphous transition sequence. We achieved to compress LDA in an isothermal, dilatometric experiment at 125 K in a stepwise fashion via HDA to VHDA. However, we can not distinguish if this stepwise process is a kinetically controlled continuous process or if both steps are true phase transitions (of first or higher order). We want to emphasize that the main focus here is to investigate transitions between different amorphous states at elevated pressures rather than the annealing effects observed at 1 bar. The vast majority of computational studies shows qualitatively similar features in the metastable phase diagram of amorphous water (cf. e.g. Fig.l in ref. 39) at elevated pressures the thermodynamic equilibrium line between HDA and LDA can be reversibly crossed, whereas by heating at 1 bar the spinodal is irreversibly crossed. These two fundamentally different mechanisms need to be scrutinized separately. 

---