Mixtures binodal

Figure C2.1.10. (a) Gibbs energy of mixing as a function of the volume fraction of polymer A for a symmetric binary polymer mixture = Ag = N. The curves are obtained from equation (C2.1.9 ). (b) Phase diagram of a symmetric polymer mixture = Ag = A. The full curve is the binodal and delimits the homogeneous region from that of the two-phase stmcture. The broken curve is the spinodal.

The thermodynamics and physical properties of the mixture to be separated are examined. VLE nodes and saddles, LLE binodal curves, etc, are labeled. Critical features and compositions of interest are identified. A stream is selected from the source Hst. This stream is either identified as meeting all the composition objectives of a destination, or else as in need of further processing. Once an opportunistic or strategic operation is selected and incorporated into the flow sheet, any new sources or destinations are added to the respective Hsts. If a strategic separation for dealing with a particular critical feature has been implemented, then that critical feature is no longer of concern. Alternatively, additional critical features may arise through the addition of new components such as a MSA. The process is repeated until the source Hst is empty and all destination specifications have been satisfied. 

A line is drawn from Rn through M to give Ex on the binodal curve and ExF and SR to meet at the pole P. It may be noted that P represents an imaginary mixture, as described for the leaching problems discussed in Chapter 10. 

If hexane is used as the low molecular weight liquid, the desired phase separation is observed when precursor mixtures containing 6-15 wt % hexane are cured isothermally at 40 °C. Further discussion of the phase separation behavior requires more detailed consideration of the schematic phase diagram, as presented in Fig. 17, which resembles the real phase diagram shown in Fig. 13. Experimentally it is found, that no phase separation occurs with hexane concentrations equal to or lower than 5 wt %. Hence the critical amount for phase separation, (j)p, is given by the intercept of the binodal line and the imaginary value of Hence no phase separation occurs if is reached before the metastable region is entered. 

Let us again consider a solid mixture (A,B)N with a solvus field similar to the one outlined in the T-Xplot in figure 3. lOB, and let us analyze in detail the form of the Gibbs free energy of mixing curve in the zone between the two binodes (shaded area in figure 3.10A). 

Figure 3.14 Stability relations in a binary mixture (A,B)N as a function of temperature. Heavy, solid line activity trend for component (B)N in the case of binodal decomposition. Dashed line activity trend in the case of spinodal decomposition.

Differentiate between binodal and spinodal decomposition in polymer mixtures. 

To be able also to measure off-critical mixtures down to the binodal within a convenient temperature range, a mixture with a higher critical temperature than for the previous investigation of the critical behavior has been chosen. The system chosen was PDMS (Mw = 16.4 kg mol Afw/Mn = 1.10) and PEMS (Afw =... 

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... 

Due to the negative Soret coefficient of PDMS/PEMS, the composition in the center of the focus evolves towards higher PDMS concentrations and, hence, towards the two phase region. The mixture crosses the binodal after a time... 

The coupling of the order parameter to the temperature gradient also leads to unexpected excursions along the concentration axis in the case of off-critical mixtures. As a consequence, equilibrium phase diagrams lose their usual meaning in thermal nonequilibrium situations, and even an off-critical blend with a temperature above the binodal can be quenched into phase separation by local heating with a laser beam. 

Tie lines of the system can be generated from the equilibrium compositions for each run and selectivities computed. The results of measurements obtained for the 5% by volume of ammonia/ethylene are represented in the binodal diagram in Fig. 3. Butene is represented as the distributed component between the solvent phase and the butadiene-rich phase. The ammonia-solvent gas mixture was considered to behave as a pseudo-solvent of fixed composition. The ratio of the integrated peaks for butene(i) and butadiene(j) was used to compute the selectivity, B (beta), defined on a solvent-free basis, as ... 

According to Equation (2F-1), a liquid mixture with a total volume fraction liquid phases with binodal compositions Gibbs energy for the mixture will thus lie on the solid line between solid line is a tangent touching the predicted curve at the binodal compositions. 

The binodal branches do not coincide with the phase diagram axes. This means that the biopolymers are limitedly cosoluble. For instance, on mixing a protein solution A and a polysaccharide solution B a mixture of composition C can be obtained. This mixed solution spontaneously breaks down into two liquid phases, phase D and phase E. Phase D is rich in protein and E is rich in polysaccharide. These two liquid phases form a water-in-water (WIW) emulsion. Hie phase volume ratio is estimated by the inverse lever rule. The phase D/phase E volume ratio equals the ratio of the tieline segments EC/CD. Point F represents the phase separation threshold, that is, the minimal critical concentration of biopolymers required for phase separation to occur. 

Computer simulations of the binodal in the phase diagrams of polymer/polymer solvent mixtures have been carried out and show the effect of the various interaction parameters on the shape of the phase diagram. ... 

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