Phase separation binodal compositions

Nowadays it is established that confocal microscopy observation can be a more sensitive method to assess die phase state of mixed biopolymer systems than the traditional centrifugation or viscometric methods (Alves et al., 1999, 2001 Vega et al., 2005). Indeed, microscopy can demonstrate that a system may be already phase-separated at compositions well below the apparent binodal line (as determined by these other methods). The report of Alves et al. (2001) demonstrates the relationship between specific compositional points in the phase diagram (Figure 7.1) and the observed microstructure (Figures 7.2 and 7.3) for water + gelatin + locust bean gum (LBG). The white areas in Figures 7.2 and 7.3 corre-... 

In Figure 2F-1 the composition where d2( G)/d 22 s equal to zero, or at the inflection point on the Gibbs energy surface, is defined as the spinodal composition. This corresponds to the boundary between an unstable solution and a metastable solution. If the necessary amount of free energy is supplied to the metastable system, the solution will phase separate into two phases with binodal compositions unstable system will always phase separate into the two phases. The temperature where the two points of inflection on the energy surface merge into a single point is defined as the critical solution temperature. 

Aharoni has reported experiments on the system tetrachloroethane/polyiso-cyanate (POIC)/polystyrene that confirm the foregoing predictions. The nematic phase separates at compositions in the range predicted polystyrene does not occur in detectable quantities in this phase. The binodal for the isotropic phase resembles the calculated curve shown in Fig. 6. 

At concentrations above ( ), a phase separation would lead to the formation of particles dispersed in a liquid matrix. The composition of such particles should be given by the binodal line. Thus such particles will still contain enough solvent to undergo a phase separation. Indeed such an internal phase separation can be used to prepare porous polymeric particles with potential for application as chromatography beads [48]. 

The growth rate, characterized by the change of the radius with time, is proportional to the driving force for the phase separation, given by the differences between 2 > the chemical composition of the second phase in the continuous phase at any time, and, its equihbrium composition given by the binodal line. The proportionahty factor, given by the quotient of the diffusion constant, D, and the radius, r, is called mass transfer coefficient. Furthermore the difference between the initial amount of solvent, (])o, and c]) must be considered. The growth rate is mathematically expressed by [101]... 

The solutions in the region inside the spinodal domain are unstable, whereas the solid solutions in the region between the binodal and spinodal lines are metastable. The presence of a miscibility gap limits the potential usefulness of these materials in device applications. Solutions with compositions lying inside the spinodal domain cannot be grown by LPE, whereas metastable solid solutions have a tendency toward phase separation and, eventually, device degradation. 

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. 

The temperature of the binodal and onset of phase separation is dependent on the composition. In a quench experiment, the time evolution of the phase separation is dependent on the end temperature and the composition. This means that the depth into the incompatibility region at a given position has an impact on the time evolution. Phase separation will then be trapped by gel formation, and it is the relative kinetics between phase separation and gel formation that determines the final morphology. Figure 13.12 gives an example of how the morphology of a discontinuous system depends on the composition and the relative kinetics of phase separation and gel formation (Loren and Hermansson 2000). 

For a polymer blend, where both mA and mB may be 1000, the critical value of x will be very small, Keep in mind what this means. Any value of x that is larger than means that the system will phase-separate at some composition. This is perhaps more easily seen if you recall that x varies approximately as 1/T, and a phase diagram can therefore be plotted as 1/x versus composition, if we so choose (Figure 11-22). Note also that the shape of the binodal and spinodal curves will depend upon the relative size of the molecules and will be skewed to one side or the other if mA is not equal to mB. 

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 points of the phase diagram between the spinodal and binodal curves correspond to metastable mixtures. The metastable homogeneous state is stable against small composition fluctuations and requires a larger nucleation event to initiate phase separation into the equilibrium phases given by the coexistence curve. This phase separation process is called nucleation and growth. 

Below the binodal, homogeneous solutions phase separate into a dilute supernatant of isolated globules and a concentrated sediment (assuming that the polymer has higher density than the solvent). The overall composition of the dilute phase of isolated globules is the lower volume fraction... 

The entire region enclosed by the outer dome represents immiscibility. The inner dome is known as the spinodal. The outer dome is known as the binodal. In the region of composition between the binodal and spinodal lines, phase separation occurs by the nucleation and growth mechanism and leads to the formation of dispersed micro-spherical glass particles in the matrix (see also Shelby, 1997). Spinodal decomposition which takes place inside the dotted region is a special type of phase separation. In order to understand this, consider two materials A and B, melts of which... 

The binodal curves (phase boundary) separate the one- and two-phase regions. Below the binodal cnrves are two-phase regions, and above the curves is a single-phase region. At the plait point of the binodal cnrve, all phase compositions are equal. The right plait point is nsnally located very close to the oil apex, and the left plait point is nsnally located very close to the water apex. In a two-phase region, the compositions of phases in eqnilibrium are connected with tie lines, along which may be found all possible proportions of the two phases, as explained in Example 7.1. Before that, we first need to review the lever rale. 

Interpretation of the phase separation fluorescence results requires that accurate values of the equilibrium binodal compositions for a particular temperature be available. These are necessary in order to calculate the volume fraction of the rich phase in the two component system. This volume fraction is assumed to be constant during the early stages of spinodal decomposition. 

Fig. 1. The phase diagram for a system showing upper critical behaviour. At temperature T3 mixtures are stable at all compositions whereas at Tt phase separation can occur. The origins of this phase separation are shown in the lower diagram which shows the plot of free energy against composition at T,. A metastable region exists between the binodal and the spinodal points ( B, and d>s, j respectiv-...

The whole composition range, 02 = 0 1, is subdivided into five sections by the binodal compositions 0 and 0f anc the spinodal compositions 0 and 0. The binodal points A and B are defined as points of common tangent to the free energy density curve. For compositions between 0 and 0 and between 0 and 1, the free energy of the mixture increases whenever it separates into two phases of... 

On the other hand, near the critical composition, the binodal and spinodal merge so that the metastable region reduces considerably in size. In this case, it is easier to pass directly into the unstable region by a thermal excursion before phase separation begins. Once in the unstable region, spinodal decomposition is the mechanism of phase separation. 

Visual inspection of films which had been heat-treated above the binodal revealed that phase separation had occurred to varying degrees depending on the nature of the heat treatment and the composition of the film. Some effort was made initially to stain the films with several chemical stains. These efforts... 

At a given pressure and temperature, the total Gibbs free energy of mixing of a one-phase polymer-solvent system of composition 2 should be necessarily minimum, otherwise the system will separate into two phases of different composition, as it is represented in a typical AG versus cp phase diagram of a binary solution (Fig. 25.3). The volume fractions at the minima (dAGIdcp = 0), cp, and (p will vary with temperature (binodal) up to critical conditions (T and (p ) where cp = tp" (Fig. 25.3b). 

Figure 25.3 Binary phase diagrams, (a) At Tj the mixture is miscible at all composition and at T2 the mixture shows phase separation (between (p and ip"). (b) Binodal and spinodal curves, and critical temperature (C.) and concentration (

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