Phase demixing

In 1970 Widom and Rowlinson (WR) introduced an ingeniously simple model for the study of phase transitions in fluids [185]. It consists of two species of particles, A and B, in which the only interaction is a hard core between particles of unlike species i.e., the pair potential v jsir) is inflnite if a P and r < and is zero otherwise. WR assumed an A-B demixing phase transition to occur in dimensions D >2 when the fugacity... 

FIG. 2 Phase diagram in the M-z plane for a square lattice (MC) and for a Bethe lattice q = A). Dashed lines Exact results for the Bethe lattice for the transition lines from the gas phase to the crystal phase, from the gas to the demixed phase and from the crystal to the demixed phase full lines asymptotic expansions. Symbols for MC transition points from the gas phase to the crystal phase (circles), from the gas to the demixed phase (triangles) and from the crystal to the demixed phase (squares). (Reprinted with permission from Ref. 190, Fig. 7. 1995, American Physical Society.)... 

The theoretical foundation for describing critical phenomena in confined systems is the finite-size scaling approach [64], by which the dependence of physical quantities on system size is investigated. On the basis of the Ising Hamiltonian and finite-size scaling theory, Fisher and Nakanishi computed the critical temperature of a fluid confined between parallel plates of distance D [66]. The critical temperature refers to, e.g., a liquid/vapor phase transition. Alternatively, the demixing phase transition of an initially miscible Kquid/Kquid mixture could be considered. Fisher and Nakashini foimd that compared with free space, the critical temperature is shifted by an amoimt... 

In state 3, polymers I and II are mixed and mutually diluted. Network I is stretched in the Flory-Rehner mode, although maximum swelling (with excess monomer) is not assumed. Demixing (phase separation) between polymer I and polymer II, with concomitant deformation of polymer II with further deformation of polymer I into a shell leads to state 4. State 4 shows a phase separated state, with a spherical domain of polymer II forming as the core. 

The demixed phase is metastable and crystals are formed after standing longer. With the complex coacervation gelatin + gum arabic (and others) no indications of metastability of the coacervate are ever observed. 

The manipulation of the size and cormectivity of demixed phases strongly depends on the fabrication parameters such as blending ratio, solvent selection, and annealing treatment, which have been discussed in detail in some recent reviews [87-92]. 

In order to keep the size of the book within bounds a description of the interface between demixed phases has not been included and the discussion of phase transition kinetics is rather brief. Also we emphasize that the references quoted do not claim to be a complete list. If the reader prefers it, (s)he can read the book at three levels. For a general idea of depletion interactions and their implications not only in coUoid science but also in systems of biological and technological interest it is recommended to study Chap. 1. At the second level one can study 2.1, 2.2, Chap. 3, 4.1, 4.2, 4.5 and 6.1-6.3, 6.5. This material could be used for 6-8 hour senior undergraduate or junior graduate course in physical chemistry or soft matter physics. The third level covers the complete text of this monograph. 

Methods. Interfacial tension was measured by the sessile bubble method. Density difference between demixed phases was measured by float method and differential re-fractometory. Details of the experimental methods have been described elsewhere. The volume ratio of separated phases was also measured to obtain the coexistence curve. The critical point was determined on the coexistence curve as a point at which the volume ratio was unity. The detailed method for ternary systems will be described elsewhere. 

Figure 17 Calculated state diagram for hard globules with diameter a dispersed In nematic rods with axial ratio L/D = too. 0s is the volume fraction of spheres, and 0r that of the rods. L/a = 10. The solid line marks the spinodal instability to the lamellar phase, and the dash-dotted line that to macroscopically demixed phases. The dotted line separates the region where self-assembled chains are of (a) the open type from that where they are of (b) the dense type. (From P. van der Schoot. J. Chem. Phys. 117 3537, 2002. With permission.)... 

Figure 6. Light reflectance vs. time recorded using the system shown in Figure 5 with a filament-lamp illuminator at 1 g. The casting-solution composition was 10% cellulose acetate, 27 % water, 63 % acetone (wt/wt). The initial thickness of the solution was 150 pm. The solid line indicates the drop in reflectance due to demixing (phase separation). Demixing begins after about 3.5 seconds and lasts approximately 3 seconds.

A phase diagram of a binary polymer blend can be derived from the Tg of the demixed phases under the following conditions ... 

In a more concentrated solution the interactions between unlike polymers provoke a demixing phase transition. In a common 0 solvent, the critical concentration scales as the overlap concentration c (in the symmetric case). In a common good solvent the critical concentration ck lies well in the semidilute regime and is governed by interactions related to corrections to the... 

Martel et al. investigated phase separation in glasses which occurs in silica-rich glasses however, some aspects as the first steps of the nucle-ation of domains with different compositions remain to be clarified as they are diffieult to eharacterize with most analytical techniques. studies and 2D Si- Si eorrelation experiments were used to characterize the Si-O-Si network after various heat treatments and are used to obtain the compositions of the two demixing phases. ... 

AFM images of a PS/PMMA/PVP film (1 1 1) cast from THF onto a SiO surface (a) as cast (b) after removal of PS by dissolution in cyclohexane (c) after removal of PMMA by dissolution in xylol. The superposition of cross sections from (a) to (c) show that the polar substrate is covered by a homogeneous PVP layer (bottom layer) which is covered by a laterally demixed phase morphology of PS (top layer) and PMMA (middle layer). 

These last results represent the idea that there is no change in the concentration of the demixed phases. 

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