Gelation and Phase Separation

For the adhesive hard-sphere model, the theoretical phase diagram in the Tg-0 plane has been partially calculated (Watts et al. 1971 Barboy 1974 Grant and Russel 1993). According to this model, there is a critical point r. c = 0.0976 below which the suspension is predicted to phase separate into a phase dilute in particles and one concentrated in them (see Fig. 7-4). The particle concentration at the critical point of this phase transition is 0c = 0.1213. This phase transition is analogous to the gas-liquid transition of ordinary 

There are, however, important differences between the phase behavior of sticky spheres and that of small molecules, which arise from differences in the relative ranges of the attractive potentials. These differences have been explored in a wonderful set of calculations and experiments by Cast et al. (1983) and Pusey and coworkers (Uett et al. 1995) for suspensions of spheres that are made to attract each other by the polymer-depletion mechanism. In such systems, the range of the attractive potential relative to the sphere size can be varied by controlling the ratio = Aj fa of the polymer depletion-layer thickness to the sphere radius. For 0 the potential is short-ranged, like that of sticky hard spheres, 

7-5 shows the phase diagrams computed for the depletion potential, Eq. (7-6), with = 0.08, 0.33, and 0.57. These predicted diagrams were confirmed by experiments on PMMA 

When rigid fractal-like structures link up to span the medium, a gel is formed. Hence, 

Below the percolation line, there is predicted to be a sample-spanning cluster of contacting spheres. Woutersen et al. (1994) found that the gel point for 47-nm octadecyl-grafted silica spheres in benzene is in reasonable agreement with the predicted percolation transition. However, Grant and Russel (1993) found that the gelation line is below the percolation  

---

Durand, D., Gimel, J.Ch., Nicolai, T. (2002). Aggregation, gelation and phase separation of heat denatured globular proteins. PhysicaA, 304,253-265. 

Manoj, P., Kasapis, S., Chronakis, I.S. (1996). Gelation and phase separation in malto-dextrin-caseinate systems. Food Hydrocolloids, 10, 407 120. 

If gelation of one or both polymers precedes phase separation, the polymer gelling first will tend to be more continuous. If phase separation precedes gelation, then a rather coarse morphology may develop. Of course, both gelation and phase separation are controlled by the kinetics of polymerization and the concentration of the crosslinkers, as well as the thermodynamics of mixing. 

Two conceptually distinct phase transitions are thought to occur during coagulation gelation and phase separation (or precipitation). Gelation is the gradual transition of the... 

This chapter studies the local and global structures of polymer networks. For the local structure, we focus on the internal structure of cross-Unk junctions, and study how they affect the sol-gel transition. For the global structure, we focus on the topological connectivity of the network, such as cycle ranks, elastically effective chains, etc., and study how they affect the elastic properties of the networks. We then move to the self-similarity of the structures near the gel point, and derive some important scaling laws on the basis of percolation theory. Finally, we refer to the percolation in continuum media, focusing on the coexistence of gelation and phase separation in spherical coUoid particles interacting with the adhesive square well potential. 

Because the hydrophobic segments on polymer chains are partly exposed to water in the postgel regime, the solution tends to separate into two macroscopic phases by hydrophobic association. Thus gelation and phase separation compete as the temperature goes up. The solution reveals an interesting multi-critical phase behavior [33]. 

A THERMORHEOLOGICAL INVESTIGATION INTO THE GELATION AND PHASE SEPARATION OF HYDROXYPROPYL METHYLCELLULOSE AQUEOUS SYSTEMS... 

Hugouvieux Virginie, Axelos A. V. Monique, and Kolb Max. Micelle formation, gelation and phase separation of amphiphilic multiblock copolymers. Soft Matter. 7 no. 6 (2011) 2580-2591. 

TAK Takahashi, M., Shimazaki, M., and Yamamoto, J., Thermoreversible gelation and phase separation in aqueous methylcellulose solutions, J. Polym. Sci. Part B Polym. Phys., 39, 91, 2001. 

In this variety of associating polymer systems, a few central questions emerge as universal themes. One concerns the structure of multipolymer aggregates. In any system with strong interpolymer forces, one could anticipate interpolymer collapse, gelation, and phase separation as three reasonable consequences of these forces. Why then do many systems exhibit stable equilibrium aggregate... 

---