Connected phase

The experimental results for 6 2 ai" also shown in Figure 3-44, along with theoretical results from Equation (3.67) for C = 0,. 2,. 4, and 1. As with the previous moduli, the experimental data are bounded by curves for C = 0 and C =. 4. The upper (parallel-connected phases) and lower (series-connected phases) bounds due to Paul (see Section 3.3) are shown to demonstrate the accuracy of the bounds in the present case where E is much greater than E. The lower bound results of Hashin and Rosen [3-8] correspond to C = 0, but their upper bound is below some of the experimental data in Figure 3-44. 

Percolation describes the geometrical transition between disconnected and connected phases as the concentration of bonds in a lattice increases. It is the foundation for the physical properties of many disordered systems and has been applied to gelation phenomena (de Gennes, 1979 Stauffer et al., 1982). At just above gelation threshold, denoting the fraction of reacted bonds as p and p=Pc + A/ , pc the critical concentration (infinite cluster), the scaling laws (critical exponents) for gel fraction (5oo) and modulus E) are ... 

Although any of the designs mentioned above will provide the location of phase boundaries (versus temperature and pressure), it is also important to know the compositions of the two phases in equilibrium. Note that while tie lines (lines connecting phases in equilibrium on T-x or p-x diagrams) are horizontal for simple binary mixtures, this is not true for phase separation in multicomponent systems (most notably polymer-fluid systems where the polymer sample contains chains of various lengths). Consequently, ports which allow withdrawal of samples following phase separation and equilibration are an important feature of view cells. Such ports also allow for the measurement of partition coefficients of solutes between, for example, aqueous and CO2 phases. 

Thermally induced phase separation (TIPS) an increased reaction temperature, or a high concentration, produces a high-connectivity phase structure so that the polymerization surpasses the phase separation using a low-temperature stage, a moderate decrease in phase separation is observed at a lower nucleation temperature (Kim et al. 2016 Padilla et al. 2011 Stieger etal.2003). 

Table 6.1 Critical Paints and Tie Lines Connecting Phases ( ) and (") Shown in 6.6...

Figure 8. Predicted interfacial area from 3D morphologies (rings, lenses, bulk connected phases) is smaller than measurements reported in the literature by as much as an order of magnitude. The area of Wfilm in drained pores increases during drainage, and when this area is added to the interfacial area, the predictions show the same trend as the data. The measurements have been normalized by the average radius of the grains or beads in each experiment.

Measurements of interfacial area reported in the literature generally exceed the predictions (Figure 8), except for very high W phase saturations. When the contribution of thin films of W in contact with NW in drained cells is included, the predictions exhibit the same trend as the data. We conclude that the experimental techniques are sensitive to the thin films as well as the interfaces between macroscopic volumes of W and N W, making a direct comparison of the predictions for 3D morphologies (pendular rings at grain contacts, lenses in pore throats, interface between bulk connected phases) impossible. The predictions... 

---