Phase behaviour separation

The boundaries separating these principal types of phase behaviour are shown on X,C, diagram (for equalsized molecules) in figure A2.5.13. For molecules of different size, but with the approximation of equation (A2.5.10). more global phase diagrams were calculated using a third parameter,... 

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

Veenstra H., Hoogvfiet R.M., Norder B., De B., and Abe P. Microphase separation and rheology of a semicrystalUne poly(ether-ester) multiblock copolymer, J. Polym. Sci. B. Polym Phys., 36, 1795, 1998. Garbrieelse W., SoUman M., and Dijkstra K., Microstmcture and phase behaviour of block copolyfether ester) thermoplastic elastomers. Macromolecules, 34, 1685, 2001. 

Leu and Robinson (1992) reported data for this binary system. The data were obtained at temperatures of 0.0, 50.0, 100.0, 125.0, 133.0 and 150.0 °C. At each temperature the vapor and liquid phase mole fractions of isobutane were measured at different pressures. The data at 133.0 and 150.0 are given in Tables 14.9 and 14.10 respectively. The reader should test if the Peng-Robinson and the Trebble-Bishnoi equations of state are capable of describing the observed phase behaviour. First, each isothermal data set should be examined separately. 

Fig. 67 Schematic of phase behaviour for blend of novolac epoxy resin with nearly symmetric poly(methyl acrylate-co-glycidylmelhacrylate)-0-polyisoprene. Ordered L can be swollen with up to about 30% of resin before macroscopic phase separation occurs, producing heterogeneous morphologies containing various amounts of L, C, worm-like micelles and pristine epoxy. At lower concentrations, disordered worm-like micelles transform into vesicles in dilute limit. According to [201]. Copyright 2003 Wiley...

Studies of the phase behaviour at ambient temperature within the separator [43] show that there is significant solubility of the product nonanal within the fluorous phase and vice versa. Although this does not present a problem for the nonanal (it will simply be recycled to the reactor and create a steady state, it does mean that fluorous solvent is always being lost. The loss of the fluorous solvent (2.8 mol% into pure nonanal), as for the catalyst and the free ligand [41] is much more significant at low conversion, so... 

In addition to Rh-catalysed hydroformylation, this special phase behaviour has been successfully applied to other continuous catalytic reactions - such as Ni-catalysed, enantioselective hydrovinylation [66] and the lipase-catalysed kinetic resolution and enantiomer separation of chiral alcohols [67]. 

In this book, we have examined the chemistry behind the possible new approaches to solving the separation problem and have discussed process designs that could be used to implement the Chemistry. In this chapter, we have addressed what we believe to be the biggest problems remaining to be solved for the different approaches described in the rest of the book and have attempted to provide pointers towards possible solutions. These should provide impetus for further research in this important area aimed at improving the chemistry, phase behaviour, differential solubility and process design and eventually lead to the commercialisation of many more homogeneous catalytic processes so as to make chemicals production much more environmentally acceptable. 

However, if the catalyst and the base required for the reaction were added, a large amoimt of the mediator is required to obtain one single phase and the solvent systems are no longer temperature dependent. Hence, in all cases a homogeneous solution is obtained after the reaction and the catalyst can not easily be recycled by a simple phase separation. This observation emphasizes again the importance of investigating the phase behaviour of the true reactive systems whenever possible. 

As we have seen, the phase behaviour of block copolymers consisting of flexible polymer coils is remarkably rich. If one of the blocks is rigid, the copolymer would be expected to exhibit even more complex phase behaviour. For example, the rigid block could be mesogenic. This leads to the possibility of self-assembly of structures consisting of domains of liquid crystalline material within a microphase-separated block copolymer superstructure. Diblock copo-... 

The phase behaviour of blends of homopolymers containing block copolymers is governed by a competition between macrophase separation of the homopolymer and microphase separation of the block copolymers. The former occurs at a wavenumber q = 0, whereas the latter is characterized by q + 0. The locus of critical transitions at q, the so-called X line, is divided into q = 0 and q + 0 branches by the (isotropic) Lifshitz point. The Lifshitz point can be described using a simple Landau-Ginzburg free-energy functional for a scalar order parameter rp(r), which for ternary blends containing block copolymers is the total volume fraction of, say, A monomers. The free energy density can be written (Selke 1992)... 

---