Cloud point polydisperse systems

Supercritical fractionation of high molecular weight alkane mixtures with propane or LPG may be used to produce products with lower polydispersity that that of molecular distillation. Operating temperatures just above the cloud point of the mixtures can be used compared to the high temperatures needed in molecular distillation. It was also shown that an optimum reflux ratio exists for every set of operating conditions. For this system it was also found that the operating costs of a supercritical fraction unit is marginally less than that of a molecular distillation unit. 

Figure 3.36 The effect of ethanol and acetone cosolvents on the cloud point pressure of the poly(ethylene-co-methyl acrylate) (90mol% ethylene and 10 mol% methyl acrylate)-propane system. The copolymer concentration is fixed at 5 wt% and the weight-average molecular weight of the copolymer is 34,000 with a molecular weight polydispersity of 2.0. This copolymer is —15% crystalline. (Hasch et al., 1993.)...

Figure 15.5 Effect of molecular weight dispersity ( )) (formerly known as polydispersity) using schematic Gibbs triangle diagrams for polymer-solvent system, generation of cloud point curve and shadow curve in temperature-composition diagram.

The binodal curve is the boundary between thermodynamically stable and metastable solutions. The term binodal is used in truly binary systems while in actual polydisperse systems the correct denomination is cloud-point curve (CPC). Thus the experimental determination of this boundary always leads to a CPC. 

The simple thermodynamic model derived in Sect. 2.1 has been useful to get a qualitative insight into the phase separation process. When one intends to apply it to an actual system, the significant influence of polydispersity is clearly evidenced. For example, Fig. 13 shows the experimental cloud-point curve for a DGEBA-CTBN binary mixture, together with binodal and spinodal curves calculated by assuming monodisperse components [66] (curves are arbitrarily fitted to the critical point). The shape of the CPC and precipitation threshold temperature (maximum of the CPC) appearing at low modifier concentrations are a clear manifestation of the rubber polydispersity [77]. 

However, a major limitation of this model is the impossibility of fitting cloud-point curves for polydisperse systems. Moreover, it cannot deal with the fractionation effect accompanying phase separation, i.e. the dispersed phase will be enriched in the highest molar-mass fractions of modifier but in the lowest molar-mass fractions of the growing thermosetting polymer. This may produce variations in stoichiometry and conversion between both phases. These phenomena can be conveniently treated taking polydispersity of constituents into account. 

The occurrence of a secondary phase separation inside dispersed phase particles, associated with the low conversion level of the p-phase when compared to the overall conversion, explains the experimental observation that phase separation is still going on in the system even after gelation or vitrification of the a-phase [26-31]. A similar thermodynamic analysis was performed by Clarke et al. [105], who analyzed the phase behaviour of a linear monodisperse polymer with a branched polydisperse polymer, within the framework of the Flory-Huggins lattice model. The polydispersity of the branched polymer was treated with a power law statistics, cut off at some upper degree of polymerization dependent on conversion and functionality of the starting monomer. Cloud-point and coexistence curves were calculated numerically for various conversions. Spinodal curves were calculated analytically up to the gel point. It was shown that secondary phase separation was not only possible but highly probable, as previously discussed. 

The spinodal curve and the critical points (including multiple critical points) only depend on few moments of the molar-mass distribution of the polydisperse system while the cloud-point curve the shadow curve and the coexistence curves are strongly influenced by the whole curvature of the distribution function. The methods used that include the real molar-mass distribution or an assumed analytical distribution replaced by several hundred discrete components have been reviewed by Kamide. In the 1980s continuous thermodynamics was applied, for example, by Ratzsch and Kehlen to calculate the phase equilibrium of a solution of polyethene in supercritical ethene as a function of pressures at T= 403.15 K. The Flory s model was used with an equation of state to describe the poly-dispersity of polyethene with a a Wesslau distribution. Ratzsch and Wohlfarth applied continuous thermodynamics to the high-pressure phase equilibrium of ethene [ethylene]-I-poly(but-3-enoic acid ethene) [poly(ethylene-co-vinylace-tate)] and to the corresponding quasiternary system including ethenyl ethanoate [vinylacetate]. In addition to Flory s equation of state Ratzsch and Wohlfarth also tested the Schotte model as a suitable means to describe the phase equilibrium neglecting the polydispersity with respect to chemical composition of the... 

Beginning in the 1990s calculations of high-pressure phase equilibria of polydisperse polymer systems were performed. For example, Enders and de Loos calculated cloud-point and spinodal curves in the high-pressure range for methylcyclohexane + poly(ethenylbenzene) and compared their results with experimental data. Enders and de Loos ° used a Gibbs-energy model with pressure dependent parameters and models that include an equation of state, such as the lattice fluid model introduced by Hu et for the monodisperse and... 

Due to the polydispersity, the demixing behavior becomes much more complicated for a polydisperse polymer in comparison with a monodisperse polymer, as shown in Fig. 1. The binodal curve in this system splits into three kinds of curves a cloud-point curve, a shadow curve, and an infinite number of coexistence curves. The meaning of these curves becomes clear if one considers the cooling process. 

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