Cloud point curves

The critical point (Ij of the two-phase region encountered at reduced temperatures is called an upper critical solution temperature (UCST), and that of the two-phase region found at elevated temperatures is called, perversely, a lower critical solution temperature (LCST). Figure 2 is drawn assuming that the polymer in solution is monodisperse. However, if the polymer in solution is polydisperse, generally similar, but more vaguely defined, regions of phase separation occur. These are known as "cloud-point" curves. The term "cloud point" results from the visual observation of phase separation - a cloudiness in the mixture. 

The recourse to the above-described procedure permitted the derivation [74] of an exact expression for function G(pi,p2). It is of utmost importance for the construction of a phase diagram of a melt or solution of interphase copolymerization products, since this function enters in the equations for the cloud point curve [82]. 

General Comments. The (P, T) cloud curve for the PIB of > -2 xlO dissolved in 2-methylbutane agreed,within experimental error, with other values reported in the literature (6,2.) The slope of the curve differed from other results but this could have been caused by the molecular weight distribution exhibited by the sample used in this study. The cloud point curve for an infinite molecular weight polymer, i.e. 0 conditions, was established from our measurements and from literature data and is shown plotted in Figure 2. It can be seen that 0 increase as a function of applied pressure with a slope (dT/dP)c of 0.56. 

Yon should prove to yourself that it makes no difference if we differentiate with respect to component A or B, nor whether we differentiate with respect to mole or volnme fraction, since the derivatives are set eqnal to zero.) The locns of points swept out by the stability condition shown in Eq. (2.36) at various temperatures is called the binodal, or cloud point curve. For example, just as we drew tangents to the... 

Cloud point curves measured for the blends of STHFS with PMMA, PEMA and PBMA, all had LCST, as expected for blends with specific interactions, and depended strongly on the degree of PS modification. For example, the lowest... 

The cloud point curves of the epoxy monomer/PEI blend and BPACY monomer/PEI blend exhibited an upper critical solution temperature (UCST) behavior, whereas partially cured epoxy/PEI blend and BPACY/PEI blend showed bimodal UCST curves with two critical compositions, ft is attributed to the fact that, at lower conversion, thermoset resin has a bimodal distribution of molecular weight in which unreacted thermoset monomer and partially reacted thermoset dimer or trimer exist simultaneously. The rubber/epoxy systems that shows bimodal UCST behavior have been reported in previous papers [40,46]. Figure 3.7 shows the cloud point curve of epoxy/PEI system. With the increase in conversion (molecular weight) of epoxy resin, the bimodal UCST curve shifts to higher temperature region. 

Figure 5.1-2. Phase behaviour of ethylene LDPE mixtures [10]. Thick line, cloud-point curve dotted line, shadow curve thin lines, co-existence curves total polymer concentration a, 6.1 wt.% b, 11.4 wt.% c, 18.6 wt.% d, 28.0 wt.% e, 36.5 wt.%.

Figure 9.7-1 Experimental cloud-point curve of the polymer blend Poly(methyl methacrylate)/Poly(styrene-co-acrylonitrile (28%AN)) as a function of pressure.

Figure 6. Conventional two-component phase behavior in poly disperse Flory-Huggins theory, shown in the (p, p0) plane for three values of % As in Fig. 5, the parent has Ln = 100 and Ly/ = 150 (hence a = 2). Along the y-axis, we plot L//p0 rather than p0 so that the dilution line p = LNp0, shown as the thick solid line in (a-c), is simply along the diagonal. With x considered as an additional variable, the dilution line constraint defines a plane (p, = L/vPq, x)- The last plot, (d), shows the cut by this plane through the phase behavior in (a-c) the solid line is the cloud point curve, and the dashed line is the spinodal stability condition.

Figure 6. Cloud-point curve for polystyrene in cyclohexane (%) determined from light scattering and (M) determined visually. The arrows indicate (from left to right) maximum of the cloud-point curve, maximum of the dissymmetry ratiof critical point.

Figure 7.1. Comparison of the cloud-point curves of poly(ethyl acrylate) (PEA), poly(butyl acrylate) (PBA), poly(ethylhexyl acrylate) (PEHA), and poly(octadecyl acrylate) (PODA) in C02. The overall polymer concentration is 5 wt % for each curve and the Mw of the polymer is given on each curve (Kirby and McHugh, 1999). The demarcations L + L and FLUID denote a two-phase and a one-phase region, respectively.

A large body of work has been developed by DeSimone and co-workers on the solubility of fluorinated polymers, especially polyfl,l-dihydroper-fluorooctylacrylate) fPFOA), in C02 (Hsiao et al., 1995 Luna-Barcenas et al., 1998). An excellent example of utilizing creative chemistry to design a C02-soluble polymer, PFOA is one of the very few fluoropolymers that dissolves in C02 at modest temperatures and pressures less than 300 bar. The characteristics needed to make a fluoropolymer soluble in C02 can be ascertained from Figure 7.2, which shows the difference in cloud-point curves for polyfvinylidene fluoride) (PDVF), a statistically random copoly-... 

Figure 2.3 Cloud point curves of diethanediol-based polyester oligomers (Mn 1 kg mol-1), dissolved in styrene the diacids used for polyester synthesis were (a) fumaric acid, (b) blend of isophthalic and fumaric acid, and (c) isophthalic acid.

Figure 8.2 Schematic phase diagrams for thermoplastic-epoxy monomer (diglycidyl ether of bisphenol A) blends, (CPC = cloud point curve, and VC = vitrification curve), (a) and (b) UCST (upper critical solution temperature) behaviour for PPE and PEI (respectively) - DGEBA n = 0.15 (c) LCST (lower critical solution temperature) behaviour for PES-DGEBA y n = 0.15. (Pascault and Williams, 2000 - Copyright 2001. Reprinted by permission of John Wiley Sons Inc.)...

Figures 8.2a and b describe a UCST behavior, while Fig. 8.2c represents an LCST behavior. It is interesting to note that in the case of an UCST behavior the cloud-point curve will usually intersect the vitrification curve, while this may not be the case for an LCST behavior.

Experimental cloud-point curves are fitted by Eq. (8.1), selecting an adequate function for /. Depending on their structures, thermoplastics are more or less soluble in epoxy monomers poly(methyl methacrylate), PMMA and poly(styrene-co-acrylonitrile), SAN are quite soluble in liquid DGEBA, but the other thermoplastics shown in Table 8.1 are only partially miscible (Pascault and Williams, 2000). 

Phase separation begins when the cloud-point curve reaches the point a at (4>mo>T ). This is defined as the cloud-point conversion, xCp, which is usually lower than the gel conversion, xgei. 

As a result of polydispersity effects, the composition of the incipient 13-phase segregated at the cloud point is located on a shadow curve, outside the cloud-point curve (point (3 in Fig. 8.4). The effects of polydispersity on phase diagrams and phase compositions may be found in specialized reviews (Tompa, 1956 Kamide, 1990 Williams et al., 1997). Because < )Mo < ( M,crit(xcp), the incipient (3-phase, which is richer in the modifier, will be dispersed in the a-phase, which is richer in the growing thermosetting polymer. The opposite occurs when < )M0 > M,crit(xcp)- It has been shown both theoretically (Riccardi et al., 1994 and 1996 Williams et al., 1997), and experimentally (Bonnet et al., 1999) that... 

In Fig. 8.4 an UCST behavior is represented. The corresponding situation for an LCST behavior is a shift of the cloud-point curve to lower temperatures as conversion increases. A similar description of the phase-separation process is valid also for the LCST case. 

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