Critical solution temperature, upper, lower

Concentration of hydroqumone. Upper critical solution temperature. Lower critical solution temperature. 

ATow.i Octanol-water partition coefficient of species i Kc Concentration-based partition coefficient of species i Kx Mole fraction-based partition coefficient of species i r Lower consolute or lower critical solution temperature (K) Upper consolute or upper critical solution temperature (K) X Set of liquid-phase mole fractions X, X2,. n Osmotic pressure (kPa)... 

Matyjaszewski et al. [2] patented a novel and flexible method for the preparation of CNTs with predetermined morphology. Phase-separated copolymers/stabilized blends of polymers can be pyrolyzed to form the carbon tubular morphology. These materials are referred to as precursor materials. One of the comonomers that form the copolymers can be acrylonitrile, for example. Another material added along with the precursor material is called the sacrificial material. The sacrificial material is used to control the morphology, self-assembly, and distribution of the precursor phase. The primary source of carbon in the product is the precursor. The polymer blocks in the copolymers are immiscible at the micro scale. Free energy and entropic considerations can be used to derive the conditions for phase separation. Lower critical solution temperatures and upper critical solution temperatures (LCST and UCST) are also important considerations in the phase separation of polymers. But the polymers are covalently attached, thus preventing separation at the macro scale. Phase separation is limited to the nanoscale. The nanoscale dimensions typical of these structures range from 5-100 nm. The precursor phase pyrolyzes to form carbon nanostructures. The sacrificial phase is removed after pyrolysis. 

It was demonstrated by Chen and co-workers that the EPDM/PP blend was immiscible below the upper critical solution temperature and above the lower critical solution temperature, i.e., the investigated EPDM/PP blend was only miscible between the aforementioned critical solution temperatures (lower and upper) [74]. 

Key words smart material, responsive polymer, lower critical solution temperature (LCST), upper critical solution temperature (UCST),phase transition. 

The third type of system gives a closed solubility curve and therefore possesses both an upper and lower critical solution temperature. The first case of this type to be established was that of nicotine and water the solubility curve is illustrated in Fig. I, 8, 3. The lower and upper consolute temperatures are 60 8° and 208° respectively below the former and above the latter the two liquids are completely miscible. 

It should be noted that the modern view is that all partially miscible liquids should have both a lower and upper critical solution temperature so that all such systems really belong to one class. A closed solubility curve is not obtain in all cases because the physical conditions under normal pressure prevent this. Thus with liquids possessing a lower C.S.T., the critical temperature (the critical point for the liquid vapour system for each component, the maximum temperature at which liquefaction is possible) may be reached before the consolute temperature. Similarly for liquids with an upper C.S.T., one or both of the liquids may freeze before the lower C.S.T. is attained. 

A few systems with both lower and upper critical solution temperatures are tabulated below., ... 

Fig. 1. Phase diagram for mixtures (a) upper critical solution temperature (UCST) (b) lower critical solution temperature (LCST) (c) composition dependence of the free energy of the mixture (on an arbitrary scale) for temperatures above and below the critical value.

We consider a binary liquid mixture of components 1 and 3 to be consistent with our previous notation, we reserve the subscript 2 for the gaseous component. Components 1 and 3 are completely miscible at room temperature the (upper) critical solution temperature Tc is far below room temperature, as indicated by the lower curve in Fig. 27. Suppose now that we dissolve a small amount of component 2 in the binary mixture what happens to the critical solution temperature This question was considered by Prigogine (P14), who assumed that for any binary pair which can be formed from the three components 1, 2 and 3, the excess Gibbs energy (symmetric convention) is given by... 

Figure 8.17 Vapor fugacity for component 2 in a liquid mixture. At temperature T, large positive deviations from Raoult s law occur. At a lower temperature, the vapor fugacity curve goes through a point of inflection (point c), which becomes a critical point known as the upper critical end point (UCEP). The temperature Tc at which this happens is known as the upper critical solution temperature (UCST). At temperatures less than Tc, the mixture separates into two phases with compositions given by points a and b. Component 1 would show similar behavior, with a point of inflection in the f against X2 curve at Tc, and a discontinuity at 7V...

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. 

Reactive compatibilization can also be accomplished by co-vulcanization at the interface of the component particles resulting in obliteration of phase boundary. For example, when cA-polybutadiene is blended with SBR (23.5% styrene), the two glass transition temperatures merge into one after vulcanization. Co-vulcanization may take place in two steps, namely generation of a block or graft copolymer during vulcanization at the phase interface and compatibilization of the components by thickening of the interface. However, this can only happen if the temperature of co-vulcanization is above the order-disorder transition and is between the upper and lower critical solution temperature (LCST) of the blend [20]. 

Using the estimated interaction parameters phase equilibrium computations were performed. It was found that the EoS is able to represent the VL2E behavior of the methane-n-hexane system in the temperature range of 198.05 to 444.25 K reasonably well. Typical results together with the experimental data at 273.16 and 444.25 K are shown in Figures 14.14 and 14.15 respectively. However, the EoS was found to be unable to correlate the entire phase behavior in the temperature range of 195.91 K (Upper Critical Solution Temperature) and 182.46K (Lower Critical Solution Temperature). 

Figure 9 Qualitative phase diagram of a polymer solution showing phase separation both on heating (at the lower critical solution temperature) and on cooling (at the upper critical solution temperature). (From Ref. 31.)...

For the two-component, two-phase liquid system, the question arises as to how much of each of the pure liquid components dissolves in the other at equilibrium. Indeed, some pairs of liquids are so soluble in each other that they become completely miscible with each other when mixed at any proportions. Such pairs, for example, are water and 1-propanol or benzene and carbon tetrachloride. Other pairs of liquids are practically insoluble in each other, as, for example, water and carbon tetrachloride. Finally, there are pairs of liquids that are completely miscible at certain temperatures, but not at others. For example, water and triethylamine are miscible below 18°C, but not above. Such pairs of liquids are said to have a critical solution temperature, For some pairs of liquids, there is a lower (LOST), as in the water-tiiethylamine pair, but the more common behavior is for pairs of liquids to have an upper (UCST), (Fig. 2.2) and some may even have a closed mutual solubility loop [3]. Such instances are rare in solvent extraction practice, but have been exploited in some systems, where separations have been affected by changes in the temperature. 

The lower critical solution temperature is another crucial polymer property, which, together with the Upper Critical Solution Temperature (UCST), defines fhe fwo solubility boundaries of polymers in solution. Typically, systems are completely miscible below the LCST but only partially miscible above the LCST and completely immiscible above the UCST. 

When there is a UCST (upper critical solution temperature), then above that temperature the components are fully mixable. When cooling down to below this UCST a region of segregation can be reached, in particular when the volume fractions do not differ too much (see MT Figure 9.3, lower part "upside down")... 

The instance we have considered here, that of a polymer in a poor solvent, results in an upper critical solution temperature (UCST) as shown in Figure 2.33. This occurs due to (a) decreased attractive forces between like molecules at higher temperatures and (b) increased solubility. For some systems, however, a decrease in solubility can occur, and the corresponding critical temperature is located at the minimum of the miscibility curve, resulting in a lower critical solution temperature (LCST). This situation is illustrated in Figure 2.34. 

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. 

In type VI phase behaviour a three-phase curve l2hg is found with an LCEP and an UCEP. Both critical endpoints are of the type (l2=li)+g and are connected by a l2=h critical curve which shows a pressure maximum. For this type of phase behaviour at constant pressure closed loop isobaric regions of l2+li equilibria are found with a lower critical solution temperature and an upper critical solution temperature. 

The phase behaviour of many polymer-solvent systems is similar to type IV and type HI phase behaviour in the classification of van Konynenburg and Scott [5]. In the first case, the most important feature is the presence of an Upper Critical Solution Temperature (UCST) and a Lower Critical Solution Temperature (LCST). The UCST is the temperature at which two liquid phases become identical (critical) if the temperature is isobarically increased. The LCST is the temperature at which two liquid phases critically merge if the system temperature is isobarically reduced. At temperatures between the UCST and the LCST a single-phase region is found, while at temperatures lower than the UCST and higher than the LCST a liquid-liquid equilibrium occurs. Both the UCST and the LCST loci end in a critical endpoint, the point of intersection of the critical curve and the liquid liquid vapour (hhg) equilibrium line. In the two intersection points the two liquid phases become critical in the presence of a... 

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