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Critical point, LCST/UCST

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. [Pg.183]

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... [Pg.50]

In a blend of immiscible homopolymers, macrophase separation is favoured on decreasing the temperature in a blend with an upper critical solution temperature (UCST) or on increasing the temperature in a blend with a lower critical solution temperature (LCST). Addition of a block copolymer leads to competition between this macrophase separation and microphase separation of the copolymer. From a practical viewpoint, addition of a block copolymer can be used to suppress phase separation or to compatibilize the homopolymers. Indeed, this is one of the main applications of block copolymers. The compatibilization results from the reduction of interfacial tension that accompanies the segregation of block copolymers to the interface. From a more fundamental viewpoint, the competing effects of macrophase and microphase separation lead to a rich critical phenomenology. In addition to the ordinary critical points of macrophase separation, tricritical points exist where critical lines for the ternary system meet. A Lifshitz point is defined along the line of critical transitions, at the crossover between regimes of macrophase separation and microphase separation. This critical behaviour is discussed in more depth in Chapter 6. [Pg.9]

For salts with univalent ions, Eq. (4) predicts critical points near room temperature for systems with e 5 [72]. Liquid-liquid immiscibilities in several electrolyte solutions are known to satisfy this criterion [5, 71, 72]. Note that these gaps do not necessarily possess an upper critical solution temperature (UCST). Theory can rationalize a lower critical solution temperature (LCST) as well, if the product esT decreases with increasing temperature. [Pg.9]

There is a large body of experimental work on ternary systems of the type salt + water + organic cosolvent. In many cases the binary water + organic solvent subsystems show reentrant phase transitions, which means that there is more than one critical point. Well-known examples are closed miscibility loops that possess both a LCST and a UCST. Addition of salts may lead to an expansion or shrinking of these loops, or may even generate a loop in a completely miscible binary mixture. By judicious choice of the salt concentration, one can then achieve very special critical states, where two or even more critical points coincide [90, 160,161]. This leads to very peculiar critical behavior—for example, a doubling of the critical exponent y. We shall not discuss these aspects here in detail, but refer to a comprehensive review of reentrant phase transitions [90], We note, however, that for reentrant phase transitions one has to redefine the reduced temperature T, because near a given critical point the system s behavior is also affected by the existence of the second critical point. An improper treatment of these issues will obscure results on criticality. [Pg.25]

The critical locus has two parts, with the portion that begins at point b (the critical point of the more volatile component) ending at the UCST (point u), and the portion that starts at point d (the critical point of the less volatile component) ending at the LCST (point 1). Although not shown in Figure 14.15, an isotherm at a temperature between T2 and T3 would show two critical points (similar to the one at T2 in Figure 14.14). One critical point would be on the critical locus line bu while the other would be on the critical locus line dl. [Pg.133]

With changing temperature the curves change for spinodals and binodals (the points of contact with the common tangent), plotted as T against q>, a picture as shown in Figure 9.3 may be obtained. In this case a lower critical solution temperature , LCST, exists, which is a maximum temperature at which, for every blending ratio, a stable homogeneous blend is possible. An upper critical solution temperature (UCST) may also exist in that case the curves are upside down. Besides, more complicated cases are possible (see also Qu. 9.4 tu. 9.7). [Pg.164]

For the system PMMA/PVDF one can estimate the volume of mixing according to Eq. (22). As the key-point, the system exhibits both LCST and UCST. The critical points are reported to be about at 325 and 140 °C for 50/50 blends [11], These data can be used to calculate, from Eqs. (18) and (19), the quantities XAB and p. [Pg.42]

The properties of a liquid mixture at or near a critical point (Stein and Allen, 1974) are complicated (Rowlinson, 1974) and will not be commented on further. Nevertheless, it seems likely that the kinetics of reactions in solvent mixtures near an LCST or a UCST may prove interesting in view of the report, admittedly not concerned with aqueous mixtures, that the rate of a Diels-Alder reaction increases by 30% within 0 01 K of the UCST for reaction in hexane + nitrobenzene mixtures (Wheeler, 1972). Measurement of the kinetics of reaction in such systems may prove difficult by spectrophoto-metric techniques because systems close to a critical point scatter light, but should be possible by electrical conductance measurements (Stein and Allen, 1973 Gammell and Angell, 1974). [Pg.297]

Figure 19 depicts plots of the temperature of the observed cloud point vs. the weight fraction w2 of CA(2.46) for each solution 55,56). The lower critical solution temperature, LCST, was determined as the minimum temperature of each cloud-point curve. Some CD-solvent systems show the existence of an upper critical solution temperature, UCST, together with LCST (Fig. 20) 57>. [Pg.27]

The thermodynamic definition of the spinodal, binodal and critical point were given earlier by Eqs. (9), (7) and (8) respectively. The variation of AG with temperature and composition and the resulting phase diagram for a UCST behaviour were illustrated in Fig. 1. It is well known that the classical Flory-Huggins theory is incapable of predicting an LCST phase boundary. If has, however, been used by several authors to deal with ternary phase diagrams Other workers have extensively used a modified version of the classical model to explain binary UCST or ternary phase boundaries The more advanced equation-of-state theories, such as the theory... [Pg.159]

Consider diffusion in a binary liquid mixture exhibiting an upper critical solution temperature (UCST) or lower critical solution temperature (LCST) (see Fig. 3.1). Let us take a mixture at the critical composition x at point A just above the UCST. Any concentration fluctuation at A will tend to be smeared out due to the effects of diffusion in this homogeneous mixture. On the other hand, any fluctuation of a system at point B, infinitesimally below the UCST, will lead to separation in two phases. Similarly, the mixture at point D, just below the LCST is stable whereas the mixture at point C, just above the LCST is unstable and will separate into two phases. [Pg.62]

Cloud-point curves or precipitation curves for different polymer-solvent systems have different shapes (Figs. 3.12 and 3.13). The maxima and minima on these curves indicate the upper critical solution temperature (UCST) and the lower critical solution temperature (LCST), respectively. As indicated in Figs. 3.12 and 3.13, the phase diagram of a polymer solution has two regions of limited miscibility (i) below UCST associated with the theta temperature (see Problem 3.16) and (ii) above LCST. [Pg.197]

If the binodal and spinodal points are determined at various temperatures and are plotted together, a phase diagram such as the one shown in Figure 6.1 b may result. The temperature at which the binodal and spinodal curves merge together is the critical temperature. The phase diagram shown illustrates a case in which the miscibility gap occurs at temperatures above the critical temperature, and the system is said to exhibit a lower critical solution temperature (LCST) behavior. A system, on the other hand, may display an upper critical solution temperature (UCST) behavior, in which the miscibility gap occurs below the critical temperature. [Pg.215]

The origin of the critical point can be traced to the temperature effect on miscibility. Patterson [1982] observed that there are three principal contributions to the binary interaction parameter, the dispersive, free volume and specific interactions. As schematically illustrated in Figure 2.16, the temperature affects them differently. Thus, for low molecular weight systems where the dispersion and free volume interactions dominate, the sum of these two has a U-shape, intersecting the critical value of the binary interaction parameter in two places — hence two critical points, UCST and LCST. By contrast, most polymer blends derive their miscibility from the presence of specific interactions, characterized by a large negative value of the interaction parameter that increases with T. The system is also affected by the free volume contribution, as well as relatively unimportant in this case dispersion forces. The sum of the interactions reaches the critical value only at one temperature — LCST. [Pg.168]

According to the type of T versus q> diagram (Fig. 25.4), the binary solution can exhibit an upper critical solution temperature (UCST), a lower critical solution temperature (LCST), or both (close-loop phase behavior). Above the UCST or below the LCST the system is completely miscible in all proportions [82], Below the UCST and above LCST a two-phase liquid can be observed between cp and cp". The two-phase liquid can be subdivided into unstable (spontaneous phase separation) and metastable (phase separation takes some time). These two kinds of mixtures are separated by a spinodal, which is outlined by joining the inflexion points (d AGIdcp ) of successive AG versus cp phase diagrams, obtained at different temperatures (Fig. 25.3b). Thus, the binodal and spinodal touch each other at the critical points cp and T. ... [Pg.478]

Class C. These binaries have both a UCST and an LCST at temperatures removed from the critical temperatures of the pure components. The locus of UCSTs intersects the VLLE line at a UCEP, while that for LCSTs intersects the VLLE line at an LCEP. The loci of UCSTs and LCSTs may or may not form a continuous line of fluid-fluid critical points. Few binaries have both UCSTs and LCSTs, so few fall into class C. [Pg.401]

Class E. In these systems one branch of the critical line originates at the critical point of the less volatile component and circles back to low temperatures and pressures, terminating at an LCEP on the three-phase VLLE curve. At low temperatures the range of liquid-liquid immiscibility ends at an LCST. So if we start at the critical point of the less volatile component, we can experimentally trace the mixture critical loci in a continuous fashion from vapor-liquid critical states through liquid-liquid critical states. Some mixtures in this class have a second region of liquid-liquid immiscibility with another UCST at still lower temperatures a miscibility gap. [Pg.402]

Certain principles mnst be obeyed for experiments where liquid-liquid equilibrium is observed in polymer-solvent (or snpercritical flnid) systems. To understand the results of LLE experiments in polymer solutions, one has to take into acconnt the strong influence of polymer distribution functions on LLE, because fractionation occnrs dnring demixing. Fractionation takes place with respect to molar mass distribution as well as to chemical distribution if copolymers are involved. Fractionation during dentixing leads to some effects by which the LLE phase behavior differs from that of an ordinary, strictly binary mixture, because a common polymer solution is a mnlticomponent system. Clond-point cnrves are measnred instead of binodals and per each individnal feed concentration of the mixtnre, two parts of a coexistence cnrve occnr below (for upper critical solution temperatnre, UCST, behavior) or above the clond-point cnrve (for lower critical solution temperature, LCST, behavior), i.e., produce an infinite nnmber of coexistence data. [Pg.12]

The following symbols are used T = temperature p = (total) pressure X = mole fraction (of component II if not indicated) c = concentration M = moldm" L = liquid phase, G = gaseous phase, S = solid phase CP I, CP II = critical point of the pme component I or II CP = critical point of a mixture UCST (LCST = upper (lower) critical solution temperature A, B, C, D, E, K = critical end point Qx, Qa = quadruple point. [Pg.106]

There are suppositions that the UCST is the more common case but one of the critical points for polymer-solvent system is observed only at high temperatures. For example, polystyrene (M = 1.1x10 ) with methylcyclopentane has LCST 475K and UCST 370K. More complete experimental data on the phase diagrams of polymer-solvent systems are published elsewhere. ... [Pg.129]


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See also in sourсe #XX -- [ Pg.5 ]




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