Lower critical point

A question of practical interest is the amount of electrolyte adsorbed into nanostructures and how this depends on various surface and solution parameters. The equilibrium concentration of ions inside porous structures will affect the applications, such as ion exchange resins and membranes, containment of nuclear wastes [67], and battery materials [68]. Experimental studies of electrosorption studies on a single planar electrode were reported [69]. Studies on porous structures are difficult, since most structures are ill defined with a wide distribution of pore sizes and surface charges. Only rough estimates of the average number of fixed charges and pore sizes were reported [70-73]. Molecular simulations of nonelectrolyte adsorption into nanopores were widely reported [58]. The confinement effect can lead to abnormalities of lowered critical points and compressed two-phase envelope [74]. 

PI Freeman, JS Rowlinson. Lower critical points in polymer solution. Polymer 1 20-25, 1960. 

The swelling behavior of poly(N-isopropylacrylamide) has been studied extensively [18,19]. It has been shown that this gel has a lower critical point due to the hydrophobic interaction. Such a swelling curve is schematically illustrated in Fig. 9. The gel is swollen at a lower temperature and collapses at a higher temperature if the sample gel is allowed to swell freely in water. The volume of the gel changes discontinuously at 33.6°C. The swelling curves obtained in this way correspond to the isobar at zero osmotic pressure. On the other hand, the friction coefficient is measured along the isochore, which is given in Fig. 9,... 

The molecular conditions for the occurrence of a lower critical point have also been investigated in several recent papers. ... 

It appears that a lower critical point is not to be observed with mixtures of spherical molecules with isotropic force fields. The phenomenon seems to be related mainly to modification of the rotational degrees of freedom of the molecules. 

In this case of water rich systems, there is no evident model of interaction and Van der Waals forces between droplets are too weak to lead to a critical point which seems to be of 01 quite different kind from the one near S2. The phase diagram of the system is possibly too complicated to study this particular point but it seems that the critical point near S is a lower critical point. In that case, one may think that entropic forces are important in the medium. In order to confirm this point, we have studied simpler systems oil free systems. 

Freeman, P.I. and Rowlinson, J.S., Lower critical points in polymer solutions. Polymer, 1, 20, 1960. 

The phase diagram of a nonionic amphiphile-water binary system is more complicated (see Figure 3.12). A classic upper critical point exists, but it is usually located below 0°C. At higher temperatures most nonionic amphiphiles show a miscibility gap, which is actually a closed loop with an upper as well as a lower critical point. The lower critical point CPp is often referred to as the cloud point temperature. The upper critical point often lies above the boiling temperature of the mixture (at 0.1 MPa). The position and the shape of the loop depend on... 

From the phase behavior of both binary mixtures (water-amphiphile and oil— amphiphile), it is now possible to account, at least qualitatively, for the three-component phase diagram as a function of temperature. The presence of a haze point on the oil-amphiphile phase diagram (critical point a) at temperature Ta shows that the surfactant is more compatible with the oil at high than at low temperature. The presence of a cloud point on the water-amphiphile phase diagram (the lower critical point (>) at temperature Tjj shows that (at least in the neighborhood of the temperature domain) the amphiphile is less compatible with water at high than at low temperature. As a consequence (the other parameters being kept constant), the amphiphile behavior depends on temperature. 

Figure 1.1 Schematic view of the phase behaviour of the three binary systems water (A) oiI (B), oil (B)-non-ionic surfactant (C), water (A)-non-ionic surfactant (C) presented as an unfolded phase prism [6]. The most important features are the upper critical point cpc, of the B-C miscibility gap and the lower critical point cpp of the binary A-C diagram. Thus, at low temperatures water is a good solvent for the non-ionic surfactant, whereas at high temperatures the surfactant becomes increasingly soluble in the oil. The thick lines represent the phase boundaries, while the thin lines represent the tie lines.

Franck, E. U., and R. Deul. 1979. Dielectric behavior of methanol and related polar fluids at high temperatures and pressures. Farad. Discuss. Chem. Soc. 66 191-198. Freeman, P. I., and J. S. Rowlinson. 1960. Lower critical points in polymer solutions. 

The discussion to be provided here will be limited to an outline of the general principles involved and certain precautions that must be observed. One important precaution involves fire and explosion hazards. Many solvent vapors, when mixed with air in certain proportions, are explosive, the degree of explosiveness depending upon the proportion of vapor to air. No explosion will occur when the vapor concentration is below a critical amount which varies from 0.5-10% according to the chemical nature of the vapor. As the vapor concentration increases above this lower critical point, the... 

The three-component model immediately makes clear that this behavior is generic [15,74]. What is unusual in, and specific to, the nonionic systems is that the triple line is traversed by varying the temperature. This is a consequence of the lower critical point that exists in these systems in addition to the usual upper critical point. That there is a lower critical point is related to hydrogen bonding, and a realistic phase diagram can be calculated only by taking this into account [75] (see Fig. 1). 

Fig. 10-6. (a) Phase diagram of a binary system with a lower critical point solid line, binodal (or cloud-point curve) dashed line, spinodal C, Critical point, (b) Composition dependence of AGe at T = To. 

Typical Data and Analysis To begin with, we illustrate in Figure 10-11 the binodal and spi nodal curves for a PS-1 (M = 200 x 10 and Mw/M = 1.05)/PVME-1 (A/w = 47 X 10 and My,./M = 1.5) blend [24]. These curves show that the system has a lower critical point at = 0.80 and Tc = 95.8°C. In what follows, we designate the volume fraction of PVME by . Actually, the dashed curve is not a binodal but a cloud-point curve, since the system is not binary (see Chapter 9). Nonetheless it is called binodal in the ensuing description. We note that the gap between the binodal and the spinodal is quite narrow. 

Fig. 2.2-1 Miscibility gaps of several binary mixtures with upper critical point Qhs), lower critical point (center), upper plus lower critical point (rhs)...

Systems with Upper and Lower Critical Solution Temperature. In the case of some liquids which are only partially miscible, complete solution is possible both above an upper C.S.T. and below a lower C.S.T., giving rise to solubility curves of the type indicated in Fig. 2.3. Despite the several examples which have been discovered where apparently the composition of both upper and lower critical points are nearly the same, there is no requirement that this be the case. 

Systems with No Critical Solution Temperature. A large number of liquid pairs form systems without upper or lower critical points. In these cases, a solid phase forms before the appearance of a lower C.S.T. on cooling, and on heating, a vapor-liquid critical condition (vapor phase of the same composition and density as one of the liquid phases) occurs. Ether... 

High-temperature alcohol supercritical extraction techniques (ASCE) bring the wet gel to the supercritical state of the solvent (usually methanol or ethanol) in an autoclave or other pressure vessel. This involves high pressures (above 8 MPa) and temperatures (above 260° C). A number of studies have been performed to examine the effects of solvent fill volume, pre-pressure, and other processing parameters (see for example Phalippou et al. [23], Danilyuk et al. [24], Pajonk et al. [25]). The low-temperature extraction techniques (CSCE) are based on supercritical extraction of CO2, which has a lower critical-point temperature than the alcohol mixture that remains in the sol-gel pores after polymerization. The CSCE methods... 

Figure 7.10 Finite-size heat capacity at constant pressure as a function of temperature t near the lower critical point of 2,6-dimethylpyridine aqueous solution at the critical composition. +, in the bulk x, 250 nm porous nickel 100 nm porous glass , lOnm porous glass.

Figure 7.11 Shift in the heat-capacity In m maxima near the lower critical point of 2,6-dime thy Ipyridine aqueous solution at the critical composition as a function of pore size Slope of the solid line is — l/v= — 1.59. +, experimental , simulation.

Figure 9.2a Pressure as a function of the total mass fraction for methylcyclohexane (A) with polydisperse poly(ethenylbenzene) (B) (M = 16 500 g mol U= ) illustrating the Lower Critical Point and Upper Critical Point...

Let us now look into the case when there is a solubility loop and focus our attention on the behavior near the lower critical point with temperature c. For the usual Ising model the critical temperature (Tc=l//3c) is dependent on the lattice geometry and the model interactions, i.e., exp(-23cJ)=Kc, with Kc fixed by the lattice geometry, determines I3c. Since in our model, we have from (4) and (5) that JO)=-ln K(, ep)/2, it follows that... 

First of all it can be shown that a lower critical point cannot be obtained by the average potential model using only second order terms. This conclusion had already been reached from the cell model (R6wun-SON [1952], Beixemans [1953]. Therefore we shall only study here the upper critical point occurihg in the case of dispersion forces (other cases can be readily studied in the same way). The case of dispersion forces is however somewhat simpler because the excess free energy is a parabolic function in xaXb when limited to second order terms in d and p. Hence the critical mole fraction is equal to 0.5. Expressions for Te are readily obtained from (1.8.3). We find ... 

Freeman, P. I., and J. S. Rowlinson, Lower Critical Points in Polymer Solutions,... 

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