Liquid-gas type transitions

For the water, AOT and decane system, light scattering experiments are in progress in view to apply the proposed interaction potential to ternary systems. As expected the first results clearly indicate that interactions increase as the system approaches the critical point. Besides preliminary calculations confirm that a liquid-gas type transition must occur very close to the experimental demixing line. 

We also note that in principle, Eq. (6.17) is really a transcendental equation for the spinodal temperature if the polymer density and/or statistical segments length depend on temperature as generally true for real systems. This aspect can lead to apparent N dependences of the spinodal temperature, which do not follow the classic Flory scaling relation of T,. N. A liquid-gas-type transition is also predicted, but since it is driven by density, not concentration, fluctuations the relevant temperature scale is independent of N, and thus is expected to be well below Tj for macromolecules. 

In order to be able to make, even qualitatively, a determination that a transition is first-order or second-order one has to apply a measuring technique probing the temperature dependence of the enthalpy FI. Very important is also the magnitude of the latent heat A//l relative to the pretransitional enthalpy change bH (see Fig. 1). Quite often it is also important to know how this ratio changes with some physical parameter like pressure or concentration (for mixtures). As a funetion of these parameters the order of the transition may, indeed, change at a tri-critical point or reach an isolated critical point (liquid-gas type transition in simple fluids). 

Liquid films There exists a certain degree of cooperative interaction between the film-forming molecules. Two types have been observed liquid expanded and liquid condensed films. The first type can be characterized by high compressibility, the absence of islands, and they show a first-order liquid-gas phase transition. Condensed films are formed by compressing expanded films. 

For larger differences between the critical temperatures, one expects liquid-liquid miscibility gaps that are well-separated from the liquid-gas transition (type II). When further increasing the dissimilarity, these liquid-liquid immiscibilities are displaced to higher temperatures, and eventually the corresponding liquid-liquid-gas (I -L -G) three-phase line interferes with the L-G critical line (type III, IV, and V). Then, the L-G critical line starting from the critical point of the more volatile component (here water) is broken at a so-called upper critical end point (UCEP), where it meets the Li-L2-g three-phase line of the liquid-liquid equilibrium. 

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340°K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175 K. Melting occurs at 239.53°K (-33.62°C) with an enthalpy increment of 2292 cal mole" and an entropy increment of 9.57 cal mole" -"K". Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function -(G°-The variation of Cp for crystalline thiazole between 145 and 175°K reveals a marked inflection that has been attributed to a gain in molecular freedom within the crystal lattice. The heat capacity of the liquid phase varies nearly linearly with temperature to 310°K, at which temperature it rises more rapidly. This thermal behavior, which is not uncommon for nitrogen compounds, has been attributed to weak intermolecular association. The remarkable agreement of the third-law ideal-gas entropy at... 

The type II isotherm is associated with solids with no apparent porosity or macropores (pore size > 50 nm). The adsorption phenomenon involved is interpreted in terms of single-layer adsorption up to an inversion point B, followed by a multi-layer type adsorption. The type IV isotherm is characteristic of solids with mesopores (2 nm < pore size < 50 nm). It has a hysteresis loop reflecting a capillary condensation type phenomenon. A phase transition occurs during which, under the eflcct of interactions with the surface of the solid, the gas phase abruptly condenses in the pore, accompanied by the formation of a meniscus at the liquid-gas interface. Modelling of this phenomenon, in the form of semi-empirical equations (BJH, Kelvin), can be used to ascertain the pore size distribution (cf. Paragr. 1.1.3.2). 

The liquid-vapour phase transition is a first-order transition. For example, the molar entropy S, being a derivative of te Gibbs potential G, S = —(8G/dT)p, where T is the temperature and p the pressure, has a discontinuity at the boiling point T = Tb. For a description of the liquid-vapour equilibrium, various approximate state equations are employed. Let us consider one of the most common equations of this type, the semiempirical van der Waals equation, written in terms of temperature T, volume V and pressure p or a gas... 

Early stability analyses employed the classical Kelvin-Helmholtz (K-H) theory for two inviscid layers (Kordyban and Ranov [33], Kordyban [34], Wallis and Dobson [35]). However, in referring to gas-liquid flows, pyp C 1, and assuming that the interfacial disturbance velocity equals the (slower) liquid layer velocity, the liquid destabilizing contribution has been degenerated. This results in a rather simple Bernoulli-type transitional criteria, whereby the suction forces in the gas-... 

The resulting phase diagram is shown in Fig. 12. We can identify a type of phase diagram predicted from the theory for intermediate stiffnesses. We do not see a coexistence between two nematic states as was predicted for very large stiffness and also no liquid-gas coexistence a lower densities. The liquid-gas coexistence point seems to be buried within the two-phase region of the isotropic-nematic transition and we have indications [23] that it may become observable when we slightly reduce the intrinsic chain stiflhiess. 

The next question is related to the critical behavior near d> = d>c. Since the coils are just beginning to overlap in the critical region, we see that the parameter P of Section IV.2.5. (giving the number of coils interacting with one of them) is of order unity. Then we expect critical exponents which are not of the mean field type but rather are related to those of the liquid-gas transition. ... 

It is no doubt that nature prefers the liquid-to-sohd transition in wet chemical methods compared to transitions from gas-to-soUd in vapor deposition techniques. Most vacuum deposition techniques such as MBE and MOVPE involve the second type of transition. It is therefore not a surprise that electrodeposited materials like ZnSe and CdTe can have superior qualities over layers grown by dry methods. Another built-in property of electrodeposition is the hydrogen passivation mechanism [49]. This is because ions mainly from the aqueous solution are attracted to... 

This quantity can provide information on phase changes within the sorbate layer, for example the transition from a lattice gas type structure, cp. Fig. 1.2, to a patch-liquid, or a dense mono-layer structure [1.3]. 

Systems of type Id (with continuous transition of liquid-liquid immiscibility into liquid-gas equilibrium, without critical phenomena in solid saturated solutions) (Figure 1.20). The three-phase equilibrium (L1-L2-G), starting at critical endpoint N (Li = L2-G), exists in these systems as well as in the systems with an isolated region of immiscibility (Figure 1.17). However, as one can see from Figure 1.20, an increase in temperature results in a three-phase equilibrium (L1-L2-G) ending not at point Ni (Li = L2-G) but at point 7 (Li = G-L2) where the compositions of gas (G) and dilute liquid solutions (Li) coincide. 

Figure 1.20 Complete phase diagram (three-dimensional P-T-X scheme (a), T-X (b), P-T (c), P-X (d) projections) for binary system A-B of the type 1 with continuous transition of liquid-liquid immiscibility into liquid-gas equilibrium (type Id) (Reproduced by permission of MAIK / Nauka Interperiodica).

It is evident that exactly the same phase behavior should be found in the complete phase diagram of type Ic when the low-temperature region of closed-loop immiscibility overlaps with the surface of crystallization for a system with two types of immiscibility region. The second high-temperature immiscibility region with continuous transition of liquid-liquid into liquid-gas equilibrium is the same as in type Ic. Such phase behaviour was established in the systems methane (CH4) - 1-hexene (C6H12) and methane (CH4) - 3.3-dimeth-ylpentane (C7H16) (Schneider, 1970, 1976, 1978). Three-dimensional P-T-X scheme for type Ic is not shown. 

The parameters of the second critical endpoint Q (Li = L2-S) and neighboring portions of ctuwes QTb (L1-L2-S) and QKb (Li = L2-S) are characterized by pressure values that are considerably higher than fliose of the supercritical transition of water from a gas-like to a hquid-like state (critical isochore or supercritical extrapolation of liquid-gas curve for pure water or those which correspond to die critical curves L = G in water-salt systems of type la (two-dots-dashed line in Figure 1.32) at the same temperature). 

It is interesting to note that it is possible to observe a tricritical point+ in binary polar/nonpolar (or quadrupolar/non-polar) systems of the type considered above. Thus if the polar component is a and is Increased, the tricritical point is observed as an Intermediary stage in the transition from class II to class III behavior. This is shown in Figure 6, the tricritical point occurring where the vapor-liquid critical curve, liquid-liquid critical curve, and the liquid-liquid-gas curve meet. (It should be noted that the formation of a tricritical point in this binary mixture does not violate the phase rule, since acts as an additional degree of freedom). 

The above examples clearly proved that the surface heterogeneity can change the character of the gas-liquid transitions in adsorbed monolayers and mechanism of the adsorbate condensation. In surface layers, one can also observe the commensurate-incommensurate-type transitions. Unfortunately, our knowledge of the behavior of incommensurate phases on nonuniform surfaces is still very limited. Only theoretical articles relevant to this problem are available [12]. 

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