Transition liquid-gas

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191]. 

McConnell et al. [196] and Andelman and co-workers have predicted [197,198] an ordered array of liquid domains in the gas-liquid coexistence regime caused by the dipole moment difference between the phases. These superstructures were observed in monolayers of dipalmitoyl phosphatidylcholine monolayers [170]. 

At lower temperatures a gaseous film may compress indefinitely to a liquid-condensed phase without a discemable discontinuity in the v-a plot. 

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The importance of the van der Waals equation is that, unlike the ideal gas equation, it predicts a gas-liquid transition and a critical point for a pure substance. Even though this simple equation has been superseded, its... 

At equilibrium, in order to achieve equality of chemical potentials, not only tire colloid but also tire polymer concentrations in tire different phases are different. We focus here on a theory tliat allows for tliis polymer partitioning [99]. Predictions for two polymer/colloid size ratios are shown in figure C2.6.10. A liquid phase is predicted to occur only when tire range of attractions is not too small compared to tire particle size, 5/a > 0.3. Under tliese conditions a phase behaviour is obtained tliat is similar to tliat of simple liquids, such as argon. Because of tire polymer partitioning, however, tliere is a tliree-phase triangle (ratlier tlian a triple point). For smaller polymer (narrower attractions), tire gas-liquid transition becomes metastable witli respect to tire fluid-crystal transition. These predictions were confinned experimentally [100]. The phase boundaries were predicted semi-quantitatively. 

A second case to be considered is that of mixtures witli a small size ratio, <0.2. For a long time it was believed tliat such mixtures would not show any instability in tire fluid phase, but such an instability was predicted by Biben and Flansen [109]. This can be understood to be as a result of depletion interactions, exerted on the large spheres by tire small spheres (see section C2.6.4.3). Experimentally, such mixtures were indeed found to display an instability [110]. The gas-liquid transition does, however, seem to be metastable witli respect to tire fluid-crystal transition [111, 112]. This was confinned by computer simulations [113]. 

Phase transitions in adsorbed layers often take place at low temperatures where quantum effects are important. A method suitable for the study of phase transitions in such systems is PIMC (see Sec. IV D). Next we study the gas-liquid transition of a model fluid with internal quantum states. The model [193,293-300] is intended to mimic an adsorbate in the limit of strong binding and small corrugation. No attempt is made to model any real adsorbate realistically. Despite the crudeness of the model, it has been shown by various previous investigations [193,297-300] that it captures the essential features also observed in real adsorbates. For example, the quite complex phase diagram of the model is in qualitative agreement with that of real substances. The Hamiltonian is given by... 

Moreover, the order parameter, which in the case of the gas-liquid transition is defined as the difference between the densities of both coexisting phases, A6 = 62 — 61, approaches zero when the temperature goes to (from below, since above T. the above order parameter is always equal to zero) as... 

To demonstrate that equation (3) describes a mean-field theory of gas-liquid transitions it will be shown how it can be obtained by minimizing a Landau free-energy function. This objective is achieved by working backwards. 

Femtochemistry at High Pressures The Dynamics of an Elementary Reaction in the Gas-Liquid Transition Region, C. Lienau, J. C. Williamson, and A. H. Zewail, Chem. Phys. Lett. 213, 289 (1993). 

Many semiempirical equations of slate with varying degree of theoretical foundations are in use. The Van der Waals equation, a two-parameter equation that gives a qualitatively correct picture of the P-V-T relations of a gas and of the gas liquid transition, is an example. 

The above analysis implies that the coil-globule transition is essentially a gas-liquid transition within a single chain. Unlike usual molecular gases, the translational entropy is absent due to the chain connectivity, and instead, the conformational entropy shows up. The collapsed state is a spherical droplet, that is, globule, to minimize the surface area, the size of which is self-adjusted to satisfy the mechanical balance between the inside and the outside of the globule. 

As early as 1878, Gibbs concluded that the breakdown or growth of a crystal was not a continuous transformation, as the gas-liquid transition was considered to be. Thomson derived what has come to be known as the Gibbs-Thomson equation, relating the vapor pressure of liquid droplets to the size of the droplets. Ostwald extended the concept to the problem of solubility, but made a numerical error later corrected by Freundlich. Similar to the Gibbs-Thomson equation, the Ostwald-Freundlich equation was expressed by... 

For the adhesive hard-sphere model, the theoretical phase diagram in the Tg-0 plane has been partially calculated (Watts et al. 1971 Barboy 1974 Grant and Russel 1993). According to this model, there is a critical point r. c = 0.0976 below which the suspension is predicted to phase separate into a phase dilute in particles and one concentrated in them (see Fig. 7-4). The particle concentration at the critical point of this phase transition is 0c = 0.1213. This phase transition is analogous to the gas-liquid transition of ordinary... 

In 1949, Turnbull and Fisher extended to the liquid-solid transition the earlier work of Becker and Doring on homogeneous nucleation of the gas-liquid transition. Their work presumed the existence in the liquid of a steady-state distribution of small crystallites which were taken to be approximately spherical in shape. The free energy of a crystallite containing i atoms was assumed to have the form... 

The critical state for the gas-liquid transition is the set of physical conditions at... 

The gas-liquid transition described above is only one of several possible transitions exhibiting a critical point. Critical phenomena are observed in liquids and solids as well, as described in Sec. 3.7. 

These trends are similar to what is observed in simpler model fluids with purely spherically s3mimotric interactions [298, 313], which is to some extent expected because the gas liquid transition in Stockmayer fluids is mainly driven by the isotropic LJ (12,6) interactions underlying this model. We show in Ref. 307 that the main effects of HS matrices on the condensation can be reproduced when the dipolar model fluid is approximated by a fluid with angle-averaged dipolar interactions that are not only spherically symmetric but also short-ranged (they decay in proportion to for r — cx)). This notion is particularly important for future simulation studies on adsorbed dipolar fluids. 

The effect of the variation of on the stability limits of a polar Stock-mayor fluid, which implies a variation of the dipolar fluid matrix coupling, is illustrated in the upper part of Fig. 7.4. All results correspond to dilute matrices that do not suppress the gas liquid transition but lead to a significant shift of that transition. In particular, the critical temperature decreases with increasing p.,n, whereas the critical density increases. This characteristic effect is referred to as preferential adsorption in other contexts. The replica integral equation results thus demonstrate, at a microscopic level, that polar... 

The normal water has the long range [T, TJ of gas-liquid transition and the complicated molecular structure. It is a good object to demonstrate the thermodynamical universality of proposed HPD-concept. The first problem is the evaluation of T-dependent FEOS-coefificients... 

Again we emphasize that wetting phenomena are not restricted to the gas-liquid transition, but analogous phenomena occur for all transitions that belong to the same universality class . A particularly, practically important, example are binary (fluid or solid) mixtures that undergo phase separation in the bulk (fig. 55). 

At the gas-liquid transition (along the boiling point line) there is a distinct break in viscosity and diffusivity curves between gases and liquids. Super-... 

Radial Flow Models. The sector models were constructed of transparent acrylic material that was packed with glass beads and initially saturated with a model oil in the lower part and gas in the upper part. Wall effects were found to be insignificant, and gas—liquid transition zones were of negligible height (1—2 cm). Further model properties are listed in Table I. The models were equipped with individual production—injection perforations in contact with specific intervals of the formation. All sector model experiments were conducted at room temperature and pressures below 1.5 bar absolute. It was possible to visually discern the presence of gas, injectant (with the aid of a dye), and model oil in the porous medium. With the aid of a strong backlight, the fluid that was present at the wall in a given location was also seen to be present across the entire model cross-section. 

In order to probe the importance of van der Waals interactions between reactants and solvent, experiments in the gas-liquid transition range appear to be mandatory. Time-resolved studies of the density dependence of the cage and cluster dynamics in halogen photodissociation are needed to extend earlier quantum yield studies which clearly demonstrated the importance of van der Waals clustering at moderate gas densities [37, 111]... 

Schroeder J and Tree J 1987 Elementary reactions in the gas-liquid transition range Ann. Rev. Phys. Chem. 38 163... 

The gas-liquid transition does, however, seem to be metastable with respect to the fluid-ciystal transition [111. 112]. This was confirmed by computer simulations [113]. 

Oxtoby, D.W., and Evans, R. (1988) Nonclassical nucleation theory for the gas-liquid transition, J. Chem. Phys. 99,151. ... 

Rovere, M., D. W. Heermann, and K. Binder 1990, The gas-liquid transition of the two-dimensional Lennard-Jones fluid . J. Phys. Condens. Matter 2, 7009. 

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