Condensation transition

MacDowell, L. G. Virnau, P. Muller, M. Binder, K., The evaporation/condensation transition of liquid droplets, J. Chem. Phys. 2004,120, 5293-5308... 

Much better agreement has been found with the results of the Deijaguin-Broekhoff-de Boer theory [10,11] (Figure 3, top). For pores wider than ca. 6 nm the equilibrium and spontaneous capillary condensation transitions predicted by the NLDFT are well approximated by the semi-empirical equations of Broekhoff and de Boer [10,11] In smaller pores, the deviations are substantial (Figure 3, bottom)... 

Pallas. N.R. Pethica, B.A. Liquid-expanded to liquid-condensed transition in lipid monolayers at the air/ water interface. Langmuir 1985, 1, 509. 

Over the years, vapour adsorption and condensation in porous materials continue to attract a great deal of attention because of (i) the fundamental physics of low-dimension systems due to confinement and (ii) the practical applications in the field of porous solids characterisation. Particularly, the specific surface area, as in the well-known BET model [I], is obtained from an adsorbed amount of fluid that is assumed to cover uniformly the pore wall of the porous material. From a more fundamental viewpoint, the interest in studying the thickness of the adsorbed film as a function of the pressure (i.e. t = f (P/Po) the so-called t-plot) is linked to the effort in describing the capillary condensation phenomenon i.e. the gas-Fadsorbed film to liquid transition of the confined fluid. Indeed, microscopic and mesoscopic approaches underline the importance of the stability of such a film on the thermodynamical equilibrium of the confined fluid [2-3], In simple pore geometry (slit or cylinder), numerous simulation works and theoretical studies (mainly Density Functional Theory) have shown that the (equilibrium) pressure for the gas/liquid phase transition in pores greater than 8 nm is correctly predicted by the Kelvin equation provided the pore radius Ro is replaced by the core radius of the gas phase i.e. (Ro -1) [4]. Thirty year ago, Saam and Cole [5] proposed that the capillary condensation transition is driven by the instability of the adsorbed film at the surface of an infinite... 

H. Dominguez, M.P. Allen and R. Evans, Monte Carlo Studies of the Freezing and Condensation Transitions of Confined Fluids, Mol. Phys. 96 (1998) pp. 209-229... 

The adsorption and desorption isotherms have been calculated for the Nj sorption at 77K in cylindrical pores of MCM-41 materials in the range 1-12 nm. The points of spinodal and equilibrium transitions are plotted in Fig. 2. There are several features worth noticing. As the pore size increases, the line of spinodal desorption saturates at the value corresponding to the spinodal decomposition of the bulk liquid. The line of equilibrium capillary condensation asymptotically approaches the Kelvin equation for the spherical meniscus and the line of spontaneous capillary condensation asymptotically approaches the Kelvin equation for the cylindrical meniscus. This asymptotic behavior is in agreement with the classical scenario of capillary hysteresis [12] capillary condensation occurs spontaneously after the formation of the cylindrical adsorption film on the pore walls while evaporation occurs after the formation of the equilibrium meniscus at the pore end. Most interestingly, the NLDFT predictions of equilibrium and spontaneous capillary condensation transitions for pores wider than 6 nm are approximated by the semi-empirical equations of the Deijaguin-Broekhoff-de Boer theory [13]. 

In the first application will will exemplify the accurate localization of the condensation transition for a coarse-grained bead-spring polymer model. As discussed above, the order parameter of the liquid-vapor transition is the monomer number density, p. The equation of state of the polymer solution is... 

K. Binder (2003) Theory of the evaporation /condensation transition of equilibrium droplets in finite volumes. Physica A 319, pp. 99-114... 

As discussed in Section 9.2.3, despite the apparent ID nature of matter filling the channels, atoms in adjacent ICs of a bundle can interact with each other. In that case, a fuUy 3D condensation transition with a nonzero critical temperature can happen where the final condensed state is an anisotropic liquid [47-49]. This state is much more stable than the ID liquid for example, the binding energy of a He system [47, 48] increases from 2 to 16 mK. Although the interchannel interaction is very weak compared with the gas-gas interaction inside the channels, its presence is enough to drive the transition. On the... 

The earliest vacancy-mediated melting theories were essentially instability theories, which predicted the temperature at which the free energy of formation of vacancies becomes negative (an example of such arguments can be found in the section on KTHNY theory above). More recent theories (such as O Reilly s) view melting as a vacancy condensation transition. Vacancy-mediated melting theories have never enjoyed wide acceptance because the concept of a vacancy is ill-defined in the liquid phase, and because such theories seem to be inapplicable to substances that contract upon melting. 

The spatial aggregation of topological defects evident in Figs, 5a- la is directly related to the other prominent feature of the dense WCA liquid extensive solid-like regions, which appear as rafts of nearly hexagonal Voronoi cells. As we will show, this dramatic spatial inhomogeneity is a consequence of the defect condensation transition that produces the liquid phase. Thus, it is the key qualitative feature of liquid structure that is required to understand 2D melting. 

General introduction/Electronic structure of metal clusters and cluster compounds/ Clusters in ligand shells/Clusters in cages/Discrete and condensed transition metal clusters in solids/Chemistry of transition metal colloids/Perspectives G.A. Somoijai, Introduction to Surface Chemistry and Catalysis, Wiley New York, 1994... 

The SJ-S2-V point is the transition point of the substance, the Sj-L-V and Sj-L-V points are melting points, and the SJ-S2-L point is a condensed transition point (7). Whether all these points can be experimentally attained depends on the empirical details of the system itself. 

Figure 3. The onset of the liquid expanded/liquid condensed transition (t ) as a function of the temperature for tricosanoyl-10 12-diynoic acid (TCDA) and pentacosanoyl-10 12-diynolc acid (PCOA). Since only two Isotherms In each case exhibited a phase transition a linear extrapolation to zero pressure was used to obtain values of Tg (the lowest temperature at which an expanded phase could exist). Previous experience indicates a linear extrapolation is a reasonable approximation and that any non-linearity would result in lowering the Tg values in Table 1 by no more than a fraction of a degree.

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