Density functional theory phase diagrams

V. V. Ginzburg and A. C. Balazs, Calculating phase diagrams of polymer-platelet mixtures using density functional theory Implications for polymer/clay composites, Macromolecules 32, 5681-5688 (1999). 

The principal tools have been density functional theory and computer simulation, especially grand canonical Monte Carlo and molecular dynamics [17-19]. Typical phase diagrams for a simple Lennard-Jones fluid and for a binary mixture of Lennard-Jones fluids confined within cylindrical pores of various diameters are shown in Figs. 9 and 10, respectively. Also shown in Fig. 10 is the vapor-liquid phase diagram for the bulk fluid (i.e., a pore of infinite radius). In these examples, the walls are inert and exert only weak forces on the molecules, which themselves interact weakly. Nevertheless,... 

Dynamic Density Functional Theory (DDFT), Fig. 2 Schematic phase diagram of a system of Brownian particles with an attractive interaction. 4> in is the depth of the attractive minimum of the interaction potential, and p is the particle density (averaged of the syston volume). Only the states above ihtfull line, the bimodal, are stable. The states between the full and the dashed lines, the spinodal, are metastable, and the states below the spinodal are linearly unstable. The system considered in Archer and Evans [7] is quenched from a stable slate circle) into the unstable region as indicated by the vertical arrow... 

Strachan A, Cagin T, Goddard WA (1999) Phase diagram of MgO from density functional theory and molecular-dynamics simulations. Phys Rev B 60 15084-15093 Streitz FH, Mintmire JW (1994) Charge-transfer and bonding in metallic oxides. J Adhesion Sci Tech 8 853-864... 

Benes, O., Zeller, R, Salanne, M., and Konings, R.J.M. (2009) Density functional theory, molecular dynamics, and differential scanning calorimetry study of the RbF-CsF phase diagram. J. Chem. Phys, 130, 134716. 

The density functional theory appears to be a powerfid tool for studying adsorption on heterogeneous surfaces. In particular, the valuable results have been obtained for adsorption in pores with chemically stractured walls. The interesting, new phenomena, such as bridging, have been discovered in this way. The phase diagrams characterizing various phase transitions in surface layers can be determined quite quickly from the functional density theory. In this context, we emphasize the economy of the computational efforts required for the application of the fimctional density methods. For this reason, the density theory can be under certain conditions, competitive with computer simulations. However, many applications of the density fimctional theory are based on rather crude, oversimplified assumptions, so the conclusions following firom the calculations should be treated very cautiously. 

FIG. 4 Phase diagram for krypton on graphite from Ref. 98. Points are experimental data and curves were obtained from the density functional theory applied by Fairobent et al. [98] using different Lermard-Jones parameters solid line—E/k = 168.5 K and a = 0.36 nm dashed line—E/k = 145 K and a = 0.36 nm. 

When the iateraction energy density is positive, equation 5 defines a critical temperature of the UCST type (Fig. la) that is a function of component molecular weights. The LCST-type phase diagram, quite common for polymer blends, is not predicted by this simple theory unless B is... 

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