Quenched-annealed mixtures

Several colloidal systems, that are of practical importance, contain spherically symmetric particles the size of which changes continuously. Polydisperse fluid mixtures can be described by a continuous probability density of one or more particle attributes, such as particle size. Thus, they may be viewed as containing an infinite number of components. It has been several decades since the introduction of polydispersity as a model for molecular mixtures [73], but only recently has it received widespread attention [74-82]. Initially, work was concentrated on nearly monodisperse mixtures and the polydispersity was accounted for by the construction of perturbation expansions with a pure, monodispersive, component as the reference fluid [77,80]. Subsequently, Kofke and Glandt [79] have obtained the equation of state using a theory based on the distinction of particular species in a polydispersive mixture, not by their intermolecular potentials but by a specific form of the distribution of their chemical potentials. Quite recently, Lado [81,82] has generalized the usual OZ equation to the case of a polydispersive mixture. Recently, the latter theory has been also extended to the case of polydisperse quenched-annealed mixtures [83,84]. As this approach has not been reviewed previously, we shall consider it in some detail. 

A major drawback of the RFIM, however, is that it focuses entirely on the aspect of disorder, whereas confinement plays no role. To accormt for this problem, more recent theoretical studies, and computer simulations, of fluids in disordered media employ the concept of a quenched-annealed (QA) mixture [290, 291]. Here, the fluid molecules (the annealed species) equilibrate in a matrix consisting of particles quenched in a disordered (configuration. Thus, QA models combine both disorder and confinement, the latter being guaranteed by the finite size of the matrix particles. In addition, preferential adsorption can be realized by assiuning attractive (or other, more complex) interactions between fluid and matrix particles. 

We presented a novel quenched solid non-local density functional (QSNLDFT) model, which provides a r istic description of adsorption on amorphous surfaces without resorting to computationally expensive two- or three-dimensional DFT formulations. The main idea is to consider solid as a quenched component of the solid-fluid mixture rather than a source of the external potential. The QSNLDFT extends the quenched-annealed DFT proposed recently by M. Schmidt and cowoikers [23,24] for systems with hard core interactions to porous solids with attractive interactions. We presented several examples of calculated adsorption isotherms on amorphous and microporous solids, which are in qualitative agreement with experimental measurements on typical polymer-templated silica materials like SBA-15, FDU-1 and oftiers. Introduction of the solid density distribution in QSNLDFT eliminates strong layering of the fluid near the walls that was a characteristic feature of NLDFT models with smoodi pore walls. As the result, QSNLDFT predicts smooth isotherms in the region of polymolecular adsorption. The main advantage of the proposed approach is that QSNLDFT retains one-dimensional solid and fluid density distributions, and thus, provides computational efficiency and accuracy similar to conventional NLDFT models. 

We shall now review experimental Bai +xFe2S4. Non-stoichiometric Baj weighed mixtures of BaS, Fe, and S in evacuated silica tubes. Figure 2.40 shows the relation between the ratio of Ba to Fe (a = 2Ba/Fe), annealing temperature (Tj,) (the samples were quenched from T ), and lattice parameters (a, Cg, Cp), measured by X-ray powder diffraction. The values of Cg and Cp are closely correlated to almost independent of nominal composition. 

Finally, C tld /,.[ = cdd = c Jm is the Fourier transform of the replica-replica direct correlation function (blocking function), and the connected function is defined as usual by cc = cdd — cdd, and similarly for hc. Let us recall that the replicated particles are the dipolar hard spheres, i.e. the annealed fluid in the partly quenched mixture. 

It is now important to report some NMR results obtained with an acid 120 Nafion sample containing an excess of water. A Nafion-water mixture is quenched from room temperature down to liquid nitrogen temperature and then rapidly put into the NMR spectrometer at a well defined temperature below 0°C. The amplitude of the line corresponding to the mobile water protons at this temperature is then recorded versus time as shown in fig (12). The observed decrease in amplitude of the line corresponds to a change in the number of the mobile water protons. During the annealing time some desorption occurs and initially mobile water molecules are frozen either outside the sample or in small holes inside this sample. 

I. An intimate mixture of 102 g.of (NaPOs)nand 266 g. of Na PgO, Is melted. The melt Is quenched, pulverized, and pressed Into tablets of 2-3 g., and these are annealed for eight hours at 500 to 525°C. Then 10 g. of the annealed reaction product is dissolved in water. The solution is evaporated over H gSO and an imstable octahydrate crystallizes out. It is dried over PgOs and thus transformed to the hexahydrate. The latter is stable. The hexahydrate can also be produced by precipitation from the solution with alcohol. 

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