Disordered matrix

The equlibrium between the bulk fluid and fluid adsorbed in disordered porous media must be discussed at fixed chemical potential. Evaluation of the chemical potential for adsorbed fluid is a key issue for the adsorption isotherms, in studying the phase diagram of adsorbed fluid, and for performing comparisons of the structure of a fluid in media of different microporosity. At present, one of the popular tools to obtain the chemical potentials is an approach proposed by Ford and Glandt [23]. From the detailed analysis of the cluster expansions, these authors have concluded that the derivative of the excess chemical potential with respect to the fluid density equals the connected part of the fluid-fluid direct correlation function (dcf). Then, it follows that the chemical potential of a fluid adsorbed in a disordered matrix, p ), is... 

First, we would like to eonsider a simple hard sphere model in a hard sphere matrix, similar to the one studied in Refs. 20, 21, 39. However, our foeus is on a very asymmetric hard sphere mixture adsorbed in a disordered matrix. Moreover, having assumed a large asymmetry of diameters of the eomponents and a very large differenee in the eoneentration of eomponents, here we restriet ourselves to the deseription of the struetural properties of the model. Our interest in this model is due, in part, to experimental findings eoneerning the potential of the mean foree aeting between eolloids in a eolloidal dispersion in the presenee of a matrix of obstaeles [12-14]. 

However, before proceeding with the description of simulation data, we would like to comment the theoretical background. Similarly to the previous example, in order to obtain the pair correlation function of matrix spheres we solve the common Ornstein-Zernike equation complemented by the PY closure. Next, we would like to consider the adsorption of a hard sphere fluid in a microporous environment provided by a disordered matrix of permeable species. The fluid to be adsorbed is considered at density pj = pj-Of. The equilibrium between an adsorbed fluid and its bulk counterpart (i.e., in the absence of the matrix) occurs at constant chemical potential. However, in the theoretical procedure we need to choose the value for the fluid density first, and calculate the chemical potential afterwards. The ROZ equations, (22) and (23), are applied to decribe the fluid-matrix and fluid-fluid correlations. These correlations are considered by using the PY closure, such that the ROZ equations take the Madden-Glandt form as in the previous example. The structural properties in terms of the pair correlation functions (the fluid-matrix function is of special interest for models with permeabihty) cannot represent the only issue to investigate. Moreover, to perform comparisons of the structure under different conditions we need to calculate the adsorption isotherms pf jSpf). The chemical potential of a... 

To the best of our knowledge, there was only one attempt to consider inhomogeneous fluids adsorbed in disordered porous media [31] before our recent studies [32,33]. Inhomogeneous rephca Ornstein-Zernike equations, complemented by either the Born-Green-Yvon (BGY) or the Lovett-Mou-Buff-Wertheim (LMBW) equation for density profiles, have been proposed to study adsorption of a fluid near a plane boundary of a disordered matrix, which has been assumed uniform in a half-space [31]. However, the theory has not been complemented by any numerical solution. Our main goal is to consider a simple model for adsorption of a simple fluid in confined porous media and to solve it. In this section we follow our previously reported work [32,33]. 

Whereas for the sample deformed to 40% a very small decrease of resistivity is obtained at 170°C not being visible in Figure 2 (very small number of excess vacancies) a slight increase results above 170°C for the sample deformed to 80%. This may be a consequence of increasing SRO within the disordered matrix before changes in LRO are enabled. 

Fig. 4. Substitution matrix based on disordered protein families. Below the diagonal are the scores for each amino acid substitution. Above the diagonal are the differences between BLOSUM 62 and the disorder matrix. On the diagonal are the scores/differences. (From Radivojac et al., 2002, PSB 2002 7, 589-600, with permission of World Scientific Publishing Co. Pte Ltd.)...

K. Hamacher, Synthesis of n.c.a. cis- and trans-4-[ F]fluoro-L-proline, radiotracers for PET-investigation of disordered matrix protein synthesis, J. Label. Compds Radiopharm. 42 (1999) 1135-1144. 

Fig. 5.15 (a) Field ion image and a domain map of a N Mo alloy which has been annealed for 5 min at 800°C with a slow heating rate to the final annealing temperature. Long range ordered domains are formed within the disordered matrix which, however, already exhibits a small degree of short range order. (Courtesy of M. Yamamoto.)... 

For synthesis of composite films with M/SC nanoparticles distributed in the volume of a dielectric matrix, method PVD is used as co-deposition of M/ SC and dielectric material vapors. A comparison of films produced by codeposition and layer-by-layer deposition PVD methods has been made on the example of BN-Fe nanocomposite films [57]. Unlike the above considered film from alternating layers of Fe and BN, which has ordered structure, co-deposited BN-Fe nanocomposite films consist of amorphous completely disorder matrix BN containing a chaotic system of immobilized Fe nanoparticles. At the same time, these particles in contrast to those of layered film have much smaller size (d — 2.3 nm) since in this case the metal atoms are inside a matrix which slowdowns the diffusion process of atoms aggregation. 

Another effects of the interaction with the surrounding disordered matrix is the increase in the one-phonon direct relaxation of Ho3+ in oxyfluoride glass ceramics due to coupling to the higher density of low-frequency phonon modes in the glass compared with the crystal (Meltzer et al., 2002). The direct relaxation time between the two lowest 5Fs sublevels (a gap of 14.5 cm-1) of Ho3+ in nanocrystals of different sizes embedded in oxyfluoride glass ceramics was measured (see fig. 14), under excitation of the second low-... 

From now on wc focus on situations where the fluid adsorbed by a disordered matrix is both homogeneous and isotropic after averaging over different mar trix configurations. In such a situation, the fluid s singlet density is just a constant that is,... 

More dramatic effects arise when the perturbation induced by the disordered matrix couples directly to the dipole moments of the fluid particles. Charged matrix particles provide an example. Their impact on a DHS fluid has been studied by Fernaud et al. [323]. They report a significant decrease of the dielectric constant and an enhanced tendency of dipoles to form aggregates at low densities. Another interesting case are dipolar fluid matrix interactions where each fluid particle feels both the dipole fields of its fluid neighbors and the additional dipole fields arising from the adsorbing medium. 

Furthermore, we show that when Co is added to the catalyst as a promoter, it is initially homogeneously distributed throughout the hemihydrate platelet. As activation proceeds, however, the Co is seen to have limited solubility in the (VO)2P207 phase and preferentially segregates into, as well as structurally stabilising, the disordered matrix material. 

Self-organization in many solution-processed, semiconducting conjugated polymers results in complex microstructures in which ordered microcrystaUine domains are embedded in an amorphous matrix [20,21]. This has important consequences for electrical properties of these materials Charge transport is usually limited by the most difficult hopping processes and is therefore dominated by the disordered matrix, resulting in low charge-carrier mobilities (<10 cm V s ) [22]. 

Schweitzer (1981) pointed out, however, that this mechanism would require that 10% of the hydrogen atoms be involved in the disorder modes and this large fraction should have been directly observable in the NMR experiments. Ngai (1981) has suggested that the relaxation is controlled by low frequency fluctuations in the disordered matrix. 

Ichikawa T, Kevan L, Bowman MK, Dikanov SA, Tsvetkov YD (1979) Ratio analysis of electron spin echo modulation envelopes in disordered matrixes and application to the structure of solvated electrons in 2-methyltetrahydrofuran glass. J Chem Phys 71 (3) 1167-1174... 

The relations given previously pertain to isotropic bodies, and for nonisotropic bodies the equations are considerably more complex. Polymeric materials are normally either amorphous or partially crystalline with randomly oriented crystallites embedded in a disordered matrix. However, any symmetry possessed by an individual crystallite can be disregarded, and the body as a whole is treated as being isotropic. 

Single crystal ENDOR measurement is an informative but not always applicable method to identify paramagnetic species in solids. It is for instance difficult to obtain single crystals of biochemical materials. In other cases the paramagnetic species are intentionally trapped in a disordered matrix or in a frozen solution. The ENDOR lines are then usually broadened by the anisotropy of the magnetic couplings. Some data that a single crystal analysis can provide are difficult to extract from a powder sample. However, a considerable amount of information can often be obtained from ENDOR spectra of disordered systems. 

In a real disordered matrix, there usually are several TLS s able to interact with a single molecule, as schematically shown in Fig. 1. The first case is that of defects in crystals, where a non-random distribution of flipping TLS s in space interacts with the probe. Dislocations or grain boundaries can give rise to such one- or two-dimensional distributions of TLS s (see Section 1.4.2). Because of the translational symmetry of crystals, we may assume in this case that all TLS s have the same... 

The success of the fluorescence spectroscopy of pentacene in p-terphenyl crystal immediately suggests including pentacene in a different, disordered matrix such as polyethylene. Several attempts in this direction failed, first because of the photoreactivity of pentacene [42] and second because the matrix can greatly influence the photophysical properties of pentacene [66]. As discussed in Section 1.2, the intersystem crossing rate from the excited singlet of pentacene strongly depends on the local site structure. Different environments around pentacene sites in p-terphenyl crystal lead to hundredfold increases of the triplet yield [74]. It is therefore likely that the highly flexible pentacene molecule has an unfavorable triplet yield when included in a polymer. 

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