Lattice adsorbed phases

Dielectric relaxation and dielectric losses of pure liquids, ionic solutions, solids, polymers and colloids will be discussed. Effect of electrolytes, relaxation of defects within crystals lattices, adsorbed phases, interfacial relaxation, space charge polarization, and the Maxwell-Wagner effect will be analyzed. Next, a brief overview of... 

NMR signals are highly sensitive to the unusual behavior of pore fluids because of the characteristic effect of pore confinement on surface adsorption and molecular motion. Increased surface adsorption leads to modifications of the spin-lattice (T,) and spin-spin (T2) relaxation times, enhances NMR signal intensities and produces distinct chemical shifts for gaseous versus adsorbed phases [17-22]. Changes in molecular motions due to molecular collision frequencies and altered adsorbate residence times again modify the relaxation times [26], and also result in a time-dependence of the NMR measured molecular diffusion coefficient [26-27]. 

From LEED measurements of H monolayers adsorbed on Fe(110) Imbihl et al. proposed a phase diagram as shown in Fig. IS. In addition to lattice gas and lattice fluid phases, two commensurate ordered phases were identifled, denoted as (2 x 1) and (3 x 1) in the figure (cf. Fig. 16). The shaded regions are interpreted as incommensurate phases or as phases composed of antiphase domains their signature is that the LEED spot does not occur at the Bragg position but rather the peak is splitted and satellites appear (Fig. 17). 

In some cases of localised adsorption the adsorbate is ordered into a two-dimensional lattice or net in a particular range of surface coverage and temperature. If the net of the ordered adsorbed phase is in registry with the lattice of the adsorbent the structure is called coherent, if not it is called incoherent (see also 1.2.4). 

A lattice theory of solutions has been proposed (.k) to describe the adsorption-desorption phenomena in zeolites. There are several reasons for this choice (a) forming a solid solution by two substances is analogous to the forming of an adsorbed phase in the cavities of a zeolite, (b) the theory of solutions is well understood and its mathematical techniques powerful, and (c) since the state-of-the-art in description of adsorption phenomena in... 

An alternative and elegant derivation of the BET equation is by a statistical mechanical treatment (Hill, 1946 Steele, 1974). The adsorbed phase is pictured as a lattice gas that is molecules are located at specific sites in all layers. The first layer is localized and these molecules act as sites for molecules in the second layer, which in turn act as sites for molecules in the third layer, and so on for the higher layers. As the surface is assumed to be planar and uniform, it follows that all surface sites are identical. It is also assumed that the occupation probability of a site is independent of the occupancy of neighbouring sites. This is equivalent to the assumption that there are no lateral interactions between adsorbed molecules. In accordance with the BET model, the probability for site occupation is zero unless all its underlying sites are occupied. Furthermore, it is assumed that it is only the molecular partition function for the first layer which differs from that for molecules in the liquid state. 

Our present model of collective multilayer adsorption also predicts critical phenomena existing in the adsorbed phase. And, because the surface coverage in the first adsorbed layer is likely to be much higher than in the next layers, the phase transition of lattice gas to the dense ordered phase will occur initially in the first layer. The critical parameters are found by solving the system of equations... 

The theory of adsorption equilibrium on homogeneous surfaces is so formalized as to be considered a set of statistico-mechanical exercises [15]. When the adsorbed molecules can be considered as structureless particles, practically all models consider the adsorbed phase as a sequence of layers, each stabilized by the adsorption field generated by the underlying one and described either as a two-dimensional (2D) lattice or as a 2D van der Waals gas. 

Liquid-phase adsorption characteristics examined by atomic force microscopy (AFM) were compared for two pyridine base molecules, pyridine and d-picoline. on (010) surfaces of two natural zeolites, heulandite and stilbite. These adsorption systems formed well-ordered. two-dimensioncJ (quasi-)hexagonal adlayers. The 2D lattice structures of the ordered adlayers w ere dependent on the adsorbate/substrate combinations. Although there existed certain habit in the orientation of the 2D lattice unit vector of the adsorbed phase with respect to the substrate(OlO) lattice vectors, the molecular arrays w ere incommensurate with the substrate atomic arrangements. 

When the adsorbate-substrate bonds are weak (of the van der Waals type), the properties of the adsorbed monolayer are less dependent on the substrate s atomic structure. In this circumstance, two-dimensional adsorbate phases exhibit lattice-gas-liquid-solid transitions as a function of coverage and temperature changes. 

A casual look at Fig. 18(b) may give the impression of the existence of a re-entrant adsorbed phase as u is increased. One should, however, realize that these figures are merely a projection on the w-u plane of three dimensional figures in which the third dimension is given by t. The value of crossover exponent (j> for the 4-simplex lattice is 0.7481 equal to the value found for HB 2,3). 

The Langmuir approach was a starting point for developing the more realistic formalism in the framework of the lattice gas theories based on the Ising model [24]. It seems intuitively obvious that the lattice gas model is well suited for representing localized adsorption. The adsorbed phase is considered a two-dimensional lattice gas. The most popular isotherm involving molecular interaction effects is the Fowler-Guggenheim equation [25]... 

The concentrations of the surface species obey the following equalities in the anion sub-lattice and in adsorbed phase ... 

Based on crystallographical analysis a new mechanism of adsorbate phase transition is discussed and theoretically modeled. Qualitative comparisons between the model isotherm and its experimental counterpart are carried out. It C2m be concluded that the hysteresis loop in the p-xylene/ZSM-5 isotherms is caused by a strong crystal lattice mediated interaction between adsorbate molecules, while the intermediate plateau is the result of this interaction and the large energetic difference between two types of adsorption sites. 

There is, of course, a mass of rather direct evidence on orientation at the liquid-vapor interface, much of which is at least implicit in this chapter and in Chapter IV. The methods of statistical mechanics are applicable to the calculation of surface orientation of assymmetric molecules, usually by introducing an angular dependence to the inter-molecular potential function (see Refs. 67, 68, 77 as examples). Widom has applied a mean-held approximation to a lattice model to predict the tendency of AB molecules to adsorb and orient perpendicular to the interface between phases of AA and BB [78]. In the case of water, a molecular dynamics calculation concluded that the surface dipole density corresponded to a tendency for surface-OH groups to point toward the vapor phase [79]. 

It is noted in Sections XVII-10 and 11 that phase transformations may occur, especially in the case of simple gases on uniform surfaces. Such transformations show up in q plots, as illustrated in Fig. XVU-22 for Kr adsorbed on a graphitized carbon black. The two plots are obtained from data just below and just above the limit of stability of a solid phase that is in registry with the graphite lattice [131]. 

The term alumina hydrates or hydrated aluminas is used in industry and commerce to designate aluminum hydroxides. These compounds are tme hydroxides and do not contain water of hydration. Several forms are known a general classification is shown in Figure 1. The most weU-defined crystalline forms ate the trihydroxides, Al(OH) gibbsite [14762-49-3], bayerite [20257-20-9], and nordstrandite [13840-05-6], In addition, two aluminum oxide—hydroxides, AIO(OH), boelimite [1318-23-6] and diaspote [14457-84-2], have been clearly defined. The existence of several other forms of aluminum hydroxides have been claimed. However, there is controversy as to whether they ate truly new phases or stmctures having distorted lattices containing adsorbed or intedameUar water and impurities. 

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