Close packed solid phase

By analogy with monomolecular films at liquid-air interfaces, surfactants at the liquid-liquid interface will normally form monolayers with various molecular packing densities ranging from relatively loosely packed arrangements normally associated with fluid phases (gases and liquids) to the close-packed solid phase. Classically, amphiphilic adsorption at interfaces has been roughly classified in terms of film types related to normal states of matter (Figure 9.13) ... 

The major difference, then, between the 3 phases we have discussed is that the solid consists of an assemblage of close-packed molecules which we have shown to have arisen when we removed enough energy from the molecules so as to cause them to condense and to form the solid state. Let us now examine the properties of atoms or molecules when they are crowded together to form a "close-packed" solid. 

Hydrogen motion has also been studied in the lutetium-hydrogen system by Barrere and Tran (1971). At the composition LuHo.17 the hydrogen is in solid solution in the close-packed-hexagonal phase of the lutetium metal. The observed rigid lattice second moment was compatible with random occupation of... 

It is generally observed that the interface between two solids which results from the growth of one phase by condensation to form a film on die other is one in which the number of nearest neighbour bonds between the two phases is maximized. The close-packed planes tend to be found at the interface, which is consequently usually nearly atomically flat and this minimizes die interfacial... 

Although Eqs. (33), (34), and especially (35), are useful they have a problem. They all predict that the hard sphere system is a fluid until = 1. This is beyond close packing and quite impossible. In fact, hard spheres undergo a first order phase transition to a solid phase at around pd 0.9. This has been estabhshed by simulations [3-5]. To a point, the BGY approximation has the advantage here. As is seen in Fig. 1, the BGY equation does predict that dp dp)j = 0 at high densities. However, the location of the transition is quite wrong. Another problem with the PY theory is that it can lead to negative values of g(r). This is a result of the linearization of y(r) - 1 that... 

There are three basic modes of transport which are employed. The first, and most common, is termed dilute phase or lean phase transport in which the volume fraction of solids in this suspension does not exceed about 0.05 and a high proportion of the particles spend most of their time in suspension. The second is transport which takes place largely in the form of a moving bed in which the solids volume fraction may be as high as 0.6 this is relevant only for horizontal or slightly inclined pipelines. The third form is dense phase transport in which fairly close packed slugs of particles, with volume fractions of up to... 

A solid emulsion is a suspension of a liquid or solid phase in a solid. For example, opals are solid emulsions formed when partly hydrated silica fills the interstices between close-packed microspheres of silica aggregates. Gelatin desserts are a type of solid emulsion called a gel, which is soft but holds its shape. Photographic emulsions are gels that also contain solid colloidal particles of light-sensitive materials such as silver bromide. Many liquid crystalline arrays can be considered colloids. Cell membranes form a two-dimensional colloidal structure (Fig. 8.44). 

Also, subcritical (hot/liquid) water can be used as a mobile phase for packed-column RPLC with solute detection by means of FID [942]. In the multidimensional on-line PHWE-LC-GC-FTD/MS scheme, the solid sample is extracted with hot pressurised water (without the need for sample pretreatment), and the analytes are trapped in a solid-phase trap [943]. The trap is eluted with a nitrogen flow, and the analytes are carried on to a LC column for cleanup, and separated on a GC column using the on-column interface. The closed PHWE-LC-GC system is suitable for many kinds of sample matrices and analytes. The main benefit of the system is that the concentration step is highly efficient, so that the sensitivity is about 800 times better than that obtained with traditional methods [944]. Because small sample amounts are required (10 mg), special attention has to be paid to the homogeneity of the sample. The system is... 

Thus, just as for incompressible single-phase flow, the pressure p constrains the velocity fields to ensure (in the case of multiphase flows) that the sum of the phase volume fractions equals unity. In the presence of mass transfer, the right-hand side of Eq. (148) is nonzero nevertheless, the role of the pressure is still the same. Finally, we should note that in gas-solid flows the maximum volume fraction of the solid phase is less than unity due to physical constraints (i.e., when particles are close packed there is still room for the gas phase so that 0solid-pressure term ps that becomes extremely large when ag approaches its minimum value (e.g., oc — 0.4). 

The right hand side of Fig. A.4.6 is contained in Fig. 3.3. Capacity measurements can readily be made at solid electrodes to study adsorption behavior. For a review see Parsons (1987). As Fig. A.4.7 illustrates, capacity potential curves of three low-index phases of silver, in contact with a dilute aqueous solution of NaF, show different minimum capacities (corresponding to the condition o = 0) and therefore remarkably different potentials of pzc. The closest packed surface (111) has the highest pzc and the least close-packed (110) has the lowest pcz these values differ by 300 mV. Such complications observed with single crystal electrodes, seem likely to have their parallel at other solid surfaces. For example, it is to be expected that a crystalline oxide will have different pzc values at its various types of exposed faces. 

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