Bare

The Reid vapor pressure is generally barely different from the true vapor pressure at 37.8°C if the light gas content —methane, ethane, propane, and butane— of the sample is small, which is usually the case with petroleum products. The differences are greater for those products containing large quantities of dissolved gases such as the crude oils shown in Table 4.13. 

When a production or injection well is drilled, it is common practice to cement in place a casing which extends across the reservoir interval. The alternative is to leave the reservoir uncased, in a so-called bare foot completion, which is rarely done. When the drilling department finishes its work on the well, it is often left in the state of a cased hole, as on the left of Figure 9.14. 

The bare foot completion, which leaves an open hole section below the previous casing, is cheap, simple and suitable for consolidated formations which have little tendency to collapse. The slotted liner s an uncemented section of casing with small intermittent slots cut along its length, which prevents the hole from collapsing, but allows no selectivity of the interval which will be produced. The cased and cemented horizontal completion does allow a choice of which intervals will be perforated and produced. None of these examples provides any effective sand exclusion it this is required a gravel pack or a pre-packed liner can be used. 

The derivation that follows is essentially that given by Langmuir [9] in 1918, in which one writes separately the rates of evaporation and of condensation. The surface is assumed to consist of a certain number of sites S of which S are occupied and Sq = S - S arc free. The rate of evaporation is taken to be proportional to 5, or equal tokiSi, and the rate of condensation proportional to the bare surface So and to the gas pressure, or equal to k PSo. At equilibrium. 

Perhaps the most fascinating detail is the surface reconstruction that occurs with CO adsorption (see Refs. 311 and 312 for more general discussions of chemisorption-induced reconstructions of metal surfaces). As shown in Fig. XVI-8, for example, the Pt(lOO) bare surface reconstructs itself to a hexagonal pattern, but on CO adsorption this reconstruction is lifted [306] CO adsorption on Pd( 110) reconstructs the surface to a missing-row pattern [309]. These reconstructions are reversible and as a result, oscillatory behavior can be observed. Returning to the Pt(lOO) case, as CO is adsorbed patches of the simple 1 x 1 structure (the structure of an undistorted (100) face) form. Oxygen adsorbs on any bare 1 x 1 spots, reacts with adjacent CO to remove it as CO2, and at a certain point, the surface reverts to toe hexagonal stmcture. The presumed sequence of events is shown in Fig. XVIII-28. 

In this equation //is the Flamiltonian (developed in the previous section) which consists of the bare system Flamiltonian and a temi coming from the interaction between the system and the light. That is. 

Consider a system governed by Hamiltonian H = H + where is the bare molecular Hamiltonian and... 

The probability for sticking is known as the sticking coefficient, S. Usually,. S decreases with coverage. Thus, the sticking coefficient at zero coverage, the so-called initial sticking coefficient,. S q, reflects the interaction of a molecule with the bare surface. 

Adsorbates can physisorb onto a surface into a shallow potential well, typically 0.25 eV or less [25]. In physisorption, or physical adsorption, the electronic structure of the system is barely perturbed by the interaction, and the physisorbed species are held onto a surface by weak van der Waals forces. This attractive force is due to charge fiuctuations in the surface and adsorbed molecules, such as mutually induced dipole moments. Because of the weak nature of this interaction, the equilibrium distance at which physisorbed molecules reside above a surface is relatively large, of the order of 3 A or so. Physisorbed species can be induced to remain adsorbed for a long period of time if the sample temperature is held sufficiently low. Thus, most studies of physisorption are carried out with the sample cooled by liquid nitrogen or helium. 

Strongin D R, Carrazza J, Bare S R and Somoqai G A 1987 The importance of Cj sites and surface roughness in the ammonia synthesis reaction over iron J. Catal. 103 213... 

Bare S R, Strongin D R and Somoqai G A 1986 Ammonia synthesis over iron single crystal catalysts—the effects of alumina and potassium J. Phys. Chem. 90 4726... 

The ppm scale is always calibrated relative to the appropriate resonance of an agreed standard compound, because it is not possible to detect the NMR of bare nuclei, even though absolute shieldings can be calculated... 

Figure Bl.20.15. Shear force as a fimction of time for (a) bare mica in toluene and (b) polystyrene-covered mica in toluene. Reproduced with pennission from [9],...

Islands occur particularly with adsorbates that aggregate into two-dimensional assemblies on a substrate, leaving bare substrate patches exposed between these islands. Diffraction spots, especially fractional-order spots if the adsorbate fonns a superlattice within these islands, acquire a width that depends inversely on tire average island diameter. If the islands are systematically anisotropic in size, with a long dimension primarily in one surface direction, the diffraction spots are also anisotropic, with a small width in that direction. Knowing the island size and shape gives valuable infonnation regarding the mechanisms of phase transitions, which in turn pemiit one to leam about the adsorbate-adsorbate interactions. 

Flead and Silva used occupation numbers obtained from a periodic FIF density matrix for the substrate to define localized orbitals in the chemisorption region, which then defines a cluster subspace on which to carry out FIF calculations [181]. Contributions from the surroundings also only come from the bare slab, as in the Green s matrix approach. Increases in computational power and improvements in minimization teclmiques have made it easier to obtain the electronic properties of adsorbates by supercell slab teclmiques, leading to the Green s fiinction methods becommg less popular [182]. 

A first step towards a systematic improvement over DFT in a local region is the method of Aberenkov et al [189]. who calculated a correlated wavefiinction embedded in a DFT host. However, this is achieved using an analytic embedding potential fiinction fitted to DFT results on an indented crystal. One must be cautious using a bare indented crystal to represent the surroundings, since the density at the surface of the indented crystal will have inappropriate Friedel oscillations inside and decay behaviour at the indented surface not present in the real crystal. 

Clusters are intennediates bridging the properties of the atoms and the bulk. They can be viewed as novel molecules, but different from ordinary molecules, in that they can have various compositions and multiple shapes. Bare clusters are usually quite reactive and unstable against aggregation and have to be studied in vacuum or inert matrices. Interest in clusters comes from a wide range of fields. Clusters are used as models to investigate surface and bulk properties [2]. Since most catalysts are dispersed metal particles [3], isolated clusters provide ideal systems to understand catalytic mechanisms. The versatility of their shapes and compositions make clusters novel molecular systems to extend our concept of chemical bonding, stmcture and dynamics. Stable clusters or passivated clusters can be used as building blocks for new materials or new electronic devices [4] and this aspect has now led to a whole new direction of research into nanoparticles and quantum dots (see chapter C2.17). As the size of electronic devices approaches ever smaller dimensions [5], the new chemical and physical properties of clusters will be relevant to the future of the electronics industry. 

More sophisticated approaches to describe double layer interactions have been developed more recently. Using cell models, the full Poisson-Boltzmann equation can be solved for ordered stmctures. The approach by Alexander et al shows how the effective colloidal particle charge saturates when the bare particle charge is increased [4o]. Using integral equation methods, the behaviour of the primitive model has been studied, in which all the interactions between the colloidal macro-ions and the small ions are addressed (see, for instance, [44, 45]). 

Figure C2.10.2. Cyclic voltammogram of Cu(l 11)/10 mM HCl and in situ measured STM micrographs revealing tire bare Cu(l 1 l)surface (-1.05 V, left) and tire (V3 x A/3)R30°-Cladsorbate superstmcture (-0.6 V, right) (from [39]).

Koinuma M and Uosaki K 1996 Atomic structure of bare p-GaAs(IOO) and electrodeposited Cu on p-GaAs (100) surfaces in H2SO4 solutions An AFM study J. Eiectroanai. Chem. 409 45-50... 

Figure C3.2.16. Dependence of measured resistance in an STM junction consisting of a bare tip a tip with one Xe atom attached, and a tip with two Xe atoms. Note that the Xe atoms facilitate tunnelling (compared to empty space). From Yazdani A, Eigler D M and Lang N D 1996 Off resonance conduction tlirough atomic wires Science 111 1921-4.

I the sum of the kinetic and potential energy of an electron in the orbital lUg in the electro-atic field of the two bare nuclei. This integral can in turn be expanded by substituting the... 

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