Adsorbed particles

The currently useful model for dealing with rough surfaces is that of the selfsimilar or fractal surface (see Sections VII-4C and XVI-2B). This approach has been very useful in dealing with the variation of apparent surface area with the size of adsorbate molecules used and with adsorbent particle size. All adsorbate molecules have access to a plane surface, that is, one of fractal dimension 2. For surfaces of Z> > 2, however, there will be regions accessible to small molecules... 

There are many other experiments in which surface atoms have been purposely moved, removed or chemically modified with a scanning probe tip. For example, atoms on a surface have been induced to move via interaction with the large electric field associated with an STM tip [78]. A scaiming force microscope has been used to create three-dimensional nanostructures by pushing adsorbed particles with the tip [79]. In addition, the electrons that are tunnelling from an STM tip to the sample can be used as sources of electrons for stimulated desorption [80]. The tuimelling electrons have also been used to promote dissociation of adsorbed O2 molecules on metal or semiconductor surfaces [81, 82]. 

Each newly cleaved mica surface is very clean. Flowever, it is known that mica has a strong tendency to spontaneously adsorb particles [45] or organic contaminants [46], which may affect subsequent measurements. The mica sheets are cut into 10 nun x 10 nun sized samples using a hot platinum wire, then laid down onto a thick and clean 100 nun x 100 nun mica backing sheet for protection. On the backing sheet, the mica samples can be transferred into a vacuum chamber for themial evaporation of typically 50-55 mn thick silver mirrors. 

Miller A R 1946 The variation of the dipole moment of adsorbed particles with the fraction of the surface covered Proc. Camb.Phil. See. 42 292-303... 

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

Pressure Drop. The prediction of pressure drop in fixed beds of adsorbent particles is important. When the pressure loss is too high, cosdy compression may be increased, adsorbent may be fluidized and subject to attrition, or the excessive force may cmsh the particles. As discussed previously, RPSA rehes on pressure drop for separation. Because of the cychc nature of adsorption processes, pressure drop must be calculated for each of the steps of the cycle. The most commonly used pressure drop equations for fixed beds of adsorbent are those of Ergun (143), Leva (144), and Brownell and co-workers (145). Each of these correlations uses a particle Reynolds number (Re = G///) and friction factor (f) to calculate the pressure drop (AP) per... 

The need for a continuous countercurrent process arises because the selectivity of available adsorbents in a number of commercially important separations is not high. In the -xylene system, for instance, if the Hquid around the adsorbent particles contains 1% -xylene, the Hquid in the pores contains about 2% xylene at equiHbrium. Therefore, one stage of contacting cannot provide a good separation, and multistage contacting must be provided in the same way that multiple trays are required in fractionating materials with relatively low volatiHties. 

Fig. 18. The repulsion force from adsorbed particles is greater than the van der Waals force between flocculated emulsion droplets under certain...

Figure 16-9 depicts porous adsorbent particles in an adsorption bed with sufficient generality to illustrate the nature and location of individual transport and dispersion mechanisms. Each mechanism involves a different driving force and, in general, gives rise to a different form of mathematical result. 

Intraparticle convection can also occur in packed beds when the adsorbent particles have very large and well-connected pores. Although, in general, bulk flow through the pores of the adsorbent particles is only a small frac tion of the total flow, intraparticle convection can affec t the transport of veiy slowly diffusing species such as macromolecules. The driving force for convec tion, in this case, is the... 

FIG. 16-9 General scheme of adsorbent particles in a packed bed showing the locations of mass transfer and dispersive mechanisms. Numerals correspond to mimhered paragraphs in the text 1, pore diffusion 2, solid diffusion 3, reaction kinetics at phase boundary 4, external mass transfer 5, fluid mixing. 

External mass tran.sfer between the external surfaces of the adsorbent particles and the surrounding fluid phase. The driving force is the concentration difference across the boundary layer that surrounds each particle, and the latter is affected by the hydrodynamic conditions outside the particles. 

General Component Balance For a spherical adsorbent particle ... 

TABLE 16-11 Rate Equations for Description of Mass Transfer in Spherical Adsorbent Particles... 

In this section, we consider the transient adsorption of a solute from a dilute solution in a constant-volume, well-mixed batch system or, equivalently, adsorption of a pure gas. The solutions provided can approximate the response of a stirred vessel containing suspended adsorbent particles, or that of a very short adsorption bed. Uniform, spherical particles of radius are assumed. These particles, initially of uniform adsorbate concentration, are assumed to be exposed to a step change in concentration of the external fluid. 

For most large-scale processes, adsorbent particle size varies from 0.06 to 6 mm (0.0025 to 0.25 in), but the adsorbent packed in a fixed bed will have a fairly narrow particle size range. Pressure drop in adsorbers can be changed by changing the diameter to bed depth ratio and by changing the particle size (see Sec. 5). Adsorbent size also determines separation performance of adsorbent columns—increasing efficiency with decreasing particle size. In hquid-phase process-... 

The heai4 of an adsorbent wheel system is a rotating cyhnder containing the adsorbent. Figure 16-55 illustrates two types horizontal and vertical. In some adsorbent wheels, the adsorbent particles are placed in basket segments (a multitude of fixed beds) to form a hori-... 

Kp, = Overall mass transfer coefficient, g/m s a = Surface area per unit volume of adsorbent particle, mVm ... 

In fluidized-bed adsorbers, the combination of high gas rate and small adsorbent particle size results in suspension of the adsorbent, giving it many of the characteristics of a fluid. Fluidized bed adsorbers, therefore, lend themselves to truly continuous, countercurrent, multistage operation. Adsorbent inventory is minimized. 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

In the last decade two-dimensional (2D) layers at surfaces have become an interesting field of research [13-27]. Many experimental studies of molecular adsorption have been done on metals [28-40], graphite [41-46], and other substrates [47-58]. The adsorbate particles experience intermolecular forces as well as forces due to the surface. The structure of the adsorbate is determined by the interplay of these forces as well as by the coverage (density of the adsorbate) and the temperature and pressure of the system. In consequence a variety of superstructures on the surfaces have been found experimentally [47-58], a typical example being the a/3 x a/3- structure of adsorbates on a graphite structure (see Fig. 1). 

A parameterization of many different surface potentials, ranging from (100) surfaces of FCC crystals to graphite surfaces, has been given by Steele [146-148]. Since most of the systems discussed below are adsorbed layers on graphite surfaces, we consider the graphite substrate in detail. The interaction potential between an adsorbate particle at the position r = (x,y, z) and all other substrate particles consists of two contributions,... 

The singlet-level theory has also been used to describe the structure of associating fluids near crystalline surfaces [30,31,76,77]. The surface consists explicitly of atoms which are arranged on a lattice of a given symmetry. The fluid atom-surface atom potential can also involve an associative term, i.e., the chemical-type bonding of the adsorbate particles with the surface may be included into the model. However, we restrict ourselves to the case of a nonassociative crystalline surface first. 

Assuming that the interaction between the adsorbed particles is confined to the first nearest neighbors, the Hamiltonian of the model reads... 

To present briefly the different possible scenarios for the growth of multilayer films on a homogeneous surface, it is very convenient to use a simple lattice gas model language [168]. Assuming that the surface is a two-dimensional square lattice of sites and that also the entire space above the surface is divided into small elements, forming a cubic lattice such that each of the cells can be occupied by one adsorbate particle at the most, the Hamiltonian of the system can be written as [168,169]... 

The simplest choice is to set all Ai = 0 in (44). Physically this means that an adsorbing particle will not experience any interactions with its prospective neighbors, and sticking is solely controled by the availability of sites. Thus the sticking coefficient becomes (for A,- = 0)... 

The sticking coefficient at zero coverage, Sq T), contains the dynamic information about the energy transfer from the adsorbing particle to the sohd which gives rise to its temperature dependence, for instance, an exponential Boltzmann factor for activated adsorption. 

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