Adsorbate, distribution

In section 2.3 of this chapter the present approach to characterisation of dose-response relationships was described. In most cases it is necessary to extrapolate from animal species that are used in testing to humans. It may also be necessary to extrapolate from experimental conditions to real human exposures. At the present time default assumptions (which are assumed to be conservative) are applied to convert experimental data into predictive human risk assessments. However, the rates at which a particular substance is adsorbed, distributed, metabolised and excreted can vary considerably between animal species and this can introduce considerable uncertainties into the risk assessment process. The aim of PB-PK models is to quantify these differences as far as possible and so to be able to make more reliable extrapolations. 

A conceptual and mechanistic model of particle interactions in silica-iron binary oxide suspensions is described. The model is consistent with a process involving partial Si02 dissolution and sorption of silicate onto Fe(OH)3. The constant capacitance model is used to test the mechanistic model and estimate the effect of particle interactions on adsorbate distribution. The model results, in agreement with experimental results, indicate that the presence of soluble silica interferes with the adsorption of anionic adsorbates but has little effect on cationic adsorbates. 

Details on the adsorbent preparation and experimental and analytical techniques are presented elsewhere (9). This paper briefly reviews the experimental results for the Fe(OH)3 and Si02 suspensions and describes a conceptual and mechanistic model for particle interactions which is qualitatively consistent with the experimental observations. Similar results were obtained for binary Al(OH)3 and Si02 suspensions (9). The constant capacitance surface complexation model is then used to test the mechanistic model and estimate the quantitative influence of the particle-particle interactions on adsorbate distribution. 

Another productive area would be in situ imaging and/or spatially localized spectroscopy of model How reactors. Pulsed-field gradient measurements could conceivably be used to characterize diffusion and pore blockage due to coking while the reaction is in progress. Xe might be similarly useful. This technique has already been used to probe adsorbate distributions in catalyst beds 1108]. 

In chemical state relaxation, a spectroscopy sensitive to chemical binding state is used to follow the evolution of an initially random adsorbate distribution into a preferred chemical state. Such techniques have quite limited apphcation for surface diffusion because (a) two easily distinguished chemical states must exist, and (b) it must be estabhshed that the transformation is diffusively mediated. 

Figure 4.26 shows the effect of the interaction parameter BpQ on the isotherm shape. Positive values of BpQ, corresponding to repulsive interactions (see Equation 4.65), cause the coverage, for fixed activity, to decrease as Bp increases. On the contrary, negative (attractive) BpQ cause faster adsorption as the activity increases notice that for BpQ < -4, a sharp rise in is observed, which can be interpreted as a bidimen-sional phase transition (Hill 1986) even when for localized adsorption on a solid surface, this concept is questionable, it means here that the adsorbate molecules are binding preferentially next to others already adsorbed. Of course, one can question for these cases the validity of the assumption of random adsorbate distribution, but nevertheless the prediction is important, as this is the simplest isotherm equation predicting such phenomena. 

To model psurf, we begin with the translational entropy of the adsorbate distributed on the surface. A lattice approach is simplest. We consider the surface of the solid to be a two-dimensional lattice having A sites (Figure 27.2). Each of the N ligand molecules occupies one site. The density 9 of the adsorbate on... 

Actual crystal planes tend to be incomplete and imperfect in many ways. Nonequilibrium surface stresses may be relieved by surface imperfections such as overgrowths, incomplete planes, steps, and dislocations (see below) as illustrated in Fig. VII-5 [98, 99]. The distribution of such features depends on the past history of the material, including the presence of adsorbing impurities [100]. Finally, for sufficiently small crystals (1-10 nm in dimension), quantum-mechanical effects may alter various physical (e.g., optical) properties [101]. 

IRE Infrared emission [110] Infrared emission from a metal surface is affected in angular distribution by adsorbed species Orientation of adsorbed molecules... 

ESDIAD Electron-stimulated desorption ion angular distribution [150-152] A LEED-like pattern of ejected ions is observed Orientation of adsorbed species... 

Fig. XI-4. Schematic diagram of the structure of an adsorbed polymer chain. Segments are distributed into trains directly attached to the surface and loops and tails extending into solution.

These concluding chapters deal with various aspects of a very important type of situation, namely, that in which some adsorbate species is distributed between a solid phase and a gaseous one. From the phenomenological point of view, one observes, on mechanically separating the solid and gas phases, that there is a certain distribution of the adsorbate between them. This may be expressed, for example, as ria, the moles adsorbed per gram of solid versus the pressure P. The distribution, in general, is temperature dependent, so the complete empirical description would be in terms of an adsorption function ria = f(P, T). 

We have considered briefly the important macroscopic description of a solid adsorbent, namely, its speciflc surface area, its possible fractal nature, and if porous, its pore size distribution. In addition, it is important to know as much as possible about the microscopic structure of the surface, and contemporary surface spectroscopic and diffraction techniques, discussed in Chapter VIII, provide a good deal of such information (see also Refs. 55 and 56 for short general reviews, and the monograph by Somoijai [57]). Scanning tunneling microscopy (STM) and atomic force microscopy (AFT) are now widely used to obtain the structure of surfaces and of adsorbed layers on a molecular scale (see Chapter VIII, Section XVIII-2B, and Ref. 58). On a less informative and more statistical basis are site energy distributions (Section XVII-14) there is also the somewhat laige-scale type of structure due to surface imperfections and dislocations (Section VII-4D and Fig. XVIII-14). 

The first term on the right is the common inverse cube law, the second is taken to be the empirically more important form for moderate film thickness (and also conforms to the polarization model, Section XVII-7C), and the last term allows for structural perturbation in the adsorbed film relative to bulk liquid adsorbate. In effect, the vapor pressure of a thin multilayer film is taken to be P and to relax toward P as the film thickens. The equation has been useful in relating adsorption isotherms to contact angle behavior (see Section X-7). Roy and Halsey [73] have used a similar equation earlier, Halsey [74] allowed for surface heterogeneity by assuming a distribution of Uq values in Eq. XVII-79. Dubinin s equation (Eq. XVII-75) has been mentioned another variant has been used by Bonnetain and co-workers [7S]. 

Fig. XVn-24. Site energy distribution for nitrogen adsorbed on Silica SB. (From Ref. 160.) (Reprinted with permission from J. Phys. Chem. Copyright by the American Chemical Society.)...

The preceding material has been couched in terms of site energy distributions—the implication being that an adsorbent may have chemically different kinds of sites. This is not necessarily the case—if micropores are present (see Section XVII-16) adsorption in such may show an increased Q because the adsorbate experiences interaction with surrounding walls of adsorbent. To a lesser extent this can also be true for a nonporous but very rough surface. 

Below the critical temperature of the adsorbate, adsorption is generally multilayer in type, and the presence of pores may have the effect not only of limiting the possible number of layers of adsorbate (see Eq. XVII-65) but also of introducing capillary condensation phenomena. A wide range of porous adsorbents is now involved and usually having a broad distribution of pore sizes and shapes, unlike the zeolites. The most general characteristic of such adsorption systems is that of hysteresis as illustrated in Fig. XVII-27 and, more gener-... 

Most microporous adsorbents have a range of micropore size, as evidenced, for example, by a variation in or in calorimetric heats of adsorption with amount adsorbed [227]. As may be expected, a considerable amount of effort has been spent in seeing how to extract a size distribution from adsorption data. 

The nature of reaction products and also the orientation of adsorbed species can be studied by atomic beam methods such as electron-stimulated desorption (ESD) [49,30], photon-stimulated desoiption (PDS) [51], and ESD ion angular distribution ESDIAD [51-54]. (Note Fig. VIII-13). There are molecular beam scattering experiments such... 

Figure Al.7.13. ESDIAD patterns showing the angular distributions of F emitted from PF adsorbed on Ru (0001) under electron bombardment, (a) 0.25 ML coverage, (b) the same surface following electron beam damage.

Figure A2.4.10. Orientational distribution of the water dipole moment in the adsorbate layer for tlu-ee...

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