Particle surface area distribution

FIGURE 12.28 Particle surface area distributions in the stratosphere (a) before Mount Pinatubo eruption, (b) August 20, 1991, over California, and (c) May 7, 1993, over California (adapted from Russell et al. (1996) and Goodman et al. (1994)). 

Monomer compositional drifts may also occur due to preferential solution of the styrene in the mbber phase or solution of the acrylonitrile in the aqueous phase (72). In emulsion systems, mbber particle size may also influence graft stmcture so that the number of graft chains per unit of mbber particle surface area tends to remain constant (73). Factors affecting the distribution (eg, core-sheU vs "wart-like" morphologies) of the grafted copolymer on the mbber particle surface have been studied in emulsion systems (74). Effects due to preferential solvation of the initiator by the polybutadiene have been described (75,76). 

Characterization. The proper characterization of coUoids depends on the purposes for which the information is sought because the total description would be an enormous task (27). The foUowiag physical traits are among those to be considered size, shape, and morphology of the primary particles surface area number and size distribution of pores degree of crystallinity and polycrystaUinity defect concentration nature of internal and surface stresses and state of agglomeration (27). Chemical and phase composition are needed for complete characterization, including data on the purity of the bulk phase and the nature and quaHty of adsorbed surface films or impurities. 

Surface Area Distribution s(D), the percentage of particles with a certain surface area plotted against the equivalent diameter. 

Figure 12.28 shows the particle surface area size distribution before the Mount Pinatubo eruption (Fig. 12.28a), inside the main aerosol layer several months after the eruption (Fig. 12.28b), and almost two years after the eruption (Fig. 12.28c). (See Chapter 9.A.2 for a description of how particle size distributions are normally characterized.) Prior to the eruption, the surface area distribution is unimodal, with typical radii of 0.05-0.09 /xrn and a number concentration of l-20 particles cm 1. In the main stratospheric aerosol layer formed after the eruption, the distribution is bimodal...

The 9-parameter is also subject to uncertainty. It is likely that Whitby s (1978) estimates of 9 (Table 10.1) do not reflect the true surface area distribution, since they were based on the average size spectrum of aerosols and assumed spherical particles. Adsorption/desorption kinetics (Kamens et al., 1995 Rounds and Pankow, 1990,1993) and relative humidity (Goss and Eisenreich, 1997 Lee and Tsai, 1994 Pankow et al., 1993 Storey et al., 1995 Thibodeaux et al., 1991) influence the adsorption of POPs onto aerosols, and the Junge-Pankow model does not take these factors into account. 

Since atmospheric aerosols comprise particles with a wide range of sizes, it is often convenient to use mathematical models to describe the atmospheric aerosol distribution (Seinfeld and Pandis, 1998). A series of mathematical models have been proposed, of which the lognormal distribution has been the most used in atmospheric applications (Seinfeld and Pandis, 1998 Horvath, 2000). Useful discussions of the various aerosol size distribution models are provided by Seinfeld and Pandis (1998) and Jaenicke (1998). In general, atmospheric aerosols size distributions are shown graphically in terms of the volume (or mass) distributions, surface area distributions, or number distributions as a function of particle size (Jaenicke, 1998). 

For the next run to narrow the small particle distribution, it was envisioned that emulsifier metering should be carried out rapidly over a short period of time. The metering would then be stopped for a given time so that micelle formation would cease. The emulsifier would be restarted to give enough emulsifier to stabilize the growing particles, yet not exceed the emulsifier level needed to cover all the growing particle surface area (not produce new micelles). With the aid of a computer controlled 190 liter reactor, this was accomplished in Run 11127-90. 

This relationship is found for each size interval. Similar expressions can be written for particle surface area or particle mass or volume. (It should be stressed again that particle volume converts directly to particle mass by multiplication of volume and particle density. Hence in plotting size distribution data, either one can be used to represent the other.)... 

The particle size and surface area distributions of pharmaceutical powders can be obtained by microcomputerized mercury porosimetry. Mercury porosimetry gives the volume of the pores of a powder, which is penetrated by mercury at each successive pressure the pore volume is converted into a pore size distribution. Two other methods, adsorption and air permeability, are also available that permit direct calculation of surface area. In the adsorption method, the amount of a gas or liquid solute that is adsorbed onto the sample of powder to form a monolayer is a direct function of the surface area of the sample. The air permeability method depends on the fact that the rate at which a gas or liquid permeates a bed of powder is related, among other factors, to the surface area exposed to the permeant. The determination of surface area is well described by the BET (Brunauer, Emmett, and Teller) equation. 

Particle Surface Area Determination Methods From the standard definitions of particle surface area, it can be seen that various determination methods are used for surface area measurement, such as adsorption (including Langmuir s equation for monolayer adsorption and the BET equation for multilayer adsorption), particle size distribution, and permeability methods. The different methods are rarely in agreement because the value obtained depends upon the procedures used and also on the assumptions made in the theory relating the surface area to the phenomena measured. The most common methods used for measuring particle surface area are described below. 

This approach was first outlined by Beckett et al. [6], where radiolabelled pollutants as orthophosphate, in atrazine, and glyphosate) were adsorbed to two Australian river colloid samples. Sedimentation FFF was used to fractionate the samples and the radioactivity of each fraction was measured. From this, it was possible to generate a surface adsorption density distribution (SADD) across the size range of the sample. The SADD is a plot of the amount of compound adsorbed per unit particle surface area as a... 

The central point of the active-site theory is that the areal density of nanoscale surface features is small and approaches the same scale as individual particle surface areas, especially in the regime of nanoparticles. The probability that a particle bears i active-sites is given by the Poisson distribution, as follows ... 

Concentration of particles in the air as well as particle size distributions can be considered either in terms of particle number or mass. In terms of number, the vast majority of airborne particles are in the ultrafine range. For example, in urban outdoor air where motor vehicle emissions are a dominant pollution source, over 80% of particulate matter in terms of number is in the ultrafine range [17]. Since outdoor particles contribute significantly to indoor particle concentrations, also in indoor air particle number concentration is usually dominated by the smallest particles. However, most of the mass of airborne particles is associated with large particles since the mass of ultrafine particles is often very small in comparison with the mass of larger particles. The particle surface area in turn is largest for particles somewhat above the ultrafine size range. 

Examples of size distribution functions are shown ill Figs. 1.4 and 1.5. Figure 1.4 shows number distributions of commercially produced silica particles in terms of the fraction of particles in the,size range around dp, dN/N d dp) = na(,dp)fNxs where is the total particle concentration. The total particle surface area corresponding to each size distribution is shown. Commercial silica manufactured by the oxidation of SiCU is used as a filler (additive) in rubber. Both coordinate axes in Fig. 1.4 are linear, and the area under each curve should be normalized to unity. A bimodal volume distribution with a minimum near a particle size of 1 is shown in Fig. 1.5. Distributions of this type are often observed for atmospheric aerosols (Chapter 13) the volume of aerosol material per unit volume of gas above and below a micron is about the same as shown by the area under the curve. Bimodal distributions are also often observed in aerosols from industrial sources as discus.sed below. 

Figure 1.4 Unimodiil number dLstribuiions for difl erent grades of comniercially produced silica particles. The fraction of the particles in the size range between any two diameters, tlpy to is proportional to the area under the curve. Also shown for eadi distribution is the total particle surface area per gram of material. (After Ettlinger et al.. 1991.)...

The release of contaminants from a solid into solution involves a number of interrelated mechanisms. Dissolution from solid to liquid occurs at the interface between the particle surface and the liquid passing over it. The overall surface area to mass or volume ratio and the intimacy of contact between the particle surface area and the liquid depend on the particle size and shape distribution and the pore structure of the solid matrix. 

Since PCBs are adsorbed on the particle surface, normally coated with a thin layer of organic matter such as humic acid, the concentration in sediment and soil samples is much more likely to be related to the particle surface area per volume unit than to the mass unit. ° For this reason, the concentration of each sample, expressed in pgg dry weight, is normalized by dividing it by the relevant calculated specific surface area, expressed in square meters of surface per cubic centimeter of dry sample (m cm ), as obtained by particle size analysis. Comparisons among concentration values of organic pollutants relevant to samples with different particle size distribution may lead to erroneous conclusions if these are expressed in a conventional way. °... 

FIGURE 2.7 Idealized schematic of the distribution of particle surface area of an atmospheric aerosol (Whitby and Cantrell 1976). Principal modes, sources, and particle formation and removal mechanisms are indicated. 

Several aerosol properties depend on the particle surface area and volume distributions with respect to particle size. Let us define the aerosol surface area distribution ns(Dp) as... 

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