Bimodal mass distribution

Fig. 1.1. Bimodal mass distributions measured with a set of special impactors and a cascade impactor. Run 14 contains many more coarse particles than the average because of construction activity upwind. Note the negligible effect of this increased concentration of coarse particles on the tine particle mode. From Whitby (1975, p. 111-21) in NRC (1979).

The carbon number distribution of Fischer-Tropsch products on both cobalt and iron catalysts can be clearly represented by superposition of two Anderson-Schulz-Flory (ASF) distributions characterized by two chain growth probabilities and the mass or molar fraction of products assigned to one of these distributions.7 10 In particular, this bimodal-type distribution is pronounced for iron catalysts promoted with alkali (e.g., K2C03). Comparing product distributions obtained on alkali-promoted and -unpromoted iron catalysts has shown that the distribution characterized by the lower growth probability a, is not affected by the promoter, while the growth probability a2 and the mass fraction f2 are considerably increased by addition of alkali.9 This is... 

FIGURE 16.1 Schematic differential (—) and integral (—) representations of amount of polymer with certain molar mass present in the sample. The narrow, broad, and bimodal molar mass distributions are shown. The typical positions of weight, viscosity, number, and z-molar mass averages are depicted. 

Other important pitfalls lie again in the low selectivity of SEC, which does not allow identifying small amounts of the macromolecular admixtures that is the minor components of polymer blends. The bell-shaped chromatograms with a broad base and a slim upper part are often erroneously proclaimed to signalize the narrow molar mass distribution of sample. On the other hand, the accumulation peaks due to presence of macromolecules excluded from the packing pores (Section 16.8.1) are interpreted as the sign of sample bimodality. The absolute detectors may also contribute to erroneous conclusions concerning sample polydispersity (Section 16.8.1). 

Eldering, A., and R. M. Glasgow, Short-Term Particulate Matter Mass and Aerosol-Size Distribution Measurements Transient Pollution Episodes and Bimodal Aerosol-Mass Distributions, Atmos. Environ., 32, 2017-2024 (1998). 

Bimodal distribution Once the rate distribution P(I) and the scaling relation in Eq. (39) are known, the molar mass distribution c(M), expressed in weight fractions, is obtained for the three basic types of experiment discussed ... 

This can be clearly seen in the comparison of viscosity functions of polystyrene 1 and polystyrene 2. If we add a very high-molecular weight component to polystyrene 2, we obtain polystyrene 3. It is therefore evident that the bimodal molar mass distribution causes the shear thinning to increase further, although not as far as the polydispersity change of the molar mass distribution between polystyrene 1 and polystyrene 2. In the case of higher shear rates, all flow curves proceed to similar viscosity functions. 

Therefore, the new variable, constrains the population balance so that it agrees with the mass balance. This means that for fixed values of /3, s, and <, the final distribution—including the maximum particle size—can be predicted. The qualitative effect of /3, s, and on the particle size distribution is realized by varying these parameters as s wn in Figs. 6.34. For most cases shown in Figure 6.34, a bimodal size distribution with one mode corresponding to nuclei that have grown... 

Broad or bimodal molecular mass distributions have been obtained using mixtures of metallocenes,452 487-491 linked homo- and heterobimetallic bis(cyclopentadienyl) complexes for broad molecular mass distribution,492 or amino-functionalized bis-Cp complexes.476... 

Liapis and McCoy [63] have assumed that the bimodal pore structure of per-fusive adsorbent particles is made of a macroporous region, in which mass transfer takes place through intraparticle convection and pore diffusion, and a microp-orous region made of spherical microparticles in which mass transfer takes place through pure diffusion. Frey et al. [61] developed a model for the analysis of mass transfer in spherical particles having a bimodal pore distribution and derived the following expression for h nt in perfusion chromatography. 

Sulfates and nitrate.s are products of gas-to-particle conversion. They frequently have multimodal di.siributions with respect to particle size, but for reasons different from tho.se that produce the bimodal mass or volume distributions discus.sed above. 

Organic compounds accumulate mainly in the submicrometer aerosol size range (McMurry and Zhang 1989), and their mass distribution is typically bimodal with the first peak around diameter 0.2 pm and the second around 1 pm (Pickle et al. 1990 Mylonas et al. 1991) (see Figure 14.7 as an example). 

HDPE HDPE ( reactor blends ) Bimodal molar mass distributions provide rmique properties that cannot he achieved by mixing the two PE grades... 

The mass distribution of EC emitted by automobiles is unimodal with a peak around 0.1 fxm. Measurements inside tunnels have confirmed that over 85% of the emitted EC mass by vehicles is in particles smaller that 0.2 /xm aerodynamic diameter (Venkataraman and Friedlander, 1994a) (Figure 13.4). However, the ambient distribution of EC in polluted areas is bimodal with peaks in the 0.05 to 0.12 /xm (mode I) and 0.5 to I.O /xm (mode II) size ranges (Nunes and Pio, 1993 Venkataraman and Friedlander, 1994b) (Figure 13.5). In... 

This polymer was also characterised by SEC. Its bimodal molar mass distribution pointed to a significant contribution from the cyclic polysiloxane fraction. The dialysis of this polymer in water permitted the separation of cyclics into the lower molar mass fraction, while the linear polymer constituted the higher molar mass fraction. The gel chromatograms of both these fractions were also compared. The two-step dialysis performed for the precursor and biocidal polymer led to a narrow polydispersity of the former, MW / Mn = 1.21 [95]. 

Asua et al. [121] and Nomura and Fujita [122,123] have analysed the case of oil-soluble initiators theoretically. The latter group [124,125] has verified the conclusions experimentally for styrene with azobis-isobutyronitrile as initiator. Below the cmc of the emulsifier suspension polymerization occurs in the monomer droplets but, in the presence of emulsifier micelles many more much smaller latex particles are produced and emulsion polymerization kinetics becomes dominant. Only the portion of the initiator partitioned into the water phase is significant in the initiation of the emulsion polymerization. The molar mass distribution of the polymer obtained is bimodal initially [125]. The molar mass of the polymer produced by suspension polymerization in the droplets is the same as that produced by bulk polymerization under comparable conditions and only about one-hundredth of that of the emulsion polymer. Wth increase of conversion the contribution of the lower molar mass component to the overall molar mass distribution becomes insignificant. 

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