Bimodal size distribution

Schiith et al. reported that Pt particles on MCM-41 show high catalytic activity in CO oxidation [13]. The Pt particles have bimodal size distribution of 2 and 20 nm. 

While clearly not strictly correct in terms of the churn of turbulent bubbles and a bimodal size distribution observed in practice, the superficial velocities to be used in commercial units were not significantly different from those used at the pilot-scale process to observe the hydrodynamics. This approach was successful in providing guaranteed performance of installed down-flow reactors. 

Fig. 18c-d. c epoxy prepared with 10 wt % hexane via the CIPS technique showing a bimo-dal size distribution d epoxy prepared with 15 wt % hexane via the CIPS technique showing a bimodal size distribution... 

Fig. 19a,b. Pore size distributions obtained from image analysis on SEM micrographs showing a narrow size distributions b bimodal size distributions... 

Fig. 21a,b. SEM micrographs showing the surface roughness of macroporous epoxy networks prepared with hexane via CIPS displaying a narrow size distribution (7.5 wt % hexane) b bimodal size distribution (15 %wt hexane)... 

Such tilted photos are shown in Fig. 21 for a sample showing (a) narrow and (b) bimodal size distribution. However such micrographs do not allow one to determine t precisely. 

The calculation of the IPD in bimodal size distributions requires the value of the volume fraction as well as the number fractions Xj and X2 and the mean diameters of the smaller and the larger domains and 2- The IPD of a bimodal distribution can be calculated [100] by iteration from... 

The previous discussion has shown that the CIPS technique allows one to produce macroporous epoxy networks with either a narrow or bimodal size distribution. However, no indication has been given on the type of phase separation mechanism to yield these morphologies. As discussed earlier, the formation of a closed cell morphology can result either from a nucleation and growth mechanism or from spinodal decomposition. 

The observation of a bimodal size distribution is the key to unravel the phase separation mechanism with respect to the kinetics of the two types of phase separation processes. 

Based on Eqs. (42) and (43), the development of a narrow or bimodal size distribution can be qualitatively explained without the detailed knowledge of the real phase diagram nor the exact dependency of the diffusion constant as a function of time. The final morphology depends mainly on the extent of reaction at which the metastable region is entered and the difference between ( )p and ( )o, as discussed below. 

In order to avoid the use of lead compounds on environmental grounds, lithium fluoride (liF) has been chosen to obtain super-rate burning of nitramine composite propellants.P7281 Typical chemical compositions of HMX composite propellants-with and without liF are shown in Table 7.4. The non-catalyzed HMX propellant is used as a reference pyrolant to evaluate the effect of super-rate burning. The HMX particles are of finely divided, crystalline (3-HMX with a bimodal size distribution. Hydroxy-terminated polyether (HTPE) is used as a binder, the OH groups of which are cured with isophorone diisocyanate. The chemical properties of the HTPE binder are summarized in Table 7.5. 

Figures 11.1 and 11.2 illustrate mercury porosimetry data of a bimodal size distribution. However, other types of less typical curves are often encountered. For example, samples of controlled porous glass exhibit intrusion-extrusion curves illustrated by Fig. 11.3, in which all the pores are essentially of one radius.

As noted above, the LUT algorithm assumes a unimodal lognormal functional form to describe stratospheric aerosols. This approximation is well suited for most non-volcanic stratospheric aerosols as shown by Pueschel et al. [7] and Yue et al. [8]. Volcanic size distributions, however, are typically bi- or trimodal. This raises the question of whether the assumption of unimodality in the LUT can introduce bias into retrieved values of Rt//, S and V. Russell et al. [1] have shown that retrieved unimodal distributions accurately describe the second, larger mode of several measured bimodal size distributions, but fail to account for the smaller particles in the first mode. The smaller particles, which contribute little to the measured extinction spectra, are not accounted for in the LUT retrievals. Unless this bias is accounted for, the values of Rtff retrieved under the assumption of a unimodal distribution will be overestimated. 

Figure 5. Left Frame Comparison between a measured post-Pinatubo bimodal size distribution (solid line) and that retrieved by the LUT from its best-fit extinction spectrum (i.e., at = 1.6) (dashed line). The fitting parameters of the measured bimodal and the LUT retrieved uni-modal are shown in the table. Right Frame Calculated extinction spectra for size distributions in the left frame The error bars on the spectrum calculated from the measured bimodal (open circles) are derived from the relative errors on coincident SAGE II and CLAES measure-...

Figure 6. Results of applying the LUT algorithm to synthetic extinction spectra calculated from measured pre- and post-Pinatubo size distributions obtained from Pueschel el al. [9], Goodman el al [10] and Deshler el al. [11,12]. R,/bimodal) is the effective radius of the measured bimodal size distribution, and R /uni modal) is the corresponding effective radius returned by the LUT. The dots are results obtained when a range of distribution widths are considered in the LUT calculations and the crosses are results obtained when at is restricted to the value that yields the best fit between calculated and measured extinction spectra. The solid and dashed curves are second order polynomial fits to the dots and crosses, respectively.

An important group of surface-active nonionic synthetic polymers (nonionic emulsifiers) are ethylene oxide (block) (co)polymers. They have been widely researched and some interesting results on their behavior in water have been obtained [33]. Amphiphilic PEO copolymers are currently of interest in such applications as polymer emulsifiers, rheology modifiers, drug carriers, polymer blend compatibilizers, and phase transfer catalysts. Examples are block copolymers of EO and styrene, graft or block copolymers with PEO branches anchored to a hydrophilic backbone, and star-shaped macromolecules with PEO arms attached to a hydrophobic core. One of the most interesting findings is that some block micelle systems in fact exists in two populations, i.e., a bimodal size distribution. 

The PEO-rich PSt-h-PEO block copolymers form spherical micelles in aqueous solutions [63]. The DLS measurements indicate the presence of a bimodal size distribution - two very narrowly distributed species. The smaller more mobile species had Rh corresponding to the star model of block copolymer micelles. However, 99% or more of the block copolymer is present as simple micelles. 

Bimodal size distribution of the microbubble-surfactant particle population... 

Taruta, S., Itou, Y., Takusagawa, N., Okada K. and Otsuka, N. Influence of aluminum titanate formation on sintering of bimodal size-distributed alumina powder mixtures , J. Am. Ceram. Soc. 80 (1987) 551-556. 

The analysis of the kinetics of crystallization of different types of zeolites from aluminosilicate gels points to the conclusion that the crystallization takes place by the simultaneous growth of the constant number N0 of nuclei-I present in the system at the very start of the crystallization process and the number Na of nuclei-II released from the gel disolved during the crystallization process. Some characteristics of the crystallization systems such as the duration of the "induction period", the shortening of the "induction period" and the increase of the crystallization rate, respectively, with the gel ageing and the bimodal size distributions in the specific cases have been discussed and explained in relation to the ratio Na/N0 of particles (nuclei)-II and particles (nuclei)-I present in the crystallizing systems. 

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