Bimodal product distributions

Figure 1 illustrates symmetry breaking in the Soai reaction that has been clearly documented in two cases by bimodal product distributions (black and... 

The bimodal velocity distribution of the 0(3Pj) fragments produced via the triplet channel in the UV photodissociation of ozone has also been observed by Syage41,43>46 and Stranges et al.AA at photolysis wavelengths of 226 and 193 nm, respectively. Both authors measured anisotropy parameters for the fast and slow product pathways separately. 

By using two or more polymerization catalysts simultaneously, polymer chemists can produce copolymers tvith a bimodal composition distribution. This is made possible by the fact that no two catalysts incorporate monomers at exactly the same rate. The net result is that short chain branches may be preferentially incorporated into either the higher or lower molecular weight fractions. Polymer manufacturers can obtain a similar result by operating two polymerization reactors in series. Each reactor produces a resin with a different copolymer distribution, which are combined to form a bimodal product. Copolymers with a bimodal composition distribution provide enhanced toughness when extruded into films. 

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... 

In Fischer-Tropsch synthesis the readsorption and incorporation of 1-alkenes, alcohols, and aldehydes and their subsequent chain growth play an important role on product distribution. Therefore, it is very useful to study these reactions in the presence of co-fed 13C- or 14 C-labeled compounds in an effort to obtain data helpful to elucidate the reaction mechanism. It has been shown that co-feeding of CF12N2, which dissociates toward CF12 and N2 on the catalyst surface, has led to the sound interpretation that the bimodal carbon number distribution is caused by superposition of two incompatible mechanisms. The distribution characterized by the lower growth probability is assigned to the CH2 insertion mechanism. 

The phenomenon of such bimodal lifetime distribution proposed for reaction 1 on the basis of direct quasiclassical trajectory calculations were tested experimentally with the reaction of diaza-[2.2.1]bicycloheptane to [2.1. Ojbicyclopentane [Equation (2)].6 8 Experimental study on reaction 2 showed that the exo isomer 5x is formed favorably over the endo isomer 5n by about 3 1 in the gas phase. One explanation for the preferential formation of 5x invokes a competitive concerted and stepwise mechanism the concerted pathway directly from 4 to 5 gives 5x with the inversion of configuration at the carbon from which N2 is departing, whereas the stepwise pathway goes through the radical intermediate and leads to both 5x and 5n in equal amount. Alternatively, the product stereochemistry can be rationalized by dynamic matching between the entrance channel to the cyclopentane-1,3-diyl radical intermediate and the exit channel to bicyclo[2.1. Ojpentane as was assumed for reaction 2. 

Pressure effect on the product distribution in supercritical media would resolve the problem. If the reaction proceeds via the competitive concerted/ stepwise mechanism, the reaction under a higher pressure is expected to give more exo isomer because the activation volume is considered to be smaller for concerted process than the stepwise one and hence more concerted reaction is expected under a higher pressure. If, on the other hand, bimodal lifetime distribution of trajectories is the origin of the stereoselection, the product ratio is expected to approach to unity under high-pressure conditions, since energy randomization is more effective under a high pressure. 

Microscopic branching refers to the observation of a bimodal product energy distribution from one reaction channel (HX) and a normal product energy distribution from the other reaction channel. It appears that the bimodal distribution occurs for the product, HX, containing the most electronegative atom. Figure 9 shows the triangle plots for the detailed vibrational state distributions for the HBr and HC1 products from H + BrCl. Bimodality is seen in the HC1 distribution. The HBr distribution from H + BrCl closely resembles the HBr distribution from H + Br2 and results from a direct reaction with the Br end of BrCl. 

Energy disposal has been studied for the reactions F + IC1 [553] and I2 [554, 555] using laser-induced fluorescence detection of the IF product. For F + IC1, the results indicate a direct reaction with the IF vibrational product distribution being inverted with a peak at v — 7. As with the Cl and Br atom reactions, the majority of the reaction energy appears as IF internal energy ( 0.14). For F + I2, the IF product vibrational state distribution appears to be bimodal [554] with peak at v = 0 and a secondary peak at v = 18 with the distribution extending up to the limit imposed by the reaction exoergicity. Trajectory... 

High-shear homogenization and ultrasound were initially used for the production of solid hpid nanodispersions [7,8], Both methods are widespread and easy to handle. However, in many cases, bimodal size distributions are obtained with one population in the micrometer range. In addition, metal contamination has to be considered if ultrasound is used. 

The addition of phosphoric acid to alumina, followed by calcination at 600 °C and deposition of an organochromium compound, also resulted in polymers having a bimodal MW distribution like the polymers made from coprecipitated aluminophosphates. In one experiment, even silica was treated with H3PO4 and calcined at 250-500 °C. When this support was treated with organochromium compounds, such as Cr(DMPD)2, the resultant catalyst also produced polymers having two contributions, one of which was the same low-MW product peak associated with phosphate. The data in Figure 191 present an example of this experiment. 

The approximate change in the size distribution that will have taken place after a 12-h intermission of new particle production is shown in Fig. 7-5 by the dashed curve. It results in a bimodal size distribution, which in addition to the accumulation peak now contains a transient peak caused by the incomplete coagulation of Aitken particles. We have previously designated this transient the nucleation mode. The ensuing size distribution gives a better representation of the natural aerosol, even though its resemblance to the size spectra in Fig. 7-1 is still marginal. 

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