Mass, distribution, conversion

The molar mass distribution of hyperbranched polymers is, therefore, always larger than diat of titeir linear homologues and tends toward infinity when conversion becomes close to 1. The use of a B3, comonomer, acting as a chain limiter and core molecule, helps in reducing polydispersity and controlling the molar mass of the final polymer.197... 

Copper bromide and pentakis-A-(heptadecafluoroundecyl)-l,4,7-triazeheptane (1 in Figure 10.9), along with an initiator, ethyl-2-bromoisobutyrate (2 in Figure 10.9), in a perfluoromethylcyclohexane-toluene biphase efficiently catalyse the polymerization of methyl methacrylate, with a conversion of 76 % in 5 h at 90 °C. The resultant polymer has a Mn = 11100 and a molar mass distribution of 1.30. After polymerization, the reaction was cooled to ambient temperature, the organic layer removed and found to contain a copper level of 0.088 % (as opposed to 1.5% if all the catalyst were to have remained in the polymer). A further toluene solution of monomer and 2 could be added,... 

In practice, when one measures the size distributions of aerosols using techniques discussed in Chapter 11, one normally measures one parameter, for example, number or mass, as a function of size. For example, impactor data usually give the mass of particles by size interval. From such data, one can obtain the geometric mass mean diameter (which applies only to the mass distribution), and crg, which, as discussed, is the same for all types of log-normal distributions for this one sample. Given the geometric mass mean diameter (/) ,) in this case and crg, an important question is whether the other types of mean diameters (i.e., number, surface, and volume) can be determined from these data or if separate experimental measurements are required. The answer is that these other types of mean diameters can indeed be calculated for smooth spheres whose density is independent of diameter. The conversions are carried out using equations developed for fine-particle technology in 1929 by Hatch and Choate. 

Table 9. Dependence of the molecular-mass-distribution of phenylglycidyl ether oligomers on conversion...

Conversion Between Translational Diffusion Coefficient Distribution and Molar Mass Distributions... 

For conversions lower than xgei the average molar mass of the polymer exhibits a continuous increase. The first two moments of the molar mass distribution are the number-average molar mass, Mn, and the mass-average molar mass, Mw, respectively. Mn is defined in terms of the number contribution of every species to the whole population. The weight factor used to define this average is the molar fraction. Mw is defined in terms of the mass contribution of every species to the whole mass, so that the mass fraction is the weight factor used in its definition. 

Davtyan et al. analyzed the problem of changes mass distribution with conversion during the polymerization of heterocycles [58], This case is interesting the question of the coexistence of one or two active centres on a single growing macromolecule is solved by means of rate equations. The results can also be applied to polymerizations of other monomers, when the conditions... 

We have shown that [Ni2+]-OMS-2 and [N 2+]-OMS-1 catalyze the selective conversion of hexane to 1-hexene. Stainless steel flow reactors of 1/4 diameter containing 0.5 g catalyst, charges of 7 g n-hexane in 2 h, 1 atm pressure and temperatures of 500°C are used in these experiments. Both gas chromatography (GC) and mass spectrometry (MS) analyses are done to monitor product distributions. Conversions as high as 60% and selectivities of 90% (to the terminal olefin) have been observed for the OMS-2 system. This may be a consequence of the better shape selectivity of [Ni2+]-OMS-2 (4.6 A tunnel) versus (Ni2+]-OMS-1 (6.9 A). The latter material is not as selective or active. Systems that do not contain N 2+ are totally inactive.91 There is precedence for dehydrogenation activity of these systems since manganese nodules have been reported to be excellent catalysts for dehydrogenation of cyclohexane.63... 

Figure 1.16 shows the chain-length distribution of the polymer at increasing extents of conversion. At short times the polymer has a narrow molar-mass distribution since the reaction mixture contains only low-molar-mass oligomers. As the reaction proceeds it... 

The molar-mass distributions for such multichain polymerizations have been calculated and shown to be narrower than for a single-chain polymerization since the probability of formation for very long chains is reduced. The polydispersity for chain growth in the presence of a multifunctional reagent Ay with functionality / then becomes, as the conversion, p, approaches unity. 

The particular features of anionic polymerization that made the polymer chains living were discussed above. The main requirement for a living polymerization is the absence of any process for spontaneous termination so that the degree of polymerization is controlled by the ratio of monomer to initiator concentrations. The molar-mass of the polymer therefore increases linearly with monomer conversion. On exhaustion of the monomer, the initiation centres remain, so chains may be re-initiated by addition of further monomer. Termination or chain transfer is controlled by the delibemte addition of a reagent to remove the living end. The resulting polymers will also have very narrow molar-mass distributions since rapid initiation ensures that all chains are initiated at the same time. 

Urban aerosols are mixtures of primary particulate emissions from industries, transportation, power generation, and natural sources and secondary material formed by gas-to-particle conversion mechanisms. The number distribution is dominated by particles smaller than 0.1 pm, while most of the surface area is in the 0.1-0.5 pm size range. On the contrary, the aerosol mass distribution usually has two distinct modes, one in the submicrometer regime (referred to as the accumulation mode ) and the other in the coarse-particle regime (Figure 8.11). 

FIGURE 12.16 Aerosol mass distributions at the time when the mass added by gas-to-particle conversion is seven times the initial mass (Seinfeld and Bassett, 1982). 

Already before reporting this combined inifer and living polymerization approach, Kennedy and coworkers developed a controlled isobutene polymerization method based on cumyl ester initiators (Scheme 8.6) with boron trichloride as activator and incremental monomer addition [28], The livingness of the polymerization was demonstrated by the linear increase of number-average molar mass and the constant number of polymer chains (A) with the amount of PIB obtained (wp, as measure for conversion) as well as the narrowing of the molar mass distribution with conversion (Fig. 8.1) [28]. 

---