Size distribution conversion

Continuous emulsion copolymerization processes for vinyl acetate and vinyl acetate—ethylene copolymer have been reported (59—64). CycHc variations in the number of particles, conversion, and particle-size distribution have been studied. Control of these variations based on on-line measurements and the use of preformed latex seed particles has been discussed (61,62). 

Suspension Polymerization. At very low levels of stabilizer, eg, 0.1 wt %, the polymer does not form a creamy dispersion that stays indefinitely suspended in the aqueous phase but forms small beads that setde and may be easily separated by filtration (qv) (69). This suspension or pearl polymerization process has been used to prepare polymers for adhesive and coating appHcations and for conversion to poly(vinyl alcohol). Products in bead form are available from several commercial suppHers of PVAc resins. Suspension polymerizations are carried out with monomer-soluble initiators predominantly, with low levels of stabilizers. Suspension copolymerization processes for the production of vinyl acetate—ethylene bead products have been described and the properties of the copolymers determined (70). Continuous tubular polymerization of vinyl acetate in suspension (71,72) yields stable dispersions of beads with narrow particle size distributions at high yields. 

Physical properties of catalysts also may need to be checked periodically, includiug pellet size, specific surface, porosity, pore size and size distribution, and effective diffusivity. The effectiveness of a porous catalyst is found by measuring conversions with successively smaller pellets until no further change occurs. These topics are touched on by Satterfield (Heterogeneous Cataly.sls in Jndustiial Practice, McGraw-Hill, 1991). 

Particles in the atmosphere come from different sources, e.g., combustion, windblown dust, and gas-to-particle conversion processes (see Chapter 6). Figure 2-2 illustrates the wide range of particle diameters potentially present in the ambient atmosphere. A typical size distribution of ambient particles is shown in Fig. 2-3. The distribution of number, surface, and mass can occur over different diameters for the same aerosol. Variation in chemical composition as a function of particle diameter has also been observed, as shown in Table 4-3. 

The pore size, the pore-size distribution, and the surface area of organic polymeric supports can be controlled easily during production by precipitation processes that take place during the conversion of liquid microdroplets to solid microbeads. For example, polystyrene beads produced without cross-linked agents or diluent are nonporous or contain very small pores. However, by using bigb divinylbenzene (DVB) concentrations and monomer diluents, polymer beads with wide porosities and pore sizes can be produced, depending on the proportion of DVB and monomer diluent. Control of porosity by means of monomer diluent has been extensively studied for polystyrene (3-6) and polymethacrylate (7-10). 

A graph paper based on this type of relationship can be obtained. It permits convenient graphical representation of size distribution data (as shown in Fig 3) even if the distribution does not follow a log-probability relationship. In addition, the assumption of a log-probability distribution as an approximation permits simple conversion from one basis of representing size distribution, mean size, or median size to another basis... 

Equations 11 and 12 are only valid if the volumetric growth rate of particles is the same in both reactors a condition which would not hold true if the conversion were high or if the temperatures differ. Graphs of these size distributions are shown in Figure 3. They are all broader than the distributions one would expect in latex produced by batch reaction. The particle size distributions shown in Figure 3 are based on the assumption that steady-state particle generation can be achieved in the CSTR systems. Consequences of transients or limit-cycle behavior will be discussed later in this paper. 

Iridium and rhodium nanoparticles have also been studied in the hydrogenation of various aromatic compoimds. In all cases, total conversions were not observed in BMI PF6. TOFs based on mol of cyclohexane formed were 44 h for toluene hydrogenation with Ir (0) and 24 h and 5 h for p-xylene reduction with lr(0) or Rh(0) nanoparticles, respectively. The cis-1,4-dimethylcyclohexane is the major product and the cisitrans ratio depends on the nature of the metal 5 1 for lr(0) and 2 1 for Rh(0). TEM experiments show a mean diameter of 2.3 nm and 2.1 nm for rhodium and iridium particles, respectively. The same nanoparticle size distribution is observed after catalysis (Fig. 4). 

The average pore size and the pore size distribution should be such that physical limitations are not placed on the conversion of reactants to products. The particle size of the carrier must also be suitable for the purpose intended (i.e., small for fluidized bed reactors and significantly larger for fixed bed applications). 

Pore size optimization is one area where developmental efforts have been focused. Unimodal pore (NiMo) catalysts were found highly active for asphaltene conversion from resids but a large formation of coke-like sediments. Meanwhile, a macroporous catalyst showed lower activity but almost no sediments. The decrease of pore size increases the molecular weight of the asphaltenes in the hydrocracked product. An effective catalyst for VR is that for which average pores size and pore size distribution, and active phase distribution have been optimized. Therefore, the pore size distribution must be wide and contain predominantly meso-pores, but along with some micro- and macro-pores. However, the asphaltene conversion phase has to be localized in the larger pores to avoid sediment formation [134],... 

In a fluidized bed reactor, entrained particles leaving in a dilute phase stream are conventionally and desirably either partially or wholly condensed into a bulk stream and returned to the bed via a centrifugally driven cyclone system. At equilibrium, or when steady state operation is attained, any particle loss rate from the cyclones, as well as the remaining bed particle size distribution, are functions of (a) the rate of any particle attrition within the system and (b) the smallest particle size that the cyclone system was designed to completely collect (i.e., with 100% efficiency), or conversely the largest size which the system cannot recover. These two functions result in an interdependency between loss rate and bed particle size distribution, eventually leading to an equilibrium state (Zenz Smith, 1972 Zenz, 1981 Zenz Kelleher, 1980). 

In 1994, we reported the dispersion polymerization of MM A in supercritical C02 [103]. This work represents the first successful dispersion polymerization of a lipophilic monomer in a supercritical fluid continuous phase. In these experiments, we took advantage of the amphiphilic nature of the homopolymer PFOA to effect the polymerization of MMA to high conversions (>90%) and high degrees of polymerization (> 3000) in supercritical C02. These polymerizations were conducted in C02 at 65 °C and 207 bar, and AIBN or a fluorinated derivative of AIBN were employed as the initiators. The results from the AIBN initiated polymerizations are shown in Table 3. The spherical polymer particles which resulted from these dispersion polymerizations were isolated by simply venting the C02 from the reaction mixture. Scanning electron microscopy showed that the product consisted of spheres in the pm size range with a narrow particle size distribution (see Fig. 7). In contrast, reactions which were performed in the absence of PFOA resulted in relatively low conversion and molar masses. Moreover, the polymer which resulted from these precipitation... 

Another example from Liu s team in this field concerns the selective hydrogenation of citronellal to citronellol by using a Ru/PVP colloid obtained by NaBH4 reduction method [112]. This colloid contains relatively small particles with a narrow size distribution (1.3 to 1.8 nm by TEM), whereas the metallic state of Ru was confirmed by XPS investigation. This colloid exhibited a selectivity to citronellol of 95.2% with a yield of 84.2% (total conversion 88.4%), which represented a good result for a monometallic catalyst. 

From the above results, one can conclude that different NiO/MgO solid-solution catalysts can have very different catalytic performances. For example, Fujimoto et aV s Nio.03Mgo.97O solid-solution catalyst exhibited relatively low activities. To reach about 82% conversion of CH4 in the presence of this Nio.03Mgo.97O catalyst, the space velocity had to be reduced to 18,670 mL (g catalyst)-1 h-1 at 1123 K (Fig. 15) (238). In contrast, Ruckenstein and Hu s NiO/MgO catalysts have very high activities (>91% conversion of CH4 and >95% selectivities of CO and H2 at the space velocity of 60,000 mL (g catalyst)-1 h-1 at 1063 K) (Fig. 14) (239). Hu and Ruckenstein (239,257,259) noted that the properties of the MgO, such as its surface area, pore size distribution, and crystal structure, have important effects on the NiO/MgO solid-solution catalysts. They found that the MgO supplied by Aldrich, which has... 

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