Monosized

Edeison L H and Giaeser A M 1988 Roie of particie substructure in the sintering of monosized titania J. Am. Ceram. See. 71 225... 

The capillary retention forces in the pores of the filter cake are affected by the size and size range of the particles forming the cake, and by the way the particles have been deposited when the cake was formed. There is no fundamental relation to allow the prediction of cake permeabiUty but, for the sake of the order-of-magnitude estimates, the pore size in the cake may be taken loosely as though it were a cylinder which would just pass between three touching, monosized spheres. If dis the diameter of the spherical particles, the cylinder radius would be 0.0825 d. The capillary pressure of 100 kPa (1 bar) corresponds to d of 17.6 pm, given that the surface tension of water at 20°C is 12.1 b mN /m (= dyn/cm). 

DpopE related to SpQpp, which is in turn related to the closeness of packing of the powder. The number of particles adjacent to a given particle is represented by The maximum packing density for monosize spheres occurs at hexagonal close packing, where = 12 and = 0.2595 for... 

Specific advancements ia the chemical synthesis of coUoidal materials are noteworthy. Many types of genera ting devices have been used to produce coUoidal Hquid aerosols (qv) and emulsions (qv) (39—43) among them are atomizers and nebulizers of various designs (30,44—50). A unique feature of produciag Hquid or soHd coUoids via aerosol processes (Table 3) is that material with a relatively narrow size distribution can be routinely prepared. These monosized coUoids are often produced by relying on an electrostatic classifier to select desired particle sizes ia the final stage of aerosol production. 

Coimectivity is a term that describes the arrangement and number of pore coimections. For monosize pores, coimectivity is the average number of pores per junction. The term represents a macroscopic measure of the number of pores at a junction. Connectivity correlates with permeability, but caimot be used alone to predict permeability except in certain limiting cases. Difficulties in conceptual simplifications result from replacing the real porous medium with macroscopic parameters that are averages and that relate to some idealized model of the medium. Tortuosity and connectivity are different features of the pore structure and are useful to interpret macroscopic flow properties, such as permeability, capillary pressure and dispersion. 

The particle size distribution is determined from the diffraction pattern. For a simplified case of monosized spherical particles, for instance, the radius... 

V. BASIC FEATURES OF MONOSIZED POLYMERIC PARTICLES PREPARED BY ACTIVATED SWELLING AND POLYMERIZATION... 

Monosized polystyrene particles in the size range of 2-10 /am have been obtained by dispersion polymerization of styrene in polar solvents such as ethyl alcohol or mixtures of alcohol with water in the presence of a suitable steric stabilizer (59-62). Dispersion polymerization may be looked upon as a special type of precipitation polymerization and was originally meant to be an alternative to emulsion polymerization. The components of a dispersion polymerization include monomers, initiator, steric stabilizer, and the dispersion medium... 

Only particles of linear or very slightly cross-linked <0.6%) polymers may be produced by dispersion polymerization. Obviously, dispersion polymerization may be used for the production of monosized seed particles, which, after transfer to aqueous conditions, are used for the production of different cross-linked and macroporous particles by the activated swelling and polymerization method. 

The effects of the concentration of divinylbenzene on pore-size distribution and surface areas of micropores, mesopores, and macropores in monosized PS-DVB beads prepared in the presence of linear polymeric porogens have been studied (65). While the total surface area is clearly determined by the content of divinylbenzene, the sum of pore volumes for mesoforms and macropores, as well as their pore-size distribution, do not change within a broad range of DVB concentrations. However, the more cross-linked the beads, the better the mechanical and hydrodynamic properties. 

The advantages of monosized chromatographic supports are as follows a uniform column packing, uniform flow velocity profile, low back pressure, high resolution, and high-speed separation compared with the materials of broad size distribution. Optical micrographs of 20-p,m monosized macroporous particles and a commercial chromatography resin of size 12-28 p,m are shown in Fig. 1.4. There is a clear difference in the size distribution between the monodispersed particles and the traditional column material (87). 

FIGURE 1.4 Optical micrograph of macroporous chromatographic column materials, (a) Monosized particles of 20 tm. (b) Commercial column filling of 12-28 tm. [Reprinted from T. Ellingsen et al. (1990). Monosized stationary phases for chromatography.7. Chromawgr. 535,147-161 with kind permission from Elsevier Science-NL, Amsterdam, The Netherlands.]... 

D. Application of Monosized Polymeric Particles in Size Exclusion Chromatography... 

A trend in chromatography has been to use monosized particles as supports for ion-exchange and size-exclusion chromatography and to minimize the column size, such as using a 15 X 4.6-mm column packed with 3-/rm polymer particles for size exclusion chromatography. The more efficient and lower back pressure of monosized particles is applied in the separation. 

Monosized macroporous polystyrene-divinylbenzene particles have been prepared in a multistep swelling process, in which particles of different sizes... 

Figure 1.5 shows the cumulative pore volume curve for 5-/rm monosized porous PS-DVB particles with 50, 60, and 70% porosity. The curves were drawn by overlapping the measurements from nitrogen adsorption-desorption and mercury intrusion. A scanning electron micrograph of 5-/rm monosized particles with 50% porosity is shown in Fig. 1.6 (87). 

Chiral nitrogen chelates derived from sugars were prepared by Ruffo [48], introducing diimines and diamines functionalities on inexpensive monoses, a-D-glucose and a-D-mannose. 

The particles build up Iqr layers because it has been found that all monosized particles can be removed from suspension by rotating at a specific speed. Thus, one runs the instrument at a series of rotational speeds, measuring the weight of the build-up layers in between each run. The overall analysis is run at specified rpm s which correspond to selected particle diameters, resulting in data sufficient to characterize the particle distribution. 

Kulin, L.-I., Flodin, P., Ellingsen, T., and Ugelstad, J., Monosized polymer particles in size exclusion chromatography. I. Toluene as solvent, /. Chromatogr., 514, 1, 1990. 

Rumpf (R4) has derived an explicit relationship for the tensile strength as a function of porosity, coordination number, particle size, and bonding forces between the individual particles. The model is based on the following assumptions (1) particles are monosize spheres (2) fracture occurs through the particle-particle bonds only and their number in the cross section under stress is high (3) bonds are statistically distributed across the cross section and over all directions in space (4) particles are statistically distributed in the ensemble and hence in the cross section and (5) bond strength between the individual particles is normally distributed and a mean value can be used to represent each one. Rumpf s basic equation for the tensile strength is... 

A comparison of the measured mean relative size with the model in Eq. (101) is shown in Fig. 28. The material was monosize glass beads. The data fit the model quite well, with the exception of fine 0.038-mm powder. It is evident that the steady-state size distribution is a function of the liquid content, and consequently, as shown by Sherrington (S9), there is an optimal granulating liquid for maximum granulation efficiency, that is, percentage of the product-grade material. 

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