Monodisperse system particles

In applying this concept, the factor of particle size must be continuously borne in mind. A heterodisperse system can reach a steady state wherein the smaller particles are agglomerated and the larger particles are dispersed, giving the apparent effect of an equiUbrium. In ideal monodisperse systems under steady conditions, however, no such effects are noted. 

Microemulsion media seem to be very useful in getting monodisperse CaCOj particles of 30 A via carbonation of calcium phenates (Marsh, 1987) this process is relevant in making lube additives. The mechanism of reaction crystallization in such systems has hardly received attention. 

DR. RAMESH PATEL (Clarkson College) It appears that studies on colloidal systems may represent an extremely important area for the future. We have also been doing some colloidal work, particularly dealing with the solution chemistry that precedes the formation of very highly monodispersed colloidal particles. One such system with iron phosphate has been included in the poster presentation. 

This chapter summarizes the present state of the art of the forced hydrolysis approach by considering specific cations, particularly those of greatest practical and theoretical interest, using aqueous solutions of common salts. In addition to being economical in the manufacture of different products, the described procedure can also help in the development of a better understanding of different processes, such as corrosion of metals or formation of minerals, to mention a few. It should be emphasized that the focus of this chapter is on dispersions of narrow particle size distributions, normally designated as monodispersed systems. While a number of genera reviews have been published on monodispersed colloids (7,9-21), this chapter specifically addresses the problems related to metal (hydrous) oxides. 

Under certain conditions both the diffusional growth and the aggregative growth pathways may lead to monodispersed" systems. As mentioned earlier, the mechanism by which the former process could yield uniform particles was proposed by Victor K. LaMer (6), whose original scheme, reproduced numerous times, is shown in Figure 1.1.4. This kind of process is most likely operational in the formation of nanosized particles or larger amorphous spheres. 

Generally, alkoxide-derived monodisperse oxide particles have been produced by batch processes on a beaker scale. However, on an industrial scale, the batch process is not suitable. Therefore, a continuous process is required for mass production. The stirred tank reactors (46) used in industrial process usually lead to the formation of spherical, oxide powders with a broad particle size distribution, because the residence time distribution in reactor is broad. It is necessary to design a novel apparatus for a continuous production system of monodispersed, spherical oxide particles. So far, the continuous production system of monodisperse particles by the forced hydrolysis... 

Despite the successes of these chemical procedures, they are still fraught with difficulties in terms of the predictability of the properties of the final products. Thus, except in a very few cases, it is impossible to predict conditions that would yield particles of a given shape. Even obtaining a desired particle size by a chemical process that can produce a monodisperse system must be established experimentally. When dealing with finely dispersed matter of internally mixed composition additional problems are encountered, because the molar ratio of constituents in the solid phase usually differs from those in solutions in which the precipitates are formed (4,5). 

In 1968, Stober et al. (18) reported that, under basic conditions, the hydrolytic reaction of tetraethoxysilane (TEOS) in alcoholic solutions can be controlled to produce monodisperse spherical particles of amorphous silica. Details of this silicon alkoxide sol-gel process, based on homogeneous alcoholic solutions, are presented in Chapter 2.1. The first attempt to extend the alkoxide sol-gel process to microemul-sion systems was reported by Yanagi et al. in 1986 (19). Since then, additional contributions have appeared (20-53), as summarized in Table 2.2.1. In the microe-mulsion-mediated sol-gel process, the microheterogeneous nature (i.e., the polar-nonpolar character) of the microemulsion fluid phase permits the simultaneous solubilization of the relatively hydrophobic alkoxide precursor and the reactant water molecules. The alkoxide molecules encounter water molecules in the polar domains of the microemulsions, and, as illustrated schematically in Figure 2.2.1, the resulting hydrolysis and condensation reactions can lead to the formation of nanosize silica particles. 

Now we compare the above osmotic pressure data with the scaled particle theory. The relevant equation is Eq. (27) for polydisperse polymers. In the isotropic state, it can be shown that Eq. (27) takes the same form as Eq. (20) for the monodisperse system though the parameters (B, C, v, and c ) have to be calculated from the number-average molecular weight M and the total polymer mass concentration c of a polydisperse system pSI in the parameters B and C is unity in the isotropic state. No information is needed for the molecular weight distribution of the sample. On the other hand, in the liquid crystal state2, Eq. (27) does not necessarily take the same form as Eq. (20), because p5I depends on the molecular weight distribution. 

This discussion of aggregates leads us to another important characteristic of dispersions we have not yet considered in sufficient detail polydispersity. Monodisperse systems are the exception rather than the rule. Even in those rare cases in which a monodisperse system exists, any aggregation that occurs will result in a distribution of particle sizes because of the random nature of the aggregation process. 

Another colloidal system with light scattering characteristics that have been widely studied is the so-called monodisperse sulfur sol. Although not actually monodisperse, the particle size distribution in this preparation is narrow enough to make it an ideal system for the study of optical phenomena. 

Data analysis methods depend upon the level of order in the sample. The degree of order, in turn, depends upon the scale of distance on which the sample is viewed. For example, casein micelles show great variation in size (20 to 300 nm diameter) and so must be treated as a polydisperse system. However, the density variations ( submicelles ) within the whole micelle are much more uniform in size. They can be treated as a quasi-monodisperse system (Stothart and Cebula, 1982) and analyzed in terms of inter-particle interference (Stothart, 1989). 

This equation again demonstrates that particle size and solubility are the main parameters affecting dissolution kinetics of drug powders, which, in turn, could affect the release profile of dosage forms if dissolution is the rate-limiting step of in vivo absorption. Table 5.1 demonstrates several examples of dissolution times of spherical particles (assuming monodispersed systems) as a function of solubility and particle size. 

Aggregation methods usually lead to the formation of polydispersed sols, mainly because the formation of new nuclei and the growth of established nuclei occur simultaneously, and so the particles finally formed are grown from nuclei formed at different times. In experiments designed to test the validity of theories, however, there are obvious advantages attached to the use of monodispersed systems. The preparation of such systems requires conditions in which nucleation is restricted to a relatively short period at the start of the sol formation. This situation can sometimes be achieved either by seeding a supersaturated solution with very small particles or under conditions which lead to a short burst of homogeneous nucleation. 

Thus far most of the relationships discussed apply to monodisperse systems in which the dispersed species have the same size and shape. Although for a monodisperse system, relative viscosity is often independent of droplet/bubble/particle size, at the high end of the dispersed phase volume fraction range the viscosity will often become influenced by size. The actual range of volume fraction for which this occurs depends strongly on the nature of a particular system, including factors such as surface rigidity [215]. 

Table I. Particle Size Measurements of Monodisperse Systems Using...

For monodisperse systems, replacement of equation 13 into equation 2, yields an approximation to the turbidity in terms of powers of the particle diameter... 

For monodisperse systems in the large particle size regime, where the extinction efficiency can be assumed constant and approximately equal to 2, equation 2 becomes... 

The equations obtained for the average particle diameter(s) should reduce to the equations developed for monodisperse systems (ie the resulting equations should reduce to equations 11) and 16 for monodisperse systems). 

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