Monodispersed systems

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. 

For a monodisperse system this result is in good agreement with the values obtained from pore size distribution measurements, but it can be significantly in error if one is dealing with a bimodal pore size distribution (see Section 6.4.2). 

Equation (31) applies to monodisperse systems. For polydisperse systems Rg reflects a high-order moment of the distribution, the ratio of the 8th to the 6th moment of the distribution in mean size. For this reason Rg will correlate with the largest sizes of a distribution. There are several advantages to Rg as a measure of size over the end-to-end distance. For branched, star and ring structures the end-to-end distance has no clear meaning while Rg retains its meaning. Further, Rg is directly measured in static scattering measurements so it maintains a direct link to experiment. 

However, ageing of these virtually monodisperse systems was shown to promote an increase in width in favour of length. There was no change from hydroxo to oxo bridges, but instead there was an alteration in polynuclear shape. While the internal structure was maintained, it was found that the polynuclears became shorter and wider, as the mononuclear ferric species released from the ends of the needles by acid cleavage redeposited on the centres of the molecules. 

There has been very little theoretical work on the problem of desorption. Recently, Cohen Stuart et al. ( 6) have proposed a theory by taking into account the polydispersity of the sample in order to explain experimentally often observed "rounded" isotherms and the apparent irreversibility. For monodisperse systems, the bulk solution concentration was estimated to be on the order of 10 a PPM for polymers in order to observe... 

In case of the anionic polymerisation, since all the chains grow at the same rate, a monodisperse system is obtained in this case. 

Membrane emulsification allows a precise control of the droplet size and monodispersity but the scale up of this process is difficult. MicroChannel emulsification is a promising technique but the low production rates restrict its use to highly monodisperse systems intended for high-technology applications. 

Sedimentation velocity gives real Mfor only monodisperse systems... 

In the past few decades, a specific kind of colloidal system based on monodis-perse size has been developed for various industrial applications. A variety of metal oxides and hydroxides and polymer lattices have been produced. Monodisperse systems are obviously preferred since their properties can be easily predicted. On the other hand, polydisperse systems will exhibit varying characteristics, depending on the degree of polydispersity. 

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. 

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). 

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. 

Das et al. [46] have studied moderately concentrated emulsions (0.7 < < > < 0.9), from both a theoretical and an experimental standpoint. Both polydisperse and distorted monodisperse systems were considered for the former, it is possible to achieve a value of 0.89 for with undistorted spheres in a tridisperse (i.e. three sphere sizes) packing. 

As can be seen, many factors affect the geometry of HIPEs. Generally, a degree of polydispersity and some cell distortion is shown in real systems and very rarely, if ever, will a truly monodisperse system be observed1. The extent of deviation from monodispersity will depend on the experimental conditions and on the physical properties of the HIPE. 

As mentioned previously, Bibette [95] has developed a very elegant method for the purification of coarse, polydisperse emulsions to produce monodisperse systems. This technique is based on the attractive depletion interaction between dispersed phase droplets, caused by an excess of surfactant micelles in the continuous phase. A phase separation occurs under gravity, between a cream layer and a dilute phase since the extent of the separation increases with increasing droplet diameter, a separation based on size occurs. By repeating this process, emulsions of very narrow size distribution can be produced. 

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. 

Even in the case of monodisperse systems, the observed decay rate of gi(s,td) (and hence the diffusion coefficient) in general depends on the angle at which the decay is measured if interparticle interference effects exist. In the case of dilute dispersions, in which interactions... 

The frequency of collisions is also expected to be greater in a polydisperse system than in a monodisperse system by the same logic as presented in item 1. 

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