Polydispersed particles

In the remainder of this section we see how the theoretical calculations of Mie account for the observed spectrum of colloidal gold. In the next section we consider the inverse problem for a simpler system how to interpret the experimental spectrum of sulfur sols in terms of the size and concentration of the particles. Both of these example systems consist of relatively monodisperse particles. Polydispersity complicates the spectrum of a colloid since the same x value will occur at different X values for spheres of different radii according to Equations (99M101). 

The formulas derived above, despite their cumbersome look, are very practical. Indeed, they present the nonlinear initial susceptibilities of a superparamagnetic particulate medium as analytical expressions of arbitrary accuracy. Another remarkable feature of the formulas of Section III.B.6 is that with respect to the frequency behavior they give the exact structure of the susceptibilities and demonstrate that those dependencies are quite simple. This makes our formulas a handy tool for analytical studies. Yet they are more convenient for numerical work because with their use the difficult and time-consuming procedure of solving the differential equations is replaced by a plain summation of certain power series. For example, if to employ Eqs. (4.194)-(4.200), a computer code that fits simultaneously experimental data on linear and a reasonable set of nonlinear susceptibilities (say, the 3th and the 5th) taking into account the particle polydispersity of any kind (easy-axes directions, activation volume, anisotropy constants) becomes a very fast procedure. 

Theoretical descriptions of the electrokinetic phenomena in the framework of these three models were developed in the literature and reviewed by Dukhin and van de Ven. The effect of particle polydispersity on the data interpretation by the different models was analyzed in the same study. ... 

Ostwald ripening obviously depends on particle polydispersity. If all the particles have the same size, there is no reason for one to grow at the expense of another. Ostwald ripening is also a function of the solubility of the oil in water and of the diffusion coefficient. This provides an excellent means to reduce its effect. The addition of a moderate amount of a water-insoluble oil such as a triglyceride is usually enough to reduce the impact of this destabilization mechanism. 

A more realistic particle polydispersity typical of that in a ferrofluid has been considered by Kristof and Szalai [164]. Their calculations for a DSS model show that, up to moderate fields, the magnetization is generally higher in the polydisperse system than in the corresponding monodisperse system where all particles have dipole moments and sizes equal to the average values. 

In the synthesis of polymer particulate material, MF polymerization provides excellent control of particle size, size distribution, morpholt, shape, and internal structure. Generally, all of these properties are controlled by the hydrodynamic means or by using a combination of hydrodynamics and macroscopic properties of the precursor liquids. The coeflBcient of variation in particle dimensions (i.e., particle polydispersity) can be as low as 1-3%. Figure 8.5a shows polymer particles synthesized by MF synthesis, while Figure 8.5b shows their size distribution [48,49]. 

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