INDEX particle model

For the case of silica as a shell material, there is no risk of interactions, since silica is electronically inert (it does not exchange charge with the gold particles). However, its refractive index is different from that of gold, and also from water and ethanol. This renders M-SiOa particles model systems for the smdy of optical properties. 

We introduce, for the sake of convenience, species indices 5 and c for the components of the fluid mixture mimicking solvent species and colloids, and species index m for the matrix component. The matrix and both fluid species are at densities p cr, Pccl, and p cr, respectively. The diameter of matrix and fluid species is denoted by cr, cr, and cr, respectively. We choose the diameter of solvent particles as a length unit, = 1. The diameter of matrix species is chosen similar to a simplified model of silica xerogel [39], cr = 7.055. On the other hand, as in previous theoretical works on bulk colloidal dispersions, see e.g.. Ref. 48 and references therein, we choose the diameter of large fluid particles mimicking colloids, cr = 5. As usual for these dispersions, the concentration of large particles, c, must be taken much smaller than that of the solvent. For all the cases in question we assume = 1.25 x 10 . The model for interparticle interactions is... 

In the general case, individual particles have differing compositions and refractive indices and to take this into account in detail is not possible from a practical point of view. To allow for a variation of refractive index, a convenient model is that of a mixture of aerosols from the several sources, each with its own extinction cross-section. The particles are assumed not to coagulate so that the aerosol is not mixed on the individual particle basis. Such an aerosol is known as an external mixture. This model would also be applicable, approximately, to an aerosol mixture whose particles are growing in size by gas-to-particle conversion. 

The model sufficiently conforms to the change in the shape index with longer treatment time, and it was proved that processing particulate materials of smaller ductility, the particle shape is more adjustable stepwise in terms of the shape index. 

Mie s Theory. Mie applied the Maxwell equations to a model in which a plane wave front meets an optically isotropic sphere with refractive index n and absorption index k [1.26]. Integration gives the values of the absorption cross section QA and the scattering cross section Qs these dimensionless numbers relate the proportion of absorption and scattering to the geometric diameter of the particle. The theory has provided useful insights into the effect of particle size on the color properties of pigments. 

Figure 1. Measured aircraft ultrafine aerosol emissions are compared with equivalent model predictions. The aerosol emission index (El) is given as the total number of particles generated for each kilogram of fuel burned, at particle sizes exceeding d>5 nm or d> 14 nm (open and filled symbols, respectively). Data were collected in the SULFUR-5 field campaign. In the simulations (lines), different initial chemiion concentrations, nio, were assumed, as indicated in the legend at the left of the figure (the first number is the value of n in /cmJ, and the second is the lower particle size cutoff diameter, nm. From [84],...

Model particle mobility has been determinated with the Tiselius method (Tiselius, 1937, 1938). This method also allows the integration of the mobility of a large number of particles even if the refractive index is very close to that of the electrolyte medium, allowing to minimize the experimental errors inherent to the classical microelectrophoretic techniques. The electrophoretic mobilities will not be transformed into surface charges because the theoretical relationship between these parameters is highly dependant on the particle radius of curvature and the electrolyte concentration in the vicinity of the particle (Hunter and Wright, 1971). For both methods, the analytical error falls below 5 %, however, it increases up to 10 % for natural composite samples and/or low mobilities. 

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

The typical results of the wide-angle light-scattering (WALS) analysis on the latex particles that were presumed to be cores are given in Table I where the theoretical model to be fitted was either S = sphere or CS = core-shell, the variance measured the goodness of fit, the modal size parameter is given by aM = 27rr/A, aQ is the log normal breadth parameter, DM is the core diameter in ym, mi the relative refractive index of the core and m2 the relative refractive index of the shell of indicated thickness. 

---