Diffusivity, monodisperse particle systems

F. 2.8 Impact of diffusion on the concentration profiles in sedimentation experiments for a monodisperse particle system left homogeneous technique, right line-start technique... 

Fig. V-34. The influence of diffusion on the Fig. V-35. The effect of diffusion on boundary position during the centrifugation of the shape of sedimentation curves system containing monodispersed particles plotted in c - AR / At coordinates...

The correlation frmction g q,T) indicates the temporal decay behavior of concentration fluctuations in the fluid as a function of delay time r. In ideal systems (dilute solution, monodisperse particles, ideal Brownian diffusion only), it exhibits a single exponential decay with decay rate r ... 

Heterodisperse Suspensions. The rate laws given above apply to monodisperse colloids. In polydisperse systems the particle size and the distribution of particle sizes have pronounced effects on the kinetics of agglomeration (O Melia, 1978). For the various transport mechanisms (Brownian diffusion, fluid shear, and differential settling), the rates at which particles come into contact are given in Table 7.2. 

Two major entry models - the diffusion-controlled and propagation-controlled models - are widely used at present. However, Liotta et al. [28] claim that the collision entry is more probable. They developed a dynamic competitive growth model to understand the particle growth process and used it to simulate the growth of two monodisperse polystyrene populations (bidisperse system) at 50 °C. Validation of the model with on-line density and on-line particle diameter measurements demonstrated that radical entry into polymer particles is more likely to occur by a collision mechanism than by either a propagation or diffusion mechanism. 

A built-in microcomputer system performs rapid quadratic least squares fit to the data, yielding D, R, a (normalized standard deviation of the intensity weighted distribution of diffusion constants) and x squares goodness of fit. The greater the value of a the larger the degree of polydispersity present in the particle sizes -a values less than 0.2 are generally considered to correspond to pure monodisperse systems. A typical result obtained for 4 x 10 3M CdS-SDS is 5= 7.25 x 10"8 cm2/s, R = 300 A, a = 0.60 and y2... 

Example 11-5 Vycor (porous silica) appears to have a pore system with fewer interconnections than alumina. The pore system is monodisperse, with the somewhat unusual combination of a small mean pore radius (45 A) and a low porosity 0.31. Vycor may be much closer to an assembly of individual voids than to an assembly of particles surrounded by void spaces. Since the random-pore model is based on the assembly-of-particles concept, it is instructive to see how it applies to Vycor. Rao and Smith measured an effective diffusivity for hydrogen of 0.0029 cm /sec in Vycor. The apparatus was similar to that shown in Fig. 11-1, and data were obtained using an H2-N2 system at 25°C and 1 atm. Predict the effective diffusivity by the random-pore model. 

For a poiydisperse aerosol, the number of particles deposited up to any point in the system can be calculated from the theory for monodisperse aerosols and then integrating over the initial. size distribution, which is the quantity sought- The experimental measure ments made with the condensation nuclei counter gives the number concentration of the poiydisperse aerosol as a function of the distance from the inlet to the diffusion battery. The recovery of the size distribution function from the measured decay In particle concentration can be accomplished in an approximate way. Various numerical schemes based on plausible approximations have been developed to accomplish the inversion (Cheng, 1993). The lower detection limit for the diffusion battery is 2 to 5 nm. Systems are not difficult to build for specific applications or can be purchased commercially. 

In order to achieve a monodisperse suspension or polydisperse system with particular particle size contribution, it is necessary to control the process of nucleation and particle growth. With most disperse systems, where the particles have some finite solubility, the smaller particles will have higher solubilities than their larger counterparts. With time, molecular diffusion occurs from the smaller to the larger particles, and this results in a shift in the particle size distribution to larger values this process is referred to as Ostwald ripening. 

For a monodisperse system of equal-sized particles, the self-collision frequency requires dividing by 2 to avoid double counting, once as a diffusing particle and once as a test particle. In this special case Eq. (8.2.6) reduces to... 

In the case of a monodisperse system (ai = U2), the expression for collision frequency needs to be divided by 2 because the same collisions are counted twice the particle is first considered as the test particle and then as the diffused particle. 

In nature, ordered colloidal systems are unusual for two reasons. First, large scale lattices require monodispersity of the individual particle units within the lattice. Second, both diffusion limited aggregation and reaction limited aggregation in solution produce fractal structures rather... 

If the suspension is entirely homogeneous and contains only particles of one definite size, the boundary between the solution and the pure solvent is sharp (apart from diffusion in the case of very small particles, which will be referred to later) and we may conclude that a monodisperse system exists. It should, of course, be emphasized that this holds only for spherical or at least for nearly spherical particles, for with elliptical particles, there may be a different adjustment of the particle axes to the direction of the field, resulting in a different rate of sedimentation of particles of the same size but of different orientation. ... 

In emulsion polymerization, the polymerization process (typically radical initiated) takes place in micellar reactors composed of monomer droplets stabilized by surfactant molecules and dispersed in water (Figure 9.1). A colloidally stable polymer dispersion or latex is formed in this reaction by a complex mechanism consisting of three distinct intervals termed Smith-Ewert intervals [ 3-5]. On addition of a dispersed phase soluble monomer to the surfactant/solvent system, the system contains monomer-swollen small surfactant micelles ( 10 nm in diameter) and large emulsion droplets of monomer. On the subsequent addition of a continuous phase soluble initiator, free radical spedes form which diffuse into the micelles. The monomer quickly polymerizes in the micelle and, as diffusion of monomer from the emulsion droplet to the micelle is rapid on the timescale of polymerization, the micelles contain both monomer and polymer. As the concentration of free monomer reduces to zero, the polymerization of the remaining monomer in the latex particles takes place, ending the reaction. Monodispersity is retained throughout the reaction to the final product as all polymerization takes place within the surfactant micelles [6, 7j. 

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