Monodisperse particle populations

Thus both the standard deviation o. in particle diameter and diffusion coefficient D can be related to experimental H values. A procedure for obtaining particle information via this route will be detailed in our discussion of monodisperse particle populations. 

The theory of coagulation will be presented in two steps. At first, we will develop an expression describing the rate of collisions between two monodisperse particle populations consisting of N particles with diameter Dpl and N2 with diameter Dp2. In the next step a differential equation describing the rate of change of a full coagulating aerosol size distribution will be derived. 

For clinical use, better defined, homogeneous and biocompatible systems will be necessary. Aspects for optimization will include a defined assembly into monodisperse particle populations preferably of small size [190] methods for the purification of polyplexes [56] which remove potentially... 

The micrographs however, revealed that the latex particle standards were not monodispersed as claimed by the suppliers. This can clearly be noted from the micrographs in Fig. U,a-e. They indicate a distinct polydispersity the micrographs of the 2T5 and 312 nm samples in fact reveal two distinct particle populations. 

This paper outlines the basic principles and theory of sedimentation field-flow fractionation (FFF) and shows how the method is used for various particle size measurements. For context, we compare sedimentation FFF with other fractionation methods using four criteria to judge effective particle characterization. The application of sedimentation FFF to monodisperse particle samples is then described, followed by a discussion of polydisperse populations and techniques for obtaining particle size distribution curves and particle densities. We then report on preliminary work with complex colloids which have particles of different chemical composition and density. It is shown, with the help of an example, that sedimentation FFF is sufficiently versatile to unscramble complex colloids, which should eventually provide not only particle size distributions, but simultaneous particle density distributions. 

It is also possible that the unexpected newly generated particles were relatively unstable and tended to associate with those of the main population. The main particle population average diau eter, as a result, was larger than that expected amd the distribution deviated significantly from the desired monodispersity. 

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. 

Thus ag is the ratio of the diameter below which 84.1% of the particles lie to the median diameter and is termed the geometric standard deviation. A monodisperse aerosol population has og = 1. For any distribution, 67% of all particles lie in the range from Dpg/ag to DpgGg and 95% of all particles lie in the range from Dpg/o2g to Dpgo2g. 

Equation (12.135) suggests that the equilibration timescale will increase for larger aerosol particles and cleaner atmospheric conditions (lower mp). The timescale does not depend on the thermodynamic properties of A, as it is connected solely to the gas-phase diffusion of A molecules to a particle. The timescale in (12.135) varies from seconds to several hours as the particle radius increases from a few nanometers to several micrometers. We can extend the analysis from a monodisperse aerosol population to a population with a size distribution n(Rp). The rate of change for the bulk gas-phase concentration of A in that case is... 

Assuming for the time being that cloud droplets are stationary, then particles are captured by Brownian diffusion. The collection of particles by a falling drop will be discussed when we consider wet deposition in Chapter 20. The collection coefficient K Dp, x) can then be estimated by (12.57). Let us estimate this collection rate assuming that the cloud has a liquid water content of 0.5 g m and that all drops have diameters of 10 /im, resulting in a number concentration of Nj = 955 cm For such a monodisperse droplet population (15.95) simplifies to... 

An alternative route to particle arrangements beyond dense packings are binary supercrystals. Such structures contain two particle populations, each of which is monodispersed with a different mean particle size. Complex crystals can be formed from such mixtures by concurrent sedimentation [63,64], butthis process is slow and unreliable. Convective particle assembly that exploits convective forces and capillary interactions has been shown to yield large, ordered domains [65] (Figure 9.9). The small particles fill the interstices between the larger ones, with the detailed structure depending both on the particle size ratio Y = s/ t and the ratio of the particle concentrations. Local fluctuations in the concentration ratio lead to domains of different structure [66]. Mixtures with y > 0.3 do not assemble into binary crystals in... 

Size Distribution. Particle populations are rarely monodispersed. The polydispersity leads the material to depart from the behaviors described by the classical equations. Generally, at a given concentration of particles, the minimum interaction between them occurs for an optimum proportion of the small particles The small particles will either isolate or lubricate the larger ones, but a too high content of small particles can induce a flocculation which can entrap a part of the continuous phase and, consequently, increase the product viscosity by artificially increasing the volume fraction. Refer to Fig. 37. 

Particle Size Distribution Determination. To consider the full PSD, a population balance or age distribution analysis on particles must be employed. Table II gives a summary of recent work concerning the determination of PSD s in emulsion systems, using both the "monodispersed" approximation and the population balance approach. More details can be found in the literature sources cited in the Table. 

However, there are a number of difficulties associated with the synthesis of colloidal semiconductor particles. The preparation of stable, monodispersed, well-characterized populations of nanosized, colloidal semiconductor particles is experimentally demanding and intellectually challenging. Small and uniform particles are needed to diminish non-productive electron-hole recombinations the mean distance by which the charge carriers need to diffuse to reach the particle surface from which they are released is necessarily reduced in small particles. Monodispersity is a requirement for the observation of many of the spectroscopic and electro-optical manifestations of size quantization in semiconductor particles. Small semiconductor particles are difficult to maintain in solution in the absence of stabilizers flocculations and Ostwald ripening... 

We have shown that fractions collected from broad particle distributions can be reinjected into the sedimentation FFF device for a second run (18). The emerging peaks are relatively narrow, reflecting their small particle size range. Quite obviously, a reinjected fraction run in a carrier of a different density will emerge at a different volume because of the effect of Ap on retention parameter X (see Equation 3). The shift in retention volume (see next section) can be used to calculate the density of the particulate material exactly as outlined for monodisperse populations. 

The development here follows that of Lichti et af. (1980). By analogy with the MWD calculation for bulk and solution polymerizations presented earlier, the MWD formalism for monodisperse emulsion systems requires the evaluation of certain types of free-radical growth time distributions. Because of the variable nature of the reaction loci (depending on the state i), a separate growth time distribution is required for the population of particles in each state i. It is therefore convenient to define the distribution of singly distinguished latex particles in state i. denoted as the... 

A second class of methods for overcoming the closure problem is to make a functional assumption regarding the NDF. The simplest is to assume that the NDF is composed of a delta function centered on the mean value of ffie internal coordinate (e.g. mi/mo), or, in other words, assume that the population of particles is monodisperse. On resorting to this approach the missing moments can be readily calculated (e.g. mk = as illustrated... 

As an example, consider a monodisperse population of particles characterized by mass as internal coordinate and moments m = mjt(O) = 1 with k = 0,..., 2N 1. This population of particles is continuously fed to a system wherein particles undergo aggregation and symmetric binary breakage with constant kernels. The equations describing the evolution of the moments are... 

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