Particle radius distribution

Figure 3. A typical imaae analysis output, (a) Particle radius distribution, (b) Particle area distribution.

Au particles generated with H2S gas showed very narrow particle radius distribution, which was dispersed in die film homogeneously. The particle diameter was about 3 nm, much smaller than that prepared by thermal decomposition. Only a very weak plasmon resonant absorption was observ for the H2S treated Au... 

FIGURE 3.2 A high-resolution TEM, obtained from image analysis of weU-dispersed Pt nanoparticles. They are deposited on a high-surface-area carbon support, together with the normalized particle radius distribution of Pt. 

Site occupation probability in percolation theory (dimensionless) Percolation threshold of site occupation probability (dimensionless) Pdclet number. Equation 1.30 Particle radius distribution function Capillary pressure (Pa)... 

FIG. 22-40 Normalized free-energy difference between distributed (II) and nondistributed (I) states of tbe solid particles versus tbree-pbase contact angle (collection at tbe interface is not considered). A negative free-energy difference implies tbat tbe distributed state is preferred over tbe nondistributed state. Note especially tbe significant effect of n, tbe ratio of tbe liquid droplet to solid-particle radius. [From Jacques, Ho-oaron ura, and Hemy, Am. Inst. Cbem. Eng. J., 25 1), 160 (1979).]... 

In the total particle size distribution, some particles of small diameter decrease in radius, and those in the larger diameter range increase in radius during Ostwald ripening. There will therefore be a radius at which particles neither decrease nor grow in size and if [Pg.210]

The particle size distribution is determined from the diffraction pattern. For a simplified case of monosized spherical particles, for instance, the radius... 

Anderson (A2) has derived a formula relating the bubble-radius probability density function (B3) to the contact-time density function on the assumption that the bubble-rise velocity is independent of position. Bankoff (B3) has developed bubble-radius distribution functions that relate the contacttime density function to the radial and axial positions of bubbles as obtained from resistivity-probe measurements. Soo (S10) has recently considered a particle-size distribution function for solid particles in a free stream ... 

In their study of the effect of particle-size distribution on mass-transfer in dispersions, Gal-Or and Hoelscher (G5) show that when the variable particle size is replaced by the surface mean radius a32, the error introduced is usually very small (see Section IV, J). Consequently if a in Eq. (144) is replaced by a32, that equation can be compared with the experimental correlations [Eq. (10) and (11)] proposed by Calderbank and Moo-Young (C4) for mass transfer in dispersions (see Fig. 9). 

Mcllvried and Massoth [484] applied essentially the same approach as Hutchinson et al. [483] to both the contracting volume and diffusion-controlled models with normal and log—normal particle size distributions. They produced generalized plots of a against reduced time r (defined by t = kt/p) for various values of the standard deviation of the distribution, a (log—normal distribution) or the dispersion ratio, a/p (normal distribution with mean particle radius, p). 

Routh and Russel [10] proposed a dimensionless Peclet number to gauge the balance between the two dominant processes controlling the uniformity of drying of a colloidal dispersion layer evaporation of solvent from the air interface, which serves to concentrate particles at the surface, and particle diffusion which serves to equilibrate the concentration across the depth of the layer. The Peclet number, Pe is defined for a film of initial thickness H with an evaporation rate E (units of velocity) as HE/D0, where D0 = kBT/6jT ir- the Stokes-Einstein diffusion coefficient for the particles in the colloid. Here, r is the particle radius, p is the viscosity of the continuous phase, T is the absolute temperature and kB is the Boltzmann constant. When Pe 1, evaporation dominates and particles concentrate near the surface and a skin forms, Figure 2.3.5, lower left. Conversely, when Pe l, diffusion dominates and a more uniform distribution of particles is expected, Figure 2.3.5, upper left. 

In contrast, the hydrodynamic radius distribution recorded for aqueous solutions of copolymers with a low grafting density is bimodal, with a contribution from small entities of = 5-30 nm, assigned to single polymer chains, and a contribution from larger particles of = 80 = 150 nm (Fig. 24b, c). The relative importance of the two populations depends on copolymer concentration the relative amount of the larger particles increases with increasing copolymer concentration. 

Any fundamental study of the rheology of concentrated suspensions necessitates the use of simple systems of well-defined geometry and where the surface characteristics of the particles are well established. For that purpose well-characterized polymer particles of narrow size distribution are used in aqueous or non-aqueous systems. For interpretation of the rheological results, the inter-particle pair-potential must be well-defined and theories must be available for its calculation. The simplest system to consider is that where the pair potential may be represented by a hard sphere model. This, for example, is the case for polystyrene latex dispersions in organic solvents such as benzyl alcohol or cresol, whereby electrostatic interactions are well screened (1). Concentrated dispersions in non-polar media in which the particles are stabilized by a "built-in" stabilizer layer, may also be used, since the pair-potential can be represented by a hard-sphere interaction, where the hard sphere radius is given by the particles radius plus the adsorbed layer thickness. Systems of this type have been recently studied by Croucher and coworkers. (10,11) and Strivens (12). 

In these cases, the values of w are used as a probing measure, and vsR2 for the spherical molecules radius of R. As a result, nm -R D2. The second method by Pfeifer and Anvir is symmetric to the first one in the sense that instead of adsorbing a set of molecules on samples with a constant particle size distribution, one adsorbs a single adsorbate (e g., N2) on a set of samples with variable particles sizes, Ra. The corresponding equations for this method are... 

An increase of the particle radius is observed at 25 C (the smaller one in the case of a two exponentials fit) as the starting concentration is increased. Furthermore, for Cq = 1.2 and 1.6 a second species of particles appears with a radius about twice larger. These two kinds of particles seem to coexist with no change of size distribution as the temperature is increased from 25to for a starting concentration of 1.6 %, Yet, at 60°C, only the smaller particle species remain in solution. 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Light scattering Modem laser light scattering instruments are very advanced devices for particle size distribution analyses. The laser light is scattered by the small dispersed particles or drops. The latter is known to be dependent on the radius of the particle. 

Colloidal CdS particles 2-7 nm in diameter exhibit a blue shift in their absorption and luminescence characteristics due to quantum confinement effects [45,46]. It is known that particle size has a pronounced effect on semiconductor spectral properties when their size becomes comparable with that of an exciton. This so called quantum size effect occurs when R < as (R = particle radius, ub = Bohr radius see Chapter 4, coinciding with a gradual change in the energy bands of a semiconductor into a set of discrete electronic levels. The observation of a discrete excitonic transition in the absorption and luminescence spectra of such particles, so called Q-particles, requires samples of very narrow size distribution and well-defined crystal structure [47,48]. Semiconductor nanocrystals, or... 

For the other extreme of the free molecular regime where Kn - oc, the particle radius is small compared to the mean free path. In this case, the thermal velocity distribution of the gas is not distorted by uptake at the surface. In effect, the gas molecules do not see the small particles. For this case, Fuchs and Sutugin (1970, 1971) show that for diffusion to a spherical particle of radius a... 

A conveniendy expressed coordinate for plotting filtration performance is the drainage number, d(G )1//2 /V, where d is the mean particle diameter in micrometers, V is the kinematic viscosity of the mother liquor in m2/s (Stokes x 10-4) at the drainage temperature, and G is (02r/g r is the largest screen radius in a conical bowl. Because the final moisture content of a cake is closely related to the finest 10—15% fraction of the solids and is almost independent of the coarser material, it is suggested that d be used at the 15% cumulative weight level of the particle size distribution instead of the usual 50% point. 

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