Diameter, average particle measurements

Avera.ge Particle Size. Average particle size refers to a statistical diameter, the value of which depends to a certain extent on the method of deterniiaation. The average particle size can be calculated from the particle-size distribution (see Size measurement of particles). 

Following the completion of the sintering study, a study was conducted to demonstrate that 663 K, the temperature at which all magnetic susceptibility measurements were taken, was indeed greater than Tq, . As discussed in the theory section, measurements were made at several temperatures until it was determined that plots of M/Mg versus H/T collapsed onto a single curve. It is clear from Figure 4 that Tqj, must be less than 450 K. That is, for any temperature above 450 K the average particle size was measured to be nearly 200 A in diameter. For smaller particles, Tq, will of course be an even lower temperature. This proves that all measurements made at 663 K were indeed accurate. 

Table III. Diameter Averages for Latex Particles Measured at...

The particle size analysis techniques outlined earlier show promise in the measurement of polydispersed particle suspensions. The asumption of Gaussian instrumental spreading function is valid except when the chromatograms of standard latices are appreciably skewed. Calc ll.ation of diameter averages indicate a fair degree of insensitivity to the value of the extinction coefficient. 

The unprotected Pt, Rh and Ru nanoclusters prepared according to the alkaline EG synthesis method in EG with metal concentrations of 0.3-3.7g/l have small average particle sizes of l.l-1.3nm and narrow size distributions from 0.7 to 2.2nm, as measured by TEM (Figure 1 and Table 1) [11]. The Os nanoclusters (3.7 g/1) prepared by this method have an average diameter of 0.9 nm and a size distribution of 0.6-1.8nm (Figure 2) [12]. 

On-line State Estimation. Optimal Sensor Selection and Control. Realistically, it is very difficult to have on-line measurements of all the major polymer or latex properties of interest, but perhaps one could rely upon one or two of the sensors available for the on-line measurement of a few states (e.g. conversion). In order to estimate some of the other states (e.g. particle diameter averages), Kalman filters or Observers should be used. A number of papers have investigated these state estimation schemes (58,6 , 67). 

Liegeois (71), using 400.0 ml of water, 280.0 gr of VCM, 280.0 mgr of potassium persulphate initiator and 2.5 gr of sodium lauryl sulphate emulsifier at 50°C, measured by electron microscopy PVC latex particle diameters close to 190 A for a conversion level of 24%. The model predicted an average particle diameter equal to 200 A for the same conversion level and for the same experimental conditions. 

Solids Circulation Rate. The solids circulation rate was obtained from the particle velocity measurements at the downcomer side by following visually the tracer particles at the wall with a stop watch. The data reported here by Yang and Keaims (1983) are for polyethylene beads (907 kg/m in density and 2800 pm in average particle size) and hollow epoxy spheres (210 kg/cm3 in density and 2800 pm in average particle size). The experiments were carried out in a semicircular transparent Plexiglas apparatus, 28.6 cm in diameter and 610 cm in height. 

Experimental results for particles in the millimeter range are shown in Fig. 12 in terms of unitary heat transfer height z/TV for different average particle diameters for both empty columns and columns with internal baffles. The various data give a range ofNH values between 2 and 7 for the 7.2-m experimental apparatus, corresponding to particle-to-gas heat transfer coefficients between 300 and 1,000 kcal/irf hr °C. The measured pressure drops for the two columns were of the order of 10 mm water gage. 

The surface area of powders is determined by subsieve-sizer which is designed for measurement of average particle sizes in the range of 0.2 to 50 microns. The relationship between average particle diameter and specific surface area (SSA) is given by the following expression ... 

To test the applicability of statistical techniques for determination of the species contributions to the scattering coefficient, a one-year study was conducted in 1979 at China Lake, California. Filter samples of aerosol particles smaller than 2 ym aerodynamic diameter were analyzed for total fine mass, major chemical species, and the time average particle absorption coefficient, bg. At the same time and location, bgp was measured with a sensitive nephelometer. A total of 61 samples were analyzed. Multiple regression analysis was applied to the average particle scattering coefficient and mass concentrations for each filter sample to estimate aj and each species contribution to light scattering, bgn-j. Supplementary measurements of the chemical-size distribution were used for theoretical estimates of each b pj as a test of the effectiveness of the statistical approach. 

As described in Appendix C, if we have a discrete set of measurements of a quantity such as the diameters of particles, one can represent the results in terms of a few useful quantities like the average diameter and standard deviation. Table 1.5 represents the frequency distribution for a hypothetical array of spheres all the numerical examples of this section are based on this sample of 400 particles. The particles have been sorted into categories called classes with a narrower range of dimensions. Each class is represented by the midpoint of the interval, a quantity called the class mark, symbolized by d, for class i. Similarly, we define the number of particles in each class as nr... 

Total partial pressure range (sum of the partial pressures of aU three MoOs vapor polymers) covered in these measurements is from about 9 X 10 to 4 X 10 s atm. Average particle diameters were 0.22 0.02 cm. Rates of uptake on the clay loam particles are shown at 0,10, and SO minutes. Dashed line indicates the rate of uptake calculated by Maxwell s equation... 

Example. Consider a sample of solid particles for which the average particle size is unknown. The particle density is known (2 g/cm3 at 20 °C) and a sedimentation column (see Figure 2.10) is filled with the solids suspended in water. Measurements indicate a terminal velocity of 0.013 cm/minute. What is the average particle diameter ... 

Figure 4. Average particle diameter as a function of nominal thickness, as determined from TEM and magnetic measurements. Included are closed shell clusters for comparison purpose, (x) TEM results, (other symbols) Magnetic measurements.

As stated previously, additional information on the sample is obtainable from band broadening (plate height) measurements. If plate height is measured as a function of flow velocity at a fixed retention level, a linear relationship is obtained, as predicted by Equation 7. The slope of the line yields the diffusivity D of the sample, and the intercept provides the polydispersity a. . The D value translates into a value for the average particle diameter d via the Stokes-Einstein relationship... 

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