Average diameters

Equation (li ) can be used to calculate uncorrected diameter averages. For the number, surface, volume, specific surface, weight and turbidity diameter averages (their definitions have been stated elsewhere (11,12), the following relations can be derived ... 

Equation (16) can be used to generate the desired moments and hence the diameter averages as a function of retention volume. 

This information together with l(o,v) which represents the number of particles in the detector cell at retention volume v, leads to the evaluation of overall sample diameter averages. 

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

Row 1. Uncorrected diameter averaged from Mie theory (Equation 13). Row 2. Diameter averages in row 1 corrected using Rayleigh correction factors (Equation 15). 

When chromatogram heights beyond X and Y were set equal to zero, the path became A BCD. Along A B and CD the order of the diameter averages were generally completely reversed. This anomaly... 

Mixtures of Latex Particles. To further assess the success of the theory in calculating particle diameter averages, two binary mixtures were considered. Mixture 1 was a mixture of 183 and 85 nm particles in the wei t ratio 38.73/61.27, while mixt ire 2 was a mixture of 183 and 109 nm particles in the wei t ratio 51-05/ U8.95 Their chromatograms are shown in Figure 10. 

The diameter averages calculated from the mixt ire rule are given in Table VI. While the first row entries for each mixture are the true values, the values that would be obtained from the analysis of the bimodal chromatograms should be compared with the third row entries since these account not only for the less than satisfactory calculations for the 183 nm sample chromatogram, but also for the incomplete recovery of the l83 nm particles. 

Figure 9. Variation of diameter averages with retention volume...

Table VI. Diameter Averages Based on Mixt ire Rule ...

Row 2. Cadculated from diameter averages for each component as given by Mie Theory. For e.g. 

The diameter averages of the mixtures evaluated using Mie Theory are presented in Table VII. For each mixture they are computed for 0 values equal to those of individual components and their mean. The averages fortunately are not very sensitive to the values between those of individual components. Computed values with mean for each mixture compare very favourably with third row entries for each mixture in Table VI. Similar results were obtained when Raylei scattering was considered. 

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. 

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). 

Tube diameter Jet nozzle diameter Average particle size Cyclone efficiency... 

Commonly when a pharmaceutical industry purchases a new compression machine, a PQ is conducted. First, the company must select some of its well-known products and prepare them until the compression phase as usual. The product must be compressed by the new equipment using the same compression conditions, such as compression force and tablet output. The obtained tablets must meet all the specifications of that product. The parameters specified could be aspect, hardness, thickness, diameter, average mass and uniformity of mass, friability, and tablet output. If the tablets obtained comply with specifications, the compression machine is considered reliable to obtain a product with good quality and in a reproducible manner and the equipment is considered performance qualified. 

The energetics data are presented in terms of heat of adsorption as a function of average zeolite pore diameter. Average pore diameter is applicable to those zeolites with elliptical pore openings, and the pore dimensions employed are those usually used to characterize the zeolite. The heat of adsorption as a function of pore diameter was predicted to exhibit a maximum around 5 A for all the alkanes studied, as shown on Fig. 11. The optimum heat of adsorption of straight-chain alkanes appears to be achieved by a pore with dimensions close to that of the 10-ring channel in ferrierite. 

---