Hatch-Choate conversion

As can be seen in Fig. 3b, it is important to specify whether data are represented as a number distribution (obtained by a counting technique such as microscopy) or as a weight distribution (obtained by methods such as sieving), since the results will not be the same. Hatch and Choate [4] have developed equations for converting one type of diameter to another the relationships between them are summarized in Table 2. Note that caution should be exercised in using the Hatch-Choate conversions if the distributions do not closely fit the log-normal model. While this distribution is the most frequently used to describe pharmaceutical systems, other distribution functions have also been developed [2,5,6],... 

Special attention must be paid to the interpretation of particle size data presented in terms of either weight or number of particles. Particle weight data may be more useful in sedimentation studies, whereas number data are of particular value in surface-related phenomena such as dissolution. Values on the basis of number can be collected by a counting technique such as microscopy, while values based on weight are usually obtained by sedimentation or sieving methods. Conversion of the estimates from a number distribution to a weight distribution, or vice versa, is also possible using adequate mathematical approaches, e.g., the Hatch-Choate equations. 

Table 2 Hatch-Choate Equations for Conversion of Diameters...

In its original form the Hatch-Choate equation for conversion of number to mass is given by... 

In practice, when one measures the size distributions of aerosols using techniques discussed in Chapter 11, one normally measures one parameter, for example, number or mass, as a function of size. For example, impactor data usually give the mass of particles by size interval. From such data, one can obtain the geometric mass mean diameter (which applies only to the mass distribution), and crg, which, as discussed, is the same for all types of log-normal distributions for this one sample. Given the geometric mass mean diameter (/) ,) in this case and crg, an important question is whether the other types of mean diameters (i.e., number, surface, and volume) can be determined from these data or if separate experimental measurements are required. The answer is that these other types of mean diameters can indeed be calculated for smooth spheres whose density is independent of diameter. The conversions are carried out using equations developed for fine-particle technology in 1929 by Hatch and Choate. 

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