A density can be related to each volume by dividing the mass by the particle volume. It is clear that for a given particle the envelope density is smaller than the apparent density which is smaller than the true density. Only the apparent density can be considered in view of the volume based overload concept. Which one is of more relevance depends on the wettability of the particle when engulfed by the macrophage fluid. However, for particles in the micron and submicron size range it is reasonable to assume that the envelope volume represents the displacement volume in the macrophage fluid. For these small particles the dimensions of the external voids are in the nanometre range and unlikely to be filled with macrophage fluid. For the definitions of density, see Fig. 2.1., which describes the corresponding definitions of the particle volume.
Among others, pycnometric methods where helium (gas) or a non-wetting liquid such as mercury (liquid) fills the pores are usually employed to measure porosity and hence the density of the material in powder form. The mercury intrusion method allows the determination of the distribution of the pore volume by variation of the pressure imposed on the mercury. The method is applied to an assemblage of (porous) particles in a container. At the low end of the pressure ramp the interparticle voids are filled with mercury. The envelope density is obtained in this pressure regime whereas the apparent powder density is usually calculated from the pycnometer value obtained at the highest pressure value because then even the smallest externally accessible pores are expected to be filled with mercury.
Recently, methods have become available that allow for the determination of the envelope density of individual particles when they are in the airborne state (Park et al, 2004, Liu, et al, 2012). These methods are based on the determination of the mass and the envelope volume of the individual particles using a combination of two well-known aerosol instruments: an electrical differential mobility analyser and a particle mass monitor. In-situ determination of the aerosol surface area can be facilitated by diffusion charging and gas absorption, for example. Gas absorption using the BET method is made on samples of powders as produced. In a recent study, Lebouf et al (2011) refined the BET method (using krypton instead of nitrogen as the absorbing gas) so that it could be employed to filter samples of material taken after aerosolization i.e. delivering a value of the specific surface area of the aerosol as delivered to the animal.