# Density and porosity - Analyses of powders

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## Chapter: Pharmaceutical Drugs and Dosage: Powders and granules

Density of powders and granules plays an important role in pharmaceutical processing.

Density and porosity - Analyses of powders

## Significance of density determination

Density of powders and granules plays an important role in pharmaceutical processing. For example, handling and processing of pharmaceutical powders often require mixing of the drug with excipients. The drug must be uniformly mixed for the dosage form to have a uniform amount of drug between different dosage units. Adequate flow of a powder and the uni-formity of mixing of two or more powders are significantly affected by powder density. Uniform mixing generally requires the powders to be of similar density. Mixing of powders whose particles have significantly dif-ferent density may not achieve uniform mixing.

## Defining powder density

Density of powders and granules is defined by their measurement technique and application to processing as follows:

·           Bulk density: BD represents the combined mass of many loosely packed particles of a powder sample divided by the total volume they occupy. This total volume reflects the interparticulate (void volume) and intraparticulate (porosity of the particle) volume occupied by air, in addition to the volume occupied by the solid component(s) of the particle. BD is important for material handling considerations because it directly measures the volume that a given mass of powder would occupy under undisturbed conditions.

·           Tapped density: Tapped density (TD) represents the settled or packed volume of a given mass of particles under well-defined rate and extent of agitation. For example, a measuring cylinder containing a given mass of powder can be manually or instrumentally tapped on a solid surface at a fixed rate and distance from surface, for a fixed number of taps, to cause the consolidation of the sample. TD is then deter-mined by dividing the combined mass of the consolidated sample by the total volume it occupies.

TD enables the determination of the extent of powder consolida-tion that may be expected under routine handling and equipment vibration conditions during pharmaceutical manufacturing. This is referred to as the compressibility index or Carr’s index (CI) of the powder. It is defined in terms of a powder BD and TD as

CI = (TDBD) / BD

Thus, CI represents the proportion of the bulk volume that gets con-solidated under vibrational and routine handling stress. In addition, a parameter that defines the ratio of consolidated to bulk volume, Hausner ratio (HR), is defined as:

HR = TD/BD

These ratios help compare the relative degree of consolidation and estimated flow characteristics of different powders.

·           True density: True density refers to the density of the solid phase of the particles. It excludes the volume contribution of both inter-and intraparticulate spaces. Therefore, true density of a powder is independent of powder porosity, compaction, and pretreatment of the sample. True density is important for understanding, for example, the solid fraction of a tablet—which represents the proportion of total volume that is occupied by the solid mass.

## Methods for quantifying powder density and porosity

The bulk and tapped powder densities are estimated using a simple volu-metric cylinder. The compendia, such as the United States Pharmacopeia (USP), have standardized the equipment and process for the measure-ment of bulk and tapped densities, and also for the pretreatment of the sample before loading in the measuring cylinder. This harmonization of testing procedure helps reduce variability due to material handling and other subjective parameters that may differ between personnel and laboratories.

True density of a powder can be determined by the following:

·           Volumetric measurement using Archimedes’ principle and Boyle’s law using an instrument called helium pycnometry.

This method is based on the penetration of an inert gas inside a chamber of known volume that contains the powder sample under constant temperature and pressure. Estimation of the actual amount of gas penetrated against that expected based on the ideal gas law, as mentioned in the following equation, allows the calculation of the vol-ume occupied by the solid mass and, thus, the determination of total porosity of the sample.

PV = nRT

where:

P is the pressure

V is the volume

n is the mole of gas

R is the gas constant

T is the temperature

The powder sample is placed inside a chamber of defined volume, which is then filled and emptied with a defined volume of an inert gas, such as helium. The pressures observed during the filling and empty-ing of the sample chamber with the inert gas allow the computation of solid phase volume of the sample.

These calculations are based on the Archimedes’ principle that fluid displacement by the solid phase of the particles is proportional to the volume of the solid phase. Boyle’s law describing the inverse proportionality of pressure and volume of a gas at a constant tem-perature allows the determination of volume occupied by the gas in the sample chamber as a function of its pressure.

This method is commonly used for true density determination of powders and granules.

Mass measurement using Washburn equation (mercury intrusion porosimetry).

Total pore volume in a defined mass of powder can be estimated by the penetration of mercury, a nonwetting (high contact angle) liquid, inside the sample under externally applied pressure.

In this technique, the sample is placed in a sealed chamber of known volume. Mercury is filled in the chamber under vacuum to occupy all interparticulate spaces (easily accessible, around the sample). This is followed by forced ingress of mercury inside the pores of the particles by application of external pressure. Total amount of mercury penetrated inside the pores is determined as a function of pressure. Washburn equation, describing the capillary penetration of a liquid as a function of its viscosity and surface ten-sion, is used to estimate pore diameter at the pressures used. A plot of pressure applied against volume of mercury penetrated into the sample allows the calculation of pore volume or size as a function of the penetrated volume—which allows the calculation of not only total penetrable porosity but also the porosity as a function of pore diameter.

Mercury intrusion porosimetry is commonly used for the compari-son of granule porosity among different samples because it represents the fluid-penetrable portion of the total porosity.

## Changing powder density and porosity

Control of particle density is important to ensure uniformity of mixing of two or more powders. Powders with significant differences in particle density tend to segregate during processing. In addition, particle density influences powder flow. Changing powder’s bulk or TD is frequently required to achieve desired flow properties. For example, a very low-density powder may not flow well. Particle density can be changed during several pharmaceutical unit operations.

The true density and porosity of particles are determined by the intrinsic or inherent characteristics of a material, which can be influenced by the material’s manufacturing process. For example, the crystalline polymorphic form of the API determines the closeness of molecular packing and the size of the cell in the crystal lattice, which impacts particle density. In the case of excipients, different density grades are sometimes available commercially. For example, Avicel PH 101 (FMC Corp.) and Avicel PH 301 have the same PSD but significantly different particle density. Particle density can be changed by changes in the manufacturing process, such as spray drying ver-sus drum drying for the preparation of raw materials, the amount of water and shear used during wet granulation, or the pressure applied on the rolls during roller compaction. Granulation techniques such as roller compaction or wet granulation lead to shear-induced consolidation of particles, in addi-tion to the binding and agglomeration of fine particulates.

High compressibility index (CI) or HR of a powder can also lead to flow problems, attributable to the consolidation and densification of powder bed in a localized region of the processing equipment such as the outlet nozzle of a hopper. This issue can be addressed by reducing the TD of the powder. The consolidation characteristics, and hence the TD, of a powder bed mainly depend on the PSD of the powder. Therefore, reducing the spread of the PSD by granulation and reduction of fines can reduce the CI or HR of a powder.

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