Micromeretics and powder rheology: Derived properties of Powders – Packing arrangement, Porosity and MCQs for GPAT, NIPER, Pharmacist and Drug Inspector Exam

DERIVED PROPERTIES OF POWDERS: There are numerous derived properties that are based on fundamental properties. Those with particular relevance to pharmacy are discussed here.

1. Packing geometry
2. Porosity
3. Density
4. Bulkiness
5. Flow property

Packing Geometry: A set of particles can be filled into a volume of space to produce a powder bed, which is in static equilibrium owing to the interaction of gravitational and adhesive/cohesive forces. By slight vibration of the bed, particles can be mobilized, and at static equilibrium, they occupy a different spatial volume than before. The change in bulk volume has been produced by rearranging the packing geometry of the particles. In general, such geometric rearrangements result in a transition from loosely packed particles to more tightly packed ones. A set of uniform-sized spherical particles can be arranged in many different geometric configurations; however, the two extreme packing arrangements are as follows:

Cubic arrangement—particles are most loosely packed and have a porosity of 48%.

Rhombohedral arrangement—particles are most densely packed and have a porosity of only 26%.

• It is to be expected that the particles of ordinary powders may have any porosity intermediate between the two extreme packing arrangements, 26–48%.
• Porosities below the theoretical minimum of 26% are possible in a powder bed with wide size range particles wherein the void spaces between coarse particles may become filled with finer particles.
• Porosities above the theoretical maximum of 48% are possible, if the particles are irregularly shaped and highly textured. Such particles arch or bridge within the powder bed through interlocking.
• Tightly packed particles require a higher driving force to produce powder flow than loosely packed particles of the same powder due to increase in cohesion between the particles.
• The porosity used to characterize packing geometry is linked to the bulk density of the powder.

Porosity (E): Porosity is a measure of the air spaces or voids in a material. In a powder bed, three types of air spaces or voids can be distinguished.

1. Open intraparticulate voids: Those within a single particle but open to the external environment.
2. Closed intraparticulate voids: Those within a single particle but closed to the external environment.
3. Interparticulate voids: The air spaces between individual particles.

Based on the types of voids, three interpretations of powder volume are proposed as shown below:

Note: M is the mass and Ub, Ug and Ut are bulk, granular and true density, respectively.

Table 1 – Three interpretations of powder volume based on the types of voids

The ratio of the total volume of void spaces (Vv) to the bulk volume of the material is often selected to monitor the progress of compression. This ratio Vv/Vb is referred to as the porosity of the material:

V_v = V_b – V_t

Therefore porosity is:

E = V_b – V_t / V_b = 1- V_t / V_b

Porosity is frequently expressed as a percentage:

E = 100 [1- V_t / V_b]

Multiple choice questions (MCQs)

1.___ equation can be used to convert number distribution to weight distributions with minimum calculation

a)Hatch Choate

b)Einstein

c)Faraday

d)Newton

2.Optical microscopy is used for determination of particle size in the range of

a)0.2 – 100µm

b)0.02-10µm

c)0.002-100µm

d)0.0002-100µm

3.____ is used for the determination of particle size distribution

a)Oven

b)Melting point apparatus

c)Potentiometer

d)Andreason apparatus

4.____ of the powder is defined as the surface area per unit volume or per unit weight

a)Angle of repose

b)Bulk density

c)True density

d)Specific surface

5.____ is not the method of adsorption for determination of surface area

a)By using a solute which forms monolayer

b)By using adsorption of gas on powder

c)Microscopy

d)Air permeability method

6.For a non porous material, bulk volume is equal to

a)Thickness

b)True volume

c)Diameter

d)Friability

7.For a porous material _____ is not equal to true volume

a)Thickness

b)Density

c)Bulk volume

d)Number

8.____ is defined as the ratio of mass of a powder and its true volume

a)True volume

b)Density

c)Bulk volume

d)Weight

9.Porous materials have internal pores or capillary spaces which are known as

a)True volume

b)Density

c)Bulk volume

d)Voids

10.____ is not the type of packing of particles

a)Closest

b)Loosest

c)Rhombohedral

d)Triangular

11.The fraction of total volume occupied by the free space between the particles is called as

a)Volume

b)Porosity

c)Tortuosity

d)Density

12.____ is not the type of density

a)True

b)Bulk

c)Granule

d)Volume

13.______ density is the density of the actual solid material devoid of free spaces

a)True

b)Bulk

c)Granule

d)Liquid

14.____ density is defined as the ratio of the given mass of a powder and its bulk volume

a)True

b)Bulk

c)Granule

d)Liquid

15.____ density is defined as the ratio of the given mass of a powder and its true volume

a)True

b)Bulk

c)Granule

d)Liquid

Solutions:

1. a)Hatch Choate
2. a) 2 – 100µm
3. d) Andreason apparatus
4. d) Specific surface
5. c) Microscopy
6. b) True volume
7. c) Bulk volume
8. b)Density
9. d) Voids
10. c) Rhombohedral
11. b) Porosity
12. d) Volume
13. a) True
14. b) Bulk
15. a) True

References:

1. GAURAV KUMAR JAIN – THEORY & PRACTICE OF PHYSICAL PHARMACY, 1st edition 2012 Elsevier, page no. 48-50.

2. Martins Physical Pharmacy, 6th edition 2011, page no. 834-835.

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