Micromeretics and powder rheology: Particle size and distribution and MCQs for GPAT, NIPER, Pharmacist and Drug Inspector exam
Micromeritics is the science and technology of small particles and includes the study of the fundamental and derived properties of individual as well as a collection of particles. The micromeritic properties of a drug can be related in a significant way to the physical, chemical and pharmacological properties of a drug.
FUNDAMENTAL PROPERTIES OF PARTICLES
The following are the five fundamental properties of powders from which other properties can be derived:
- Particle size and size distribution
- Particle volume
- Particle number
- Particle shape
- Particle surface area
Particle Size and Size Distribution-
Spherical or symmetrical particle: The size of a spherical particle can be expressed in terms of its diameter. The surface area is proportional to the square of the diameter, and the volume is proportional to the cube of the diameter. Thus, for a perfect sphere, the surface area is given by
S = πd^{2} (1)
And the volume is given by
V = πd^{3} / 6 (2)
As the volume of a sphere is πd3/6, the diameter of a spherical particle with a volume V is given by
d = 3√ 6V / π (3)
Nonspherical or asymmetrical particle: In naturally occurring particulate solids and milled solids, the shape of particles is irregular with different numbers of faces. An asymmetric particle has a definite surface area and volume, but its length varies with its orientation. As the degree of asymmetry increases, so does the difficulty of expressing size in terms of meaningful diameter. Hence, an asymmetric or a nonspherical particle is often considered to be approximate to a sphere that can then be characterized by determining its diameter. Because measurement is then based on a hypothetical sphere, which represents only an approximation to the true shape of the particle, the dimension is referred to as the equivalent spherical diameter of the particle. The size of the particle is expressed in terms of equivalent spherical diameters by using some measurable properties such as surface area, volume, diameter or density. Thus,
- Surface diameter, ds, is the diameter of a sphere having the same surface area as that of the asymmetric particle in question.
- Volume diameter, dv, is the diameter of a sphere having the same volume as the asymmetric particle in question.
- Projected diameter, dp, is the diameter of a sphere having the same observed area as the asymmetric particle in question when viewed normal to its most stable plain. This diameter is usually determined by the microscopic technique.
- Stokes’ diameter, dst, is the diameter of a sphere with the same density as the asymmetric particle in question and which undergoes sedimentation as the same rate as the asymmetric particle in a given fluid within the range of Stokes’ law. This diameter is usually measured by the sedimentation method.
The other two diameters, the values of which are dependent on both the orientation and the shape of the particles, are Feret’s diameter and Martin’s diameter.
- Feret’s diameter is the mean distance between two tangents on the opposite sides of the particle parallel to some fixed direction.
- Martin’s diameter is the length of the line that bisects the particle. The line may be drawn in any direction but must be in the same direction for all the particles measured.
Fig 1 – Equivalent diameters of asymmetric particle (taken from micromeretics.pdf page 1)
Particle size distribution: A particle population that consists of spheres or equivalent spheres with uniform dimensions is monosized and its characteristics can be described by a single diameter or an equivalent diameter. However, most pharmaceutical powders are polydisperse (i.e. consists of a mixture of particles of varying sizes and shapes). Therefore, it is necessary to know not only the size of particle in the sample but also the number of particles of each size present in the sample. This is called the particle size distribution.
Table 1 – Particle size distribution data obtained by particle size analysis
Particle size range (µm) | Mean particle diameter d (µm) | Frequency n (no. of particles in each
diameter) |
Frequency (%) | nd |
10–30 | 20 | 100 | 4.5 | 2000 |
30–50 | 40 | 200 | 9.1 | 8000 |
50–70 | 60 | 400 | 18.2 | 24,000 |
70–90 | 80 | 800 | 36.4 | 64,000 |
90–110 | 100 | 400 | 18.2 | 40,000 |
110–130 | 120 | 200 | 9.1 | 24,000 |
130–150 | 140 | 100 | 4.5 | 14,000 |
Ɛn = 2200 | Ɛnd = 17,600 |
Multiple choice questions (MCQs)
1.One micrometer is equal to
a)10^{-6} cm
b)10^{-3 }cm
c)10^{-6} m
d)10^{-3 }m
2.Which of the following properties of a particle significantly affects the physical, chemical and biological properties of the drug?
a)Density
b)Sedimentation
c)Size
d)Surface area
3.It is difficult to express the size of particle in a meaningful diameter
a)Irregular in shape
b)Irregular surface
c)Spherical shape
d)Uniform in size
4.The type of particle diameter obtained largely depends on
a)Method by which it is determined
b)Nature of the powder
c)Procedure by which it is calculated
d)Way it is defined and described
5.When cumulative percent frequency on a probability scale is plotted against logarithm of the particle size, 50 percent on the probability scale gives the powder particle diameter of
a)Arithmetic mean
b)Arithmetic mode
c)Geometric mean
d)Harmonic mean
6.Which one of these distributions is more important in the design of dosage forms?
a)Gaussian
b)Normal
c)Number
d)Weight
7.In the formulation development of emulsion and suspensions, what type of diameter is important?
a)Length number
b)Projected
c)Sieve
d)Stokes
8.Sieving method is used for size distribution analysis of powder. The disadvantage of this method is:
a)Agglomerates can be identified
b)Attrition of powder is possible
c)Large number of sieves are required
d)Tedious and time consuming
9.While using sedimentation method for size analysis, addition of a deflocculating agent to a suspension is necessary in order to
a)Accelerate the process of sedimentation
b)Make the particles spherical
c)Prevent the aggregation
d)Satisfy Reynolds number
10.Stoke’s law cannot be used, if Reynolds number is more than
a).2
b)1.8
c)9.0
d)18.0
11.Andreasen apparatus consist of
a)Balance
b)Electrodes
c)Hydrometer
d)Pipette
12.When coulter-counter apparatus is employed for powder analysis, the following criteria is important
a)Dispersion medium should be colored
b)Dispersion medium should be conducting
c)Suspended particles should be charged
d)Suspended particles should be suspended
13.In coulter-counter, as the particles move through the orifice, the event that occurs is
a)Conductance between the electrodes increases
b)Electronic scanners produce photographs for volume measurement
c)Resistance between the electrodes increases
d)Sedimentation increases
14.Fisher subsieve sizer is used to determine the surface area of the powder. The surface area is measured based on the change in
a)Light transmission of gas that reaches the detector
b)Pressure across the compacted powder
c)Thermal conductivity of gas across the powdered pack
d)Weight of powder when air is passed through the powdered pack
15.High repose angle of the granules indicated
a)Bulk density of the granules
b)Porosity of the granules
c)Roughness of the granule surface
d)Smoothness of the granule surface
Solutions:
- c) 10^{-6} m
- d) Surface area
- a) Irregular in shape
- a) Method by which it is determined
- c) Geometric mean
- d) Weight
- d) Stokes
- b) Attrition of powder is possible
- c) Prevent the aggregation
- a) 0.2
- c) Hydrometer
- b) Dispersion medium should be conducting
- c) Resistance between the electrodes increases
- d) Weight of powder when air is passed through the powdered pack
- c) Roughness of the granule surface
References:
1. GAURAV KUMAR JAIN – THEORY & PRACTICE OF PHYSICAL PHARMACY, 1st edition 2012 Elsevier, page no. 24-27.
2. Martins Physical Pharmacy, 6th edition 2011, page no. 800-802.
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