Pharmaceutics II – Micrometrics
1.
Definition
2. Particle Size
2.1 Overview
2.2 Statistical Diameters
3.
4.
5.
Particle Size Distribution
Comparing Different Distributions
Particle Shape and Surface Area
6.
6.1
6.2
6.3
6.4
Particle Size Analysis
Microscopy
Sieving
Sedimentation
Coulter Counter
Dr M. Skinner
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Pharmaceutics II – Micrometrics
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DEFINITION
Micrometrics is the science and technology of small particles.
Examples of Particle Size in Pharmaceutical Disperse Systems
μm
mm
0.5 – 10
0.0005 – 0.010 Suspensions, fine emulsions
10 – 50
0.010 – 0.050
Coarse emul., flocculated, suspensions
50 – 100
0.050 – 0.100
Fine powder range
150 – 1000
0.150 – 1.000
Coarse powder range
1000 – 3360 1.000 – 3.360
Average granule size
•
Knowledge and control of the size and size range of particles is of
profound importance in pharmacy.
•
Size and surface area can be related in a significant way to the physical,
chemical and pharmacologic properties of a drug.
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Pharmaceutics II – Micrometrics
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IMPORTANCE IN FORMULATION AND PRODUCTION
•
Suspensions - stability and rheological properties depend on particle size.
•
Mixtures of powders - individual components should be roughly same size
for ease of mixing otherwise de-mixing or segregation will occur.
•
Powders of different sizes have different flows and packing properties which
alter the volume of powder during each encapsulation or tablet compression
event resulting in fluctuation in content of product. Direct Compression.
•
Granule size - used in tables and capsules must be controlled - for good flow
properties & inter-batch uniformity. Granulation to reduce settling etc.
•
Filtration during manufacture - if a solid is to be separated from a fluid, it is
essential to know the size of particle to be removed. Selection of filter.
•
Mass Transfer – efficiency dependent on size and area. Dissolution.
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Pharmaceutics II – Micrometrics
2 PARTICLE SIZE
2.1 Overview
•
In a collection of particles of more than one size (polydisperse
samples) 2 aspects are important, viz:
•
shape of individual particles;
•
size range and number of particles and therefore the total surface
area – dependent on size distribution.
•
When a large solid is milled -
Dr M. Skinner
smaller fragments
fine particles
irregular
different numbers of faces
difficult to determine more than
one dimension.
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Pharmaceutics II – Micrometrics
•
The size of a sphere readily expressed in terms of its diameter but
•
As the degree of asymmetry increases expressing size in terms of a
meaningful diameter is difficult.
•
Under these conditions there is no one unique diameter for a
particle.
•
Resort to the equivalent spherical diameter
•
Relates the size of the particle to
the diameter of a sphere which has the same length
(diameter), surface area or volume.
•
Measurement based on a hypothetical sphere
Represents only an approximation of the true shape of the particle.
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Pharmaceutics II – Micrometrics
2.2 Statistical Diameters
•
Theoretical diameters which represent asymmetric particles as
symmetric particles.
dln -
length mean diameter
(length number)
dsn - surface mean diameter
(surface number)
dvn – volume mean diameter
(volume number)
dst – Stokes diameter
Median Diameter
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Pharmaceutics II – Micrometrics
•
dln - length mean diameter (length number)
-
•
The usual way to express a mean .
(measure the length of the particle).
Acceptable if the size range is narrow
and distribution is normal.
However these conditions are rarely
found in pharmaceutical powders.
dsn – surface mean diameter (surface number)
-
Diameter of a sphere having the same
surface area as the particle in question.
This is a function of the surface area of
the particles.
Size is expressed as the mean surface diameter.
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Pharmaceutics II – Micrometrics
•
dvn – volume mean diameter (volume number)
Diameter of a sphere having the same volume
as the particle in question.
The packing and flow of a powder or granule
depends on its volume.
If packing / filling etc is a prime consideration
this is useful.
•
dst – Stokes diameter.
Describes an equivalent sphere undergoing
sedimentation at the same rate as the
asymmetric particle.
Important in referring to the size of particles
in suspensions.
•
Median diameter.
-
-
The diameter for which 50% of the particles measured are less than
the stated size
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Pharmaceutics II – Micrometrics
Dr M. Skinner
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Pharmaceutics II – Micrometrics
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PARTICLE SIZE DISTRIBUTION
•
•
•
•
The frequency of distribution of particle sizes.
As important as the size itself.
Presented graphically.
Concise and allows easy visualization of the results.
•
•
Size distribution is broken down into different size ranges.
Present data in a histogram.
•
Plot the number (or weight) of particles lying within a certain size
range vs. the size range or mean particle size.
•
A frequency distribution curve is obtained
•
Can compare the characteristics of 2 or more powders.
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Pharmaceutics II – Micrometrics
Dr M. Skinner
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Pharmaceutics II – Micrometrics
•
Provides a visible representation of data that an average diameter
calculation cannot achieve.
•
Immediately apparent what particle size occurs most frequently.
e.g. Comparison of 2 samples with the same average diameter but different
distributions.
•
This is the mode and it separates a normal curve into 2 identical halves.
•
Normal distribution i.e. distribution is symmetric about the mean.
•
The standard deviation, σ , is an indication of distribution about the mean.
•
In a normal population:
68% lie ±1 σ from the mean
95.5 lie ±2 σ from the mean
99.7 lie ±3 σ from the mean
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Pharmaceutics II – Micrometrics
•
In pharmaceutical powders, a normal distribution is not commonly
found.
•
These systems tend to have an un-symmetric or skewed distribution.
•
When data are plotted as frequency versus the logarithm of the particle
diameter, a typical bell-shaped curve is frequently obtained.
A log-normal distribution.
•
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Pharmaceutics II – Micrometrics
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COMPARING DIFFERENT DISTRIBUTIONS
(a) Normal distribution where mean = mode.
(b) This frequency distribution curve has an elongated tail towards
higher size ranges - positively skewed.
(c) More than 1 mode can occur - bimodial frequency distribution.
- Milled powders - Coarser particles from the unmilled remain.
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Pharmaceutics II – Micrometrics
5
PARTICLE SHAPE AND SURFACE AREA
•
A knowledge of the shape and surface area of a particle is desirable.
•
Shape affects
•
Area is significant in mass transfer processes.
flow
packing properties
surface area.
•
Equation expressing mass transfer.
•
W = D A ( C1 - C2 ) t
L
•
Operations such as dissolution, evaporation, extraction and drying
will be influenced directly by particle size and area.
A = Surface Area
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Pharmaceutics II – Micrometrics
6
PARTICLE SIZE ANALYSIS
•
Various methods attempt to express the “size” of an irregular, 3D
particle.
•
Measurements must be carried out on a sample representative of
the whole.
•
Generally, it is not sufficient to remove a small amount from the top
of a container:
Segregation may have occurred during transport.
Preliminary mixing of contents.
One container may not be representative of the entire
batch.
•
Statistical sampling methods must be used to ensure a good
representation.
Dr M. Skinner
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Pharmaceutics II – Micrometrics
6.1 MICROSCOPY
•
•
An effective procedure
Only direct measurement method.
•
•
0.2 to 100 μm
0.01 μm and above
•
The technique involves:
- calibration of the microscope
- visual measurement of particle size
- sample as an emulsion or suspension, diluted or undiluted,
- mounted slide or ruled cell
- mechanical stage
- eyepiece is fitted with a micrometer
- by which the size of the particles may be estimated.
- also projected onto a screen, or a photograph can taken
- size determined therefrom.
ordinary microscope
electron microscope
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Pharmaceutics II – Micrometrics
Advantages and disadvantages
•
The only method which enables direct visualization of the particle.
•
Tedious and time-consuming method
A large number of measurements must be made.
Number of measurements must be large enough so that the result will not
change on continued measuring
Recommended number is at least 625
If the size distribution is large, this number may have to be increased.
•
Shape
- Particles measured along an arbitrarily chosen, fixed line, generally made
horizontally across the center of the particle.
- It is necessary to decide on one linear dimension to represent the
particle.
- e.g. consider a cylindrical particle. Which measurement should be used?
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Pharmaceutics II – Micrometrics
• Particle Position
- Using a microscope, we see a 2-D representation of a 3D object.
- A particle will assume the position of maximum stability on the
microscopic slide.
- A laminar particle will appear to be much larger than if it was measured
by a different method.
• Aggregation
- Aggregation on the slide will produce anomalous results as the
aggregate will be indistinguishable from a single particle.
• Sampling
- special sampling techniques must be used as only a relatively small
number of particles is measured. Like the counting and measuring
procedures, sampling techniques must be rigidly standardised.
Dr M. Skinner
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Pharmaceutics II – Micrometrics
6.2 SIEVING
•
•
•
Most simple method.
Inexpensive
Rapid
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Pharmaceutics II – Micrometrics
Dr M. Skinner
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Pharmaceutics II – Micrometrics
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The powder is passed over a perforated screen:
- Particles sufficiently small will pass through
- Oversize particles will be retained on the sieve
- Sieving is a “go/no go” test which divides the powder into 2
fractions above and below a specified size.
•
USP method for testing powder fineness – USP 32 <786> pg 307:
- Definite mass of sample is placed on the proper sieve in a
mechanical shaker.
- The powder is shaken for a definite period of time.
- Material that passes through one side and is retained on the next
finer sieve is collected and weighed.
Dr M. Skinner
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Pharmaceutics II – Micrometrics
•
When a detailed analysis is desired:
- Sieves may be arranged in a nest of about 5
- Coarsest sieve at the top.
- A weighed sample of the powder is placed on the top sieve.
- After the sieves are shaken for a predetermined period of time,
the powder retained on each sieve is weighed.
•
Results of sieve analysis:
- Best presented in the form of a cumulative oversize curve.
- A log-normal distribution is assumed.
- Cumulative % by weight of powder retained on the sieves is
plotted against the logarithm of the arithmetic mean size of 2
successive screens.
- This will be plotted on semi-log paper.
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Pharmaceutics II – Micrometrics
BP APPENDIX XV11
A. Particle Size of Powders
The degree of coarseness or fineness of a medicinal or pharmaceutical
substance in powder form is differentiated and expressed by reference
to the nominal mesh aperture size of the sieves used, or, where the use
of the sieves is inappropriate, it is expressed in terms of the particle size
as determined by suitable microscopic examination.
The following terms are used in the description of powders: e.g.
Coarse powder. A powder all the particles of which pass through a sieve with
a nominal mesh aperture of 1700 μm and not more than 40.0% by
weight pass through a sieve with a nominal mesh aperture of 355 μm.
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Pharmaceutics II – Micrometrics
To summarise the results (changes in current BP):
Sieve (μm) through which Sieve (μm) through which not
Grade of powder all particles must pass
more than 40% of particles pass
Coarse
1700
355
Moderately coarse
710
250
Moderately fine
355
180
Fine
180
125
Very fine
125
45
Microfine:
Not less than 90% by weight of the particles pass through a sieve of
45 μm
Superfine:
Not less than 90% by number of the particles are less than 10 μm in
size
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Pharmaceutics II – Micrometrics
•
When the fineness of a powder is described by a number, it is intended
that all particles of the powder shall pass through a sieve of which the
nominal mesh aperture, in μm, is equal to that number.
•
The limit for the 2nd sieve is to place a limit on “fines” in the coarser
grade of powders. The ideal, of course, is that none of the powder should
pass through the lower sieve.
•
No lower limit is placed on the microfine powder.
•
Superfine powders will be determined by microscopy.
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Pharmaceutics II – Micrometrics
•
•
Standards for sieves
-
As powders are standardized by sieves, the sieves themselves must
meet stringent specifications – ISO specificiations.
-
Wire mesh sieves are identified by numbers indicating the nominal
mesh aperture in micrometers.
-
This is the distance between the wires.
-
The sieves should be made of suitable materials with square meshes.
-
There must be no reaction between the material of the sieve and the
substance being sifted.
REFERENCE: Table in Appendix XVII of the BP
Dr M. Skinner
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Pharmaceutics II – Micrometrics
•
Problems using sieving
-
Although a simple technique, it is difficult to obtain accurate results
for a number of reasons.
-
Particle shape
-
Only spheres can pass through the sieve without having to assume a
specific orientation.
-
Therefore the further the particle departs from the spherical shape,
the greater the difficulty it will have in passing through the aperture.
-
Consider a cylindrical particle, lying lengthways will not pass through
the sieve, but if it was end on, it would be able to pass through.
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Pharmaceutics II – Micrometrics
From this we can conclude that a sieve will classify a particle as less than the
dimension of the mesh, provided that the particle is less than the mesh size
in one plane and that the sifting process is carried on for sufficient time for
the particle to become suitably orientated to the mesh opening.
•
Humidity
- Can affect particles of hygroscopic materials and lead to aggregation.
•
Aggregates
- Due to electrostatic charges, fine particles tend to form aggregates which
do not pass through the sieve.
•
Particle size distribution
- Particles that are well below mesh size will pass through early.
- Those that are ≥ 0.75 of mesh opening tend to form aggregates which block
the sieve.
- Similarly, particles up to 1.5 times the mesh size tend to block the sieve.
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Pharmaceutics II – Micrometrics
•
Technique and completion of sieving
- Disturbance of the bed of particles by shaking or vibration is necessary for
sieving to occur.
- Standardisation is necessary, especially with regard to the end-point, since
it is virtually impossible to sieve to completion.
- Some sort of end-pt must therefore be set such as a specified time.
•
Fines
- Prolonged sieving can lead to fines formation by attrition of the coarser
particles between each other and against the sieve.
•
Number of data points obtained
- Usually only a few data points are obtained i.e. depending on the number
of sieves used.
- The average size of particles held on any one sieve must be assumed to be
the average of the aperture sizes of the sieves on either side of the sample.
- This may be inaccurate.
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Pharmaceutics II – Micrometrics
6.3 SEDIMENTATION
•
The sedimentation rate of various particles within the sample is measured.
•
The sedimentation rate may be expressed using Stokes’Equation:
V = d2 ( ρS - ρL ) g
18 η
- V = velocity (m/s),
- d = diameter
- g is gravitational acceleration (m/s2),
- ρS is the mass density of the particles (kg/m3),
- ρL is the mass density of the fluid (kg/m3).
- η is viscosity of the fluid.
•
This applies to: - an ideal situation
- with spherical particles
- in a dilute suspension
- falling freely without hindrance
- at a constant rate.
•
It is important to note that [ V α d2 ] since all other parameters remain constant for a
given situation.
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Pharmaceutics II – Micrometrics
•
Andreasen Pipette Method
-
This method combines ease of analysis,
accuracy and economy of equipment.
-
Apparatus consists of a 550 ml vessel
containing a 10 ml pipette sealed into
a ground-glass stopper.
-
When the pipette is in place in the
cylinder, its lower tip is 20 cm below the
surface of the suspension.
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Pharmaceutics II – Micrometrics
-
A 1% suspension of particles in a
medium containing a suitable deflocculating
agent is introduced into the vessel and
brought to the 550 ml mark.
-
The vessel is shaken to distribute particles
uniformly.
-
At various time intervals, 10 ml samples
are withdrawn and discharged by means of
the 2-way stopcock.
-
The samples are evaporated and weighed or
analyzed by other means.
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Pharmaceutics II – Micrometrics
-
Use a modification of Stoke’s
Law:
d = SQRT .
18 η h .
( ρS - ρL ) g t
-
‘h’ is the height of the liquid
above the lower end of the
pipette at the time each sample
is removed
-
From the data obtained a
size VS less than stated size
graph can be plotted.
-
Using the semi-log arithmetic
plot (log size vs %) the
geometric mean diameter and
SD can be calculated.
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Pharmaceutics II – Micrometrics
6.4 COULTER COUNTER
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Pharmaceutics II – Micrometrics
•
Measures the volume of particles rather than particle size.
-
The CC works on the principle that a change in electrical resistance
occurs when a particle suspended in a conducting liquid passes through a
small orifice, on either side of which are electrodes.
-
A known volume of a dilute suspension is pumped through the orifice,
and if it is sufficiently dilute, the particles pass through one at a time.
-
A constant voltage is applied across the electrodes so as to produce a
current.
-
As the particle travels through the orifice, it displaces its own volume of
electrolyte and this results in a change in resistance between the 2
electrodes.
-
This change in resistance causes a voltage pulse that is amplified and fed
to a pulse height analyser calibrated in terms of particle size.
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Pharmaceutics II – Micrometrics
-
In practice, the electronic counter is set within 2 threshold values, such
that it will not count the particles which pass through the aperture that
cause an impulse that does not fall within the threshold i.e. those
particles that are either larger or smaller than a given size.
-
By repeating the process at various threshold values, data can be
obtained as to the number and distribution of the particle sizes.
-
The instrument is capable of counting particles at the rate of
approximately 4000 per second
-
Both gross counts and particle size distributions are obtained fairly
rapidly. Useful over the range 0.5 – 100 μm.
-
The main disadvantage is with aqueous soluble particles, however, there
are non-aqueous electrolytes that can be used to suspend the particles.
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