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Techno1
Dr.Ahmed Bani Jaber
Sheet#6
Done by: Noor Aswad
Particle size analysis (PSA)
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Particle size analysis is an important step in the pharmaceutical industry because it is
needed to characterize certain steps & processes:
1. One of the steps that are needed to be characterized is milling or micronization.
- Milling or micronization are needed to enhance the dissolution of hydrophobic drugs.
So, after milling, particle size analysis should be performed to know the average size
that was given by the milling process.
- If we want to compare between two milling equipments, particle size analysis is down to
reach a conclusion which of these two equipments is more efficient & reduce the
particle size.
2. The second process in which size analysis is needed, is to characterize the granulation
(size enlargement process). The main aim of granulation is to enhance flowability (
movement of the particles relative to each others).
- Fine powders have poor flowability because of the high surface area that leads to high
cohesive & frictional forces (cohesive forces are due to electrostatic charge or van der
waals forces while frictional forces are due to surface roughness).
- We can do a simple experiment, bring a funnel & once put confectioner’s sugar & once
put crystalline sugar (while the funnel is closed) &then open the funnel &by having a
stop watch see how much time the funnel will take to empty the sugar. ↑flow (faster)
→ the funnel will empty faster.
- Coarse sugar (crystalline) has a better flow than fine sugar (confectioner’s sugar).
- After granulation, particle size analysis is usually done to characterize the size
enlargement process & to know the mean size that was given.
3. To characterize certain dosage forms; mainly suspensions & emulsions and they’re
called two-phase systems: they have dispersed phase & continuous phase, dispersed
phase in suspension is solid & in emulsion is liquid. In either dosage form, the dispersed
phase may change with respect to its size.
- Usually, during accelerated stability studies of suspensions or emulsions, these dosage
forms are characterized for particle size analysis to make sure that the mean particle
size of the dispersed phase remains statistically the same with no significant shift.
- Even when we manufacture these dosage forms, particle size is a specification that has
to be checked against tolerance limits.
Particle Size Data
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Data of particle size as a “frequency distribution curve” that is a plot of frequency (yaxis) versus size (x-axis). This frequency distribution curve may be normally distributed
or skewed, (see the next figures).
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Techno1
Dr.Ahmed Bani Jaber
Sheet#6
Done by: Noor Aswad
(Right skewed)
Normal Distribution
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Normally distributed curve is
bell-like in shape.
The middle value is the mean.
Area above the mean=50% &
area below the mean= 50%, so
in normal distribution: area
above the mean=area below
the mean & the total area is 1
or 100%.
The area between the mean
±1σ is 68% (i.e. 34% between
the mean and mean + 1 σ and
34% between the mean and
mean – 1 σ).
σ→ stands for standard
deviation (SD).
The area below mean – 1 σ is 16%. The area below mean + 1 σ is 84%.
Percentile: the observation below which X percent of the observations lies.
50th percentile: is the observation below which 50% of the observations lie.
Example: if you got in the exam 23\30, and you’re the 80th percentile, this is mean that
80% of the students are below 23 and 20% of the students are above 23.
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Techno1
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Dr.Ahmed Bani Jaber
Sheet#6
Done by: Noor Aswad
Mean is the 50th percentile.( Mean + 1 σ) is the 84th percentile.(Mean – 1 σ) is the 16th
percentile.
Example: the marks of an exam showed normal distribution curve with a mean of 20,
and standard deviation of 5, what is the 84th percentile & what is the 16th percentile?
Answer: 84th percentile is 25 (Mean + 1 σ =20+5), 16th percentile is 15 (Mean – 1 σ =205), the 50th percentile is 20.
If we take :
(mean-1 σ)-mean = σ
84th percentile-50th percentile = σ (e.g. in the above example 25-20=5= σ)
Similarly mean-(mean-1 σ)= σ
50th percentile-16th percentile= σ (e.g. in the above example 20-15=5= σ)
Skewed distribution
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Usually the data is not normally distributed (in milling, granulation,… all these processes
give skewed distributions).
If the data is skewed we should normalize the data or the curve, but how can we
manage to normalize the curve?
1. Plot frequency versus particle size, but we plot the particle size in the logarithmic
scale (on semilog paper, called semilog because one scale is logarithmic & the other
is normal)(i.e. when we go in particle size from 1 to 2 to 3 to 4… the scale is
becoming smaller till 10, after 10 the width will become more smaller to reach 100).
In this case
mean= antilog(log 50th)= 50th
and σ = antilog(log 50th –log 16th)= 50th /16th or σ = 84th / 50th .
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Techno1
Dr.Ahmed Bani Jaber
Sheet#6
Done by: Noor Aswad
2. Plot log(size) versus frequency on normal scale (size not in logarithmic scale but in
normal scale).
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Here :
mean= antilog (50th percentile)
& σ= antilog (50th -16th) or σ= antilog (84th – 50th)
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In normalizing cases (both 1 & 2) → both give almost normal distributed curve.
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Data for particle size analysis we have it as a table called “frequency distribution table” :
Frequency
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Frequency in particle size analysis can either be number (e.g. we have 20 or 2 or 3
particles have that size range) or weight.
If the frequency is in terms of number of particles, it takes a symbol of ni, but if it is in
terms of weight it takes a symbol of wi. We use number or weight depending on the
method used for PSA.
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Techno1
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Dr.Ahmed Bani Jaber
Sheet#6
Done by: Noor Aswad
Mean of Size Range is di.
∑N= total frequencies.
PSA Steps:
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First step in PSA is making a plot of frequency (or % frequency)(ni or wi) versus particle
size (mid interval size or mean of size range = di).
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Then after plotting, we must know whether the data is normally distributed or skewed.
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If the data is normally distributed, then we calculate the mean and σ, which are called
arithmetic mean (da) & standard deviation of the arithmetic mean (σa), respectively.
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