Particle size

Question 1

Why is particle size measurement

important?

Answer 1

• Size influences physical properties of pharmaceutical materials
– Powder flow, tablet formation

• It tells us if a process has been successful
– Milling of a solid; homogenization of emulsions

• Gives an indication of product stability
– Emulsion droplet size on storage

• Quality control of products – Increases confidence that a product is same as previous batches
• Indicative of in-vivo behavior – Absorption rate of insulin from IM injection depends on crystal size – Nanosized particles can accumulate in ‘leaky’ cancerous tissues via EPR effect (enhanced permeability and retention)

Question 2

Equivalent diameters

Answer 2

• We need to find a way of defining a single size for a particle that may be irregularly shaped
• To do this we use the concept of equivalent diameter – the diameter of a sphere that is in some unique way similar to the particle in question
• Simplest to do this by volume

Question 3

What is dV

Answer 3

Simplest is Volume Equivalent Diameter (dV) – the diameter of a sphere that has the same volume as the irregular particle – it’s unambiguous, as particles have a well-defined volume

Question 4

Distributions of particle size - mode

Answer 4

Size with most particles is called the mode

Question 5

Distributions of particle size - mean

Answer 5

the weighted arithmetic mean size

Question 6

Distributions of particle size - median

Answer 6

the size with half the particles on each side

Question 7

Distributions of particle size - standard deviation

Answer 7

The width can be defined as the standard deviation

Question 8

Cumulative frequency representation

Answer 8

This is the percentage of particles above or below a given size

Question 9

Techniques for measuring particle size

Answer 9

– Sieving
– Sedimentation
– Microscopy
– Light scattering

Question 10

Choice of technique to measure particle size depends on

Answer 10

– Applicable size range for sample
– Cost
– Time taken
– Skill required
– Precision
– Quantity of material needed
– How much data they provide (e.g. full distribution or just an average)

Question 11

Sieving

Answer 11

• Oldest method, inexpensive, widely available
• Separates fine material from course material by means of a series of woven or perforated surfaces. The proportion of different size particles are recorded and analysed.
• Sieves are precision-woven square mesh, from steel or
bronze wire
• Smallest size is about 50 µm – smaller particles don’t pass through readily, fine meshes are easily damaged and clogged
• Method defines a ‘sieve equivalent diameter’ – the size of the sphere which will pass through the square hole

Question 12

Sieving method

Answer 12

• Standard size sieves stacked into a ‘nest’ of decreasing mesh size – bottom is a closed tray
• Sample put in top and shaken - particles fall through until mesh size is too small – at which point the particles
will be retained
• When shaking is completed, the amount of particles in each sieve is weighed

Question 13

Errors in sieving

Answer 13

• Errors are readily visualised with sieving.
– Sieve holes may vary in size due to manufacture or damage – Powder may coat the wires leading to sieve apertures being reduced
– Particles may be cohesive – stick together so that they don’t pass through the mesh
– Vibration from shaking may damage the particles leading to erroneous ‘fines’
– Stack may not be shaken for long enough to get particles to their final sieve
– Sieve may be overloaded – only works well for a light load
– Particle shape may cause problems (e.g. needle-like particles)

Question 14

Sedimentation - theory

Answer 14

• The rate at which suspended particles settle has long been used for size measurement
• The connection between particle size and settling rate or ‘sedimentation velocity’ is given by Stokes’ law

Question 15

equation

Answer 15

v = 2r2 (ρ2-ρ1)g/9η

Question 16

Sedimentation in practice

Answer 16

• Settling velocity is not measured directly
• Can measure the amount of material settled in a particular time (e.g. on to an immersed balance pan) – a sedimentation balance
• Can measure the amount remaining in suspension vs time by passing a beam of light or x-rays through the sample

Question 17

How does gravity effect settling

Answer 17

Because settling can be slow under gravity, instruments usually use centrifugal sedimentation to speed things up - g in Stokes’ law is then replaced by r2ω, where r is the centrifuge radius and ω the angular velocity

Question 18

Andreasen pipette

Answer 18

Remove samples over time (hours/days) and analyse for particle content; calculate size distribution

Question 19

Sedigraph III

Answer 19

Insert sample and push button

Question 20

Microscopy and image analysis

Answer 20

• More sophisticated and expensive technologies
• Many different types of microscopy e.g.. Light, electron, atomic force etc.
• Uses very small volume of sample
• Measures 1 nm – millimetres depending on technique
• Computer thresholds image then simply counts pixels in each region, constructs histogram, computes statistics as required

Question 21

Disadvantage and advantage of Microscopy

Answer 21

Disadvantage- Measures relatively few particles
Advantage - One of the few methods of getting
shape information

Question 22

Particle size analysis by light scattering and its advantages

Answer 22

• Light scattering methods now account for the majority of size measurements and instruments

• Advantages:
– Rapid
– Easy to use
– Wide applicability
– Wide size range

Question 23

The diffraction pattern

Answer 23

determined by the particle size and shape

Given the particle size we can compute the scattering
pattern – its not a simple calculation!

Question 24

Disadvantage for light scattering

Answer 24

• Measuring the diffraction pattern

* Finding the particle size distribution from it

Question 25

Operation of a laser diffraction sizer

Answer 25

- Particles in dilute suspension
Scattering is measured from many particles
- Laser light source
High intensity
Single colour
single direction
- Array detector
Similar to digital camera sensor
Measures light intensity at each point

Question 26

How does the calculation work?

Answer 26

• It guesses the size distribution! (The ‘trial’ distribution)
• It calculates the scattering pattern of the trial distribution
• It compares the trial distribution scattering pattern with the measured scattering pattern (of course they don’t match at first)
• It adjusts the trial distribution
• Recalculates scattering pattern of trial distribution
• Goes round loop, adjusting trial distribution until its scattering pattern is the same as the measured scattering pattern
• The size measured is a representation of the hydrodynamic radius, this is defined as the size of a sphere that moves at an identical rate to the particle

Question 27

Particle counting

Answer 27

• Problem with previous methods is that they tell you the size distribution, but do not tell you how many particles are present.
• For some applications, the number of particles is critical (e.g. cell counting, or particle contamination in injections).
• The classic instrument for this is the Coulter Counter or electrical zone sensing (EZS) technique

Question 28

Electrical zone sensing

Answer 28

• The volume of suspension drawn through the aperture is determined by the suction potential created
• Now lets put an electrode in each chamber and add a battery; the only way we could pass a current through the circuit would be if it goes through the aperture:
• If a particle is sucked through the aperture, it will briefly occlude the hole and stop part of the current reducing the electrical current.
• We can suck a known amount of suspension (e.g. 1 ml or 10 ml) through the aperture and the instrument will count the number of times the current is blocked.
• From the amount of blockage we can also measure the size of each particle, and the instrument can build up a size distribution
• Sufficiently small apertures (15 micrometres is the smallest commercially supplied aperture)

Question 29

Optical particle counting

Answer 29

• A similar particle counter can be made using optical sensing of particles
• Particles in dilute suspension are passed through a narrow beam of light
• As they pass they cast a shadow which is measured by a
photodetector
• This is the principle of the Hiac counter which is the method used in pharmacopoeial tests for particles in injections