W4 Particle size analysis (ZM) 17.10

Question 1

How do you calculate arithmetic mean?

Answer 1

(d1 + d2)/2

Question 2

How do you calculate geometric mean?

Answer 2

√(d1xd2)

Question 3

Particle size distribution looking at a:
Histogram- incremental distribution
(for info)

Answer 3

Shows how many particles fall within a given size increment

Question 4

Particle size distribution looking at a:
Cumulative distribution- what does it show?
(for info)

Answer 4

Shows how much material lies above or below a particular size

Question 5

Normal distribution (rare for particle size distributions:

Answer 5

Normal distribution is symmetrical about the mean

Arithmetic mean = sum of particle sizes divided by total number of particles

Question 6

Particle diameters:
Skewed distributions: How may they be normalised?
-for info

Answer 6

Skewed distributions may be normalised by replotting the equivalent particle diameters using a logarithmic scale (lognormal distributions)

Question 7

What is Bimodal/multimodal distribution?

Answer 7

Neither normal nor lognormal
two or multiple mode values

Question 8

Dispersion
What is central tendency?

If Particles in a sample are all of the same size its called..?
If a range of particle sizes exists its called..?

Answer 8

Tendency of the particle size to cluster around a particular value
e.g. Mean/mode/median

*To report an average value without a its dispersion or deviation is however meaningless
*In a real sample of material there will be a range of particle sizes spread about the average
= monodisperse
=polydisperse

Question 9

What is Coefficient of variation (CV%)

Answer 9

Coefficient of variation (CV%) = (SD/ Mean) x100

Normalise the standard deviation through division by the mean

To compare the degree of variance between multiple sample populations

Also known as relative standard deviation (RSD)

Question 10

What is D90/D10 Ratio?

Answer 10

Used by the pharmaceutical industry to describe polydispersity of powders, regardless of the distribution model.
Useful measure of dispersion for multimodal distributions

e.g. D90/D10= 1300um/750um =1.73
No unit
Expressed with 2 d.p.
The closer it is to 1.00, the more narrow the dispersion is around the median value

Question 11

What are the different particle sizing methods?

Answer 11

1. Sieving
2. Microscopy
3. Andreasen pipette
   -defines size by sedimentation
4. Electrical sensing zone
5. Laser light diffraction
6. Photon correlation spectroscopy
7. Cascade impactor

Question 12

Particle sizing methods:
Sieving
What are the brief steps?

Answer 12

1. Fill, seal, agitate, weigh

(Clamping device, Sieve pan, Vibrating base)

e.g. lactose (excipient) poured in at top, shaken and falls down from large to small mesh (filtered)

Be aware of rod like particles- overestimate of under-size

Question 13

What does sieving measure?

Answer 13

• Mesh number = number of openings in one linear inch of screen
  -A 100-mesh screen has 100 openings per inch
• Sieve equivalent diameter (ds) = the size of a sphere that will just pass through the aperture of a particular sieve
  -A two-dimensional value

(square-hole sieve and round-hole sieve)

Question 14

Particle sizing methods:
Microscopy
What are the types of microscopes?

Answer 14

• Light microscope
• Electron microscope (SEM/TEM)
• Atomic force microscope

Question 15

Microscope measurements:
What is projected area diameter (da)?

Answer 15

The diameter of a circle having the same area as the particle viewed normally to a plane surface on which the particle is at rest in a stable position

Question 16

Microscope measurements:
What is Martin’s diameter? (dm)

Answer 16

The length of the line which bisects the image of particle

Question 17

Microscope measurements:
What is Feret’s diameter (df)?

Answer 17

The distance between two tangents on opposite sides of the particle, parallel to some fixed direction

Question 18

Particle sizing methods:
What does Andreasen pipette measure?

Answer 18

Measures sedimentation
Stokes’ Law can be used to calculate stokes diameter.

Question 19

What is stokes diameter?

Answer 19

Diameter of a sphere with the same density and settling velocity as the particle

Question 20

What should you be careful of during extended measurements of particle size?

Answer 20

Particle interaction/re-aggregation

Question 21

What are 2 Electrical sensing zone methods?

Answer 21

Coulter Counter
- Particles 1-1000 um
Qnano
- Particles 1-1000nm

Limited to those particles that can be suitably suspended in an electrolyte solution

Question 22

Particle sizing methods:
Describe Laser Diffraction:
(Static light scattering)

Answer 22

*Light waves diffracted on the particle surface change their direction of travel dependent upon particle size

*Detectors placed at fixed angles measure the intensity of light scattered at each position

*The amount of light hitting the outer circles of the bull’s eye detector can be used to calculate the amount of diffracted light and thus the mean particle size

Question 24

Particle sizing methods:
Photon correlation spectroscopy (Dynamic Light Scattering)
What does it measure?

Answer 24

Measures Brownian motion and relates this to the size of the particles

• Particle diffuses within a fluid
• The scattered light of the incident laser can be detected at different angles (θ)

Measures Hydrodynamic diameter (dhyd) = Diameter of a sphere that diffuses at the same rate in a liquid as the particle

Question 25

Particle diffusion methods- Photo correlation spectroscopy
What is the Mie Theory?

What causes the intensity of the beam to fluctuate?

Answer 25

The Mie model takes into account both diffraction and diffusion of the light around the particle in its medium

• High intensity (scatter more light), slow fluctuations (move slower)
• Low intensity (scatter less light), rapid fluctuations (move faster)

Brownian motion

Question 26

Be careful of…

Answer 26

Small amounts of large aggregates or dust particles can disturb the size determination (especially if the main population is significantly smaller in size)
The intensity of scattering is proportional to d6