Particle size analysis

-Chapter 3

Size and hence surface area of particles affect:

The rate of drug dissolution and release from dosage forms

Flow properties of granules and powders.

Proper mixing of granules and powders.

Physical stability for suspensions.

Grittiness for topical formulation (powder must be

impalpable).

Irritation of the eyes for ophthalmic suspensions (small

particle must be used).

Importance of PSA

When determining the size of large solid usually we need to

measure at least three dimensions.

When determining the size of a sphere, it is possible to describe

the size using one dimension (diameter).

If a particles of powder is perfectly spherical, than it is possible

to describe the particle size by measuring the diameter of the

particle.

Dimensions

However, particles are often irregular and not perfectly

spherical.

Such irregular particles are considered to approximate to a

sphere (equivalent sphere), which can then be characterized

by determining its diameter.

Because the measurement is based on an hypothetical sphere,

which represents only an approximation to the true size of the

particle, the dimension is called equivalent sphere diameter.

Dimensions

It is possible to generate more than one sphere which is

equivalent to a given irregular particle shape.

Equivalent sphere diameter

Different equivalent diameters constructed around the same

particle. (Aulton’s 3rd ed.)

Equivalent sphere diameter

The equivalent spherical diameter, relates the size of a particle to the

diameter of a sphere having the same surface area or volume or

sedimentation rate or other factors. Examples of types of equivalent

diameters:

Surface diameter (ds) is the diameter of a sphere having the same

surface area as the particle in question.

Volume diameter (dv) is the diameter of a sphere having the same

volume as the particle in question.

Stokes diameter (dst) is the diameter of a sphere undergoing

sedimentation in a specific medium at the same rate as the asymmetric

particle.

Equivalent sphere diameter

Two topics will be covered in this Chapter:

1. Particle size distribution.

2. Methods for particle size analysis.

Particle size distribution

A powder population (a bulk of powder) which consists of

spheres or equivalent spheres of the same diameter is said to

be monodispersed and its characteristics can be described

by a single equivalent sphere diameter.

However, in pharmaceutical systems this situation is almost

never encountered.

Most powders contain particles with a range of different

equivalent diameters, i.e. they are polydispersed.

In order to be able to define the size distribution of

polydisperse powder samples, the size distribution can be

broken down into different size ranges, which can be

presented in the form of a histogram (or curve).

The histogram presentation allows also to compare the

characteristics of two or more polydisperse powder samples.

Particle size distribution

When the number (or weights) of particles lying within a

certain size range is plotted against a size range (or mean

particle size), a frequency distribution curve is obtained.

Such plots give a visual representation of the distribution that

an average diameter cannot achieve.

0

10

20

30

40

50

60

0.75 1.25 1.75 2.25 2.75 3.25 3.75

Mean of Size Range (um)

# o

f P

art

icle

s i

n E

ach

Siz

e

Ran

ge

PSD - Frequency distribution

The figure shown in the previous slide is representative of a normal

distribution: the particles are symmetrically distributed about a central

value.

The peak frequency value (called mode) separated the normal curve in

two identical halves, because the size distribution is fully symmetrical

(normal).

For normal distribution, mean = median =mode

mean – ‘average’ size of a population

median – size where 50% of the population is

below/above

mode – size with highest frequency

PSD - Normal distribution

In many cases, rather than plotting the number of particles (or

weight), laying within a specific size range, the percent particles

(or weight) in each size range (% frequency) can be plotted.

Size Range

(μm)

Mean of

Size Range,

di (μm)

Number of

particles in each

size range, ni

% Frequency

(ni/N)*100%

0.50 – 1.00 0.75 2 1.7

1.00 – 1.50 1.25 10 8.5

1.50 – 2.00 1.75 22 18.6

2.00 – 2.50 2.25 54 45.8

2.50 – 3.00 2.75 17 14.4

3.00 – 3.50 3.25 8 6.8

3.50 – 4.00 3.75 5 4.2

N=Σ ni= 118 100

PSD - % Frequency

PSD – Number vs Weight distributions

Number distributions imply that the data were collected by a

counting technique (microscopy, Coulter counter).

We are frequently interested in obtaining data based on weight

(weight distribution) which can be achieved by using

sedimentation or sieving techniques.

We can still convert number data (i.e. obtained by microscopy)

to weight data given the assumption that the general shape

and density of the particles are independent of the size range

of the sample.

Not all particles’ populations are characterized by normal size

distributions and the frequency distributions of such populations

exhibit skewness.

In this case, mean median mode.

PSD- Skewed distribution

Skewed distribution can sometimes be normalized by

replotting the equivalent particle diameter using a

logarithmic scale.

This is often referred to as log-normal distribution.

0

10

20

30

40

50

60

70

0 5 10 15 20

Mean of Size Range, um

# o

f P

art

icle

s

0

10

20

30

40

50

60

70

1 10 100

Mean of Size Range, um

# o

f P

arti

cle

s

PSD- Skewed distribution

a) Normal distribution: the mode separates the curves into two symmetrical

halves.

b) Positively skewed: a frequency curve with an elongated tail towards the

higher size range.

c) Negatively skewed: a frequency curve with an elongated tail towards

the lower size range.

d) Bimodal: the frequency curve containing two peaks (two modes).

PSD- Skewed distribution

Then, % frequency can then be used to produce the

cumulative percent frequency.

Cumulative % oversize: The total percent of particles

with size higher than the lower

limit of each class interval

Cumulative % undersize:

The total % of particles with size

lower than the upper limit of

each class interval

PSD – Cumulative frequency distribution

PSD – Cumulative frequency distribution

The median particle diameter corresponds to

the point that separates the cumulative

frequency curve into two equal halves,

above and below which 50% of the particles

lie (point a)

Just as the median divides a symmetrical

cumulative size distribution curve into two

equal halves, so the lower and upper quartile

points at 25% (b) and 75% (c) divide the

upper and lower ranges of a symmetrical

curve into equal parts.

PSD - Cumulative frequency distribution

Not all particle populations are characterized by symmetrical

or normal size distributions and the frequency distributions of

such populations exhibit skewness.

The degree of skewness can be estimated by determining the

interquartile coefficient of skewness (IQCS):

PSD - IQCS

a is the median diameter and b and c

are lower and upper quartile points.

The IQCS can take any value between

−1 and +1. If the IQCS is zero then the

size distribution is practically symmetrical

between the quartile points

)()(

)()(

baac

baacIQCS

PSD - IQCS

Methods of PS analysis

1. Sieve analysis method.

2. Microscopy.

3. Sedimentation in a liquid or gas.

4. Electrical sensing zone method

5. Laser light scattering

1. Sieving method

The most widely used method for measuring PSD (simple,

cheap, rapid and with little variability).

This method uses a series of standard calibrated sieves.

Sieves are generally used for grading coarser particles.

ISO range (45 – 1000 microns)

Equivalent diameter measured is the Sieve diameter (dA):

the width of the minimum square opening which the

particle will pass.

Sample preparation

Sieve analysis is usually carried out using dry powders.

For powders in liquid suspension wet sieving can be used.

Also for powders which tends to agglomerates during dry

sieving, wet sieving can be used.

1. Sieving method

Equipment

Sieve analysis uses wire woven stainless steel meshes

with known aperture diameters which form a

physical barrier to particles.

Most sieve analysis use a stack or nest of sieves

which has the smallest mesh above a collector tray

followed by meshes that become progressively

coarser towards the top of the stack of sieves.

1. Sieving method

Principle of measurement

The sieves are mounted on a mechanical shaker.

Powder is loaded on to the coarsest sieve at the

top of the assembled stack and the nest is

subjected to mechanical vibration.

After suitable time the particles that passes

through one sieve and retained on the next finer

sieve are collected and weighed.

Frequently the powder is assigned the size of the

screen through which it passes, on which it is

retained or the mean of the two values.

1. Sieving method

Limitations

Sieving errors would result from a number of variables including sieve

loading, intensity and time of agitation. Care must be taken to ensure

that the correct techniques are employed.

For materials >150 μm, a sieve analysis and particle size distribution is

accurate and consistent. However, for material that is finer than <150

μm, dry sieving can be significantly less accurate.

Sieve analysis assumes that all particles will be round (spherical). Less

spherical particles (e.g. elongated or flat) will give less reliable results.

Unsuitable for material that adheres to the sieve or forms clumps.

1. Sieving method

Standards for powders based on sieving

In order to characterize the particle size of a given powder,

the USP uses these standards descriptive terms: very coarse,

coarse, moderately coarse, fine, and very fine.

These terms are related to the proportion of powder that is

capable of passing through the openings of standard sieves.

1. Sieving method

Standards for powders based on sieving Very coarse (No. 8): All particles pass through a

No. 8 sieve and not more than 20% pass through

a No. 60 sieve. Coarse (No. 20): All particles pass through a No.

20 sieve and not more than 40% pass through a

No. 60 sieve.

Moderately coarse (No. 40): All particles pass

through a No. 40 sieve and not more than 40%

pass through a No. 80 sieve.

Fine (No. 60): All particles pass through a No. 60 sieve and not more than 40% pass through a No.

100 sieve

Very fine (No. 80): All particles pass through a No.

80 sieve. There is no limit to greater fineness.

1. Sieving method

Microscopy

Equivalent diameter:

da, dp, dF, dM can be determined

Range of analysis:

Light microscope: 1-1000 microns

Scanning electron microscope (SEM): 0.05 - 1 microns

Transmission electron microscope (TEM): 0.001 – 0.05

microns

2. Microscopy

Equivalent diameter

dp: perimeter diameter is based on a

circle having the same perimeter as the

particle.

da: projected area diameter is based

on a circle of equivalent area to that of

the projected image of a particle;

2. Microscopy

Equivalent diameter:

dF: Feret’s diameter is the distance between two parallel

tangents to the projected particle perimeter.

dM: Martin’s diameter is the is the length of a line that divides a

randomly oriented particle into two equal areas.

dF, dM are diameters which are averaged over many different

orientations to produce a mean value for each particle diameter.

dM corresponds to the dotted lines

2. Microscopy

Light microscopy - procedure

A suspension, diluted or undiluted, is

mounted on a slide and placed on a

mechanical stage.

The microscope eyepiece is fitted with a

micrometer by which the size of the

particles can be estimated.

The field can be projected onto a screen

where the particles are measured more

easily.

2. Microscopy

1. The number of particles that must be

counted (300-500) to obtain a good

estimation of the distribution makes the

method slow and tedious.

2. The diameter is obtained from only two

dimensions of the particle: length and

breadth. No estimation of the depth

(thickness) of the particle is ordinarily

available. (E.g. for a flaky particle the size

measurement might be overestimated).

Disadvantages

2. Microscopy

Advantage

Microscopic examination of a sample should be undertaken

even when other methods of particle size analysis are

available, because the presence of agglomerates and

particles of one or more than one component can be

detected properly by microscopy but overlooked by other

methods.

2. Microscopy

Equivalent diameter: dst(Stokes diameter)

Stokes equation:

gt

hd

os

st)(

18

dst= (Stokes diameter)

h = height or sedimentation distance

η = viscosity of the medium

v = rate of settling

t = time

ρs = density of the particles

ρo = density of dispersion medium,

g = acceleration due to gravity

18

0

2 gd

t

hv sst

3. Sedimentation method

The Stoke’s equation holds exactly only for spheres falling freely

without hindrance and at a constant rate.

The law is applicable to irregularly shaped particles of various

sizes as long as one realizes that the diameter obtained is a

relative particle size equivalent to that of sphere falling at the

same velocity as that of the particles under consideration. (i.e.

equivalent Stokes diameter).

The particles must not be aggregated or clumped together in

the suspension since such clumps would fall more rapidly than

the individual particles, and erroneous results would be

obtained (deflocculating agent may be needed).

3. Sedimentation method

Range of analysis:

Gravitational sedimentation: 5-1000 microns

Centrifugal sedimentation: 0.5-50 microns

3. Sedimentation method

Pipette method (Andreasen pipette)

The Andreasen apparatus usually consists of a

550-mL vessel.

In contains 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.

3. Sedimentation method

Pipette method (Andreasen pipette)

Particle size distribution can be determined by examining the

powder as it sediments.

The powder is dispersed uniformly or introduced as a thin layer in

a fluid.

The powder should not be soluble in the fluid, but should be

easily dispersed (wetting agent might be added to the fluid).

3. Sedimentation method

Balance method

The increase in weight of sedimented particles falling onto a

balanced pan suspended in fluid is recorded with respect to

time.

3. Sedimentation method

Alternative techniques

One of the limitations of gravitational sedimentation it is that it is

not suitable for particles < 5 microns:

in this case the test becomes too slow and less accurate.

This can be minimized by increasing the driving force of

sedimentation by replacing the gravitational force with a larger

centrifugal force (centrifugal sedimentation).

3. Sedimentation method

The electrical sensing zone method of particle characterization is

also known as Coulter Counter.

Equivalent diameter: dV (Volume diameter)

dV Diameter of the sphere having the same volume as the

particle

Range of analysis:

0.1- 1000 microns

4. Electric sensing zone method

Powder samples are dispersed in an electrolyte solution to form

a very diluted suspension.

The particle suspension is drawn through an orifice where

electrodes are situated on either side and surrounded by

electrolyte solution.

As the particle travels through the orifice, it displaces its own

volume of electrolyte solution.

The change in electrical resistance between the electrodes is

proportional to the volume of the particle (volume of the

electrolyte solution displaced).

4. Electric sensing zone method

4. Electric sensing zone method

This is a very accurate method of measurement, yet very

expensive and sophisticated.

Moreover dispersions must be sufficiently diluted to avoid the

occurrence of coincidence. Coincidence is when more than

one particle is present in the orifice at any one time. This may

result in two or more particles counted as one and therefore

inaccurate measurement (i.e. the equivalent diameter is based

on the volume of two particles rather than one).

4. Electric sensing zone method

Low angle light scattering

Equivalent diameters:

da and dV

Principle of measurement:

Scattering of light upon incidence with particle suspended in

air or a liquid.

Detection range:

0.5 to 1000 microns

5. Laser light scattering

Low angle light scattering

For particles (i.e. >1 µm) that are much larger than the wavelength of light,

any interaction with particles causes light to be scattered in a forward

direction with only a small change in angle (Fraunhofer diffraction). The

angle of scatter is inversely proportional to the particle diameter.

Laser light is passed through a dilute suspension of the particles. The light is

scattered by the particles, and is detected by detector which measures

light intensity over a range of angles.

5. Laser light scattering

Dynamic light scattering

Based on the Brownian movement (random motion of small

particles caused by collisions with the smaller molecules of the

suspended fluids).

It analyses the constantly changing patterns of laser light,

scattered by particles in Brownian movement.

The rate of change of scattered light can be related to the

particle size.

Range of analysis: 0.001 – 1 microns.

5. Laser light scattering