The process of grinding. sifting. mixing.
INTRODUCTION
The importance of size reduction in relation to pharmaceutical active agents and
excipients is well known, and the aim of this chapter is to identify methods for particle size reduction, discuss how particle size and shape are characterized, and recognize the importance of controlling particle characteristics to ensure the success of pharmaceutical powder processing and the manufacture of elegant pharmaceutical products. An initial overview of the implications of size reduction within pharmaceutics and the importance of comminution in relation to variability of active pharmaceutical ingredient (API) surface area, effi cacy, and ultimately dosing regimen required to maintain optimum therapeutic effects will be addressed. This will encompass examples from a diverse range of dosage forms, including oral, parenteral, and topical systems. The effects of particle size on the essential characteristics of powders intended for compression (tablets, capsules) such as fl uidity and compressibility will be addressed. The need for uniformity of size and the effects of particle size distribution on the homogeneity of mixing/blending and in essence on the uniformity of APIs within the fi nal manufactured dosage form will be highlighted.
MILLING EQUIPMENT
There are many factors that must be taken into consideration in choosing milling
equipment. Some of these factors are related to required product specifi cations such as particle size distribution, but additionally, physical and chemical properties of the material such as particle shape and moisture content must also be taken into
consideration. Furthermore, other factors that are related to production requirements (mill capacity and the required production rate) must be carefully balanced to ensure the correct choice of milling equipment.
Ball Mill
A ball mill consists of a hollow cylinder mounted such that it can be rotated on its
horizontal longitudinal axis (Figure 1 ). The length of the ball mill is slightly greater than its diameter. A ball mill reduces particle size by subjecting particles to impact and attrition forces generated by moving steel balls or pebbles (grinding medium) that typically occupy 30 – 50% of the total volume of the mill. It is common for a ball mill to contain balls of different diameters that aid size reduction. Generally, larger diameter balls have a higher tendency to act upon coarse feed materials
FIGURE 1 Ball mill in operation showing correct cascade action. whereas smaller diameter balls facilitate the formation of fi ne product by reducing
void spaces between the balls.
The most important factors governing the performance of the mill and the
achievement of the desired particle size are as follows:
1. Amount of material required for subsequent testing (sample volume)
2. Speed of rotation of ball mill
A high volume of powder feed produces a cushioning effect whereas small
sample volumes cause a loss of effi ciency and abrasive wear of the mill parts. The
amount of material to be milled in a ball mill may be expressed as a material – to – void ratio (ratio of the volume of material to that of the void in the ball charge). As the amount of material is increased, the effi ciency of a ball mill is increased until the void space in the bulk volume of ball charge is fi lled; then, the effi ciency of milling is decreased by further addition of material.
Rotational speed is the most signifi cant factor controlling the particle size specifi
cation. The optimum speed of rotation is dependent on mill diameter. At low
angular velocities the balls move with the drum until the force due to gravity
exceeds the frictional force of the bed on the drum, and the balls then slide back
to the base of the drum. This sequence is repeated, producing very little relative
movement of balls so that size reduction is minimal. At high angular velocities the
balls are thrown out onto the mill wall by centrifugal force and no size reduction
occurs. At about two – thirds of the critical angular velocity where centrifuging occurs,
a cascading action is produced. Balls are lifted on the rising side of the drum until
their dynamic angle of repose is exceeded. At this point they fall or roll back to the
base of the drum in a cascade across the diameter of the mill. By this means, the
maximum size reduction occurs by impact of the particles with the balls and by
attrition.
The critical speed of a ball mill is the speed at which the balls just begin to centrifuge
with the mill. Thus, at the critical speed, the centrifugal force is equal to the
weight of the ball. At and above the critical speed, no signifi cant size reduction
occurs. The critical speed n c is given by the equation
n D c 76 6 .
where D is the diameter of the mill.
A larger mill reaches its critical speed at a slower revolution rate than a smaller
mill. Ball mills are operated at from 60 to 85% of the critical speed. Over this range,
the output increases with the speed; however, the lower speeds are for fi ner grinding.
An empiric rule for the optimum speed of a ball mill is
n57−40logD
where n is the speed in revolutions per minute and D is the inside diameter of the
mill in feet.
In practice, the calculated speed should be used initially in the process and modifi
ed as required.
The use of a ball mill is advantageous in that it may be used for both wet and
dry milling and additionally can be successfully employed in batch and continuous
operation. Also, the installation, operation, and labor costs involved in ball milling
are extremely low in comparison to other techniques, which makes this technique
economically favorable.
6.7.2.2 Fluid Energy Mill
Fluid energy milling acts by particle impaction and attrition that are generated by
a fl uid, usually air (Figure 2 ). Fluid energy mills can reduce the particle size to
approximately 1 – 20 μm. A fl uid energy mill consists of a hollow toroid that has a
diameter of 20 – 200 μm, depending on the height of the loop, which may be up to
loop with the high – velocity air, giving rise to zones of turbulence into which solid
particles are fed. The high kinetic energy of the air causes the particles to impact
with other particles with suffi cient momentum for fracture to occur. Turbulence
ensures that the high levels of particle – particle collision produce substantial size
reduction by impact and attrition.
The design of fl uid energy mills provides an internal classifi cation system according
to their particle size in which the fi ner and lighter particles are discharged and
the heavier, oversized particles, under the effect of centrifugal force, are retained
until reduced to a signifi cantly smaller size.
FIGURE 2 Fluid energy mill. Centrifuging action throws coarser particles outward
Classifier removes fine particles and fluid Solids inlet Fluid inlet jets Zone of Turbulence Fluid inlet jets
FIGURE 2 Fluid energy mill.
6.7.2.3 Hammer Mill
The main mechanism of size reduction produced by a hammer mill is by impaction
that is generated from a series of four or more hammers hinged on a central shaft
and enclosed within a rigid metal case (Figure 3 ). During milling the hammers swing
out radially from the rotating central shaft. The angular velocity of the hammers
produce strain rates up to 80 s − 1 , which are so high that most particles undergo brittle
fracture. As size reduction continues, the inertia of particles hitting the hammers
reduces markedly and subsequent fracture is less probable, so that hammer mills
tend to produce powders with narrow particle size distributions. Particle retention
within the mill is achieved using a screen, which allows only suffi ciently milled particles
(defi ned particle size) to pass through. Particles passing through a given mesh
can be much fi ner than the mesh apertures, as particles are carried around the mill
by the hammers and approach the mesh tangentially. For this reason, square, rectangular,
or herringbone slots are often used. According to the purpose of the operation,
the hammers may be square faced or tapered to a cutting edge or have a
stepped form.
The particle size achieved may be controlled variation in the speed of the hammers
and additionally by careful selection of the size and type of screen. During the
operation of a hammer mill the speed of rotation is critical such that below a critical
impact speed the rotor turns so slowly that a blending action rather than milling is
obtained. Such operating conditions result in signifi cant rises in temperature. Moreover,
at very high speeds, there is the probability of insuffi cient time between successive
passes of the hammers for a signifi cant mass of material to fall from the
grinding zone.
The hammer mill is particularly useful in achieving particles in the approximate
size range of 20 – 40 μm and additionally in producing a particle size distribution that
is extremely narrow. The equipment offers ease of use and high levels of fl exibilty
(speed and screen may be rapidly changed allowing rapid variation in achievable
particle size), is easy to clean, and can be operated as a closed system, thus avoiding
operator exposure to potent dusts and potential explosion hazards.
6.7.2.4 Cutting Mill
Particle size reduction using a cutting mill involves successive cutting or shearing a
sample using a series of knives attached to a horizontal rotor (Figure 4 ). This rotary
motion pushes the sample against a series of stationary knives that are attached to
the mill casing. Size reduction occurs by fracture of particles between the two sets
of knives, which have a clearance of approximately a few millimetres. As with a
hammer mill a screen is fi tted at the base of the mill casing and acts to retain material
until a suffi cient degree of size reduction has occurred.
6.7.3 POWDER CHARACTERIZATION TECHNIQUES
6.7.3.1 Powder Sampling
Powdered materials are used in a wide range of industries, no more so than in the
pharmaceutical industry wherein powders are used for the manufacture of a wide
range of dosage forms, the two most common being tablets and hard gelatin capsules.
Orally administered solid dosage forms are the preferred and most patient
convenient, primarily because of the ease of administration and the convenience of
handling. Pharmaceutically, orally administered solid dosage forms are generally
more favorable because of increased stability in comparison to their liquid counterparts
(suspensions, syrups) and the increased control they offer in manipulating
drug dissolution in vivo to suit end – use requirements. Solid dosage forms administered
via the oral route are an intricate blend of pharmaceutical excipients (diluents binders, disintegrants, glidants, lubricants, and fl avors) and APIs. In order to successfully
manufacture acceptable pharmaceutical products, these materials must
be adequately mixed and/or granulated to ensure that the resultant agglomerates
possess the required fl uidity and compressibility and, in addition, avoid demixing
during postgranulation processes. Moreover, the fi nal characteristics of tablets or
capsules such as drug dissolution rate, disintegration time, porosity, friability and
hardness are signifi cantly infl uenced by the properties of the powder blends used
during their manufacture.
During product manufacture large volumes of powder blends are fed through
production equipment/processes, and it is essential to be able to accurately
determine, defi ne, and control powder properties to ensure reproducible manufacture
and product performance. Therefore the characterization of the physicochemical
properties of powder blends is extremely important. It is well accepted
that there are inherent diffi culties in characterizing the entire mass of a bulk
powder blend or process stream, so it is essential to remove and analyze discrete
samples.
Sampling is a useful technique that allows an appropriate aliquot to be withdrawn
from the bulk so as to collect a manageable amount of powder which is representative
of the batch [3] , in other words, every particle should have an equal chance of
being selected [4] . However, there are many circumstances that may result in the
selection of nonrepresentative samples and hence the defi nition of powder characteristics
that are not a true estimation of the entire bulk powder. Typically, powder
masses with an extremely wide particle size distribution or diverse physical properties
are highly likely to be heterogeneous, which may result in high levels of variability
and samples that do not represent bulk mass. Moreover, powder characteristics
may change because of the attrition and segregation during transfer that can make
sampling extremely diffi cult.
It is well accepted that two types of sampling errors are possible when removing
small masses of powder from bulk [5] .
1. Segregation errors, which are due to segregation within the bulk and can be
minimized by suitable mixing and the use of a large number of incremental
samples to form a larger test sample.
2. Statistical errors, which arise because the quantitative distribution in
samples of a given magnitude is not constant but is subject to random fl uctuations.
Consequently, it is an example of a sampling error that cannot
be prevented but can be estimated and indeed reduced by increasing the
sample size.
Therefore, sampling procedures are of the greatest importance in order to reduce
the effect of nonuniform size segregation and nonrandom homogeneity of a system
to achieve statistically meaningful sampling results. Careful attention and faithful
observance must be demonstrated and it is extremely important that sampling
occurs when the powders are in motion [6] and samples are withdrawn from the
whole stream for equal periods of time, rather than part of the stream for all of the
time [3] .
TABLE 1 Stationary Bulk Sampling
Sampling Devices Procedure of Sampling Application and Characteristics Low volume powder
sampler (Figure
When released the spring – loaded T bar will close the sampling chamber.
Used for small quantity of sample powders. The sampler has a sampling chamber volume approximately equal to 2 mL.
Pneumatic lance sampler (Figure 5 c )
A gentle fl ow of air out of the nozzle allows the probe to move through the powder bed. At the
site, the air is slowly reversed to draw up a sample, which is collected against a porous plate
at the end of the probe [7] .
Minimizes powder disturbance and therefore is better than a sample thief, but bias still cannot
be avoided [8] .
Scoop sampler A single swipe of the scoop completely across the powder bulk collects the sample. Each collection should use opposite directions.
Suitable only for materials that are homogeneous within the limits set by the quantity of material
taken by the scoop. It may be used for non – free – fl owing or damp materials where instrumental methods are inappropriate [9] .
Thief/spear probe sampler (Figure 5 b ) One or more cavities are stamped in a hollow cylinder enclosed by an outer rotating sleeve. The thief is inserted into sample with the cavities closed, once opened the sample fi lls the hole.
The cavities are closed and the thief is withdrawn. It must be ensured that samples are withdrawn from different locations Thief samplers belong to two main classes, side sampler (has one or more cavities along the probe) and end sampler (has a single cavity at the end of the probe), which are the most common used for stored non – fl owing material [10] .
There are a number of sampling techniques for particle sampling, which can be
classifi ed in many different ways. Here, particle sampling techniques are divided
into three parts: stationary bulk sampling (Table 1 and Figure 5 ), fl owing stream
sampling (Table 2 and Figure 6 ), and subsampling (Table 3 and Figure 7 ). The
sampling devices, procedures and application overview of the common used techniques
in corresponding fi elds are shown as follow.
6.7.3.3 Particle Density and Voidage
Particle density may be defi ned as the total mass of the particle divided by its total
volume; however, depending upon the different defi nitions of the total volume (or
the different ways to measure the particle volume), there are various defi nitions of
particle density in existence (see Table 4 ).
In order to get clear understanding of the subtle differences between the defi nitions
of various particle density types, an illustration can be formed as shown in
Figure 8 .
Particle Density Methods Density is defi ned as the ratio of mass to volume, so
the density determination can be separated into two steps: measurement of mass
and measurement of volume. Determining the mass of an object is rather straightforward;
however, it is much more diffi cult to directly determine the volume of a
solid. The volume of a solid object with a regular geometric shape may be calculated mathematically; however, in most conditions, the shape of a particle is often irregular,
especially in powder technology, which makes it extremely diffi cult to measure
geometrically. Therefore, various methods have been developed to determine the
volume of particles and powders. The two most in use in both laboratory and industrial
settings are liquid and gas displacement methods. The different values of particle
density can also be expressed in a dimensionless form, as “ relative density ” (or
specifi c gravity), which is the ratio of the density of the particle to the density of
water.
The discussion that follows will give an overview of the common methods used
in particle density measurement.
Measurement of Particle Density
1. Liquid Pycnometry Method There are several British standards that deal
with liquid pycnometry applied to specifi c materials [18 – 23] . A pycnometer bottle
is weighted empty (M1), and then full of liquid (M2). Following these two initial
measurements, two subsequent measurements are made: a sample of powder
approximately one – third of maximum container volume (M3) and the bottle fi lled
to capacity containing the sample and water (M4). Great care is required in the fi nal
step to ensure that the liquid is fully wetted and all the air removed. Variations in
recorded weight also arise depending on how much liquid escapes when the ground
glass stopper is inserted in the liquid – fi lled container. It is extremely important that
the liquid used in this procedure does not solubilize or react with the solid particles.
Moreover, the solid particles must not absorb the selected fl uid.
2. Gas Pycnometry Method Principally this method is similar to liquid pycnometry
in that volume determination is achieved by detecting the pressure or volume
change associated with the displacement of a gas (rather than liquid) by a solid
object. Given that this method is largely dependent upon the diffusivity of the gas,
helium is often used since it has a low molecular weight and a small atomic radius,
allowing high diffusivity into small pores. Sample volumes are often displayed on a
TABLE 3 Subsampling
Sampling Devices Procedure of Sampling Application and Characteristics Coning and
Quartering (Figure
A cross – shaped cutter is used to separate the sample heap (which is fi rst fl attened at
the top) into four equal parts. The segments are drawn apart and two
opposite quadrants are combined together. This procedure is repeated at least 4 times until a small enough sample has been generated.
The fi rst choice for non – free – fl owing powders and nonfl owing powders. Prone to operator bias as fi ne particles remain in the center of the cone and should never be used with free – fl owing powders [13] .
Oscillating hopper sample divider (Figure 7 c )
Hopper (paddle) oscillates and powder falls into two collectors placed under the hopper (paddle).
Used for small quantity of samples. Sample size can be controlled by monitoring time over each collector [7] .
Revolving sample splitter (Figure
The revolving feeder distributes the sample material equally (in time) over a number of radial
chutes, assuming constant rotational speed [14] .
Very easy to perform and several versions are available that are suitable for free – fl owing
powders, dusty powders, and cohesive powders. Handling quantities can vary from
Riffl e/chute splitter (Figure 7 e )
The sample is introduced to a rectangular area, divided by parallel chutes leading to two separate receptacles [14] .
Well – accepted method for sample reduction that is highly suitable for free – fl owing powders. Used to produce samples with a minimum volume of 5 mL.
Spinning riffl er (Figure 7 d ) a steady stream of powder is run into a rotating basket of containers [8] .
Useful in subsampling large samples [15] . Suitable for free – fl owing materials [13] .
Table sampler (Figure 7 b )
In a sampling table, powder fl ows down from the top of an inclined plane, holes and
prisms splitting the powder. The powder that reaches the bottom of the plane is the sample.
Used for sample reduction with the advantages of low price and lack of moving parts. digital counter on the testing equipment [24] ; however, such volumes are easily calculated using the pressure change and the ideal gas law, PV = nRT . The true density of the particle can be measured using this method if the particles have no closed pores, while the apparent particle density can be measured if there are any closed pores. Additionally, if open pores are fi lled with wax, envelope volumes may the open – pore volume, which is sometimes used as a measure of porosity.
3. Hydrostatic Weighing Method The volume of a solid sample is determined
by comparing the mass of the sample in air with the mass of sample immersed in a
liquid with a known density. The volume of sample may be calculated using the
difference between the two measured mass values divided by the density of the
liquid. This method can be used to determine the bulk or apparent volume. It is
extremely important that the suspending liquid does not interact with the powder
under investigation.
4. Float – Sink or Suspension Method This method involves placing a solid
sample into a liquid with known and adjustable density. The density of liquid is
incrementally adjusted until the sample begins to sink – fl oat (ASTM C729 – 75 [25] ),
or is suspended at neutral density in the liquid (ASTM C693 – 93 [26] ). At the point
of equilibrium the density of the sample is equal to the density of the liquid.
5. Bed Pressure Drop Method This technique is based on making measurements
of bed pressure drop as a function of gas velocity at two voidages, when gas
is passed through the bed of powder in the laminar fl ow regime [24] . During measurement
pressure changes for at least four velocities must be measured. The effective particle density ρp can be calculated using the equation where s is the gradient of pressure drop with gas velocity, ρb is the bulk density, ρp
is the particle effective density.
6. Sand Displacement Method The sand displacement method is another useful
way of measuring the envelope density of a particle using fi ne sand as the displacement
media. Sand is mixed with a known amount of particles, then the density of
the sample particles can be determined from the difference of the bulk density
between sand alone and that with samples.
7. Mercury Porosimetry Method Mercury is a nonwetting liquid that must be
forced to enter a pore by application of external pressure. Consequently it is an
extremely useful and convenient liquid for measuring the density of powders and/or
particles. This method can measure the apparent and true density of one sample by applying different pressures. At atmospheric pressure, mercury will resist entering
pores smaller than about 6 μm in diameter, but at pressures of approximately 60,000
psi (414 MPa) mercury will be forced to enter pores with diameters as small as
0.003 μm [27] .
Measurement of Bulk Density Bulk density is very important in determining the
size of containers used for handling, shipping, and defi ning storage conditions for
pharmaceutical powders and granules. It is a property that is also pertinent in defi ning
the size of hoppers and receivers for milling equipment and for sizing blending
equipment in the scale – up to pilot and to commercial production [28] . The concept
of bulk density is the mass of particles divided by the bulk volume, which includes
not only the envelope volume of particles but also the spaces between particles, so
it should not be confused with particle density [24] .
The most convenient method to measure bulk density is to fi ll the particles into
a known volume container (usually cylindrical), level the surface, and weigh the
particles in the container. The bulk density is calculated by the mass of the particles
divided by the volume that can be read from the scale of the measuring cylinder.
In order to minimize experimental errors, the container should be ideally at least
recommended to leave the sample for approximately 10 min to achieve an equilibrium
volume (density) value before making readings.
Given that the bulk volume associated with the particle mass is a mixture of air
and solid material, the bulk density value is highly dependent on sample history
prior to measurement. Calculation of the tapped density can then be achieved by
tapping the bulk powder a specifi ed number of times (to overcome cohesive forces
and remove entrapped air) to determine the tapped volume of the powder. The
tapped and bulk density values can be used to defi ne the fl owability and compressibility
of a powder using Carr ’ s index and the Hausner ratio.
6.7.3.4 Particle Surface Area
Surface area is one of the most important characteristics in particle technology.
Particles with a different surface area will express different physical properties
that will subsequently affect many applications and ultimately fi nal dosage form
properties.
Similar to particle density, there are various defi nitions relating to particle surface
area [16] :
1. Adsorption surface area : the surface area calculated from an adsorption
method.
2. BET surface area : the surface area calculated from the Brunauer, Emmett,
and Teller theory of multilayer adsorption of a gas on a solid surface.
3. Calculated surface area : the surface area of a powder calculated from its particle
size distribution.
4. Effective permeability mass – specifi c surface : the effective volume – specifi c
surface divided by the effective solid density, determined by permeametry.
5. Effective permeability volume – specifi c surface : the effective surface area
divided by the effective solid volume, determined by permeametry.
6. Permeability surface area : the surface area of a powder calculated from the
permeability of a powder bed under stated conditions.
7. Specifi c surface area ( S w ): the surface area of a unit mass of material determined
under stated conditions, where S w is usually expressed in centimeters
squared per gram or meters squared per gram and can be used for quality
control purposes [28] .
Particle Surface Area Determination Methods From the standard defi nitions of
particle surface area, it can be seen that various determination methods are used
for surface area measurement, such as adsorption (including Langmuir ’ s equation
for monolayer adsorption and the BET equation for multilayer adsorption), particle
size distribution, and permeability methods. The different methods are rarely in
agreement because the value obtained depends upon the procedures used and also
on the assumptions made in the theory relating the surface area to the phenomena
measured. The most common methods used for measuring particle surface area are
described below.
1. Gas Adsorption Method Gas adsorption methods measure the surface area
of particles/powders through measurement of the amount of gas adsorbed onto the
sample surface. The methods can measure both external and internal surfaces
(including open pores in the particles) and can yield physically meaningful average
particle sizes with nonporous materials [24] . The amount of gas adsorbed depends
upon the nature of the solid (adsorbent) and the pressure at which adsorption takes
place. The amount of gas (adsorbate) adsorbed can be found by determining the
increase in weight of the solid (gravimetric method) or the amount of gas removed
from the system due to adsorption by application of the gas laws (volumetric
method [6] ). The adsorption used in this method is physical adsorption, which is a
relatively weak interaction between samples and gases and therefore can be removed
by evacuation.
In this method, a graph of the number of moles of gas adsorbed per gram of
solid, at constant temperature, against the equilibrium gas pressure is called an
adsorption isotherm. A point must be chosen on this isotherm corresponding to the
completion of the adsorbed monolayer in order to calculate S w [29] .
2. Permeametry Method This method is based on the fact that the fl ow rate of
a fl uid through a bed of particles depends on the pore space, the pressure drop
across the bed, the fl uid viscosity, dimensional factors such as the area of the bed,
and specifi c surface area ( S w ). The determination of permeability can be made either
under continuous steady – state fl ow (constant fl ow rate) or under variable – fl ow
(constant – volume) conditions.
All of the permeability methods are based on the Kozeny – Carman equation,
which is used to calculate a surface area of a packed powder bed from its permeability.
The Kozeny – Carman equation is expressed as [16]
where S k = effective permeability volume – specifi c surface of powder assuming only
viscous fl ow occurs in determination (Kozeny – Carman term)
A = cross – sectional area of bed of powder perpendicular to direction of fl ow
of air
ε= porosity of bed of powder
Δp = pressure difference across bed of powder
K = Kozeny constant
L = linear dimension of bed of powder parallel to direction of fl ow of air
(commonly known as height of powder bed)
η= viscosity of air at its temperature at time of determination
q = rate of fl ow of incompressible fl uid through bed of powder
The specifi c surface area calculated here only involves the walls of the pores of
the bed and excludes the pores within the particles. Therefore, the surface area
measured in this method can be much smaller than the total surface area measured
by gas adsorption methods [24] .
3. Particle Size Distribution Method The surface area of particles can be determined
using particle size and particle shape values. The “ equivalent spherical diameter
” is used in this technique and many attempts to measure the surface area using
this method have led to values that are signifi cantly less than the true value (large
deviations arising from inability to defi ne particle shape due to surface irregularities
and porosity). Surface area values calculated from particle size distribution methods
will in effect establish the lower limit of surface area due to the implicit assumptions
of sphericity or other regular geometric shapes and by ignoring the highly irregular
nature of real surfaces [30] .
Besides the three methods introduced above, there are many other methods of
surface area determination: Any surface – dependent phenomenon can be used for
such measurement [24] . Some available methods (mercury porosimetry, adsorption
from solution, adsorption of dyes, chemisorption, density methods, and secondary
ion mass spectroscopy) are explained in more detail elsewhere [6, 30, 31, 32] .
6.7.3.5 Particle Shape
Particle behavior is a function of particle size, density, surface area, and shape.
These interact in a complex manner to give the total particle behavior pattern [28] .
The shape of a particle is probably the most diffi cult characteristic to be determined
because there is such diversity in relation to particle shape. However, particle shape
is a fundamental factor in powder characterization that will infl uence important
properties such as bulk density, permeability, fl owability, coatablility, particle
packing arrangements, attrition, and cohesion [33 – 36] . Consequently it is pertinent
to the successful manipulation of pharmaceutical powders that an accurate defi nition
of particle shape is obtained prior to powder processing.
A number of methods have been proposed for particle shape analysis, including
shape coeffi cients, shape factors, verbal descriptions, curvature signatures, moment
invariants, solid shape descriptors, and mathematical functions (Fourier series expansions or fractal dimensions); these are beyond the scope of this chapter but
have been adequately described in other texts [37] .
In the most simplistic means of defi ning particle shape, measurements may be
classifi ed as either macroscopic or microscopic methods. Macroscopic methods
typically determine particle shape using shape coeffi cients or shape factors, which
are often calculated from characteristic properties of the particle such as volume,
surface area, and mean particle diameter. Microscopic methods defi ne particle
texture using fractals or Fourier transforms. Additionally electron microscopy
and X – ray diffraction analysis have proved useful for shape analysis of fi ne
particles.
Particle Shape Measurement
1. Shape Coeffi cients and Shape Factors There are various types of shape
factors, the majority based on statistical considerations. In essence this translates to
the use of shape factors that do refer not to the shape of an individual particle but
rather to the average shape of all the particles in a mass of powder. However, a
method developed by Hausner [38] that uses three factors — elongation factor, bulkiness
factor, and surface factor — may be used to characterize the shape of individual
particles (Table 5 ).
2. Determining Particle Shape by Fourier Analysis Fourier transforms have
been previously used to determine particle shape and the rollability of individual
particles from the coeffi cients of the resulting series [39] . Moreover, fast Fourier
transforms have been successfully used to determine coeffi cients and a particle
“ signature ” by plotting ln Aversus ln n , where Ais the n th Fourier coeffi cient
and n is the frequency [29, 40, 41] . In brief, Fourier method consists of fi nding the
centre of gravity of a particle and its perimeter, from which a polar coordinate
system is set up. Amplitude spectra of a fi nite Fourier series in closed form are used
as shape descriptors of each particle [42] . Several research papers have focused on
the characterization of individual particle shape using Fourier grain analysis or
morphological analysis [43 – 44] . The method has also been extended to the measurement
of particle shapes in a blend [45] and to relate particle attrition rate in a milling
operation to particle shape [46] .
3. Determining Particle Shape by Electron Microscopy Electron microscopy
has been used for the examination of fi ne powder dispersions and will provide
information on particle shape perpendicular to the viewing direction. Standard
shadowing procedures may be useful in obtaining information on shape in the third
dimension. Scanning electron microscopy can give direct and valuable information
on the shape of large particles [47] .
4. Determining Particle Shape by X – Ray Diffraction Broadening The broadening
of X – ray diffraction lines is primarily a measure of the departure from single –
crystal perfection and regularity in a material and can therefore be used to
characterize particle shape. This is the only method that gives the size of the primary
crystallites, irrespective of how they are aggregated or sintered, and is of great value
for determining the properties of fi ne powders [48, 49] .
5. Other Methods for Particle Shape Determination Gotoh and Finney [50]
proposed a mathematical method for expressing a single, three – dimensional body by sectioning it as an equivalent ellipsoid with the same volume, surface area, and
average projected area as the original body. Moreover, wedge – shaped photodetectors
to measure forward light – scattering intensity have also been explored for determination
of crystal shape [51] . More recently a technique referred to as time of
transition (TOT) that was fi rst introduced in 1988 has also been used for the analysis
of particle size and shape [52, 53] .
