http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
The Compaction of Pharmaceutical Powders
by Oluwatoyin A. Odeku
The compaction properties of pharmaceutical powders are characterised by their
compressibility and compactibility. While compressibility is the ability of the powder to
deform under pressure, compactibility is the ability to form mechanically strong compacts.
Compaction as applicable to a pharmaceutical powder consists of the simultaneous processes
of compression and consolidation of a two-phase (particulate solid-gas) system due to an
applied force.
In the pharmaceutical industry, the effects of such forces are particularly important in the
manufacture of tablets and granules, in the filling of hard-shell gelatin capsules and in
powder handling in general. The phenomena and mechanisms involved during compaction of
pharmaceutical materials have become an important concept in the design and development
of solid dosage forms. This is due to the fact that systematic investigations are facilitated by
the use of instrumented single-station and multi-station tablet presses, universal testing
machines and integrated compaction research systems, also known as compaction simulators.
The parameters monitored during compaction vary widely in these studies. Data obtained
from the measurements of forces on the punches and the displacement of the upper and lower
punches, axial to radial load transmission, die wall friction, ejection forces, temperature
changes and other miscellaneous parameters have been used to assess the compaction
behavior of a variety of pharmaceutical powders and formulations. More than fifteen
different mathematical descriptions of the compaction process have been compiled in the
literature and several of these including those of Heckel, Kawakita and Ludde, and Adams
have been validated for pharmaceutical systems. Focus is now changing from the
mathematical modelling of compressibility to the development and evaluation of a
compactibility characteristic where primarily a linear model in the relevant pressure region is
investigated. The interesting question whether a correlation between compressibility and
compactibility exists is being considered.
Introduction
Compactibility is the ability of a powder bed to form a mechanically strong tablet; whereas
the compressibility is the ability of a powder bed to be compressed and consequently be
reduced in volume. The characterisation of powder compression and compaction plays an
important role in the manufacturing of tablets and granules, in the filling of hard-shell gelatin
capsules and in powder handling in general. Compaction as applicable to a pharmaceutical
powder consists of the simultaneous processes of compression and consolidation of a twophase (particulate solid-gas) system due to an applied force (1,2). Compaction of powders is
generally used to describe the situation in which these materials are subjected to some level
of mechanical force. In the pharmaceutical industry, the effects of such forces are particularly
important in the manufacture of tablets.
Pharmaceutical powders
Powders are subdivided solids which are classified in the British Pharmacopoeia, BP (3)
according to the size of their constituent particles which range from less than 1.25 mm to 1.70
mm in diameter. The term ‘powder’ when used to describe a dosage form, however, describes
a formulation in which a drug powder has been mixed with other powdered excipients to
produce the final product. The function(s) of the added excipients depends upon the intended
use of the product (4). Some powders are intended to be used orally e.g. Compound
Magnesium trisilicate oral powder BP, and others externally e.g. dusting powder. However,
the use of powders as oral dosage forms has been reduced because of problems associated
1
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
with administration of powders which include the undesirability of taking bitter or unpleasant
tasting drugs in this manner, the difficulty of protecting from decomposition those powders
containing hygroscopic, deliquescent, or aromatic materials, and the time and expense
required in the preparation of uniform powders. Hence, the largest use of powder
pharmaceutically is in the production of tablets and capsules. Powders intended for
compression must possess two essential properties: fluidity and compressibility.
Powder fluidity is required so that the material can be transported through the hopper of the
tabletting machine and provide adequate filling of the dies to produce tablets of consistent
weight and strength. Uneven powder flow can result in excess of entrapped air within
powders which in some high speed tabletting conditions may promote capping and
lamination. Powder flow can be improved by the incorporation of a glidant such as silicon
dioxide, talc, or by making the particles as spherical as possible e. g. by spray-drying. The
most popular method of increasing powder flow is by granulation. Icing sugar, for example,
has poor flow properties which can be improved by granulation with water (4). Thus,
granulation is also the pharmaceutical process that converts a mixture of powders which have
poor cohesion, into aggregates capable of compaction.
Powder density
Bulk density, ρB , is a characteristic of a powder and is given by the mass, M, of a powder
occupying a known bulk volume, VB , according to the relationship:
ρB = M / VB
(1)
Bulk density depends on particle shape. As the particle becomes more spherical in shape,
bulk density increases (5). The bulk density of a powder bed is always less than the particle
or true density (ρT) of its component particles, because the powder contains inter-particle
pores or voids. Hence, a powder can possess a single true density but have many bulk
densities depending on the way it is packed and the porosity of the powder bed. However, a
high bulk density value does not necessarily imply a closed-packed low porosity bed since
bulk density is directly proportional to true density.
i.e.
ρB = ρR . ρT
(2)
or
ρR
(3)
= ρB / ρT
The proportionality constant, ρR , is known as the relative density or packing fraction of the
powder bed which is a dimensionless quantity. During compression process, the relative
density increases to a maximum of unity when all air spaces have been eliminated.
Also:
E = 1 - ρR
(4)
where E is the fractional voidage or porosity of the powder bed which is usually expressed as
percentage and termed the powder porosity (6).
Compression of powdered solids
Compression refers to a reduction in the bulk volume of materials as a result of displacement
of the gaseous phase. Stages involved in the bulk reduction of powdered solids are shown in
Fig. 1.
At the onset of the compression process, when the powder is filled into the die cavity, and
prior to the entrance of the upper punch into the die cavity, the only forces that exist between
the particles are those that are related to the packing characteristics of the particles, the
density of the particles and the total mass of the material that is filled into the die (Fig. 1. I).
The packing characteristics of the powder mass will be determined by the packing
characteristics of the individual particles (1,2).
2
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
Fig.1: Stages involved in compression (I - III) and decompression.
When external mechanical forces are applied to a powder mass, there is usually a reduction in
volume due to closer packing of the powder particles, and in most cases, this is the main
mechanism of initial volume reduction (Fig. 1. II). However, as the load increases,
rearrangement of particles becomes more difficult and further compression leads to some
type of particle deformation (Fig. 1. III). If on removal of the load, the deformation is to a
large extent reversible, i. e. it behaves like rubber, then the deformation is said to be elastic.
All solids undergo elastic deformation when subjected to external forces. With several
pharmaceutical materials such as acetylsalicylic acid, elastic deformation becomes the
predominant mechanism of compression within the range of maximum force encountered in
practice.
In other groups of powdered solids, an elastic limit is reached, and loads above this level
result in deformation not immediately reversible on the removal of the applied force. Bulk
volume reduction in these cases results from plastic deformation and/or viscous flow of
particles, which are squeezed into the remaining void spaces, resembling the behaviour of
modelling clay. This mechanism predominates in materials in which the shear strength is less
than the tensile or breaking strength. Plastic deformation is believed to create the greatest
number of clean surfaces. Because plastic deformation is a time dependent process (2,7,8)
higher rate of force application should lead to the formation of less new clean surfaces and
thus resulting in weaker tablets. Furthermore, since tablet formation is dependent on the
3
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
formation of new clean surfaces, high concentration or over mixing of materials that form
weak bonds result in weak tablets.
Magnesium stearate for example, forms weak bond and easily wet surfaces. Therefore over
mixing of magnesium stearate may lead to weak tablets (2).
Conversely, in materials in which the shear strength is greater than the tensile strength,
particles may be preferentially fractured, and the smaller fragments then help to fill up the
adjacent air spaces. This is most likely to occur with hard, brittle particles and is known as
brittle fracture; sucrose behaves in this manner. The ability of a material to deform in a
particular manner depends on the lattice structure; in particular whether weakly bonded
lattice planes are inherently present. Brittle fracture creates clean surfaces that are brought in
intimate contact by applied load.
Irrespective of the behaviour of large particles of materials, small particles may deform
plastically through a process known as microsquashing, and the proportion of fine powders in
a sample may therefore be significant. Asperities that are sheared off larger, highly irregular
particles could also behave in this way; hence particle shape is an important factor.
Summarily, four stages of events are encountered during compression (1,2):
(i)
Initial repacking of particles.
(ii)
Elastic deformation of the particles until the elastic limit (yield point) is reached.
(iii) Plastic deformation and/or brittle fracture then predominate until all the voids
are virtually eliminated.
(iv) Compression of the solid crystal lattice then occurs.
Consolidation
Consolidation has been described as the increase in the mechanical strength of a material as a
result of particle/particle interactions (2). Various mechanisms of powder consolidation are
discussed below.
When the surfaces of two particles approach each other closely enough (e.g. at a separation of
less than 50nm), their free surface energies result in a strong attractive force through a
process known as cold welding. The nature of the bonds so formed are similar to those of the
molecular structure of the interior of the particle surface (on a molecular scale), but the actual
surface area involved may be small. This hypothesis is favoured as a major reason for the
increasing mechanical strength of a bed of powder when subjected to rising compressive
forces.
On the macro scale, most particles encountered in practice have an irregular shape, so that
there are many points of contact in a bed of powder. Any applied load to the bed must be
transmitted through this particle contacts. However, under appreciable forces, this
transmission may result in the generation of considerable frictional heat. If this heat is
dissipated, the local rise in temperature could be sufficient to cause melting of the contact
area of the particles, which would relieve the stress in that particular region. When the melt
solidifies, fusion bonding occurs, which in turn results in an increase in the mechanical
strength of the mass.
All the deformation effects may be accompanied by the breaking and formation of new bonds
between the particles, which give rise to consolidation as new surfaces are pressed together.
Another possible mechanism of powder consolidation is asperitic melting of the local surface
of powder particles (9,10). During compression, the powder compact typically undergoes a
temperature increase usually between 4 and 30 o C, which depends on the friction effects, the
specific material characteristics, the lubrication efficiency, the magnitude and rate of
4
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
application of compression forces, and the machine speed (9,11). As the tablet temperature
rises, stress relaxation and plasticity increases while elasticity decreases and strong compacts
are formed (12). Therefore, compression of material at elevated temperature with increase in
ductility should result in stronger tablets (2). Asperitic melting is believed to be important
only with relatively low melting point materials for which even very hard asperities are
pushed into a more plastic material.
The final tablet properties are also affected by the consolidation (i.e. bonding) mechanisms of
the powder which is influenced by its chemical nature, the surface area of the contact point,
contamination (including film coating, such as magnesium stearate) and interparticulate
distance (2).
Jones (13) has divided the compression event into a series of time periods, and from this,
proposed a number of useful definitions.
These are:
(i)
Consolidation time: time to reach maximum force.
(ii)
Dwell time: time at maximum force.
(iii) Contact time: time for compression and decompression excluding ejection time.
(iv) Ejection time: time during which ejection occurs.
(v)
Residence time: time during which the formed compact is within the die.
Fig. 2 is a diagrammatic representation of the lower punch force trace from an eccentric press,
and shows Jones' definitions in this context. Dwell time cannot be shown is such a situation,
since force reaches a maximum value and then immediately decreases, i.e. a peak is obtained
with no plateau. However, in some studies, the maximum force is maintained for prolonged
periods and so "dwell time" has a meaning in such circumstances. Furthermore, in rotary
presses, a definite though extremely short dwell time is encountered.
Fig. 2. Events during the compression process (13).
5
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
Decompression
In tabletting, the compression process is followed by a decompression stage, as the applied
load is removed. Most compression theories and their related equations describe only the
compression stage of the tabletting process, whereas a complete tabletting cycle involves
compression, decompression and ejection stages. These theories have in effect proved
inadequate to explain some of the compression problems often encountered in routine tablet
production. For instance, why some pharmaceutical powders and formulations form crumbly
tablets while others form fractured tablets with strong individual pieces; or why minor
changes in processing and formulation significantly affect the tabletting characteristics of
materials and quality of formed tablets.
It is now realized that the decompression stage is as important as (but not independent of) the
compression stage in determining whether or not a tablet formulation will form satisfactory
tablets. For example, some deformation processes are time-dependent and occur at various
rates during the compaction sequence, so that the tablet mass is never in a state of
stress/strain equilibrium during the actual tabletting process. This means that the rate at which
load is applied and removed may be a critical factor in materials for which dependence on
time is significant. More specifically, if a plastically deforming solid is loaded (or unloaded)
too rapidly for the process to take place, the solid may exhibit brittle fracture. In view of this,
research investigations in recent years have shifted to relating the capping and lamination
tendencies of tablet formulations to their plastic and elastic behaviour during the
compression/ decompression/ ejection cycle (14-18). The same deformation characteristics
that come into play during compression play a role during decompression (2).
Decompression leads to a new set of stresses within the tablet as a result of elastic recovery,
which is augmented by the forces necessary to eject the tablet from the die. Irrespective of the
consolidation mechanism, the tablet must be mechanically strong enough to withstand these
new stresses, otherwise structural failure will occur. In particular, the degree and rate of stress
relaxation within tablets, immediately after the point of maximum compression have been
shown to be characteristic of a particular system (1). This phase of the cycle can provide
valuable insight into the reasons behind inferior tablet quality and may suggest a remedy.
If the stress relaxation process involves plastic flow, it may continue after all compression
force has been removed, and the residual die wall pressure will decay with time. David and
Augsburger (19) have been able to interpret plastic flow in terms of viscous and elastic
parameters in series. This interpretation leads to the relationship of the form:
ln(Ft ) = ln(Fm) - K t
(5)
where Ft is the force left in the visco-elastic region at time t, Fm is the total magnitude of the
force at time t=0 (i.e. when decompression begins) and K is the visco-elastic slope and a
measure of the degree of plastic flow.
Materials with higher K values undergo more plastic flow and such materials often form
strong tablets at relatively low compaction forces. On the other hand, the changing thickness
of the tabletting mass due to the compactional force and subsequently due to elastic recovery
(ER) during unloading can be used to obtain a measure of plastoelasticity ER/PC; Where PC
is the plastic compression of the material under constant load.
Force transmission through a powder bed
The process of tabletting involves the application of massive compressive forces, which
induce considerable deformation in the solid particles (Fig. 3). During normal tablet
operations, consolidation is accentuated in those regions adjacent to the die wall, owing to the
intense shear to which the material is subjected to, as it is compressed axially and pushed
along the wall surface.
6
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
Fig. 3: Diagram of a cross section of a typical single punch and die assembly used for
compaction studies.
The resistance to differential movement of particles caused by their inherent cohesiveness
results in the applied force not being transmitted uniformly throughout the entire mass. In the
case of single-station press, the force exerted by the upper punch diminishes exponentially at
increasing depths below it. Thus, the relationship between upper punch force, FA , and lower
punch force, FL , may be expressed in the form:
FL = FA . e - kH/D
(6)
where k is an experimentally determined material-dependent constant that includes a term for
the average die-wall frictional component. H and D are the height and diameter of the tablet
respectively.
The discrepancy between the two punch forces should be minimized in pharmaceutical
tabletting operations, so that there is no significant difference in the amount of compression
and consolidation between one region of the tablet and another. The effect of die wall friction
can be reduced by having smaller tablet-to-diameter ratios and by adding lubricants (1,20).
The distribution of force in an isolated punch and die set is shown in Fig. 4, with force being
applied to the top of a cylindrical powder mass.
Fig. 4. Force distribution through a powder bed
Since there must be an axial (vertical) balance of forces:
FA = FL + FD
(7)
where FA is the force applied to the upper punch, FL is that proportion of it transmitted to the
lower punch, and FD is the reaction of the die wall due to the friction at this surface. Because
of this inherent difference between the force applied at the upper punch and that affecting
material close to the lower punch, a mean compaction force, FM , has been proposed, where:
7
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
FM = (FA + FL ) / 2
(8)
FM offers a practical friction-independent measure of compaction load, which is generally
more relevant than FA (1). In single-station presses, where the applied force transmission
decays exponentially as in equation 6, a more appropriate geometric mean force, FG , might
be:
FG
=
( FA . FL ) 0.5
(9)
The use of these parameters is probably more appropriate than the use of F A when
determining the relationships between compressional force and such properties as tablet
strength.
As the compressional force is increased and the repacking of the tabletting mass is completed,
the material may be regarded as a single solid body. Then, the compressive force applied in
one direction (e.g. vertical) results in a decrease, H, in the height, i.e. a compressive stress.
In the case of an unconfined solid body, this would be accompanied by an expansion in the
horizontal direction of D. The ratio of these two dimensional changes are known as the
Poisson ratio (λ) of the material, defined as:
λ
= D / H
(10)
The Poisson ratio is a characteristic constant for each solid material and may influence the
tabletting processes. Under the conditions illustrated in Fig 4, the material is not free to
expand in the horizontal plane because it is confined in the die. Consequently, a radial diewall force FR develops perpendicularly to the die-wall surface, materials with larger Poisson
ratios giving rise to higher values of FR. Classical friction theory can be applied to deduce
that the axial frictional force FD is related to FR by the expression:
FD
=
μW . FR
(11)
where μW is the coefficient of die-wall friction. FR is reduced when materials of small
Poisson ratios are used, and in such cases, axial force transmission is optimum.
The frictional effects represented by μW arise from the shearing of adhesions that occurs as
the particles slide along the die-wall. Hence, its magnitude is related to the shear strength, S,
of the particles (or the die-wall-particle adhesions if these are weaker) and the total effective
area of contact, Ae, between the two surfaces. Therefore, optimal force transmission is also
realized when FD values are reduced to a minimum, which is achieved by ensuring adequate
lubrication at the die wall (lower S) and maintaining a minimum tablet height (reducing Ae).
A common method of comparing degrees of lubrication has been to measure the applied and
transmitted axial forces and determine the ratio FL / FA. This is called the coefficient of
lubrication, or R value (1). The ratio approaches unity for perfect lubrication (no wall
friction), and in practice, values as high as 0.98 may be realized. Values of R should be
considered as relating only to the specific system from which they are obtained, because they
are affected by other variables, such as compressional force and tablet H/D (height /
diameter) ratio.
Compaction data analysis
The phenomena and mechanisms involved during compaction of pharmaceutical materials
have become an important concept in the design and development of solid dosage forms. This
is due to the fact that systematic investigations are facilitated by the use of instrumented
single-station and multi-station tablet presses, universal testing machines and integrated
compaction research systems, also known as compaction simulators (21-23). The parameters
monitored during compaction vary widely in these studies. Data obtained from the
measurements of forces on the punches and the displacement of the upper and lower punches,
axial to radial load transmission, die wall friction, ejection force, temperature changes and
8
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
other miscellaneous parameters have been used to assess the compaction behavior of a
variety of pharmaceutical powders and formulations (24). Many empirical relationships have
been proposed to describe the resulting data which may be expressed equivalently in term of
stress-strain, pressure-volume or pressure –density since the natural strain, for example, is
equal to the natural log of the ratio of the initial bed height or volume to the current height or
volume respectively (25).
A compaction equation relates some measure of the state of consolidation of a powder, such
as porosity, volume (or relative volume), density or void ratio, with a function of the
compaction pressure. The initial purpose of fitting experimental data to an equation is usually
to linearize the plots so as to make comparisons easier between different sets of data (26).
The parameters of the fitting equation can also be used for comparison purposes. A second
reason is a practical one of predicting the pressure to obtain a required density. The large
range of pressures over which compaction studies can be made, makes it obvious and
reasonable to plot pressures logarithmically, so as to spread out the data in a distinguishable
form. This was done by Walker (1923) who plotted the relative volume (VR) of the powder
compact against the logarithm of the applied axial pressure (Pa) as shown in the following
equation (26):
VR = a1 – K1 In Pa
(12)
Later, many other compaction equations have been proposed and today, more than fifteen
different mathematical descriptions of the compaction process have been compiled in the
literature (24,25) and several of these including those of Heckel (27,28), Kawakita (25) and
Adams (29,30) have been validated for pharmaceutical systems. However, it is highly
unlikely that a single compaction equation will fit all the compaction mechanisms. In
interpreting compaction curves, it is therefore essential to know which mechanisms are
operating, or not, over different region of pressure. A good compaction curve should be able
to indicate changes in the compression mechanism.
1. Heckel equation
Powder packing with increasing compression load is normally attributed to particle
rearrangement, elastic and plastic deformation and particle fragmentation as have been
previously discussed. The Heckel analysis is a popular method of determining the volume
reduction mechanism under the compression force (24, 27, 28) and is based on the
assumption that powder compression follows first order kinetics with the interparticulate
pores as the reactants and the densification of the powder as the product. According to the
analysis, the degree of compact densification with increasing compression pressure is directly
proportional to the porosity as follows:
dρR / dP
= kE
(13)
where ρR is the relative density at pressure, P, and E is the porosity.
The relative density is defined as the ratio of the density of the compact at pressure, P, to the
density of the compact at zero void or true density of the material (see equation 3).
The porosity (see equation 4) can also be defined as:
E = (Vp - V) / Vp = 1 - ρR
(14)
where Vp and V are the volume at any applied load and the volume at theoretical zero
porosity, respectively.
Thus, equation 14 can be expressed as:
dρR / dP = k ( 1 - ρR )
(15)
and then transformed to:
9
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
ln[1 / (1 - ρR )] = k P + A
(16)
Plotting the value of ln [1 / (1 - ρR )] against applied pressure, P, yields a linear graph having
slope, k and intercept, A. The reciprocal of k yields a material-dependent constant known as
yield pressure, Py which is inversely related to the ability of the material to deform plastically
under pressure. Low values of Py indicate a faster onset of plastic deformation(31). This
analysis has been extensively applied to pharmaceutical powders for both single (32,33) and
multi-component systems (31,34-38).
The intercept of the extrapolated linear region, A, is a function of the original compact
volume. It represents two stages of densification - one due to the initial relative density of the
powder and the other due to densification by particle rearrangement. From the value of A, the
relative density, DA, which represents the total degree of densification at zero and low
pressures (31,33,39,40), can be calculated using the equation (41,42):
A
= ln[1 / (1 - DA )]
(17)
Thus,
DA = 1 - e - A
(18)
The relative density of the powder bed at the point when the applied pressure equals zero, D0 ,
is used to describe the initial rearrangement phase of densification as a result of die filling. D0
is determined experimentally and is equal to the ratio of bulk density at zero pressure to the
true density of the powder (43). The loose packing of granules at zero pressure tends to yield
low D0 values (18, 31).
The relative density, DB , describes the phase of rearrangement of particles in the early stages
of compression and tends to indicate the extent of particle or granule fragmentation, although
fragmentation can occur concurrently with plastic and elastic deformation of the constituent
particles (44). The extent of the rearrangement phase depends on the theoretical point of
densification at which deformation of particles begins. DB can be obtained from the equation:
DB = DA - D0
(19)
The particular value of Heckel plots arises from their ability to identify the predominant form
of deformation in a material. They have been used:
(i)
to distinguish between substances that consolidate by fragmentation and those
that consolidate by plastic deformation.
(ii)
as a means of assessing plasticity. Materials that are comparatively soft readily
undergo plastic deformation. Conversely, materials with higher mean yield
pressure values usually undergo compression by fragmentation first, to provide a
denser packing. Hard, brittle materials are generally more difficult to compress
than soft ones.
Hersey & Rees (45) and York & Pilpel (46) classified powders into three types A, B and C.
The classification is based on Heckel plots and the compaction behavior of the material. With
type A materials, a linear relationship is observed, with the plots remaining parallel as the
applied pressure is increased indicating deformation apparently only by plastic deformation
(Fig. 5A). An example of materials that exhibit type A behavior is sodium chloride. Type A
materials are usually comparatively soft and readily undergo plastic deformation retaining
different degrees of porosity depending on the initial packing of the powder in the die. This is
in turn influenced by the size distribution, shape, e. t. c., of the original particles.
For type B materials, there is an initial curved region followed by a straight line (Fig. 5B).
This indicates that the particles are fragmenting at the early stages of the compression process
i. e. brittle fracture preceds plastic flow. Type B Heckel plots usually occur with harder
10
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
materials with higher yield pressures which usually undergo compression by fragmentation
first, to provide a denser packing. Lactose is a typical example of such materials.
For type C materials, there is an initial steep linear region which become superimposed and
flatten out as the applied pressure is increased (Fig. 5C). York and Pilpel (43) ascribed this
behavior to the absence of a rearrangement stage and densification is due to plastic
deformation and asperity melting.
Fig. 5:The 3 different types of Heckel plots.
Type A Heckel plots usually exhibit a higher final slope than type B which implies that the
former materials have a lower yield pressure. This is so because fragmentation with
subsequent percolation of fragments is less efficient than void filling by plastic deformation.
11
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
In fact, as the porosity approaches zero, plastic deformation may be the predominant
mechanism for all materials.
The two regions of Heckel plots in type B are thought to represent the initial repacking stage
and subsequent deformation process, the point of intersection corresponding to the lowest
force at which a coherent tablet is formed. In addition, the crushing strength of tablets can be
correlated with the values of k of the Heckel plot; larger k values usually indicate harder
tablets. Such information can be used as a means of binder selection when designing tablet
formulations. Heckel plots can be influenced by the overall time of compression, the degree
of lubrication and even the size of the die, so that the effects of these variables are also
important and should be taken into consideration.
Roberts and Rowe (47) carried out some work involving the application of the Heckel
relationship to a wide range of powders. They observed that there was a reasonable
agreement between the yield stresses obtained with the Heckel relationship and values
measured independently using indentation hardness. The Heckel equations have also proved
useful in characterizing the compressional properties of some pharmaceutical excipients
developed locally in Nigeria. Itiola (33) showed that three different local starches, namely
cassava (from Manihot utilissima ), potato (from Ipomea batatas ) and yam (from Discorea
rotundata ) starches deform mainly by plastic flow as has been observed for many official
and proprietary starches. This equation has also been used to evaluate the compressional
characteristics of tablet formulations containing local gums (31,36,37,48,49) and starches
(44) as binding agents. It was believed that Heckel plots generally exhibit linearity for
materials at high pressures (24). However, Odeku and Itiola (31) while working on the
compressional properties of paracetamol tablet formulations found that the Heckel plots
exhibited some degree of linearity at both low and high pressures. Normally, it would be
expected that the formulations would consolidate by fragmentation first at low pressures as
normally evidenced by an initial curvilinear portion, but the apparent linearity at low
pressures suggests that some degree of plastic deformation was also taking place. This is
probably due to the fact that the system would start deforming plastically from the moment
the yield value for one particle is exceeded during compression. Thus, it should be expected
that the process of fragmentation of the granules would occur, to some extent, simultaneously
with plastic and elastic deformation of the constituent particles. However, the fact that
plasticity is measurable more accurately at higher pressures was evidenced by the higher
values of correlation coefficient of the linear second region of the Heckel plots for the
formulations. Furthermore, binding agents were shown to facilitate the plastic deformation of
pharmaceutical materials with the degree of plasticity increasing with increase in the
concentration of the binding agent. With the phenomenon of plastic deformation being timedependent (50,51), the rate of plastic flow may be more important than the total plastic flow
for the production of tablets without lamination and capping problems. The rate of
deformation could be very important for tabletting considerations considering the fact that
most tabletting machines have short dwell or compression time.
2. Kawakita equation
The Kawakita equation was developed to study powder compression (25) using the degree of
volume reduction, C, a parameter equivalent to the engineering strain of the particle bed and
is expressed as:
C = (V0 - Vp ) / V0 = a b P / (1+ bP)
(20)
In practice, the Kawakita equation can be rearranged to give:
P / C = P / a + 1 / ab
(21)
where C is the degree of volume reduction, V0 is the initial volume of the powder bed and V p
is the powder volume after compression; a and b are constants which are obtained from the
12
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
slope and intercept of the P/C versus P plots respectively. The constant a is equal to the
minimum porosity of the bed prior to compression while b, which is termed the coefficient of
compression, is related to the plasticity of the material. Values of 1 – a yield the initial
relative density of the material, D I which have been shown to provide a measure of the
packed initial relative density of tablets with the application of small pressure or what may be
referred to as tapping (31,44,52). The reciprocal of b yields a pressure term, P k , which is the
pressure, required to reduce the powder bed by 50% (53,54). The value of P k provides an
inverse measurement of plastic deformation during the compression process. The lower the
value of P k , the higher the degree of plastic deformation occurring during compression
(30,44).
Celik (24) reported that the Kawakita equation appeared to be applicable to materials in
powder form only. The equation can be adapted by substituting the initial compaction volume
with an initial bulk volume in order to have a better fit to the Kawakita equation for
granulated materials. Another limitation of the Kawakita equation as reported by Celik (24) is
that using this method, the compaction process can be described up to a certain pressure
above which the equation is no longer linear. It is now generally accepted that the Kawakita
equation is best used for low pressures and high porosities (26). The equation is applied
frequently with some success to tapping and vibrational densification (i.e. the higher
porosities). In these cases, the pressure term is replaced by the number of taps or time in the
case of machine vibration (25).
It has been shown that the Kawakita relationship may be employed to determine the tensile
strength of agglomerates provided that the influence of the friction at the die wall of the
compaction cell has been taken into account since it is well established that wall friction
significantly increase resistance to deformation (25,30). Kawakita and Ludde stated that the
equation holds best for soft fluffy pharmaceutical powders and stated that particular attention
must be paid to the measurement of the initial volume, Vo, and that deviation from this
equation is sometimes due to the measured value of Vo. The Kawakita equation however, has
also been applied to granules which cannot be described as light and fluffy (31,44,48). Odeku
and Itiola (31) have shown that the pressure term, P k provides a measure of the total amount
of plastic deformation occurring during compression. Recent studies carried out in our
laboratory have shown that the tensile strength of paracetamol tablets containing pigeon pea,
plantain and corn starches as binding agent, was inversely related to the values of P k values
of the various formulations (55). This supports the assertion that as has been previously
established that higher total plastic deformation would lead to more contact points for
interparticulate bonding to produce stronger tablets (30,44,56).
The Heckel and Kawakita plots have been employed to evaluate and describe the
compressional characteristics of paracetamol formulations (31). Both plots have their
limitations and are believed to generally exhibit linearity for materials at high and low
pressures, respectively (24). Thus both plots have been used with the hope of obtaining more
accurate information on the compressional characteristics of the paracetamol tablet
formulations. Research has shown that the Heckel and Kawakita plots gave largely different
indications for the plasticity of the formulations (31). The observed differences between P y
and P k for the different binders are probably due to the fact that the P y values relate
essentially to the onset of plastic deformation during compression while the P k values appear
to relate to the amount of plastic deformation occurring during the compression process,
especially with plastic deformation being a time-dependent phenomenon (50,51). Thus, the
more the time allowed for plastic deformation to occur (i. e. increase in dwell time), the more
the difference between the values of P y and P k would be, although it should be remembered
that for every material, there would be a limiting dwell time after which no more plastic
deformation would occur. Furthermore, it should be noted that differences between P k and P
13
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
would be observable more for materials that deform mainly by plastic flow than for those
that deform mainly by fragmentation (47).
y
It should be possible, therefore, to obtain more information on the deformation profile of a
material from the combined use of P k and P y . For example, to obtain optimum plasticity,
there may not be much point in using a long dwell time for a material with a low P y but a
high P k . On the other hand, it should be of significant benefit to use a long dwell time for a
material with a high P y but low P k values. However, material with low P y and P k values
should not give any appreciable problems on any type of tabletting machine, while materials
with a combination of high P k and P y values would give compressional problems on virtually
any type of tabletting machine, and reformulation or the addition of plastic materials may be
necessary in such cases.
3. Adams Equation
The Adams equation (29,30) was derived in order to estimate the fracture strength of single
granules from in-die compression data. It models the bed of granules in the die as a series of
parallel load-bearing columns. The following equation was derived:
In P = In (тo’ / α’ ) +α’ ε + In (1 – e (-α’ε) )
(22)
where P is the applied pressure and ε is the natural strain which is given by:
ε = In (Ho / Hp )
(23)
where Ho and Hp are the initial and current height of the bed respectively. The quantity тo’ is
the apparent single agglomerate strength which is related to the actual strength, тo , as
follows:
тo’ = k1 тo
(24)
where k1 is a constant. The quantity α ’ is related to the pressure coefficient, α of the
agglomerate strength by the following expression:
α ’ = k2 α
(25)
where k2 is a constant.
At higher values of natural strain, the last term of the Adams equation becomes negligible
and can be omitted, leaving a linear function. The intercept and slope of this linear part of the
profile were used to calculate the compression parameter тo’ .
Nicklasson & Alderborn (56) have used the Adams and Kawakita equations to analyse the
compression mechanics of pharmaceutical agglomerates. They found that both 1/ b (Pk ) from
Kawakita and т o ’ from Adams were related with agglomerates porosity and composition. The
two parameters were related to the intergranular pore structures and tensile strength of the
tablets formed from the agglomerates. They concluded that 1/ b and тo’ may be interpreted as
measure of agglomerate shear strength during uniaxial confined compression and as such
may be used as indications of tabletting performance of the agglomerates.
Conclusion
The understanding of the principles involved in compressibility and compactibility are
required to characterise the compaction profiles of pharmaceutical materials. Both
phenomena are important in the tabletting of the materials. The importance of each will
depend largely on the type of compact required i.e. whether soft or hard and on the brittle
properties of the materials. Various mathematical equations have been used to describe the
compaction process. The use of one single equation is unlikely to be adequate since different
materials consolidate by different mechanism depending on their properties. Some progress
has been made in this direction with prominence of some relevant parameters obtained from
the more useful compression equations. The rate and extent of plastic deformation are now
14
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
more completely characterized by the combined use of P y and P k from the Heckel and
Kawakita equations respectively. There is also promise of additional indices from newer
approaches to the study of the compression process. More work is however required.
References
1. Marshall, K., Compression and consolidation of powdered solids. In : The Theory and Practice of
Industrial Pharmacy. Lachman, L., Lieberman, H. A. and Kanig, J. L. (Eds.) 3 rd Edition (1986)
Lea & Febiger, Philadelphia , pp. 66-99.
2. Bodga, M. J. (2002) Tablet compression: Machine theory, design and process troubleshooting. In:
Encyclopedia of Pharmaceutical Technology. Swarbrick J and Boylan J (Eds). Marcel and Dekker
Inc., USA . Vol. 3: 2669 – 2688.
3. British Pharmacopoeia (1998) HMSO, London .
4. Summers, M. P. Granulation. In : Pharmaceutics: The science of dosage form design. Aulton, M.
E. (Ed.) ELBS. 1 st Edition (1988), Longman grp. Ltd., U. K. pp. 616-628.
5. Banker, G. S. and Anderson, N. R., Tablets. In : The Theory and Practice of Industrial Pharmacy.
Lachman, L., Lieberman, H. A. and Kanig, J. L. (Eds.) 3 rd Edition. (1986) Lea & Febiger,
Philadelphia , pp. 301-303.
6. Staniforth, J. N. Powder flow. In : Pharmaceutics: The science of dosage form design. Aulton, M.
E. (Ed.) ELBS. 1 st Edition (1988), Longman grp. Ltd., U. K. pp. 600-615.
7. Armstrong N. A. (1989) Time dependent factors involved in powder compression and tablet
manufacture. Int. J. Pharm. 49: 1-13.
8. Ayorinde, J. O. Odeku, O. A. and Itiola, O. A. (2005) The survival of B. Subtilis spores in
dicalium phosphate, lactose and corn starch and their binary mixtures during tableting.
Pharmaceutical Technology 29 (12):56-67.
9. Rankell, A. S. and Higuchi, T. (1968) Physics of tablet compression: XV. J. Pharm. Sci., 57: 574577.
10. York, P. and Pilpel, N. (1973) The tensile strength and compression behaviour of lactose, four
fatty acids and their mixtures in relation to tabletting. J. Pharm. Pharmacol., 25: 1P-11P.
11. Hanus, E. J. and King, L. D. (1968) Thermodynamic effects on the compression of solids. J.
Pharm. Sci., 57: 677-684.
12. Esezobo, S. and Pilpel, N. (1986) The effect of temperature on the plasto-elasticity of some
pharmaceutical powders and on the tensile strength of their tablets. J. Pharm. Pharmacol., 38:
409-413.
13. Jones, T. M. (1981) The physicotechnical properties of starting materials used in tablet
formulation. Int. J. Pharm. Prod. Manuf., 2: 17-24.
14. Carless, J. E. and Leigh, S. (1974) Compression characteristics of powders: Radial die wall
pressure transmission and density changes. J. Pharm. Pharmacol., 26: 189-297.
15. Hiestand, E. N., Wells, J. E., Poet, C. B. and Ochs, J. F. (1977) Physical processes of tabletting. J.
Pharm. Sci. 66 : 510 - 519.
16. Rees, J. E. and Rue, P. J. (1978) Time-dependent deformation of some direct compression
excipients. J. Pharm. Pharmacol. , 30: 601-607.
17. Krycer, I. , Pope, D. G. and Hersey, J. A. (1982) The role of intragranular porosity in powder
compaction. Powder Technol., 33: 101-111.
18. Itiola, O. A. and Pilpel, N. (1986) Tabletting characteristics of metronidazole formulations. Int. J.
Pharm. 31: 99-105.
19. David, S. T. and Augsburger, L. L. (1977) Plastic flow during compression of directly
compressible fillers and its effect on tablet strength. J. Pharm. Sci., 66: 155-159.
15
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
20. Briscoe B. J. and rough S.L. (1998) The effects of wall friction on the ejection of pressed ceramic
parts. Powder Technol. 99: 228- 233.
21. Higuchi, T., Rao, A. N., Busse, L. W. and Swintosky, J. V. (1953) The Physics of tablet
compression, 2: the influence of degree of compression on properties of tablets. J. Am. Pharm.
Assoc. Sci. Ed. 42: 194-200.
22. Higuchi, T., Nelson, E. and Busse, L. W. (1954) The physics of tablet compression, 3: design and
construction of an instrumented tabletting press. J. Am. Pharm. Assoc. Sci. Ed. 43: 344-348.
23. Train, D. (1954) An investigation into compaction of powders. J. Pharm. Pharmacol. 8: 745-761.
24. Celik, M. (1992) Overview of compaction data analysis techniques. Drug Dev. Ind. Pharm., 18:
767-810.
25. Kawakita, K. and Ludde, K. H. (1970/71) Some considerations on powder compression equations.
Powder Technol., 4: 61-68.
26. Denney P.J. (2002) Compaction equations: a comparism of the Heckel and Kawakita equations
Powder Technol. 127: 162 – 172.
27. Heckel, R. W. (1961) Density-pressure relationships in powder compaction. Trans. Metall. Soc.
AIME., 221: 671-675.
28. Heckel, R. W. (1961) An analysis of powder compaction phenomena. Trans. Metall. Soc. AIME.,
221: 1001-1008.
29. Adams , M. J. Mullier M. A. and Bircall, J. D. (1994) Agglomerates strength measurements using
a uniaxial confined compression test. Powder Technol . 78: 5-13.
30. Adams, M. J. and McKeown, R. (1996) Micromechanical analysis of the pressure-volume
relationships for powders under confined uniaxial compression. Powder Technol . 88: 155-163.
31. Odeku, O. A and Itiola O. A. (1998) Evaluation of khaya gum as a binder in a paracetamol tablet
formulation. Pharm Pharmacol Commun ., 4: 183-188.
32. Duberg, M. and Nystrom, C. (1986) Studies on direct compression of tablets. XVII. Porositypressure curves for the characterization of volume reduction mechanisms in powder compression.
Powder Technol. , 46: 67-75.
33. Itiola, O. A. (1991) Compressional characteristics of three starches and the mechanical properties
of their tablets. Pharm. World J., 8(3) : 91-94.
34. Kurup, T. R. R. and Pilpel, N. (1978) Compression characteristics of pharmaceutical powder
mixtures. Powder Technol., 19: 147-155.
35. Garr, J. S. M. and Rubinstein, M. H. (1992) Consolidation and compaction characteristics of
three-component particulate system. Int. J. Pharm., 82: 71-77.
36. Adeyemo, O. A. and Itiola, O. A. (1993) Effects of khaya gum and gelatin on the compressional
characteristics of a griseofulvin tablet formulation. J. West Afr. Pharm . 7: 27-29s
37. Odeku, O. A. and Itiola, O. A. (2002) Characterisation of khaya gum as a binder in a paracetamol
tablet formulation. Drug Dev. Ind. Pharm. 28 (3); 329-337
38. Odeku, O. A., Itiola O. A. and Adeniran, A. A. (1998) Effects of Yam and Corn Starches on the
Mechanical and Disintegration of Paracetamol Tablets. Proceedings of the 1 st International
Workshop on Herbal Medicinal Products , pp. 193-200
39. Paronen, P. and Juslin, M. (1983) Compressional characteristics of four starches. J. Pharm.
Pharmacol., 35: 627-635.
40. Mitrevej, A., Faroongsarng, D. and Sinchaipanid, N. (1996) Compression behaviour of spray
dried rice starch. Int. J. Pharm., 140: 61-68.
41. Humbert-Droz, P., Gurny, R., Mordier, D. and Doelker, E. (1983) Densification behaviour of
drugs presenting availabilty problems. Int. J. Pharm. Tech, Prod. Mfr., 4: 29-35.
16
http://www.pharmainfo.net/reviews/compaction-pharmaceutical-powders
42. Roberts, R. J. and Rowe R.C (1985) The effect of punch velocity on the compaction of a variety
of materials. J. Pharm. Pharmacol., 37: 377 - 384.
43. Chowhan, C. T. and Chow, Y. P. (1981) Compression behaviour of granulations made with
different binders. Int. J. Pharm. Tech. Prod. Mfr. 2(1) : 29-34.
44. Odeku, O. A., Awe, O. O., Popoola, B. Odeniyi, M. A. and Itiola, O. A. (2005) Compression and
mechanical properties of tablet formulations containing corn, sweet potato, and cocoyam starches
as binders. Pharm. Tech. 29 (4): 82-90.
45. Hersey, J. A. and Rees, J. E. (1971) Deformation of particles during briquetting. Nature, 230: 96.
46. York, P. and Pilpel, N. (1972) The effect of temperature on the mechanical properties of some
pharmaceutical powders in relation to tabletting. . J. Pharm. Pharmacol., 24: 47P-56P.
47. Roberts, R. J. and Rowe, R. C. (1986) The effect of the relationship between punch velocity and
particle size on the compaction behaviour of materials with varying deformation mechanisms. J.
Pharm. Pharmacol. , 38: 566-571.
48. Odeku, O. A. (2005) Assessment of Albizia zygia gum as binding agent in tablet formulations.
Acta Pharm. 55 (3):263-276.
49. Odeku, O. A. and Patani, B. O. (2005) Evaluation of dika nut mucilage (Irvingia gabonensis) as a
binder in metronidazole tablet formulations. Pharm. Dev. Tech. 10: 439-446.
50. Rees, J. E. and Rue, P. J. (1978) Time-dependent deformation of some direct compression
excipients. J. Pharm. Pharmacol. , 30: 601-607.
51. Akande, O. F., Ford, J. L. Rowe, P. H. and Rubinstein, M. H. (1998) The effects of lag-time and
dwell-time on the compaction properties of 1:1 paracetamol/microcrystalline cellulose tablets
prepared by pre-compression and main compression. J. Pharm. Pharmacol. , 50: 19-28.
52. Podczeck, F. and Sharma, M. (1996) The influence of particle size and shape of components of
binary powder mixtures on the maximum volume reduction due to packing. Int. J. Pharm., 137:
41-47.
53. Shivanand, P. and Sprockel, O. L. (1992) Compaction behaviour of cellulose polymers. Powder
Technol., 69: 177-184.
54. Lin, C. and Cham, T. (1995) Compression behaviour and tensile strength of heat-treated
polyethylene glycols. Int. J. Pharm., 118: 169-179.
55. Dare, K., Akin-Ajani, D. O., Odeku, O. A., Odusote O. M. and Itiola, O. A. (2006) Effects of
pigeon pea and plantain starches on the compressional, mechanical and disintegration properties
of paracetamol tablets. Drug Dev. Ind. Pharm . 32: (In Press)
56. Nicklasson, F and Alderborn, G. (2000) Analysis of the compression mechanics of
pharmaceutical agglomerates of different porosity and composition using the Adams and
Kawakita equation. Pharm. Res. 17 (8): 949-954.
17