The Heckel equation is used to analyze compaction data and determine the mechanism of volume reduction under compression force. It relates the natural log of relative density to applied pressure in a linear relationship. The slope (k) is related to the ability of the material to deform plastically, with a lower yield pressure (Py=1/k) indicating faster plastic deformation. The intercept (A) relates to the original compact volume and initial densification from die filling before plastic deformation sets in. The Heckel analysis provides insight into particle rearrangement, elasticity, plasticity and fragmentation during powder compaction.

1. Compression and Compaction
By:
Mr. Santosh A. Payghan
(Asst. Professor)
Tatyasaheb Kore college of
Pharmacy, Warananagar.

2. Powder Properties
Solid particles are made up of molecules that are held in
close proximity to each other by intermolecular forces.
The strength of interaction between two molecules is due
to the individual atoms within the molecular structure.
For example, hydrogen bonds occur as a result of an
electrostatic attraction involving one hydrogen atom and
one electronegative atom, such as oxygen.
For molecules that cannot hydrogen bond, attraction is due
to van der Waal's forces. dipole-dipole (Keesom),dipole-
induced dipole (Debye) and induced dipole-induced dipole
(London) forces.

3. Derived properties of powdered solids
1. The solid-air interface 4. Mass-volume relationships
2. Angle of repose 5. Density
3. Flow rates
AngleDensity
Mass-volumeRates of relationships
The solid-air interface
Flowrepose
HeliumTan-1VOLUME
1. θ = Pycnometer 2. θ = cos D/
Liquid displacement method
Compressibility indexdensityPOROSITY -1 of (l1+l2)
(h/r)
VCOHESION: Methods topossible Angle gravity bottle used.Flow
= V /U maximum angle measure here,
The -U x[U types of
Different-U ] : Consolidation/Repose
t
here,
c 1 2 1 s Pycnometer or specific
 Truevolume betweent)freeparticle.  Carr’sVIndex(% ) of) base-w )/(w -w )
volume and index)
(V
(Carr's consolidationlike standing True density= w /(w -w = (w
a. Attraction of sample
Vt = Fixedheight of pile
true = funnel
E = V / Vb
between the surface of pile , D = diameter
h 3 4 2 2 1 4 2
Vc=true= radius stainless base)of the pile w = wt. ofl1Pycnometer opposite sides of pile
Experienced by]x100 spheres
I r=volume of of the (V
cone[1-v/vo particles
method.
Granule volumesteel g in bulk. here 1 5-15 +l2 = the Excellent
ofθ the powder and the w = Wt. of Pycnometer + sample or
here, =density: b) ρt=M/vt VV =Wt. of Pycnometer with powder glass beads
angle of repose 2
 Bulk volume (V
True box method.
U1=Volume of empty cell
b. Tilting Void volume
w 12-16 Wall is linedfilled with
&
ADHESION: plane.FLOW
horizontal
U1-U2=Volume occupied by the std. sample
4=
VSTATICvolume KINETIC/DYNAMICGood by sandpaper
b = Bulk A.R.
 Relative volume unlike particle.
V = Tapped Volume
ANGLE OF REPOSE
c. Attraction between (Vr)
solvent
Revolving cylinder method.
U1-Us = volume occupied by
(Ø) ρ
Granule density:sample g=M/vg noww2-w1 Wt. of sample Fair To Passable
w3 , = = A.R.
V0= Volumebytparticles at surface. w*18-21
Vr = V/ V
Experienced before tapping 4-w2 Volume of liquid displaced by the solid
= Vb –V
=
Voidangle of (VV)It is anglet of repose deter-
volume
Resistance to movement ρbparticles It is
Bulk density:< 25 of =M/v
EXCELLENT b
*23-35 Poor
Therefore, Porosity (E) =(Vb–Vt3rdVb
repose mined by the )/ method
Vr tends to become unity factors:-
is affected by two as all air is
eliminated25-30 the mass GOODtheρ/ ρtPorosity when expressed as percentage
relative density: duringr=
from ρ determined by It is preferred since they
a. Electrostatic forces.
compression process
st 33-38
1 two methods most closelyPoor the
Very mimic
*30-40 PASSABLE E =100.[(Vb–Vt)/ Vb]
b. Adsorbed layer of moisture on (a. & b.) manufacturing situation in
>40 VERY POOR >40 Very Very Poor
particles. Tapped which powder is in motion.
density-tester
Specific gravity bottle

4. Powder compression
COMPRESSION:
The reduction in the bulk volume of a material as a result
of the removal of the gaseous phase (air) by applied
pressure.
„ CONSOLIDATION:
Involves an increase in the mechanical strength of a
material resulting from particle-particle interactions.
„ COMPACTION:
The compression and consolidation of a 2 phase (solid +
gas) system due to an applied force.

5. Compression
When external mechanical forces are applied to a powder
Powder fluidity
mass, there is reduction in bulk volume as follows,
 required to transport the material
1.Repacking 3.Brittle fracture: e.g., sucrose
 provide adequate filling of the dies to produce tablets of
2.Particle weight 4.microquashing
consistent and strength.
deformation
 Powder compression
Elastic e.g., acetyl salicylic acid, MCC
 Depends on density and packing characteristics of
deformation
powder - when elastic limit or yield point
is reached.
Plastic
deformation
Microsquasing: Irrespective of the behavior of larger particles smaller
particles may deform plastically.

6. Stages involved in compression
1. Initial repacking of
particles.
2. Elastic deformation of the
particles until the elastic
limit (yield point) is
reached.
3. Plastic deformation and/or
brittle fracture then
predominate until all the
voids are virtually
eliminated.
4. Compression of the solid
crystal lattice then occurs.
On Decompression

7. Stages involved in compression
Elastic deformation:
Plastic deformation
1. The only forces that exist between the particles are those
 1. that areof the load, the deformation reversible on the the like
On removal related to immediatelycharacteristicsbehaves
Deformation not the packing is reversible - it of removal
rubber
of the applied force.
particles, the density of the particles and the total mass of
 2. the material elastic deformation whendie
All solids undergo that materials in which the shear strength is
Predominant in is filled into the subjected to external forces.
2. External forcetensile or breaking strength. closer packing
less than the - reduction in volume due to
 Some materials, e.g. paracetamol, are elastic and There is very little
3. of the powder(eitherthe greatest mechanismclean surfaces
permanent change particles- main number of of caused by
Believed to create plastic flow or fragmentation) initial
4. volume deformation is a time dependent process, higher
Plastic reduction
compression:
3. As the load increases, rearrangementformation ofbecomes
leads to the of particles less
rate of force application elastically) When the compression load
 The material rebounds (recovers
is released. If bonding is weak the compact will self-destruct some type
more clean surfaces - weaker tablets. leads to and the top
new difficult and further compression
will detach (capping) Else, whole cylinder cracks into horizontal layers
5. of particle deformation is dependent on the formation of
Since tablet formation
(lamination).
new clean surfaces, high concentration or over mixing of
 Elastic materials require a particularly plastic tableting matrix or wet
materials that form weak bonds result in weak tablets
massing to induce plasticity.
e.g. Mg stearate

8. Compression events
 Consolidation time:
Time to reach maximum force.
 Dwell time:
Time at maximum force.
 Contact time:
Time for compression decompress-
ion excluding ejection time.
 Ejection time:
Time during which ejection occurs.
 Residence time:
Time during which the formed
compact is within the die.

9. Consolidation
Definition: increase in the mechanical strength of a
material as a result of particle/particle interactions
Various Hypothesis:
 During compression, the powder compact typically undergoes a
 If this heatincrease usually isthe local rise in temperature
temperature is dissipated,between
When the sufficientthetwo particles4 approach each area of
Any applied load to of cause melting andthe C
surfaces to bed transmitted 30 contact other
could be on of through particle
 Depends
contacts.
closely enough (e.g. at a separation of less than 50nm),
theFriction effects
 particles
theirMaterial characteristics,
 free surface energies result in a strong attractive
forceLubricationa process known as cold welding .result in
Under appreciable forces, this transmission may
 When the melt solidifies, fusion bonding occurs, which in
 through efficiency
the generationin an increase in the mechanical strength of
results of considerable frictional heat.
turn This hypothesisapplication of compression forces
 Magnitude and rate of is favoured as a major reason for
theMachine speed
mass.
the increasing mechanical strength of a bed of powder
 As the tablet temperature rises, stress relaxation and plasticity
when subjected elasticity decreases and strong compacts are
increases while to rising compressive forces.
formed

10. Compaction:
Steps involved in compaction of powders under an applied force.

11. Stages of Compaction
Particle rearrangement/inter particle slippage
Deformation of particulates
Bonding/Cold welding
Deformation of the solid body
Elastic recovery/expansion of the mass as a whole
Bonding/Cold Welding
Deformation of the Solid Body
Particle Rearrangement
Deformation Recovery: of Materials
Mechanisms
a) As Occurs at low a result the bonded solid is consolidated
MajorThe compact pressures.melting, crystallization, axial
1.1. deformation increases, of allowing radial and sintering,
Solid bridges (as
pressure is ejected,
Material
chemical reaction, and binder hardening)
mechanism(s)
2. Reduction in the relativeby plastic and/or elastic
toward a limiting density volume of powder bed.
recovery. Ascorbic acid, Dicalcium
Fragmentation as a result of movable liquids (capillary and surface
b)deformation.phosphate, Maltose,
Bonding
3.2. Small particles flow intoto revert the compact particles
Elastic character tends voids between larger to its
tension forces) Phenacetin, Sodium
leading to Citrate, Sucrose packing arrangement As pressure
a closer
originalmovable binder bridges (viscous binder and
shape.
c) Non freely
increases, Ibuprofen, Paracetamol
Fragmentation and relative particle movement becomes
adsorption layers)
elastic impossible, inducing deformation
deformation
d) Attraction betweenmonohydrate,
Fragmentation and Lactose solid particles (molecular and electrostatic
plastic deformation Microcrystalline cellulose
forces)
Plastic deformation NaHCO3, NaCL, Pre
e) Mechanical interlocking (irregular particle size and size
gelatinized starch
distribution) Starch
Elastic deformation

12. Compaction data analysis
The ideal requirements for a compression / compaction equation
 The compaction monitored relates compaction of densification these
A
 The parameters
equation
model should cover during
some measure of the state of
the whole range vary widely in with
studies. accuracy.a powder, such as porosity, volume (or relative
consolidation of
sufficient
volume), density or void ratio, with a function of the compaction
 Various parameters havebe related to physical the compaction behavior
 The parameters should been used to assess relevant properties of the
pressure.
of a variety of pharmaceutical powders and formulations
powder.
 Forces on the punches
 Many compaction equations have been proposedformulation and
The parameters should be sensitive to changes in like; Heckel ,
Kawakita and of the upperandbeen validated at least proportional to minor
 displacement Adams have lower punches, for pharmaceutical systems.
experimental variables
and
insensitive or
 axial to radial load transmission,
changes in normalisation factors like density or initial volume.
However,friction,
 die wall it is highly unlikely that a single compaction equation will fit
 The model and itsmechanisms.should be easily estimated by general
 the compaction parameters
all ejection force,
available computer programs.
 temperature changes
 In interpreting compaction curves, it is therefore essential to know
The model should significantly differentiate between powders and
 Resulting data may be expressed equivalently in term of stress-
which mechanisms are operating, or not, over different region of
dissimilar compression characteristics.
strain, pressure-volume or pressure –density since the natural
pressure.
 strain, for example, model should be evaluatedof thecombinationinitial
The quality of the is equal to the natural log by a ratio of the of the
bed height or volume tocovered and height orto indicate to the observed
range of compaction curve current be able volume respectively in the
A good densification the should the goodness-of-fit changes
data.
compression mechanism

13. Heckel equation
where ρR is the relative density at pressure P, and E is the porosity.
Powder packing with increasing compression load is
The relative density is definedparticle rearrangement, the compact
normally attributed to as the ratio of the density of elastic and
at pressure, P, to the density of particle fragmentation true density of
plastic deformation and the compact at zero void or
the material
The porosity cananalysis is a popular method of determining
The Heckel also be defined as:
the volume reduction mechanism under the compression
E =(Vp –V)/V p= 1 - ρ R
force
where V p and V are the volume at any applied load and the volume at
theoretical zero porosity, respectively. powder compression follows
Based on the assumption that
Thus, equationkinetics kE cantheexpressed as:
first order dρR/dP= with be interparticulate pores as the
reactants andR /dP= k( 1-ρ R )
dρ the densification of the powder as the
product.
and then transformed to:
 According to [1/(1-ρR)]= kP+A i.e (y = mx +c)
In the analysis, the degree of compact
Plotting the value of In [1/(1-ρR)] against applied pressure, P, yields a is
densification with increasing compression pressure
linear graph having slope, k and intercept, A.
directly proportional to the porosity as follows:
 dρ R / dP = kE

14. Heckel equation
 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.
 This analysis has been extensively applied to
pharmaceutical powders for both single and multi-
component systems.
 The intercept of the extrapolated linear region, A, is a
function of the original compact volume.

15. Heckel equation
 From the value of A, the relative density, D A , which represents
the total degree of densification at zero and low pressures can be
calculated using the equation
A =In 1/(1-DA )
DA=1-e - A
 The relative density of the powder bed at the point when the
applied pressure equals zero = D0
 Describes 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
 The loose packing of granules at zero pressure tends to yield low
D0 values

16. Heckel equation
 The relative density, DB describes the phase of rearran-
gement of particles in the early stages of compression
 Indicates the extent of particle or granule fragmentation,
 The extent of the rearrangement phase depends on the
theoretical point of densification at which deformation of
particles begins. D B can be obtained from the equation:
DB=DA- D0

17. Based on Heckel equation – 3 types of powder-A, B & C
1. 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
2. An example of materials that
exhibit type A behavior is sodium
chloride.
3. 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.
In [1/(1-ρR)]=kP + A
4. This is in turn influenced by the
size distribution, shape, e. t. c., of
the original particles.

18. Based on Heckel equation – 3 types of powder-A, B & C
1. For type B materials, there is an
initial curved region followed by
a straight line
2. This indicates that the particles
are fragmenting at the early
stages of the compression
process
3. Type B Heckel plots usually
occur with harder materials with
higher yield pressures which
usually undergo compression by
fragmentation first, to provide a
denser packing. Lactose is a
In [1/(1-ρR)]=kP + A typical example of such
materials.

19. Based on Heckel equation – 3 types of powder-A, B & C
1. For type C materials, there is
an initial steep linear region
which become superimposed
and flatten out as the applied
pressure is increased
2. This behavior to the absence of
a rearrangement stage and
densification is due to plastic
deformation and asperity
melting.
In [1/(1-ρR)]=kP + A

20. Application of Heckel equation
 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.

21. Kawakita equation
The Kawakita equation was developed to study powder
compression using the degree of volume reduction, C, a
parameter equivalent to the engineering strain of the
particle bed
C =(V0-Vp)/V0=abP/(1+bP)
can be rearranged to give:
P/C=P/a+1/ab
Where,
C is the degree of volume reduction,
V 0 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 slope and intercept of the
P/C versus P plots

22. Methods of Evaluating the Compaction Process
„Compaction profiles (Force-time, Displacement-
time)
„ Tablet expansion
„ Pressure-Volume relationships
„ Pressure transmission
„ Energy of Compaction
„ Radial vs Axial Force
„ Acoustics
„ Temperature