PM3125: Lectures 19 to 21
Content of Lectures 19 to 20:
Compression and compaction (of powder solids):
The solid-air interface, angle of repose, flowrates,
mass-volume relationship, density, heckel plots,
consolidation, friability, compression.
Prof. R. Shanthini
05 Nov 2012
Compaction characteristics of powder
solids as applied to tabletting:
Compressibility
is the ability of the powder bed to be
compressed (under pressure) and
consequently be reduced in volume.
Compactibility
is the ability of a powder bed to form
mechanically strong compacts (tablets).
Prof. R. Shanthini
05 Nov 2012
Powders intended for compression
must possess two essential properties:
- Compressibility
- Fluidity (how to meaure it?)
Prof. R. Shanthini
05 Nov 2012
The Solid-Air Interface
Cohesion is the attraction between like particle;
Experienced by particles in bulk.
Adhesion is the attraction between unlike particle;
Experienced by particles at surface.
Resistance to movement of particles is affected
by two factors:
a) Electrostatic forces
b) Adsorbed layer of moisture on particles
Prof. R. Shanthini
05 Nov 2012
Angle of Repose
The maximum angle possible between the surface
of pile of non-cohesive (free-flowing) material and
the horizontal plane.
Angle of repose
is an indication
of the flowability
of the material.
Prof. R. Shanthini
05 Nov 2012
Angle of Repose (θ)
θ = tan-1(h/r)
where
h = height of pile
h
r = radius of the base of the pile
r
Excellent flowability
Good flowability
Passable flowability
Very poor flowability
Prof. R. Shanthini
05 Nov 2012
o
if θ < 25
o
o
if 25 < θ < 30
if 30o < θ < 40o
if θ > 40o
Factors affecting Angle of Repose
- coefficients of friction between particles
- size of the particles
- moisture affects the angle of repose
Prof. R. Shanthini
05 Nov 2012
Methods to measure Angle of Repose
• Fixed funnel method
• Tilting method
• Revolving cylinder method
Method by which the angle of repose is
measured can also affect the measurement.
Prof. R. Shanthini
05 Nov 2012
Methods to measure Angle of Repose
Fixed funnel method:
The material is poured through a
funnel to form a cone.
The tip of the funnel should be held
close to the growing cone and slowly
raised as the pile grows, to minimize
the impact of falling particles.
Stop pouring the material when the
pile reaches a predetermined height
or the base a predetermined width.
Prof. R. Shanthini
05 Nov 2012
Manual powder flow tester
Methods to measure Angle of Repose
Fixed funnel method:
Find the ratio by dividing the height of
the cone by half the width of the base
of the cone.
The inverse tangent of this ratio is the
angle of repose.
θ = tan-1(h/r)
where
h = height of the cone
r = radius of the base of the cone
Prof. R. Shanthini
05 Nov 2012
Manual powder flow tester
Methods to measure Angle of Repose
Tilting box method:
This method is appropriate for fine-grained, non-cohesive
materials, with individual particle size less than 10 mm.
The material is placed within a box with a transparent side
to observe the granular test material.
It should initially be level and parallel to the base of the
box.
The box is slowly tilted at a rate of approximately 3
degrees/second.
Tilting is stopped when the material begins to slide in bulk,
and the angle of the tilt is measured.
Prof. R. Shanthini
05 Nov 2012
Methods to measure Angle of Repose
Revolving cylinder method:
The material is placed within a cylinder with at least one
transparent face.
The cylinder is rotated at a fixed speed and the observer
watches the material moving within the rotating cylinder.
The granular material will assume a certain angle as it
flows within the rotating cylinder.
This method is recommended for obtaining the dynamic
angle of repose, and may vary from the static angle of
repose measured by other methods.
Prof. R. Shanthini
05 Nov 2012
Mass-Volume relationships
Type of voids (or air spaces):
• Open intraparticulate voids
• Closed intraparticulate voids
• Interparticulate voids
Prof. R. Shanthini
05 Nov 2012
Mass-Volume relationships
Types of Volume:
• True volume (VT)
• Granule volume (VG)
• Bulk volume (VB)
• Relative volume (VR)
VR = VB / VT
VR tends to become unity as all air is eliminated
from the mass during the compression process.
Prof. R. Shanthini
05 Nov 2012
Mass-Volume relationships
Types of Density:
• True density
(ρT = M / VT )
• Granule density
(ρG = M / VG )
• Bulk density
(ρB = M / VB)
• Relative density
(ρR = M / VR)
ρR = ρB / ρ T
M is the mass of powder
Prof. R. Shanthini
05 Nov 2012
Mass-Volume relationships
Fractional voidage or Porosity (E ):
E = VV / VB
where VV = Void volume = VB – VT
E = (VB – VT) / VB = 1– VT / VB
= 1– ρB / ρT = 1 – ρR
= 100 (1– ρR)
Prof. R. Shanthini
05 Nov 2012
when expressed in %
Measuring Compressibility
Carr’s (Compressibility) Index
= [(VB – VTap) / VB] x 100 ≈ E
where
VB = Freely settled volume of a given mass of powder
VTap = Tapped volume of the same mass of powder ≈ VT
Carr’s (Compressibility) Index
= [(ρTap – ρB) / ρTap] x 100 ≈ E
where
ρB = Freely settled bulk density of the powder
ρTap = Tapped bulk density of the powder ≈ ρT
Prof. R. Shanthini
05 Nov 2012
Measuring Compressibility
Excellent flowability
if 5 < Carr’s Index < 15
good flowability
if 12 < Carr’s Index < 16
Passable flowability
if 18 < Carr’s Index < 21
poor flowability
if 23 < Carr’s Index < 35
Very poor flowability if 33 < Carr’s Index < 38
Very very poor flowability
if Carr’s Index > 40
Prof. R. Shanthini
05 Nov 2012
Methods to measure volume of powder
• Helium pycnometer
• Liquid displacement method
(specific gravity bottle method)
Prof. R. Shanthini
05 Nov 2012
Compression of powdered solids
Compression refers to a reduction in the
bulk volume of materials as a result of
displacement of the gaseous phase.
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 individual particles.
Prof. R. Shanthini
05 Nov 2012
Compression of powdered solids
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.
As the load increases, rearrangement of
particles becomes more difficult and
further compression leads to some type
of particle deformation.
Prof. R. Shanthini
05 Nov 2012
Compression of powdered solids
If on removal of the load, the deformation is to a large
extent reversible, then the deformation is said to be
elastic.
All solids undergo elastic deformation when subjected
to external forces.
Prof. R. Shanthini
05 Nov 2012
Compression of powdered solids
In other groups of powdered solids, an elastic limit (or yield
point) 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.
This mechanism predominates in materials in which the shear
strength is less than the tensile or breaking strength.
Prof. R. Shanthini
05 Nov 2012
Compression of powdered solids
If shear strength is greater than the tensile or breaking
strength, particle may fracture.
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).
Prof. R. Shanthini
05 Nov 2012
Compression of powdered solids
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.
Prof. R. Shanthini
05 Nov 2012
Effect of applied forces
Microsquasing:
Irrespective of the behavior of larger particles
smaller particles may deform plastically.
Prof. R. Shanthini
05 Nov 2012
Effect of applied forces
Summarily, four stages of events are encountered during
compression:
(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.
Prof. R. Shanthini
05 Nov 2012
Effect of applied forces
DEFORMATION:
Strain: The relative amount of deformation produced on a
solid body due to applied force.
It is dimensionless quantity.
Prof. R. Shanthini
05 Nov 2012
Effect of applied forces
Prof. R. Shanthini
05 Nov 2012
Effect of applied forces
Prof. R. Shanthini
05 Nov 2012
Effect of applied forces
Ho
∆H
Prof. R. Shanthini
05 Nov 2012
Compressive strain, Z = ∆H / Ho
Effect of applied forces
Shear strain
Prof. R. Shanthini
05 Nov 2012
Effect of applied forces
DEFORMATION:
Stress(σ):
σ=F/A
where, F is force required to produce strain in area A
Prof. R. Shanthini
05 Nov 2012
Effect of applied forces
Prof. R. Shanthini
05 Nov 2012
Consolidation
Consolidation is the increase in the
mechanical strength of a material as a
result of particle-particle interactions.
Prof. R. Shanthini
05 Nov 2012
Mechanisms of Consolidation
When the surfaces of two particles approach each other
closely enough (e.g. at a separation of less than 50 nm),
their free surface energies result in a strong attractive
force through a process known as cold welding.
Prof. R. Shanthini
05 Nov 2012
Mechanisms of Consolidation
On the macro scale, most particles 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.
Prof. R. Shanthini
05 Nov 2012
Mechanisms of Consolidation
Another possible mechanism of powder consolidation is
asperitic melting of the local surface of powder
particles.
During compression, the powder compact typically
undergoes a temperature increase usually between 4 and
30oC, which depends on the friction effects, the specific
material characteristics, the lubrication efficiency, the
magnitude and rate of application of compression forces,
and the machine speed.
As the tablet temperature rises, stress relaxation and
plasticity increases while elasticity decreases and strong
compacts are formed.
Prof. R. Shanthini
05 Nov 2012
Consolidation
Mechanisms (summary):
1. Cold welding (particle distance < 50nm)
2. Fusion bonding (caused due to frictional heat)
3. Asperitic melting
Consolidation process is influenced by,
- chemical nature of materials
- extent of available surface
- presence of surface contaminants
- inter-particulate distance
Prof. R. Shanthini
05 Nov 2012
Tabletting cycle
Division of tabletting cycle into a series of time periods:
(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.
Prof. R. Shanthini
05 Nov 2012
Tabletting cycle
Prof. R. Shanthini
05 Nov 2012
Decompression
In tabletting, the compression process is followed by a
decompression stage, as the applied load is removed.
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.
Prof. R. Shanthini
05 Nov 2012
Decompression
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.
This phase of the cycle can
provide valuable insight into the
reasons behind inferior tablet
quality and may suggest a
remedy.
Prof. R. Shanthini
05 Nov 2012
Decompression
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.
ln(Ft ) = ln(Fm) – K t
Ft = Fm e-Kt
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)
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.
Prof. R. Shanthini
05 Nov 2012
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.
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.
Prof. R. Shanthini
05 Nov 2012
Force transmission through a powder bed
Axial balance of forces in punches:
FA = FL + FD
where,
FA = force applied to the upper punch
FL = force transmitted to the lower punch
FD = reaction of the die wall due to the
friction
FA
FD
Prof. R. Shanthini
05 Nov 2012
FL
Force transmission through a powder bed
Relationship between
upper punch force FA and lower punch force FL:
FL = FA × e-kH/D
where,
k = constant (material dependent);
H = height of tablet
FA
D = diameter of tablet
FD
Prof. R. Shanthini
05 Nov 2012
FL
Force transmission through a powder bed
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 as:
FM = (FA + FL) / 2
= (FA + FA × e-kH/D ) / 2
= FA (1 + e-kH/D ) / 2
where,
FA = upper punch force
FL = lower punch force
Prof. R. Shanthini
05 Nov 2012
FM offers a practical frictionindependent measure of
compaction load, which is
generally more relevant than FA.
Force transmission through a powder bed
In single-station presses, where the applied force
transmission decays exponentially, a more appropriate
measure is the geometric mean force, FG, defined as:
FG = (FA × FL)0.5
= (FA × FA × e-kH/D )0.5
= FA × (e-kH/D)0.5
= FA × e-kH/2D
where,
FA = upper punch force
FL = lower punch force
Prof. R. Shanthini
05 Nov 2012
Poisson ratio
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
Prof. R. Shanthini
05 Nov 2012
= D / H
The Poisson ratio is a characteristic
constant for each solid material and
may influence the tabletting processes.
Poisson ratio
∆D
∆H
Prof. R. Shanthini
05 Nov 2012
λ
= D / H
Poisson ratio
Under the conditions in the die, the material is not free to
expand in the horizontal plane because it is confined in the die.
Consequently, a radial die-wall force FR develops
perpendicularly to the die-wall surface, materials with larger
Poisson ratios giving rise to higher values of FR.
Axial frictional force FD is related to FR
by :
FA
FD = μW . FR
where μW is the coefficient of die-wall
friction.
Prof. R. Shanthini
05 Nov 2012
FR
FD
FL
Poisson ratio
FA = FL + FD
FD = μW . FR
FR is reduced when materials of small Poisson ratios are used,
and in such cases, axial force transmission is optimum.
FA
FR
FD
Prof. R. Shanthini
05 Nov 2012
FL
Minimizing frictional effects
FA = FL + FD
FD = μW . FR
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 FR
wall (lower S) and maintaining a
minimum tablet height (reducing Ae).
Prof. R. Shanthini
05 Nov 2012
FA
FD
FL
Minimizing frictional effects
FA = FL + FD
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.
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.
Prof. R. Shanthini
05 Nov 2012
FA
FR
FD
FL
Compaction data analysis
Data obtained from the measurements of
forces on the punches,
the displacement of the upper and lower punches,
axial to radial load transmission,
die wall friction,
ejection force,
temperature changes and
other miscellaneous parameters
have been used to assess the compaction behavior of a
variety of pharmaceutical powders and formulations.
Many empirical relationships have been proposed to
describe the resulting data.
Prof. R. Shanthini
05 Nov 2012
Compaction Equations
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.
Walker (1923) related the relative volume (VR) of the
powder compact against the logarithm of the applied axial
pressure (Pa) as:
VR = a1 – K1 In Pa
Today, more than fifteen different mathematical descriptions
of the compaction process.
Prof. R. Shanthini
05 Nov 2012
Compaction Equations (Hackel 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
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.
Prof. R. Shanthini
05 Nov 2012
Compaction Equations (Hackel equation)
Degree of compact densification with increasing compression
pressure is directly proportional to the porosity as follows:
dρR / dP = k E
where
ρR is the relative density at pressure (P)
E is the porosity
Prof. R. Shanthini
05 Nov 2012
Compaction Equations (Hackel equation)
dρR / dP = k E
The relative density is defined as:
ρR = ρp / ρ
which is the ratio of the density of the compact at
pressure P (ρp) to the density of the compact at zero
void or true density of the material (ρ).
The porosity is defined as:
E = (Vp - V) / Vp
= 1 - ρR
where Vp and V are the volume at any applied load and
the volume at theoretical zero porosity, respectively.
Prof. R. Shanthini
05 Nov 2012
Compaction Equations (Hackel equation)
Therefore,
dρR / dP = k (1 - ρR)
which is transformed to:
In [1 / (1 - ρR )] = k P + A
Plotting the value of In [1 / (1 - ρR )] against applied pressure,
P, yields a linear graph having slope, k and intercept, A.
In [1 / (1 - ρR )]
Slope = k
Intercept = A
Prof. R. Shanthini
05 Nov 2012
P
Compaction Equations (Hackel equation)
Yield pressure (Py) = 1/k
Py is a material-dependent constant.
Low values of Py indicate a faster onset of plastic deformation.
In [1 / (1 - ρR )]
In [1 / (1 - ρR )] = k P + A
Prof. R. Shanthini
05 Nov 2012
Slope = k
Intercept = A
P
Compaction Equations (Hackel equation)
Let us say, when P = 0, ρR = DA
where DA is the relative density representing the total
degree of densification at zero and low pressures.
Therefore, A = ln[1 / (1 - DA )]
Thus,
DA = 1 - e-A
In [1 / (1 - ρR )]
In [1 / (1 - ρR )] = k P + A
Prof. R. Shanthini
05 Nov 2012
Slope = k
Intercept = A
P
Compaction Equations (Hackel equation)
For Type A materials:
- a linear relationship is observed
- deformation apparently only by plastic deformation
- An example of materials that exhibit type A behavior is
sodium chloride (soft material).
Prof. R. Shanthini
05 Nov 2012
Compaction Equations (Hackel equation)
For Type B materials:
- an initial curved region followed by a straight line
- brittle fracture preceds plastic flow
- An example of materials that exhibit type A behavior is
lactose (harder materials).
Prof. R. Shanthini
05 Nov 2012
Compaction Equations (Hackel equation)
For Type C materials:
- an initial steep linear region followed by a flatten region
with increased applied pressure
- densification is due to plastic deformation and asperity
melting
Prof. R. Shanthini
05 Nov 2012