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Two major components to the frictional force can be distinguished

 Interparticulate friction:

• friction between particle/particle and expressed as coefficient of “interparticulate

• It is more significant at low applied loads.

• addition of glidants reduces it.

Ex: colloidal silica, talc, corn starch


Die wall friction:

• arises as material being pressed to die wall and moved down it, can be
expressed as “coefficient of die wall friction”

This effect become dominant at high applied forces when particle
rearrangement has ceased and is particularly important in tabletting

Most tablets contain a small amount of an additive design to reduce die
wall friction; such additives are called lubricants.

Ex: magnesium stearate, talc, PEG, waxes, stearic acid


Force volume relationship

 After the completion , compression air spaces are removed i.e. Vb=Vt and E=0.

 Residual porosity is required, a relation exists between applied force FA and
remaining porosity ‘E’. Decreased porosity was due to. Filling of air spaces by
interparticulate slippage Filling of small voids by deformation (or) fragmentation at
higher loads. This process was expressed as

E0= initial porosity

E = porosity at pressure P

K1 K2 K3 K4 = constants
But this data applies to only few materials such as alumina and magnesia and

establishes that degree of compression depends upon E0. To eliminate this experiment
are carried out on tablet masses of same Vt and variable initial values of Vb


More complex events in compression involves 4 stages

• Initial repacking materials followed by elastic deformation.

• Elastic limit is reached, plastic deformation/brittle fracture dominates.

• All voids are eliminated.

• Compression of solid crystal lattice.

In tabletting process after applying compressional force the relation b/n applied
pressure (P) and porosity (E) become linear over the range of pressure.

Shapiro equation:

– K.P E0= Porosity when the pressure is ‘o’

K = Constant

Walker equation:



Heckel equation is based upon analogous behavior to a first order reaction, where
the pores in the mass are reactant.

Ky= material dependent const, but inversely proportional to material yield

Ky= 1/3s

Kr= related packing stage (E0)
These relations may be established by measuring applied force (F) and movements

of Punches during compression cycle and translating this data into applied pressure (P),
for a cylindrical tablet.

D= diameter of tablet



W= weight of tablet
= true density

H= thickness of tablet at that point.

 Heckel plots identifies the predominant form of deformation for a given sample.

 Soft materials undergo plastic deformation readily, retains different degrees of
porosity based on initial packing of die, which was influenced by the size distribution,
shape etc of original particles.

 Harder materials have high yield strength undergo compression by fragmentation
i.e. breakdown of larger particles to form denser packing.

 Type (a) plots have higher slope than type
(b) from this we can expect that these materials have lower yield strength(S).

 Hard, brittle materials are more difficult to compress than softer ones,
fragmentation occurs in hard materials & plastic deformation in soft materials.


Two regions of Heckel plots represents

1. Initial repacking stage

2.Subsequent deformation process

 Crushing strength can be correlated with value of Ky. i.e Ky larger – harder
tablets. This information was utilized for binder selection to particular material.

Heckel plots are influenced by:
o Degree of lubrication, Size of the die.

 Residual porosity in particular formulations provide good mechanical
strength, rapid water intake and hence good disintegration characteristics.


 Removal of applied force, so new stresses are formed during decompression due to
elastic recovery and it was opposed by ejection induced forces.

 Degree and role of relaxation with in tablets immediately after point of maximum
compression is characteristic for a particular system. Recording the above cycle will give
be added to system to avoid structural failure.(PVP – Plastically deforming component)

 If plastic flow occurs in a system it will continue after the removal of all forces during
stress relaxation process.

Plastic flow can be interpreted by viscous and elastic flow parameters and related as

Ft = force left in the visco elastic region at a time t.
Fm= total magnitude of Ft force at t=0
K = visco elastic slope

High K value – plastic flow – strong tablets at low compaction forces. Plasto elasticity
determines change in thickness of tablet mass due to the compactional force, elastic
recovery during unloading of forces

H0 = thickness of tab mass at onset of loading
Hm = thickness at point of max. force
Hr = thickness on ejection from die.
Y If >9 – tablets are laminated and capped


Force Distribution

 Most of the investigations of the fundamentals of tabletting have been
carried out on single station presses or even on isolated punch and die sets in
conjunction with a hydraulic press.

 This compaction system provides a convenient way to examine the
process in greater detail.
More specifically the following basic relationships apply.


The axial balance of forces:


FA=force applied to the upper punch
FL= force transmitted to the lower punch
FD= reaction at the d

The mean compaction force (FM):

FM = (FA+FL)/2
A recent report confirms that FM offers a practical friction- independent

measure of compaction load, which is generally more relevant than FA.

The geometric mean force (FG):

FG = (FA . FL)0.5

ie wall to the friction at this surface.


 Development of radial force

 After compression process the material was regarded as single solid body. As
with all other solids if compressional force is applied I one direction i.e., vertical
results in decrease in height and I unconfined body accompanied by an expansion
in the horizontal direction.

Poisson ratio λ is the ratio between these two dimensional changes

λ =ΔD/ΔH

 λ is characteristic constant for each solid. If material is confined to die then
it is not free to

expand in the horizontal plane. A radial die wall force FR develops
perpendicular to die wall

surface .Materials with larger Poisson ratios giving rise to higher FR values.


Classic friction theory can then be applied to deduce that the
axial frictional force FD is related to FR by the expression:

FD = mw.FR

Where mw is the coefficient of die wall friction.

Note that FR is reduced when material of small Poisson ratio are
used, and that in such cases, axial force transmission is optimum.



 Most pharmaceutical tablet formulation require the addition of a lubricant
to reduce friction at the die wall .

 Die wall lubricant function by interposing a film of low shear strength at the
interface between the tabletting mass and the die wall.

 Preferably, there is some chemical bonding between this boundary
lubricant and the surface of the die wall as well as the edge of the tablet.

 The best lubricant are those with low shear strength but strong cohesive
tendencies in direction at right angles to the plane of shear.



 Radial die wall forces and die wall friction also effect the ease with
which the compressed tablet can be removed from the die.

 The force necessary to eject a finished tablet follows distinctive pattern
of three stage.

 The first stage involves the distinctive peak force required to initiate
ejection, by braking of tablet/die wall adhesions.

 A smaller force usually follows, namely that required to push the tablet
up the die wall.

 The final stage is marked by declining force of ejection as the tablet
emerges from the die.


 Variation on this pattern are sometimes found, especially when
lubrication is inadequate and/or “slip-stick” condition occur between the
tablet and the die wall, owing to continuing formation and breakage of
tablet die wall adhesion.

 A direct connection is to be expected between die wall frictional forces
and the force required to eject the tablet from the die, FE.

 For e.g. well lubricated systems have been shown to lead to smaller FE



Compaction data obtained from tabletting
machines are of 3 types:

 Force-time profile
Force-displacement profile
Die wall force profile


.Force-Time profile:

Compression force-time profiles are used to characterize the compression
behavior of the active ingredients and excipients.
On a rotary tablet press, the force-Time curves are segmented in to three
phases; Phases of compression events.

a) Compression phase:
horizontal and vertical punch movement

b) Dwell phase:
only horizontal punch movement

c) Decompression / Relaxation phase :
both punches moving away from upper &
lower surface


Compression phase:
Compression is the process in which maximum force is applied on powder
bed in order to reduce its volume.

Dwell phase: When compression force reaches a maximum value, this
maximum force is maintained for prolonged period before decompression.
The time period between the compression phase and decompression
phase is known as DWELL TIME.

Decompression phase: Removal of applied force on powder bed i.e, both
punches moving away from upper and lower surfaces.

1. Compression phase – horizontal and vertical movement of punch
movement 2. Dwell phase – only horizontal punch movement (punch head
is under compression roller


Compression event divided in to series of time periods.

Consolidation time : Time period to reach maximum force.
Dwell time : Time at maximum force.
Contact time : Time for compression and decompression.
Ejection time : Time during which ejection occurs.
Residence time : Time during which the formed tablet is with in die.


The compression area A 1 and compression slope (sl c ) describe
the compression phase.

The area ratio A 6 /A 5 and peak offset time(t off ) characterize the
dwell phase.

The A 5 and A 6 are obtained by drawing a parallel line to X-axis
from starting to end point of dwell phase.

The decompression area A 4 and the decompression slope (Sl d )
describe the decompression phase.


 A 1 (compression phase) is small for powders having high density ( low volume;
due to less void spaces)
Example :Dicalcium phosphate dihydate.

A 1 (compression phase) large for powders having low density (more void
Example : Microcrystalline cellulose.

Plastic materials show a decrease in force over dwell time , in contrast a
plateau is observed for brittle materials.

The dwell phase coefficient (A 6 / A 5 ) can be used to measure the plasticity of
a substance mixture.



Peak offset time is the difference between the time of maximum pressure and
middle of dwell time.

At a given F max ,short t off values are characteristics of materials that
consolidate mainly by brittle fracture, whereas large values indicates an
increase in plastic flow.


Force-Displacement profile:

 Assessment of the compaction behavior of materials is done by force-
displacement profile.

Force-displacement profile can be used to determine the behavior of plastic
and elastic materials.

 Stress relaxation is observed to be minimal in case of plastic deformation;
where as materials that undergoes elastic deformation tend to relax to a greater
extent during and/or after decompression

 At a given f max the displacement area of plastic deformation is more when
compared to the displacement area of elastic deformation.


Most of the materials undergo plastic and elastic deformation at different
stages, hence the work required for compression is the sum of work
necessary to rearrange the particles, deform and finally to fragment them.

 Net work of compaction (NWC) is calculated by subtracting the work of
elastic relaxation (WER) from the gross work of compaction (GWC).

GWC = W f + W p + W e +W fr

W f = work against friction W e = work of elastic deformation
W p = work of plastic deformation W fr = work of fragmentation.

This information can be used to predict the compaction behavior of
pharmaceutical materials.

Ex: Lesser the amount of work needed to compress indicates higher
the compressibility of material and vice versa.



 During tableting friction arises between the material and the die wall and
also between particles (Interparticulate or internal friction).

Internal friction is significant only during particle slippage and rearrangement
at low applied pressures.

 The coefficients of friction related to tableting process are;
a) Static friction
b) Dynamic friction.

Static friction : Force require to initiate sliding
Dynamic friction : Force to maintain sliding between two surfaces


Static friction (µ 1 ) = maximum axial frictional force / maximum radial force
Dynamic friction (µ 2 ) = Ejection force / residual die wall force

 Friction phenomena can be determined from upper and lower punch force and

 Lubrication ratio (R value) is the ratio of the maximum lower punch force to
the maximum upper punch force .

The die wall force reaches a maximum just after the maximum upper and
lower force, and a constant residual value after upper and lower forces become
zero. When the ejection process starts it increases again.

 The residual die wall force is the average of values in the constant region at
zero upper punch force, The difference of displacement between upper and
lower punch gives a measure of the tablet area contact with the die wall.



The high die wall force during ejection is a sign of adhesion of
powders to the die.

S.No. Material Residual die wall

1 plastic large

2 brittle medium

3 elastic low