Prof. R. Shanthini 05 Nov 2012 Content of Lectures 19 to 20: Compression and compaction (of powder...
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Transcript of Prof. R. Shanthini 05 Nov 2012 Content of Lectures 19 to 20: Compression and compaction (of powder...
Prof. R. Shanthini 05 Nov 2012
Content of Lectures 19 to 20: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.
PM3125: PM3125: Lectures 19 to 21Lectures 19 to 21
Prof. R. Shanthini 05 Nov 2012
CompressibilityCompressibility is the ability of the powder bed to be
compressed (under pressure) and consequently be reduced in volume.
CompactibilityCompactibility
is the ability of a powder bed to form mechanically strong compacts (tablets).
Compaction characteristics of powder Compaction characteristics of powder solids as applied to tabletting:solids as applied to tabletting:
Prof. R. Shanthini 05 Nov 2012
- Compressibility- Compressibility
- Fluidity - Fluidity (how to meaure it?)(how to meaure it?)
Powders intended for compression Powders intended for compression must possess two essential propertiesmust possess two essential properties::
Prof. R. Shanthini 05 Nov 2012
The Solid-Air InterfaceThe Solid-Air Interface
CohesionCohesion is the attraction between like particle; Experienced by particles in bulk.
AdhesionAdhesion is the attraction between unlike particle; Experienced by particles at surface.
Resistance to movement of particlesResistance 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
The maximum angle possible between the surface of pile of non-cohesive (free-flowing) material and the horizontal plane.
Angle of ReposeAngle of Repose
Angle of repose is an indication of the flowability of the material.
Prof. R. Shanthini 05 Nov 2012
Angle of Repose (θ)Angle of Repose (θ)
θ = tan-1(h/r)
where h = height of pile
r = radius of the base of the pile
Excellent flowability if θ < 25o
Good flowability if 25o < θ < 30o
Passable flowability if 30o < θ < 40o
Very poor flowability if θ > 40o
h
r
Prof. R. Shanthini 05 Nov 2012
- coefficients of friction between particles
- size of the particles
- moisture affects the angle of repose
Factors affecting Angle of ReposeFactors affecting Angle of Repose
Prof. R. Shanthini 05 Nov 2012
• Fixed funnel method
• Tilting method
• Revolving cylinder method
Method by which the angle of repose is measured can also affect the measurement.
Methods to measure Angle of ReposeMethods to measure Angle of Repose
Prof. R. Shanthini 05 Nov 2012
Methods to measure Angle of ReposeMethods 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.
Manual powder flow tester
Prof. R. Shanthini 05 Nov 2012
Methods to measure Angle of ReposeMethods 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.
Manual powder flow tester
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
Methods to measure Angle of ReposeMethods 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 ReposeMethods 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
Type of voids (or air spaces):
Mass-Volume relationshipsMass-Volume relationships
• Open intraparticulate voids
• Closed intraparticulate voids
• Interparticulate voids
Prof. R. Shanthini 05 Nov 2012
• 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.
Types of Volume:
Mass-Volume relationshipsMass-Volume relationships
Prof. R. Shanthini 05 Nov 2012
• True density (ρT = M / VT )
• Granule density (ρG = M / VG )
• Bulk density (ρB = M / VB)
• Relative density (ρR = M / VR)
ρR = ρB / ρT
Types of Density:
Mass-Volume relationshipsMass-Volume relationships
M is the mass of powder
Prof. R. Shanthini 05 Nov 2012
E = VV / VB
where VV = Void volume = VB – VT
E = (VB – VT) / VB = 1– VT / VB
= 1– ρB / ρT = 1 – ρR
= 100 (1– ρR) when expressed in %
Fractional voidage or Porosity (E ):
Mass-Volume relationshipsMass-Volume relationships
Prof. R. Shanthini 05 Nov 2012
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
Measuring CompressibilityMeasuring Compressibility
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 CompressibilityMeasuring 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
• Helium pycnometer
• Liquid displacement method (specific gravity bottle method)
Methods to measure volume of powderMethods to measure volume of powder
Prof. R. Shanthini 05 Nov 2012
Compression of powdered solidsCompression 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 solidsCompression 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 deformationparticle deformation.
Prof. R. Shanthini 05 Nov 2012
Compression of powdered solidsCompression 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 solidsCompression 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 solidsCompression 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 solidsCompression 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
Microsquasing: Microsquasing:
Irrespective of the behavior of larger particles smaller particles may deform plastically.
Effect of applied forcesEffect of applied forces
Prof. R. Shanthini 05 Nov 2012
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.
Effect of applied forcesEffect of applied forces
Prof. R. Shanthini 05 Nov 2012
DEFORMATION:DEFORMATION:
Strain: The relative amount of deformation produced on a solid body due to applied force.
It is dimensionless quantity.
Effect of applied forcesEffect of applied forces
Prof. R. Shanthini 05 Nov 2012
Effect of applied forcesEffect of applied forces
Compressive strain, Z = ∆H / Ho
∆H
Ho
Prof. R. Shanthini 05 Nov 2012
DEFORMATION:DEFORMATION:
Stress(σ):
σ = F / A
where, F is force required to produce strain in area A
Effect of applied forcesEffect of applied forces
Prof. R. Shanthini 05 Nov 2012
Consolidation is the increase in the mechanical strength of a material as a result of particle-particle interactions.
ConsolidationConsolidation
Prof. R. Shanthini 05 Nov 2012
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.
Mechanisms of ConsolidationMechanisms of Consolidation
Prof. R. Shanthini 05 Nov 2012
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.
Mechanisms of ConsolidationMechanisms of Consolidation
Prof. R. Shanthini 05 Nov 2012
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.
Mechanisms of ConsolidationMechanisms of Consolidation
Prof. R. Shanthini 05 Nov 2012
Mechanisms (summary): Mechanisms (summary): 1. Cold welding (particle distance < 50nm)
2. Fusion bonding (caused due to frictional heat)
3. Asperitic melting
Consolidation process is influenced byConsolidation process is influenced by, - chemical nature of materials
- extent of available surface
- presence of surface contaminants
- inter-particulate distance
ConsolidationConsolidation
Prof. R. Shanthini 05 Nov 2012
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.
Tabletting cycleTabletting cycle
Prof. R. Shanthini 05 Nov 2012
In tabletting, the compression process is followed by a decompression stage, as the applied load is removed.
DecompressionDecompression
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
DecompressionDecompression
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
DecompressionDecompression
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
The process of tabletting involves the application of massive compressive forces, which induce considerable deformation in the solid particles.
Force transmission through a powder bedForce transmission through a powder bed
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
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
Force transmission through a powder bedForce transmission through a powder bed
FA
FL
FD
Prof. R. Shanthini 05 Nov 2012
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
D = diameter of tablet
Force transmission through a powder bedForce transmission through a powder bed
FA
FL
FD
Prof. R. Shanthini 05 Nov 2012
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
FM offers a practical friction-independent measure of compaction load, which is generally more relevant than FA.
Force transmission through a powder bedForce transmission through a powder bed
Prof. R. Shanthini 05 Nov 2012
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
Force transmission through a powder bedForce transmission through a powder bed
Prof. R. Shanthini 05 Nov 2012
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
Poisson ratioPoisson ratio
The Poisson ratio is a characteristic constant for each solid material and may influence the tabletting processes.
Prof. R. Shanthini 05 Nov 2012
Poisson ratioPoisson 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 :
FD = μW . FR
where μW is the coefficient of die-wall friction.
FA
FL
FD
FR
Prof. R. Shanthini 05 Nov 2012
Poisson ratioPoisson ratio
FR is reduced when materials of small Poisson ratios are used, and in such cases, axial force transmission is optimum.
FD = μW . FR
FA = FL + FD
FA
FL
FD
FR
Prof. R. Shanthini 05 Nov 2012
Minimizing frictional effectsMinimizing frictional effects
FD = μW . FR
FA = FL + FD
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).
FA
FL
FD
FR
Prof. R. Shanthini 05 Nov 2012
Minimizing frictional effectsMinimizing 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 valuecoefficient 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.
FA
FL
FD
FR
Prof. R. Shanthini 05 Nov 2012
Compaction data analysisCompaction 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 EquationsCompaction 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)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)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)Compaction Equations (Hackel equation)
dρR / dP = k E
The relative density is defined as:
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.
ρR = ρp / ρ
Prof. R. Shanthini 05 Nov 2012
Compaction Equations (Hackel equation)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 )]
P
Slope = kIntercept = A
Prof. R. Shanthini 05 Nov 2012
Compaction Equations (Hackel equation)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 )]
P
Slope = kIntercept = A
In [1 / (1 - ρR )] = k P + A
Prof. R. Shanthini 05 Nov 2012
Compaction Equations (Hackel equation)Compaction Equations (Hackel equation)
In [1 / (1 - ρR )]
P
Slope = kIntercept = A
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 )] = k P + A
Prof. R. Shanthini 05 Nov 2012
Compaction Equations (Hackel equation)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)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).