Prof. R. Shanthini 05 Nov 2012 Content of Lectures 19 to 20: Compression and compaction (of powder solids) : The solid-air interface, angle of repose,

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


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:


- 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::


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


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.


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


- coefficients of friction between particles

- size of the particles

- moisture affects the angle of repose

Factors affecting Angle of ReposeFactors affecting 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.

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



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



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.



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.


Type of voids (or air spaces):

Mass-Volume relationshipsMass-Volume relationships

• Open intraparticulate voids

• Closed intraparticulate voids

• Interparticulate voids


• 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:



• 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:


M is the mass of powder


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 ):



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


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


• Helium pycnometer

• Liquid displacement method (specific gravity bottle method)

Methods to measure volume of powderMethods to measure volume of powder


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.



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.



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.



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.



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).



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.


Microsquasing: Microsquasing:

Irrespective of the behavior of larger particles smaller particles may deform plastically.

Effect of applied forcesEffect 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.



DEFORMATION:DEFORMATION:

Strain: The relative amount of deformation produced on a solid body due to applied force.

It is dimensionless quantity.








Compressive strain, Z = ∆H / Ho

∆H

Ho



Shear strain


DEFORMATION:DEFORMATION:

Stress(σ):

σ = F / A

where, F is force required to produce strain in area A





Consolidation is the increase in the mechanical strength of a material as a result of particle-particle interactions.

ConsolidationConsolidation


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


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.



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 (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


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


Tabletting cycleTabletting cycle


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.



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.



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.


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.


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

FL

FD


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


FA

FL

FD


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.



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



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.



λ = D / H

∆H

∆D



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



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


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


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


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.


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.


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.



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



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



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



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


In [1 / (1 - ρR )] = k P + A



In [1 / (1 - ρR )]

P


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



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).



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).



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

Documents

Prof. R. Shanthini 05 Nov 2012 Content of Lectures 19 to 20: Compression and compaction (of powder solids) : The solid-air interface, angle of repose,