PHYSICS OF TABLET COMPRESSION
COMPRESSIBILITY: ability of a powder to decrease in volume under pressure.
Compression: compression of a powder means reduction in the bulk volume of a material as a result of displacement of the gaseous phase under pressure.
Compaction: compaction of a powder is a general term used to describe a situation in which powdered material is subjected to some level of mechanical force.
The physics of compaction may be simply stated as the compression & consolidation of two phase [particulate solid & gas] systems due to the applied force.
Consolidation: consolidation is an increase of a material resulting particle-particle interaction.
Decompression, in tablet manufacturing:
During tablet manufacturing the compressional process is followed by a decompression stage, as the applied force is removed. This leads a new set of stresses within the tablets as a result of elastic recovery which is augmented [increased] by the forces necessary to eject the tablet from the die.
Deformation: change of geometry of a solid when it is subjected to opposing forces. The amount of deformation is called strain.
The process of compression: in pharmaceutical tablet manufacturing an appropriate volume of granules in a die cavity is compressed between an upper & lower punch to consolidate the material into a single solid matrix which is subsequently ejected from the die cavity as an intact tablet.
The events that occur in the process of compression:
[a] Transitional repacking.
[b] Deformation at point of contact.
[c] Fragmentation &/or deformation.
[e] Deformation of the solid body.
[a] transitional repacking :
$: the particle size distribution of the granulation & the shape of the granules determine the initial packing [bulk density] as the granulation movement occurs at lower pressure.
$: the granules flow with respect to each other with the finer particles entering the void between the larger particles & the bulk density of the granulation is increased. Spherical particles undergo less particle rearrangement then irregular particles, as the spherical particles tend to assume a close packing arrangement initially.
[b] Deformation at the point of contact: when the particles of the granulation are so closely packed that no further filling of the void can occur, a further increase of compression force causes deformation at the point of contact.
*elastic deformation: if the deformation is disappear completely [returns to the original shape] upon release of stress, it is an elastic deformation.
*plastic deformation: a deformation that doesn’t completely recover after release of the stress is known as a plastic deformation.
Yield stress: the force required to initiate a plastic deformation is known as yield stress.
[c]fragmentation & deformation:
At higher pressure, fracture occurs when the stress within the particle become great enough to propagate cracks.
Fragmentation cause furthers densification with the infiltration of the smaller fragments into the void space.
With some materials fragmentation doesn’t occur because the stresses are released by plastic deformation. Plastic deformation may be thought of a change in particle shape & as the sliding of groups of particles in an attempt to release the stress [visco-elastic flow]. Such deformation produces new clean surfaces that are potential areas.
Bonding: several mechanism of bonding in the compression process has been conceived but they have not been substantiated by experimentation & have not been useful in the prediction of the compressional properties of the materials.
Three theories are
* The mechanical theory.
* The intermolecular theory.
* The liquid surface film theory.
[e] Deformation of the solid body: as the applied pressure is further increased the bonded solid is consolidated toward a limiting density by plastic &/or elastic deformation of the tablet within the die
[e] Decomposition: the success or failure to produce an intact tablet depends on the stresses induced by elastic rebound & the associated deformation processes during decompression & ejection.
As the upper punch is withdraw from the die cavity the tablet is confined in the die by a radial pressure. Consequently any dimensional change during decompression must occur in the axial direction.
[f] Ejection: as lower punch rises & pushes the tablet upward there is a continued residual die wall friction. As the tablet is removed from the die the lateral pressure is relived & the tablet undergoes elastic recovery with an increased [2-10 %] in the volume of that portion of the tablet removed from the die.
BONDING IN TABLET: [THE MECHANICAL THEORY]
• The mechanical theory proposes that under pressure the individual particles undergo elastic/plastic or & brittle deformation & that the edges of the particles intermesh deforming a mechanical bond.
• If only the mechanical bond exists, the total energy of compression is equal to the sum of the energy of deformation, heat & energy absorb for each constituent.
• Mechanical interlocking is not a major mechanism of bonding in pharmaceutical tablet.
• The molecules [or ions] at the surface of solid have unsatisfied forces [surface free energy] which interact with the other particles in true contact.
• Under pressure the molecules in true contact between new clean surfaces of the granules are close enough so that vender-walls forces interact to consolidate the particles.
• Materials containing plenty OH groups may also create hydrogen bonds between molecules.
[LIQUID SURFACE FILM THEORY]
• The liquid-surface film theory attributes bonding to the presence of a thin liquid film which may be the consequence of fusion or solution at the surface of the particle induced by the energy of compression.
It may be classified in two ways
1. Hot welding.
2. Cold welding.
HOT WELDING: the relation of pressure & melting point is expressed by the clapeyron equation,
dT/dP = T(VL-VS)/ ^H…….
• dT/dP is the change in melting point with a change in pressure.
• T is the absolute temperature.
• ^H is the molar latent heat of fusion.
• VL & VS are the molar of the liquid melt & the solids respectively.
For an ideal process in which the material is exposed to a uniform pressure, the relation reduced to the Clapeyron equation .if the pressure of true contact is exerted only on the solid & liquid phase is subjected to a constant atmospheric pressure, the relationship simplifies to equation 2.
dT/dPS = TVS/ ^H…………..
As dT/dPS is positive, regardless of the expansion or contraction of the solid, the pressure acting locally at the points of true contact lowers the melting point.
• For surface fusion at the points of true contact a localized temperature at least equal to the melting point of the material is attained.
• With some mixtures, the melting point may be depressed by other ingredients & fusion will occur at a temperature lower then the melting point of the pure material.
• Upon release of the pressure, solidification of the fused material would form solid bridge between the particles.
The poor compressibility of most water insoluble & the relative ease of compression of water soluble materials suggest that pressure-induced solubility is important in tableting.
The pressure distribution in compression is such that the solubility is increased with increasing pressure.
With an increasing in solubility at the point of true contact, solution usually occurs in the film of absorbed moisture of the surface of the granule. When the applied pressure is released and the solubility is decreased the solid dissolved in the absorbed water crystallizes in small crystal between the particles & thus form bridges.
EFFECT OF MOISTURE:
The moisture may be present as that retain from the granulating solution after drying or that absorbed from the atmosphere.
Granulations that are dry have poor compressional characteristics.
Water or saturated solutions of the material being compressed may form a film that act as lubricant & if release force is utilized in compression & bonding & the ejection force is reduced.
In formulations using solution of hydrophilic granulating agent, there may be optimum moisture content.
DESCRIPTION OF PROCESS OF COMPRESSION:
The process of compression have been described in term of relative volume [ratio of the volume of the compressed mass to the volume of the mass at zero void] & pressure as shown in fig-4.
In transitional repacking the granules are immobile & the number of intergranular point of contact has increased.
• AE: the decrease in relative volume during transitional repacking is represented by the segment AE.
• EF: with further increase in pressure temporary supports between the particles are formed as represented by segment EF.
• FG: fragmentation &/or plastic deformation is represented by the segment FG.
• GH: as some higher pressure bonding & consolidation of the solid occur to some limiting value as indicted by segment GH.
THE HACKEL EQUATION: for the compression process, Hackle proposed the following equation
ln V/V-V> = k P + V0/V0- V>……………………..
• V is the volume at pressure P.
• V0 is the original volume of the powder including void.
• K is a constant related to the yield value of the powder.
• V> Is the volume of solid.
The Heckel relationship may be written in terms of relative density Prel rather then volume.
Log 1/1- Prel = KP/2.303 + A………. 
P is the applied pressure.
K & A are constants.
THE SIGNIFICANCE OF HECKEL PLOT:
1. The Heckel constant k
has been related to the reciprocal of the mean yield pressure, which is the minimum pressure required to cause deformation of the material under compression.
2. The intercept
Of the curve portion of the curve at low pressure represents a value due to densification by particle rearrangement.
3. The intercept
Obtained from the slop of the upper portion of the curve is a reflection of the densification after consolidation.
4. A large value of the Heckel constant indicates the onset of plastic deformation at relatively low pressure.
5. A Heckel plot permits an interpretation of the mechanism of bonding.
log @x = log @max – b E…………….
@x is the redial tensile strength.
@max is the theoretical tensile strength at zero voids.
E Is the porosity.
b Is the constant.
The increase in concentration of starch fro 1.2 to 4.5 % increases the radial tensile strength 47% to at a porosity of 25%.
The increase in starch increase the redial tensile strength only 12% as zero voids is approached.
* It appears that the concentration of binder has a greater influence in more porous tablet than in those approached zero void. As the P is increased & the porosity of tablet is decreased, the inter particular distance through which bonding force operate are shorten, thus the bonding force of the materials is stronger at lower porosity & a lesser quality of binder is required to produce a tablet of desired strength.
Properties of tablets influenced by compression
The relationship between applied pressure & weight, thickness, density & the force of ejection are relatively independent of the material being compressed.
Hardness, tensile strength, friability, disintegration & dissolution are properties that depend predominately on the formulation.
However, the developmental scientist should realized that processing & formulation are integrated disciplines, & effect of one on a pharmaceutical product cannot be totally separated from the other.
Following properties are significantly affected by compressional pressure.
Density & porosity.
Hardness & tensile strength.
Density & porosity: the apparent density of the tablet is exponentially related to the applied pressure [or compression force], as shown in the figure-2 until the limiting density of the material is approached.
As shown in figure-7 a plot of the apparent density against the logarithm of applied pressure is linear except at high pressure.
As the porosity & apparent density are inversely proportional, the plot of porosity against the logarithm of applied pressure is linear with a negative slope, as shown in figure-8.
Hardness & tensile strength: the ability of a tablet to withstand mechanical handling & transport has been evaluated by various types of test.
o Diametral crushing.
However the data from the tests seldom can be correlated in a precise manner.
Although hardness is not a fundamental property, diametral crushing is most frequently used for in-process control because of its simplicity.
Hardness & tensile strength:
There is a linear relationship between tablet hardness & the logarithm of applied pressure except at high pressure. As shown in figure 9 for lactose-aspirin tablets. Compressed mixtures have hardness value between those of tablet composed of the individual ingredients.
RADIAL & AXIAL TENSILE STRENGTH:
The strength of a tablet may be expressed as a tensile strength [breaking stress of a solid unit cross section in kg/m2] as shown in fig-10; the radial tensile strength is proportional to the applied pressure.
For an isotropic, homogenous tablet, the radial and axial tensile strength is equal. In practice the distribution of pressure, differences in density within the tablet and the mixture of several ingredients contribute to the non-homogeneity of the tablet & to the non-uniformity of the tensile strength.
The radial tensile strength @x is determined by a diametral compression test in which the maximum force to cause tensile failure[fracture] is measured. The radial tensile strength is then calculated by equ-6
D is diameter
& t is the thickness of the tablet.
The axial tensile strength is determined by measurement of the maximum force F@ to pull the tablet apart in tensile failure.
Effect of binders on tensile strengths:
A blend of powders may be granulated with a granulating solution to increase the adhesiveness of a formulation. The influence of the concentration of povidone on the tensile strengths of hydrous lactose is shown in fig-11.
The radial strength is little affected by the concentration of povidone but axial tensile strength is increased by increased concentration of povidone to strength greater then the radial strength.
Specific surface :
The specific surface is increased to a maximal value[four times that of the initial granules] indicating the formation of new surfaces due to fragmentation of the granules.
Further increase in applied pressure produce a progressive decrease in specific surface as the particles bond.
Usually as the applied pressure used to prepare a tablet is increased the disintegration time linear.
Frequently there is an exponential relationship between the disintegration time & the applied pressure as shown for aspirin & lactose in fig-16
There is a minimal value when the applied pressure is plotted against the logarithm of disintegration time as shown in figure-17.
Disintegration : for tablets compressed at low pressures, there is a large void & the contact of starch, grains in the inter particulate space is discontinuous. Thus, there is a lag time before the starch grains which are swelling due to the imbitition of water contact & exart a force on the surrounding tablet structure.
For tablets compressed at a certain applied pressure, the contact of the starch grain is continuous with the tablet structure & the swelling of the starch grains immediately exerts pressure causing the most rapid disintegration as demonstrated by a minimum in a plot of applied pressures against the logarithm of disintegration time.
The effect of applied pressure on dissolution rate may be considered from the view point of non-disintegrating tablets & disintegrating tablets.
Shah & parrott have shown that under skin conditions the dissolution rate is independent of applied pressures for non-disintegrating spheres of aspirin & salicylic acid an equimolar mixture of aspirin & salicylic acid & an equimolar mixture of aspirin & caffeine.
Micchella & savil found the dissolution rate of aspirin disks to be independent of pressure & independent of the particle size of the granules used to prepare disks.
The effect of applied pressure on the dissolution of disintegrating tablets is difficult to predict. However for a conventional tablet it is dependent on the pressure range, the dissolution medium & the properties of the medicinal compound & the excipient.
If fragmentation of the granules occurs during compression the dissolution is faster as the applied pressure is increased & the fragmentation increases the specific surface.
If the bonding of the particles is the predominate phenomenon in compression, the increase in applied pressure cause a decrease in dissolution.
THE FOUR MOST COMMON DISSOLUTION-PRESSURE RELATIONSHIPS ARE
1. The dissolution is more rapid as the applied pressure is increased.
2. The dissolution is slowed as the applied pressure is increased.
3. The dissolution is faster to a maximum as the applied force is increased & than a further increase in applied pressure slows dissolution.
4. The dissolution is slowed to a minimum as the applied pressure is increased & then further increase in applied pressure speeds dissolution.
The most popular estimate of tablet strength has been crushing strength. So may be defined as ‘that compressional force [Fc] which, when applied
Diametrically to a tablet just fracture it.’
Most practical test involves placing the tablet on or against a fixed anvil & transmitting the force to it by means of a moving plunger until the tablet just fractures.
Since tablets are isotropic & test conditions rarely provide well defined uniform stresses full & exact findings is difficult.
With flat faced anvil & plunger the tablet may be compressive.[tablet is crushed]
If one of then is knife-edged, however, it is more likely to be tensile.
The tensile strength of tablet is expressed by the following equation…
It has been suggested that the work Wf required to cause tablet failure correlates better with other mechanical strengths costs & is a more sensitive parameter for comparison with other tabletting parameters.
F is the force applied to the tablet.
Z is the deformation resulting from it.