PM3125: Lectures 19 to 21

1. 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.

2. 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).

3. Powders intended for compression must possess two essential properties: - Compressibility - Fluidity (how to meaure it?)

4. 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

5. 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.

6. Angle of Repose (θ) θ = tan-1(h/r) where h = height of pile r = radius of the base of the pile h r Excellent flowability if θ < 25o Good flowability if 25o < θ < 30o Passable flowability if 30o < θ < 40o Very poor flowability if θ > 40o

7. Factors affecting Angle of Repose - coefficients of friction between particles - size of the particles - moisture affects the angle of repose

8. 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.

9. 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. Manual powder flow tester

10. 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 Manual powder flow tester

11. 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.

12. 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.

13. Mass-Volume relationships Type of voids (or air spaces): • Open intraparticulate voids • Closed intraparticulate voids • Interparticulate voids

14. 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.

15. 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 / ρT M is the mass of powder

16. 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) when expressed in %

17. 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

18. 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

19. Methods to measure volume of powder • Helium pycnometer • Liquid displacement method • (specific gravity bottle method)

20. 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.

21. 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.

22. 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 deformationwhen subjected to external forces.

23. 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.

24. 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).

25. 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.

26. Effect of applied forces Microsquasing: Irrespective of the behavior of larger particles smaller particles may deform plastically.

27. 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.

28. Effect of applied forces DEFORMATION: Strain: The relative amount of deformation produced on a solid body due to applied force. It is dimensionless quantity.

29. Effect of applied forces

30. Effect of applied forces

31. Effect of applied forces Ho ∆H Compressive strain, Z = ∆H / Ho

32. Effect of applied forces Shear strain

33. Effect of applied forces DEFORMATION: Stress(σ): σ = F / A where, F is force required to produce strain in area A

34. Effect of applied forces

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

36. 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.

37. 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 bondingoccurs, which in turn results in an increase in the mechanical strength of the mass.

38. Mechanisms of Consolidation Another possible mechanism of powder consolidation is asperitic meltingof 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.

39. 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

40. 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.

41. Tabletting cycle

42. 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.

43. 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.

44. 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 = Fme-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.

45. 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.

46. 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 FL

47. 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 D = diameter of tablet FA FD FL

48. 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 FM offers a practical friction-independent measure of compaction load, which is generally more relevant than FA.

49. 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

50. 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     =   D / H   The Poisson ratio is a characteristic constant for each solid material and may influence the tabletting processes.