Understanding Material Properties in Pharmaceutical Product ...

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Product and Process Design.Coordinated by Yihong Qiu]

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“Product and Process Design” discusses scientific and technical principles associated with pharmaceutical product development useful to practitioners in valida-tion and compliance. We intend this column to be a useful resource for daily work applications. The pri-mary objective for this feature: Useful information.

Reader comments, questions, and suggestions are needed to help us fulfill our objective for this column. Please send your comments and suggestions to col-umn coordinator Yihong Qiu at [email protected] or to journal coordinating editor Susan Haigney at [email protected].

KEY POINTSThe following key points are discussed in this article:

•Mechanical property is the relationship between applied force and the resulting deformation of a material

•Stress and strain are the basic descriptors of the applied force and deformation in the characterization of mechanical property

•Deformation may be categorized as elastic, plastic, or fracture. Elastic deformation is reversible but plastic deformation and fracture are permanent and irreversible

•Viscoelasticity refers to a combination of both elastic and plastic deformation. Virtually all materials exhibit this property under appropriate conditions. Viscoelas-tic deformation is dependent on the rate of strain

•Typical stress-strain behavior includes initial elas-tic deformation, yielding, and plastic deformation, followed by work-hardening and eventual fracture. Brittle fracture occurs when applied stress exceeds the elasticity limit

•Mass flow and funnel flow are the two basic flow patterns of bulk powder

Understanding Material Properties in Pharmaceutical Product Development and Manufacturing:Powder Flow and Mechanical Properties

ABOUT THE AUTHORSDeliang Zhou, Ph.D., is a principal pharmaceutical scientist in Oral Drug Products, Manufacturing Science & Technology at Abbott Laboratories. He may be reached by e-mail at [email protected]. Yihong Qiu, Ph.D., is a research fellow and associate director in Global Pharmaceutical Regula-tory Affairs CMC, Global Pharmaceutical R&D at Abbott Laboratories. He may be reached by e-mail at [email protected].

Deliang Zhou and Yihong Qiu

66 Journal of Validation technology [Spring 2010] i v t home.com

Product and Process Design.

•Arching, rat-holing, and inadequate flow can cause disruption to manufacturing, unacceptable weight variability, and segregation

•Powder flow is a deformation under shear stresses•The barrier to powder flow is the interparticu-

late interactions. Cohesive powder tends to flow poorly

•Powder cohesiveness also depends on stress history or pre-consolidation, which may be deemed as one aspect of the structure of a powder

•Stresses in bulk solids can be described by Mohr’s stress circle

•Unconfined yield strength is a characteristic of pow-der cohesiveness and resulting flowability. Uncon-fined yield strength of a particular powder depends on the pre-consolidation

•Flow function is the relationship between the unconfined yield strength and the pre-consolida-tion pressure

•Time is a factor in the pre-consolidation process that leads to timed consolidation and further complicates analysis of powder flow

•Yield locus analysis, along with Mohr’s stress circle, has been used to quantitatively characterize the cohesiveness of powders and is widely used in pow-der flow characterization

•Various semi-empirical methods such as angle of repose, Carr indices, and critical orifice diam-eter have also been widely used in powder flow characterization

•Powder compaction is the process of significant pow-der consolidation under compaction pressure, lead-ing to sufficient bonding and formation of tablets

•Van der Waals interaction is primarily responsible for particle-particle interaction. Particle-to-particle attraction is spontaneous when they are brought into close contact

•Tableting is the disarranging of barriers that mechan-ically interfere with increased number of particles coming close together

•Elastic deformation, plastic deformation, and brittle fracture are the three major events during compac-tion. Plastic deformation is the primary contributor to tablet bonding

•Solid fraction or porosity is a basic parameter of a compact and can be deemed as the structure of the compact or the state of consolidation

•Tensile strength and hardness serve as the indicators of the strength of a compact

•Compressibility, compactibility, and tabletability are the three terms commonly used to describe the

relationships among compaction pressure, tensile strength, and the solid fraction of the compacts. Solid fraction is a key in determining the properties of a compact

•Various Hiestand indices have been used to char-acterize the properties of a material with respect to their tableting performance

•Material properties may be understood from three levels: chemistry, solid phase, and particle.

INTRODUCTIONSolid drug products are formed using various powder ingredients. For example, tablets are made by mixing solid ingredients (e.g., filler, binder, disintegrant, and drug substance) followed by compaction. In phar-maceutical development, material properties of these solid ingredients, particularly mechanical properties, often play an important role in the fabrication of drug products. In certain cases, thermal properties may also become important (e.g., in a melt-extrusion process). By definition, mechanical properties are those of a material under an applied stress, including hardness, elasticity, plasticity, brittleness, the Poisson ratio, yielding stress and elongation, etc. They are used as measurements of how materials behave under a load. Scientific under-standing of these properties and their impact on product design, performance, and manufacturing is essential to the rational development and successful production of solid dosage forms.

Powder handling is an essential part in the devel-opment and manufacture of solid dosage forms. It is involved in virtually every stage of drug product manu-facture such as conveying, blending, transfer, storage, feeding, and compaction. Two basic aspects of powder handling are powder flow and powder compaction, both of which depend on physicochemical and mechanical properties of the solid materials used.

MECHANICAL PROPERTIES OF PHARMA-CEUTICAL POWDERSTo help understand the relationship between applied force and behavior of a material, some basic concepts are described in the following sections.

Stress And StrainStress is a measure of the average amount of force exerted per unit area of a surface within a deformable body (i.e., σ = F / A where F is the force applied and A is the area of the plane of interest). Forces may be categorized as tensile (pulling), compressive (pushing), bending/tor-sion, and shearing. However, any arbitrary external force


Coordinated by Yihong Qiu.

may be decomposed into only two independent com-ponents: the normal force, Fn, which is perpendicular to the plane, and the shear force, Fs, which is parallel to the plane. Stresses corresponding to these normal and shear forces can, therefore, be defined as: normal stress, σ = Fn / A, and the shear stress, τ = FS / A. Stress has the unit of pressure.

Strain is a measure of the extent of deformation. It is defined as the relative displacement in a material. Normal stress causes normal strain (i.e., stretch or com-pression in the normal direction), and shear stress causes distortion associated with the sliding of plane layers over each other (i.e., shear strain).

In one-dimensional deformation, strain is often defined as the ratio between the change of the dimen-sion of a material and the original dimension: γ = Δ l/lo where l0 is the original dimension, and Δ l = l - l0 is the change of the dimension, or displacement (Figure 1). Shear strain may also be defined by the angular distor-tion caused by the shear stress (i.e., γ = Δ l / l0 = tan α) (Figure 1). Bulk strain is also represented as the fractional change of volume of the material, γ = ΔV/V0.

Elastic Deformation And Modulus Of ElasticityIn the absence of external force, molecules are in their equilibrium positions with lowest free energy as deter-mined by the inter-atomic and intermolecular forces. In response to an applied stress, molecules or their parts will change their mutual positions from their original equilib-rium positions to new positions with higher free energy. Thermodynamics then compels molecules to return to the original positions with the lowest free energy, resulting in a returning elastic force that counterbalances the applied stress. At the new equilibrium position, the internal elas-tic force equals to the applied external force.

Within a limited extent, the deformation of a solid body is reversible. This type of deformation is referred to as the elastic deformation. Elastic deformation obeys the Hook’s Law, which states that the deformation is pro-portional to the applied stress. Three types of modulus of elasticity may be defined for a material that undergoes elastic deformation, as follows:

•Bulkmodulus,Κ, is defined as the proportionality constant between pressure (stress) and the fractional volume change, per equation 1:

[Equation 1]

Κ is the reciprocal of isothermal compressibility and has the unit of pressure

•Young’smodulus, Ε, is obtained in a tensile experi-ment. It is defined as proportionality coefficient between the tensile stress and the strain, as in equa-tion 2:

[Equation 2]

Elongation along the tensile direction, x, is usually accompanied by contraction along the directions perpendicular to the tensile stress (i.e., y and z). The Poisson ratio, ν, is defined as the ratio between the strains in the y or z directions to that in the x direc-tion, as in equation 3:

[Equation 3]

The Poisson ratio is one-half for materials that are incompressible, and is less than one-half for materials whose elongation is accompanied by volume expan-sion (most typical).•Shear modulus, or rigidity, G, is defined as the pro-

portionality factor between shear stress and shear strain, as in equation 4:

[Equation 4]

The bulk modulus, Young’s modulus, Poisson ratio, and shear modulus are connected by the following relationships, as in equation 5:

[Equation 5]

Figure 1: Illustration of strains caused by a tensile (top) and a shear (bottom) stresses.

α

Δ

Δ

Δ

α



These three moduli are therefore not entirely independent.

Plastic DeformationPlastic deformation refers to irreversible changes in the internal molecular structure (or microstructure) of a material subject to applied stress. Plastic deformation is a result of viscous flow, as described as follows.

The characteristic of a liquid is the non-fixed positions of its constituent molecules. As a result, liquid has no particular shape. Therefore, the deformation of a liquid itself does not produce elastic force as in elastic solids because the microenvironment of each molecule stays as the same before and after deformation. However, the process of deformation is related to the shear stress. The higher the shear stress, the more rapid the deformation. Viscous flow is related to the rate of deformation or rate of strain, denoted as γ = dγ/dt.

The relationship between shear stress and strain rate in viscous flow is related to the viscosity. For a Newtonian liquid, equation 6 holds:

[Equation 6]

where, η is the viscosity. It is also shown the strain rate is the same as the velocity gradient along the direction perpendicular to the shear stress.

ViscoelasticityViscoelasticity is a combination of viscosity and elasticity. The majority of mechanical bodies exhibit both elastic and viscous behavior. The viscoelasticity of a material may be better characterized by a combination of elastic springs and viscous damping elements. For example, the Maxwell’s model consists of an elastic spring and a viscous dashpot in series, while the Kelvin (or Voigt) model con-sists of these two elements in parallel (Figure 2).

A mathematic model can be constructed based on the behavior of each of the basic spring and/or dash pot. For example, the Maxwell and Kelvin models satisfy the fol-lowing equations, respectively:

[Equation 7]

[Equation 8]

Under constant shear stress, the Maxwell model predicts strain increase linearly with time. On the contrary, the Kelvin model predicts an exponentially asymptotic behavior (Figure 2). The Maxwell model is useful to describe the stress relaxation of a material;

while the Kelvin model provides insights into creeping of a material.

Under dynamic conditions such as those encountered using a rotary tablet press, the strain may be represented as a sinusoidal wave, and the resulted stress will also vary sinusoidally, but with a phase lag. Viscoelasticity of many materials are more complicated than what can be described by the simple Maxwell or Kelvin model. Improved rep-resentation may be achieved using various combinations of the two elements; however, it can rarely be reproduced perfectly. The situation with nonlinear viscoelasticity is even more complicated. Nevertheless, viscoelasticity makes the compaction behavior of a material more difficult to predict from one set of conditions to another.

Stress-Strain BehaviorFigure 3 shows some typical stress-strain behavior of materials. Elastic deformation is designated by the linear

Figure 2: Maxwell and Kelvin models (top) and the predicted behavior (bottom).



portions of the stress-strain curves. For brittle materi-als, the fracture will occur when the stress exceeds the elastic limit. Non-brittle material initially exhibits the elastic deformation. When the applied stresses increase beyond the capability of the material to balance them by elastic forces, the material will yield, and the elastic region ends when material reaches its yield strength. Subsequently, plastic deformation or plastic flow starts, which is irreversible. This region is clearly one of non-linear viscoelasticity. Polymeric materials may extend at constant stress in this region that is often referred to as cold drawing. A strain-hardening (or work-hardening) region may also occur due to the strength enhancement caused by plastic deformation. Finally, material will eventually fracture.

FLOW PROPERTIES OF PHARMACEUTICAL POWDERSThe following sections discuss the flow properties of pharmaceutical powders.

Powder FlowIn most cases, pharmaceutical powders fall into the cat-egory of fine powders (less than 100 µm). Fine powders often exhibit significant two-phase (i.e., solid/air) inter-actions when they are handled in bins, hoppers, and processing vessels. Flow of fine powders is very complex and generally more difficult to handle.

Flow refers to the deformation of powder bed under shear stresses. Powder flow is a reflection of the mechani-cal behavior of powder under relatively low shear stresses. On the contrary, powder compaction is a revelation of the mechanical properties of powder under much higher (compressive) pressures. During flow, the powders gain sufficient shear force such that they can overcome the

inter-particulate interactions and frictions and move along the direction of shear.

Intuitively, the flowability of bulk powder is depen-dent on the inter-particulate attractions. Because of the multi-component nature of formulated powders, the attractive forces between individual particles are often called adhesive forces. However, interactions among particles of the same kind should be more correctly termed as cohesion. Van der Waals interaction is primar-ily responsible for these inter-particulate forces, which include dipole-dipole (Keesom force), dipole-induced dipole (Debye force), and induced dipole-induced dipole (dispersion or London force) interactions. These van der Waals forces decrease quickly with distance (1/r6) and, therefore, only become important when atoms/mol-ecules are in close proximity.

The number of particle contacts is another important factor in the inter-particulate interactions of bulk pow-der. Perfectly spherical particles have the least possible number of contacts and are usually the most readily flowable. Most pharmaceutical powders are irregularly shaped. The number of contacts is generally higher and contacting faces may even be possible. Smaller par-ticles have relatevely higher numbers of contacts and the total adhesive forces are greater. As a rule, fine powder generally flows more poorly than large particle size powder. Increased inter-particulate interactions may also result from particle bridging. Particle bridging may be caused by physical locking, or by crystallization following partial dissolution, by sintering around the contact points, by plastic deformation at the particle contacts, or by various other physical, chemical, or bio-logical processes. The formation of bridging increases the number of contacts or contact area and hence the total adhesion/cohesion.

Powder flowability is a consequence of the inter-par-ticulate interactions. From a material science point of view, this interparticulate interaction depends on chem-istry, crystal structure, and powder structure. Certain powder structures may be altered by mechanical forces. Application of external forces can increase the number of particle contacts, cause plastic deformation around the contacts, and increases the contact area. These in turn lead to a change in the overall adhesiveness, the powder structure, and flow characteristics. Even without exter-nal forces, bulk powder during storage will consolidate under gravity, which is called timed consolidation. It is a revelation of the viscoelasticity of the powder. Timed consolidation causes increased particle-particle interac-tion and may eventually lead to caking, which signifi-cantly alters the flow behavior.

Figure 3: Illustration of stress-strain behavior.



In brief, the easiness of powder flow depends strongly on the interparticulate interactions in the powder, the latter of which is determined by molecular structure, crystal structure, and powder structure. The stronger the interparticulate interaction, the less flowable is the powder, and the more shear is required to render flow.

Powder Flow Pattern Adequate powder flowability (1-5) is key to the success of many unit operations in the manufacture of solid products. Powder flow properties are known to influ-ence the fluidization behavior in the granulation and drying operation and mixing during blending operation. However, it also has a significant impact on tablet com-pression or encapsulation. Consistently good flowabil-ity is critical in producing quality tablets and capsules. Typical issues related to powder flow are caused by poor flow of materials in the bins, through hoppers, or into die cavities. The problems may include lack of flow due to arching or rat-holing, unacceptable weight variability of final dosage units, and/or poor content uniformity because of powder segregation.

Powder flow pattern in a hopper may be classified as mass flow or funnel flow (Figure 4). In mass flow mode, all materials are in motion, albeit at the differ-ent velocities. In funnel flow, an active flow channel forms above the outlet while no powder flows in the periphery, forming a dead zone. Mass flow provides a first-in-first-out flow sequence and is desired. Funnel flow corresponds to first-in-last-out flow sequence, and materials only flow through the center flowing channel. The non-flowing powder may collapse into the active flow channel as the amount of powder depletes, but in an uncontrolled manner that often leads to segrega-tion. Funnel flow is often manifested as rat-holing or

arching. Rat-holing is the result of funnel flow leading to the formation of the flow channel above the hopper outlet to the top of powder filling. Arching refers to the formation of an arch around the outlet of the hopper due to the cohesiveness of the powder that prevents further powder flow. The arch may or may not collapse without external interruption. However, when this occurs, erratic flow, such as flooding, may arise.

Characterization Of Powder FlowStress Distribution in Bulk Powder. Stress is dis-tributed unevenly throughout a powder bed when a force is exerted. Typically this can be illustrated with a simplified 2D plane stress analysis. A horizontal stress σx develops as a result of the stress σy in the vertical direc-tion. The ratio between σx and σy is called the stress ratio (typically 0.3 - 0.6). Stresses in other directions are con-sidered below.

For any arbitrary plane with an angle θ to the hori-zontal direction, the stresses can be represented by the normal stress, σ

θ, the shear stress, τ

θ. The plane is also

referred to as a cutting plane. Based on equilibrium principles (force and momentum), the following rela-tionships can be derived, as follows:

[Equation 9]

[Equation 10]

Hence the stress pair (σθ, τ

θ) of all possible cutting planes

form a circle in the σ, τ-diagram (Figure 5). This circle is called the Mohr’s (stress) circle, introduced by Otto Mohr in 1882.

The Mohr’s circle is centered at σ = (σy + σx)/2 and τ = 0, with a radius of (σy - σx)/2. It has exactly two points of inter-section with the σ–axis, which correspond to the directions where the shear stress τ =0. The normal stresses defined by these two intersections are called principal stresses. The larger one, which equals to σy, is called the major principal stress (designated as σ1). The smaller one, which equals to σx, is called the minor principal stress (designated as σ2). The plane where τ = 0 (i.e., no shear stress) is called the principal plane, corresponding to the horizontal or vertical direction (θ = 0 or θ = 90°) where only compressive stress exists. The maximum shear stress occurs at θ = 45° while the minimum occurs at θ = 135°. Fractures of many solid materials have been observed at an angle of approximately 45° from the applied force, which is the direction where the maximum shear stress occurs.

Mohr’s circle has been a leading tool to visualize the relationships between normal and shear stresses, and

Figure 4: Illustration of mass flow (left) and funnel flow (right).

Act

ive

flo

w c

han

nel

No

n-fl

ow

reg

ion



to estimate the maximum stresses and principal plane. In characterizing powder flow, Mohr’s circle provides a quantitative means to characterize the cohesiveness of a powder. Figure 5 is based on 2D plane stress analysis but Mohr’s circle can also be used to deal with general 3D stresses.

Uniaxial Compression Test, Shear Cell Test, Unconfined Yield Strength, Flow Function, and Yield Locus Analysis. Flow properties of bulk powder depend on the consolidation state of the powder (or “powder structure”), which is often achieved by pretreat-ments such as pre-shearing (e.g., during shear cell test) or pre-consolidation (e.g., during uniaxial compression test) by applying a defined normal load to the powder bed. After the powder structure is defined, all subsequent tests may then be performed under reduced normal loads, usually without the confinement of a wall.

The unconfined yield strength can be readily demon-strated using a uniaxial compression test. In this test, a powder is loaded into a cylinder and preconsolidated under a defined normal force. Following removal of the

confining wall, a normal stress lower than the pre-con-solidation pressure is re-established and subsequently increased gradually until the powder bed fails (i.e., flows). The stress causing powder failure is the unconfined yield strength, σc. The relationship of the unconfined yield strength σc versus the pre-consolidation pressure σ1 is known as the flow function (FF). This test is essen-tially designed for the characterization of the strength of the powder structure formed by pretreatments. The flow function coefficient, ffc, is the ratio between the pre-consolidation pressure and the unconfined yield strength. The larger the ffc, the more flowable is the powder. Value of ffc can be used to define the category of powder flow (Figure 6). It should be noted that flow function often exhibits curvature and ffc is not constant (Figure 6). Hence, powder flowability has to be inter-preted under specific conditions. A powder may flow freely under one set of conditions but may not flow at all under another.

It has been shown that yield strength obtained from uniaxial compression test is often too low for practi-

Figure 5: Stress distribution in bulk powder and the Mohr’s stress circle.

ϴ

ϴ20

σy

σ1 = σy

σ2 = σx

σσθ

τθ

τ

τθ

σy σy

σx σx σxσθ



cal applications and data from the shear cell test are more relevant. There are two basic types of shear cell designs, the translational shear (e.g., Jenike) and the rotational shear (e.g., Schulze). Both tests operate using very similar principles and provide similar information on flow characterization. In shear cell analysis, the pre-consolidation is achieved by pre-shearing to reach a steady-state flow under a defined normal load. The pre-shear normal stress and the steady-state shear stress (σpre, τpre) define the powder structure under the specific test condition. The pre-consolidated powder is then sheared under a reduced normal stress until the shear force goes through a maximum that corresponds to the failure of the structured powders (i.e., flow). The cor-responding shear stress and the normal stress at failure (σsh, τsh) represents a yield point in the (σ, τ) plane. The process of pre-shearing followed by shear to failure under different reduced normal load is repeated multiple times until the yield loci are adequately characterized (Figure 7). The yield locus is characteristic of the physical and mechanical properties of the powder under the defined test conditions.

Because all stresses in a bulk powder can be represent-ed by the Mohr’s circle, Mohr’s circles can be constructed from the yield locus to gain a quantitative understanding of the cohesiveness of the bulk powder. The preshear normal stress is an experimentally known quantity that equals to the major principal stress σ1 according to previous discussion. The minor principal stress σ2 is not known a priori, and the same is the Mohr’s circle. How-ever, τpre represents the steady-state shear stress under preconsolidation pressure σpre, hence these relationships must be reflected on the Mohr’s circle. Graphically, the

(greater) Mohr’s circle can be constructed such that it is centered on the σ-axis, intersects with the σ-axis at (σpre, 0), and is tangential to the yield locus on the point where τ = τpre. The minor principal stress σ2 can then be obtained as the other point of intersection of the Mohr’s circle with the σ-axis. The unconfined yield strength of the consolidated powder is obtained by drawing a smaller Mohr’s circle with σ2 = 0 (i.e., corresponding to unconfined yielding), while tangent to the yield locus. The major principal stress of the smaller Mohr’s circle corresponds to the unconfined yield strength σc.

Greater Mohr’s circle represents the structure of the powder under the pre-consolidation conditions. It can be used to construct the “cohesiveness” of the powder. A tangent line of the greater Mohr’s circle can be drawn through the origin, which is the effective yield locus as defined by Jenike in his original derivation (1). The angle of this line with the σ-axis (φe) is defined as the effective angle of internal friction of the powder at steady-state flow. The larger φe, the more cohesive is the powder. This internal friction angle is required for hopper and silo design to achieve mass flow according to Jenike’s theory (1, 6). Shear cell test not only provides a quantitative measure on powder cohesiveness, but also provides a methodology to modify equipment (e.g., hopper angle and surface finish) designs for achieving mass flow and mitigating flow problems. It is superior to empirical methods for characterization of powder flow.

Empirical Methods for Characterization of Powder Flow. The shear method described above is based on sound physical principles and yields quanti-tative and reproducible results in the characterization of powder cohesiveness. It also provides a clear depic-tion of the powder flow. Nevertheless, several empirical methods have also been widely used in the industry due to their simplicity and practicality. Among them, the angle of repose, critical orifice of flow, Carr indices (including the compression index and the Hausner ratio) are most common. These methods have been shown to correlate with powder flowability though they were not based on (or derived from) fundamental principles. One of the main drawbacks of these methods is that the results are often more variable. The reproducibility of the data often depends on multiple factors, such as how the experiments are performed or the powders are pre-treated. Small variations in experimental settings can sometimes lead to large differences in test results.

•Angle of Repose (AoR). Angle of repose is a char-acteristic related to the cohesiveness of the pow-der. It is the angle formed by a cone-like pile of the powder. Cohesive powder has higher interparticle

ffc = 1

ffc = 2

ffc = 4

ffc = 10

Figure 6: Illustration of flow function.



friction which resists flow hence the angle will be larger. Smaller angles indicate better flowability. As a rule of thumb, AoR value of less than 30° is most desirable while greater than 55° may indicate serious flow problems. However, the method is not very robust.

•Compression Index (CI). Cohesive powder tends to resist consolidation by its own weight. Hence, larger differences exist between the tapped and untapped bulk volume (or density). Com-pression index is a measurement of the relative difference between tapped (Vt) and untapped volume (V0) of the powder, as follows:

[Equation 11]

Hausner ratio (HR) is closely related to the compres-sion index, as follows:

[Equation 12]

A CI value of less than 10% indicates good flow while greater than 25% suggests potential problems with powder flow.•Critical Orifice Diameter (COD). Critical

orifice diameter is another parameter related to powder flow. A cohesive powder tends to resist flow and does not pass through small orifice by gravity. Therefore, orifice diameter can be used as an indicator of flowability. COD of less than 10mm indicates good flowability while larger than 24mm indicates poor flow.

MECHANICAL PROPERTIES OF POWDER COMPACTSThe compressed tablet is the most preferred dosage form because of its convenience, flexibility, cost effectiveness, and high production throughput. One of the objectives of compression is to obtain tablets that are sufficiently strong to withstand subsequent processing and transportation. Mechanical properties of materials dictate the behavior of powder mixtures both during and after compaction. However, tablet compaction of mixed solid ingredients is still a very complex physical process (7-11). A good understanding of the tableting process requires multi-disciplinary knowledge in physics, engineering, materials, and mathematics. Nevertheless, a basic comprehension of the principles that govern the compaction process is beneficial for those involved in the design, operation, and troubleshooting of tablet production.

Compaction And Bonding The compression of powders and granules to form tab-lets occurs at high applied pressures. Under high load conditions, powders undergo significant consolidation and volume reduction. The behavior of the powders under pressure determines the mechanical strength of the resulted compacts. At the particle level, compression is the disarranging of barriers that mechanically interfere with increased number of atoms coming close to form inter-atomic attraction (i.e., bonding) (10). During tab-let compression, particles may slide against each other, fracture, or deform plastically in order to fit themselves closely together. Attraction between particles is ther-modynamically favorable when they are brought close enough to form interfacial contact. Once the bonding is formed, it will resist separation, resulting in a mechani-cally strong compact.

As discussed previously, particles under applied load may undergo plastic and elastic deformation or brittle fracture. Elastic deformation is reversible and does not contribute to the tablet bonding upon decompression. Plastic deformation occurs when the stress exceeds the yielding strength of the material. It causes particles to flow and fill into the inter-particulate spaces, as well as weld together with the neighboring particles. These processes result in the increased contact number, contact-ing area, and thus tablet bonding. Plastic deformation is a form of viscous flow and is dependent on the rate of strain. Brittle fracture is the result of exceeding the limit of material elasticity. It leads to smaller particles, resulting in increased particle-particle contact numbers and increased bonding opportunities. It is often cited as a major bonding mechanism for brittle materials. However, this process alone is unlikely to produce the

Steady-state flow

0σ2

φe

σC σ1στ

Figure 7: Illustration of yield locus.



bonding needed for the formation of strong tablets. It may be argued that plastic deformation is still the pri-mary bonding mechanism in the compaction of brittle materials, while brittle fracture provides an aid to the consolidation process.

Viscoelasticity is commonly observed in organic mate-rials. Because viscoelastic deformation is dependent on the rate of strain, it often plays a significant role in com-pression operation for certain materials. Depending on the relative contributions of elasticity and viscosity of a powder mixture, the primary deformation mechanism may vary with compaction speed. Viscoelasticity causes elasticity to dominate when a stress is applied quickly, but allows more viscous flow with a longer compaction time. Hence plastic deformation does not always translate from one compaction speed (or scale) to another.

According to Hiestand (10), (tablet) bonding is the summation of inter-atomic attraction between particles that manifest as tablet strength during separation. The nature of this inter-atomic attraction is primarily van der Waals forces in pharmaceutical tablets. H-bond-ing requires specific distance and direction and is not expected to be a significant contributor to tablet strength. Attraction results when two particles are brought into close proximity. Further reduction in the interparticulate distance results in an increase in repulsive forces. At equi-librium, the attraction and repulsion are balanced and the particles are at a minimum in the potential energy. Therefore, once the equilibrium is established, parti-cles will remain in their equilibrium positions after the compressive force is removed, and a tablet forms. When external tensile or other types of forces are applied to a tablet, the inter-atomic attraction will resist these forces. Breakage of tablet occurs only when the external forces exceed the overall inter-atomic interactions in the tablets. Therefore, the strength of a tablet depends on the number of bonding sites and the strength of bonding between particles. Contrary to powder flow, the more cohesive a powder is the better the chance for the powder to form a strong tablet.

Tensile Strength And Hardness Of TabletsTensile Strength. Tensile strength is a measure of bonding in a tablet. It is directly related to the attrac-tion between particles. The tensile strength of compacts is always much less than the strength under compression. Tensile strength (σ

Τ) can be measured using the transverse

compression between two platens for square compacts or using the conventional diametrical hardness testing for circular compacts. Both methods measure the force to cause the tensile fracture of a tablet.

The transverse compression of square tablets produces tensile stresses at the center of the compact and provides highly reproducible results (12). In the transverse com-pression method, when the platens are 0.4 of the width of the compact, the tensile strength is 0.16 times the mean stress under the platens. The ratio between the major principle stress and the minor principal stress at the center of the compact is 3.7, which renders the stress distribution to be readily analyzed using the Mohr’s circle on a common scale. Diametrical hardness test-ing is routinely used in in-process monitoring during tablet compression. Tensile strength determination of pharmaceutical tablets based on this method has been demonstrated (13). However, the fraction mode of a tablet subject to such a test is not guaranteed to be truly tensile in origin. Visual inspection of the tablet failure is therefore necessary. In addition, the conversion from breaking force to tensile strength is only well defined for relatively simple tablet geometries such as circular and round.

Tablet tensile strength between 0.1 and 4 MPa has been reported in the pharmaceutical literature. As a rule of thumb, a tensile strength higher than 2 MPa is desirable in ensuring that the tablet will withstand subsequent operations such as coating and transportation.

Dynamic Indentation Hardness. Dynamic inden-tation hardness of a compact is usually measured using a pendulum impact device. The tablet is subjected to impact with a sphere (made of stainless steel) released at an initial height, hi. The impaction causes rebound of the ball (at height hr), while leaving a permanent dent (deformation) on the tablet. The difference between the initial height and the rebound height corresponds to the energy lost during the impaction process, which is used to produce the dent (with chordal diameter a). The dynamic indentation hardness is calculated as this energy divided by the volume of the dent (12, 14), as follows:

[Equation 13]

Where m is the mass of the ball, g is gravity accelera-tion, and r is the radius of the indenter.

Quasi-static Hardness. Quasi-static hardness is measured under a different condition. In this test, a stain-less steel ball is pressed into the tablet surface by applying a static force for a much longer time (e.g., 15-30 min). The hardness is then calculated as the force divided by the area of the projected chordal, as follows:

[Equation 14]



Where a is the chordal radius of the indent. The slow stress relaxation during this hardness test allows for plas-tic deformation to develop more fully. Therefore, quasi-static hardness is much smaller than the dynamic inden-tation hardness for materials that are viscoelastic.

Porosity, Compressibility, Compactibility, And TabletabilityPorosity or solid fraction is a basic parameter character-istic of a compact. Porosity is the fraction of pores of the total volume in the compact that are accessible for particle packing. Solid fraction is the fraction of compact vol-ume that is occupied by particles. Porosity (ε) and solid fraction (SF) can be calculated from the tablet mass (M), tablet volume (V), and true density (ρtrue), as follows:

[Equation 15]

Porosity or solid fraction represents the structure, or a state, of a compact. Many properties of a compact such as tensile strength and hardness are highly dependent on the porosity of the compact. Therefore, comparisons of compact properties should be made based on similar porosity (or solid fraction) of the compacts.

A number of relationships have been developed and are central to the understanding of compaction behavior/ properties. Compressibility is the relationship between compaction pressure and porosity or solid fraction of the compact. Compatibility refers to the relationship between the tensile strength of and porosity of the result-ing compact. Tabletability is the relationship between the tensile strength of the tablet and the compaction pressure. These three relationships are not independent of each other: one can be derived once the other two are given. In pharmaceutical manufacturing, the relationship between tablet crushing force and the compression force is routinely checked during compression operations to monitor tableting behavior. It should be noted that the compression force is linked to the compaction pressure and the crushing force is related to the tensile strength of the tablet. Under the same crushing forces, the tensile strength depends significantly on tablet sizes and shapes because the tensile strength of a tablet is also a function of geometry and dimension of the tablet. Therefore, this relationship cannot be used to compare different prod-ucts or strengths of different size.

Among compressibility, compactibility, and tabletabil-ity, compactibility is a more fundamental parameter as it describes the relationship between the structure (i.e., the porosity) and the strength of a compact, which is analogous to the structure-property relationship widely

adopted in material science. Other relationships such as compressibility and tabletability are influenced by com-pressing equipment settings (i.e., pre-compression, dwell time, punch vertical velocity) and material properties. On the contrary, the compactibility is largely independent of the processes by which compacts are made (15).

Hiestand Tableting IndicesOne of the useful approaches for characterizing the compact properties is to use Hiestand’s indices which include bonding index (BI), brittle fracture index (BFI), and viscoelastic index (VE). These dimensionless indices provide insight into the relative tableting performance of materials.

Bonding Index (BI). Bonding index is defined as the ratio between tensile strength and hardness of a tablet. It is a measurement of the survival of tablet bonding during decompression. Maximum contacts (bonding) between particles are established at the end of compres-sion. However, some bonding may be lost (broken) dur-ing the decompression due to elastic recovery. A large BI indicates strong bonding due to a relatively small fraction of lost bonding. A bonding index exceeding 0.01 is typically desired. The largest BI value reported for pharmaceutical compacts are about 0.06. Bonding index is calculated as follows:

[Equation 16]

Brittle Fracture Index (BFI). Brittle fracture index measures the brittleness of a material. It is determined by comparing the tensile strength of a tablet with that of the same tablet but with a small axially-oriented hole in the center. The strength of a tablet is weakened by the presence of a hole. However, if the material can effectively re-distribute the stress, the strength of the holed tablet will be approaching that of the intact tablet. For brittle material, the tensile strength can be shown theoretically to be approximately one-third of that of the intact tablet. BFI is calculated according to the following equation such that the very brittle material will have a BFI close to 1, as follows:

[Equation 17]

BFI values less than 0.3 are indicative of relatively non-brittle materials, while BFI values larger than 0.8 may indicate severe fracture problems. BFI values exceeding unity are rare but may also occur. Methenamine, eryth-romycin, ibuprofen, sucrose, and phenacetin exhibit high values of BFI, which can cause fracture during decom-



pression. The bonding index should also be considered when assessing the brittleness of a material. A material may be brittle yet may withstand decompression without fracture if the BI is also high (e.g., erythromycin).

Viscoelastic Index (VE). The viscoelastic index (16) is the ratio between the dynamic indentation hardness and the quasi-static hardness of a tablet, as follows:

[Equation 18]

During the dynamic indentation hardness testing, the tablet is rapidly deformed, while during the quasi-static testing, the compact will have more time to undergo plastic deformation, potentially resulting in formation of stronger bonding. Hence, VE provides an assessment on the viscoelastic properties of the material. The larger the difference between these two hardness values, the more is the strain-rate dependence of the material.

APPLICATIONS OF MATERIAL PROPERTIESMaterial properties may be understood from at least three levels. The constituent molecules (chemical spe-cies) determine the first level of material properties. The second level involves how these molecules/atoms are arranged spatially (i.e., structure in the condensed states such as non-crystalline and crystalline structures including polymorphs). For example, the compaction properties can vary drastically among amorphous and crystalline phases. Slip planes are particularly important when considering compaction behavior of crystalline solids. Acetaminophen and sulfamerazine are two good examples where one crystal form is more compressible than the other due to the presence of slip planes. Similar observations have also been reported with different salt forms (e.g., L-lysine). The third level is more complex and involves particle morphology, particle size, and other particle characteristics such as moisture sorption, pore structure (e.g., granule structure), and consolida-tion, etc. All three levels of material properties usually play significant roles in handling pharmaceutical pow-ders. The first level is more important during formula-tion development, while the second and third levels are more relevant during scale-up and manufacture after the formulation is fixed.

Powder flow is related to the internal friction between powder particles. Besides the chemical com-position, the particle size and distribution, morphol-ogy, and powder attributes such as granule structure and moisture content determine the overall flow char-acteristics. Powder flow is also a function of equip-ment and operating conditions. Improvements of

powder flow may be achieved using two approaches: changing the material characteristics to improve flow, and/or modifying the equipment design so that flow problem can be eliminated or mitigated.

Similar principles can also be applied in tablet com-pression. First, the intrinsic material properties of a drug substance and excipients need to be well understood and built in the selection and design of formulation and manufacturing process. Solid-state forms, particle morphology, size and distribution, and moisture content may be altered and controlled to improve the mechanical properties of a drug substance. For solid dosage form containing high loading of a drug substance with poor compactibility and/or flow properties, particle agglom-eration (e.g., granulation) is often required in addition to use of excipients that counteract poor compressing properties. Equally important are the design of compac-tion process and equipment settings. Given that many materials with viscoelastic compaction mechanism (e.g., starch and microcrystalline cellulose) exhibit a large degree of stress relaxation with time-dependent defor-mation, proper selection of the compaction conditions (e.g., dwell time, vertical punch velocity, etc.) and their ranges will also play an important role in addressing potential compaction issues such as capping and lamina-tion, picking and sticking, and low tablet strength.

SUMMARYUnderstanding material properties is essential in the successful development, scale-up, and manufactur-ing of solid dosage forms. Mechanical properties determine powder flow, powder compaction, and the strength of powder compacts. Powder flow depends on interparticulate interactions. Flowability decreases with increasing cohesiveness of the powder. On the contrary, interparticulate interaction is exploited in the formation of a tablet. The success of powder compac-tion is highly dependent on the material properties. Elastic and plastic deformations and brittle fracture occurs during tablet compaction. Plastic deformation is the primary contributor to tablet bonding. Visco-elasticity is fairly common in pharmaceutical powders and should be considered when dealing with many problems often encountered during compression opera-tion. Many techniques, ranging from more quantitative to semi-empirical approaches, have been used in the characterization of powder flow and compaction. A general understanding of these topics should be helpful for validation and compliance personnel.



REFERENCES1. Jenike, A. W., “Storage and Flow of Solids,” Bulletin 123 of

the Utah Engineering Experimental Station, 53, 1964 (Revised 1980).

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