Heckel Equation Research Articles

Pharmaceutical powders compaction: Experimental and numerical analysis of the density distribution

This paper investigates the axial density distribution during the single action compaction of pharmaceutical powders in rigid dies. Experimental results of the compaction of microcrystalline cellulose are compared to those predicted with an analytical model and with numerical analysis. The axial density distribution within tablets compacted at different loads are measured using a mercury porosimeter of slices from tablets. The analytical model based on the Janssen–Walker analysis coupled with the Heckel equation is applied to determine the axial density distribution. Representing the mechanical behaviour of the powder compaction with the Drucker-Prager/Cap model and by measuring the die wall friction, computation of the axial density within the tablet is also obtained by solving the boundary problem with finite element method for the loading–unloading cycle. Results of the axial density obtained with the analytical model and numerical method at end of the loading step show a qualitative agreement with the measured data. However, the measurements are better predicted with the numerical results obtained with the simulation of the loading–unloading phases.

Some Compaction Characteristics of the Hot Water Leaf Extract ofNauclea latifiola

This study aims to develop a suitable tablet dosage form of Nauclea latifolia, a potential antimalarial agent. The compaction characteristics of the oven dried water extract were studied using the Heckel equation. The mechanical properties of the compacts were also determined. This preliminary information will be useful in developing a suitable dosage form of the extract for use in the management of malaria. The results showed that N. latifolia extract exhibited high densification due to dye filling while the subsequent rearrangement of the granules did not contribute, significantly, to their densification. The granules had enhanced plasticity as shown by the low yield point, Py. The tablets produced from the extract had good mechanical properties, with hardness increasing via compression pressure while the friability decreased. However, the tablets had poor disintegration properties; it is concluded that while tablets of suitable physical properties can be produced from the extract, a disintegrant would need to be included in the formulation to ensure adequate drug release.

Evaluation of Dika Nut Mucilage (Irvingia gabonensis) as Binding Agent in Metronidazole Tablet Formulations

Dika nut mucilage obtained from the nuts of Irvingia gabonensis (O'Rorke) Bail (family Irvingiaceae) has been evaluated as a binding agent in metronidazole tablet formulations in comparison with gelatin BP. The compressional properties of metronidazole formulations were analyzed using density measurements and the Heckel equations as assessment parameters, whereas the mechanical properties of the tablets were assessed using the tensile strength (T), brittle fracture index (BFI), and the friability of the tablets. The drug release properties of the tablets were assessed using disintegration and dissolution times of the tablets. The results obtained indicate that formulations containing dika nut mucilage as binding agent show faster onset of plastic deformation under compression pressure than those containing gelatin. The tensile strength of the tablets increased with increase in concentration of the binding agents, whereas the BFI and friability values decreased. Furthermore, tablets containing dika nut mucilage generally showed lower tensile strength but higher brittleness and friability than those containing gelatin. The results also showed that tablets containing dika nut mucilage generally showed higher disintegration and dissolution times than those containing gelatin BP. The results suggest that dika nut mucilage could be useful in achieving various tablet strength and drug release properties.

Evaluation of a new coprocessed compound based on lactose and maize starch for tablet formulation.

The development of new direct compression excipients should include a comprehensive and rapid determination of deformation properties. The aim of this study was to characterize StarLac, a new coprocessed compound for direct compression based on lactose and maize starch. For this purpose, the effects of the base materials (maize starch and spray-dried lactose) were considered and the influence of the spray-drying process was investigated. This was performed by comparing the physical mixture of starch and spray-dried lactose at the same ratio as for StarLac. For analysis of the deformation behavior, the 3-D model and the Walker equation were applied; for verification, the Heckel equation and the pressure time function (a modified Weibull equation) were used. The advantages of StarLac are its good flowability depending on the spray-drying process, an acceptable crushing force due to its lactose content, its rapid disintegration depending on starch, and a brilliant fast release of an active ingredient, such as theophylline monohydrate. The volume-pressure deformation properties of StarLac were dependent on the lactose properties. Only at high maximum relative density (rho(rel, max)) did the influence of starch cause a change in these properties. A network-like structure can be observed using scanning electron microscopy pictures. Overall, StarLac deformed plastically with a low portion of elasticity. The physical mixture exhibited a more elastic behavior than StarLac. However, the part of the powder that was irreversibly compressed was much lower than was observed for the single substances. This behavior is caused by an interaction between the components, which in StarLac is prevented by spray drying.

A Novel Method for Deriving True Density of Pharmaceutical Solids Including Hydrates and Water-Containing Powders

True density is commonly measured using helium pycnometry. However, most water-containing powders, for example, hydrates, amorphous drugs and excipients, and most tablet formulations, release water when exposed to a dry helium atmosphere. Because released water brings significant errors to the measured true density and drying alters the nature of water-containing solids, the helium pycnometry is not suitable for those substances. To overcome this problem, a novel method has been developed to accurately calculate powder true density from compaction data. No drying treatment of powder samples is required. Consequently, the true density thus obtained is relevant to tableting characterization studies because no alteration to the solid is induced by drying. This method involves nonlinear regression of compaction pressure-tablet density data based on a modified Heckel equation. When true density values of water-free powders derived by this novel method were plotted against values measured using pycnometry, a regression line with slope close to unity and intercept close to zero was obtained. Thus, the validity of this method was supported. Using this new method, it was further demonstrated that helium pycnometry always overestimates true densities of water containing powders, for example, hydrates, microcrystalline cellulose (MCC), and tablet formulations. The calculated true densities of powders were the same for different particle shapes and sizes of each material. This further suggests that true density values calculated using this novel method are characteristic of given materials and independent of particulate properties. © 2004 Wiley-Liss, Inc. and the American Pharmacists Association

Wall Friction and its Effects on the Density Distribution in the Compaction of Pharmaceutical Excipients

The effect of powder-die wall friction during the compaction of pharmaceutical excipients has been investigated for three modes of lubrication: lubricated die, non-lubricated die and with the lubricant mixed with the powder. Coulomb friction is assumed and the wall friction coefficient was evaluated from the transmission ratio (applied pressure/transmitted pressure), the transfer ratio (radial pressure/axial pressure) and the aspect ratio (height/diameter of tablet). The friction coefficient of three pharmaceutical excipients was measured with respect to the relative density of the tablet by means of an instrumented press. It was found that the behaviour of the friction depends on the powder and the lubrication mode. Mixing the powder with a lubricant reduces the friction with respect to that of the lubricated die, but the evolution of the friction coefficient with the densification is different. The effect of the wall friction on the axial density distribution in the tablet was investigated by experiment and by modelling. The model was based on Janssen-Walker analysis coupled with the Heckel equation. For comparison, only the single action compaction in a non-lubricated die was considered. It was found that the measured and predicted axial density decrease from the top to the bottom of the tablet. Moreover, the predicted and measured density had the same tendency, but different values. However, the analysis should not be applied to the compaction of the powder mixed with lubricant because no physical parameter for this mode of lubrication is taken into account in the model.

Compression behaviour of the enzyme β-galactosidase and its mixture with microcrystalline cellulose

The behaviour of β-galactosidase powder under compaction was investigated to get more information on powder properties and to further characterise tablet excipients. The enzyme β-galactosidase, the model excipient microcrystalline cellulose and several mixtures of these two substances were compressed at different compaction forces. The relative density of the obtained tablets was calculated and the Heckel equation as well as the modified Heckel equation was used to characterise the bulk powders and their mixtures. Microcrystalline cellulose is known as a model substance for plastic powders, the used β-galactosidase was found to be a brittle substance. In further experiments, the activity loss of the compacted enzyme powder was investigated and used to characterise the behaviour of the binary mixtures in various ratios. Data interpretation with percolation theory led to a critical β-galactosidase concentration of 20%. Between 100 and 20%, the enzyme builds a lattice and dominates the binary system. For β-galactosidase amounts below 20% in mixtures with plastic excipients, the activity loss increases strongly because of higher shearing forces during compaction due to the system dominance of the plastic particles.

Comparative Evaluation of Granules Made with Different Binders by a Fluidized Bed Method

Granules were prepared using three different binders, pregelatinized starch (PGS), gelatin (GEL), and polyvinylpyrrolidone (K30) by a fluidized bed method. As a quantitative measurement of mechanical strength or abrasion resistance, granules were subjected to a friability test for certain periods of time, and friability indexes (FI) as a function of time were calculated. The data obtained were analyzed by applying standard mathematical models. According to the derived parameters of the logistic and Weibull models, which fit best to the data, mechanical strength of granules made with K30 was observed to be lower than that of the granules of PGS and GEL which have similar values of model parameters. Flow properties, consolidation, and compressibility behaviors of unfriabled (UFR) and friabled (FR) granules, which were selected based upon their Weibull time parameter, were investigated as comparative. The flow rate of granules decreased due to diminishing particle size depending on binder type and friability, but the values of angle of repose were within the acceptable limits. Regarding consolidation behavior, the change of relative density vs. the number of taps, i.e., packing rate for FR granules of GEL was slower than that of its UFR form, whereas FR granules of PGS and K30 showed faster change in relative density compared to their UFR forms. According to the parameters obtained from the Heckel equation, PGS and K30 were found to produce softer, more plastic and readily deformable granules than GEL, and the compressibility of their FR forms was not influenced negatively.

Compaction equations: a comparison of the Heckel and Kawakita equations

The background and theoretical and experimental requirements of powder compaction equations have been briefly reviewed. There have been many equations proposed. However, the equations most commonly used today are the Heckel and Kawakita ones, because they alone have claimed to be able to relate to the physical properties of the materials being compacted. There has been much discussion about their relative merits, and in their form, they appear very different. The two equations are discussed in detail and examples are given, and their relative merits are discussed. However, it is first shown for applied pressures, which are low compared to the yield strength of the particles, that they are identical in form. It is then shown mathematically that if a pressure dependent term is used in the Heckel equation then the resulting modified equation is very similar to the Kawakita one and, in fact, becomes identical in form for a particular, likely value of the pressure dependency term. It is concluded that the Kawakita equation is a special case of the more general, modified Heckel equation. It is further concluded that compaction equations need further development to take into account the anisotropy in compacts made by uniaxial compaction. It is shown that the Poisson's ratio of compacts will also increase with applied pressure, and this must be considered.

Influence of Elastic Deformation of Particles on Heckel Analysis

The Heckel equation is one of the most useful equations for describing the compaction properties of pharmaceutical powders. Important material properties (e.g., yield strength) of powders can be derived using Heckel analysis. Two types of Heckel analysis are in common use. One is the “out-of-die,” or “zero-pressure” method, the other is the “in-die” or “at-pressure” method. Because particles undergo elastic deformation under pressure, which tends to lower the porosity of the powder bed, the “out-of-die” method describes powder consolidation and compaction more accurately than the “in-die” method. However, “in-die” Heckel analysis has been widely used because of the speed and ease of data collection. Using L-lysine monohydrochloride dihydrate as a model compound, this work analyzes quantitatively the effects of elastic deformation on the calculation of porosity of a tablet, and therefore on the Heckel analysis. The effects of a small change in porosity, ε, on Heckel analysis are presented mathematically. It is found that a decrease in porosity of 0.001, when the porosity is lower than 0.05, causes a significant increase in the value of −ln ε. Therefore, data at ε < 0.05 should be interpreted with caution when using Heckel analysis. Elastic deformation causes positive deviations in the Heckel plot, and therefore leads to a yield strength that is lower than the true value. The lower the elastic modulus of the powder, the greater is the deviation from the true value. Therefore, the “in-die” method gives values of yield strength that are significantly lower than the true values for most pharmaceutical powders.

Impact of particle density and initial volume on mathematical compression models

In the calculation of the coefficients of compression models for powders either the initial volume or the particle density is introduced as a normalising factor. The influence of these normalising factors is, however, widely different on coefficients derived from the Kawakita, Walker and Heckel equations. The problems are illustrated by investigations on compaction profiles of 17 materials with different molecular structures and particle densities. It is shown that the particle density of materials with covalent bonds in the Heckel model acts as a key parameter with a dominating influence on the derived apparent yield pressures. Substances with ionic bonds or macromolecular materials with amorphous structures do not show this dependency on the particle density. The influence of density is demonstrated by performing non-linear regression on the Heckel equation where the optimal particle density is estimated. The a parameter in the Kawakita equation is not influenced to a greater degree by variation in the initial volume.

A critical evaluation of the Heckel equation

Great differences between published Heckel parameters, obtained from ‘at pressure’ data or the ‘in-die’ method, are outlined. The general validity of the concept of yield pressures derived from slopes of such Heckel plots is questioned. When the ability of the Heckel and the Walker equations is compared to fit density/pressure data from tabletting different pharmaceutical powders, a generally better fit is obtained with the Walker equation in the region of 5–100 MPa. The ability to discriminate between materials by data from the compression phase is improved by using the Walker model. For Emcompress®, apparent yield pressures derived from Heckel plots are dependent strongly on the maximum pressure of the compression process.

Pressure susceptibility of polymer tablets as a critical property: A modified heckel equation

The pressure susceptibility (χp), which is defined as the decrease of porosity (ε) under pressure was investigated. Of special interest are compacts obtained at very low pressures, because of the transition between the state of a powder and the state of a tablet. This range was found to be critical in respect to a diverging pressure susceptibility. Above a critical porosity (εc) or below the corresponding relative density (ρc), no pressure susceptibility can be defined, because of no rigid structure exists. To take this into account, a simple function was proposed for the pressure susceptibility: χp ∝ 1/(εc − ε). This proposal leads to a new porosity vs pressure relationship. The new model was compared to the Heckel equation that involves a constant pressure susceptibility. Various polymers were tested from “out of die” measurements, and the new relationship was found superior to the Heckel equation. As a conclusion, the pressure susceptibility exhibits a curvature that can be called critical at low relative densities. Consequently, a better understanding evolves as to why the Heckel equation is not valid at low pressures. The new model has proven to be adequate for polymer tablets but, so far it is not clear whether other substances exhibit the same performance. Especially tableting materials exhibiting brittle fracture will be of interest considering their importance in compaction technology.

The Effect of Wax on Compaction of Microcrystalline Cellulose Beads Made by Extrusion and Spheronization

The effect of wax on the deformation behavior and compression characteristics of microcrystalline cellulose (Avicel® PH-101) and acetaminophen (APAP) beads is described. Beads of Avicel PH-101 and APAP formulations were prepared using extrusion and spheronization technology. A waxy material, glyceryl behenate, N.F. (Compritol ®), was added to the formulations in amounts ranging from 10% to 70% of total solid weight. Beads with a selected particle size range of 16-30 mesh were compressed with an instrumented single punch Manesty F press utilizing a 7/16-in. flat-faced tooling set. Compaction profiles were generated for the tablets to evaluate the effect of wax on the densification of beads containing wax. Beads made without wax (the control formulation) required greater compression forces to form cohesive tablets. As the amount of wax in the bead formulation was increased, the beads become more plastic and compressible. The Heckel equation which relates densification to compression pressure was used to evaluate the deformation mechanisms of the bead formulations. The analysis shows that as the level of wax in the bead formulation is increased, the yield pressure decreases, indicating that the beads densify by a plastic deformation mechanism.

An Investigation of the Influence of the Core Material Properties on the Compression and Properties of Dry-Coated Tablets

The effect of core material properties on the process of compression and physical properties of compression-coated tablets were investigated using microcrystalline cellulose as the coating material (mantle). Three model core materials: borosilicate glass, silicone rubber, and steel, each of different Young's modulus, were selected to give a range of core mechanical properties. Coated tablets were prepared using a single-punch press, with facilities for monitoring the compression cycle and analysis of data using the Heckel (1) equation. This analysis showed a considerable effect of different core materials on the compression process, (i) as an unanchored core, and (ii) due to core material type with differing Young's modulus.

A compaction study on ceramic powders

In this investigation, a compaction study was performed on magnesia, zirconia and titania ceramic powders. All the powder samples were compacted in an opposed anvil apparatus at different pressures upto a maximum pressure of 1100 MPa. The Heckel equation, which is used to describe compaction behaviour of metallic powders, is modified in the present study by incorporating the tap density term so that it can be successfully applied to ceramic powders. The modified equation is found to fit very neatly to the experimental data obtained for the powders used in the investigation. The validity of the equation is established theoretically.

A Comparative Evaluation of the Mechanical Properties of Various Celluloses.

The influence of basic properties such as physicochemical or particle properties on the mechanical properties of celluloses with different average degrees of polymerization ((DP)^^-), which included powdered α-cellulose and its degradation products as well as commercial microcrystalline celluloses, was investigated. The particle shape approached that of a sphere with a reduction in (DP)^^-, causing an increase in flowability and a decrease in the cohesion of cellulose powders. Hmax and γ in the Leuenberger equation, which were considered to reflect the compactibility and compressibility of powders, respectively, were higher at a lower (DP)^^-, suggesting that the particle shape and/or crystallinity of materials affected the bonding properties of a substance in tablet preparation. The mechanical strength was estimated using the crushing test for a granule and the diametral compression test for a tablet. Crushing work, W, increased with a decrease in (DP)^^-, which was probably due to a decrease in granule porosity. The compression behavior of granules was estimated by the static method, using the Heckel equation. The compression coefficient, K, in this equation decreased with the crushing work of a granule, thus the reciprocal of K was expected to be a measure of granule strength. The tensile strength of a tablet increased with the crushing work of a granule in the relatively high (DP)^^- region. When the (DP)^^- was low, the crushing work of granule was high and tablet strength tended to reach a maximum.

Compaction simulator studies of a new drug substance: effect of particle size and shape, and its binary mixtures with microcrystalline cellulose.

The compaction characteristics of a new drug substance with two crystal habits and particle size fractions as well as its binary mixtures with microcrystalline cellulose were studied using an integrated compaction research system under 300 and 450 MPa pressures. The results indicate that the drug substance has poor intrinsic compaction properties. The three-dimensional hexagonal crystal habit or smaller particle size consistently produced a slightly higher total work of compaction as compared with the cubic brick habit or larger particle size, respectively. However, neither crystal habit produced a coherent compact. The compactability of the drug substance was improved by the inclusion of microcrystalline cellulose, and the crushing strength of the compacts increased as the amount of microcrystalline cellulose in the binary mixture was increased. Such correlation was not observed when the compaction data were evaluated using either the Heckel equation or the percentage porosity change as a function of applied pressure.

Application of a Compaction Simulator to the Design of a High-Dose Tablet Formulation. Part I

AbstractThe compaction properties of an investigational drug are studied by the use of a compaction simulator. The effects of punch velocity over the range of 30-640 mm−1 on the compaction properties of the pure drug and a variety of formulas incorporating a high dose of the active compound have been investigated. The data were analyzed by applying the Heckel equation. The pure drug was found to have a high yield pressure at a relatively low punch velocity of 31 mm−1. As the punch velocity was increased there was a decrease in crushing strength, primarily as a result of increasing yield pressure. These findings indicate that the pure drug predominantly consolidated by fragmentation and elastic deformation, with a slow plastically deforming component. The information obtained on the consolidation mechanism of the pure drug and, subsequently, on model formulas were instrumental in the design and selection of a robust formula and granulation process. The advantages of conducting dosage form design and charac...

Effect of particle size and sorbed moisture on the compression behaviour of some hydroxypropyl methylcellulose (HPMC) polymers

A study has been made of the moisture sorption-desorption and the compressional characteristics of some powdered HPMC polymers with different particle size, methoxy/hydropropoxy substitution and molecular size. Moisture sorption-desorption isotherms, at 25°C, have been measured and analysed according to the Young and Nelson and the GAB equations, which distinguish moisture distribution in different physical forms. Compression data were obtained after storage at various environmental relative humidities by two methods: the tablet-in-die and the ejected-tablet method. The rearrangement or packing of HPMC particles and their deformation under pressure during tableting were determined by means of the Heckel equation. The externally adsorbed and normally condensed moisture were found to decrease with the particle size increase and the methoxy/hydropropoxy substitution ratio while the internally absorbed moisture increased mainly due to the particle size increase. No simple and general change due to molecular size was observed in the moisture distribution results. The particle packing and deformation of the HPMC powders were found to be related with the moisture distribution effects due to the particle size and the methoxy/hydropropoxy substitution ratio changes while no correlation was observed with the molecular size alteration.