Heckel Equation Research Articles

An Investigation Into Properties of Foam‐Mat‐Dried Spinach Powder and Physical Properties of Spinach Cube

Today, producing fruit or vegetable cubes with high solubility and dispersibility can attract consumers’ attention, diminish agricultural waste, and raise people’s access to important nutritional sources. In recent years, it seems that cube‐making preserves the appearance and marketability of food. In this study, the physicochemical properties of foam‐mat‐dried spinach powders with thicknesses of 3 and 5 mm produced at 40°C, 50°C, 60°C, and 70°C were investigated. The resulting powder was used to produce spinach cubes. The physicochemical properties of the powders were evaluated. With an increase in foam thickness, the water activity, moisture content, dissolution time, particle size, density, and porosity increased, whereas the hygroscopicity and glass transition temperature decreased. The lowest chlorophyll content (0.166 mg/g spinach) was observed in samples dried at 70°C and 5 mm. The samples dried at 70°C and 3 mm had the highest L∗ and higher stability (lower moisture content and water activity and higher Tg). The Heckel equation showed that the highest k value was related to the spinach powder produced at 70°C and 5 mm. The cubes with the greatest heights, the highest chlorophyll content (0.245 mg/g spinach), and the lowest dissolution time were obtained from powders produced at 40°C and 3 mm. The cube of the powder produced at 70°C and 5 mm had the longest dissolution time. All cubes had a non‐Fickian release in both dissolution media. The product of this research is dried spinach powder and its cubes. This product provides easy access to the valuable nutritional compounds of spinach in all conditions. This product is used as an additive in soup. It can also be used with yogurt and smoothies.

Analysis of electrical resistance measurements as a potential determination method for coating thickness on powders

The electrical resistance of conductive and non-conductive coatings on non-conductive and conductive powders, respectively, is investigated under increasing external load. A specially designed equipment was used to deposit coatings on small and light as well as heavy powdery substances by DC magnetron sputtering. Several reference methods to predict or measure the absolute film thickness on powders are discussed.When measuring the electrical resistance of insulating powders coated with a metal, in this case hollow glass microspheres (HGMs) coated with copper, under increasing load, a typical resistance curve is found. This resistance curve is discussed in terms of percolation theory and the Heckel equation for powder compaction. The influence of coating thickness of the conductive coating is then evaluated and other factors like inhomogeneity of the coating are discussed. To reduce the influence of measurement parameters, selected experiments are interpreted under the concept of a force per grain, which is introduced and explained.To further substantiate the typical electrical resistance curve, stabilized and non-stabilized NMC811 powder is coated with aluminium and zirconium oxides of different thicknesses, corresponding to a conductive powder with an insulating coating. When comparing measurements for stabilized and non-stabilized powder, the perspective for electrical resistance measurements under increasing load becomes apparent, as it is possible to even detect surface modifications which are not known a priori.

Compression prediction from single pellet press to industrial production presses

A single pellet press is commonly used to study the ring die pelleting (RDP) process. However, it is a challenge to apply the results obtained from studying the single pellet press to ring die pellet mill. The aim of this study is to model a prediction from single pelleting (SP) to RDP. In this study, SP was divided into two stages: compression and extrusion. The compression stage was analyzed based on the Kawakita equation and the Heckel equation, while the mechanical model for the extrusion stage was derived based on plastic mechanics. The compression pressure of the SP could be converted into that of RDP by analyzing the kinematics and mechanics of the ring die and roller. Those models were validated through experiments and simulations of SP and RDP. The results showed that all the models have good fitness (R2 > 0.95), and SP can be used to predict RDP by compression pressure.

Comparative Evaluation of the Disintegrant Properties of Starches from Three Cultivars of Dioscorea rotundata (Poir)

Poir starches from three cultivars (Lagos, Giwa, and Sule) were evaluated asexo-disintegrants (5 and 10%w/w) in paracetamol tablet formulations to determine whether the similarity in their physicochemical and material properties translates to performance in tablet formulation. The tablets were prepared by wet granulation and were evaluated for compressional properties (Heckel equation), mechanical strength (crushing strength and friability), and drug release (disintegration and dissolution times). Plastic deformation occurred in all tablets with rank order for the onset of plastic deformation Lagos>Giwa>Sule. An increase in the concentration of disintegrants in the tablets led to a decrease in mean yield pressure, total relative precompression density, and relative density at low pressure, but an increase in relative density at zero pressure. The crushing strength and disintegration times of the tablets were dependent on the disintegrants' concentration. All tablets passed the disintegration test (≤15min) with tablets containing the Sule cultivar producing the fastest disintegration (p<0.05). Tablets containing 10% of the Sule cultivar had the fastest release of paracetamol (t80=32.1min), though it failed the compendial standard for immediate release tablets (t80≤30min). Starches from the three cultivars despite their similar physicochemical and material properties exhibited different disintegrant properties and could find different applications as excipients in tablet formulations.

Negative porosity issue in the Heckel analysis: A possible solution

A parameterization of compaction simulator generated dynamic compression profile with a few grams of powder provides important information about the material deformation and compact elasticity. The Heckel equation is by far the most popular choice among pharmaceutical scientists for such parametrization. A general approach of Heckel analysis uses pycnometric powder density (ρP0) for relative density calculation. However, as ‘in-die’ tablet bulk density at applied compression pressure (ρBP) becomes greater than or equal to the measured ρP0, the general approach typically poses a negative porosity challenge at high compression pressure regions. It is only theoretically possible to have a tablet with zero or negative porosity. Negative porosity may be detected during ‘in-die’ compression analysis, but it will not exist after ejection of the tablet in practical aspect. Thus, the present work proposes a new approach to using pycnometric tablet density (ρPP) in the relative density calculations of Heckel analysis. This ρPP may be a better representation of actual tablet particle volume, as it is composed of non-accessible intra-particulate pores, which are broken under applied compression pressure. A new approach showed its immunity for Heckel high-pressure negative porosity. It enables the utilization of the compression and decompression phases of dynamic compression profiles to evaluate macroscopic compaction performance. The proposed approach was validated with a reported modified Heckel approach. The Heckel parameters computed with both methodologies for microcrystalline cellulose and lactose were not statistically different. However, a modified Heckel approach was unable to compute Heckel parameters of poorly compacting starch unlike the new approach. A modified Heckel approach became invalid during starch compaction at low compression pressures (below 400 MPa), where starch was forming weaker but still intact tablets. Certainly, a complete Heckel profiling with a new approach could save time and costs in an early development stage for designing and screening scientifically based lead prototype formulations.

Investigation on mechanical and microstructural evolution of lithium-ion battery electrode during the calendering process

To increase battery capacity and improve electronic conductivity and electrochemical performance, lithium-ion battery electrodes are produced using a calendering process. This work aims to reveal the evolution of mechanics and microstructure during the calendering process, while a predictive model was derived to determine the thickness and porosity. Here, the discrete element method simulations and calendering experiments were adopted to analyze the microscale and macroscale responses. A predictive model was supplemented using the Heckel equation. Furthermore, the electrodes were manufactured under incremental line load. According to the electrode morphology, the deformation mechanism was summarized: Particle pulverization, secondary particle fusion, binder network compression and the current collector's surface deformation. The increase of the electronic conductivity is related, on the one hand, to the conductive path inside the electrode being improved and, on the other hand, to the tightening of the contact between the coating and the current collector • The discrete element method is taken to analyze the microscale and macroscale response. • A predictive model is derived for the determination of the thickness and porosity. • The deformation mechanism is summarized according to the electrode morphology.

Studies on the influence of high-shear granulation process on the compressibility of microcrystalline cellulose

Microcrystalline cellulose (MCC) is a diluent for oral solid dosage forms. The wet granulation process was selected to prepare losartan potassium tablets using MCC as a model for a predictive study. It was found that the hardness of the tablets could not satisfy the quality standards. In this study, the effect of the high-shear granulation process on the compressibility of MCC was characterized by plotting the compression characteristics curve, as well as the mechanism of the effect from the perspectives of mechanical properties, powder properties. The solid-state properties were also analyzed. Combined with the Heckel equation, the Ryshkewitch-Duckworth equation, the energy method, PXRD, SEM, and other evaluation methods, the results suggest that the high-shear granulation process reduced the compressibility of MCC, which may be caused by the reduced plastic deformation capacity of MCC and the change of the particle morphology structure. The method applied in this study can also be applied to other excipients, which is an important guideline for solving possible problems and process selections during the preparation stage of solid formulations.

Evaluation of gravitational consolidation of binary powder mixtures by modified Heckel equation

Consolidation of powders by tapping is an important quality test but it is time and material consuming, which encourages the use of mathematical modelling. This article aims to study this gravitational consolidation dynamics by using nine binary mixtures consisting of cellets and powdered microcrystalline cellulose (MCC102), differing in size, shape, and consolidation properties. To describe the correlation between number of taps and powder bed density/ porosity, the modified Heckel equation. (MH) was newly introduced and compared to the models by Kawakita (KW) and Varthalis & Pilpel (VP). High coefficients of determination were observed by applying the traditional KW model up to 80% of cellets, while a comparable fitting adequacy was obtained with the MH equation up to 50% of cellets in the mixtures. An increased content of MCC102 increased fitting adequacy in the MH and KW model, whereas a nearly opposite mixture trend was observed for the VP model. • Three models were used to study the consolidation dynamics of binary mixtures. • A cellet concentration-dependent relationship was noted for the Hausner ratio. • The Kawakita model fitted consolidation dynamics well up to 80% ( w /w) of cellets. • The modified Heckel model fitted the data comparably up to 50% (w/w) of cellets. • The best but opposite mixture trend was noted with Varthalis & Pilpel model.

A Simplified Model Structure for Compression Characterization of Pharmaceutical Tablets

Despite -or maybe because- many shortcomings, Heckel's equation is by far the most investigated compressibility model for decades. The somewhat overlooked Gurnham equation is proposed as a more stable and better fitting compressibility model. Combining this equation with a linear model for the strength/pressure relation provides a composite function identical with the often-used Ryshkewitch equation for the relation between strength and porosity. It is thus questioned whether the three-dimensional compression characterization presented in USP monograph <1062> is correct. Substantial errors in computed parameters are revealed with consequences for reproducibility or inter-lab assessments. Elastic recovery is proposed as a more interesting and relevant characteristic in relation to pharmaceutical tablet formulation.

Effect of Moisture of Pharmaceutical Material MCC Avicel PH102 and Tablet Diameter on the Compression Process and Tablet Strength

Abstract This paper focuses on the effect of moisture of powder material on the process of tablet compression and on tablet mechanical strength. The powder used in the experiments was Avicel PH102 microcrystalline cellulose, as it is the most widely used excipient in direct tablet compression. The compression process is described using the Heckel equation and the strength of the tablets was determined using a Brazilian test. To introduce the reader to the issue, the first part of the paper is devoted to a theoretical introduction. The second part of the work is devoted to the description of experimental equipment and work procedure. The last part of the paper presents the results of the experiment and their evaluation. The reason for this experiment was the assumption that the moisture of the raw material significantly affects the compression process and the mechanical strength of the tablet. A series of experiments demonstrated this effect, which can be seen in the respective graphs.

Effect of Physical Properties and Chemical Substitution of Excipient on Compaction and Disintegration Behavior of Tablet: A Case Study of Low-Substituted Hydroxypropyl Cellulose (L-HPC)

As final attributes of dosage form largely depend on the properties of excipients used, understanding the effect of physicochemical properties of excipients is important. In the present study, six grades of L-HPC with varying degrees of particle size and hydroxypropyl content and the influence of the grade on compaction as well as disintegration behavior were studied. All grades of L-HPC were compressed at different compression loads to achieve different tablet porosity. Compressibility and compactibility of L-HPC grades were evaluated using a modified Heckel equation and percolation model. Further effects of particle size and hydroxypropyl content of L-HPC on tablet porosity and disintegration time were evaluated using a 32 full-factorial design. From compaction studies, it was found that compressibility of L-HPC largely depends upon the particle size with lower particle size grade showing lower compressibility. Whereas consolidation/bonding behavior of L-HPC is independent of particle size and % hydroxypropyl content. By factorial design, it was found that particle size and % hydroxypropyl content have a significant effect on the disintegration behavior of L-HPC. It was found that smaller particle sizes and higher hydroxypropyl content of L-HPC show longer disintegration time. Thus, careful consideration of excipients selection should be made to achieve desired quality attribute of the product.

Oral Dispersible Tablets of GK-2 [bis-(N-Monosuccinyl-L-Glutamyl-L-Lysine) Hexamethyleneamide]: Optimization of Pressing Process by Mathematical Modeling Based on the Heckel and Kawakita Equations

Oral Dispersible Tablets of GK-2 [bis-(N-Monosuccinyl-L-Glutamyl-L-Lysine) Hexamethyleneamide]: Optimization of Pressing Process by Mathematical Modeling Based on the Heckel and Kawakita Equations

Study on effect of SuperTab 40LL on compression characteristics of musk sustained-release mini-tablets based on mathematical models

In this paper, co-processed lactose SuperTab 40 LL was selected as fillers to study the preparation of musk sustained-release mini-tablets in the Xihuang multiple-unit drug release system. Musk sustained-release tablets containing different proportions of SuperTab 40 LL and MCC were prepared under various pressures, and then the compressibility and compactibility of these prescriptions were evaluated by Walker, Heckel and Ryshkewitch-Duckworth equations. In addition, the fluidity of the prescriptions was evaluated by parameters of Kawakita equation. There was a comprehensive analysis of the effect of SuperTab 40 LL on musk sustained-release mini-tablets combined with the appearance of SuperTab 40 LL and their tensile strength. The results shown that SuperTab 40 LL had better compression process through the Heckel equation, and the direct compression process of drug powders with excipients can be analyzed by the Kawakita and Ryshkewitch-Duckworth equations. As a new type of co-processed lactose, SuperTab 40 LL had a good fluidity and compactibility. SuperTab 40 LL may undergo particle crushing and plastic deformation during the compression process, which increased the contact area and bonding sites between the particles, and aggregated and shaped the mixed powder easy. Moreover, MCC showed a synergistic effect, and the combined application with SuperTab 40 ll could effectively improve the fluidity and compressibility of the musk sustained-release powder. When the ratio of SuperTab 40 LL and MCC was 2∶1, musk sustained-release mini-tablets had a high drug loading capacity and good compactibility in line with the design objectives.

Morphological effect on high compaction density nickel-rich layered oxide cathodes during electrochemical lithiation and delithiation

The morphological effect of the blended single-crystalline Li[Ni0.8Co0.1Mn0.1]O2(NCM-C) and spherical secondary polycrystalline Li[Ni0.8Co0.1Mn0.1]O2(NCM-SP) cathodes (3:7 in weight) were systematically investigated. Calendering properties of the NCM-C, NCM-SP, and blended cathode were tested on a pilot-scale compactor. The values of maximal coating density and compaction resistance fitted by Heckel's equation indicate that the addition of moderate amounts of NCM-C into NCM-SP produced a significant improvement in the compaction degree and electrical conductivity of cathode laminate. The addition of NCM-C is also found to help reduce the generated electrode stress during electrochemical lithiation and delithiation which is confirmed by using the multi-beam optical sensor (MOS) technique. In the pouch-type full cell test utilizing artificial graphite as the negative electrode, the retained capacity is about 85.3% of its initial capacity by applying 1.0 C current at 25 °C after 700 cycles. The rate capability is also improved in the blended cathode even at a 2.0 C discharge rate, keeping 97.3% of its initial specific capacity (0.33C rate). It is suggested that the mixed electrode is considered to be a quite promising cathode electrode material to be applied for lithium-ion batteries.

Ockham's Razor Applied on Pharmaceutical Powder Compaction Models

This investigation contains a critical survey of a collection of five well-known and often used standard models in pharmaceutical technology. The basic idea is to use the recognised Ockham's razor as a tool in search for simpler methods or explanations for these models. The study includes the indirect tensile strength of tablets, Pitt's equation for tensile strength of biconvex tablets, Adams' model for strength of agglomerates, Weibull's distribution for variability of strength measurements and Heckel's equation for compressibility. In all these cases simpler and equally valid solutions and explanations are presented and subsequently preferred rather than the original.

Evaluation of Lactose-Based Direct Tableting Agents' Compressibility Behavior Using a Compaction Simulator.

A compaction simulator (CS) is a single-punch instrument that records data during the powder compaction process. The aim of the study was to determine the behavior of lactose-based direct tableting agents (DTAs) by CS. The data recorded were used to evaluate the flowability and compressibility of powders. The focus of the study was on comparing the compressibility of StarLac® [alpha lactose monohydrate (85%) and white maize starch (15%)] and FlowLac®100 (spray-dried alpha lactose monohydrate) in order to make tablets containing poorly flowable paracetamol. Two lactose-based DTAs were used. Physical characterization of these powders was done by measuring bulk, tapped, and true densities alongside scanning electron microscopy analysis. Flow properties were then calculated by the angle of repose, Hausner ratio, and Carr's compressibility index. Force, in-die thickness, and punch displacement data produced by the CS were captured during in-die compression. Compressibility was calculated using the Heckel equation. The physical characterization test results showed no significant difference between the two DTAs. Hardness results revealed that tablet formulations containing FlowLac® had higher sensitivity to an increase in compression force in comparison with StarLac®. From the Heckel plots generated by the CS during the compression cycle, yield pressure (Py) values were calculated for FlowLac®100 and StarLac®. The Heckel parameter (Py) for FlowLac®100 and StarLac® was calculated as 87.5 MPa and 85.2 MPa, respectively, during the compaction cycle at 5 kN. These data indicated that both powders are compressible and have brittle behavior. StarLac® is less brittle, which was shown by its lower sensitivity to compression force. Py values obtained from the Heckel equation described the plasticity of particles, which gives distinct information on the compressibility of both DTAs in real time during the compaction cycle.

Employing Multivariate Statistics and Latent Variable Models to Identify and Quantify Complex Relationships in Typical Compression Studies.

The effect of storage condition (% RH) on flufenamic acid:nicotinamide (FFA:NIC) cocrystal compressibility, compactibility, and tabletability profiles was not observed after visual evaluation or linear regression analysis. However, multivariate statistical analysis showed that storage condition had a significant effect on each compressional profile. Shapiro and Heckel equations were used to determine the compression parameters: porosity, Shapiro's compression parameter (f), densification factor (Da), plastic yield pressure (YPpl), and elastic yield pressure (YPel). Latent variable models such as exploratory factor analysis, principal component analysis, and principal component regression were employed to decode complex hidden main, interaction, and quadratic effects of % RH and the compression parameters on FFA:NIC tablet mechanical strength (TMS). Statistically significant correlations between f and Da, f and YPpl, and Da and YPel supported the idea that both rearrangement and fragmentation, and plastic deformation are important to FFA:NIC TMS. To the authors knowledge, this is the first time that simultaneously operating dual mechanisms of fragmentation and plastic deformation in low and midrange compression, and midrange plastic deformation have been identified and reported. A quantitative PCR model showed that f, Da, and YPel had statistically significant main effects along with a significant antagonist storage condition-porosity "conditional interaction effect". f exhibited a 2.35 times greater impact on TMS compared to Da. The model root-mean-square error at calibration and prediction stages were 0.04MPa and 0.08MPa, respectively. The R2 values at the calibration stage and at the prediction stage were 0.9005 and 0.7539, respectively. This research demonstrated the need for caution when interpreting the results of bivariate compression data because complex latent inter-relationships may be hidden from visual assessment and linear regression analysis, and result in false data interpretation as illustrated in this report.

PM compaction equations applied for the modelling of titanium hydride powders compressibility data

ABSTRACTThe suitability of compaction equations commonly used in PM was investigated for the modelling of TiH2 powder compaction. Compressibility data of TiH2 powder fractions (<45, <150 and <355 μm) were obtained up to 800 MPa and fitted to the Heckel equation, as well as to the models of Gerdemann and Jablonski and Cooper and Eaton. Although a partial correlation was observed for the Heckel equation, the model provided a consistent approximation of TiH2 powder yield strength. An accurate fit was observed for the Gerdemann and Jablonski equation; however, considering the brittleness of TiH2, a more realistic depiction of the physical process was verified from the Cooper and Eaton model. By the addition of an exponential term to the original equation an excellent fit was attained, and compaction of TiH2 powders could be appropriately described according to the mechanisms of initial density, particle rearrangement, fragmentation and plastic deformation.

Mechanism of "unification of drugs and excipients" for Chinese medicine semi-extract based on powder compression behavior analysis

In this paper, five representative Chinese herbal decoction pieces of Scutellariae Radix, Paeoniae Radix Alba, vinegar-processed Corydalis Rhizoma, Polygoni Multiflori Radix Praeparata and Lonicerae Japonicae Flos were selected to prepare the corresponding fine powder of pieces, extract powder, semi-extract powder and physical mixed powder. The physical properties of 20 kinds of powders, such as related parameters of particle size, density, stability and flowability, were evaluated comprehensively. The compression curves of powder porosity and tensile strength changing with pressure were plotted, and the Heckel equation and the Kawakita equation were used to describe the powder compression behavior. The results showed that compared with the fine powder of pieces, the compressibility of the semi-extract powder and the extract powder was significantly improved. Compared with the extract powder, the particle size and relative uniformity of the semi-extract powder were increased, indicating that the uniformity of the powder was improved. Besides, the semi-extract powder could reduce the hygroscopicity of the powder. Particularly, the semi-extract powder of Scutellariae Radix, Paeoniae Radix Alba and vinegar-processed Corydalis Rhizoma could maintain the porous structure of the tablet even under a high tableting pressure, which was beneficial to tablet disintegration. For some traditional Chinese medicines(such as Lonicerae Japonicae Flos), the semi-extract powder could reduce the viscosity, which avoided the sticking in the die compression. The semi-extract powder and the physical mixture powder prepared by the same Chinese herbal decoction pieces had similar physical properties and compression behaviors. Principal component analysis(PCA) was carried out on the 17 physical attributes and 5 compression parameters of the powder. It was found that the first principal component mainly reflected the differences among the material sources, while the second principal component could reflect the differences among fine powder of pieces, extract powder, semi-extract powder and physical mixed powder originating from the same Chinese herbal decoction pieces. In this paper, the mechanism of &quot;unification of drugs and excipients&quot; of Chinese medicine semi-extract powder was explained in terms of physical properties and compression behavior of powders, which provided reference for the formulation design and process development of Chinese medicine tablets.

Determination of maximum flowable liquid-loading potential of Neusilin® US2 and investigation of compressibility and compactibility of its liquisolid blends with PEG (400)

The objective of the present study was to determine the maximum flowable liquid-loading potential of a solid carrier material (Neusilin® US2) and to investigate the compressibility and compactibility of its liquisolid blends with PEG (400). Liquid-solid blends using an increasing amount of a non-volatile liquid (PEG 400) sorbed onto the solid carrier were prepared to determine its flowable liquid-loading potential. The solid carrier and liquisolid blends were then compressed at various compression pressures. The compression data were fitted into Walker, Kawakita, and Heckel equations to determine the compressibility of Neusilin® US2 and the liquisolid systems, and into Leuenberger and Ryshkewitch-Duckworth equations to determine their compactibility. It was observed that Heckel and Leuenberger equations were the most suitable mathematical models to quantify the compressibility and compactibility of solid carrier and its liquisolid blends, respectively. The values of mean yield pressure, Py, calculated from Heckel plot and compactibility parameter, σtmax, determined using Leuenberger equation were found to decrease with an increase in the liquid-loading. In addition, a good correlation was observed between the mean yield pressure, Py, and compactibility parameter, σtmax, of the liquisolid systems. Thus in the present study, compressibility and compactibility of liquisolid systems were successfully determined for formulation development of liquisolid compacts.