In-die compressibility as a surrogate for lubrication-induced changes in tabletability

Abstract

Lubricants are indispensable in tableting, as their impact extends beyond facilitating ejection to altering compressibility and tablet strength. However, the extent to which lubrication affects in-die compressibility, and whether these effects can be exploited for tensile strength modeling, remains insufficiently understood. This study systematically investigated the effects of lubricant type (magnesium stearate, sodium stearyl fumarate), concentration, and blending time on microcrystalline cellulose, dicalcium phosphate anhydrous, and an ibuprofen-based formulation using compaction simulation and compressibility analysis. Regression analysis confirmed that lubricant effects were expressed in the early compression phase. A nonlinear white-box model, based on tablet mass and onset density, accurately modeled tensile strength with mean squared errors ≤ 0.20 MPa across all materials and settings within the investigated dataset. These findings demonstrate that lubrication-driven variations in tabletability are inherently captured in compressibility data, enabling robust characterization of tensile strength without explicit lubricant information. Beyond model development, this work advances the understanding of lubrication effects in compressibility-based modelling and highlights its potential as a formulation-independent strategy for tabletability assessment within quality-by-design frameworks.

Introduction

Lubricants play a crucial role in the manufacturing of pharmaceutical tablets. They affect the friction between the punches, the die walls, and the compressed material,1 reducing thermal stress,2 influencing punch sticking,3, 4 and facilitating smooth ejection of the formed tablet from the die cavity.5 However, their influence extends beyond the manufacturing process, as lubricants also impact the critical quality attributes of the final tablets. In addition to prolonging disintegration time6 and altering the dissolution,7, 8 they also influence tablet strength,9, 10 depending on the properties of the compressed material.11, 12 These overlubrication effects depend not only on the type and concentration of the lubricant used, as well as on the properties of the formulation, but can also be influenced by the blending time and intensity with which the lubricant is incorporated into the powder blend.13 In this context, not only the actual blending time is of interest. Additional mechanical stress may also occur in downstream processing, such as within the force feeder systems of rotary tablet presses, which can further intensify the effect.14 Given these complexities, a comprehensive understanding of the relationships between lubrication and tablet properties, as well as the ability to represent these effects within modeling frameworks, is of high industrial and academic interest.

Despite the well-established relevance of lubrication in the process of tablet manufacturing and its known effects on tablet properties, surprisingly limited attention has been paid to its influence on in-die compressibility. The compressibility of a material describes its resilience to compression over the reduction of the bulk volume. It is characterized by the relationship between solid fraction, porosity, or a suitable surrogate and pressure in the tableting process. In this context, in-die compressibility specifically refers to the relationship between compaction pressure and, for example, apparent density during the compression phase within the die cavity. In classical compression analysis, empirical or semi-mechanical regression models are established based on the parameters of pressure and volume reduction. Examples of such analytical approaches include those developed by Heckel,15 Walker,16 Kawakita,17 Kuentz and Leuenberger,18 Johanson,19 and Sun.20 As in-die compressibility can be derived solely from machine process data, potentially in combination with material properties and the readily determined tablet mass, it represents an attractive variable for use in mechanistic and empirical modeling approaches. This concept has already been explored in the literature using a range of different methodological approaches.21, 22

Investigations into how lubricant concentration and blending time influence the parameters of compressibility are scarce. For example, Patel et al.23 observed that prolonged lubricant blending altered the

parameter in the Kawakita model. Additionally, he describes the lubrication-dependent changes of the force-displacement curve during compression, reflecting effects on the energy dissipation and mechanical behavior. An increase in compressibility after addition of a lubricant was observed in a ternary mixture system containing three excipients.24 Such findings are likely attributable to changes in bulk material properties induced by lubrication. Historically, magnesium stearate was used to enhance powder flow in some formulations, although it has since been largely supplanted by highly dispersed silicon dioxide for this purpose. Still, magnesium stearate and similar lubricants have been shown to impact bulk properties.25, 26, 27 Increasing concentrations of magnesium stearate, for instance, can decrease the dynamic density of powders.25 Moreover, Shah and Mlodozeniec13 demonstrated that lubricant mixing time decreases powder bulk volume, which in turn may affect compressibility parameters like those in the Kawakita model.28

Although various models have incorporated lubrication effects into model tablet strength, they often lack comprehensiveness. Nassar et al.29 introduced a model to describe the relationship between lubrication and tensile strength, but it considered only a narrow range of lubricant concentrations and ignored the effect of mixing time. As a result, potential changes in compressibility remain unaccounted for, despite high reported model fits. Kushner and Moore30, 31 proposed a framework that considers both lubricant blending time and intensity for tablet strength modelling, yet they did not connect the change in tabletability to changes in compressibility. Studies by Puckhaber et al.24, 32 addressed lubricant effects on compactability but required surface area ratios derived from BET measurements. Moreover, the vast majority of these studies focus solely on magnesium stearate, with limited attention given to alternative lubricants such as sodium stearyl fumarate. It was demonstrated that the lubrication effect of sodium stearyl fumarate appears to be less strongly influenced by mixing and shear effects and overall, less influencing on the tablet properties.33, 34, 35 Models describing the influence of lubrication that operate independently of material-specific properties of the lubricant are not found in any published study. Given that compressibility reflects the correlation between the material’s deformation and compression pressure, and therefore the deformation mechanics of the material under pressure, its use as an input for modeling tablet strength is appealing, particularly in models aiming for broad applicability and reduced experimental burden. However, this requires that variations in tabletability due to lubrication are adequately captured in the compressibility data.

The questions that remain unanswered in the current literature can be summarized as follows: (1) Do the effects of concentration and mixing on compressibility-related parameters differ between magnesium stearate and sodium stearyl fumarate? (2) Can the compressibility effects of both lubricants be leveraged to develop a lubricant-independent model that relates formulation tabletability to compressibility-related factors?

Conventionally, compressibility parameters are interpreted as regression coefficients of predefined models. However, this risks overlooking relevant features of powder behavior. In this study, we adopt a broader definition of compressibility parameters as measures of bulk properties, or their temporal evolution, within the die at specific time points or intervals. This perspective enables a comprehensive description of dynamic powder behavior during compression.

The objective of this study is to systematically investigate the influence of lubricant concentration and blending time on the compressibility of pharmaceutical materials, specifically focusing on magnesium stearate and sodium stearyl fumarate. Subsequently, the study aims to demonstrate that these changes in compressibility can be leveraged to model lubrication effects on tabletability. This will allow us to evaluate whether models relying exclusively on compaction simulator data, without explicit knowledge of lubrication parameters, can account for such effects. Drawing from prior literature, we hypothesize that the early phase of compression, particularly the pressure onset, is especially sensitive to lubrication-induced changes and will therefore be central to our analysis. To reduce subjectivity in data interpretation, we therefore propose an algorithm for the systematic detection of compression pressure onset, thereby minimizing operator bias in identifying this critical region of the compaction curve.

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Materials

Gian Mensch, Najeeb Abdelrahman, Stefan Klinken-Uth, In-die compressibility as a surrogate for lubrication-induced changes in tabletability, Journal of Pharmaceutical Sciences, 2026, 104417, ISSN 0022-3549, https://doi.org/10.1016/j.xphs.2026.104417.

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