Effect of particle size on the dispersion behavior of magnesium stearate blended with microcrystalline cellulose

experiments during the development of new tablet formulations


Introduction
The majority of industrial tablet formulations contain particulate lubricants, which facilitate tablet ejection by reducing the interfacial friction between the lateral tablet surface and inner die wall.However, the internal addition of lubricants is known to bear the risk of reducing the mechanical tablet strength [1][2][3][4][5].The reduction in mechanical strength is caused by the coverage of the surfaces of matrixforming diluent particles with lubricant particles [5,6].The extent of mechanical strength reduction strongly depends on the deformation behavior of the lubricated material [1].Plastically deforming materials are especially sensitive to lubrication, as they typically generate only a limited amount of fresh, unlubricated surfaces during compaction [7,8].Thus, the coverage of diluent surfaces by lubricant particles may critically affect the interparticulate interactions if excessive amounts of lubricants are added.In contrast, brittle fracturing excipients generate substantial amounts of new particle surfaces during compaction, which explains their insensitivity towards lubrication with regard to their mechanical tablet strength [9,10].Generally, produced tablets must exhibit sufficient mechanical strength to enable successful subsequent processing (such as transport, coating, and packaging) into commercial medicines [11].Consequently, for plastically deforming materials, in-depth knowledge of the correlation between lubricant surface coverage and mechanical tablet strength is necessary to reduce the number of time-and cost-intensive experiments during the development of new tablet formulations.characterize the underlying mechanisms and extent of surface coverage by lubricant particles experimentally using different measurement techniques.The majority of studies focused on the investigation of the distribution of magnesium stearate (MgSt), which is the predominantly applied pharmaceutical lubricant.Initial studies applied scanning electron microscopy (SEM) to investigate the distribution of MgSt on surfaces, which showed a sufficient contrast to identify MgSt particles [5,6].By combining SEM and energy dispersive X-ray analysis, the surface coverage of NaCl [12] and API crystals [15] was quantitatively evaluated.Additionally, secondary ion mass spectometry [16] and raman spectroscopy [17] were found to be suitable to quantify the distribution of MgSt.All these methods have in common that the determination of surface coverage by lubricant particles is experimentally very laborious and has therefore only been carried out for selected substance combinations in order to elucidate fundamental mechanisms.Generally, the extent to which the lubricant addition affects tablet properties depends on the type of applied lubricant [18][19][20], the lubricant amount [1,20], the lubricant particle size [21], the applied mixing device [4,22], the mixing time [2,13] and, if applied, the paddle feeder passage [23][24][25].The high number of influencing factors and their complex interplay hinders, so far, the development of generally applicable models that are capable of precisely predicting the impact of lubrication on the final tablet tensile strength.Thus, previous research has been focused on developing suitable methods to characterize individual sub-processes.The most prominent model to capture the effect of lubrication on tablet strength was introduced by Kushner et al. [4,26,27].They developed a mathematical model that allows for scaling-up the mixing process for lubricated formulations in free-fall mixers by taking into account the effects of several process parameters (blender volume, headspace, and number of blender revolutions).However, as pointed out by the authors themselves, their model is not able to capture the effect of changes in the formulation.Thus, if the formulation is altered, time-consuming experiments to reparametrize the model are necessary, which are economically unfavorable.The effect of lubricant concentration on the reduction of compactibility was recently quantitatively modeled by our research group by introducing an empirical model for binary formulations [28].Subsequently, the model was combined with the model of Reynolds et al. [29] and, by that, extended to more complex formulations [30].The effect of lubricant concentration on structural and mechanical tablet properties was modeled by theoretically estimating the surface coverage based on the initial particle size distributions of applied excipients.However, the experiments were limited to very short mixing times in a given blender setup, and by that, only a limited process setup was investigated.Generally, it would be desirable to extend the available formulation knowledge in order to predict the extent to which the mechanical strength is altered if one excipient is replaced with another grade exhibiting a different particle size.Therefore, in this study, a comprehensive evaluation of the mechanical strength of binary tablets consisting of MCC and MgSt of different particle sizes for various lubricant concentrations and mixing times was performed.By calculating the theoretical surface coverage of MCC particles by lubricant particles, a unifying relationship between theoretical surface coverage and compactibility reduction due to lubrication independent of the applied excipient particle size was derived for short mixing times.Afterwards, for a given lubricant concentration, blending experiments, in which the mixing time was greatly varied between 2 -600 min, were executed, and the derived compactibility reduction was modeled by adapting the dispersion model proposed by Schilde et al. [31].

Methods and Materials
2.1 Particle size analysis Particle size distributions were measured by means of laser diffraction (MasterSizer 3000, Malvern Panalytical, USA).Powders were dispersed by using the dry dispersion unit AERO S and applying a dispersion pressure of 0.5 bar.Samples were measured in triplicate, and an average particle size distribution was calculated.Additionally, the specific surface area S m,LD was calculated based on the particle size distribution and considering the solids density ρ s .
2.2 Solids density Solids densities ρ s were measured by means of helium pycnometry (Ultrapyc 1200e, Micromeritics, USA).For each material, three samples were investigated in a ten-fold measurement and an average solids density was calculated.
2.3 Scanning election microscopy Particle morphology was investigated by means of scanning electron microscopy (SEM; Helios G4 CX, Thermo Fisher Scientific, USA).Samples were sputtered with gold (LEICA EM ACE600, Leica microsystems GmbH, Germany).
2.4 Gas adsorption analysis Specific surface areas of lubricants were analyzed by gas adsorption measurements (ASAP 2460, micromeritics, USA) applying the 5-point BET method.Samples were conditioned under vacuum at 25 °C overnight.Nitrogen was used as an adsorptive.Powders were analyzed in triplicate and an average specific surface area S m,BET was calculated.
2.5 Blending Blends of 50 g were produced by means of a Turbula mixer (T2F, Willy A. Bachofen GmbH, Germany) using 1 L glass bottles.For all blends, a rotation frequency of 49 min -1 was applied.The effect of lubricant concentration on the mechanical tablet strength was evaluated by systematically varying the lubricant concentration between 0.25 and 2 wt.% and applying a mixing time of 2 min.In order to examine the effect of mixing time on mechanical strength, binary blends of MCC and MgSt were produced with a fixed lubricant concentration of 0.5 wt.% for varying mixing times (2 -600 min).Additionally, binary blends of MCC and MgSt with very small to medium amounts of MgSt (0.02 -1 wt.%) were produced by applying a mixing time of 120 min.
2.6 Compaction Tablets were produced by a compaction simulator (Stylone evolution, Medelpharm, France), which was equipped with 11.28 mm round, flat-faced tooling.In the case of formulations containing MCC fine or MCC medium , dies were filled by hand after manually weighing the desired powder mass.For MCC coarse , a gravity feeder was applied to fill the dies.Independently of the filling method, a tablet weight of approximately 450 mg was used.The compression profile of a StylCam (Medelpharm, France) with a rotation frequency of 5 min -1 was simulated.The compression stress was systematically varied between 50 and 300 MPa.For each set of process parameters, five tablets were produced and stored under lab conditions (20 ± 1 °C, 40 ± 10% r.H.).
2.7 Tablet analysis After measuring the tablet weight m t , the tablet height h t and tablet diameter d t were determined by a tablet tester (MultiTest 50 FT, Dr. Schleuniger, Switzerland).By relating the resulting tablet density ρ tablet to the solids density ρ s , the tablet porosity ε was calculated: Afterwards, the tablet breaking force F B was measured by a diametral compression test (MultiTest 50 FT, Dr. Schleuniger, Switzerland) with a loading rate of 0.35 mm s -1 .The resulting tablet tensile strength σ t was calculated according to the equation of Fell and Newton [32]:

Materials
Three different grades of microcrystalline cellulose (Vivapur 101 (MCC fine ), Vivapur 102 (MCC medium ) and Vivapur 200 (MCC coarse ), all JRS Pharma, Germany) were considered in this study.For lubrication, four different grades of magnesium stearate (Carl Roth, Germany (MgSt 1 ); Faci, Italy (MgSt 3 ); Ligamed MF-2-V, Peter Greven GmbH, Germany (MgSt 2 ); Ligamed MF-3-V, Peter Greven GmbH, Germany (MgSt 4 )) were used.Prior to application, lubricants were deagglomerated by using a 355 µm sieve.The morphology and particle size of the investigated lubricants were investigated by means of SEM images.The nomination of MgSt grades follows their median particle size (cf.Figure 1 and Figure 2b).MgSt 2 , MgSt 3 , and MgSt 4 exhibit a comparable particle morphology in which the platelet-shaped primary particles are agglomerated into coarser secondary particles.It is generally believed that during blending processes, acting shear stress results in the dispersion of these primary lubricant particles for prolonged mixing times [5,33].In contrast, MgSt 1 consists of considerably larger primary particles, which showed a limited surface roughness to which smaller particles are attached.Generally, all investigated MgSt grades exhibit a monomodal particle size distribution whereby the median particle size ranges between 17.2 µm (MgSt 1 ) and 6.9 µm (MgSt 4 ) (Table 1 and Figure 2).The applied MCC grades possess considerably larger particles, as shown in Figure 2a.The cumulative particle size distributions revealed expected differences between the applied MCC grades, as the median particle sizes significantly differed between 70 µm (MCC fine ) and 261 µm (MCC coarse ) (Table 1).Additionally, the specific surface areas of the lubricants determined by gas adsorption substantially differ between 0.95 m 2 g -1 (MgSt 1 ) and 34.45 m 2 g -1 (MgSt 4 ) and do not follow the order of median particle size.This discrepancy can be attributed to the different primary particle size of the lubricant particles examined which determine the S m,BET values.Contrarily, the x 50 values correspond to the secondary particle size of the visible lubricant agglomerates.Thus, the investigated lubricants show significant differences in their particulate structure, the influence of which on the dispersion behavior is investigated in this study.Table 1: Bulk properties of investigated diluents and lubricants.Specific surface area values represent average values ± standard deviation.

Impact of lubricant concentration on mechanical strength of tablets
In a first step, the impact of lubrication on the mechanical strength of MCC tablets was investigated by applying short mixing times of 2 min and systematically varying the MgSt concentration between 0.25 and 2 wt.%.Here, the relationship between tablet porosity and tensile strength, the compactibility, was evaluated.The compactibility is only slightly impacted by changes in compaction kinetics [34] and thus, can be seen as a fundamental relationship that describes the bondability of the formulation.Rumpf's model suggests that the bondability of a compact depends on the quantity and strength of bonds formed on the aggregate [35] and can be calculated based on porosity, coordination number, particle surface area, and bonding force.The internal lubricant addition results in the surface coverage of diluent particles by lubricant particles [5,6].In the case of lubricated MCC, it can be hypothesized that the negative impact on mechanical strength can be explained by two different mechanisms [36]: First, the presence of lubricants on the surface acts as a physical barrier, preventing, amongst other adhesive forces, strong hydrogen bonding between MCC particles [37] and replacing them with weaker bonding between lubricant and MCC particles.Second, the decreased bonding force of lubricated MCC particles enhances the extent of relaxation during decompression [38] and by doing so, increases the interparticulate distance, reducing effective particle interaction areas.In this study, MCC was applied as a model material, as its tensile strength is highly sensitive to the addition of lubricants [39], especially due to the limited generation of new, unlubricated surfaces during compaction [7,8].Consequently, this high sensitivity enables the correlation of the dispersion behavior of MgSt with the process and formulation parameters used in this study.As expected, increasing the concentration of internally applied lubricants results in a severe decrease in the compactibility of binary formulations of MCC and MgSt (Figure 3).The compactibility of tablets was quantified by applying the equation of Ryshkewitch-Duckworth [40,41]: Where σ 0 is the theoretical maximal tensile strength for a non-porous tablet and k b is the bonding capacity.
In a previous study of our research group, it was shown that the k b values of lubricated MCC grades are virtually constant for different MgSt concentrations [28].Thus, in order to limit the effect of lubrication to the reduction of σ 0 , the compactibility profiles of lubricated MCC formulations are fitted by the Ryshkewitch-Duckworth equation while using the k b values of the unlubricated diluents k b,dil, respectively.The empirical fit parameters of the unlubricated MCC grades were determined beforehand based on their compactibility profiles (Figure S1) and are enlisted in Table 2 [28], the subsequently derived theoretical maximal tensile strength values decrease for rising lubricant concentrations (Figure 4).Obviously, if finer MgSt grades (e.g., MgSt 4 ) are applied, smaller σ 0 values result for a given lubricant concentration.This detrimental effect of smaller lubricant particles on the mechanical tablet strength is well known [21,42] and can be explained by the higher number of lubricant particles for a given lubricant concentration, resulting in a higher coverage of diluent particles.Consequently, a greater fraction of comparably stronger MCC-MCC bonds is replaced by weak MCC-MgSt or MgSt-MgSt bonds and by that, the tablet strength decreases.Additionally, for a given lubricant grade and concentration, the application of coarser MCC particles results in a considerably higher reduction of compactibility (cf. Figure 4a and Figure 4c).This effect is caused by the smaller available diluent surface, which, if the same number of lubricant particles are applied, will be covered to a greater extent by lubricant particles.It is obvious that the extent of compactibility reduction depends on both applied diluent and lubricant particle size for binary formulations of MCC and MgSt, due to the different resulting surface coverages.In previously conducted studies [21,42], the same qualitative explanatory approach was used, but no quantitative correlation taking into account the particle sizes of both excipients was derived.In the course of this study, the dispersion mechanisms proposed by Shah and Mlodozeniec are considered [5].The dispersion of MgSt due to shear stress can thereby be distinguished in two consecutive steps: First MgSt stearate agglomerates adhere to the diluent surfaces resulting in a macroscopic distribution of the lubricant.If further shear stress is applied, the lubricant agglomerates deagglomerate or delaminate, due to their lamellar structure, into smaller particles and which consecutively cover additional diluent surfaces (Figure 5).The resulting macroscopic lubricant distribution was theoretically estimated by calculation of the geometric surface coverage according to the approach of Meyer [43].It is assumed that each lubricant particle occupies a hexagonal area on the diluent surface according to its median particle size x 50 (Figure 5).For this methodology, several assumptions are drawn: 1.For short mixing times, the lubricant agglomerates are distributed on the diluent surfaces due to acting shear stresses and occupies the diluent surface.No further deagglomeration or delamination has taken place.2. The different lubricant particle sizes after the macroscopic distribution can be represented by a characteristic particle size (x 50 ), which can reliably be measured by laser diffraction.3. The available diluent surface can be estimated by the specific surface area calculated from particle size distributions measured by laser diffraction.4. The deposition of lubricant agglomerates on free diluent surfaces is favored in terms of the formation of lubricant multilayer on the diluent surface Naturally, those assumptions do not represent the distributed nature of particle properties of both diluents and lubricants as well as the irregular shape of those entities.However, in a previous publication, this approach was successfully applied to link the effect of lubrication to the prediction of multi-component mixtures [30] and to identify a common relationship between compactibility reduction and lubricant particles size of chemically different lubricants [19].The total available diluent surface S dil can be calculated by multiplying the specific surface area S m,LD with the total diluent mass m dil : The occupied area by lubricant particles S lub can be derived by [43]: Where x 50,lub is the median particle size of the investigated lubricant and m lub is the total lubricant mass.Afterwards, the particle size-based theoretical surface coverage SC theo can be calculated: By relating SC theo to σ 0 values of lubricated blends, a unifying relationship for binary blends of a given MCC grade and different MgSt grades was identified (Figure 6a-c).For all applied MCC grades, an exponential decrease of σ 0 for rising SC theo values was observed.SC theo [-] Fit acc. to (8) (d) Figure 6: Correlation between σ 0 and SC theo for binary blends of MCC fine (a), MCC medium (b), MCC coarse (c) and four different grades of MgSt.Correlation between σ 0,norm and SC theo for all investigated blends of three different MCC and four different MgSt grades (d).In case of unlubricated MCC tablets, despite being generally comparable, a slight trend of higher σ 0 values for finer MCC grades was determined (Table 2).This difference in initial compactibility impedes the direct comparison of σ 0 values of lubricated MCC grades.In order to allow a meaningful comparison of different grades, the derived σ 0,lub values of lubricated formulations were normalized by the σ 0,dil values of the unlubricated MCC grade, respectively: Plotting σ 0,norm against SC theo reveals a unifying compactibility reduction for higher SC theo values.This finding indicates that the initial MgSt dispersion is governed by the macroscopic distribution of lubricant agglomerates, as previously assumed [5], and depends on the initial particle sizes of applied excipients.The reduction of σ 0,norm was modeled by fitting the data with an appropriate dispersion kinetic.Here, the dispersion kinetic published by Schilde et al. was adapted [31], which depicts a modified Michaelis-Menten kinetic: 0 =  0, + ( 0, - 0, ) •  ℎ  ℎ +   (8) Where σ 0,end describes the minimal σ 0 value and K Macro represents an empirical kinetic constant.By considering equation (7), equation ( 9) can be yielded: Generally, it can be hypothesized that the minimal value of σ 0,norm should be close to zero due to the weak interactions between MgSt particles, however, results shown in later chapters indicate that the threshold value will most likely be different to zero.Additionally, it is questionable if the threshold can be reasonably assessed, as a further increase of SC theo resulted in obvious tablet defects.As the investigated lubricant concentrations are well within the industrially applied range, higher lubricant concentrations were not examined.Generally, alternative dispersion models [4,23] were also evaluated, but resulted in poorer correlation (data not shown).As shown in Figure 6d, the adapted dispersion kinetic accurately describes the plotted data (R 2 ~ 0.95) and thereby, once parametrized by a limited number of experiments, can be used to predict the compactibility loss due to lubrication of MCC for different excipient particle sizes.However, as 12 individual combinations of materials are taken into account, a maximum deviation of approx.15% of single values from the model occurs.Consequently, the proposed approach represents an interesting tool for formulation development, as it requires only comparatively easily measurable particle properties and allows the adaptation to partially unavoidable changes in the starting material quality.

Impact of mixing time on mechanical strength of tablets
The interplay of MgSt and MCC particle sizes on the dispersion behavior of MgSt for prolonged mixing times was evaluated by creating binary formulations with a fixed MgSt concentration of 0.5 wt.% and systematically varying the mixing time between 2 and 600 min.For longer mixing times, it is proposed that MgSt deagglomerates and delaminates resulting in an increased coverage of MCC surfaces (Figure 5).Accordingly, with increased mixing time, the compactibility is reduced (Figure S2) and can be quantified by applying the Ryshkewitch-Duckworth equation (3).Analogous to the impact of lubricant concentration, the k b,dil value of the unlubricated MCC grades was used to limit the effect of lubricant addition to σ 0 .Subsequently, the σ 0 vs. t mix plots were evaluated by applying the adapted dispersion kinetic of Schilde et al. [31]: Where K Micro is a kinetic constant describing the half life time until 50% of the absolute difference between σ 0,dil and σ 0,end is reached.The compactibility for a mixing time of 0 min was estimated by applying the σ 0 value of the unlubricated diluent σ 0,dil .The σ 0,dil values have been quantified beforehand (Table 2), leaving only σ 0,end and K Micro to be determined.(c) Figure 7: Effect of mixing time t mix on σ 0 values of binary blends of MCC fine (a), MCC medium (b), MCC coarse (c) and different grades of MgSt for a lubricant concentration of 0.5 wt.%.The σ 0 value for a mixing time of 0 min was estimated by σ 0,dil .As shown in Figure 7, the determined σ 0 values decrease with rising mixing time whereby two phases can be identified: A drastic reduction rate for short mixing times followed by a considerably smaller reduction rate for long mixing times.This reduction rate represents the lubricant dispersion rate.Generally, the majority of investigated formulations approach a common threshold (σ 0,end ) between 2.5 -4 MPa for all investigated formulations.Contrary to this finding, if MgSt 1 in combination with MCC fine or MCC medium is applied, the minimum σ 0 value is slightly higher.Those visible differences are not completely resembled by the σ 0,end values due to the extrapolating nature of the applied fit function (Figure 8a).
The minimal compactibility for long mixing times can be interpreted as an equilibrium state of lubricant dispersion.Assuming that the mixing time of 600 min excludes a limitation due to an insufficient number of stress events, three different scenarios can be envisioned (amongst others) to explain this equilibrium state: 1) The shear stress is insufficient to induce further MgSt delamination due to an increase of shear strength with decreasing particle size of MgSt during mixing.The equilibrium state reflects the maximum surface coverage depending on the lubricant shear strength, lubricant mass and available diluent surface.
2) The shear stress exceeds the shear strength of MgSt at any given time during mixing, resulting in a complete dispersion of the applied MgSt mass.The resulting number and size of MgSt particles is insufficient to cover the available MCC surface.The equilibrium state is defined by the lubricant mass and available MCC surface.
3) The shear stress is sufficiently high to disperse MgSt into particles, which size and number is sufficient to cover the available MCC surface.The equilibrium state is defined by the remaining bonding potential of lubricated MCC surfaces.Based on the results shown, the deviating results for MgSt 1 + MCC fine /MCC medium could be explained by scenario 1, indicating an increased shear strength of the applied MgSt 1 compared to the other grades.This hypothesis is supported by the fact that MgSt 1 is a technical grade of MgSt in contrast to MgSt 2 -MgSt 4 that resemble pharmaceutical grades.Technical grades with a higher stearate content are known to exhibit higher shear strength [44].If the coarsest MCC grade with a decreased total surface is applied, the resulting particle size and number of particles after delamination of MgSt 1 is sufficient to cover the available MCC surface, similar to the other MgSt grades (Figure 7c).If Scenario 2 would be valid, for a given lubricant mass the total surface to be covered determines the fraction of surface coverage and by that, the minimal compactibility.As the total surface to be covered is determined by the MCC grade, coarser MCC grades should generally exhibit smaller compactibility values.In fact, a slight tendency for an opposing effect is apparent: coarser MCC grades show slightly higher σ 0,end values (Figure 8a).It could be hypothesized that larger MCC particles exhibit a greater absolute deformation during compaction, which could result in an increased interference with the lubricant coverage.Additionally, a small degree of fragmentation was identified for coarse MCC grades by Roberts and Rowe [45].Both mechanisms could result in an increase of fresh, unlubricated surfaces that are available for bonding, which could explain the slightly higher σ 0,end values of coarser MCC grades.However, though it may prevail during the whole dispersion process, this specific effect can only be differentiated towards σ 0,end because at lower dispersion states, the higher surface coverages of coarser MCC particles overrule this effect by lower strength compared with smaller MCC particles.This finding in combination with the general similarity of the found σ 0,end values contradicts scenario 2.  11) and K Macro derived of Figure 6d.Thus, it can be hypothesized that scenario 3 best describes the equilibrium state for the majority of investigated formulations.To check this hypothesis, it was investigated whether the identified common equilibrium state is the consequence of the constant added lubricant mass or refers to the saturation of the majority of available MCC surfaces.Therefore, binary mixtures of all MCC grades and MgSt grades were created by applying a mixing time of 120 min and systematically varying the lubricant concentration between 0.02 -1 wt.% (for MgSt 1 also 2 wt.%) (Figure S3).The mixing time of 120 min was chosen in order to ensure a sufficiently high number of stress events to achieve higher dispersion and to come close to a possible equilibrium while simultaneously keeping the experiments feasible in terms of time.Afterwards, the compactibility profiles were mathematically quantified by applying the Ryshkewitch-Duckworth equation while assuming that the bonding capacity can be estimated by the bonding capacity of the unlubricated diluent k b,dil .The resulting σ 0 values are plotted against the SC theo , which represents the surface coverage of MCC after the macroscopic lubricant dispersion.It is evident, that a common relationship between σ 0 and SC theo irrespective of the applied formulation can be identified (Figure 9).The resulting σ 0 values rapidly decrease between initial SC theo values of 0 -0.01 and subsequently approach a threshold of σ 0 between 3 -4 MPa, similar to the results shown in Figure 7. Thereby, if a sufficient amount of lubricant is added to the formulation, a similar equilibrium state of compactibility results.This indicates that this equilibrium describes the residual bonding potential of lubricated MCC surfaces.Interestingly, higher MgSt 1 concentrations also results in a comparable minimum σ 0 values.This can be seen as confirmation that the deviating results for MgSt 1 + MCC fine /MCC medium is in fact attributed to its enhanced shear strength and does not indicate an entirely different behavior.Generally, the dataset can be divided into a rapid decrease of σ 0 followed by a very slow decrease of σ 0 .The transition area is located at SC theo values of 0.01, which can be seen as a minimum value to ensure a common equilibrium state for high mixing times.This correlates to lubricant concentrations between 0.1 wt.% (MCC coarse + MgSt 4 ) and 1 wt.% (MCC fine + MgSt 1 ) and is well within the commonly applied range of pharmaceutical lubricant concentrations.Thus, from a practical point of view, a common minimal compactibility value can be assumed.For SC theo values below 0.01, considerably higher σ 0 values were found.This increased compactibility could either be caused by an insufficient lubricant mass or an insufficient number of stress events.As those small lubricant concentrations are typically not applied, no further laborious experiments with prolonged mixing times were performed.Thereby, following the stress model for comminution processes by Kwade [46], it can be hypothesized that the complete saturation of available MCC surfaces by MgSt particles can be achieved if the following criteria are met: 1.During mixing, the stress energy during stress events is sufficiently high to enable the lubrication dispersion, i.e. by deagglomeration and delamination.2. The applied mixing time is sufficiently long in order to ensure a sufficient number of successful stress events, which result in lubricant delamination.3. The applied lubricant mass is sufficiently high, so that the number and size of generated lubricant particles after delamination is sufficient to cover the available MCC surfaces.Assuming that the σ 0,dil values are known and σ 0,end values can be reasonably estimated, the dispersion behavior is mainly governed by the dispersion rate.The dispersion rate describes the rate of which a given MCC surface is covered by lubricant particles and is quantified by the kinetic constant, K Micro .Here, K Micro represent the necessary mixing time until σ 0 is reduced by 50% of the difference between σ 0,dil and σ 0,end .Thus, smaller K Micro values represent a fast dispersion rate and vice versa.Correlating the kinetic constant K Micro to SC theo , which represents the macroscopic lubricant dispersion, reveals a rapid decrease of K Micro for increasing SC theo values (Figure 8b).This relationship can be mechanistically understood as the probability that an individual available MCC surface spot is covered by MgSt in a given time step.It is envisioned, that the delamination of lubricant particles due to shear stresses acting during mixing occurs if a lubricant particle is stressed between two MCC particles, which effectively act comparable to grinding media [46].If a higher degree of MCC surface is already covered by lubricant particles after the macroscopic lubricant dispersion, the probability to stress a lubricant particle during a stress event is increased.Thereby, the dispersion rate during MgSt delamination directly depends on the macroscopic dispersion state.It is assumed that the different consecutive realized dispersion states of the investigated formulations are comparable, irrespective of the applied particle sizes (Figure 10).Thus, higher SC theo values can be understood as a headstart, which results in short necessary mixing times, and by that smaller K Micro values, to completely cover the diluent surface.Figure 10: Schematic representation of proposed dispersion states of MgSt as a function of the macroscopic and microscopic lubricant distribution.Additionally, it can be assumed that the minimal compactibility of lubricated MCC is comparable independent of the type of distribution (be it macroscopic or microscopic) if sufficient amounts of lubricant are applied.Following, σ 0,dil and σ 0,end can be estimated to be equal.Assuming that the dispersion kinetics for the influence of concentration and mixing time coincide for a mixing time of 2 min, the dependence of K Micro on SC theo can be determined analytically.Therefore, equation ( 8) and ( 10) are equated for t mix = 2 min and solved for K Micro : ) Plotting the resulting predicted K Micro values (Figure 8b) showed a correct trend between the predicted and experimental K Micro values.This finding is valuable as it allows the prediction of the dispersion behavior for prolonged mixing times without performing any mixing experiments for prolonged times.Instead, once the impact of lubricant addition on tablet compactibility for a small number of lubricant concentrations is established (c.f. Figure 6d) and modeled by equation ( 8), the dispersion behavior can already be reasonable predicted.In summary, the influence of particle size on delamination behavior of MgSt on MCC particles can be divided into two aspects.The minimal compactibility for long mixing times appears to be comparable for the vast majority of investigated formulations with a given MgSt concentration, indicating that this equilibrium state is controlled by the residual bonding strength between lubricated MCC surfaces.The kinetics of dispersion, on the other hand, depend significantly on the set particle size-based surface coverage due to the macroscopic distribution of MgSt after short mixing times, as it directly affects the probability that a MgSt particle is stressed during MCC particle contact.The findings shown here allow to quantitatively model the particle size influence on the tablet strength of binary mixtures of MCC and MgSt for prolonged mixing times for the first time and by that, can provide a substantial improvement of the available formulation knowledge.In future studies, it would be desirable to quantify the lubricant particle strength and relating it to stress conditions during relevant pharmaceutical unit operations, e.g.mixing, to further rationalize the lubricant selection.Additionally, as these study has focused on a given set of process parameters, it would be desirable to combine this approach with models which take into account the effect of mixing process parameters on the tablet strength, e.g. the model of Kushner [4].Finally, an extension of the findings on multi-component mixtures would represent a considerable economic benefit, as it would allow minimizing the number of required experiments.

Conclusions
In this study, the influence of the excipient particle size on the compactibility of binary mixtures of MCC and MgSt was investigated using three grades of MCC and four grades of MgSt.The impact of formulation was quantified by estimating the theoretical surface coverage and subsequently, correlated with the reduction of compactibility.Here, the effect of lubricant concentration and mixing time on this correlation was investigated in detail.It was shown that the compactibility reduction for short mixing times could be modeled independent of the grades used by introducing theoretical surface coverage, which describes the surface coverage of diluents surfaces after the macroscopic lubricant distribution for short mixing times.The theoretical surface coverage requires only easily measurable formulation properties and allows predicting the compactibility reduction if components are replaced by other grades with different particle sizes.In addition, it was shown that, for a sufficient lubricant amount, the minimum compactibility for long mixing times is comparable for the majority of the formulations investigated, if a industrially common low threshold (< 0.5 wt.%) is overcome.This allows to mathematically limit the influence of the lubricant addition on the compactibility for prolonged mixing times to the dispersion rate.It could be shown that this dispersion rate mainly depends on the given theoretical surface coverage, since it determines the probability that a lubricant particle is stressed during an MCC particle contact and, by that, the probability of successful lubricant dispersion events.Accordingly, the relationships shown in this framework represent a significant improvement in formulation knowledge regarding the linkage of applied excipient sizes on the compactibility reduction of lubricated MCC tablets.This knowledge can be transferred to other formulation components and can be used to streamline the development of new tablet formulations, minimizing the necessary empirical testing.This approach can also be applied directly for granules, which are quite frequently used for tableting.It could even be extended to materials causing too high ejection stresses and tablet defects for the unlubricated case, when external lubrication is applied to assess their compactibility data.

Figure 2 :
Figure 2: Cumulative particle size volume distributions of the investigated grades of MCC (a) and MgSt (b) determined by laser diffraction for a dispersion pressure of 0.5 bar.

Figure 3 :
Figure 3: Compactibility plots of binary formulations of MCC and MgSt for different lubricant concentrations and a mixing time of 2 min.Lines represent fits acc. to equation (3) with a fixed k b value determined from the unlubricated MCC grades, named k b,dil (a) MCC fine + MgSt 1 (b) MCC fine + MgSt 4 (c) MCC coarse + MgSt 1 (d) MCC coarse + MgSt 4

Figure 4 :
Figure 4: Correlation of lubricant concentration and theoretical max.tensile strength σ 0 for binary mixtures of MCC fine (a), MCC medium (b), MCC coarse (c) and four different grades of MgSt for a mixing time of 2 min.Measuring the extent of surface coverage by lubricant particles is experimentally challenging and timeconsuming.As discussed above, quantitative values of surface coverage by MgSt are typically based on SEM measurements.However, identifying MgSt on MCC particles is extremely challenging as the debris of MCC and MgSt exhibit comparable morphologies[5] and MCC particles do not exhibit the required smooth particles surfaces[15].

Figure 5 :
Figure 5: Schematic representation of the proposed dispersion mechanisms during mixing of MgSt and diluent particles.Initially, lubricant agglomerates adhere to the diluent surface and occupy a hexagonal shaped area according to their x 50 .If further shear stress is applied, MgSt particles deagglomerate or delaminate into platelets, which consecutively cover additional diluent surfaces.

Figure 8 :
Figure 8: Derived σ 0,end (a) and K Micro (b) values by fitting σ 0 vs. t mix plots with equation (10) for different binary combinations of MCC and MgSt grades.Line in (b) represents prediction of K Micro based on equation (11) and K Macro derived of Figure 6d.

Figure 9 :
Figure 9: Reduction of σ 0 as a function of SC theo for different binary mixtures of MCC and MgSt for a mixing time of 120 min.