# Characterization of Mechanical Property Distributions on Tablet Surfaces

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{®}PH 200 (FMC BioPolymer, Philadelphia, Pa, USA) (MCC-A), Pharmacel

^{®}102 (DFE Pharma, Nörten-Hardenberg, Germany) (MCC-P), Tablettose

^{®}100 (Meggle Pharm, Wasserburg am Inn, Germany) (LAC), and DI-CAFOS

^{®}D160 (Budenheim, Budenheim, Germany) (CAPH). The first two constitute two grades of microcrystalline cellulose with a different particle size distribution: Tablettose

^{®}100 is a lactose monohydrate, whereas the main component of DI-CAFOS

^{®}D160 is dicalcium phosphate dihydrate.

#### 2.2. Powder Characterization

#### 2.3. Tableting

^{®}100 and DI-CAFOS

^{®}D160, each of these batches is internally lubricated by blending 1% (w/w) of magnesium stearate (MgST) (Magnesia 4264; Magnesia GmbH, Lüneburg, Germany) in a powder mixer ERWEKA AR-403/-S (ERWEKA GmbH, Heusenstamm, Germany) with a 3.5-L cubic container for 3 min at 16 rpm before tableting. All four grades of powder freely flowed from the feeder to the die, precisely limiting the fill volume by the position of the lower punch. The excess of powder was scraped off the die, yielding reproducible fill and tablets with constant weights for the same processed batch.

#### 2.4. Tablet Characterization

#### 2.5. Microindentation

^{2}, respectively.

## 3. Results and Discussion

#### 3.1. Powder Characterization

_{50}values in the range comprised between 200–250 µm, while MCC-P and LAC are also comparable in size, but ranging from 80–110 µm, which is approximately half the size of the former. The polydispersity of both MCC grades is comparable, according to their span values, whereas CAPH and LAC constitute two opposite examples of PSD broadness: 0.79 for CAPH and 2.48 for LAC.

#### 3.2. Tablet Quality Parameters: Tensile Strength, In-Die Elastic Recovery and 24 h Elastic Recovery

#### 3.3. Evaluation of Densification Mechanism

#### 3.4. Sensitivity Analysis of Maximum Indentation Force and Structural Inhomogeneity

#### 3.5. Evolution of Stiffness with Compaction Pressure at Different Locations of the Tablet (Upper, Lower, and Lateral Faces)

_{2}beads, which are a hard/brittle slightly cohesive material, Strege et al. studied the structural anisotropy from an in situ reconstruction of the contact alignment and arrangement by means of X-ray microtomography [50]. Beginning with an initial perfectly isotropic configuration, anisotropy increased with pressure, reaching a maximum value. Due to the continuous presence of friction, the anisotropy was meant to exist even for infinitive pressure.

#### 3.6. Cumulative Property Analysis

**a**) MCC-P 138.0 MPa with measurements at the upper face; and (

**b**) LAC 197.0 MPa also at the same tablet face.

^{TM}(Table 2). Figure 15 accounts for the representation of the fitted cumulative gamma distributions for ${E}_{mod}$. The scale factor θ increases with the increasing compaction pressure for all of the analyzed materials, clearly indicating the wider dispersion of stiffness at the highest degree of compaction. These results contradict the notion that the higher the degree of densification of the structure, the more compact and thus, more homogeneous it should be [18]. However, this effect may have its origin in the accumulation of effects ruling different stages of compaction: rearrangement, elasto-plastic deformation for ductile materials, fragmentation, and dislocations interlocking for brittle materials. This complex interplay of stress events, with some of them predominant through successive stages of compaction, leads to an increasingly heterogeneous structure with compaction pressure. Additionally, at the border, compaction is hindered because the contact formation is reduced and the elastic expansion after ejection from the die yields the highest stresses perpendicular to the radial direction on the circumference of the tablet.

#### 3.7. Property Distribution over Tablet Faces

^{®}in order to obtain the stiffness distribution at the surface of the compacts [53]. The results of this analysis are displayed in representative color diagrams for MCC-P (Figure 16) and LAC (Figure 17) tablets.

^{®}PH 101 based on a continuum modeling via FEM by applying the modified Drucker–Prager Cap model, keeping the position of the lower punch constant and exerting pressure with the upper punch [55]. Considering a frictional term on the formulation of the model, during compression, decompression, and ejection, stress distributions were irregular, causing a non-uniform density distribution. As a result of that, the top and the bottom corners were the most and the least densified regions, respectively, with each of them having a peak difference to the overall average density of the tablet of around 12%. Not identifying this highly densified region at the top corner of the tablet in Figure 16 and Figure 17 is plausible because of the symmetrical movement of the punches for the current analysis. However, a reduced sampling of the adjacent regions of the edges due to the impossibility of satisfactorily performing an indent from a relative radial distance to the center of 0.95 (560 µm) may not allow in any case identifying an overall lateral hardening.

^{®}PH 102 and cylindrical instrumentation, they traced the density distribution by admixing steel balls to the formulation, which permitted the density reconstruction by X-ray imagery. They identified regions of high density in contact with the top punch and a vector force acting outwards with respect to the loading axis. A frictional force at the die wall impedes the powder movement, and as a result, an uneven pressure distribution is generated. Toward the lower part of the tablet, particles experience less compressive force, which explains the lower density.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**Left**) Schematic view of indentation with a frustum-shaped indenter with an opening angle $\theta $ = 40° and a punch radius $a$ = 50 µm. ${F}_{max}$ corresponds to the maximum indentation force and $\delta $, the indentation depth at this force; (

**Right**) Microscope acquisition of the 100 µm flat punch.

**Figure 2.**Relative position of the indentation locations throughout the flat face of the cylindrical tablets.

**Figure 3.**Example of force–displacement curve on a tablet. Material: Pharmacel

^{®}102. Compaction pressure: 175 MPa. Max. indentation force: 500 mN.

**Figure 4.**SEM acquisitions of the excipient powders prior to compaction: (

**a**) MCC-A; (

**b**) MCC-P; (

**c**) LAC; (

**d**) CAPH. MCC-A: Avicel

^{®}PH 200 (FMC BioPolymer, Philadelphia, PA, USA); MCC-P: Pharmacel

^{®}102 (DFE Pharma, Hardenberg, Germany); LAC: Tablettose

^{®}100 (Meggle Pharm, Wasserburg am Inn, Germany); CAPH: DI-CAFOS

^{®}D160 (Budenheim, Budenheim, Germany).

**Figure 6.**Elastic recovery after compaction of MCC-A/P, LAC, and CAPH granules: (

**a**) In-die axial elastic recovery; (

**b**) Axial recovery after 24 h; (

**c**) Radial recovery after 24 h; (

**d**) Axial vs. radial elastic recovery after 24 h (arrows pointing towards the direction of increasing solid fraction).

**Figure 7.**Surface area determination with Brunauer, Emmett, and Teller (BET) (n = 4, for each material and compaction pressure); (

**a**) MCC-A; (

**b**) MCC-P; (

**c**) LAC; (

**d**) CAPH.

**Figure 8.**Median elastic modulus of MCC-P tablets as a function of the maximum indentation force for different nominal compaction pressures (n = 79 for each compaction pressure (CP) and indentation force).

**Figure 9.**Median elastic modulus of CAPH tablets as a function of the maximum indentation force for different nominal compaction pressures (n = 79 for each CP and indentation force).

**Figure 10.**Elastic ratio ($\epsilon $) of MCC-P tablets as a function of the maximum indentation force for different nominal compaction pressures.

**Figure 11.**Elastic ratio ($\epsilon $) of CAPH tablets as a function of the maximum indentation force for different nominal compaction pressures.

**Figure 12.**Normalized force–displacement indentation curves. Confidence intervals for n = 30 assuming normally distributed results for a 95% of probability. Material: MCC-P. Compaction pressure: 100 MPa.

**Figure 13.**Elastic modulus as a function of the solid fraction of tablets for different excipients; (

**a**) MCC-A; (

**b**) MCC-P; (

**c**) LAC; (

**d**) CAPH. Sampling size: eight tablets per solid fraction (SF) and face, 164 indents at each tablet.

**Figure 14.**Fitted number cumulative distributions (${Q}_{0}$); (

**a**) MCC-P 138.0 MPa upper face; (

**b**) LAC 197.0 MPa upper face. The legend summarizes the fitted parameters for each distribution and the result of the Kolmogorov–Smirnov (K–S) hypothesis test. Sampling size: eight tablets per SF and face, 79 indents at each tablet.

**Figure 15.**Fitted volumetric/weight cumulative gamma distributions (${Q}_{0}$) as a function of the maximum compaction pressure for the upper and lower tablet faces of the following excipients; (

**a**) MCC-A; (

**b**) MCC-P; (

**c**) LAC; (

**d**) CAPH. Sampling size: eight tablets per SF and face, 79 indents at each tablet.

**Figure 16.**${E}_{mod}$ distribution over tablet surface for MCC-P tablets. Coordinates [0, −5.625] correspond to the frontal part during compaction. The filling shoe approaches from [−5.625, 0] with a rotational cycle, and it withdraws following its same path to [5.6250, 0]. Sampling: eight tablets per pressure and face; 79 indents at each tablet face.

**Figure 17.**${E}_{mod}$ distribution throughout the tablet surface for LAC tablets. Coordinates [0, −5.625] correspond to the frontal part during compaction. The filling shoe approaches from [−5.625, 0] with a rotational cycle and it withdraws following its same path to [5.6250, 0]. Sampling: eight tablets per pressure and face; 79 indents at each tablet face.

**Figure 18.**Radial evolution of ${E}_{mod}$ at the lower surface of the tablet for the following materials; (

**a**) MCC-A; (

**b**) MCC-P; (

**c**) LAC; (

**d**) CAPH. Sampling: eight tablets per SF and face, six indents at each radial distance.

**Table 1.**Physical properties of the powders of interest: particle size distribution (PSD) from volumetric/mass cumulative distributions and true/skeletal density.

Material | x_{10} (Q_{3}) (µm) | x_{50} (Q_{3}) (µm) | x_{90} (Q_{3}) (µm) | Span (-) | Measuring Technique | True Density (kg·m^{−3}) | Measuring Technique |
---|---|---|---|---|---|---|---|

MCC-A | 82.9 | 224.6 | 379.3 | 1.32 | Dynamic particle image analysis | 1541.1 | Helium pycnometry |

MCC-P | 28.3 | 86.5 | 173.8 | 1.68 | 1533.7 | ||

CAPH | 131.6 | 210.5 | 298.4 | 0.79 | 1763.3 | ||

LAC | 34.3 | 107.8 | 302.0 | 2.48 | Laser diffraction | 2766.0 |

**Table 2.**Fitting volumetric/weight cumulative parameters for gamma distributions (${Q}_{0}$) as a function of the maximum compaction pressure for the upper and lower tablet faces.

Material | Compaction Pressure (MPa) | Face | Gamma $\mathit{k}$ Factor (-) | Gamma $\mathit{\theta}$ Factor (-) |
---|---|---|---|---|

MCC-A | 27.0 | Upper | 11.20 | 29.29 |

Lower | 13.10 | 42.95 | ||

79.2 | Upper | 24.15 | 23.41 | |

Lower | 24.15 | 23.41 | ||

136.8 | Upper | 27.27 | 25.36 | |

Lower | 10.77 | 64.40 | ||

197.0 | Upper | 11.40 | 62.24 | |

Lower | 10.32 | 79.97 | ||

MCC-P | 26.7 | Upper | 24.75 | 11.34 |

Lower | 25.98 | 10.02 | ||

80.1 | Upper | 8.43 | 59.07 | |

Lower | 22.17 | 20.86 | ||

138.0 | Upper | 23.10 | 31.33 | |

Lower | 9.78 | 67.52 | ||

196.7 | Upper | 6.90 | 105.84 | |

Lower | 6.90 | 108.56 | ||

LAC | 134.6 | Upper | 8.98 | 118.56 |

Lower | 10.77 | 64.40 | ||

197.0 | Upper | 8.20 | 150.08 | |

Lower | 7.81 | 159.26 | ||

CAPH | 79.0 | Upper | 8.09 | 103.87 |

Lower | 2.95 | 176.51 | ||

135.9 | Upper | 7.61 | 112.02 | |

Lower | 3.70 | 176.57 | ||

198.4 | Upper | 4.59 | 187.66 | |

Lower | 4.56 | 167.26 |

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**MDPI and ACS Style**

Cabiscol, R.; Finke, J.H.; Zetzener, H.; Kwade, A.
Characterization of Mechanical Property Distributions on Tablet Surfaces. *Pharmaceutics* **2018**, *10*, 184.
https://doi.org/10.3390/pharmaceutics10040184

**AMA Style**

Cabiscol R, Finke JH, Zetzener H, Kwade A.
Characterization of Mechanical Property Distributions on Tablet Surfaces. *Pharmaceutics*. 2018; 10(4):184.
https://doi.org/10.3390/pharmaceutics10040184

**Chicago/Turabian Style**

Cabiscol, Ramon, Jan Henrik Finke, Harald Zetzener, and Arno Kwade.
2018. "Characterization of Mechanical Property Distributions on Tablet Surfaces" *Pharmaceutics* 10, no. 4: 184.
https://doi.org/10.3390/pharmaceutics10040184