Pharm Res DOI 10.1007/s11095-017-2273-5
RESEARCH PAPER
Dependence of Friability on Tablet Mechanical Properties and a Predictive Approach for Binary Mixtures Shubhajit Paul 1 & Changquan Calvin Sun 1
Received: 10 August 2017 / Accepted: 27 September 2017 # Springer Science+Business Media, LLC 2017
ABSTRACT Purpose To systematically assess the dependence of friability on tablet mechanical properties, compaction pressure, and tablet porosity. Methods Several common excipients and their mixtures exhibiting diverse mechanical properties were analyzed. Tablet elastic modulus, hardness, brittleness, porosity, and tensile strength were determined using standard techniques and then were correlated to tablet friability both individually and as a group to derive a universal model. Results Viscoelastic starch exhibits the highest friability followed by brittle excipients (mannitol, DCPA, and LM) and then ductile excipients (HPC and MCC). A reasonably accurate model for predicting pharmaceutically relevant range of friability, up to 3%, of binary mixtures is presented based on friability of individual components. In addition, a multivariate model between friability and different mechanical parameters was developed, based on which the weight loss propensity of tablets may be predicted. Conclusions The experimental findings and predictive model are useful for expedited development and optimization of tablet formulation using a minimum amount of API.
KEY WORDS friability . mechanical properties . mixture . modelling . tablet Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11095-017-2273-5) contains supplementary material, which is available to authorized users. * Changquan Calvin Sun
[email protected] 1
Pharmaceutical Materials Science and Engineering Laboratory Department of Pharmaceutics, College of Pharmacy University of Minnesota, 9-127B Weaver-Densford Hall 308 Harvard Street S.E, Minneapolis, MN 55455, USA
ABBREVIATIONS ε σ DCPA E Fr H HPC KIc LM MCC TBI
Porosity Tablet tensile strength Dicalcium phosphate anhydrate Tablet elastic modulus Friability Indentation hardness Hydroxypropyl cellulose Stress intensity factor Lactose monohydrate Microcrystalline cellulose Tablet brittleness index
INTRODUCTION More than 70% of the drugs are formulated into tablets, because of the advantages of stability and economy. (1) To ensure robust commercial manufacturability of high quality tablet products, tablet formulation and manufacturing processes need to be optimized. Friability assesses a tablet’s susceptibility to the loss of component particles due to abrasion, friction, or mechanical shock, such as that experienced during tablet coating. (2) Low tablet friability is one of the critical attributes required for a high quality tablet product. For a given formulation, a certain minimal tablet strength is required to maintain low tablet friability, when subjected to mechanical shock during operation, handling, and storage. The USP acceptance criterion is <1.0% weight loss for a minimal weight of 6.5 g of a given batch of tablets after 100 drops in a rotating drum of a friabilator, which simulates the impact and attrition in real life situations. (3) The current USP friability method is primarily used for quality control of finished tablet batches, instead of guiding the formulation development and optimization or trouble shooting. However, an expedited and material-sparing friability method was recently introduced to allow facile measurement of tablet friability as a function of
Paul and Sun
tablet properties or compaction parameters. (4) The knowledge of friability allows the direct determination of suitable conditions, such as tooling design, tableting speed, compaction pressure, for manufacturing tablets that meet the USP friability criterion. (5) Ready access to friability information makes routine assessment of the influence of material mechanical properties on friability possible, which can thereby guide tablet formulation development. Tablet friability is affected by both impact conditions (velocity of impact, height of freefall, sliding distance) and tablet properties (tensile strength, brittleness, hardness, Young’s modulus, ability of a material to bounce back after an impact). (6–8) For examples, more brittle tablets or tablets with lower tensile strength tend to exhibit higher friability. (4,9) Material loss from a tablet usually occurs in the form of edge chipping or surface abrasion where particles randomly detach from the tablet. Correspondingly, both attrition and abrasion mechanisms of weight loss have been proposed. (6,10,11) These two mechanisms are related to mechanical properties differently, (8) which allows independent quantification. Moreover, analyzing tablet friability in light of the two mechanisms facilitates the development of new insight for the design of robust formulation free from problems associated with high tablet friability. Using common pharmaceutical excipients of diverse mechanical properties and their mixtures, we have studied the impact of material mechanical properties on friability, using the expedited method. The results were modelled to allow prediction of the friability of mixtures from that of the individual constituents. Finally, we also attempted to elucidate predominant mode of weight loss for cylindrical tablets.
MATERIALS AND METHODS Materials Microcrystalline cellulose (MCC; Avicel PH102, FMC Biopolymers, Philadelphia, PA), hydroxypropyl cellulose (HPC, Sigma Aldrich, St Louis, MO), starch (Starch 1500®, Colorcon Inc., Harleysville, PA), lactose monohydrate (LM; Fastflo® NF, Foremost Farms, Clayton, WI), mannitol (Pearlitol 200 SD, Roquette America Inc., Keokuk, IA), and dicalcium phosphate anhydrate (DCPA, JRS Pharma, Patterson, NY) were the chosen common tablet excipients, e.g., fillers or binders. Magnesium stearate (Mallinckrodt, St Louis, MO) was used as a lubricant. Both pure excipients and binary mixtures were studied. The binary mixtures of each of the excipients with MCC were prepared in 25% (w/w) increments. Two mixtures of brittle excipients, LM-DCPA (3:1) and LM-mannitol (3:1), were also included.
Methods Preparation of Powders for Tableting Approximately, 10 g of each powder with 0.5% magnesium stearate were passed through a #30 mesh sieve (United States Standard Sieves) and mixed in a blender (Turbula, Glen Mills Inc., Clifton, NJ) for 2.5 min at 100 rpm. All powders were conditioned at 32% RH (saturated MgCl2 solution) at room temperature for 48 h prior to the compaction study. Direct Compression of Powders Tableting was conducted on a compaction simulator (Presster; Metropolitan Computing Corporation, NJ) simulating a Korsch XL100 (10 stations) press at a speed corresponding to 25 ms dwell time (49,300 tablets/h) using 9.5 mm round flat-faced punch-die sets. For each batch, two sets of tablets were prepared in the pressure range of 30–300 MPa for friability and diametric breaking tests. Tablet weight was kept at 300 mg throughout this study. This study was carried out at ambient conditions (~23°C and 31–38% RH). The use of nearly constant tablet weight in this work eliminated the possible complication in data interpretation due to different impact intensity during free fall of tablets. Determination of Powder True Density For water-containing MCC and HPC, powder true density (ρt) was determined by nonlinear fitting of the tablet density (ρ) as a function of compaction pressure (P) data according to Eq. (1), (12) For other water-free powders, true density was measured using helium pycnometry (Quantachrome Instruments, Ultrapycnometer 1000e, Byonton Beach, Florida). 2 0 ρ 13 1− 16 ρ ρt C7 B P ¼ 4ð1−εc Þ− −εc ln@ ð1Þ A5 εc C ρt where 1/C and εc are constants. The true density of each binary mixture (ρ1,2) was calculated from the individual components, 1 and 2, according to Eq. (2), (12) 1 x1 x2 ¼ þ ρ1;2 ρt;1 ρt;2
ð2Þ
where x refers to the weight fraction of constituent binary components. Tablet porosity (ε) was calculated according to Eq. (3). ε ¼ 1−
ρ ρt
ð3Þ
Tablet friability, mechanical properties, and prediction
Determination of Powder Plasticity The powder consolidation behavior of each excipient, i.e., ε reduction as a function of P was analyzed by the KuentzLeuenberger compressibility equation (Eq. 4), (13) 1 ε ð4Þ ε−εc −εc ln P¼ C εc Nonlinear fitting of data provides two parameters, C and εc, where 1/C is related to plasticity of the material, and εc denotes the porosity at which a powder bed attains an initial state of gaining mechanical rigidity. Expedited Friability Test Tablets were first individually coded and then subjected to USP friability test using a friabilator (Pharma Alliance Group Inc., Model F2, Santa Clarita, CA) for 100 drops (25 rpm over a period of 4 min). Each tablet was weighed on an analytical balance with 0.01 mg accuracy before and after the friability test. (4) The percentage of weight loss was obtained from the weight change after the friability test. Particles on tablet surface were carefully removed with a soft brush before weighing. Assessment of Tablet Tensile Strength
2F πdh
ð5Þ
where F, d, and h are the breaking force, diameter, and thickness of the tablet, respectively. Determination of Tablet Elastic Modulus Tablet elastic modulus (E) was estimated from Eq. (6): E¼
stress
P strain ¼ ðh−h0 Þ=h0
ð6Þ
Where h0 and h are in-die and out-of-die tablet thickness, respectively. Determination of Tablet Brittleness Index (TBI) Tablet brittleness was calculated using Eq. (7) according to the method described previously. (9,15) T BI ¼
tablet diameter maximum elastic deformation
Determination of Compact Hardness The intrinsic hardness of compacts containing MCC, LM, DCPA and mannitol were measured by macroindentation. (16) Due to weak strength of starch, tablets were made over a wide range of compaction pressures, i.e., 50–350 MPa with a 5 min holding time. Briefly, a spherical indenter (diameter 3.175 mm) was used to apply an accurately known force (F) in the range of 15–30 N with a holding time of 3 min. The indent area (A) was clearly demarcated by rubbing against a carbon paper and subsequently determined using a calibrated digital microscope (Dino-Light, AnMo electronic Corp., Hsinchu, Taiwan). Indentation hardness (H) was calculated using Eq. (8): H¼
F A
ð8Þ
Modelling Friability of Binary Mixtures Friability (Fr) was found to follow an exponential relationship with porosity (ε), as shown by Eq. (9) (4)
Tablets were broken diametrically on a texture analyzer (Texture Technologies Corp., Surrey, UK) at a test speed of 0.01 mm/s. Tablet tensile strength, σ, was determined from Eq. (5), (14) σ¼
The maximum elastic deformation was extracted from the tablet breaking force - displacement profile using MATLAB (Mathworks, Natick, MA).
ð7Þ
F r ¼ F 0 e ε: F 1
ð9Þ
Where F0 and F1 are constants, which represent the friability of a material at zero porosity and the sensitivity of friability to porosity, respectively. The power mixing rule, which was successfully used before for predicting tabletability and TBI, (17,18) was used to predict friability of mixtures. The power mixing rule suggests that F0 and F1 of a binary mixture of a and b, i.e., F0,m and F1,m, can be obtained from those of the individual components using Eqs. (10) and (11): v v F 0;m ¼ F 0;a a F 0;b b
ð10Þ
v v F 1;m ¼ F 1;a a F 1;b b
ð11Þ
where va and vb are volume fraction of components a and b, respectively. The volume fractions of individual components, vi, were obtained from their weight fraction (n) and ρ1,2 as per Eq. (12): vi ¼
ni ρ1;2 ρi
ð12Þ
Replacing Eqs. (10) and (11) to Eq. (9) leads to Eq. (13), which can be used to predict the friability of a binary mixture
Paul and Sun
from its porosity (εm), provided friability parameters of the constituent components of the mixtures are known. F r;m ¼ F m0 e ð F m1 εm Þ
ð13Þ
Regression Analysis Regression analysis was conducted to identify parameters that significantly (p = 0.05) correlate with friability using Design Expert 8.0.7 package (Stat-Ease, Inc., Minneapolis, MN). The mechanical parameters, σ, E, H, and TBI, of individual tablets for all excipients were included in the regression analysis.
RESULTS AND DISCUSSION The friability and compaction pressure followed a power-law relationship, i.e., log-log linear, and friability-tablet porosity followed an exponential relationship, i.e., log linear, (Fig. 1). The goodness of fitting in all cases was acceptable (R2 ≥ 0.95). Similar trends were previously reported for MCC and DCPA. (4) Thus, these relationships appear to hold for materials with diverse deformation properties. The points corresponding to >30% weight loss for starch and DCPA are not included in
b
100
HPC MCC LM DCPA Starch Mannitol
Weight loss (%)
10
1
0.1
1
0.1
0.0
100
0.6 HPC MCC LM DCPA Starch Mannitol
0.5
0.4
0.3
0.2
0.1
50
100
150
200
250
Compaction pressure (MPa)
0.1
0.2
0.3
Porosity
Compaction pressure (MPa)
0.0
HPC MCC LM DCPA Starch Mannitol
0.01
0.01
c
10
Weight loss (%)
a
Porosity
Fig. 1 Dependence of friability on (a) compaction pressure and (b) tablet porosity; (c) compressibility of different excipients.
subsequent analysis due to their little relevance to industrial practice. Generally, friability decreased with increasing compaction pressure, provided it led to a stronger tablet and lower porosity. The quantitative relationships were different among different powders (Fig. 1a). Highly plastic materials, such as HPC and MCC, exhibited friability much lower than 1.0% even at a low pressure (< 25 MPa) as observed before. (4,9) In fact, HPC exhibited the lowest friability in the series. Brittle LM and DCPA showed an intermediate friability behavior, where meeting the 1.0% friability criterion requires compaction pressures of ~100 MPa for LM and ~170 MPa for DCPA. Starch exhibited the highest friability, which required a much higher compaction pressure (~ 300 MPa) to meet the friability criterion. The friability of mannitol was intermediary between DCPA and LM. Except for mannitol, higher friability curve was associated with larger slope (Fig. 1a). Mannitol exhibited a smaller slope than LM and DCPA, and its friability curve crossed those of LM and DCPA (Fig. 1a). In the typical tableting pressure range of 100–300 MPa, friability followed the order of starch > DCPA ~ mannitol > LM > > MCC > HPC. The exponential dependence of friability on porosity (Fig. 1b) indicates the strong influence of tablet microstructure on weight loss. The evolution of tablet microstructure can be semi-quantitatively evaluated from the compressibility profiles
300
350
0.4
0.5
Tablet friability, mechanical properties, and prediction
of different excipients (Fig. 1c). (13,19) At 300 MPa, the plastic HPC and MCC formed tablets of nearly zero porosity when compressed, and the weight loss was essentially negligible for those highly consolidated tablets. In contrast, the hard DCPA could only form tablets with porosity of ~0.36. LM and mannitol exhibited similar compressibility profiles with porosities of ~0.08 at 300 MPa, while starch formed tablets with approximately 0.16 porosity. Thus, powder consolidation behavior of different materials corresponded well with their mechanical properties, where more plastic materials formed tablets of lower porosity. The plasticity parameter, 1/C, followed the order: HPC < MCC < Mannitol < LM < Starch < DCPA (Table I). By this measure, plasticity follows the reverse order: HPC > MCC > Mannitol > LM > Starch > DCPA. When normalized by porosity, tablet friability did not always follow the trend of plasticity (Fig. 1b). For example, friability at 0.2 porosity follows the order of Starch > Mannitol ≥ LM > > MCC > HPC > DCPA. Hence, thorough assessment and reliable prediction of tablet friability require knowledge of both the tablet porosity and mechanical properties. This is a result of the substantial difference in the bonding strength among materials. To examine the contributions of tablet strength on friability, weight loss - σ data were analyzed (Fig. 2a). Since a tablet can only be tested for either σ or friability, the weight loss and σ of tablet at the same porosity were determined separately from σ-porosity (Fig. S1) and friability-porosity (Fig. 1b) plots using two sets of tablets. The friability - σ plots thus generated followed a power-law relationship. As shown previously, (4) the empirical criterion of 2 MPa σ for tablet mechanical strength is again found generally sufficient for meeting the <1% friability in this work. The σ at 1.0% friability follows the order: LM < MCC < Starch < DCPA < Mannitol, where mannitol required σ slightly greater than 2 MPa. It is interesting that viscoelastic starch required lower tensile strength to meet the 1.0% weight loss criterion than DCPA and mannitol, which exhibited better tabletability than starch. Although more plastic materials generally tend to require lower tensile strength for meeting the 1% friability criterion, it is not the case for mannitol, which required higher σ than the less plastic
Table I Plasticity Parameters, 1/C and H0, of the Excipients
Excipient
1/C (MPa)
H0 (MPa)
HPC MCC LM DCPA Starch Mannitol
52.8 (6.3)b 76.1 (6.8)a 504.4 (19.2)a 3856 (146.7)a 600.1 (24.5)b 455.2 (12.4)a
16.8 (1.1)b 124.8 (8.3)a 393.1 (23.6)a 6798 (865)a 348.9 (18.8)b 263.2 (12.1)a
a
From the literature (20)
b
This work, see Fig. S2
DCPA and starch (Table II). Thus, plasticity alone does not fully account for the dissipation of stress during the process of collision and rebound in a friabilator, which may also be affected by elasticity. If so, reliable prediction of tablet friability will also benefit from a consideration of other mechanical properties in addition to σ and plasticity. Therefore, the correlations of tablet elastic modulus (E), hardness (H), and brittleness (TBI) with friability were also examined. Similar to the relationship between weight loss and σ (Fig. 2a), a power law relationship between tablet elastic modulus (E) and friability was also observed, where friability increased with decreasing E (Fig. 2b). A higher E suggests an intrinsically stiffer tablet, arising from either stronger interparticulate bonds, lower porosity, or both. The E corresponding to 1% friability for different materials followed the order; HPC < MCC << LM < DCPA < Starch < Mannitol. The E vs. porosity profiles (R2 > 0.99) are shown in Fig. 2c. The E at zero porosity followed the order of HPC ≈ MCC < LM ≈ Mannitol < Starch < DCPA. This implies that DCPA was intrinsically the most rigid material. However, the E of compressed tablets of DCPA and mannitol was comparable, because the porosity of mannitol tablet was much lower than that of DCPA tablet. It has been shown that more rigid or elastic materials have poorer ability to dissipate stress during an impact and thus can be more friable. In addition, the number of rebound increases with increasing tablet elasticity. (7) This coincides with the observation that mannitol had the highest E at 1% friability (Fig. 2b), and it concomitantly required greater σ at the corresponding friability than any other excipients (Fig. 2a). Friability - hardness and friability - TBI profiles (Fig. 3) were generated using values predicted at the same porosities from respective plots against porosity. Usually a harder material tends to have a higher E and TBI, both depend on the tablet porosity. The hardness corresponding to 1% friability follows the order: HPC << MCC < LM < Mannitol ≈ DCPA < Starch (Fig. 3a), while the hardness at zero porosity (H0) follows the order: HPC << MCC < Mannitol < Starch < LM << DCPA (Table I). The different rank ordering is attributed to different tablet porosities of different excipients corresponding to 1% friability. From the TBI vs. friability profiles (Fig. 3b), TBI corresponding to the 1% friability followed the order: Mannitol < MCC < Starch < DCPA < LM. Harder LM and DCPA exhibited larger TBI than the plastic MCC, suggesting some degree of correlation between H and TBI. In fact, greater friability was always associated with both greater H0 and higher TBI0 for the materials studied here. The σ and TBI profiles of HPC were not available, because HPC tablets did not fail under diametrical breaking test. However, the 1/C and H0 data (Table I) suggest that HPC was the most plastic material among these excipients, thus TBI is expected to be the lowest.
Paul and Sun
a
b5
5 MCC LM DCPA Starch Mannitol
HPC MCC LM DCPA Starch Mannitol
4
Weight loss (%)
4
We i g h t l o s s ( % )
Fig. 2 Relationship between friability and (a) tensile strength, and (b) elastic modulus, and (c) elastic modulus vs. porosity. HPC is not included in (a) because most HPC tablets did not break during diametrical break test.
3
2
3
2
1
1
0 0
2
4
6
8
σ (MPa)
0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
E (GPa)
c HPC MCC LM DCPA Starch Mannitol
E (GPa)
1
0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Porosity
A good correlation of tablet friability (Fr) with several key tablet mechanical properties, i.e., E, H, TBI, and σ, was individually shown in Figs. 2 and 3. In addition, a correlation with a set of mechanical properties was modelled by a multivariate regression analysis of all data, which led to a quadratic equation (Eq. (14) with an adjusted R2 of 0.87: lnðFr Þ ¼ −2:7 þ 0:88⋅E−0:96⋅σ þ 0:05⋅TBI þ 0:02⋅H −0:074⋅E⋅TBI −0:036⋅σ⋅TBI −0:02⋅σ
ð14Þ
2
The model shows that E, H, σ, and TBI all influence Fr at a statistically significant level (p < 0.05). Friability positively
Table II Fitted Parameters, F0 and F1, from Eq. (9) for Different Excipients from Friability vs. Porosity Relationship. Standard Errors of Fitting are Shown in Parentheses Excipients
F0
F1
HPC MCC LM DCPA Starch Mannitol
0.0076 (0.0003) 0.013 (0.001) 0.079 (0.007) 0.024 (0.002) 0.033 (0.001) 0.33 (0.03)
6.75 (0.46) 8.55 (0.25) 12.9 (1.6) 16.3 (1.0) 23.1 (3.2) 7.48 (0.41)
correlates with E, H, and TBI while negatively correlates with σ. This relationship is revealing as the regression analysis quantifies the relationship covers a range of each mechanical property due to variations in tablet porosity. Thus, prediction of Fr does not require the knowledge of tablet porosity, which is required if individual mechanical properties were used. Fig. 4 shows the contour plots of friability in the E - H and TS - TBI spaces. Since the excipients covered a wide range of materials and tablet mechanical properties, the contour plots can be used to guide efforts in developing tablet formulations that meet <1% friability criterion based on knowledge in these tablet mechanical properties, which can be routinely measured. The weight loss due to impact is related to attrition or abrasion. Attrition is the wear in a material due to impact or collision, while abrasion refers to removal of asperities due to shearing between surfaces. (8) We have observed that the attrition mechanism dominated at the tablet edges, resulting from breakage due to the large scale fracture of the tablet. Fig. 5 shows the images of tablets of different excipients after a friability run. It is evident that HPC and MCC tablets were minimally impacted by the edge attrition, while LM and mannitol tablets exhibited clear edge chipping. Severe edge chipping propagated to the tablet surface leading to partial or even complete loss of tablet edge for DCPA and starch.
Tablet friability, mechanical properties, and prediction
b
5 HPC MCC LM DCPA Starch Mannitol
W e i g h t l o s s ( %)
4
3
5
4
Weight loss (%)
a
Fig. 3 Dependence of friability on (a) hardness (H) and (b) TBI.
2
3 MCC LM DCPA Starch Mannitol
2
1
1
0
0 0
25
50
75
100
125
150
175
200
50
100
150
H (MPa)
It was suggested that the severity of abrasion inversely relates to the hardness. (10,21) In contrast, the ratio of material hardness (H) to critical stress intensity factor (KIc) directly relates to the weight loss during impact wear that mostly influences tablet attrition as shown in Eqs. (15) and (16). (6,11) KIc is an intrinsic material property related to the ability to resist propagation of a crack. Other things being equal, K Ic is higher for ductile materials than brittle materials. −
dm H m ðmass lossÞ ¼ ρ 1:5 dt E K Ic
ξ ðfractional mass lossÞ ¼ α
ð15Þ
ρv2 lH K 2Ic
ð16Þ
where E is Young’s modulus of the material, m and ρ are the mass and density of the tablet. Parameters v and l are the impact velocity and size of the particle.
a
b
182.4
8.0
6.0 4.0
2.0
95.8
300
350
400
Since the term, KH1:5 , measures material brittleness, (22) both Ic
equations imply that the weight loss strongly relates to material brittleness. However, KIc can be difficult to measure for pharmaceutical materials. Here, we report an empirical relationship, shown in Eq. (17), between friability and some readily accessible mechanical parameters of pharmaceutical tablets, including TBI, the 1/(C* σ), and the ratio of E to H. The parameter k can be regarded as a material constant. Fr ¼ k
1 E lnðTBI Þ C*σ H
ð17Þ
The parameter, C1* σ, takes account the effect of both plasticity and tensile strength. For example, at a given tensile strength, a more plastic material would exhibit lower friability. E/H could be considered an intrinsic material property, which includes combined effects of both elastic and plastic deformation on tablet friability. The positive, but nonlinear,
6.0
4.3
1.0
3.4
0.1
2.6 1.7
0.5
52.4
250
5.1
(Mpa)
H (Mpa)
139.1
200
TBI
1
0.9
5 10
0.0
9.1
380.8
337.1
293.5
249.9
206.3
3.5
162.7
E (GPa)
2.7
119.1
1.8
75.5
1.0
31.9
0.2
TBI
Fig. 4 Contour plots of effects of tablet mechanical properties on tablet friability (a) E - H and (b) σ - TBI. Lines correspond to specific tablet friability as labelled.
Paul and Sun
HPC
LM
DCPA
MCC
Mannitol
Starch
Fig. 5 Top view of tablet surface made of different materials at 100 MPa compaction pressure after a friability run (100 drops).
dependence between friability and E/H for the excipients studied is shown in Fig. S3. The larger coefficient for E than H in the regression analysis (Eq. 14) also suggests greater effect of E on friability than H. In contrast to plastic materials, tablets of largely elastic materials undergo significantly more collisions to dissipate their initial kinetic energy, (7) which leads to greater weight loss. This is consistent with the physical meaning of E/H ratio that, at the same mechanical strength, brittle tablets tend to exhibit higher friability. Figure 6 shows data fitting according to the Eq. (17) for the diverse excipients. An acceptable correlation (R2 > 0.98) was obtained in all cases. Excluding starch, the profiles appeared followed a global trend. Further research is required to verify and explain this interesting trend using a wider range of materials. Regardless of the underlying physical basis, Eq. (17) appears valid for diverse materials.
The strong correlation between tablet properties and friability suggests the possibility to predict the friability of a binary mixture from those of individual components. (17,23) Porosity appears centrally important, because it can strongly influence all other tablet properties, including friability. Table II lists the F0 and F1 parameters for different materials, where MCC and HPC show a low F0 due to their ductile nature and brittle LM, and Mannitol show large F 0 . However, F0 for DCPA was unexpectedly low. This could be attributed to the fact that DCPA tablets under the compaction pressures used in this study had high porosities. It is possible that the friability of DCPA tablets could be extremely low at zero porosity because of the exceptionally high mechanical strength. An analogous argument can be made for starch. The F1 parameter was overall low for plastic materials, implying that the friability of plastic materials is less sensitive to a change in tablet porosity. In the next step, Eq. (13) was employed to predict friability of binary mixtures. To challenge the robustness of Eq. (13), mixtures of two brittle excipients, i.e., LM-DCPA and LMmannitol, were also included in the data set. The experimentally determined friability of tablets of different mixtures was then correlated with the predicted values for a set of 14 formulations, totalling 153 tablets (Fig. 7). It was found that within 3% weight loss (140 tablets out of 153), an acceptable R2 (~0.95) and a slope value (0.97) close to unity was obtained. The good correlation suggests that the power mixing rule is reliable for predicting friability of a binary mixture from its constituents. However, when friability higher than 3% (up to 18%) was also included for analysis using Eq. (13), R2 and slope were only 0.9 and 0.73, respectively. Thus, the power mixing rule does not work satisfactorily for predicting friability of weak tablets. Fortunately, this does not have major impact in practice, because accurate prediction of friability around
Fr (% weight loss)
10
8
6 MCC LM DCPA Mannitol Starch
4
2
0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
. 1 Fig. 6 Friability vs. (C:σ Þ⋅ðHE )∙ln(TBI) relationship for different excipients.
Predicted Friability (% weight loss)
12 2.5
y = 0.97x
2.0
1.5
R2 ~ 0.95
1.0
0.5
0.0 0.0
0.5
1.0
1.5
2.0
2.5
Actual Friability (% weight loss) Fig. 7 Predicted vs. actual friability of binary mixtures with a friability window of 0–3%.
Tablet friability, mechanical properties, and prediction
1% is important in tablet formulation development. Overall, the predictive approach was successful for cylindrical tablets of a fixed weight (~300 mg). The model for predicting tablet friability of mixtures can potentially be used to assist future material-sparing tablet formulation development. The list of common excipients employed in routine tablet formulation development in a given company is usually not extremely large for cost and logistics reasons. Thus, if the F0 and F1 of an API and those of the common set of excipients are known, friability of formulated tablets could be predicted in silico using Eq. (13). This can lead to a computationally optimized tablet formulation, which is then experimentally verified using a small amount of API. Compared to concave or capsule shaped tablets, cylindrical tablets experienced impact force that was less evenly distributed over the tablet surface. Thus, for cylindrical tablets, the attrition mechanism is expected to play a more important role in the observed friability than concaved tablets. However, when the friability is high (> 5%, by visual observation), the extensive chipping rounded the edges and transformed the tablets eventually into a more concave shape. Thus, a transition in the dominating friability mechanism from attrition to abrasion took place. As the edges become more round, the surface defects facilitate crack propagation, which is required for removing particles from the surface. Moreover, the change in tablet shape also affects the contact between tablet and friabilator wall, which leads to different stress distributions during an impact. (8) This explains the poorer predictions in the friability range above 3% using Eq. (13). For tablets of mixed powders, higher friability always corresponded to a higher proportion of brittle material.
REFERENCES 1. 2.
3. 4. 5.
6. 7.
8. 9. 10. 11.
12.
13.
14. 15.
16. 17.
CONCLUSION The dependence of friability on tablet mechanical properties, compaction pressure, tablet porosity has been systematically analyzed for several common excipients and their mixtures exhibiting diverse mechanical properties. Viscoelastic starch exhibits the highest friability followed by brittle excipients (mannitol, DCPA, and LM) and then ductile excipients (HPC and MCC). A reasonably accurate model for predicting pharmaceutically relevant range of friability (0–3%) of binary mixtures is presented, which may be useful for expedited development and optimization of tablet formulation using a minimum amount of API.
18. 19. 20.
21. 22. 23.
Dexheimer SL. Terahertz Spectroscopy: Principles and Applications. Boca Raton: CRC Press; 2007. Seitavuopio P, Heinamaki J, Rantanen J, Yliruusi J. Monitoring tablet surface roughness during the film coating process. AAPS PharmSciTech. 2006;7:E31. USP. USP37/NF32 (Online), General Chapters. Tablet Friability. Rockville: United States Pharmacopoeial Convention; 2014. Osei-Yeboah F, Sun CC. Validation and applications of an expedited tablet friability method. Int J Pharm. 2015;484:146–55. Perumalla SR, Paul S, Sun CC. Enabling the Tablet Product Development of 5-Fluorocytosine by Conjugate Acid Base Cocrystals. J Pharm Sci. 2016;105:1960–6. Ghadiri M, Zhang Z. Impact attrition of particulate solids. Part 1: A theoretical model of chipping. Chem Eng Sci. 2002;57:3659–69. Bharadwaj R, Smith C, Hancock BC. The coefficient of restitution of some pharmaceutical tablets/compacts. Int J Pharm. 2010;402: 50–6. Kodam M. Attrition of pharmaceutical tablets. Doctoral dissertation: Purdue University; 2010. Gong XC, Sun CC. A new tablet brittleness index. Eur J Pharm Biopharm. 2015;93:260–6. Archard JF. Contact and Rubbing of Flat Surfaces. J Appl Phys. 1953;24:981–8. Duncan-Hewitt WC. Predicting the Relative Rate of Wear of Pharmaceutical Compacts Using the Mechanical-Properties of Their Constituent Crystals. Powder Technol. 1990;60:265–72. Sun CC. A novel method for deriving true density of pharmaceutical solids including hydrates and water-containing powders. J Pharm Sci. 2004;93:646–53. Kuentz M, Leuenberger H. Pressure susceptibility of polymer tablets as a critical property: A modified Heckel equation. J Pharm Sci. 1999;88:174–9. Fell JT, Newton JM. Determination of tablet strength by the diametral-compression test. J Pharm Sci. 1970;59:688–91. Gong XC, Chang SY, Osei-Yeboah F, Paul S, Perumalla SR, Shi LM, et al. Dependence of tablet brittleness on tensile strength and porosity. Int J Pharm. 2015;493:208–13. Patel S, Sun CC. Macroindentation hardness measurementModernization and applications. Int J Pharm. 2016;506:262–7. CY W, Best SM, Bentham AC, Hancock BC, Bonfield W. A simple predictive model for the tensile strength of binary tablets. Eur J Pharm Sci. 2005;25:331–6. Paul S, Sun CC. Lubrication with magnesium stearate increases tablet brittleness. Powder Technol. 2017;309:126–32. Sun CC. Microstructure of tablet—pharmaceutical Significance, assessment, and engineering. Pharm Res. 2017;34:918–28. Paul S, Sun CC. The suitability of common compressibility equations for characterizing plasticity of diverse powders. Int J Pharm. 2017;532:124–30. Hornbogen E. The role of fracture toughness in the wear of metals. Wear. 1975;33(2):251–9. Lawn BR, Marshall DB. Hardness, Toughness, and Brittleness: An Indentation Analysis. J Am Ceram Soc. 1979;62:347–50. Michrafy A, Michrafy M, Kadiri MS, Dodds JA. Predictions of tensile strength of binary tablets using linear and power law mixing rules. Int J Pharm. 2007;333:118–26.
