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(sometimes called hardness), and friability, as well as their disintegration and dissolution characteristics. Then plot each attribute or characteristic as a function of the com- paction force. Figure 1 shows a tabletability profile, which plots tensile strength as a function of the applied compaction pressure. The compaction pressure, which can be calculated from the applied force and cross-sectional area of the punch face (Equation 1), allows you to compare the load- ing of different sizes of tablets. Equation 1: Tensile strength, which can be calculated from the breaking force and tablet dimensions, allows you to com- pare the mechanical strength of different sizes of tablets. The tablets for the experiments summarized here were made using round, flat-faced punches and the values were calculated using the Fell-Newton equation [2], where F is the breaking force, D is the diameter of the tablet, and T is the tablet thickness (Equation 2). Equation 2: Compaction pressures of 100 to 200 megapascals (MPa) are typical for pharmaceutical tablets, while pres- sures greater than 200 MPa are common for dietary sup- plement tablets. (The difference is due to the very high percentage of active ingredients dietary supplement tablets contain. Pharmaceutical tablets may contain less than 10 percent active and high percentage of binders.) There are many factors that will determine the target tablet strength, although 1 to 2 MPa of tensile strength is typically required for the tablet to remain intact through post-compaction processes, such as coating, transport/ handling, and packaging. From the example in Figure 1, it's clear that from a mechanical strength evaluation, microcrystalline cellulose (MCC) [3] with 0.5 percent magnesium stearate [4] provides the strongest compact. This is mainly due to the plastic deformation characteris- tics of MCC. The lactose monohydrate [5] with 0.5 per- cent magnesium stearate also provides a robust tablet at reasonable compaction pressures. But by blending the two excipients it's possible to add multiple functions to the formulation's performance, including plastic and brit- tle deformation characteristics. A 3-to-1 ratio of lactose- to-MCC provides a slightly stronger tablet than one made from pure lactose. With the evaluation of the mechanical strengths of the tablets at different compaction pressures complete, we can turn to evaluating the solid fraction. It indicates how much of the tablet's total volume is solid material. The solid fraction of a tablet corresponds to the ratio of the tablet's apparent density and absolute density, as mea- sured by a helium pycnometer [6]. The tablet's density can be calculated from its weight and volume. The con- verse of density is porosity—the total volume occupied by voids or air—and it is calculated by subtracting the solid fraction from 1. See equations 3 and 4. Equation 3: Equation 4: Figure 2 depicts a compactibility profile, which is the tablet's tensile strength as a function of the solid fraction. The MCC behavior is consistent with the tabletability profile we calculated above and yields the strongest com- pact, in this case at the lowest solid fraction. The 3-to-1 blend of lactose-to-MCC provides a stronger compact than lactose does at a given solid fraction. Figure 3 depicts the compressibility profile, which assesses how readily the material undergoes a change in volume when compressed. As the applied compaction pressure increases, so does the material's solid fraction. At a specific compaction pressure, the MCC yields the low- est solid fraction, whereas the lactose and the 3-to-1 lac- tose-to-MCC blend provide very similar solid fraction results. Now that we know the compaction characteristics of the excipients, let's add an API to the mix. Figure 4 depicts the tabletability profile of the 1) 3-to-1 lactose- to-MCC blend, 2) the 3-to-1 blend with the addition of 10 percent acetaminophen (APAP), and 3) the 3-to-1 blend with the addition 20 percent APAP. If a tensile Figure 1 Tabletability profile Compaction pressure (MPa) 0 50 100 150 200 250 Tensile strength (MPa) 7 6 5 4 3 2 1 0 MCC* Lactose* Lactose-MCC 3-to-1 blend Figure 2 Compactibility profile Solid fraction 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Tensile strength (MPa) 7 6 5 4 3 2 1 0 MCC* Lactose* Lactose-MCC 3-to-1 blend * Includes 0.5% magnesium stearate * Includes 0.5% magnesium stearate Tablets & Capsules September 2016 21 Pressure = Force Area Porosity = 1 – Tablet Density True Density Solid Fraction = Tablet Density True Density σ t = 2F DT