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Tablets & Capsules January 2015 29 The RI can also be obtained from surface reflectance using a simple expression derived from the Fresnel equations and assuming a 90-degree angle of incidence (Equation 3). h 5 [ 1 1 r ] Equation 3 1 2 r where r 5 Intensity of the sample reflection and n air 5 1 Intensity of a reference mirror reflection Studies on surface-density mapping of compacts using terahertz imaging spectrometers have shown excellent results [6, 7]. Surface-reflectance RI measurements are independent of ribbon thickness and therefore have no restriction on ribbon dimensions. However, the reflec - tance mode is generally less accurate than the trans - mission mode when measuring bulk RI. This is because factors such as surface roughness, which causes scat tering, can significantly decrease sample reflection intensity but have little effect on phase. In addition, the surface density may not be representative of the bulk sample. Terahertz sampling modes Figure 4 shows three terahertz sampling modes, each with a different design geometry, for measuring the density of roller-compacted ribbons. For transmission, the emitter-detector pair is placed on opposite sides of the ribbon (Figure 4a.) Laser micrometers may be mounted on the terahertz elements to provide a serial reading of the moving ribbon's thickness, followed by a terahertz reading at the same location. This combination allows nearly real- time density measurements. For most static samples, such as those measured for QA/QC, ribbon thickness would be recorded manually and the results entered into software as a sample parameter in the calculation of RI. Depending on the roller compactor's design and operating conditions, material may exit the rollers as a rigid, freestanding ribbon or it may adhere as a layer to the roller surface until a scraper removes it, which generally reduces the ribbon to flakes before they enter the mill. Rigid ribbons can be analyzed by transmission, but when they flake, density must be measured while the ribbons adhere to the roller. Alternatively, the ribbon can be measured in trans - flectance mode, where the roller serves as a metallic reflector between the angled emitter-detector pair (Figure 4b). In that case, because the terahertz waves must pass through the ribbon twice, its path is twice as long as it is in transmission. While that enhances sensitivity when measuring thin ribbons, it reduces the maximum thickness that can be measured. Because there is no practical way to measure thickness while a ribbon adheres to the roller, the minimum roller gap—plus a fixed percentage increase to account for the ribbon's elastic recovery—can provide a reasonable gauge of ribbon thickness for in-line applications. The surface-reflectance sampling mode shown in Figure 4c—essentially identical to the transflectance geometry in the absence of a metallic reflector—is included here for completeness. This mode is useful for surface characterization but is generally not as accurate as transmission or transflectance and is not a bulk measurement. Single-point density measurements Terahertz spectroscopy measures the RI of a solid directly, and converting the RI results to density, solid fraction, and percentage porosity requires calibration. The easiest conversion entails preparing powder compacts at different compaction forces and measuring them with an analyzer like the one in the photo on the next page. Apparent density is calculated from the sample weight and envelope volume, which are easily obtained by directly measuring the cylindrical compacts. Figure 5a shows the linear correlation between RI and apparent density for fresh and relaxed compacts of microcrystalline cellulose (MCC). The plot demonstrates the sensitivity of terahertz spectroscopy when measuring the elastic recovery of materials after compression. It also demonstrates the need to measure envelope volume simultaneous to terahertz analysis of freshly made compacts. To convert apparent density to percentage Figure 4 Sampling modes for terahertz measurements Laser micrometers Ribbon a. Transmission b. Transflectance c. Surface reflectance Detector Detector Detector Metallic reflector Emitter Emitter Emitter Figure 5 Correlation of refractive index (RI) to apparent density and to percentage porosity for fresh and relaxed MCC compacts over a range of compaction forces a. RI vs. apparent density b. RI vs. percentage porosity 1.9 1.85 1.8 1.75 1.7 1.65 1.6 1.1 1.2 1.3 1.4 1.5 Apparent density (g/cm 3 0 5 10 15 20 25 RI 1.9 1.85 1.8 1.75 1.7 1.65 1.6 % Porosity RI Fresh Relaxed Linear (fresh) Linear (relaxed) Fresh Relaxed Linear (fresh) Linear (relaxed)