Dielectric Spectroscopy: Choosing the Right Approach - Pharmaceutical Technology

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Dielectric Spectroscopy: Choosing the Right Approach
This tutorial paper is meant to aid in dielectric-sensor selection


Pharmaceutical Technology
Volume 9, Issue 32, pp. 8293

Benefits associated with preconcentrators include improved sensitivity and versatility with various analytes. However, with the use of preconcentrators, sensor response is subject to hysterisis because the sensitive layer cannot reach immediate equilibrium with the environment.


Figure 3 (ALL FIGURES ARE COURTESY OF THE AUTHORS.)
Single frequency or spectroscopy? Relaxation processes in dielectric spectroscopy are very similar to relaxation processes in the optical regime. However, the interrogation frequencies used in dielectric spectroscopy are lower than optical frequencies, so this technique studies molecular interactions such as polymer reconfiguration within a matrix, percolation processes, and moisture diffusion. A major advantage of dielectric spectroscopy is that it can be performed over a wide band of measurement frequencies. The lowest boundary for frequency in existing dielectric spectroscopy is around 1 μHz, and the highest is in THz range. It is rarely practical to go to such extremes; most practical industrial measurements are accomplished in the range from 1 Hz to 100 MHz. In the PAT context, time available for inline measurements can be a limitation for a spectroscopic approach. This can be overcome by selecting frequencies at which the response to properties of interest provides adequate sample resolution. In this section, experimental data is analyzed using a spectroscopic approach, and, after some postprocessing, a single frequency optimum for measurements is selected.


Figure 4 (ALL FIGURES ARE COURTESY OF THE AUTHORS.)
A spectroscopic approach involves a detailed study of various processes that occur at different frequencies. Application of an oscillating electromagnetic field to samples results in either ionic charge transport, at low frequencies, or dielectric loss caused by energy dissipation at higher frequencies. These phenomena are dependant on physical properties of the dielectrics such as viscosity, density, and moisture content. Therefore, the response of a sample over a range of excitation frequencies provides information pertaining to the physical structure and composition. Figure 3, Figure 4, and Figure 5 provide an example of spectroscopic measurement. The impedance spectra of tablets with 25, 50, 75, and 100% coatings were measured. Figure 3 shows a monotonic trend in capacitance with coating levels. In Figure 3, the smooth trend in the frequency spectrum is a characteristic of dielectric spectroscopy measurements. Unlike other technologies such as NIR, measurement peaks resulting from relaxation times are visible with wide frequency bands spanning several decades. Moreover, the separation between samples at lower frequencies is greater because at lower frequencies the system is not as dissipative. It should be noted that the discontinuity in measurement from 1 kHz to 2 kHz is a result of the switching of internal circuitry in the measurement instrumentation and does not reflect dielectric behavior. Figure 4 shows the conductance spectrum for the four samples. At lower frequencies, the conductance measurements are too low for instrumentation. At low frequencies, conductance is a result of charge transport processes. Figure 5 shows the variation in phase spectrum with various coating thicknesses.


Figure 5 (ALL FIGURES ARE COURTESY OF THE AUTHORS.)
All chemicals that constitute a pharmaceutical sample influence the output of the sensor. Hence it is important to isolate the effect of the analyte under study on the sensor output from those from other chemicals. This is a complex problem that requires extraction and isolation of the contributions of each constituent based on a weighted convolution of their known relaxation processes and that observed in the mixture.

A simple solution is to create a calibration-based estimation model that uses the spectroscopic data from a narrow frequency range and makes approximations on the type of relaxations, transport mechanism, and chemical processes being observed (30–32). This method is most commonly used in situations in which the variations in the composition are in a narrow range and speed is of more importance than accuracy.


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