Broadband Dielectric Spectroscopy

TDR High-Frequency Dielectric Spectroscopy

TDR Dielectric Spectroscopy uses an innovative approach to high frequency dielectric spectroscopy. The sensing electrodes are measured not with a continuous frequency wave, but with a rapid voltage pulse containing a broad range of frequencies at once. [1-3] The reflected signal is captured after an appropriate propagation delay, separating sensor response from connecting-line artifacts on the basis of delay time.

The advantage of this approach is that the reflected signal is displayed in either time or frequency domain.  In the frequency domain the signal is Fourier-Transformed to a dipole rotation spectrum, providing detailed quantitative information on the changing rotation spectrum. In the time domain the signal is monitored in its direct transient form, providing simple qualitative indicators of the changing rotation spectrum and allowing instrument artifacts to be diagnosed more easily.

TDR Dielectric Spectroscopy is related to conventional Time- Domain- Reflectometry used in closed-circuit fault testing [9-10]. However, TDR Spectroscopy focuses on a time and frequency analysis from a lumped capacitance sensor while conventional TDR focuses on spatial differences along a distributed transmission line. Details are given in references below.

TDR High-Frequency Examples

A typical TDR spectrum obtained in our laboratory for ethanol is shown below. On the left is real permittivity and on the right is the imaginary permittivity, both shown over a frequency range 100 MHz to 10 GHz. The data shows the expected dipolar relaxation around 1 GHz, which continues to trail off in permittivity and loss to around 10 GHz. A theoretical model based on Debye theory of viscous rotation [10] is overlaid on both real and imaginary components for comparison.

The relaxation spectrum shifts with typical variations in material parameters such as temperature, viscosity, molecular weight, mixture concentration, etc.  For example, the data below shows the ethanol relaxation varying with temperature, with the loss peak increasing to around 2 GHz at 55°C.  Similar changes are seen with other material variations such as addition of water or substitution of different molecular-weight alcohols. 

The data can also be presented in Cole-Cole or complex impedance format, to further aid in the analysis [9]. For example, the data below shows a complex impedance arc in cement paste immediately after mixing, at higher frequencies and shorter cure times than allowed by low-frequency measurement. An arc in the complex impedance plane demonstrates that material behaves as an electrolyte resistance in parallel with an interelectrode capacitance, allowing the bulk resistance to be quantified independent of electrochemical effects at the electrodes.

Low-Frequency Dielectric Spectroscopy

We also provide low-frequency dielectric and impedance spectroscopy using standard HP4192 Impedance Analyzer methods.  Samples are placed in 4-wire capacitance cell and measured over a frequency range 10 Hz to 10 MHz.  Results can be modeled in the Cole-Cole permittivity plane or complex impedance plane as appropriate.

An example of low-frequency dielectric spectroscopy is a cured epoxy thermoset shown below. The epoxy shows polymer-chain relaxation in the 1 kHz to 1 MHz range, with a broad roll-off in permittivity seen on the left, and a similarly broad loss peak seen on the right.

Another example is a porous glass sample shown below. The sample shows strong low-frequency dispersion due to surface currents along pore edges accompanied by interfacial charging at grain boundaries (Maxwell-Wagner effect).  As the sample is heated to drive off moisture the low-frequency dispersion disappears, and only reappears as the sample is returned to ambient for a period of time.

Combined High- and Low-Frequency Dielectric Spectroscopy

TDR and low-frequency measurement can be combined over an extremely wide frequency range.  The data below shows the real permittivity of curing cement over a frequency span of 9 decades, from 10 Hz to 10 GHz. Two relaxations are seen in the figure below, a low-frequency relaxation due to the mobility of free ions, and high-frequency relaxation due to the mobility of bound water.  The high-frequency relaxation straddles both TDR and low-frequency measurements. 

These are some examples of high- and low-frequency dielectric spectroscopy and numerous others exist.  Please contact us for information about additional applications. 

Technical References

Additional information on TDR Dielectric Spectroscopy, TDR fault detection, and general dielectric theory can be found at:

1. N.E. Hager III, R.C. Domszy, M.R. Tofighi, "Smith-chart diagnostics for mult-GHz Time Domain Reflectometry Dielectric Spectrscopy, Rev. Sci. Instrum. 83, 025108 (2012). downloadable pdf* msi_smith_rsi_2012.pdf 

2. R. H. Cole, J. G. Berberian, S. Mashimo, G. Chrssikos, A. Burns, and E. Tombari, "Time domain reflection methods for dielectric measurements to 10 GHz", J. Appl. Phys 66, 793 (1989)

3. N.E. Hager III, "Broadband Time-Domain-Reflectometry Dielectric Spectroscopy using variable-time-scale Sampling", Rev. Sci. Instrum. 65(4), April 1994, p 887. downloadable pdf* msi_tdr_rsi_1994.pdf 

4. H. Fellner-Feldegg, J. Chem Phys. 73, 616 (1969).

5. M. Merabet and T. K. Bose, Dielectric measurements of water in the radio and microwave frequencies by Time Domain Reflectometry", J. Chem. Phys. 92 (1988) 6149.

6. R. H. Cole, G. Delbos, P. Winsor IV, T. K. Bose, J. K. Moreau, "Study of dielectric properties of water/oil and oil/water microemulsions by Time Domain and Resonance Cavity Methods", J. Phys. Chem., 89, 3338-3343 (1985).

7. Satoru Mashimo and Toshihiro Umehara, "Structures of water and primary alcohol studied by microwave dielectric analysis", J. Chem. Phys. 95 (9), 1 November 1991. 

8. J. Barthel, K. Bachhuber, R. Buchner and H. Hetzenauer. "Dielectric spectra of some common solvents in the Microwave Region. Water and Lower Alcohols" Chem. Phys. Letters 165 (4) 19 January 1990 369.

9. N. Asaka, N Shinyashiki, T. Umehara, S. Mashimo "Dielectric Dispersion of primary alcohols in polymer complex" J. Chem. Phys. 93 (11) 1 December 1990 8273. 

10. "Time Domain Reflectometry Clearinghouse": http://www.iti.northwestern.edu/tdr

11. Hewlett-Packard Application Note 62, "TDR Fundamentals".

12. A. K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics Press, London (1983).

13. Arthur R. Von Hippel, Dielectric Materials and Applications, Wiley, New York (1954).
     

1 Copyright 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Review of Scientific Instruments and may be found at http://link.aip.org/link/?RSI/83/025108 

2 Copyright 2004 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Applied Physics and may be found at http://link.aip.org/link/?jap/96/5117.