Understanding Electrical Properties of Materials for Capacitance and Dielectrics

1. Electrical Properties of Materials Materials can do 2 things: • Polarize • Initial alignment of charge with applied voltage • Charge proportional to voltage • Temporary short-range alignment • Conduct • Continuous flow of charge with applied voltage • Current proportional to voltage • Continuous long-range movement

2. Capacitance • Electric potential always proportional to charge • Point • Sheet • Wire • Define capacitance as ratio: • ) • Measure of geometry’s ability to store charge • Know voltage and capacitance, calculate charge

3. Dielectrics • Polarizable material increases capacitance • Ability to “cancel” charge on plates draws more charge for given voltage, increases capacitance • Capacitance becomes • Actually k isn’t a “constant”. Can vary with frequency, temperature, orientation, etc.

4. Capacitance and Dielectrics • Typical capacitors

5. Capacitance and Dielectrics Constant electric field between two conducting sheets Potential between sheets Capacitance across sheets With Dielectric between

6. Dielectric constants

7. Examples of Capacitance • Problems 31,32,33,34 C = Q/V • Problems 35 • Problem 37 E = σ/εo Q = σA • Problem 38 E = σ/εo Q = σA • Problem 39 V = Q/C E = V/d • Problem 36 Q1 = CV1 Q2 = CV2

8. Dielectric Spectroscopy (Nat’s Research) • Most insulators contain polar molecules and free ions • These can align as a function of frequency (up to a point) • Where they fail to align is called “relaxation frequency” • Characteristic spectrum www.msi-sensing.com

9. TDR Dielectric Spectroscopy • Sensor admittance from incident and reflected Laplace Transforms. • Sample complex permittivity from sensor admittance. • Differential methods • Bilinear calibration methods.1 • Non-uniform sampling.2

10. Dielectric Permittivity in Epoxy Resin 1 MHz -1 GHz • Aerospace resin Hexcel 8552. • High frequency range 1 MHz – 1 GHz. • Temperature constant 125°C, transition decreases with cure. • TDR measurement method. www.msi-sensing.com

11. Permittivity in Epoxy Resin during Complete Cure Cycle www.msi-sensing.com

12. Application to cement hydration • Cement Conductivity - Variation with Cure • Imaginary counterpart of real permittivity (’’). • Multiply by  to remove power law (o’’). • Decrease in ion conductivity, growth of intermediate feature with cure • Frequency of intermediate feature does not match permittivity www.msi-sensing.com

13. Basic signal evolution in cement paste3 • Permittivity (ε’ ) and conductivity (εoωε’’) from 10 kHz to 3 GHz. • Initial behavior at zero cure time. • Evolution with cure time. • Low, medium, and high (free) relaxations.

14. Dielectric modeling in cement paste • 1 Cole-Davidson, 2 Debye relaxations4-7 www.msi-sensing.com

15. Model evolution with cement cure • Free-relaxation decreases as water consumed in reaction. • Bound-water8, grain polarization9 forms with developing microstructure. • Variations in frequency and distribution factor. • Conductivity decrease does not match free-water decrease. www.msi-sensing.com

16. Energy stored in capacitor • Work to move charge across V • Define • Example 17-11 • Energy Density • Energy Density proportional to field squared! V + 0