Her current research includes quantitative measurement of optical constants for solid and liquid materials. She is the author of over 40 refereed publications.
He worked as a postdoctoral fellow at the University of Southern California before his year career at the Pacific Northwest National Laboratory, primarily practicing infrared spectroscopy of clusters and gases. He is now retired and living happily ever after. Matt Taubman.
Quantum Mechanical Simulations of Biopolymer Vibrational Spectra
Systems that Dr. Russ Tonkyn. He received his PhD for work on ion-molecule reaction in the gas phase in , followed by post-doctoral work at Brookhaven National Lab where he studied the pulsed field ionization of extremely high Rydberg states prepared by single photon absorption. He has been at PNNL since and has worked on many diverse projects over the years, including various gas, liquid and solid databases using FTIR and Raman spectroscopy.
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Parsons, R. Lovett, and D. Ferraro and Louis J. Figure 1. Sinusoidal Current Response in a Linear System. The excitation signal, expressed as a function of time, has the form. An expression analogous to Ohm's Law allows us to calculate the impedance of the system as:. If we plot the applied sinusoidal signal E t on the X-axis of a graph and the sinusoidal response signal I t on the Y-axis, the result is an oval see Figure 2.
This oval is known as a "Lissajous Figure". Analysis of Lissajous Figures on oscilloscope screens was the accepted method of impedance measurement prior to the availability of modern EIS instrumentation. The potential is described as,. Look at Equation 9 in the previous section. If the real part is plotted on the X-axis and the imaginary part is plotted on the Y-axis of a chart, we get a "Nyquist Plot" see Figure 3.
Notice that in this plot the Y-axis is negative and that each point on the Nyquist Plot is the impedance at one frequency. Figure 3 has been annotated to show that low frequency data are on the right side of the plot and higher frequencies are on the left. On the Nyquist Plot the impedance can be represented as a vector arrow of length Z.
Nyquist Plots have one major shortcoming. When you look at any data point on the plot, you cannot tell what frequency was used to record that point. The Nyquist Plot in Figure 3 results from the electrical circuit of Figure 4. The semicircle is characteristic of a single "time constant". Electrochemical impedance plots often contain several semicircles.
Often only a portion of a semicircle is seen. Another popular presentation method is the Bode Plot. The Bode Plot for the electric circuit of Figure 4 is shown in Figure 5. Unlike the Nyquist Plot, the Bode Plot does show frequency information. Figure 5. Bode Plot with One Time Constant. Electrical circuit theory distinguishes between linear and non-linear systems circuits.
Impedance analysis of linear circuits is much easier than analysis of non-linear ones. The following definition of a linear system is taken from Signals and Systems by Oppenheim and Willsky:. A linear system Mathematically, let y 1 t be the response of a continuous time system to x 1 t ant let y 2 t be the output corresponding to the input x 2 t. Then the system is linear if:.
For a potentiostated electrochemical cell, the input is the potential and the output is the current. Electrochemical cells are not linear!
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Doubling the voltage will not necessarily double the current. However, Figure 6 shows how electrochemical systems can be pseudo-linear. If you look at a small enough portion of a cell's current versus voltage curve, it appears to be linear. With such a small potential signal, the system is pseudo-linear. We don't see the cell's large nonlinear response to the DC potential because we only measure the cell current at the excitation frequency.
If the system is non-linear, the current response will contain harmonics of the excitation frequency. A harmonic is a frequency equal to an integer multipled by the fundamental frequency. Some researchers have made use of this phenomenon. Linear systems should not generate harmonics, so the presence or absence of significant harmonic response allows one to determine the systems linearity. Other researchers have intentionally used larger amplitude excitation potentials. They use the harmonic response to estimate the curvature in the cell's current voltage curve. Measuring an EIS spectrum takes time often up to many hours.
The system being measured must be at a steady state throughout the time required to measure the EIS spectrum. A common cause of problems in EIS measurements and analysis is drift in the system being measured. In practice a steady state can be difficult to achieve. The cell can change through adsorption of solution impurities, growth of an oxide layer, build up of reaction products in solution, coating degradation, or temperature changes, to list just a few factors. Standard EIS analysis tools may give you wildly inaccurate results on a system that is not at steady state.
Time and Frequency Domains and Transforms.