Impedance Spectroscopy: Applications to Electrochemical and Dielectric Phenomena
Vadim F. Lvovich
Language: English
Pages: 8
ISBN: 0470627786
Format: PDF / Kindle (mobi) / ePub
This book presents a balance of theoretical considerations and practical problem solving of electrochemical impedance spectroscopy. This book incorporates the results of the last two decades of research on the theories and applications of impedance spectroscopy, including more detailed reviews of the impedance methods applications in industrial colloids, biomedical sensors and devices, and supercapacitive polymeric films. The book covers all of the topics needed to help readers quickly grasp how to apply their knowledge of impedance spectroscopy methods to their own research problems. It also helps the reader identify whether impedance spectroscopy may be an appropriate method for their particular research problem. This includes understanding how to correctly make impedance measurements, interpret the results, compare results with expected previously published results form similar chemical systems, and use correct mathematical formulas to verify the accuracy of the data.
Unique features of the book include theoretical considerations for dealing with modeling, equivalent circuits, and equations in the complex domain, review of impedance instrumentation, best measurement methods for particular systems and alerts to potential sources of errors, equations and circuit diagrams for the most widely used impedance models and applications, figures depicting impedance spectra of typical materials and devices, extensive references to the scientific literature for more information on particular topics and current research, and a review of related techniques and impedance spectroscopy modifications.
representation of complex impedance data for ideal electrical circuits It is convenient to start the discussion of the fundamentals of impedance data representation with an analysis of very simple systems. If a sinusoidal voltage is applied to a pure resistor of value R, then the measured complex impedance is entirely resistive at all frequencies as Z* = R and the impedance magnitude | Z | = R. If a sinusoidal voltage is applied across a pure capacitor, the measured impedance can be calculated
capacitance is composed of a series combination of the compact Helmholtz layer and the diffuse-layer capacitances as: — = c DL +— — c (5-15) c HELMHOLTZ DIFFUSE The Helmholtz capacitor CH£LMHOLTZ (F/cm2) is potential-independent and is expressed by a capacitor formula: C HELMHOLTZ εε = --2- (5-161 τ ^ "' The thickness of the compact Helmholtz layer (LH ~ 1-2 nm) is approximately equal to the length of closest proximity where the discharging ions can approach the interface. For
finite diffusion for transmitting or absorbing boundaries or rises at -90° as a purely capacitive response for blocking or reflecting boundaries [40]. The problem of combining various types of diffusion processes, including diffusion with finite boundaries and homogeneous reactions were addressed earlier [34, 36]. One of the studied cases was finite reflecting boundary diffusion, which also shows a capacitive dispersion [37]. A total expression for diffusion impedance was derived as a
when high-conductivity suspended matter reaches a certain volume fraction Φ, the impedance spectrum is often unable to resolve the time constants, and the complex modulus spectrum is preferred in order to see two arcs [4, p. 200]. The Maxwell-Wagner model describes dispersions and composites as conducting spheres suspended in a continuous insulating medium [4, pp. 192198]. Several different models for a two-phase microstructure are possible: 1. "Series layer model" represents two phases stacked
possible to show that the minimum voltage VM[N required for the DEP force to exceed the thermal force scales as the inverse of the electrode radius r (or principal dimension) and the 1.5th power of the particle radius [27]: VMIN~"3/2/r (7-49) AC electrokinetic fields work optimally with microscale particles and devices, integrating seamlessly with microfluidics and miniaturized electrochemical impedance-based sensors [18, 21]. Microfluidic technologies reduce detection times, reduce biological