MIT10_626S11_lec05

# MIT10_626S11_lec05 - Lecture 5 Impedance spectroscopy MIT...

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Unformatted text preview: Lecture 5. Impedance spectroscopy MIT Student Last time we talked about the non-linear response to DC voltage, and today we will discuss about the AC linear response at frequency ω . A simplified model of voltage response of galvanic cell can be written as V(I,Q)=V (Q)-η (I,Q) If we consider small perturbations around a reference state (constant current), voltage, current and charge can be expressed as Δ V=V-V ref Δ I=I-I ref Δ Q=Q-Q ref Since we are assuming small changes (perturbation), we can use taylor expansion to express ∆ V ≃ voltage, ∆ ! ! !"# where + R !"# ∆ I …(1) ! ! !"# = ! ! ! ! ! !"# , ! !"# = ! ! ! ! ! ! !"# , ! !"# − ! ! ! ! ! !"# , ! !"# , C !"# = differencial capacitance R !"# = ! ! ! ! ! !"# , ! !"# = − ! ! ! ! ! !"# , ! !"# , R !"# = differencial resistance ∆ I = ∂ ∆ Q ∂ t Consider alternating-current (AC) sinusoidal perturbations at frequency ω and introduce complex amplitudes for the perturbations (to induce phase lag): Δ V=Re( V e i ω t )= V cos( ω t) ; chose t to fit real number for Δ V, V :real number) i Δ I= Re( I e ω t )= ϐ I ϐ cos( ω t+ ϕ ) i t Δ Q= Re( Q e ω ) , where I =i ω Q since ∆ I = ! ∆ ! !...
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MIT10_626S11_lec05 - Lecture 5 Impedance spectroscopy MIT...

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