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0581.5271 Electrochemistry for Engineers
LECTURE 12
Lecturer: Dr. Brian Rosen Office: 128 Wolfson
Office Hours: Sun 16:00
Final Exam • No books• No notes• Calculator required (no graphing calculators)• Equation sheet provided• Standard reduction potentials provided • Question types
– Open answer– Drawing graphs / identifying graphs– Calculations
• 3 hours (test designed for 2 hours)
Coupled Characterization Examples
• Spectraelectrochemistry • Sum Frequency Generation• Scanning Electrochemical Microscopy• Synchrotron Radiation
– In Situ XRD, XPS• Electrochemical Quartz Crystal Microbalance• Electrochemical AFM
Polarization using incident E-M field
No net polarization(Centrosymmetric)
Molecules have a polarizability, P, which describes how E-M radiation polarizes molecules
Pnet=0
Pnet≠0
Linear vs. Nonlinear Optics
• Linear Optics: Polarizability depends on the first order susceptibility term χ (1):E
• Nonlinear Optics: Polarizability depends on higher order terms e.g. χ (2):EE
• SFG is a second order nonlinear process and is dependent on χ (2):EE
P=εo (χ (1):E + χ (2):EE + χ (3):EEE +……)Second order (and ALL even orders) susceptibility term is zero in Centrosymmetric media (i.e. bulk of most materials) because it is athird rank tensor
SFG is Surface Selective
• χ (2) is nonzero at the surface because the molecules are no longer centrosymmetric
• Consequence 1: SFG does NOT probe the bulk• Consequence 2: SFG can be a good in-situ
electrochemical technique
Bulk vs. Surface
Sum Frequency Generation (SFG)must be Infrared and Raman active
Virtual electronic state(i.e. no resonance)
ν=0
ν=1
Infrared Raman-Stokes SFG
ωIRωIR
ωVIS ωSFG
ωIR
ωIR
ωSHG
ν=2
SHG
Sum Frequency Generation (SFG)must be Infrared and Raman active
Virtual electronic state(i.e. no resonance)
ν=0
ν=1
Infrared Raman-Stokes SFG
ωIR ωIR
ωVIS ωSFG
SAME SELECTION RULES AS IR AND RAMAN
Conventional SFG
• In conventional SFG, an IR beam coherently and resonantly excites the first transition.
• The excited population (υ=1) is up-regulated by a visible laser to a virtual (non-resonant) state.
• Frequency resolution is given by scanning the IR laser across different infrared frequencies.
• Disadvantage: No time resolution! Not so useful for in-situ electrochemical system when you want to scan electrode bias.
Second order Susceptibility has 2 contributions
χ (2) = χ(nr) (2) + χ(r) (2)
• Susceptibility has a non-resonant and resonant contribution. (we only care about the resonant)– Resonant: vibrational modes – Non-Resonant: electronic transitions of metal surface.
• Both contributions are subject to so-called Free Induction Decay (covered later)
Coherent Waves• Coherence: Waves always have same relative
phase, θ. (Leads to stationary interference i.e. constructive and destructive)
Free Induction Decay (FID) Illustrated
= Molecule with polarization, P, and a vibrational mode oscillating at a frequency, ω
ω
ω ω ω+dω
Weak H-bonding
Moderate H-bonding
Strong H-bonding
ω-dωDue to inhomogeneous environment, the SFG signalfrom different molecules (from the same resonant transition)will have slightly different frequencies and will eventually become incoherent, causing decay in the SFG signal.
Consequences of Time-Bandwidth Product
Because Fourier Transform sets a constant limitfor the value of the TB-P for a given waveform,
longer pulses will have narrower bandwidths and
shorter pulses will have wider bandwidths.
Broadband (BB-SFG)
• Rather than scanning the IR laser, a spectrally broad femtosecond (fs) IR beam pulses with a large linewidth, Γ, to probe the surface.
• All vibrations with resonances in the band will have a population excited (υ=01) .
• BB-SFG resolution comes from a temporally long (spectrally short) VIS pulse such that the resonant population is excited to a virtual state.
Frequency Resolved BB-SFG
1. IR pulse coherently excites υ=01 transition and VIS pulse (overlapping temporally and spatially) up-regulates this population to virtual electronic state.
2. Spectrally narrow and temporally long VIS pulse gives good frequency resolution and no time resolution.
Time Resolved: Offset IR – VIS
1. IR pulse coherently and resonantly excites υ=01 transition
2. Coherence decays at T due to FID
3. Duration of VIS pulse MUST be less than T or no coherence will remain (VIS pulse spectrally wide).
Disadvantage: multiple resonant modes
In many experiments, having two resonant transitions is unwantedbecause it convolutes the analysis of the SFG spectra.
If the both the IR and VIS pulses are spectrally wide, the probability of overlapping with a resonance in another electronic state is high, leading to poor ω-resolution.
SECM Collection Modes • Substrate generation tip collection (SG/TC)• Tip generation substrate collection (TG/SC)• Competitive • Constant current or constant height
Competitive
Synchrotron Radiation
Acceleration of electrons using powerful magnets creates radiation in the tangential direction. At 99.9% the speed of light, this is most X-ray radiation
10,000+’s more powerful than laboratory X-ray sources
Subtract Background, Convert Energy Space to K-Space
k is the “wavenumber” and had units of inverse distance
Producing X-Rays at APS
• https://www.youtube.com/watch?v=NQygZ1sikdI
Electrochemical Quartz Crystal Microbalance
Quartz is a piezoelectricResonant frequency dependent on the mass of the quartz electrode