Broadband Sum Frequency Generation Studies of Surface Intermediates Involved in Fuel Cell Electrocatalysis - Fuel Cell Catalysis: A Surface Science Approach - page 375

were used to show that both devices remained well synchronized throughout the
duration of each SFG-electrochemistry run. The potentiostat scanned the electrode
potential at 1 - 5 mV/s, while the CCD was usually read out at 5 spectra/s.
We have performed a detailed analysis of laser heating in Pt - CO experiments in
the TLE configuration, using methods described in [Lu et al., 2005; Hare et al.,
1998]. We first determined the adiabatic temperature jump DT after a single pulse,
and then a steady-state DT at 1 kHz. At 2050 cm 21 , the electrolyte absorption coeffi-
cient is 400 cm 21 [Bertie and Lan, 1996]. For an IR fluence of 20 mJ/cm 2 , in the elec-
trolyte, DT never exceeds 1.2K. The pulses are also absorbed by the electrode; the
femtosecond IR pulse being most important owing to its higher intensity. At the elec-
trode surface, electrons, phonons, and adsorbates are not in thermal equilibrium on the
femtosecond time scale. Based on ultrafast laser heating and pump-probe measure-
ments, we were able to estimate the heat jump at the Pt surface [Venkatakrishnan
et al., 2002]: DT ¼ 30K. However, it takes time for a hot Pt surface to heat the CO
adsorbates. During the time interval of order1 ps when the SFG signal is emitted
[Persson and Ryberg, 1981], the temperature jump of CO [Bonn et al., 2000] is
about 10K. These estimates were tested by varying the laser pulse energies, and we
observed no changes in the spectra when the pulse intensities were reduced by up
to a factor of four.

12.3 ANALYSIS OF SFG SPECTRA

For adsorbates on a metal surface, an SFG spectrum is a combination of resonant mol-
ecular transitions plus a nonresonant background from the metal. (There may also be
a contribution from the water - CaF 2 interface that can be factored out by following
electrode potential effects; see below.) The SFG signal intensities are proportional
to the square of the second-order nonlinear susceptibility [Shen, 1984]:

I SFG / j x (2) j 2 (12 : 1)

For simplicity, we assume nonresonant visible pulses and ignore the tensor nature of
x (2) which describes the well-known polarization conditions. For adsorbates on a metal
surface [Backus and Bonn, 2005; Cho et al., 2002],

b av (v IR , v vis )
[1 þ a av (v IR )U(0)][1 þ a e U(0)] 2

x (2)

SFG ¼

(12 : 2)

a av and b av are the linear molecular polarizability and the molecular hyperpolarizabil-
ity respectively, a e is the electronic polarizability, and U(0) is the local field in the
long-wavelength (k ¼ 0) limit. The linear polarizability is given by Persson and
Ryberg [1981] as

a av ¼ X

M

c m a m
1 þ [a m (v IR ) a av (v IR )]Q

(12 : 3)

m ¼ 1