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Because electron–phonon coupling times are of the order of 1–10 ps,
subpicosecond light pulses create nonequilibrium conditions within the
optical absorption depth of a metal. Because the electronic heat
capacity is typically an order of magnitude smaller than the lattice
heat capacity, the electrons are heated to temperatures approximately an
order of magnitude greater than those achieved by the lattice.
Electronic temperatures in range of several 1000’s of Kelvin can be
routinely generated, while the lattice remains below the melting point
of the metal.
The
“Empirical Friction Model”
In the early 1990’s, J. Misewich, T. Heinz and coworkers, and W. Ho and
coworkers, found that these nonequilibrium electrons can effectively
drive molecular chemistry at metal surfaces through diabatic excitation
of adsorbates. Two regimes of excitation have been suggested: multiple
electronic excitation of the adsorbate (understood in terms of a
modified Menzel-Gomer-Redhead model) and “electronic friction” (which
can be thought of as annihilation of electron hole pairs, or inelastic
electron scattering events resulting in transfer of energy to the
adsorbate). The former explicitly considers promotion of the adsorbate
from its ground electronic state to an excited state, with coupling to
the surface invoked only to describe the transition rate between the two
states; the latter considers evolution of the adsorbate within a
continuum of adsorbate–substrate states with coupling to the substrate
being explicitly identified with the substrate–adsorbate energy transfer
rate.
A useful phenomenological approach to modeling the dynamics that can
capture both types of substrate–adsorbate energy transfer has been
dubbed the “Empirical Friction Model” (see, for example, the work of M.
Wolf, G. Ertl, M. Bonn and coworkers). In this model, a third
temperature, the adsorbate temperature, is appended to the
two-temperature model and the energy transfer is parameterized in terms
of friction terms that couple the electronic heat bath and the lattice
heat bath to the adsorbate temperature bath. This adsorbate temperature
is understood to represent the degree of excitation along the relevant
reaction coordinate in a simple 1-D model.
(Left) A schematic illustration of the empirical friction model. The
adsorbate excitation is understood to be the result of frictional
coupling between the electronic and lattice degrees of freedom of the
metal and adsorbate. (Right) A schematic energy level diagram
illustrating how generation of a hot electron distribution in the metal,
resulting in population of energy states in resonance with the density
of states of the adsorbate, can result in electron transfer from the
metal to the adsorbate
Efficient Photoinduced Chemistry
Perhaps the simplest example of the chemistry that can be induced by
ultrafast pulses is desorption: the metal surface is heated by the laser
pulse, energy is coupled into the molecule–surface degrees of freedom
(molecule–surface stretch, frustrated rotation, frustrated translation)
and the adsorbate departs the surface as a neutral species. Such a
photoinduced desorption process can be readily observed in ultrahigh
vacuum by a quadrupole mass spectrometer as illustrated in the cartoon
below.
Early on it was found that photoinduced processes driven by ultrafast
laser pulses can be very efficient: a single pulse of on the order of
ten millijoules per square centimeter can desorb on the order of ten
percent of a monolayer. Furthermore, the yield is a highly non-linear
function of the fluence; the yield, Y, goes as the fluence, F,
to the power of n, where n is in the range of 4 to 9 or
more. This behavior does not directly reflect a multiple-photon process,
rather it reflects other non-linearities such as the exponential
dependence of the desorption yield on the adsorbate temperature (see
below). Furthermore, the non-linear behavior distinguishes this process
from photoinduced desorption resulting from single electronic
transitions driven by nanosecond ultraviolet pulses. Specifically, in
the non-linear regime, desorption can be efficiently driven by visible
and near-infrared photoexcitation where the photon energy is not high
enough to result in electronic excitation of the adsorbate by a
single-photon process, in contradistinction to excitation in the UV
where a linear response is observed.
(Left) Illustration of the photoinduced desorption of CO from Pd and
detection by a quadrupole mass spectrometer. (Right) An example
measurement of the dependence of the desorption yield on the absorbed
laser fluence, for CO desorption from Pd(111). The laser wavelength is
~800 nm.
Time-Resolved Measurements
Insight into the adsorbate–substrate energy coupling involved in surface
chemical reactions can be derived from time-resolved surface dynamics
measurements. A simple approach to time-domain observations is a
two-pulse correlation measurement, where the excitation pulse is split
into two pulses separated by a variable delay. The desorption (or
reaction) yield is then measured as a function of the delay between the
pulses. Because the response is non-linear (see above) there is a strong
enhancement of the yield at short delays; the desorption yield is
generally 5–10 times larger at zero delay than at long (~10–100 ps)
delays.
The two-pulse correlation measurement measures the overall relaxation
rate of the energy transferred from the metal surface into the reaction
coordinate. In a simplified picture, this be understood by viewing the
experiment as a “pump-probe” measurement where the first pulse
“pre-heats” the adsorbate–substrate complex and the second pulse induces
desorption. Thus, the amount of desorption is a measure of the level of
excitation of the system when the second pulse arrives. A more refined
understanding involves using a model, such as the empirical friction
model, to extract energy transfer rates from the measurement.
A schematic illustration of the two pulse correlation setup. The results
of such experiments can be viewed in the
research highlights
Linking Ultrafast Photoinduced Chemistry to Heterogeneous Catalysis
We are interested in examining the connections and contrasts between
ultrafast photoinduced chemistry and conventional surface chemistry. One
way in which the two may be connected can be understood at a basic level
by considering the mechanism for the photoinduced chemistry as a
two-step process. In the first step, the energy deposited in the
substrate is transferred to the adsorbate by coupling to the electronic
temperature bath. In the second step, the hot adsorbate desorbs with a
probability determined by the adsorbate–substrate potential energy
surface.
The empirical friction model can be used to estimate the
(time-dependent) rate of photoinduced reaction (e.g., simple
desorption or associative desorption) by assuming an Arrhenius rate
expression for the desorption rate:
Rd
=
q
n
exp[– Ea / kB Tads]
where the (time-dependent) temperature, Tads, is taken
from the result of the empirical friction model simulation, Ea,
is the activation energy for the desorption, kB is
Boltzmann’s constant,
n
is the preexponential factor, and
q
is the coverage. Under the provisional assumption that the
preexponential factor,
n,
and the activation energy for desorption, Ea, are
equal to those that describe the thermal (non-photoinduced) process,
this model can be understood as “pseudo-thermal”: the coupling of energy
from the substrate to the adsorbate is a non-thermal, multiple
electronic process, whereas the evolution of the adsorbate following the
energy transfer proceeds on the same potential energy surface that
governs thermal desorption.
Although this model is simple, it at least provides a means for us to
begin to get a quantitative handle on the ultrafast photoinduced process
and for comparing and contrasting ultrafast photoinduced chemistry and
conventional surface chemistry. Some of our efforts have been directed
toward testing the applicability of this model.
An illustration of the “pseudo-thermal” model for ultrafast photoinduced
desorption. The mechanism is understood in terms of two steps: (i) coupling
of energy from the substrate to the adsorbate occurs via a non-thermal,
multiple electronic process, and (ii) evolution of the adsorbate
proceeds on the same potential energy surface that governs thermal
desorption. |
