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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Catalytic resonance theory | 3/3 | https://en.wikipedia.org/wiki/Catalytic_resonance_theory | reference | science, encyclopedia | 2026-05-05T10:46:31.645312+00:00 | kb-cron |
== Characteristics of Dynamic Surface Reactions == Catalytic reactions on surfaces exhibit an energy ratchet that biases the reaction away from equilibrium. In the simplest form, the catalyst oscillates between two states of stronger or weaker binding, which in this example is referred to as 'green' or 'blue,' respectively. For a single elementary reaction on a catalyst oscillating between two states (green & blue), there exists four rate coefficients in total, one forward (k1) and one reverse (k−1) in each catalyst state. The catalyst switches between catalyst states (j of blue or green) with a frequency, f, with the time in each catalyst state, τj, such that the duty cycle, Dj is defined for catalyst state, j, as the fraction of the time the catalyst exists in state j. For the catalyst in the 'blue' state:
D
B
=
τ
B
τ
t
o
t
a
l
{\displaystyle D_{B}={\frac {\tau _{B}}{\tau _{total}}}}
The bias of a catalytic ratchet under dynamic conditions can be predicted via a ratchet directionality metric, λ, that can be calculated from the rate coefficients, ki, and the time constants of the oscillation, τi (or the duty cycle). For a catalyst oscillating between two catalyst states (blue and green), the ratchet directionality metric can be calculated:
λ
=
k
1
,
b
l
u
e
D
B
+
k
1
,
g
r
e
e
n
(
1
−
D
B
)
k
−
1
,
b
l
u
e
D
B
+
k
−
1
,
g
r
e
e
n
(
1
−
D
B
)
{\displaystyle \lambda _{\ }={\frac {k_{1,blue}D_{B}+k_{1,green}(1-D_{B})}{k_{-1,blue}D_{B}+k_{-1,green}(1-D_{B})}}}
For directionality metrics greater than 1, the reaction exhibits forward bias to conversion higher than equilibrium. Directionality metrics less than 1 indicate negative reaction bias to conversion less than equilibrium. For more complicated reactions oscillating between multiple catalyst states, j, the ratchet directionality metric can be calculated based on the rate constants and time scales of all states.
λ
=
∑
j
τ
j
k
1
,
j
∑
j
τ
j
k
−
1
,
j
{\displaystyle \lambda _{\ }={\frac {\sum _{j}\tau _{j}k_{1,j}}{\sum _{j}\tau _{j}k_{-1,j}}}}
The kinetic bias of an independent catalytic ratchet exists for sufficiently high catalyst oscillation frequencies, f, above the ratchet cutoff frequency, fc, calculated as:
f
c
=
k
I
I
D
I
I
4
(
2
−
1
)
{\displaystyle f_{c}={\frac {k_{II}D_{II}}{4({\sqrt {2}}-1)}}}
For a single independent catalytic elementary step of a reaction on a surface (e.g., A* ↔ B*), the A* surface coverage, θA, can be predicted from the ratchet directionality metric,
θ
A
=
1
1
+
λ
{\displaystyle \theta _{A}={\frac {1}{1+\lambda }}}
== Experiments and Evidence == Catalytic rate enhancement via dynamic perturbation of surface active sites has been demonstrated experimentally with dynamic electrocatalysis and dynamic photocatalysis. Those results may be explained in the framework of catalytic resonance theory but conclusive evidence is still lacking:
In 1978, the electro-oxidation of formic acid on a platinum electrode was studied under the application of constant potentials and square-wave pulsed potentials. The latter was found to enhance the current density (and thus catalytic activity) by up to 20 times compared to the potentiostatic conditions, with the optimal wave amplitude and frequency of 600 mV and 2000 Hz, respectively. In 1988, the oxidation of methanol on a platinum electrode was conducted under pulsed potentials between 0.4 and 1.18 V, resulting in an average current almost 100 times higher than the steady-state current at 0.4 V. Using the formic acid electro-oxidation reaction, oscillation of the applied electrodynamic potential between 0 and 0.8 volts accelerated the formation rate of carbon dioxide more than an order of magnitude higher (20X) than what was achievable on platinum, the best existing catalyst. The maximum catalytic rate was experimentally observed at a frequency of 100 Hz; slower catalytic rates were observed at higher and lower electrodynamic frequencies. The resonant frequency was interpreted as the oscillation between conditions favorable to formic acid decomposition (0 V) and conditions favorable to form CO2 (0.8 V). The concept of implementing periodic illumination to improve the quantum yield of a typical photocatalytic reaction was first introduced in 1964 by Miller et al. In this work, they showed enhanced photosynthetic efficiency in the conversion of CO2 to O2 when the algal culture was exposed to periodic illumination in a Taylor vortex reactor. Sczechowski et al. later implemented the same approach for heterogeneous photocatalysis in 1993, where they demonstrated 5-fold increment in photoefficiency of formate decomposition by cycling between light and dark conditions with periods of 72 ms and 1.45 s respectively. They hypothesized that upon illumination of the catalyst, there is a critical illumination time during which absorbed photons generate oxidizing species (hvb+) on the surface of the catalyst. The generated species or their intermediates go on to react with substrates on the surface or in the bulk. During dark period, adsorption, desorption, and diffusion generally occurs in the absence of photons. After a critical recovery period in the dark, the photocatalyst can efficiently use photons again when photons are reintroduced. A summary of work involving “dynamic” photocatalysis was provided by Tokode et al. in 2016. Dynamic promotion of methanol decomposition was demonstrated on 2 nm Pt nanoparticles using pulsed light. The rate acceleration to form H2 relative to static illumination was attributed to the selective weakening of adsorbed carbon monoxide, thereby also increasing the quantum efficiency of applied light. In 2021, Sordello et al. experimentally demonstrated a 50% increase of the quantum yield for the Hydrogen Evolution Reaction (HER) over Pt/TiO2 nanoparticles via formic acid photoreforming under Controlled Period Illumination (CPI). Implementation of catalyst dynamics has been proposed to occur by additional methods using oscillating light, electric potential, and physical perturbation.
== References ==