Leighton cycle and chemical system equations

Kinetic derivation · steady state · photochemical anticorrelation

1. Basic chemical system (NO–NO₂–O₃)

The so-called Leighton cycle is the dynamic closure between three species (NO, NO₂ and O₃), involved in the three fundamental reactions of the tropospheric photo-oxidative cycle:

(R1) — nitrogen dioxide photolysis

hν: UV radiation
O(³P): ground-state atomic oxygen

(R2) — ozone formation

M: third body (air, N₂, O₂), stabilises the reaction energy

(R3) — ozone titration

Leighton Cycle — Fig. 1 — The three fundamental reactions of the photo-oxidative cycle

2. Complete kinetic equations

Definitions:

\(\ce{NO}\), \(\ce{NO2}\), \(\ce{O3}\)
J: photolysis coefficient of \(\ce{NO2}\) (s^-1)
k₃: rate constant of the \(\ce{NO}\)+\(\ce{O3}\) reaction

loss: photolysis
production: NO oxidation

production from photolysis
loss via reaction with ozone

3. Elimination of O(³P)

Applying the steady-state approximation to atomic oxygen:

The ozone production rate therefore becomes:

4. Final equation for O₃

5. Steady state

At photochemical equilibrium, production equals destruction:

6. Leighton relationship

7. Physical meaning

The ratio \([\ce{NO2}]/[\ce{NO}]\) depends on:

solar radiation intensity \((J)\)
available ozone concentration
kinetic constant \(k_3\) of the titration reaction

As a direct consequence, if \(\ce{O3}\) increases:

the conversion \( \ce{NO -> NO2} \) increases
therefore \( [\ce{NO2}]/[\ce{NO}] \) increases

8. Origin of the NO₂/O₃ anticorrelation

NO emission (e.g. traffic, volcanism)

\([\ce{NO}]\uparrow\) → \([\ce{O3}]\downarrow\) by titration (R3)
\([\ce{NO2}]\uparrow\) as product of (R3)

Strong solar irradiance

\(J\uparrow\) → \([\ce{NO2}]\downarrow\) by photolysis (R1)
\([\ce{O3}]\uparrow\) through production via (R2)

The \(\ce{NO2}\)/\(\ce{O3}\) anticorrelation is therefore a direct consequence of photo-stationary cycle conservation, not a statistical coincidence.

9. Nocturnal regime

At night \(J = 0\): photolysis stops and the system is governed by (R3) alone:

The inverse proportionality follows directly:

Day and night regime — Fig. 3 — Daytime and nocturnal regime

10. When the Leighton cycle is not sufficient

Volatile Organic Compounds (VOCs)

Peroxy radicals \(\ce{RO2}\) convert \(\ce{NO}\) to \(\ce{NO2}\) without consuming ozone:

This produces \(\ce{O3}\) in excess of the Leighton prediction (breaking the anticorrelation).

Other perturbing factors

\(\ce{HO_x}\) radicals (\(\ce{OH}\), \(\ce{HO2}\), radical chains): introduce strong non-linearities
Long-range atmospheric transport (non-local \(\ce{O3}\), local \(\ce{NO2}\)): decouples the variables
Volcanic emissions (\(\ce{SO2}\), secondary oxidations, aerosol formation): alters ozone chemistry

11. Complete system

Including the additional terms due to VOCs:

\(P_{\text{background}}\) represents background ozone production (tropospheric transport, stratosphere); \(L_{\text{chem}}\) denotes the loss terms: reaction with \(\ce{OH}\) (chemical) and dry deposition (physical removal at the surface, not a reaction).

12. Conclusions

The Leighton cycle provides a fundamental framework for understanding ozone chemistry under steady-state conditions, but is only a starting point for describing the complexity of real atmospheric chemistry, which includes numerous additional species and processes.

References

Leighton, P. A. (1961). Photochemistry of Air Pollution (Vol. 9). Academic Press.
Seinfeld, J. H., & Pandis, S. N. (2016). Atmospheric Chemistry and Physics: From Air Pollution to Climate Change (3rd ed.). John Wiley & Sons.
Finlayson-Pitts, B. J., & Pitts Jr, J. N. (2000). Chemistry of the Upper and Lower Atmosphere: Theory, Experiments, and Applications. Academic Press.
Mannschreck, K., Gilge, S., Plass-Duelmer, C., Fricke, W., & Berresheim, H. (2004). Assessment of the applicability of NO-NO₂-O₃ photostationary state to long-term measurements at the Hohenpeissenberg GAW Station, Germany. Atmospheric Chemistry and Physics, 4(5), 1265–1277. https://doi.org/10.5194/acp-4-1265-2004 (Mannschreck et al., 2004)