Rayleigh Isotopic Fractionation

Dynamic plots of Rayleigh Isotopic Fractionation. The classical Rayleigh fractionation applies for reactions with one substrate (s) and one product (p). The Branched Rayleigh applies for reaction netowrks where the substrate is converted to two products (p1 and p2). Here, the parameter `n' defines the fluxes through the network to p1.

x-axis: fraction consumed f (0 = fresh substrate, 1 = fully consumed)  |  y-axis: δ (‰) relative to standard

Classical Rayleigh
Equation (exact form)
δ̄p = [(1 + δ₀/1000) · (1−(1−f)α) / f − 1] · 1000
δ₀ substrate (‰)
α
ε = 1000(α−1) = −70.0 ‰ | 1000·ln α = −72.5 ‰
Branched Rayleigh
Equations (exact form)
δ̄p1 = [(1 + δ₀/1000) · (α₂α₁ / (nα₂+(1−n)α₃)) · (1−(1−f)α₁) / (α₁·f) − 1] · 1000
δ̄p2 = [(1 + δ₀/1000) · (α₃α₁ / (nα₂+(1−n)α₃)) · (1−(1−f)α₁) / (α₁·f) − 1] · 1000
δ₀ substrate (‰)
α1
α2
α3
n branching fraction
αeff = α₂α₁/(nα₂+(1−n)α₃) = 0.9295 | εeff = −70.5 ‰