Licht-im-Terrarium: Literaturdatenbank

Enthält alle gekoppelten Differentialgleichungen, Absorptionsspektren und Quanteneffizienzen für die Berechnung des Vitamin-D3-Gleichgewichts.

Eq 2:
Photoisomer concentrations Ci
i = 1: 7DHC, 2: preD3, 3:Tach, 4:Lumi, 5:Tox
dC1/dt = int dλ I∗(λ) [−ε1(λ)C1φ12 + ε2(λ)C2φ21]
dC2/dt = int dλ I∗(λ) [−ε2(λ)C2φ21 + ε1(λ)C1φ12
− ε2(λ)C2φ23 + ε3(λ)C3φ32
− ε2(λ)C2φ24 + ε4(λ)C4φ42
− ε2(λ)C2φ25]
dC3/dt = int dλ I∗(λ) [−ε3(λ)C3φ32 + ε2(λ)C2φ23]
dC4/dt = int dλ I∗(λ) [−ε4(λ)C4φ42 + ε2(λ)C2φ24]
dC5/dt = int dλ I∗(λ) [ε2(λ)C2φ25]

Eq. 3, ref. to [17]
photokinetic factor
I∗(λ) = I0(λ) * [ 1 − 10^[−D(λ)] ]/D(λ)

Eq. 1
total absorbance of the solution
D(λ) = l sum(i=1:5) εi(λ) Ci

quantum yields φij
for the reversible photoreactions: Ref[18]
for the irreversible photoconversion: Ref[19]
Fig 1
φ12 = 0.26 7DHC → preD3
φ21 = 0.015 preD3 → 7DHC
φ23 = 0.48 preD3 → Tach
φ32 = 0.10 Tach → preD3
φ24 = 0.42 preD3 → Lumi
φ42 = 0.03 Lumi → preD3
φ25 = 0.039 preD3 → Tox

absorbance spectra εi(λ)
Fig 2

At t=0 the initial conditions for the concentrations are C1=100% and C2=C3=C4=C5=0

Fig. 4 shows an example of calculated kinetics under monochromatic irradiation at the wavelengths 254, 282, 296 and 305 nm. The calculations were performed for the intensity I0 = 1 mW/cm²/nm, initial concentration of provitamin D (7DHC) C0 = 0.002% and l = 0.5 cm