Déformation photoinduite dans les films minces contenant des ...

Appendix B 162( 1Since λ 2 = −(ψ + ξ) = − +τ 1 )< 0 the second addend of Equation B.7T → Cτ C → Tvanishes for t ≫ 1. Moreover, we can reasonably suppose that no molecules are in theCIS state at t = 0, so x 0 2 = 0. This leads to:x(t) =[(1 ξ/ψ1 + ξ/ψ 1)x 0 1](B.8)It is now straightforward to obtain the ratio x 1 /x 2 for t ≫ 1, which provides an expressionof the photostationary equilibrium that can be observed:x 1x 2∣∣∣t→∞= ξ ψ⇒N∣ τ T RANS ∣∣t→∞ T → C=N CIS τ C → T(B.9)pastel-00527388, version 1 - 19 Oct 2010Considering eq. B.3 and B.4 we can express the photostationary equilibrium as:[N∣T RANS ∣∣t→∞= γ C1 + hνN CIS γ T P ·= γ [C1 + P ]thγ T P1γ C τ thC → T]=(B.10)hνwhere P th = indicates the power such that the TRANS → CIS isomerizationγ C τ thC → Thas the same probability to be induced either optically or thermally.In particular, for sufficiently low power densities, that is P ≪ P th , the photostationaryequilibrium is essentially dependent on P :N∣T RANS ∣∣t→∞≃ γ CN CIS γ T[ ] PthP(B.11)On the other hand, for P ≫ P th the photostationary equilibrium can be considered asindependent from P :N∣T RANS ∣∣t→∞≃ γ CN CIS γ T(B.12)