Déformation photoinduite dans les films minces contenant des ...

Appendix B 161• P is the light power density• C is the molecule concentration in the considered volume• hν is the photon energy• ρ T , ρ Care the quantum yields for the isomerization of TRANS and CIS forms• α T , α Care the absorption coefficients of the material when all the molecules arerespectively in the TRANS and CIS forms• τ this the CIS → TRANS time constant due to the CIS form thermal relaxation.C → TConsidering:pastel-00527388, version 1 - 19 Oct 2010• x 1 (t) = N T RANS (t), x 2 (t) = N CIS (t), x(t) =• ψ = 1/τ T → C,ξ = 1/τ C → Twe can rewrite the model in the following form:dx(t)dt=whose solution can be written as:x(t) =( )x1 ˙x˙2+=(−ψ ξψe λ 1t(ξ/ψ1 + ξ/ψ 1e λ 2t1 + ξ/ψ(1−1−ξ) (x1 (t)x 2 (t)(x1 (t)x 2 (t)))(B.5))(x01 + x 0 )2 + (B.6)) (x 0 1 − ξ ψ x0 2)where(x01x 0 2)is the initial condition, λ 1 = 0 and λ 2 = −(ψ + ξ), which gives:x(t) =[(1 ξ/ψ1 + ξ/ψ 1)(x01 + x 0 )2 + e−(ψ+ξ)t(1−1) (x 0 1 − ξ ψ x0 2) ] (B.7)