7.4 Modified model of photodegradation
7.4.1 Model based on multiple photodegradation pathways
It is apparent from Figs. 7.8, 7.9 and 7.11 that the evolution of F(β) with time cannot be fitted to a single exponential. The deviation from the expected single exponential needs to to be investigated to develop a more realistic model. Better understanding of the photodegradation mechanism is important to develop new methods for enhanced optical stability of the chromophores. The departure ofF(β) plot from single exponential was reported previously from measurements on 10 wt.% PYR-3/APC thin films [24, 118] where the measurements are done without a pinhole and hence it was expected that the departure from a single exponential could be due to a varying laser intensity across the film [24, 118, 121]. However, this is not
144 Chapter 7. Photostability of NLO Chromophores
the case in the new set of experiments we made because we used an expanded laser beam and a 100µm pinhole to ensure that the intensity was constant across the film. Experiments were repeated using a further expanded beam and a 1 mm pinhole to avoid the diffraction effect caused by the small pinhole in the range of film thickness. This was confirmed by optical microscopy after photodegradation where the resultant bleached area was circular and with the same diameter as the pinhole. Most of the previous reports of chromophore photo-bleaching also find that Eq. 7.9 does not provide a good fit for all times and hence Equation. 7.9 is used to model the data for short times only [114, 122]. This has also been done for our data and we show in Fig. 7.11 T(t) and F(t) for 5 wt.% PYR-3/APC and 15 wt% PYR-3/APC whereB = 1100 and 1400, respectively.
The failure of Eqs. 7.9 and 7.10 to provide a good fit to the data over a large time range suggests that there is a polarisation-dependent photodegradation or there is a distribution in the photodegradation quantum efficiencies. The first possibility could occur if the S0 to S1 transition probabilities strongly depend on the polarisa-
tion of the incident beam. Simulation results provided by Quilty [123] showed light polarised perpendicular to the bridge contributes less than 10% of the absorption and shows peaks at higher energies which are attributable to transitions within the donor and acceptor rings [67]. Thus, the absorption cross section depends on the angle between the electric field of the incident light and the principal chromophore axis, which results in a orientational distribution of the absorption cross section if PYR-3 is randomly orientated in the PYR-3/APC films. The second possibi- lity could occur if, for example, there existed an intermediate product that then photodegraded [124, 125]. However, we expect this is unlikely in our case because there is no evidence for another absorption peak above 450 nm during bleaching and there is no significant absorption above 450 nm after complete bleaching. Note that trans- and cis- isomers of PYR-3 might be expected to occur in the film be- cause NMR of the starting powder shows that both isomers exist. However, the
S0 to S1 transition probabilities are not expected to be significantly different for
both isomers. To be able to characterise our photostability data, we consider a model where there are 3 photodegradation quantum efficiencies and/or 3 different absorption cross sections arising from a polarisation dependent transition proba- bility and/or a distribution in the photodegradation quantum efficiency. We also include oxygen diffusion into the films and oxygen-mediated photodegradation. The resultant differential equations can be written as [67],
7.4. Modified model of photodegradation 145 ∂m(β, z) ∂z =−σN¯ (β, z)m(β, z) (7.17) ∂N(β, z) ∂β =−σm¯ (β, z) Nox(β, z) Nox(0) 3 ∑ i=1 Ni(β, z) σi ¯ σBi (7.18) ∂Nox(β, z) ∂β =D ′∂2Nox(β, z) ∂z2 + ∂N(β, z) ∂β (7.19)
where β(t) = n0 ×t, m(β, z) = n(t, z)/n0, n(t, z) is the photon flux at time
t and at distance z into the film, N(β, z) is the total chromophore concentration,
Nox(β, z) is the oxygen concentration in the films,D´=D/n0, andDis the oxygen
diffusivity in the films. The three chromophore concentrations areN1(β, z),N2(β, z),
and N3(β, z) where the corresponding absorption cross sections are σ1,σ2, andσ3,
and the average number of photons required to degrade a chromophore at room temperature and pressure are B1, B2, and B3, respectively. We previously showed
that the average number of photons required to degrade a chromophore is inversely proportional to the oxygen partial pressure. The average absorption cross section is ¯
σ= [σ1N1(0) +σ2N2(0) +σ3N3(0)]/N(0).
Figure 7.12– Plot of the transmittance againstβ/2.67×1019 (solid curves) for (a) a
2.4µm thick 5% PYR-3/APC films and (b) a 2.05µm thick 15% PYR-3/APC film. The arrows show increasing intensity of 1 mW/mm2, 5 mW/mm2, and 50 mW/mm2 for the
5% films and 0.47 mW/mm2, 6.8 mW/mm2, and 29 mW/mm2 for the 15% films. The excitation wavelength was 532 nm. Also shown are the modelled data assuming three B´ values (dashed curves) and a time-dependent reduction in the oxygen concentra- tion by chromophore photodegradation. Insets: Corresponding plots of the transmit- tance againstβ/(η2.67×1019) whereη is the photostability enhancement factor for (a)
1 mW/mm2(solid curve) 5 mW/mm2(dashed curve) and 50 mW/mm2(dot dash curve)
and (b) for 0.47 mW/mm2(solid curve), 6.8 mW/mm2(dashed curve) and 29 mW/mm2
(dotted curve).
One of the key merits of this model is that it removes the dependence on the initial photon flux and enables data to be compared when the incident photon flux
146 Chapter 7. Photostability of NLO Chromophores
is varying. Analytical solution similar to that derived for the Dubois model [114, 24] is, unfortunately, not possible for this differential equations. A fit to the experimen- tal transmittance data was found via numerical solution using the finite difference method in pascal. The data in Fig. 7.12 were modelled using this model where the optical intensities are low enough so that the oxygen concentration in the films can be considered constant. It can be seen that the use of 3 photodegradation quantum efficiencies and/or absorption cross sections provide a good fit to the data. The measured average absorption cross section, at 532 nm was 5.5×10−17 cm−2 for the 5 wt% PYR-3/APC film and 7.8×10−17 cm−2 for the 15 wt.% PYR-3/APC film.
Table 7.2– Table of parameters used to model the transmittance data in Fig. 7.11 and Fig. 7.12 for 2.4µm thick 5% PYR-3/APC films at 532 nm. The initial chromophore number density,N(0), was 8.37×1019cm−3.
Light intensity,I (mW/mm2) 1 5 50 N1(0)/N(0) 0.7 0.71 0.71 N2(0)/N(0) 0.23 0.2 0.2 N3(0)/N(0) 0.07 0.09 0.09 B1′ 980 980 980 B2′ 6900 6900 6900 B3′ 29400 78400 78400 Nox(0) (cm−3) 3.36×1018 3.36×1018 3.36×1018 D(cm2s−1) – 3.2×10−8 3.2×10−8
The resultant fit parameters are listed in Tables 7.2 and 7.3 where Bi′ = ¯σσ iBi. The 5% PYR-3/APC film can be fitted with a main component where B1′ = 980. The corresponding main component for the 15 wt.% PYR-3/APC was B1′= 1073. These values are similar and indicate that the main photodegradation quantum efficiency does not strongly depend on the PYR-3 concentration. The results from photodegradation measurements at a range of intensities for 5 wt.% PYR-3/APC and 15 wt.% PYR-3/APC films are plotted in Fig. 7.12, where the film thicknesses were 2.4µm and 2.05µm, respectively. The transmittance data are plotted against
β/2.67×1019 where 2.67×1019 cm−2 is the photon flux for an incident intensity of 100 mW/mm2. Note that the maximum optical intensities are below the thermal
7.4. Modified model of photodegradation 147
Table 7.3 – Table of parameters used to model the transmittance data in Fig. 7.11 and Fig. 7.12 for 2.05µm thick 15% PYR-3/APC films at 532 nm. The chromophore number density,N(0), was 2.51×1020cm−3.
Light intensity, I (mW/mm2) 0.47 6.8 29 N1(0)/N(0) 0.66 0.62 0.64 N2(0)/N(0) 0.12 0.28 0.26 N3(0)/N(0) 0.22 0.1 0.1 B1′ 1073 1073 1073 B2′ 5360 7660 25300 B3′ 8940 35800 31600 Nox(0) (cm−3) 3.36×1018 3.36×1018 3.36×1018 D(cm2s−1) – 1.35×10−8 1.35×10−8
The transmittance data were modelled using Eqs. 7.17 - 7.19. The best-fit curves for some of the data are plotted in Fig. 7.12 and the resultant best-fit parameters are listed in Tebles 7.2 and 7.3. Note thatNox(0) is in the range of values obtained from
solubility measurements on some other polymers where saturated oxygen concen- trations range from approximately 1.9×1018 to 1.9×1019 cm−3[126]. The oxygen
diffusivities are reasonable given that measurements on some other polymers pro- vide diffusivities as low as 2.4×10−8 cm2s−1[127]. We first consider the results from fitting the 5 wt.% PYR-3/APC thin film data. It is clear in Table 7.2 that the data can essentially be fitted with the same parameters and the only change is an increase inB′ for the small fraction (N3) that has the highestB′ value. This shows that the
photostability enhancement for high incident optical intensities can be reasonably described by oxygen-mediated photodegradation for low PYR-3 concentration.
It can be seen that T(β) increases slowly for samples bleached at higher optical intensities. This enhancement can also be seen in the insets to Fig. 7.12 whereT(β) is plotted against β/η where η is the photostability enhancement factor obtained by scaling to the data with the lowest optical intensity. The data fall on a common curve for low intensities. For high intensities there is a small deviation for large β
values. The resultant photostability enhancement factor is plotted in Fig. 7.13 for the different PYR-3 concentrations and a range of optical intensities, where it can show that the enhancement factor is higher for the higher PYR-3 concentrations.
148 Chapter 7. Photostability of NLO Chromophores 1 10 1 10 Intensity (mW /mm 2 )
Figure 7.13– Plot of the photostability enhancement factor,η,against light intensity at 532 nm for (a) a 2.4µm thick 5% PYR-3/APC (filled circles) and (b) a 2.05µm thick 15% PYR-3/APC (open circles).