Quantification of photoinduced bending of dynamic molecular crystals: from macroscopic strain to kinetic constants and activation energies

Precise measurement of bending kinematics induced by a photochemical reaction in a single crystal can be used to extract the kinetic parameters of the underlying reaction with high accuracy.

. Screen snapshot of the software used to record the crystal bending showing the procedure for measurement of the crystal curvature and length. S4  Table S1. Combination of crystal samples and temperatures used to verify the reproducibility of the measurements under conditions of uniform both-sides irradiation of single crystal of 1-N and thermal reversion of the resulting 1-O. S8 Note 2. This reaction has already been used by us to relate the quantum yield of photoisomerization and the mechanical stress that originates from external loading 52 or thermal expansion.

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Note 3. The characteristic light penetration depth x 0 is calculated as the reciprocal of the absorption coefficient μ in the Beer-Lambert law. The absorption coefficient is connected with the molar extinction coefficient ε by ln(10) C    , where C is the molar concentration of the absorbing substance.
Note 4. A thermal equilibrium between 1-O and 1-N was assumed in some previous works. 59,66 In such case, the measured value of the thermal isomerization rate constant would be equal to the sum of the two rate constants, those of the forward (nitrito-nitro) and backward (nitro-nitrito) thermal reactions, The relation between the two thermal constants is defined by the equilibrium constant K and the corresponding Gibbs energy change ΔG, with the hypothesis of a thermal equilibrium between the two isomers in the crystal. Should the 1-O isomer still be present, its amount does not exceed 5% (mol). The corresponding value of ΔG at this temperature then should not be greater than -10 kJ/mol. In the present study, where the temperatures did not exceed 363 K, the thermal nitro-nitrito isomerization can be safely neglected, and the heating can be assumed to result exclusively in nitrito-nitro 1-O  1-N transformation.
Note 5. The average residuals did not exceed 2 × 10 -2 cm -1 , that is, less than 1% of general magnitude of the curvature in the experiments.
Note 6. Equation 4 was obtained for the simplest possible assumption that the absorption coefficient  is constant and the photoreaction constant ph k does not depend on the transformation degree. 1 The same equation also holds in more general cases, when α and  are substituted with the corresponding functions of the transformation degree (and, possibly, other parameters, such as temperature or mechanical stress). The additional difference in more general cases of non-constant values will be in introducing two different absorption coefficients in this equation:  appearing as a separate coefficient in Eq. 4 will be the total absorption coefficient in the substance (including absorption by the reactant and by the product), while  in the rate constant ph k will correspond to the absorption contributed by reactant only. The analysis of the stationary crystal curvature with the approximate eq 4 is reasonable in order to estimate the temperature dependence of the relation between the constants th ph kk as it gives the most impact in the resulting stationary curvature due to high temperature dependence of the kk. Note 7. The reaction 1-N → 1-O results not only in expansion of the crystal along its longest axis but also in compression normal to that axis (along axis a; the maximum strain is -2.4% after complete transformation, see Fig. S3 in the SI). This compression is known to lower the quantum yield. 57 As the maximum transformation extent decreases with increasing temperature because of the increased contribution of the reverse reaction 1-N ← 1-O, the lattice contraction along a decreases as well, thus contributing to higher quantum yield. Taken together, these results show that both the thermal expansion and the decrease in the average transformation extent at higher temperatures contribute to higher quantum yield of photoisomerization.
Note 8. The absorbance of the nitrito form is thus estimated to be 5 to 7 times lower than that of the nitroisomer. This difference is larger, than that measured for the two isomers in aqueous solutions. However, absorption in solution may differ from absorption in the solid state. There is presently no direct experimental information on the UV-Vis absorption of the nitrito-isomer of [Co(NH 3 ) 5 ONO]Cl(NO 3 ) in the solid state to assess the result. Additionally, the absorption in crystals depends not only on the oscillator strength of the corresponding electronic transition, but also on the crystallographic orientation of the absorbing species and the polarization plane of the irradiation causing the excitation. So, the lower predicted absorption of nitrito form as compared to solution data can be a consequence of a specific relative orientation of incident light and the dipole moment of corresponding transition in the nitrito-isomer in the irradiated crystals.
Note 9. The value of I 0 is the highest estimated value of the used light source. It has been measured outside of the experimental setup (see the Experimental details). Real photon flux on the crystal installed inside the measurement camera can be somewhat lower because of the intensity loss on the camera window and because of inevitable irreproducibility of the crystal installation relative the light spot inside the camera. We assume that up to two-fold total photon flux density decrease may result from the different crystal installations comparing to the initial value of I 0 .
Note 10. The same reasoning can be given for the interaction of differently oriented nitrito-isomers with light. However, since the nitrito-isomers in the crystal are no longer involved into the phototransformation, we have assumed for the sake of simplicity the light absorption by all the nitrito-isomers to be the same and isotropic.