Quantitative Evaluation of Photoinduced Bending Speed of Diarylethene Crystals

We investigated photoinduced crystal bending behavior of various photochromic diarylethenes. In all the diarylethene derivatives we used in this work, the relationship between the initial photoinduced bending speed and the crystal thickness was well explained by the easy-handled Timoshenkoʼs bimetal model. Moreover, we proposed a quantitative analysis method to reveal the relationship between the bending speed and the molecular structure of diarylethenes. These results provide the quantitative evaluation method of the photoinduced crystal bending speed.

There are two types of bending directions in photoinduced crystal bending: bending away from ultraviolet (UV) light and bending toward UV light.The crystal bending away from UV light is caused by the expansion of the photoreacted crystal layer upon UV irradiation.In contrast, the crystal bending toward UV light is due to the contraction of the irradiated part of the crystal upon irradiation with UV light.In both types, the photoinduced crystal bending is caused by heterogeneous photoisomerization in depth because of high absorption of the crystal in UV region.To analyze and evaluate the photoinduced crystal bending behavior, the development of the easy-handled simplified model is required.
We have reported the crystal thickness dependence of photoinduced crystal bending of diarylethene derivatives [11,15].It has been experimentally clarified that the initial speed of bending depends on the thickness of the crystal.When the crystal thickness is thin, the crystal bends largely and rapidly.To discuss photoinduced bending behavior in the easy-handled model, we have introduced the Timoshenko's equation known as the simplified bimetal model [34].The correlation between the initial speed of the curvature change and the crystal thickness was well explained by the Timoshenko's bimetal model in both types of bending, bending away from UV light and bending toward UV light.Naumov and Bardeen have also independently reported the more sophisticated mathematical treatments based on the fact that the concentration of the photoreacted product throughout the crystal continuously changes for other phoreactive compounds [35,36].Such a rigorous analysis of the experimental fact is necessary for the development of the research field.On the other hand, the quantitative argument of the bending speed among different molecular crystals in easy-handled model is attractive and required to establish the general analysis method that can be widely used by other chemists.
Herein, we report on the quantitative evaluation of photoinduced bending speed among various diarylethene crystals (Scheme 1).All the diarylethenes 1-6 exhibited the photoinduced crystal bending caused by expansion or contraction of the photoreacted crystal layer and their bending speeds depended on the crystal thickness.The correlation between the initial speed of the curvature change and the crystal thickness in all the diarylethene crystals can be well explained by the Timoshenko's bimetal model.Moreover, the normalized relative bending speed in each crystal could be determined by focusing on the relationship between the thickness and the actuation strain of photoreacted layer in bimetal model.

Results and Discussion
In all the diarylethenes 1-6, their rod-like crystals can be crystallized out by slow evaporation of solvents.The space groups of the crystals of 1-6 were P1  S1.Diarylethene molecules in all the crystals of diarylethenes 1-6 exist in an antiparallel conformation.The distance between the reactive carbons was shorter than 4.2 Å, which is short enough for photoisomerization from the open-ring isomer to the closed-ring isomer to take place in the crystalline phase [37].
The initial velocity of the curvature change (Vinit) for various samples having different crystal thicknesses was estimated by fitting in a polynomial function to the curvature change against UV irradiation time and the differential of the function at t = 0.The dependence property of Vinit on the crystal thickness in the photoinduced bending was investigated in all the diarylethene crystals.Figure 2 shows the relationship between Vinit and the crystal thickness of diarylethene derivatives 1-6.When the crystal thickness is thin, Vinit becomes large.It can be well explained by the Timoshenkoʼs bimetal model.The illustration and equation of the Timoshenko's bimetal model are shown in Figure 3 and Equation (1) [34].Thickness / μm Thickness / μm where R is the curvature radius, αi (i = 1, 2) are the actuation strains, hi (i = 1, 2) are the layer thicknesses, m = h1/h2, n = E1/E2, and Ei (i = 1, 2) are the Youngʼs moduli.Actuation strain α means the coefficient of expansion or contraction of the layer in the absence of the other layer upon UV irradiation.In the non-photoreacted layer, the value of actuation strain α1 is always zero because the layer cannot expand or contract.In the type of bending away from UV light, the value of α2 is the coefficient of expansion.In contrast, it is the coefficient of contraction when the crystal bends toward UV light.Moreover, the assumption that the Youngʼs modulus E1 is the same as E2 is introduced because only a few % of diarylethene molecules in the crystal are converted from the open-ring isomer to the closed-ring isomer in the initial stage of the bending.As a result, the Timoshenkoʼs equation becomes very simple, as shown in Equation ( 2).This equation can be applied to the explanation of the relationship between the initial velocity of the curvature change of photoinduced bending and the thickness of crystal.That is, the initial velocity of α2 is expressed as α2,init.The values of h2 and α2,init can be obtained by the best fitting curve (Equation ( 3)) to the experimental data.
The values of h2 and α2,init in diarylethenes 1-6 are summarized in Table 1.When the depth of photoreaction from the crystal surface (h2) is the same, a potential capacity of bending in each crystal can be compared by only the value of α2,init.However, the potential capacity of each crystal cannot be compared by only the value of α2,init when the value of h2 is different in each crystal.The new analytical method to evaluate the unique value in each crystal is required.Here, we have focused on the relationship between h2 and α2,init in the same crystal.The value of h2 in the same crystal depends on the faces irradiated with UV light because of the difference of the absorption coefficient due to the molecular orientation viewed from the faces.The value of α2,init is proportional to the conversion rate from the open-ring isomer to the closed-ring isomer in the photoreacted layer.The number of photoreacted molecules is the same even when the face irradiated with UV light is different.Therefore, the value of multiplication of α2,init and h2 is always constant, as shown in Figure 4 and Equation ( 4).In other words, the value of α2,init is proportional to h2 −1 , as shown in Equation ( 5).
To discuss whether Equation ( 4) is suitable for the crystal of the same compound, the dependence of the photoinduced bending speed on the faces irradiated with UV light was investigated for diarylethene 1.The face indices of the rod-like crystal of 1 were determined as shown in Figure S1.When the crystal was irradiated from the (0 0 1) face with UV light, the movement of the crystal was small and slow.In contrast, when the crystal was irradiated from the (0 1 0) face, it was bent largely and rapidly [11].Figure 5 shows the dependence property of the bending speed on the crystal thickness when the UV irradiation was performed to the (0 0 1) and (0 1 0) faces of the crystal of 1.In the case of irradiation with UV light to the (0 1 0) face, h2 = 1.0 μm and α2,init = 0.46%•s −1 were obtained.On the other hand, h2 = 5.0 μm and α2,init = 0.10%•s −1 were obtained in the case of irradiation with UV light to the (0 0 1) face.This result means that the values of h2 and α2,init are different when the face irradiated with UV light is different.
Figure 6 shows the relationship between α2,init and h2 −1 in diarylethenes 1-6.In the case of irradiation with UV light to the (0 0 1) and (0 1 0) faces of diarylethene 1, the plots of α2,init against h2 −1 ride on a line through the origin.This result indicates that the value of α2,init is proportional to h2 −1 in experimental.By using this relationship, the effect of h2 on the value of α2,init can be normalized.In other words, the slope of a line through the origin is the unique value in each crystal.Here, we introduce the potential capacity of bending speed (C) that normalized the crystal thickness and the depth of the photochromic reaction from the crystal surface.The C value in each crystal can be calculated from the slope of the line.The relative C values of diarylethenes 1-6 were 1.0, 0.61, 1.2, 2.0, 3.0, and 1.2, respectively, as summarized in Table 1.These values indicate that the potential capacity of diarylethene crystal 5 is the largest value among the six compounds and is three times as large as that of 1.Thus, we have succeeded in the quantitative evaluation for the potential capacity of photoinduced bending speed among different diarylethene crystals.

General
The photoinduced bending behavior of diarylethene crystals was observed using a Keyence VHX-500 digital microscope.UV irradiation was carried out using a Keyence UV-LED UV-400 (365-nm light).The light intensity was 55 mW•cm −2 on the crystal surface.Visible light irradiation was carried out using a halogen lamp (100 W).Single crystal X-ray crystallographic analysis was carried out using a Rigaku RAXIS RAPID imaging plate diffraction instrument or a Rigaku VariMax with Saturn CCD single crystal X-ray diffraction instrument with MoKα radiation (λ = 0.71073 Å) monochromated by graphite.The crystal structures were solved by a direct method using SIR92 and refined by the full-matrix least-squares method on F 2 with anisotropic displacement parameters for non-hydrogen atoms using SHELXL-97.

Determination of the Initial Speed of the Curvature Change
The edge of a rod-like crystal was fixed to a glass capillary, and a fluorescent material was painted on the glass capillary.The fluorescence of the glass capillary shows the onset time of UV irradiation.The value of the curvature against UV irradiation time (t) was fitted by a polynomial function.The initial speed of the curvature change was calculated by the differential of the function at t = 0.The error of the initial speed determined by the method was less than 8%.The standard deviation of the repeating experiments using the same crystal was smaller than the error.

Conclusions
We have investigated the photoinduced bending behavior of various diarylethene crystals.All the diarylethenes showed the photoinduced crystal bending behavior caused by expansion or contraction of the photoreacted crystal surface.Their bending speeds depended on the crystal thickness.The correlation between the initial bending speed and the crystal thickness in all the diarylethene crystals can be well explained by the Timoshenko's bimetal model.When the thickness of the photoreacted layer (h2) in the bimetal model is the same even in different diarylethene crystals, the bending speed can be compared quantitatively using the value of α2,init.However, the h2 values are different depending on the molecular structure and the molecular packing.The multiplication of h2 and α2,init led to a constant value of C in the same crystal.By using this relationship, the effect of h2 on the value of α2,init can be normalized.Therefore, the value of C means the potential capacity of bending speed.

Scheme 1 .
Scheme 1. Diarylethene derivatives used in this work: (a) bending away from UV light; (b) bending toward UV light.

hν (a) Bending away from UV light h 2 h 1 (b) Bending toward UV light hν h 2 h 1 Figure 3 .
Figure 3. Illustration of Timoshenkoʼs bimetal model in the case of (a) bending away from UV light and (b) bending toward UV light.

Figure 4 .
Figure 4. Illustration of the relationship between h2 and α2 when the UV light irradiation is conducted to the different face in the same crystal.