Open Access
Add to BibSonomy
Abstract
Terahertz spectroscopy provides a powerful and informative link between infrared spectroscopy and microwave spectroscopy, and is now beginning to make its transition from initial development to broader use by chemists, materials scientists and biologists. In this study, utilizing terahertz spectroscopy we monitored the crystallization and isomerization of azobenzene. In flash-frozen trans-azobenzene solutions, the processes of crystallization and phase transition were observed. A new phase has been experimentally confirmed to exist stably at low temperatures. The results on gradual-frozen experiment indicate that the formation of the observed new phase is determined by the cooling rate. Besides, based on the distinctive spectral features of the isomers, the thermal- and photo-induced isomerization processes of azobenzene were investigated. This work presents that the terahertz spectroscopy has a great potential to study the phase transitions and crystallization of liquid samples under different freezing conditions.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Azobenzene (AB) consists of two benzene rings attached by a diazo bridge and can undergo reversible isomerization during heating or irradiating. The stable trans isomer can isomerize to the metastable cis isomer under ultraviolet (UV) irradiating, and the reverse process occurs by visible (vis) light irradiating or heating. Upon isomerization, the electronic dipole moment and molecular shape will change significantly. This reversible geometric effect has been utilized in many fields such as photoswitches [1], energy storage [2], drug release [3] and biomolecular control [4]. So far, the isomerization processes of AB have been investigated using a number of different techniques, including Raman [5], infrared spectroscopy [6], transient fluorescence [7], and UV-vis absorption [8], where the excited-state structure, isomerization dynamics and pathways of the AB can be evaluated. However, there is rare study on the low-frequency vibrations, which are especially sensitive to the molecular configuration. Terahertz photon energy, which matches with weak interactions and conformational changes in molecule, promises terahertz spectroscopy a powerful method to investigate the isomerization of AB molecule [9].
The terahertz (THz) region lies between the microwave and infrared regions and the terahertz time domain spectroscopy (THz-TDS) containing enormous physical, chemical and optical information is thought of a powerful and informative tool to investigate the low-frequency vibrational activities, torsional and rotational modes and intermolecular interactions. Although it just begins to make transition from initial development, THz-TDS has already presented promising application in the fields of physics [10], chemistry [11,12], material [13], optics [14] and biology [15–17]. In particular, terahertz photon energy of meV matches well with collective vibrational mode and conformational changes of molecule. This allows THz-TDS an excellent method to investigate the isomerization and crystallization of AB molecules. In our previous work in 2018 [9], THz-TDS was employed to monitor cis-to-trans isomerization of AB molecule by observing the low-frequency vibrational modes of the cis- and trans-AB. The spectra of AB were collected in solid tablet to avoid the difficulties in spectral analysis of liquid samples where long-range order and well-defined intermolecular bonding are absent.
In this work, we investigated the feasibility of terahertz spectroscopy on identify spectral difference of trans- and cis-AB solutions at frozen state. Based on the obtained spectral feature of the isomers, we monitored their spectral evolution in the melting process immediately after flash freezing and gradually freezing. It is surprising that a stable new phase of trans-AB was observed using the proposed method. Furthermore, the thermal- and photo-induced isomerization processes of AB in cyclohexane were investigated. This work presents that the terahertz spectroscopy has a great potential to study the phase transitions and crystallization of liquid samples under different freezing conditions.
2. Materials and methods
2.1 Materials
The trans-azobenzene (trans-AB) was purchased from J&K Scientific Co., Ltd with a purity of 98% and the cis-azobenzene (cis-AB) was obtained by the photo-induced isomerism of trans-AB. The prepared trans-AB in ethanol solution was illuminated under an ultraviolet lamp (consumed power 250 W, wavelength 365 nm) and about 40% trans-AB transferred to cis-AB within two hours. After illumination, the solution was purified by column chromatography with silica gel (200 mesh) as the stationary phase and petroleum ether and ethyl acetate mixed solvent (40:1, v/v) as eluents. After column chromatography, the solute was volatilized, and the obtained trans-AB granules and cis-AB granules were separately preserved in brown vessels at about 277 K for stability. Thus, both of trans-AB and cis-AB were ready for the freezing experiments. Cyclohexane and tetradecane, that have purities of 99.5% and 99%, respectively, were purchased from Aladdin and used without further purification.
In following experiments, the cyclohexane solution of trans- and cis-AB with concentration of 0.33 mol/L were prepared directly from the trans- and cis-AB granules obtained with the method described in the material section.
2.2 Sample freezing
In a flash freezing experiment, the AB solution was contained in a polytetrafluoroethylene (PTFE) cuvette with sample thickness of 5 mm. The cuvette was immersed in liquid nitrogen for 30 seconds and then was stuck onto a liquid nitrogen cooled metal platform and gradually equilibrated to the room temperature. In this natural warming-up process, the terahertz time-domain spectrum of the sample was collected every 100 seconds. A thermometer probe was utilized to monitor the temperature changes during the measurements. The initial temperature recorded immediately after freezing was about 240 K, and after about 40 minutes, the temperature raised up to 283 K at which the samples had melted. The freezing and transfer processes were operated under dry air environment, so there is no water condensation.
In the gradual freezing experiment, solution was sealed in a quartz cuvette with sample thickness of 5 mm. The cuvette was set into a cryostat (Janis ST-300, Janis Research Company) which kept pressure under 0.1 Pa to avoid heat dissipation and sealed with two terahertz-transparent diamond windows. The solution was gradually cooled from 296 K to 240 K with a rate of 1 K per 5 min, and then heated up to 296 K at the same rate.
2.3 Isomerization of AB
The stable trans isomer can isomerize to the metastable cis isomer under ultraviolet (UV) irradiating, and the reverse process occurs by visible (vis) light irradiating or heating as indicated in Fig. 1. In thermal isomerization experiment, cis-AB cyclohexane solution was bathed in water at 333 K (60 °C). To monitor the thermal induced cis-to-trans isomerization, the terahertz spectra of the solution were recorded every one hour at 240 K. For the photo-induced trans-to-cis isomerization of AB, the trans-AB cyclohexane solution circulated through a quartz cell which was irradiated with a 310 nm UV light. The terahertz spectra of the solution were recorded for every two hours.
2.4 Terahertz spectroscopy
The terahertz spectra were performed on a broadband 8-f confocal THz-TDS system (TAS7400TS, Advantest Corporation, Japan). The effective spectrum band of the spectrometer is 0.3 to 3.5 THz, while, in the gradual freezing experiment, the spectra in the frequency region >2.8 THz is not reliable due to the attenuation of the terahertz by the quartz cuvette and windows of cryostat. During measurements, the terahertz path was fully sealed and flushed with dry air continuously to avoid vapor absorption from the atmosphere. Each terahertz spectrum comprised the averaged data of 256 scans for the good signal-to-noise ratio. The absorption of samples was extracted from transmitted terahertz signal with the spectrum of empty quartz cuvette or PTFE cuvette as reference.
3. Results and discussion
3.1 Crystallization of the AB solution by flash freezing
The trans- and cis-AB solutions were monitored by terahertz spectroscopy during warming up process directly after the flash freezing. Temperature-dependent spectra of the trans-AB in cyclohexane and tetradecane solutions are presented in Fig. 2(a) and (b), respectively. In Fig. 2(a), the green curve indicates the spectrum of trans-AB solution in flash frozen state (240 K) and presents three absorption peaks at 2.07, 2.48 and 3.03 THz. It can be observed clearly that the spectral feature of the frozen AB cyclohexane sample evolved dramatically in the warming up process after flash freezing. Particularly, with the temperature elevation, the above three absorption peaks disappear abruptly at around 268 K, while four new peaks at 1.45, 1.77, 2.58 and 2.94 THz arise during the warming-up process. As temperature continued to rise, the sample melted and a broad absorption band at around 2.6 THz was observed, which shows the spectral signature of the liquid solution. The same process and evolution of terahertz spectra were also observed in trans-AB tetradecane solution as shown in Fig. 2(b), which suggests that the observed changes of the spectra are dominated by the AB solute rather than the solvent. This is further improved by the featureless spectra of frozen cyclohexane and tetradecane, as presented by the dashed black curves in Fig. 2(a) and (b), respectively. Thus, it can be concluded that the appearance of absorption peaks was caused by the crystallization of AB in frozen solutions. The flashing decrease of temperature caused the dramatic decrease of the solubility of AB, and thus AB precipitated quickly and crystalized into microcrystals. While, the quick evolution of the spectra of AB cyclohexane from 268 K to 270 K indicates a phase transition process of crystallization during the warming-up process directly after flash freezing.
Fig. 2. The evolutions of terahertz spectra of the trans-AB in (a) cyclohexane and (b) tetradecane solution during the warming-up process after flash freezing. Curves are shifted vertically for clarity.
Comparing the spectra of trans-AB tablet and the spectra of AB cyclohexane solution at 240 K and 270 K, it is obvious that the four peaks of flash-frozen trans-AB solution at 270 K (yellow curve) matches very well with the peaks of trans-AB tablet at 270 K (black curve) in Fig. 3(a). It is worthy to mention that these four peaks in tablet were assigned to twisting or wagging of the benzene rings and collective vibrations of AB molecules in our previous study [9]. This observation indicates that at 270 K, trans-AB molecules are stabilized as solid monoclinic crystal [18]. However, the obvious different spectrum at 240 K and the abrupt changes of spectral features at around 268 K suggest that at 240 K directly after flash-freezing trans-AB microcrystals stay at a different phase.
Fig. 3. (a) The extracted spectra of trans-AB cyclohexane solution after flash freezing at specific temperature and the spectrum of pure trans-AB powder tablet. (b) Terahertz spectra of trans-AB cyclohexane solution during warming-up process. The solution sample was prepared by the flash-freezing method and then stored in liquid nitrogen for 180 hours. Curves are shifted vertically for clarity. (c) Measured and calculated XRD results of trans-AB powder and solutions.
The new phase may stem from the formation of AB-cyclohexane complex or the steric effect of solvent to the crystallization of trans-AB [19]. The formation of solute-solvent complex at low temperatures can occur under specific composition in the field of binary phase diagram research, such as the two-component system of acetonitrile-benzene [20], NaCl-H2O [21] or sodium-potassium [22], and the formed compound would decompose into the original binary components at the incongruent melting point. However, the spectral feature of flash-frozen trans-AB tetradecane solution indicate that the new phase is not caused by the formation of a complex between the AB molecule and the solvent, because changes in molecular composition will cause significant differences in the terahertz spectrum. Thus, the result suggests that the new phase, which has three absorption peaks at around 2.07, 2.48 and 3.03 THz, originates from the steric effect of solvent to the crystallization of trans-AB.
Now the question is whether the observed new phase is a stable or a metastable state. To verify its stability, we performed THz-TDS experiment on the flash-frozen trans-AB cyclohexane sample, which was remained in liquid nitrogen for 180 hours. The collected terahertz spectra of the sample during warming up process are shown in Fig. 3(b). It is obvious that the three peaks at around 2.07, 2.48 and 3.03 THz which presenting the formation of new phase can still be clearly observed, and the phase transition process can also be observed during warming-up process. The results indicate that the new phase formed by flashing freezing can exist stably for a long time at low temperature.
Furthermore, we measured the XRD patterns of the frozen trans-AB solution and compared it with the pattern of the powder, as shown in Fig. 3(c). Two peaks were observed in the XRD pattern of flash-frozen trans-AB solution at 240 K, as indicated by the green arrows. While the temperature increased to 268 K, these two peaks disappeared, and several peaks at different positions emerged, as indicated by the yellow arrows. It can be found that the peaks indicated by the green arrows do not match the patterns of AB powder (blue line in panel c) or frozen cyclohexane (black curve in panel c), while the peaks emerged at 268 K were basically consistent with the powder pattern. These results agree with the observation in terahertz spectra, and prove the formation of a new phase of AB microcrystals after the direct flash-freezing of AB cyclohexane solution. It is worthy to mention that to the best of our knowledge, the observed new phase of trans-AB has not been reported before and the calculated XRD pattern using reported parameters [23] agree well with the pattern of tablet sample as shown in the bottom curve of Fig. 3(c). In addition, the XRD pattern of the gradual-frozen trans-AB solution was presented by the top curve in panel c, where the signatures of new observed phase in flash-frozen experiment are missing. This indicates that the formation of the new phase is related to the cooling rate. The details will be discussed in the gradual cooling experiment section below.
Figure 4 presents the temperature-dependent spectra of the cis-AB. It can be found that cis-AB solution in flash frozen state (240 K) presents three absorption peaks at 0.65, 1.79 and 2.54 THz, as shown by the green line in Fig. 4(c). With the temperature elevation, the absorption peaks slightly shift to the lower frequencies around 0.57, 1.72 and 2.49 THz. As the temperature continues to rise, the sample melted and all the absorption peaks vanished. Similar phenomenon was observed in cis-AB tetradecane solution, as shown in Fig. 4(b). Comparing with trans-AB solution, there are two obvious differences identified in the temperature-dependent spectra of flash-frozen cis-AB solution. First, the spectra of flash-frozen cis-AB solution at 240 K and 270 K are very similar, as indicated by the green and yellow curves in Fig. 4(c). In other words, there is no phase transition observed in flash-frozen either cis-AB cyclohexane or cis-AB tetradecane solutions. Second, the absorption peaks of frozen sample at 270 K do not agree well with the peaks in the spectrum of cis-AB tablet at 270 K (black line in Fig. 4(c)). Thus, the spectral difference between the frozen cis-AB solution and the tablet seems to be caused by the influence of the solvent surrounding the crystal on its vibration mode rather than the temperature effect. This might be because the orthorhombic cis-AB crystal structure is more easily affected by the solvent than that of trans-AB whose crystal structure is monoclinic [24,25].
Fig. 4. The evolutions of terahertz spectra of the cis-AB in (a) cyclohexane and (b) tetradecane solution during the warming-up process after flash freezing. (c) The extracted spectra of cis-AB cyclohexane solution after flash freezing at specific temperature and the spectrum of pure cis-AB powder tablet. Curves are shifted vertically for clarity.
3.2 Gradual cooling–heating cycle of the AB solution
The crystallization process usually depends on the cooling rate, and different cooling rates may lead to different crystal shapes and structures [26–28]. For comparing with the flash-freezing experiment, in this section we studied the gradual cooling and heating processes of the trans- and cis-AB cyclohexane solutions using THz-TDS. The terahertz spectra of trans-AB cyclohexane solution in cooling and heating process in temperature range of 240 to 296 K are shown in Fig. 5(a) and (b), respectively. In Fig. 5(a), at temperatures above 260 K, the trans-AB cyclohexane solution shows a featureless low absorption below 2.0 THz and a strong absorption band at around 2.60 THz. While, at temperatures below 260.5 K, the absorbance increased distinctly and new peaks emerged, indicating the liquid-solid phase transformation. The frozen sample exhibits three absorption peaks at 1.49, 1.82 and 2.62 THz, which are basically consistent with the spectra of trans-AB tablet shown as black line in Fig. 3(a). However, with the temperature decrease further, the spectrum remains. This is different from the results in flash-frozen trans-AB solution, which shows different spectral feature at temperatures of 240 K and 270 K. This means that the phase transition observed in flash freezing experiment is absent in the gradual-freezing process, which is also confirmed by the XRD pattern of gradual-frozen trans-AB solution, as shown by the top curve in the Fig. 3(c). In the heating cycle (Fig. 5(b)), the evolution of absorbance was almost the reverse process of cooling cycle, except that the phase-transition temperatures were noticeably shifted to higher temperatures and the phase-transition processes were more moderate. For clarity, the normalized integral absorbance intensity from 1.5 THz to 2.5 THz were plotted as a function of temperature in both of cooling and heating cycles as blue and red dots in Fig. 5(c), respectively. In the cooling cycle, there are two distinguishable segments shown in the blue curve: the steady stage with low absorbance form 296 K to 260.5 K (liquid phase), and the high absorbance stage from 260 K to 240 K (solid phase). In the heating cycle, the transition stage shifted to higher temperature compared with that of the cooling cycle. This shift is consistent with the widely observed freezing-melting hysteresis [29–31], and the hysteresis originated from the super-cooling effect in the solutions. In addition, before melting, there is a stage where the absorbance gradually increases. This is due to the partial melting of the sample, and the heterogeneous sample will have a scattering effect on the terahertz. Unlike the case in flash freezing experiment, in both cooling and heating cycles of the gradual freezing experiment, there was no solid-solid phase transition. The results indicate that formation of the new phase in trans-AB depends on the cooling rate.
Fig. 5. Terahertz spectra of AB cyclohexane solution during cooling and heating processes in the temperature range of 240 to 296 K. (a, b) The terahertz absorption spectra of 0.33 mol/L trans-AB solution in the cooling (a) and heating (b) processes. (c) The temperature-dependent hysteresis curves of the integral intensity of absorbance from 1.5 THz to 2.5 THz. (d-f) The results of 0.22 mol/L cis-AB solution. A relative low concentration of cis-AB was chosen due to its strong absorption of terahertz.
Terahertz spectra of cis-AB cyclohexane solutions in cooling and heating processes were presented in Fig. 5(d-f). As shown in the Fig. 5(d), the absorbance of the cis-AB cyclohexane solution has relatively low and smooth absorption spectra without obvious absorption peak in the studied region (0.3-3.5 THz) at temperatures above 270 K. When the temperature dropped below the phase transition point, the absorbance increased dramatically, while the spectra above 2.5 THz are not reliable due to the strong absorption. However, the red wing of the absorption was observed clearly and two sharp peaks emerged at 0.59 THz and 1.71 THz. The heating cycle was the reverse process of cooling cycle and the results were shown in Fig. 5(e). The temperature-dependent hysteresis curves of the integrated absorbance intensity from 1.5 THz to 2.5 THz in both cooling and heating cycles was represented as blue and red dots in Fig. 5(f), respectively. In cooling cycle, the phase transition happened precipitously at about 270 K. In heating cycle, the phase-transition temperature was slightly shifted to higher temperatures and the phase transition process was more gradually. In general, the results of gradual freezing of cis-AB solution are consistent with that of the flash freezing experiment.
3.3 Thermally and photo-induced isomerization of AB
Based on the above analysis of the terahertz spectra of frozen trans-AB solution and cis-AB solution, THz-TDS was used to monitor the thermal induced cis-to-trans isomerization process of AB in cyclohexane. In thermal isomerization experiment, cis-AB solution was bathed in water at 333 K (60 °C) for 7 hours, and the spectra of the AB solutions were taken for each hour. The temperature at which the spectra were collected is about 250 K. Figure 6(a) shows the evolution of terahertz spectra during thermal induced isomerization process. One could focus on the spectra collected at in the first four hours. The terahertz absorption peaks of the cis-AB at 0.65 and 1.79 THz were clearly observed at the beginning of the experiment. After 1 hour of thermal-isomerization, two peaks of the trans-AB at 2.59 and 2.98 THz appeared, which indicates that partially isomerization of cis-AB to trans-AB. Over time, the peaks of cis-AB at 0.65 and 1.79 THz gradually vanished. Meanwhile, the peaks of trans-AB at 1.49, 1.77, 2.59 and 2.98 THz become more obvious with isomerization time. It is interesting that two peaks at 2.08 and 2.47 THz appeared after 5 hours of thermal isomerization. These peaks have been discussed above and indicated the formation of the new phase trans-AB in the thermal isomerization. The results reveal that the formation of the new phase of trans-AB may rely on concentration, which could lead to different crystal phase during crystallization [32], or be interfered by the presence of cis-AB. The peak amplitude at 0.65 THz with baseline correction [33] was plotted as a function of isomerization time in Fig. 6(b). The data were fitted using the exponential function y = y0 + Ae(-x/τ) as shown by the red line, and the obtained τ is about 2.5 h for the isomerization at 333 K.
Fig. 6. Terahertz absorption spectra of AB cyclohexane solution at different time intervals during thermally induced cis-to-trans isomerization. (a) The spectra of samples frozen by flash cooling method. The spectra were measured at 250 K. Curves are shifted vertically for clarity. (b) The peak amplitude at 0.65 THz as a function of thermal-isomerization time.
Furthermore, the UV (310 nm) photoinduced trans-to-cis isomerization of AB in cyclohexane at room temperature was studied and the result are presented in Fig. 7. As shown in Fig. 7(a), before irradiation, the trans-AB cyclohexane presented absorption peaks at 2.08, 2.47 and 3.03 THz, which are the fingerprint of new phase. Over the irradiation time, the trans-AB isomerized to cis-AB and the corresponding peaks of cis-AB at 0.65 and 1.79 THz increased gradually. After 4-hour irradiation, the peaks at 2.08, 2.47 and 3.03 THz indicating the new phase of trans-AB disappeared due to the decrease of trans-AB concentration. However, the characters of trans-AB, such as the peaks at 1.49, 2.59 and 2.98 THz, became stable rather than vanished after 12 hours of irradiation, which means the trans-AB could not completely isomerize to cis-AB. This is because a photostationary state was reached in the isomerization [34]. The peak amplitude at 0.65 THz was plotted as a function of isomerization time in Fig. 7(b). The cis-AB content increased with increasing isomerization time and the isomerization reached a photostationary state after 12 h. The data were fitted using the exponential function y = y0 + Ae(-x/τ) and the obtained τ is about 11 h. The measured data did not perfectly match the mono-exponential fitting and showed some fluctuations. This might be caused by the unevenly irradiation on the sample which was circulated in the experiment.
Fig. 7. Terahertz absorption spectra of AB cyclohexane solution at different time intervals during photo-induced trans-to-cis isomerization. (a) The spectra of samples frozen by flash cooling method. Each spectrum was measured at 250 K. Curves are shifted vertically for clarity. (b) The peak amplitude at 0.65 THz as a function of thermal-isomerization time.
4. Conclusions
In summary, we studied the crystallization and phase transition processes of AB cyclohexane and tetradecane solutions using THz-TDS. For trans-AB cyclohexane solution in flash freezing experiment, we found a formation of an unreported new phase indicated by three distinct fingerprint peaks at around 2.07, 2.48 and 3.03 THz. This phase can only exist at temperature below 268 K and would transform to the ordinary crystal structure after heating. The new phase was further proven to be a stable state by THz-TDS on long time frozen solutions. In the gradual freezing experiment, the trans-AB has shown characteristic absorption peaks at 1.49, 1.82 and 2.62 THz, while the three peaks corresponding to new phase were absent. This observation indicates that the formation of new phase depends greatly on the cooling rate. For the cis-AB cyclohexane solution, there was no feature of new phase observed, and the frequency-shift relative to spectrum of powder tablet was assigned to steric effect of solvent. Based on the understanding of terahertz spectra of trans-AB solution and cis-AB solution, we monitored thermally induced cis-to-trans isomerization and photoinduced trans-to-cis isomerization of AB in cyclohexane solutions by utilizing THz-TDS at flash frozen state. We believe that the freezing method could expand the application of THz-TDS and may provide a new perspective for terahertz spectral analysis of liquid samples.
Funding
National Key Research and Development Program of China (2017YFA0701004); National Natural Science Foundation of China (61705163, 61875150, 61935015); Tianjin Municipal Fund for Distinguished Young Scholars (18JCJQJC45600).
Acknowledgments
This work was supported by the National Key Research and Development Program of China (Grant No. 2017YFA0701004), the National Science Foundation of China (Grant Nos. 61875150, 61935015, and 61705163), the Tianjin Municipal Fund for Distinguished Young Scholars (Grant No. 18JCJQJC45600), and the National Defense Science and Technology Innovation Special Zone.
Disclosures
The authors declare no conflicts of interest.
References
1. T. Ikeda and O. Tsutsumi, “Optical switching and image storage by means of azobenzene liquid-crystal films,” Science 268(5219), 1873–1875 (1995). [CrossRef]
2. L. Dong, Y. Feng, L. Wang, and W. Feng, “Azobenzene-based solar thermal fuels: design, properties, and applications,” Chem. Soc. Rev. 47(19), 7339–7368 (2018). [CrossRef]
3. J. Liu, W. Bu, L. Pan, and J. Shi, “NIR-triggered anticancer drug delivery by upconverting nanoparticles with integrated azobenzene-modified mesoporous silica,” Angew. Chem. Int. Ed. 52(16), 4375–4379 (2013). [CrossRef]
4. A. A. Beharry and G. A. Woolley, “Azobenzene photoswitches for biomolecules,” Chem. Soc. Rev. 40(8), 4422–4437 (2011). [CrossRef]
5. T. Fujino and T. Tahara, “Picosecond time-resolved Raman study of trans-azobenzene,” J. Phys. Chem. A 104(18), 4203–4210 (2000). [CrossRef]
6. P. Hamm, S. M. Ohline, and W. Zinth, “Vibrational cooling after ultrafast photoisomerization of azobenzene measured by femtosecond infrared spectroscopy,” J. Chem. Phys. 106(2), 519–529 (1997). [CrossRef]
7. C. W. Chang, Y. C. Lu, T. T. Wang, and E. W. Diau, “Photoisomerization dynamics of azobenzene in solution with S1 excitation: a femtosecond fluorescence anisotropy study,” J. Am. Chem. Soc. 126(32), 10109–10118 (2004). [CrossRef]
8. M. Quick, A. L. Dobryakov, M. Gerecke, C. Richter, F. Berndt, I. N. Ioffe, A. A. Granovsky, R. Mahrwald, N. P. Ernsting, and S. A. Kovalenko, “Photoisomerization dynamics and pathways of trans- and cis-azobenzene in solution from broadband femtosecond spectroscopies and calculations,” J. Phys. Chem. B 118(29), 8756–8771 (2014). [CrossRef]
9. L. Zhou, L. Chen, G. Ren, Z. Zhu, H. Zhao, H. Wang, W. Zhang, and J. Han, “Monitoring cis-to-trans isomerization of azobenzene using terahertz time-domain spectroscopy,” Phys. Chem. Chem. Phys. 20(42), 27205–27213 (2018). [CrossRef]
10. D. Wang, B. Yang, W. Gao, H. Jia, Q. Yang, X. Chen, M. Wei, C. Liu, M. Navarro-Cía, J. Han, W. Zhang, and S. Zhang, “Photonic Weyl points due to broken time-reversal symmetry in magnetized semiconductor,” Nat. Phys. 15(11), 1150–1155 (2019). [CrossRef]
11. A. Shalit, S. Ahmed, J. Savolainen, and P. Hamm, “Terahertz echoes reveal the inhomogeneity of aqueous salt solutions,” Nat. Chem. 9(3), 273–278 (2017). [CrossRef]
12. A. I. McIntosh, B. Yang, S. M. Goldup, M. Watkinson, and R. S. Donnan, “Terahertz spectroscopy: a powerful new tool for the chemical sciences?” Chem. Soc. Rev. 41(6), 2072–2082 (2012). [CrossRef]
13. S. A. Bretschneider, I. Ivanov, H. I. Wang, K. Miyata, X. Zhu, and M. Bonn, “Quantifying polaron formation and charge carrier cooling in lead-iodide perovskites,” Adv. Mater. 30(29), 1707312 (2018). [CrossRef]
14. Z. Zhang, M. Kang, X. Zhang, X. Feng, Y. Xu, X. Chen, H. Zhang, Q. Xu, Z. Tian, W. Zhang, A. Krasnok, J. Han, and A. Alù, “Coherent perfect diffraction in metagratings,” Adv. Mater. 32(36), 2002341 (2020). [CrossRef]
15. Y. Li, C. Chang, Z. Zhu, L. Sun, and C. Fan, “Terahertz wave enhances permeability of the voltage-gated calcium channel,” J. Am. Chem. Soc. 143(11), 4311–4318 (2021). [CrossRef]
16. H. Cheon, H.-j. Yang, S.-H. Lee, Y. A. Kim, and J.-H. Son, “Terahertz molecular resonance of cancer DNA,” Sci. Rep. 6(1), 37103 (2016). [CrossRef]
17. Y. C. Sim, J. Y. Park, K.-M. Ahn, C. Park, and J.-H. Son, “Terahertz imaging of excised oral cancer at frozen temperature,” Biomed. Opt. Express 4(8), 1413 (2013). [CrossRef]
18. C. J. Brown, “A refinement of the crystal structure of azobenzene,” Acta Crystallogr. 21(1), 146–152 (1966). [CrossRef]
19. L. Chen, G. Ren, L. Liu, P. Guo, E. Wang, L. Zhou, Z. Zhu, J. Zhang, B. Yang, W. Zhang, Y. Li, W. Zhang, Y. Gao, H. Zhao, and J. Han, “Terahertz signatures of hydrate formation in alkali halide solutions,” J. Phys. Chem. Lett. 11(17), 7146–7152 (2020). [CrossRef]
20. J. R. Goates, J. B. Ott, and A. H. Budge, “Solid-liquid phase equilibria and solid compound formation in acetonitrile-aromatic hydrocarbon systems,” J. Phys. Chem. 65(12), 2162–2165 (1961). [CrossRef]
21. L. Chen, G. Ren, L. Liu, P. Guo, E. Wang, Z. Zhu, J. Yang, J. Shen, Z. Zhang, L. Zhou, J. Zhang, B. Yang, W. Zhang, Y. Gao, H. Zhao, and J. Han, “Probing NaCl hydrate formation from aqueous solutions by terahertz time-domain spectroscopy,” Phys. Chem. Chem. Phys. 22(32), 17791–17797 (2020). [CrossRef]
22. J. B. Ott, J. R. Goates, D. R. Anderson, and H. T. Hall, “Solid-liquid phase equilibria in the sodium + potassium system,” Trans. Faraday Soc. 65, 2870–2878 (1969). [CrossRef]
23. J. A. Bouwstra, A. Schouten, and J. Kroon, “Structural studies of the system trans-azobenzene/trans-stilbene. I. A reinvestigation of the disorder in the crystal structure of trans-azobenzene, C12H10N2,” Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 39(8), 1121–1123 (1983). [CrossRef]
24. A. Mostad and C. Rømming, “A refinement of the crystal structure of cis-azobenzene,” Acta Chem. Scand. 25(10), 3561–3568 (1971). [CrossRef]
25. P. C. Chen and Y. C. Chieh, “Azobenzene and stilbene: a computational study,” J. Mol. Struct.: THEOCHEM 624(1-3), 191–200 (2003). [CrossRef]
26. W. Xu, Q. Zhu, and C. T. Hu, “The structure of glycine dihydrate: implications for the crystallization of glycine from solution and its structure in outer space,” Angew. Chem. Int. Ed. 56(8), 2030–2034 (2017). [CrossRef]
27. N. Denkov, S. Tcholakova, I. Lesov, D. Cholakova, and S. K. Smoukov, “Self-shaping of oil droplets via the formation of intermediate rotator phases upon cooling,” Nature 528(7582), 392–395 (2015). [CrossRef]
28. A. W. Crawford, R. H. Groeneman, D. K. Unruh, and K. M. Hutchins, “Cooling-rate dependent single-crystal-to-single-crystal phase transition in an organic co-crystal,” Chem. Commun. 55(22), 3258–3261 (2019). [CrossRef]
29. O. Petrov and I. Furó, “Curvature-dependent metastability of the solid phase and the freezing-melting hysteresis in pores,” Phys. Rev. E 73(1), 011608 (2006). [CrossRef]
30. I. Hitchcock, E. M. Holt, J. P. Lowe, and S. P. Rigby, “Studies of freezing–melting hysteresis in cryoporometry scanning loop experiments using NMR diffusometry and relaxometry,” Chem. Eng. Sci. 66(4), 582–592 (2011). [CrossRef]
31. O. Petrov and I. Furó, “A study of freezing–melting hysteresis of water in different porous materials. Part I: Porous silica glasses,” Microporous Mesoporous Mater. 138(1-3), 221–227 (2011). [CrossRef]
32. X. Ni and A. Liao, “Effects of cooling rate and solution concentration on solution crystallization of L-glutamic acid in an oscillatory baffled crystallizer,” Cryst. Growth Des. 8(8), 2875–2881 (2008). [CrossRef]
33. F. Qu, L. Lin, C. Cai, B. Chu, Y. Wang, Y. He, and P. Nie, “Terahertz fingerprint characterization of 2,4-dichlorophenoxyacetic acid and its enhanced detection in food matrices combined with spectral baseline correction,” Food Chem. 334, 127474 (2021). [CrossRef]
34. H. M. D. Bandara and S. C. Burdette, “Photoisomerization in different classes of azobenzene,” Chem. Soc. Rev. 41(5), 1809–1825 (2012). [CrossRef]
