The effect of solvent viscosity on the quenching by oxygen of S1 and T1 states was investigated for a number of meso-substituted anthracene derivatives. The solvent viscosity, r], was varied by applying hydrostatic pressure at several temperatures. The fluorescence from the S1 state of the anthracene derivatives that have one or two electron-donating substituents was quenched nearly collisionally, and the dependence of the rate constant for fluorescence quenching, kS, on r] was shown to be described satisfactorily by the empirical function, Aq". It was shown for 9-methylanhracene in methylcyclohexane that the exponent, a, has a value of 0.68 f 0.06, which is independent of temperature and pressure but that thevalue of the constant of proportionality, A, is temperature dependent. The dependence of A on temperature was described empirically using the functions P.36 or exp(-AEIRT). An alternative function for is (T/r])@, but this function failed to describe correctly the dependence of kt on 9 and T. The fractional power dependence of k: on 4 suggests that the rate constant for the intrinsic fluorescence quenching reaction, kaCt, is not significantly larger than the rate constant for diffusion.The values of k: for the anthracene derivatives containing one or two electron-attracting substituents were smaller than that found for anthracene, decreased with Hammett's up parameter, and could not be described by the empirical function A?* with a constant value for a. A typical example is 9,lO-dicyanoanthracene whose values for k: exhibit a convex dependence on In r]. In accordance with this, the activation energy associated with k: was negative at low viscosities and displayed a transition from negative to positive values as the viscosity was increased. The values of the rate constant for the quenching by oxygen of the T1 states of the anthracene derivatives, k t , did not vary significantly, all being approximately 3 X lo9 M-1 s-l at 25 OC and 0.1 MPa. The logarithmic values of k;, when plotted as a function of In r], displayed appreciable downward curvature for all of the anthracene derivatives examined in this work.

The mechanism for the quenching by oxygen of the singlet and triplet states of several anthracene derivatives in methylcyclohexane (MCH) under pressures of up to 700 MPa was investigated. The value for the rate constant of fluorescence quenching, k s, at 0.1 MPa is found to vary from (3.2 f 1.1) X lo9 M-' s-* for 9,10-dicyanoanthracene (DCNA) to (2.88 f 0.27) X IOy0 M-l s-I for 9-methylanthracene (MEA), whereas values for the rate constant of the triplet-state quenching process, k at 0.1 MPa are similar for each of the anthracenes, being in the range (3.0-3.8) X IO9 M-' s-I. The values for the pressure increase. A linear relation between In k," and In 7 is found for anthracene (A) and MEA, with slopes of -0.57 f 0.04 and -0.64 f 0.02, respectively. However, plots of this relation show a distinct downward curvature for 9,lO-dichloroanthracene (DCLA) and DCNA. It is also found that In kqT does not vary linearly with In 7 for any of the derivatives examined. The activation volumes of k," for A and MEA are estimated to be in the range 12-14 cm3 mol-I. These values are about 2 times larger than those determined for k T, but are only half of the value reported for the activation volume of the viscosity of MCH. The ratio of k, ' to k: for MkA and DCLA at 0.1 MPa is reasonably close to the predicted value of 1/9 and increases with pressure, reaching a value of approximately 4 9 for DCLA at 700 MPa. These results suggest that, is not conserved, may come to play an important role in the quenching of the triplet state as the pressure is increased. Dynamic aspects of the fluorescence quenching are also discussed in terms of the transient decay feature characterized by the function predicted by the Smoluchowski model. k: and k, P' decrease with increasing pressure, mainly as a result of the increase in viscosity of the solvent that accompanies in addition to '(AOz)*, encounter complexes of the form 3(AOz)* or / (A02)*, for which the total spin angular momentum IntroductionMolecular oxygen is an efficient quencher of the electronically excited states of many organic molecules. In most cases, the quenching by oxygen is so eMicient that the reaction rate is believed to be diffusion-limited. However, quenching rate constants reported in the literature vary from compound to compound, for example, 3.3 X IO'O M-' s-' for p-methoxybiphenyl and 4.4 X lo9 M-l s-I for flu0ranthene.I Despite this wide range of magnitudes,

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In this study, we show the formation of frequency band structures in origami-based mechanical metamaterials composed of the Triangulated Cylindrical Origami (TCO). Interestingly, the folding behavior of this structure can exhibit both axial and rotational motions under external excitations. Therefore, these two motions can be strongly coupled with each other, which leads to unique dynamic behavior, particularly wave mixing effects. To analyze the folding behavior of the TCO cells, we model their triangular facets into a network of linear springs. We assemble a 1D chain of multiple TCO unit cells stacked vertically in various arrangements, e.g., changing their stacking sequences and/or orientation angles. We study frequency responses of this system to investigate wave mixing effects between axial and rotational motions under dynamic excitations. This dynamic analysis on the multi-cell structure demonstrates the formation of tunable frequency band structures, which can be manipulated by the arrangement of the unit cells and their initial configurations. By taking advantage of their unique dynamic mechanisms, the origami-based mechanical metamaterials have great potential to be used for controlling structural vibrations in an efficient manner.