[en] This article investigates the robustness of switched multiple equilibrium points systems (SMEPSs) with unstable subsystems. Each subsystem has a unique equilibrium point that is different from all equilibrium points of the other subsystems. Unlike the most commonly used Lyapunov function method, the analytical solutions and numerical solutions are calculated to analyze the boundedness of the solutions for perturbation discrete-time and continuons-time SMEPSs, respectively. The given perturbation systems have good robustness if the ratio of total dwell time of unstable subsystems and the total dwell time of stable subsystems is less than or equal to a constant. A numerical example is employed to validate the correctness of the theoretical results.

[en] We show that unsymmetric BODIPY compounds with one, two, and three methyl groups can be synthesized easily and efficiently by the unsymmetric reaction method. Their steady state and time-resolved fluorescence properties are examined in solvents of different polarity. These compounds show high fluorescence quantum yields (0.87 to 1.0), long fluorescence lifetimes (5.89 to 7.40 ns), and small Stokes shift (199 to 443 cm⁻¹). The methyl substitution exhibits influence on the UV-Vis absorption and fluorescence properties, such as the blue shift in emission and absorption spectra. It is the number rather than the position of methyls that play major roles. Except for 3 M-BDP, the increase in the number of methyls on BODIPY core leads to the increase in both fluorescence quantum yield and radiative rate constant, but causes the decrease in fluorescence lifetime. H-bonding solvents increase both the fluorescence lifetime and quantum yields. The methylated BODIPYs show the ability to generate singlet oxygen (¹Δ_g) which is evidenced by near-IR luminescence and DPBF chemical trapping techniques. The formation quantum yield of singlet oxygen (¹Δ_g) for the compounds is up to 0.15 ± 0.05.

[en] To get consistent data for ten rhodamine dyes, the fluorescence lifetime, fluorescence quantum yield and spectral properties were measured under the same conditions in four typical solvents by using time-correlated single photon counting and steady state fluorometer. The comparable data make it possible to discuss the mechanism that controls the fluorescence properties of the rhodamine dyes. The data showed that the molecular structure and solvent have remarkable effects. The second alkyl and the rigidity of the alkyls on N atoms are the determining factors for fluorescence lifetime and quantum yields, whereas the substitution on phenyls has little influence. The increase of the solvent polarity decreases both the fluorescence lifetime and fluorescence quantum yield. These results support that the intra-molecular photoinduced electron transfer (PET) may occur from the xanthene moiety to the linked phenyl. The rate constant of radiation process, however, shows no dependence on both the chemical structure and solvents but a constant value (0.21×10⁹ s⁻¹). The rate constant of nonradiation process, on the other hand, is varied with both the structure and the solvent used. -- Highlights: • The fluorescence lifetime and quantum yield of ten rhodamine dyes were measured. • The mechanism that controls the fluorescence properties of the dyes was suggested. • Intra-molecular photoinduced electron transfer occurs within Rhodamine B. • The second alkyl and the rigidity of the alkyls on N atoms are the determining factors

[en] The aggregation (inter-layer π–π interaction) and self-rolling up (intra-layer π–π interaction) of chemically derived graphene (CDG) sheets in aqueous dispersion were evidenced by spectral and TEM methods. Their effects on optical properties were studied by UV–vis–NIR absorption spectra, fluorescence emission spectra and fluorescence lifetime measurements under various CDG concentrations. At pH 8.3, CDG sheets formed carbon nanoscrolls by self-rolling up when its concentration is lower than 10 μg/mL. When the concentration is higher than that, CDG sheets aggregated. Upon aggregation, CDG exhibited the decrease of absorptivity, the change of band shape and the deviation from Lambert–Beer law due to inter-layer π–π interaction. The aggregation effect on CDG fluorescence includes the decrease of emission efficiency, the shortening of fluorescence lifetime and the relative increase of the contribution from short-lived emitting species. On the other hand, CDG self-rolling up caused the occurrence of new absorptions (500 and 960 nm) and new emission (after 500 nm), the decrease of fluorescence quantum yield and shortening of fluorescence lifetime. -- Highlights: ► Aggregation of CDG (chemically derived graphene) occurs, when its concentration>10 μg/mL. ► Self-rolling up of CDG sheets occurs and forms carbon nanoscrolls, when its concentration <10 μg/mL. ► The optical properties of carbon nanoscrolls were discussed for the first time. ► CDG aggregation (CDGA) causes the decrease of absorptivity, the change of band shape. ► CDGA induces the decrease of emission efficiency, the shortening of fluorescence lifetime. ► CDGA causes the relative increase of the contribution from short-lived emitting species

[en] Highlights: • Excited triplet state T₁ properties for BODIPY parent compound (BDP) are reported for the 1st time. • The singlet oxygen formation efficiency of BDP is measured in different solvents. • Molecular oxygen strongly increases the T₁ and singlet oxygen formation efficiency. • Fluorescence lifetime and quantum yield are quenched by oxygen. • The oxygen enhancing mechanism is due to: BDP(S₁) + O₂ .→ BDP(T₁) + ¹O₂(¹Δ_g). -- Abstract: Excited triplet state (T₁) properties and formation efficiency are key issues in photodynamic therapy (PDT) and organic light emitting diode (OLED). We report hereby the T₁ properties, T₁ formation efficiency and mechanism for BODIPY parent compound (BDP) using laser flash photolysis technique. We also disclose the singlet oxygen ¹O₂(¹Δ_g) formation ability of BDP based on NIR phosphorescence and chemical trapping method. More importantly we show that molecular oxygen can strongly increase the T₁ and singlet oxygen formation efficiency of BDP up to 5-fold compared to its intrinsic ability due to intersystem crossing. Combining with time-resolved and steady state fluorescence methods, we conclude that the oxygen enhancing mechanism is due to that the energy transfer from the excited singlet state (S₁) of BDP to molecular oxygen leads to both T₁ and ¹O₂ formation: BDP(S₁) + O₂ → BDP(T₁) + ¹O₂(¹Δ_g). This O₂ enhancing mechanism for T₁ and ¹O₂ formation is important to understand and design BODIPY photosensitizers in various applications including PDT and OLED.

[en] Highlights: • BODIPY parent compound (BDP) is synthesized. • BDP shows high fluorescence quantum yield (Φ_f) in all solvents (Φ_f > 0.80). • BDP has long fluorescence lifetime (τ_f) in all solvents (τ_f > 6.0 ns). • Oxygen quenches S₁ of BDP and generates singlet oxygen. • Fluorescence lifetime and fluorescence quantum yield correlates with refractive index of the solvent. -- Abstract: The BODIPY (boron-dipyrromethene) parent compound is synthesized to measure its fluorescence properties and singlet oxygen generation ability. The ground state, excited singlet state S₁ and triplet state T₁ geometry and properties in gas, solid state and organic solvents are calculated by DFT method. This unsubstituted BODIPY (BDP) has good solubility in all solvents ranging from non polar n-hexane to highly polar water. BDP exhibits bright green fluorescence with high fluorescence quantum yield (Φ_f) and long fluorescence lifetime (τ_f) values in all solvents, Φ_f of BDP varies from the lowest 0.79 in toluene to the highest 0.98 in water, while τ_f varies from the shortest 6.02 ns in toluene to the longest 7.36 ns in water. τ_f and Φ_f show good linear correlation with the refractive index (n) of a solvent: τ_f = 17.13 – 7.36·n and Φ_f = 2.51–1.16·n (for air-saturated solution). The fluorescence lifetime in each solvent, however, becomes longer in deoxygenated solutions, suggesting that the presence of molecular oxygen leads to the formation of BDP T₁ and singlet oxygen: BDP(S₁)+O₂ → BDP(T₁)+¹O₂. Singlet oxygen formation quantum yield was measured to be up to 0.083. The absorption and emission maximum (λ_abs and λ_em), however, are only slightly changed by solvent nature: λ_abs= 500 ± 4 nm and λ_em= 510 ± 4 nm. The spectral shape and peak maximum for its absorption and emission are little affected by solvent nature. DFT calculation reveals that the geometry difference between S₀ and S₁ state of BDP is very small, so that the dipole moment change is also small. The calculated charges of carbon atoms, however, are very different and can well explain their different reactivity to nucleophiles. The calculated absorption spectra (peak maximum λ_cal) by TD-DFT method shows a good linear relation with experimental value λ_exp: λ_exp = 1.19 λ_cal. These results provide the basis for elucidating the mechanism or photophysical processes involving BODIPY as the functional units.

[en] The optical absorption and fluorescence properties of five rhodamine dyes in solid-state are measured and show large difference from that in their gas phase or liquid solvents. All solid-state rhodamine dyes strongly absorb all light in UV and visible region, but emit only red and NIR fluorescence (680–800 nm, >100 nm red-shifted from that in solution). Further more, the absorption maxima of a solid-state rhodamine show a large red-shifted band (~100 nm) and blue-shifted peak (~125 nm) compared to that in solutions, indicating a strong molecular exciton coupling between molecules. All solid-state rhodamines still show reasonably good fluorescence quantum yield (Φ_f). In particular, solid-state Rhodamine B butyl ester and sulfonyl Rhodamine B showed a much longer emission lifetime (τ_f) than that of the corresponding molecular rhodamine, i.e. 4.12 and 4.14 ns in solid state compared to 1.61 and 2.47 ns in solution. The chemical structure of a rhodamine molecule showed dramatic effect on Φ_f and τ_f values for solid state rhodamine. The larger substituent in the benzene moiety favors higher Φ_f and τ_f values of rhodamine solids. These effects can be elucidated by the relation between structure-molecular distance and molecular exciton couplings. - Highlights: • Optical properties of solid rhodamines show large difference from that in solutions. • Solid-state rhodamine dyes emit red and NIR fluorescence (680–800 nm). • Solid-state rhodamines still show reasonably good fluorescence quantum yield. • Solid-state rhodamines have much longer fluorescence lifetimes than that in solutions

[en] meso-phenyl and meso-naphthyl substituted BODIPY derivatives were synthesized as singlet oxygen photosensitizers. Strengthening the electron donating ability of the phenyl or naphthyl by attaching OCH₃ or OH group makes these BODIPYs efficiently generate singlet oxygen in polar solvents accompanied by strong fluorescence quenching. The BODIPYs exhibited higher fluorescence quantum yields in non polar solvents, but became much less emissive in polar solvents. The results are explained by the involvement of photoinduced electron or charge transfer process in the lowest lying excited singlet state (S₁). These results indicate that these BODIPY dyes can be potential singlet oxygen photosensitizers for the application in PDT and theranostics.

[en] Six rhodamine dyes for which the benzoate is modified with NH₂ or COOH were studied by time-correlated single photon counting and steady state fluorescence technique. The absorption and fluorescence spectra, the fluorescence quantum yield as well as fluorescence lifetime values were measured in typical solvents. The data showed that molecular rigidity, the substituent type and position on the benzoate, as well as solvent have remarkable effects on fluorescence properties. NH₂ on the benzoate showed very different effect from that of COOH. NH₂ modified rhodamines exhibit much smaller fluorescence quantum yields and much shorter lifetimes, due to the very fast intramolecular photoinduced electron transfer (PET). On the substituent position effect, 5′-COOH on the benzoate leads to larger band maximum, lower fluorescence quantum yield and shorter fluorescence lifetime than that of 6′-COOH. For NH₂ substitution, however, it is 6-NH₂ that shows larger band maximum, lower fluorescence quantum yield and shorter fluorescence lifetime than that of 5′-COOH. Although the rate constant of nonradiation process for the rhodamines is varied in several orders with structure and solvent, the rate constant of radiation process, however, shows a constant value (0.18×10⁹ s⁻¹). Quantum chemical calculations on B3LYP/6-31+G(d) level was also carried out to obtain molecular structures and free energy change to confirm the presence of PET. - Highlights: • Flurescence of benzoate-modified rhodamine dyes was studied in detail. • Large change in flurescence efficiency and lifetime occurred upon substitution. • Molecular rigidity, the substituent and position on the benzoate are main factors. • Fluorescence change is due to fast intramolecular photoinduced electron transfer. • Rate constant of radiation process is a constant value for the six rhodamine dyes.