Transition Rates Research Articles

Temperature-dependent law of transition probability associated with main emission states in YVO4:Re3+ (Re3+=Sm3+, Dy3+ and Eu3+)

The understanding of how radiative transition probabilities change with temperature is crucial for comprehending the relationship between fluorescence behavior and temperature. However, although various models have been proposed to explain the patterns of transition probabilities (A) with temperature changes, they lack consistency due to their derivation from distinct microscopic perspectives. In this study, the macroscopic law of the temperature-dependent A for the 4G5/2, 4F9/2, and 5D0 energy states in YVO4:Re3+(Re3+=Sm3+, Dy3+ and Eu3+) was obtained. Three rare earth ions (Re3+) were identified for each with unique energy level properties conducive to validating the general rules of A. These ions share a common characteristic: in the visible spectrum, their main emissions originate from the radiative transitions from the same higher energy level (4G5/2 in Sm3+, 4F9/2 in Dy3+, and 5D0 in Eu3+) to lower energy levels, respectively. The A of the main emission levels, varying with T, were obtained by fitting the fluorescence decay curves. The exponential law governing non-radiative transitions was revealed after separating the radiative transition rate (WR) from A. The macroscopic law of temperature-dependent transition probabilities of 4G5/2, 4F9/2, and 5D0 energy states in YVO4:Ln3+ (Ln3+ = Sm3+, Dy3+ and Eu3+) has been found to follow the Boltzmann distribution. The results indicate that the non-radiative transitions of the main emission levels of the rare-earth ions are processes from the excited state to adjacent lower energy levels. This macroscopic pattern may serve as a foundational rule for understanding the impact of microscopic factors on A.

Preparation and Judd-Ofelt Analysis of Warm Red Luminescent Eu3+ Complexes for Semiconductor Lasing Devices.

Six novel red photoluminescent Eu3+ complexes with 3-formyl chromone as the primary sensitizer (L) were synthesized using the solution precipitation method. These complexes are [Eu(L3).X] where X is 2H2O (C1), phen (C2), neo (C3), bipy (C4), dmph (C5), and biquno (C6). These complexes were characterized by elemental analysis, EDAX analysis, SEM, FT-IR, thermo-gravimetric analysis (TGA/DTA) and photoluminescence spectra. The transition rates, quantum efficiency, and J-O intensity parameters were calculated using emission data and luminescence decay time (τ). Complexes exhibit a strong emission peak (5D0 → 7F2) of the Eu3+ ion in their luminescence emission spectra in solid and solution states, making them an effective emitter of the red color in OLEDs. The branching ratio of these complexes ranges from 80.67-82.92 in solid and 50.53-62.65 in solution state; CIE color coordinate of complexes falls in the red region. The color purity ranges [CP(%)] values for solid 95.26-97.27% and for solution ranges 85.11-93.43%. Correlated color temperature (CCT) of the complexes (C1-C6) ranged from 2710 to 3049K in the solid state and 1775 to 2450K in the solution state. These complexes are promising red emitters in OLEDs, semiconductors, and leasing devices.

The Role of Precursor Disturbances on the Modulation of Western Pacific Tropical Cyclogenesis by the Madden‐Julian Oscillation

AbstractThe present study considers tropical cyclogenesis as a multi‐stage process in which pre‐cursor disturbances develop first and a fraction of them further strengthen to become a tropical cyclone (TC). Using this framework, we analyze the impact of Madden‐Julian oscillation (MJO)‐ associated anomalous large‐scale environmental conditions on the triggering of tropical convective clusters (TCCs)—a type of pre‐cursor disturbance—and the TCC‐to‐TC transition in the western Pacific. We find that, within the MJO's lifecycle, the modulation of the TCC frequency by the MJO drives TC genesis frequency anomalies earlier than the TCC‐to‐TC transition rate. Also, the fluctuation of TCC occurrence frequency is most strongly associated with the MJO's large‐scale ascent and relative humidity anomalies, while that of the transition of TCCs to a TC is mainly associated with the MJO's vorticity anomalies. Our results suggest the distinct roles of large‐scale environmental variables in different stages of tropical cyclogenesis.

Steady-state probabilities for Markov jump processes in terms of powers of the transition rate matrix.

Several types of dynamics at stationarity can be described in terms of a Markov jump process among a finite number N of representative sites. Before dealing with the dynamical aspects, one basic problem consists in expressing the a priori steady-state occupation probabilities of the sites. In particular, one wishes to go beyond the mere black-box computational tools and find expressions in which the jump rate constants appear explicitly, therefore allowing for a potential design/control of the network. For strongly connected networks admitting a unique stationary state with all sites populated, here we express the occupation probabilities in terms of a formula that involves powers of the transition rate matrix up to order N - 1. We also provide an expression of the derivatives with respect to the jump rate constants, possibly useful in sensitivity analysis frameworks. Although we refer to dynamics in (bio)chemical networks at thermal equilibrium or under nonequilibrium steady-state conditions, the results are valid for any Markov jump process under the same assumptions.

Effects of measurement power on state discrimination and dynamics in a circuit-QED experiment

We explore the effects of driving a cavity at a large photon number in a circuit-QED experiment where the “matterlike” part corresponds to a unique Andreev level in a superconducting weak link. The three many-body states of the weak link, corresponding to the occupation of the Andreev level by 0, 1, or 2 quasiparticles, lead to different cavity frequency shifts. We show how the nonlinearity inherited by the cavity from its coupling to the weak link affects the state discrimination and the photon number calibration. Both effects require treating the evolution of the driven system beyond the dispersive limit. In addition, we observe how transition rates between the circuit states (quantum and parity jumps) are affected by the microwave power, and compare the measurements with a theory accounting for the “dressing” of the Andreev states by the cavity. Published by the American Physical Society 2024

Direct WIMP detection rates for transitions in isomeric nuclei

The direct detection of dark matter constituents, in particular the weakly interacting massive particles (WIMPs), is central to particle physics and cosmology. In this paper we study WIMP induced transitions from isomeric nuclear states for two possible isomeric candidates: Ta180 and Ho166. The experimental setup, which can measure the possible decay of Ta180 induced by WIMPs, was proposed. The corresponding estimates of the half-life of Ta180 are given in the sense that the WIMP-nucleon interaction can be interpreted as ordinary radioactive decay.

Intertwined quantum phase transitions in the zirconium and niobium isotopes

Nuclei in the A ≈ 100 region exhibit intricate shape-evolution and configuration crossing signatures. Exploring both even–even and their adjacent odd-mass nuclei gives further insight on the emergence of deformation and shape-phase transitions. We employ the algebraic frameworks of the interacting boson model with configuration mixing and the new interacting boson-fermion model with configuration mixing in order to investigate the even–even zirconium with neutron number 52–70 (40Zr) and odd-mass niobium (41Nb) isotopes with 52–62. We compare between the evolution in energy levels, configuration and symmetry content of the wave functions, two neutron separation energies and E2 transition rates, alongside comparison with the experimental data. The comparisons between the two chains of isotopes denote the occurrence of two types of QPTs, a crossing of normal and intruder configurations (named Type II QPT), and a shape-evolution of the intruder configuration (named Type I QPT). The latter QPT begins from spherical shape to axially deformed rotor in the Zr isotopes and from weak to strong coupling scenario in the Nb isotopes. This occurrence, named intertwined quantum phase transitions (IQPTs), in the even–even Zr chain is thus demonstrated to persists when coupling a proton to the boson core for the odd-mass Nb chain, even as deformation increases.

Looking Back and Moving Forward: COVID-19’s Impact on the Teacher Labor Market and Implications for the Future

Throughout the COVID-19 pandemic teachers reported high levels of stress and burnout, raising concerns about a potential increase in teacher turnover and future teacher shortages. We use administrative data from the 2018 to 2019 through 2022 to 2023 school years to examine how the pandemic affected teacher turnover in Arkansas. We find relatively stable turnover entering the 2020 to 2021 and 2021 to 2022 school years but an increase of 5 percentage points (20%) over pre-pandemic levels entering the 2022 to 2023 school year, representing both higher rates of transitions out of the education sector but also more likely movements to other positions outside regular teaching within the education sector. Importantly, we also find significant heterogeneity in turnover by teacher and school characteristics suggesting a decline in aggregate teacher quality, diversity, and experience. These results suggest potential lasting effects on the composition and quality of the teacher labor force.

Lessons learned: avoiding bias via multi-state analysis of patients' trajectories in real-time.

Many studies have attempted to determine the disease severity and patterns of COVID-19. However, at the beginning of the pandemic, the complex patients' trajectories were only descriptively reported, and many analyses were worryingly prone to time-dependent-, selection-, and competing risk biases. Multi-state models avoid these biases by jointly analysing multiple clinical outcomes while taking into account their time dependency, including current cases, and modelling competing events. This paper uses a publicly available data set from the first wave in Israel as an example to demonstrate the benefits of analysing hospital data via multi-state methodology. We compared the outcome of the data analysis using multi-state models with the outcome obtained when various forms of bias are ignored. Furthermore, we used Cox regression to model the transitions among the states in a multi-state model. This allowed for the comparison of the covariates' influence on transition rates between the two states. Lastly, we calculated expected lengths of stay and state probabilities based on the multi-state model and visualised it using stacked probability plots. Compared to standard methods, multi-state models avoid many biases in the analysis of real-time disease developments. The utility of multi-state models is further highlighted through the use of stacked probability plots, which visualise the results. In addition, by stratification of disease patterns by subgroups and visualisation of the distribution of possible outcomes, these models bring the data into an interpretable form. To accurately guide the provision of medical resources, this paper recommends the real-time collection of hospital data and its analysis using multi-state models, as this method eliminates many potential biases. By applying multi-state models to real-time data, the gained knowledge allows rapid detection of altered disease courses when new variants arise, which is essential when informing medical and political decision-makers as well as the general population.

Symmetry Molecular Design Strategy for Highly Efficient Blue Electroluminescence with Hot Exciton Mechanisms

AbstractEmitters with a hot exciton mechanism are regarded as one of the most promising candidates for organic light‐emitting diodes (OLEDs). In this study, a deep‐blue emitter with the hot exciton mechanism is reported, namely 2An‐PCz, by integrating a pair of carbazole groups with a 9,9′‐bi‐anthracene nucleus. Owing to the symmetric molecular architecture and intrinsic local excited state character, multiple high‐lying reverse intersystem cross (hRISC) channels and large overlaps of frontier molecular orbits (FMOs) can be formed, facilitating rapid hRISC processes as well as enhancement of radiative transition rates simultaneously. Combined with the strong luminescence properties brought by the unique X‐packing mode, a high photoluminescence quantum yield of 60.5% is achieved in the non‐doped state. Strikingly, non‐doped deep‐blue OLEDs exhibited a maximum external quantum efficiency (EQE) of 10.50% with minimal efficient roll‐off, which is one of the highest values for deep‐blue organic light‐emitting devices based on hot exciton emitters thus far. The magneto‐electroluminescence (MEL) experiment and transient electroluminescence measurements corroborated that both the high EQE and suppressed efficiency roll‐off are attributable to the rapid “hot exciton” channels.

Robustness of reaction–diffusion PDEs predictor-feedback to stochastic delay perturbations

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction–diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The stabilization problem under consideration involves random perturbations modeled by a finite-state Markov process that further obstruct the actuation path at the controlled boundary of the infinite-dimension plant. This scenario is useful to describe several actuation failure modes in process control. Employing the recently introduced infinite-dimensional representation of the state of an actuator subject to stochastic input delay for ODEs (Ordinary Differential Equations), we convert the stochastic input delay into r+1 unidirectional advection PDEs, where r corresponds to the number of jump states. Our stability analysis assumes full-state measurement of the spatially distributed plant’s state and relies on a hyperbolic–parabolic PDE-PDE cascade representation of the plant plus actuator dynamics. Integrating the plant and the nominal stabilizing boundary control action, all while considering probabilistic delay disturbances, we establish the proof of mean-square exponential stability as well as the well-posedness of the closed-loop system when random phenomena weaken the nominal actuator compensating effect. Our proof is based on the Lyapunov method, the theory of infinitesimal operator for stability, and C0-semigroup theory for well-posedness. Our stability result refers to the L2-norm of the plant state and the H2-norm of the actuator state. Furthermore, our study presents a qualitative analysis of the maximum deviation of the stochastic disturbance relative to the nominal delay, which is expressed as a function of the severity of the plant instability, namely, the magnitude of the reactivity coefficientand the known upper bound of the transition rate of the underlying stochastic perturbations. Extensive simulation results illustrate the viability of the robustness study.

Amelioration activity of the high bioaccessible chrysanthemum (Gongju) phenolics on alcohol-induced oxidative injury in AML-12 cells

The main bioavailable phenolics from of Gongju (GJ) and their mechanism for hepato-protection remain unclear. To select the GJ phenolics with high bioavailability, chrysanthemum digestion and Caco-2 cells were used and their hepato-protective potential were examined by using AML-12 cells. The digestive recovery and small intestinal transit rate of the main phenolic compounds ranged from 28.52 to 69.53% and 6.57% ∼ 15.50%, respectively. Among them, chlorogenic acid, 3,5-dicaffeoylquinic acid, and 1,5-dicaffeoylquinic acid, showed higher small intestinal transit rates and digestive recoveries. Furthermore, we found that by increasing intracellular Catalase (CAT) and Superoxide dismutase (SOD) viability and lowering Malondialdehyde (MDA) level (P < 0.05), 3,5-dicaffeoylquinic acid significantly mitigated the oxidative damage of AML-12 liver cells more than the other two phenolics. Our results demonstrated that 3,5-dicaffeoylquninic acid was the primary phenolic compounds in GJ that effectively reduced liver damage, providing a theoretical basis for the development of GJ as a potentially useful resource for hepatoprotective diet.

Sphaleron damping and effects on vector and axial charge transport in high-temperature QCD plasmas

We modify the anomalous hydrodynamic equations of motion to account for dissipative effects due to quantum chromodynamic (QCD) sphaleron transitions. By investigating the linearized hydrodynamic equations, we show that sphaleron transitions lead to nontrivial effects on vector and axial charge transport phenomena in the presence of a magnetic field. Due to the dissipative effects of sphaleron transitions, a wave number threshold kCMW emerges characterizing the onset of chiral magnetic waves. Sphaleron damping also significantly impacts the time evolution of both axial and vector charge perturbations in a QCD plasma in the presence of a magnetic field. Based on our analysis of the linearized hydrodynamic equations, we also investigate the dependence of the vector charge separation on the sphaleron transition rate, which may have implications for the experimental search for the chiral magnetic effect in heavy ion collisions. Published by the American Physical Society 2024

Continuous tuning of optical transition properties and phonon spectrum in Er3+ doped germano-tellurite glass system

With the development of science and the progress of technology, novel and advanced rare earth ions doped luminescent materials with higher performance are demanded in the both emerging and traditional applications. Understanding the rules for tuning the spectroscopic properties of these materials is crucial for their development. However, achieving precise control over the optical properties of rare earth doped materials using traditional design and synthesis methods, such as altering dopants and their concentrations or modifying the preparative conditions, still remains challenging. This work aims to adjust the optical transition characteristics of Er3+ doped germano-tellurite glasses by changing the glass components. First, the Er3+ doped germano-tellurite glass series were synthesized using a high-temperature melt-quenching method at optimized melting temperatures. The tuning of band gap energy and refractive index of the glasses were revealed, and it was found that both of them can be monotonically and continuously tuned by changing the glass composition. The optical transition intensity parameters of Er3+ in the glasses were calculated in the framework of traditional three-parameterized Judd-Ofelt theory using the absorption spectra, and furthermore the corresponding optical transition parameters including radiative transition rates and intrinsic lifetimes for some interested levels were alsoconfirmed. The results demonstrated that the optical transition parameters could be efficiently modulated by changing the glass composition, indicating that the spectral properties of Er3+ doped germano-tellurite glasses can be tuned for the practical applications. The reliability of the deduced tuning rule was validated by comparing the theoretical and experimental transition rate ratios of 2H11/2 → 4I15/2 to 4S3/2 → 4I15/2. Furthermore, the tuning regulation of the phonon spectra in relation to the glass composition was discovered, showing a concordance between theoretical predictions and experimental results. From the above facts, it can be concluded that the optical transition properties of Er3+ in germano-tellurite glasses can be substantially adjusted by modifying the glass composition. This work provides a new perspective for designing and developing novel luminescent materials to meet specific application needs.

Essential roles of Rad6 in conidial property, stress tolerance, and pathogenicity of Beauveria bassiana

ABSTRACT Rad6 functions as a ubiquitin-conjugating protein that regulates cellular processes in many fungal species. However, its role in filamentous entomopathogenic fungi remains poorly understood. This study characterizes Rad6 in Beauveria bassiana, a filamentous fungus widely employed as a critical fungicide globally. The results demonstrate a significant association between Rad6 and conidial properties, heat shock response, and UV-B tolerance. Concurrently, the mutant strain exhibited heightened sensitivity to oxidative stress, cell wall interfering agents, DNA damage stress, and prolonged heat shock. Furthermore, the absence of Rad6 significantly extended the median lethal time (LT50) of Galleria mellonella infected by B. bassiana. This delay could be attributed to reduced Pr1 proteases and extracellular cuticle-degrading enzymes, diminished dimorphic transition rates, and dysregulated antioxidant enzymes. Additionally, the absence of Rad6 had a more pronounced effect on genetic information processing, metabolism, and cellular processes under normal conditions. However, its impact was limited to metabolism in oxidative stress. This study offers a comprehensive understanding of the pivotal roles of Rad6 in conidial and hyphal stress tolerance, environmental adaptation, and the pathogenesis of Beauveria bassiana.

Room Temperature Dynamics of an Optically Addressable Single Spin in Hexagonal Boron Nitride.

Hexagonal boron nitride (h-BN) hosts pure single-photon emitters that have shown evidence of optically detected electronic spin dynamics. However, the electrical and chemical structures of these optically addressable spins are unknown, and the nature of their spin-optical interactions remains mysterious. Here, we use time-domain optical and microwave experiments to characterize a single emitter in h-BN exhibiting room temperature optically detected magnetic resonance. Using dynamical simulations, we constrain and quantify transition rates in the model, and we design optical control protocols that optimize the signal-to-noise ratio for spin readout. This constitutes a necessary step toward quantum control of spin states in h-BN.

Habitat opening fostered diversity: impact of dispersal and habitat‐shifts in the evolutionary history of a speciose afrotropical insect group

The opening of habitats associated with the emergence of C4 grasslands during the Neogene had a massive influence on the evolution of plant and animal communities. Strikingly, the impacts of grassland expansion on species diversification in Africa, where the largest surface of grasslands and savannas in the world is located, are not well understood. To explore the impact of habitat opening, we investigate the evolution of noctuid stemborers, a group of moths mostly associated with open habitats, and whose diversity is centered in the Afrotropics. We generate a dated molecular phylogeny for ca 80% of the known stemborer species, and assess the role of habitat opening on the evolutionary trajectory of the group through a combination of parametric historical biogeography, ancestral character state estimation, life history traits and habitat‐dependent diversification analyses. Our results support an origin of stemborers in Southern and East Africa ca 20 million years ago (Ma), with range expansions linked to the increased availability of open habitats to act as dispersal corridors, and closed habitats acting as potent barriers to dispersal. Early specialization on open habitats was maintained over time, with shifts towards closed habitats being rare and invariably unidirectional. Analyses of life history traits showed that habitat changes involved specific features likely associated with grassland adaptations, such as variations in larval behavior and color. We compare these findings to those previously inferred for an Afrotropical butterfly group that diversified roughly in parallel with the stemborers but distributed predominantly in closed habitats. Remarkably, these two groups show nearly opposite responses in relation to habitat specialization, whether in terms of biogeographical patterns, or in terms of rates of transition between open and closed habitats. We conclude that habitat opening played a major role in the evolutionary history of Afrotropical lineages through dispersal and adaptation linked to habitat shifts.

Core@Shell Heterostructured NiMoPx@Ni5P4 Nanorod Arrays Promoting Direct Electro‐Oxidation of Methanol and Hydrogen Evolution under Industry Conditions

AbstractMethanol‐electrooxidation‐reaction (MOR) to value‐added formate is a promising alternative to water oxidation for cost‐efficient hydrogen production. It is generally proposed that the MOR kinetics on Ni‐based catalysts are highly limited by the transition rate of Ni(OH)2/NiOOH. Yet, how to define the catalyst following the direct pathway without Ni2+/Ni3+ transition remains challenging. Herein, a core@shell heterostructured NiMoPx@Ni5P4 catalyst is developed to selectively promote the MOR at a large current density (&gt; 500 mA cm−2). A series of operando spectroscopic studies reveal negligible formation of NiOOH with 1.0 m methanol in a wide potential range, where MOR is predominant. Theoretical calculations demonstrate that the Ni‐P site of NiMoPx@Ni5P4 favors the adsorption of *CH3OH over *OH while the heterostructure contributes to the significantly reduced energy barrier of *OCH3 →*OCH2, hence promoting the MOR along a direct pathway without the formation of NiOOH. Moreover, further study suggests that the catalyst also performs well toward cathodic hydrogen evolution reaction (HER). As a result, an electrode pair of NiMoPx@Ni5P4//NiMoPx@Ni5P4 is employed to enable concurrent MOR/HER electrolysis at 1.81 V to yield formate/H2 with FEs of ca. 90/100% and long‐term (100‐h) sustainability at 500 mA cm−2 under the industrial conditions (6.0 m KOH, 65 °C).

Silver nanoparticles stabilized by chitosan-polyvinyl alcohol polymers mediated by Pistacia extract for treatment of functional dyspepsia and gastric cancer

The impact of the nanoparticles on the dyspepsia mice gut microbiota is evaluated through the utilization of the 16S rRNA technique. Various methods were employed to characterize the NPs. In the textile, culinary, paper, leather, and printing sectors, synthetic dyes are frequently employed as coloring agents. Because these dye molecules are harmful to both the environment and living things, it is difficult to remove them sustainably. Here, we have produced nanoparticles embedded in chitosan-polyvinyl alcohol hydrogel (CS-PVA) by using bark's Pistacia under ultrasonic irradiation. The reduction of Ag + ions into Ag0 NPs was detected by a visual change in the colors. UV–Vis analysis indicated that the characteristic SPR band appeared near ∼440–450 nm. UV/Vis, EDX-elemental mapping, SEM, TEM, ICP-OES, and XRD analysis were applied to characterize the Ag NPs/CS-PVA nanocomposite. The recent study focused on the cellular and molecular aspects. The MTT assay was conducted for 48 h to evaluate the anti-human gastric cancer and cytotoxicity efficacies of the treated cells with nanocomposite. The assessment was performed on normal (HUVEC) and gastric cancer cells, namely MKN45 and NCI–N87. The IC50 values of nanocomposite against MKN45 and NCI–N87 were 180 and 151 μg/mL, respectively. The dose-dependent reduction in malignant gastric cell viability was observed in the nanocomposite presence. Furthermore, the nanocomposite induced cell apoptosis by 40–50%, leading to an increase in the expression of pro-apoptotic markers (Bax and cleaved caspase-8) and a decrease in the expression of the anti-apoptotic marker, Bcl-2. Furthermore, the nanocomposite showed inhibitory effects on colony formation. Our results indicate that the nanocomposite can increase p53 expression and decrease the expression of STAT3 in treated cells. This indicates that p53 and STAT3 play crucial roles in the biological effects induced by the extract in human gastric carcinoma cells. The data from the gut microbiome suggested that nanocomposites have the ability to control the rebalancing of homeostasis and microbiome composition by decreasing the levels of harmful bacteria, and at the same time, increasing the levels of beneficial bacteria. Following the introduction of nanocomposite, there was an observed rise in the levels of gastrointestinal hormones in the serum, including gastrin and motilin, while the levels of vasoactive intestinal peptide decreased. The application of nanocomposite led to an improvement in gastrointestinal movement, encompassing a rise in the rate of transit through the small intestine and the rate of gastric emptying. These findings offer that the Ag NPs/CS-PVA nanocomposite could be a promising anticancer treatment for functional dyspepsia and gastric cancer.

Singlet oxygen generation proportion from triplet state of porphyrin in water

The proportion of singlet oxygen (R) produced from the triplet state of porphyrin in aqueous solutions was investigated by substituting porphyrin molecules with the metalloporphyrin Platinum(II) meso-tetraphenylporphyrin (Pt-TPP). The feasibility of using platinum porphyrin as a substitute for porphyrin to study the photophysical properties in photodynamic therapy (PDT) was confirmed. The model of first-order decay in a water-methanol mixed solution encompasses potential deactivation processes of the excited triplet states and was built, which was confirmed by monitoring the change in the total transition rate of the T1 state (A0) value at different water contents under anoxic environments, obtained through measuring the phosphorescence lifetime (τp) of Pt-TPP. Combined with A0 and the quenching rate constant of T1 by O2 (kq), the formula for R in relation to changes in oxygen can be deduced in pure water.