High-Sensitivity Differential Helmholtz Photoacoustic System Combined with the Herriott Multipass Cell and Its Application in Seed Respiration.

A highly sensitive photoacoustic detection system using a differential Helmholtz resonator (DHR) combined with a Herriott multipass cell is presented, and its implementation to sub-ppm level carbon dioxide (CO2) detection is demonstrated. Through the utilization of erbium-doped optical fiber amplifier (EDFA), the laser power was amplified to 150 mW. Within the multipass cell, a total of 22 reflections occurred, contributing to an impressive 33.6 times improvement in the system sensitivity. The normalized noise equivalent absorption coefficient (NNEA) was 8.64 × 10-11 cm-1·W·Hz-1/2 [signal-to-noise ratio, (SNR) = 1] and according to the Allan variance analysis, a minimum detection limit of 500 ppb could be achieved for CO2 at 1204 s, which demonstrates the long-term stability of the system. The system was applied to detect the respiration of rice and upland rice seeds. It is demonstrated that the system can monitor and distinguish the respiration intensity and respiration rate of different seeds in real time.

Photoionization and Dissociative Photoionization of Acetaldehyde in the 10.0-13.7†eV Range by Synchrotron Photoelectron Photoion Coincidence Spectroscopy.

Photoionization and dissociative photoionization of acetaldehyde (CH3CHO) in the 10.0-13.7 eV energy range are studied by using synchrotron radiation double imaging photoelectron photoion coincidence spectroscopy (i2PEPICO). The X2A' and A2A" electronic states of CH3CHO+ as well as the Franck-Condon gap region between these two states have been populated with several vibrational sequences and assigned in the high-resolution slow photoelectron spectrum (SPES). The adiabatic ionization energies (AIEs) of the X2A' and A2A" states are measured at 10.228±0.006 and 12.52±0.05 eV, respectively. The present results show that the X2A' state is a stable state while the A2A" state is fully dissociative to produce CH3CO+, CHO+ and CH4 + fragment ions. The 0 K appearance energies (AE0K) of CH3CO+ and CHO+ fragment ions are determined through the modeling of the breakdown diagram, i. e., AE0K(CH3CO+)=10.89±0.01 eV (including a reverse barrier of ~0.19 eV) and AE0K(CHO+)=11.54±0.05 eV. In addition, the dissociation mechanisms of CH3CHO+ including statistical dissociation, direct bond breaking and isomerization are discussed with the support of the calculated dissociation limits and transition state energies.

Accurate Kinetic Studies of OH + HO2 Radical-Radical Reaction through Direct Measurement of Precursor and Radical Concentrations with High-Resolution Time-Resolved Dual-Comb Spectroscopy.

The radical-radical reaction between OH and HO2 has been considered for a long time as an important reaction in tropospheric photochemistry and combustion chemistry. However, a significant discrepancy of an order of magnitude for rate coefficients of this reaction is found between two recent experiments. Herein, we investigate the reaction OH + HO2 via direct spectral quantification of both the precursor (H2O2) and free radicals (OH and HO2) upon the 248 nm photolysis of H2O2 using infrared two-color time-resolved dual-comb spectroscopy. With quantitative and kinetic analysis of concentration profiles of both OH and HO2 at varied conditions, the rate coefficient kOH+HO2 is determined to be (1.10 ± 0.12) × 10-10 cm3 molecule-1 s-1 at 296 K. Moreover, we explore the kinetics of this reaction under conditions in the presence of water, but no enhancement in the kOH+HO2 can be observed. This work as an independent experiment plays a crucial role in revisiting this prototypical radical-radical reaction.

Measurements of absolute line strength of the ν1 fundamental transitions of OH radical and rate coefficient of the reaction OH + H2O2 with mid-infrared two-color time-resolved dual-comb spectroscopy.

Absolute line strengths of several transitions in the ν1 fundamental band of the hydroxyl radical (OH) have been measured by simultaneous determination of hydrogen peroxide (H2O2) and OH upon laser photolysis of H2O2. Based on the well-known quantum yield for the generation of OH radicals in the 248-nm photolysis of H2O2, the line strength of the OH radicals can be accurately derived by adopting the line strength of the well-characterized transitions of H2O2 and analyzing the difference absorbance time traces of H2O2 and OH obtained upon laser photolysis. Employing a synchronized two-color dual-comb spectrometer, we measured high-resolution time-resolved absorption spectra of H2O2 near 7.9 µm and the OH radical near 2.9 µm, simultaneously, under varied conditions. In addition to the studies of the line strengths of the selected H2O2 and OH transitions, the kinetics of the reaction between OH and H2O2 were investigated. A pressure-independent rate coefficient kOH+H2O2 was determined to be [1.97 (+0.10/-0.15)] × 10-12 cm3 molecule-1 s-1 at 296 K and compared with other experimental results. By carefully analyzing both high-resolution spectra and temporal absorbance profiles of H2O2 and OH, the uncertainty of the obtained OH line strengths can be achieved down to <10% in this work. Moreover, the proposed two-color time-resolved dual-comb spectroscopy provides a new approach for directly determining the line strengths of transient free radicals and holds promise for investigations on their self-reaction kinetics as well as radical-radical reactions.

A Coin-Sized Oxygen Laser Sensor Based on Tunable Diode Laser Absorption Spectroscopy Combining a Toroidal Absorption Cell.

Laser gas sensors with small volume and light weight are in high demand in the aerospace industry. To address this, a coin-sized oxygen (O2) sensor has been successfully developed based on a small toroidal absorption cell design. The absorption cell integrates a vertical-cavity surface-emitting laser (VCSEL) and photodetector into a compact unit, measuring 90 × 40 × 20 mm and weighing 75.16 g. Tunable diode laser absorption spectroscopy (TDLAS) is used to obtain the O2 spectral line at 763 nm. For further improving the sensitivity and robustness of the sensor, wavelength modulation spectroscopy (WMS) is utilized for the measurement. The obtained linear correlation coefficient is 0.9994. Based on Allen variance analysis, the sensor achieves an impressive minimum detection limit of 0.06% for oxygen concentration at an integration time of 318 s. The pressure-dependent relationship has been validated by accounting for the pressure factor in data processing. To affirm its efficacy, the laser spectrometer underwent continuous atmospheric O2 measurement for 24 h, showcasing its stability and robustness. This development introduces a continuous online laser spectral sensor with potential applications in manned spaceflight scenarios.

Peroxy radical chemistry during ozone photochemical pollution season at a suburban site in the boundary of Jiangsu-Anhui-Shandong-Henan region, China.

Ambient peroxy radical (RO2⁎ = HO2 + RO2) concentrations were measured at a suburban site in a major prefecture-level city (Huaibei) in the boundary of Jiangsu-Anhui-Shandong-Henan region, which is the connecting belt of air pollution in the Beijing-Tianjin-Hebei region and the Yangtze River Delta. Measurements were carried out during the period of September to October 2021 to elucidate the formation mechanism of O3 pollution. The observed maximum concentration of peroxy radicals was 73.8 pptv. A zero-dimensional box model (Framework for 0-Dimensional Atmospheric Modeling, F0AM) based on Master Chemical Mechanism (MCM3.3.1) was used to predict radical concentrations for comparison with observations. The model reproduced the daily variation of peroxy radicals well, but discrepancies still appear in the morning hours. As in previous field campaigns, systematic discrepancies between modelled and measured RO2⁎ concentrations are observed in the morning for NO mixing ratios higher than 1 ppbv. Between 6:00 and 9:00 am, the model significantly underpredicts RO2⁎ by a mean factor of 7.2. This underprediction can be explained by a missing RO2⁎ source of 1.2 ppbv h-1 which originated from the photochemical conversion of an alkene-like chemical species. From the model results it shows that the main sources of ROx (= OH + HO2 + RO2) are the photolysis of oxygenated volatile organic compounds (OVOCs, 33 %), O3 and HONO (25 %), and HCHO (24 %). And the major sinks of ROx transitioned from a predominant reaction of radicals with NOx in the morning to a predominant peroxy self- and cross-reaction in the late afternoon. The introduction of an alkene-like species increased RO2 radical concentration and resulted in 14 % increase in net daily integrated ozone production, indicating the possible significance of the mechanism of alkene-like species oxidation to peroxy radicals. This study provides important information for subsequent ozone pollution control policies in Jiangsu-Anhui-Shandong-Henan region.

Photophysical oxidation of HCHO produces HO2 radicals.

Formaldehyde, HCHO, is the highest-volume carbonyl in the atmosphere. It absorbs sunlight at wavelengths shorter than 330 nm and photolyses to form H and HCO radicals, which then react with O2 to form HO2. Here we show HCHO has an additional HO2 formation pathway. At photolysis energies below the energetic threshold for radical formation we directly detect HO2 at low pressures by cavity ring-down spectroscopy and indirectly detect HO2 at 1 bar by Fourier-transform infrared spectroscopy end-product analysis. Supported by electronic structure theory and master equation simulations, we attribute this HO2 to photophysical oxidation (PPO): photoexcited HCHO relaxes non-radiatively to the ground electronic state where the far-from-equilibrium, vibrationally activated HCHO molecules react with thermal O2. PPO is likely to be a general mechanism in tropospheric chemistry and, unlike photolysis, PPO will increase with increasing O2 pressure.

Rate constant and branching ratio of the reaction of ethyl peroxy radicals with methyl peroxy radicals.

The cross-reaction of ethyl peroxy radicals (C2H5O2) with methyl peroxy radicals (CH3O2) (R1) has been studied using laser photolysis coupled to time resolved detection of the two different peroxy radicals by continuous wave cavity ring down spectroscopy (cw-CRDS) in their AÃ-X̃ electronic transition in the near-infrared region, C2H5O2 at 7602.25 cm-1, and CH3O2 at 7488.13 cm-1. This detection scheme is not completely selective for both radicals, but it is demonstrated that it has great advantages compared to the widely used, but unselective UV absorption spectroscopy. Peroxy radicals were generated from the reaction of Cl-atoms with the appropriate hydrocarbon (CH4 and C2H6) in the presence of O2, whereby Cl-atoms were generated by 351 nm photolysis of Cl2. For different reasons detailed in the manuscript, all experiments were carried out under excess of C2H5O2 over CH3O2. The experimental results were best reproduced by an appropriate chemical model with a rate constant for the cross-reaction of k = (3.8 ± 1.0) × 10-13 cm3 s-1 and a yield for the radical channel, leading to CH3O and C2H5O, of (ϕ1a = 0.40 ± 0.20).

Dimeric Product of Peroxy Radical Self-Reaction Probed with VUV Photoionization Mass Spectrometry and Theoretical Calculations: The Case of C2H5OOC2H5.

Organic peroxy radicals (RO2) as key intermediates in tropospheric chemistry exert a controlling influence on the cycling of atmospheric reactive radicals and the production of secondary pollutants, such as ozone and secondary organic aerosols (SOA). Herein, we present a comprehensive study of the self-reaction of ethyl peroxy radicals (C2H5O2) by using advanced vacuum ultraviolet (VUV) photoionization mass spectrometry in combination with theoretical calculations. A VUV discharge lamp in Hefei and synchrotron radiation at the Swiss Light Source (SLS) are employed as the photoionization light sources, combined with a microwave discharge fast flow reactor in Hefei and a laser photolysis reactor at the SLS. The dimeric product, C2H5OOC2H5, as well as other products, CH3CHO, C2H5OH and C2H5O, formed from the self-reaction of C2H5O2 are clearly observed in the photoionization mass spectra. Two kinds of kinetic experiments have been performed in Hefei by either changing the reaction time or the initial concentration of C2H5O2 radicals to confirm the origins of the products and to validate the reaction mechanisms. Based on the fitting of the kinetic data with the theoretically calculated results and the peak area ratios in the photoionization mass spectra, a branching ratio of 10 ± 5% for the pathway leading to the dimeric product C2H5OOC2H5 is measured. In addition, the adiabatic ionization energy (AIE) of C2H5OOC2H5 is determined at 8.75 ± 0.05 eV in the photoionization spectrum with the aid of Franck-Condon calculations and its structure is revealed here for the first time. The potential energy surface of the C2H5O2 self-reaction has also been theoretically calculated with a high-level of theory to understand the reaction processes in detail. This study provides a new insight into the direct measurement of the elusive dimeric product ROOR and demonstrates its non-negligible branching ratio in the self-reaction of small RO2 radicals.

Portable cavity ring-down spectrometer for an HO2 radical measurement: instrument's performance and potential improvement using a narrow linewidth laser.

We report the development of a portable cavity ring-down spectrometer (CRDS) for direct and absolute measurement of HO2 radical concentration using a distributed feedback (DFB) diode laser operating at 1506 nm. The spectrometer has a compact design with all optics in a 1000 × 400 × 140 mm3 box. At a pressure of 100 mbar and a ring-down time (τ0) of 136 µs, the detection limit of the CRDS spectrometer was ∼ 7.3 × 107 molecule/cm3 (1σ, 10s). The corresponding detection sensitivity was 1.5 × 10-11 cm-1, which was close to the state-of-the-art performance. By replacing the DFB diode laser with a narrow linewidth erbium-doped fiber (EDF) laser, the amplitude fluctuation caused by the laser phase noise was reduced and the cavity mode injection efficiency was improved. The sensitivity was improved to 3.9 × 10-12 cm-1 with a short data-acquisition time of 0.2 s. Compared with the DFB laser, the improvement was nearly an order of magnitude. The use of the narrow linewidth laser is attractive. The instrument can achieve very high sensitivity without the need for a complex locking technique, ensuring simple and ease of use in future field applications.

Self-Reaction of Acetonyl Peroxy Radicals and Their Reaction with Cl Atoms.

The rate constant for the self-reaction of the acetonyl peroxy radicals, CH3C(O)CH2O2, has been determined using laser photolysis/continuous wave cavity ring down spectroscopy (cw-CRDS). CH3C(O)CH2O2 radicals have been generated from the reaction of Cl atoms with CH3C(O)CH3, and the concentration time profiles of four radicals (HO2, CH3O2, CH3C(O)O2, and CH3C(O)CH2O2) have been determined by cw-CRDS in the near-infrared. The rate constant for the self-reaction was found to be k = (5.4 ± 1.4) × 10-12 cm3 s-1, in good agreement with a recently published value (Zuraski, K., et al. J. Phys. Chem. A 2020, 124, 8128); however, the branching ratio for the radical path was found to be ϕ1b = (0.6 ± 0.1), which is well above the recently published value (0.33 ± 0.13). The influence of a fast reaction of Cl atoms with the CH3C(O)CH2O2 radical became evident under some conditions; therefore, this reaction has been investigated in separate experiments. Through the simultaneous fitting of all four radical profiles to a complex mechanism, a very fast rate constant of k = (1.35 ± 0.8) × 10-10 cm3 s-1 was found, and experimental results could be reproduced only if Cl atoms would partially react through H-atom abstraction to form the Criegee intermediate with a branching fraction of ϕCriegee = (0.55 ± 0.1). Modeling the HO2 concentration-time profiles was possible only if a subsequent reaction of the Criegee intermediate with CH3C(O)CH3 was included in the mechanism leading to HO2 formation with a rate constant of k = (4.5 ± 2.0) × 10-14 cm3 s-1.

Cl-Initiated oxidation of methacrolein under NOx-free conditions studied by VUV photoionization mass spectrometry.

The Cl-initiated oxidation of methacrolein (MACR, C4H6O) under NOx-free conditions has been investigated in a fast flow tube by using a home-made vacuum ultraviolet (VUV) photoionization mass spectrometer complemented by high-level theoretical calculations. The key species such as intermediates and radicals together with products involved in the oxidation are observed online and confirmed in photoionization mass spectra. The reaction potential energy surfaces of the transient C4H5O and C4H6OCl radicals, formed from the hydrogen-abstraction reaction and the addition reaction of MACR with Cl atoms, with oxygen have been theoretically calculated to illuminate the formation of the peroxy radicals of C4H5OO2 and C4H6OClO2. The photoionization processes of these peroxy radicals, whose cations are not stable, and their individual self-reactions as well as bimolecular reactions with HO2 radical are studied and discussed. In addition, kinetic experiments are also performed to get the time evolution of specific products and compared with theoretical models, providing a detailed insight into the reaction mechanism of the Cl-initiated oxidation of MACR.

Data of chemical composition of the particles from OH-initiated oxidation of 1,3,5-trimethylbenzene.

This paper presents the data of chemical composition of the particles from OH oxidation reaction of 1,3,5-trimethylbenzene (1,3,5-TMB). The particle-phase compositions are measured on-line by using a vacuum ultraviolet (VUV) photoionization aerosol mass spectrometer. The assignments of the major peaks of photoionization mass spectrum, as well as their molecular structures, are presented. The optimized structures of the reactants, intermediates and transition states involved in the reaction of the bicyclic peroxy radical with HO2 are shown. The reaction routes of the OH-initiated oxidation of the deuterated 1,3,5-TMB sample are also calculated and displayed for comparison. The data presented here is related to the paper "Direct observation of the particle-phase bicyclic products from OH-initiated oxidation of 1,3,5-trimethylbenzene under NOx-free conditions" by Lin et al. (2022).

Reaction kinetics of 1,4-cyclohexadienes with OH radicals: an experimental and theoretical study.

This work presents the OH-initiated oxidation kinetics of 1,4-cyclochexadiene (1,4-CHD). The temperature dependence of the reaction was investigated by utilizing a laser flash photolysis flow reactor and laser-induced fluorescence (LPFR/LIF) technique over the temperature range of 295-438 K and a pressure of ∼50 torr. The kinetics of the reaction was followed by measuring the LIF signal of OH radicals near 308 nm. The reaction of OH radicals with 1,4-CHD exhibited a clear negative temperature dependence. To discern the role of various channels, ab initio and RRKM-based ME calculations (RRKM-ME) were performed over temperatures of 200-2000 K and pressures of 0.76-7600 torr. The computed energy profile revealed that the reaction proceeds via the formation of a pre-reaction van der Waals complex at the entrance channel. The complex was found to be more stable than that usually seen in other alkenes + OH reactions. Both the addition channel and the abstraction reaction of allylic hydrogen were found to have negative energy barriers. Interestingly, the abstraction reaction exhibited a negative temperature dependence at low temperatures and contributed significantly (∼37%) to the total rate coefficients even under atmospheric conditions. At T ≥ 900 K, the reaction was found to proceed exclusively (>95%) via the abstraction channel. Due to the competing channels, the reaction of OH radicals with 1,4-CHD displays complicated kinetic behaviours, reflecting the salient features of the energy profile. The role of competing channels was fully characterized by our kinetic model. The calculated rate coefficients showed excellent agreement with the available experimental data.

Vacuum ultraviolet photochemistry of sulfuric acid vapor: a combined experimental and theoretical study.

We present a vacuum ultraviolet (VUV) photoionization study of the gas-phase sulfuric acid (H2SO4) molecule in the 11-14 eV energy range by using the method of synchrotron radiation-based double imaging photoelectron photoion coincidence (i2PEPICO) spectroscopy complemented with accurate theoretical calculations. The slow photoelectron spectrum (SPES) of H2SO4 has been acquired and the three electronic states of H2SO4+, X2A, A2A and B2A have been populated and assigned. The adiabatic ionization energy of the H2SO4 molecule towards the X2A cationic ground state is measured at 11.684 ± 0.006 eV, in accordance with high-level calculated findings. With increasing photon energies, the H2SO4+ cation dissociates into HSO3+ and OH fragments and their adiabatic appearance energy is measured at 13.498 ± 0.007 eV. Then, the enthalpies of formation for the species involved in the photoionization and dissociative photoionization have been determined through a thermochemical cycle.

Vacuum ultraviolet photochemistry of the conformers of the ethyl peroxy radical.

We study the conformers of the ethyl peroxy radical (C2H5O2), the simplest peroxy radical having more than one conformer, by combining synchrotron radiation vacuum ultraviolet (VUV) photoionization mass spectrometry with theoretical calculations. The ethyl peroxy radical is formed in a microwave discharge flow tube through the reaction of the ethyl radical (C2H5) with oxygen molecules, where C2H5 is generated via the hydrogen-abstraction reaction of ethane with fluorine atoms. Two kinds of C2H5+, originating from photoionization of C2H5 and from dissociative photoionization of C2H5O2, whose cation is not stable, have been identified and separated in photoionization mass spectra. The photoionization spectrum corresponding to C2H5O2 is obtained and assigned with Franck-Condon calculations. The present findings show that the gauche conformer (G-C2H5O2) of C2H5O2 has favorable Franck-Condon factors in the ionization transitions, whereas the contribution of the trans conformer (T-C2H5O2) to the photoionization spectrum is minor or negligible due to its large geometric changes in the photoionization process. Moreover, the reason for the instability of C2H5O2+ and its detailed dissociation mechanisms have been unraveled with the aid of the calculated potential energy curves.

Palm-Sized Laser Spectrometer with High Robustness and Sensitivity for Trace Gas Detection Using a Novel Double-Layer Toroidal Cell.

A palm-sized laser spectrometer has been developed for detecting trace gases based on tunable diode laser absorption spectroscopy in combination with a novel double-layer toroidal cell. With the benefit of a homemade electronic system and compact optical design, the physical dimensions of the sensor are minimized to 24 × 15× 16 cm3. A toroidal absorption cell, with 84 reflections in 2 layers for an effective optical path length of 8.35 m, was used to enhance the absorption signals of gaseous species. A homemade electronic system was designed for implementing a distributed feedback (DFB) diode laser controller, an analog lock-in amplifier, data acquisition, and communication. Calibration-free scanned wavelength modulation spectroscopy was employed to determine the concentration of the gas and reduce the random fluctuations from electronical noise and mechanical vibration. The measurement of CH4 in ambient air was demonstrated using a DFB laser at 1.653 µm. The rise time and fall time for renewing the gas mixture are approximately 16 and 14 s, respectively. Vibration and temperature tests have been carried out for verifying the performance of the spectrometer, and standard deviations of 0.38 ppm and 0.11 ppm for 20 ppm CH4 at different vibration frequencies and temperatures, respectively, have been determined. According to the Allan deviation analysis, the minimum detection limit for CH4 can reach 22 ppb at an integration time of 57.8 s. The continuous measurement of atmospheric CH4 for 2 days validated the feasibility and robustness of our laser spectrometer, providing a promising laser spectral sensor for deploying in unmanned aerial vehicles or mobile robots.

Identifying isomers of peroxy radicals in the gas phase: 1-C3H7O2vs. 2-C3H7O2.

The two isomers of the propylperoxy radical 1-C3H7O2 and 2-C3H7O2, together with their individual rotamers, are identified and assigned by threshold photoelectron spectroscopy with the aid of high-level theoretical computations, from which their accurate adiabatic ionization energies are derived. This study paves the way to probing elusive peroxy radicals and their isomers in advanced mass spectrometry analysis of combustion and atmospheric reactions.

Implementation of the toroidal absorption cell with multi-layer patterns by a single ring surface.

We developed a type of toroidal multi-pass cell with multi-layer patterns based on the off-axis model. The effective path length of the original toroidal multi-pass cell is extended several roundtrips in comparison with the single-layer pattern, since the inner surface of the toroidal multi-pass cell is more efficiently utilized. The light pattern has been achieved by using the simple ring surface, which is easy to fabricate. The exact analytical equations for the design of the toroidal multi-pass cell were derived based on analytical vector calculations. A series of numerical ray tracing simulations is presented, and the maximum theoretical optical path length that can be reached is 30 m with a setup of 5 cm column radius. Furthermore, two practical spot patterns are demonstrated with a path length of 8.3 m for a two-layer pattern and 10 m for a three-layer pattern, with respective effective volumes of 63 mL and 94 mL. Furthermore, the fringe effect is substantially reduced to less than 0.5% by the usage of our designed mask.

Threshold photoelectron spectroscopy of the HO2 radical.

We report a synchrotron radiation vacuum ultraviolet photoionization study of the hydroperoxyl radical (HO2), a key reaction intermediate in combustion and atmospheric chemistry as well as astrochemistry, using double imaging photoelectron photoion coincidence spectroscopy. The HO2 radical is formed in a microwave discharge flow tube reactor through a set of reactions initiated by F atoms in a CH4/O2/He gas mixture. The high-resolution threshold photoelectron spectrum of HO2 in the 11 eV-12 eV energy range is acquired without interferences from other species and assigned with the aid of theoretically calculated adiabatic ionization energies (AIEs) and Franck-Condon factors. The three vibrational modes of the radical cation HO2 +, the H-O stretch, the H-O-O bend, and the O-O stretch, have been identified, and their individual frequencies are measured. In addition, the AIEs of the X3A″ ground state and the a1A' first excited electronic state of HO2 + are experimentally determined at 11.359 ± 0.003 eV and 11.639 ± 0.005 eV, respectively, in agreement with high-level theoretically computed results. Furthermore, the former AIE value provides validation of thermochemical networks used to extract the enthalpy of formation of the HO2 radical.