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The kinetic data of cyclopentadiene C5H6 oxidation reactions are significant for the construction of aromatics oxidation mechanism because cyclopentadiene C5H6 has been proved to be an important intermediate in the aromatics combustion. Kinetics for the elementary reactions on the potential energy surface (PES) relevant for the C5H6 + HO2 reaction are studied in this work. Stationary points on the PES are calculated by employing the CCSD(T)/cc-pVTZ//B3LYP/6-311G(d,p) level of theory. High-pressure limit and pressure-dependent rate constants for elementary reactions on this PES are calculated using conventional transition state theory (TST), variational transition-state theory (VTST) and Rice-Ramsberger-Kassel-Marcus/master equation (RRKM/ME) theory. In this work, the reaction channels for the C5H6 + HO2 reaction, which include H-abstraction channels from C5H6 by HO2 to form the C5H5 + H2O2 and the addition channels through well-skipping pathways to form the bimolecular products C5H7 + O2 or C5H6O + OH, or through C5H7O2 stabilization and its unimolecular decomposition to form the bimolecular products C5H7 + O2 or C5H6O + OH, namely sequential pathways, are studied. Also, the consuming reaction channels for the compounds C5H6O and C5H7 in the addition products are studied. The dominant reaction channels for these reactions are unraveled through comparing the energy barriers and rate constants of all elementary reactions and it is found: (1) HO2 addition to cyclopentadiene C5H6 is more important than direct H-abstraction. (2) in the HO2 addition channels, the well-skipping pathways and sequential pathways are competing and the well-skipping pathways will be favor in the higher pressures and the sequential pathways will be favor in the higher temperature. (3) The major consumption reaction channel for the five-member-ring compound C5H6O is the reaction channel to form C4H6 + CO and the major consumption reaction channel for the five-member-ring compound C5H7 is the reaction channel to form C3H5 + C2H2. High-pressure limit rate constants and pressure-dependent rate constants for elementary reactions on the PES are calculated, which will be useful in modeling the oxidation of aromatic compounds at low- and medium-temperatures.
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A self-consistent state specific (SS) method in the framework of TDDFT is presented to account for solvent effects on absorption and emission processes for molecules in solution. In these processes, the initial state is an equilibrium state, while the polarization of the solvent is in nonequilibrium with the electron density of the solute in the final state. Nonequilibrium solvation free energy is calculated based on a novel nonequilibrium solvation model with constrained equilibrium manipulation. The bulk solvent effects are considered using the polarizable continuum method (PCM), where the solvent-solute interaction is described with a reaction field. Molecular orbitals and orbital energies in the presence of the reaction field corresponding to the excited state are employed and the response of the solvent is not included in the TDDFT calculations. A self-consistent procedure is designed to obtain the excited state reaction field. The equations based on this new nonequilibrium solvation model in the framework of the self-consistent SS-PCM/TDDFT method for calculation of vertical absorption and emission energies are presented and implemented in the Q-Chem package. Vertical absorption and emission energies for several small molecules in solution using the newly developed code are calculated and compared with available experimental data and the results of other theoretical studies. Solvent shifts of absorption and emission energies are reasonably reproduced with this approach. The new model is a promising approach to study nonequilibrium absorption and emission processes in solution.
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The isodesmic reaction method is applied to calculate the potential energy surface (PES) along the reaction coordinates and the rate constants of the barrierless reactions for unimolecular dissociation reactions of alkanes to form two alkyl radicals and their reverse recombination reactions. The reaction class is divided into 10 subclasses depending upon the type of carbon atoms in the reaction centers. A correction scheme based on isodesmic reaction theory is proposed to correct the PESs at UB3LYP/6-31+G(d,p) level. To validate the accuracy of this scheme, a comparison of the PESs at B3LYP level and the corrected PESs with the PESs at CASPT2/aug-cc-pVTZ level is performed for 13 representative reactions, and it is found that the deviations of the PESs at B3LYP level are up to 35.18 kcal/mol and are reduced to within 2 kcal/mol after correction, indicating that the PESs for barrierless reactions in a subclass can be calculated meaningfully accurately at a low level of ab initio method using our correction scheme. High-pressure limit rate constants and pressure dependent rate constants of these reactions are calculated based on their corrected PESs and the results show the pressure dependence of the rate constants cannot be ignored, especially at high temperatures. Furthermore, the impact of molecular size on the pressure-dependent rate constants of decomposition reactions of alkanes and their reverse reactions has been studied. The present work provides an effective method to generate meaningfully accurate PESs for large molecular system.
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Nonequilibrium solvation effects need to be treated properly in the study of electronic absorption processes of solutes since solvent polarization is not in equilibrium with the excited-state charge density of the solute. In this work, we developed a state specific (SS) method based on the novel nonequilibrium solvation model with constrained equilibrium manipulation to account for solvation effects in electronic absorption processes. Time-dependent density functional theory (TD-DFT) is adopted to calculate electronic excitation energies and a polarizable continuum model is employed in the treatment of bulk solvent effects on both the ground and excited electronic states. The equations based on this novel nonequilibrium solvation model in the framework of TDDFT to calculate vertical excitation energy are presented and implemented in the Q-Chem package. The implementation is validated by comparing reorganization energies for charge transfer excitations between two atoms obtained from Q-Chem and those obtained using a two-sphere model. Solvent effects on electronic transitions of coumarin 153 (C153), acetone, pyridine, (2E)-3-(3,4-dimethoxyphenyl)-1-(2-hydroxyphenyl)prop-2-en-1-one (DMHP), and uracil in different solvents are investigated using the newly developed code. Our results show that the obtained vertical excitation energies as well as spectral shifts generally agree better with the available experimental values than those obtained using the traditional nonequlibrium solvation model. This new model is thus appropriate to study nonequilibrium excitation processes in solution.
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Intramolecular H-migration reaction of hydroperoxyalkylperoxy radicals (â¢O2QOOH) is one of the most important reaction families in the low-temperature oxidation of hydrocarbon fuels. This reaction family is first divided into classes depending upon H atom transfer from -OOH bonded carbon or non-OOH bonded carbon, and then the two classes are further divided depending upon the ring size of the transition states and the types of the carbons from which the H atom is transferred. High pressure limit rate rules and pressure-dependent rate rules for each class are derived from the rate constants of a representative set of reactions within each class using electronic structure calculations performed at the CBS-QB3 level of theory. For the intramolecular H-migration reactions of â¢O2QOOH radicals for abstraction from an -OOH substituted carbon atom (-OOH bonded case), the result shows that it is acceptable to derive the rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. For the abstraction from a non-OOH substituted carbon atom (non-OOH bonded case), rate rules for each class are also derived and it is shown that the difference between the rate constants calculated by CBS-QB3 method and rate constants estimated from the rate rules may be large; therefore, to get more reliable results for the low-temperature combustion modeling of alkanes, it is better to assign each reaction its CBS-QB3 calculated rate constants, instead of assigning the same values for the same reaction class according to rate rules. The intramolecular H-migration reactions of â¢O2QOOH radicals (a thermally equilibrated system) are pressure-dependent, and the pressure-dependent rate constants of these reactions are calculated by using the Rice-Ramsberger-Kassel-Marcus/master-equation theory at pressures varying from 0.01 to 100 atm. The impact of molecular size on the pressure-dependent rate constants of the intramolecular H-migration reactions of â¢O2QOOH radicals has been studied, and it is shown that the pressure dependence of the rate constants of intramolecular H-migration reactions of â¢O2QOOH radicals decreases with the molecular size at low temperatures and the impact of molecular size on the pressure-dependent rate constants decreases as temperature increases. It is shown that it is acceptable to derive the pressure-dependent rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. The barrier heights follow the Evans-Polanyi relationship for each type of intramolecular hydrogen-migration reaction studied. All calculated rate constants are fitted by a nonlinear least-squares method to the form of a modified Arrhenius rate expression at pressures varying from 0.01 to 100 atm and at the high-pressure limit. Furthermore, thermodynamic parameters for all species involved in these reactions are calculated by the composite CBS-QB3 method and are given in NASA format.
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Ta2O5 has been an appealing contender for the resistance switching random access memory (ReRAM). The resistance switching (RS) in this material is induced by the repeated formation and rupture of the conducting filaments (CFs) in the oxide layer, which are accompanied by the almost inevitable randomness of the switching parameters. In this work, a 1 to 2 nm-thick Ti layer was deposited on the 10 nm-thick Ta2O5 RS layer, which greatly improved the RS performances, including the much-improved switching uniformity. The Ti metal layer was naturally oxidized to TiOx (x < 2) and played the role of a series resistor, whose resistance value was comparable to the on-state resistance of the Ta2O5 RS layer. The series resistor TiOx efficiently suppressed the adverse effects of the voltage (or current) overshooting at the moment of switching by the appropriate voltage partake effect, which increased the controllability of the CF formation and rupture. The switching cycle endurance was increased by two orders of magnitude even during the severe current-voltage sweep tests compared with the samples without the thin TiOx layer. The Ti deposition did not induce any significant overhead to the fabrication process, making the process highly promising for the mass production of a reliable ReRAM.
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Hydrogen abstraction from toluene by OH, H, O, CH3, and HO2 radicals are important reactions in oxidation process of toluene. Geometries and corresponding harmonic frequencies of the reactants, transition states as well as products involved in these reactions are determined at the B3LYP/6-31G(2df,p) level. To achieve highly accurate thermochemical data for these stationary points on the potential energy surfaces, the Gaussian-4(G4) composite method was employed. Torsional motions are treated either as free rotors or hindered rotors in calculating partion functions to determine thermodynamic properties. The obtained standard enthalpies of formation for reactants and some prodcuts are shown to be in excellent agreement with experimental data with the largest error of 0.5 kcal mol(-1). The conventional transition state theory (TST) with tunneling effects was adopted to determine rate constants of these hydrogen abstraction reactions based on results from quantum chemistry calculations. To faciliate its application in kinetic modeling, the obtained rate constants are given in Arrhenius expression: k(T) = AT(n) exp(-EaR/T). The obtained reaction rate constants also agree reasonably well with available expermiental data and previous theoretical values. Branching ratios of these reactions have been determined. The present reaction rates for these reactions have been used in a toluene combustion mechanism, and their effects on some combustion properties are demonstrated.
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By using three monochromator! detecting systems, the light emissions of excited-state OH*, CH* and C* radicals during the transient combustion of methylcyclohexane at high temperatures behind the reflected shock wave have been measured. The dependence of the time-history and the relative intensity of excited radicals on the temperature have been obtained. The reflected shock temperatures are 1 200-1 700 K, the shock pressure is 1.5 atm, the mole fraction of methylcyclohexane is 0.1% and the equivalence ratio is 1.0. At the beginning of the combustion process, these three radicals were produced at the same time. The durations of these radicals became shorter when the temperature increases. At the same ignition temperature, the durations of CH* and OH* are longer than that of C2*. The C2* signal disappears below 1 400 K. The emission intensities of OH* and CH* are not sensitive to the temperature at T < 1 400 K. However, at high temperature (T > 1 400 K), the peak intensity of CH* increases rapidly as temperature increases, while C2* and OH* increase slowly. Current results were compared to the simulation results of corresponding chemical reaction mechanism. The obtained time-history of OH* radical matches well with the prediction of mechanism at low temperatures, but shows difference at high temperatures. The time-history of CH* radical matches well between experimental and simulated results at high temperatures, however, the simulated durations of CH* are longer than the experimental results at low temperatures. Current work provides experimental data to validate and optimize corresponding chemical reaction mechanism containing excited-state species.
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SiO2 is the most significantly used insulator layer in semiconductor devices. Its functionality was recently extended to resistance switching random access memory, where the defective SiO2 played an active role as the resistance switching (RS) layer. In this report, the bias-polarity-dependent RS behaviours in the top electrode W-sputtered SiO2-bottom electrode Pt (W/SiO2/Pt) structure were examined based on the current-voltage (I-V) sweep. When the memory cell was electroformed with a negative bias applied to the W electrode, the memory cell showed a typical electronic switching mechanism with a resistance ratio of ~100 and high reliability. For electroforming with opposite bias polarity, typical ionic-defect-mediated (conducting filament) RS was observed with lower reliability. Such distinctive RS mechanisms depending on the electroforming-bias polarity could be further confirmed using the light illumination study. Devices with similar electrode structures with a thin intervening Si layer between the SiO2 and Pt electrode, to improve the RS film morphology (root-mean-squared roughness of ~1.7 nm), were also fabricated. Their RS performances were almost identical to that of the single-layer SiO2 sample with very high roughness (root-mean-squared roughness of ~10 nm), suggesting that the reported RS behaviours were inherent to the material property.
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The measurement system for the detection of soot production as high-temperature pyrolysis of hydrocarbon fuels behind the reflected shock wave was established. By using the laser extinction method, the soot yields of toluene/argon mixtures were measured at high temperatures. The mole fractions of toluene were 0.25% and 0.5% while the pressures were approximate 2 and 4 atm. The temperatures ranged from 1 630 to 2 273 K. The dependence of soot yield on the temperature, pressure and fuel concentration was obtained. With the changes of temperature, the soot yield is a Gauss distribution. The soot yield increases as the pressure or fuel concentration increases. The maximum of soot yield was as high as 55%. The peak temperature of soot yield was not changed dramatically with the pressure. However, it changed from 1 852 to 1 921 K as the concentration of toluene increase from 0.25% to 0.5%. Moreover, we compared the soot yield between toluene and methylcyclohexane at pressure of 4 atm with fuel concertation of 0.5%. During the pyrolysis of methylcyclohexane, the peak temperature of soot yield was 2 045 K, which is about 135 K higher than that of toluene. However, the maximum soot yield of methylcyclohexane is only 1/8 of toluene. This work provides experimental reference for the research of soot particle emission in the engines and the mechanism of soot formation.
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BACKGROUND: Recently, several studies assessed the effectiveness of Tai Chi for Parkinson's disease (PD), but the role of Tai Chi in the management of PD remained controversial. Therefore, the purpose of this systematic review is to evaluate the evidence on the efficacy of Tai Chi for PD. METHODS: Six English and Chinese electronic databases, up to April 2014, were searched to identify relevant studies. The risk of bias in eligible studies was assessed by Cochrane Collaboration's tools. The primary outcomes were motor function, balance and gait in individuals with PD. Standardized mean difference (SMD) and 95% confidence intervals (CI) of random-effect model were calculated. And heterogeneity was assessed based on the I2 statistic. RESULTS: 7 randomized controlled trials and 1 non-randomized controlled trial were eligible. The aggregated results suggested that Tai Chi showed beneficial effects in improving motor function (SMD, -0.57; 95% CI -1.11 to -0.04; pâ=â0.03), balance (SMD, 1.22; 95% CI 0.80 to 1.65; p<0.00001) and functional mobility (SMD, 1.06; 95% CI 0.68 to 1.44; p<0.00001) in patients with PD, but not in improving gait velocity (SMD, -0.02; 95% CI -0.58 to 0.54; pâ=â0.94), step length (SMD, -0.00; 95% CI -0.57 to 0.56; pâ=â0.99), or gait endurance (SMD, 0.53; 95% CI -0.07 to 1.12; pâ=â0.08). Comparing with other active therapies, however, Tai Chi only showed better effects in improving balance (SMD, 0.74; 95% CI 0.38 to 1.10; p<0.0001). CONCLUSION: Tai Chi should be a valid complementary and alternative therapy for PD, especially in improving motor function and balance. However, more studies with long follow-up are warrant to confirm the current finding of Tai Chi for PD.
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Marcha/fisiologia , Destreza Motora/fisiologia , Doença de Parkinson/reabilitação , Equilíbrio Postural/fisiologia , Tai Chi Chuan , Humanos , Doença de Parkinson/fisiopatologiaRESUMO
Low-lying states of Ga2P and Ga2As are investigated with the equation-of-motion coupled-cluster approach for ionized states at the singles and doubles level (EOMIP-CCSD) as well as at the CCSDT-3 level together with CCSD, CCSD(T), and DFT. Except for the asymmetric stretching b2 mode of the (2)B2 and (2)A1 states, all these approaches provide structures, frequencies and adiabatic electron affinities that are in reasonable agreement with each other. According to our results, the lowest-energy state of these two molecules is the (2)A' state of C(s) symmetry and the (2)B2 state is the ground electronic state with C(2v) symmetry. As for the b2 mode, CCSD and CCSD(T) afford real frequencies for the (2)B2 state, while EOM approaches and DFT with most exchange-correlation functionals give rise to imaginary frequencies. The (2)B2 and (2)A1 states couple with each other due to distortion along b2 mode through the pseudo-Jahn-Teller effect. Analysis on results shows that EOM approaches afford reasonable b2 frequencies for the two states and DFT approaches, except for BP86 and PBE, provide qualitatively correct b2 frequencies for the (2)B2 state. In addition, a potential matrix is introduced to describe the vibronic coupling between the (2)B2 and (2)A1 states and parameters in the matrix are fitted to the adiabatic potential curves from EOMIP-CCSD results.
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Within the framework of constrained density functional theory (CDFT), the diabatic or charge localized states of electron transfer (ET) have been constructed. Based on the diabatic states, inner reorganization energy λin has been directly calculated. For solvent reorganization energy λs, a novel and reasonable nonequilibrium solvation model is established by introducing a constrained equilibrium manipulation, and a new expression of λs has been formulated. It is found that λs is actually the cost of maintaining the residual polarization, which equilibrates with the extra electric field. On the basis of diabatic states constructed by CDFT, a numerical algorithm using the new formulations with the dielectric polarizable continuum model (D-PCM) has been implemented. As typical test cases, self-exchange ET reactions between tetracyanoethylene (TCNE) and tetrathiafulvalene (TTF) and their corresponding ionic radicals in acetonitrile are investigated. The calculated reorganization energies λ are 7293 cm(-1) for TCNE/TCNE(-) and 5939 cm(-1) for TTF/TTF(+) reactions, agreeing well with available experimental results of 7250 cm(-1) and 5810 cm(-1), respectively.
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Elétrons , Etilenos/química , Compostos Heterocíclicos/química , Nitrilas/química , Teoria Quântica , Termodinâmica , Estrutura MolecularRESUMO
We present a further interpretation of reaction class transition state theory (RC-TST) proposed by Truong et al. for the accurate calculation of rate coefficients for reactions in a class. It is found that the RC-TST can be interpreted through the isodesmic reaction method, which is usually used to calculate reaction enthalpy or enthalpy of formation for a species, and the theory can also be used for the calculation of the reaction barriers and reaction enthalpies for reactions in a class. A correction scheme based on this theory is proposed for the calculation of the reaction barriers and reaction enthalpies for reactions in a class. To validate the scheme, 16 combinations of various ab initio levels with various basis sets are used as the approximate methods and CCSD(T)/CBS method is used as the benchmarking method in this study to calculate the reaction energies and energy barriers for a representative set of five reactions from the reaction class: R(c)CH(R(b))CR(a)CH2 + OH(â¢) â R(c)C(â¢)(R(b))CR(a)CH2 + H2O (R(a), R(b), and R(c) in the reaction formula represent the alkyl or hydrogen). Then the results of the approximate methods are corrected by the theory. The maximum values of the average deviations of the energy barrier and the reaction enthalpy are 99.97 kJ/mol and 70.35 kJ/mol, respectively, before correction and are reduced to 4.02 kJ/mol and 8.19 kJ/mol, respectively, after correction, indicating that after correction the results are not sensitive to the level of the ab initio method and the size of the basis set, as they are in the case before correction. Therefore, reaction energies and energy barriers for reactions in a class can be calculated accurately at a relatively low level of ab initio method using our scheme. It is also shown that the rate coefficients for the five representative reactions calculated at the BHandHLYP/6-31G(d,p) level of theory via our scheme are very close to the values calculated at CCSD(T)/CBS level. Finally, reaction barriers and reaction enthalpies and rate coefficients of all the target reactions calculated at the BHandHLYP/6-31G(d,p) level of theory via the same scheme are provided.
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Aromatic hydrocarbon fuels, such as toluene, are important components in real jet fuels. In this work, reactive molecular dynamics (MD) simulations employing the ReaxFF reactive force field have been performed to study the high-temperature oxidation mechanisms of toluene at different temperatures and densities with equivalence ratios ranging from 0.5 to 2.0. From the ReaxFF MD simulations, we have found that the initiation consumption of toluene is mainly through three ways, (1) the hydrogen abstraction reactions by oxygen molecules or other small radicals to form the benzyl radical, (2) the cleavage of the C-H bond to form benzyl and hydrogen radicals, and (3) the cleavage of the C-C bond to form phenyl and methyl radicals. These basic reaction mechanisms are in good agreement with available chemical kinetic models. The temperatures and densities have composite effects on toluene oxidation; concerning the effect of the equivalence ratio, the oxidation reaction rate is found to decrease with the increasing of equivalence ratio. The analysis of the initiation reaction of toluene shows that the hydrogen abstraction reaction dominates the initial reaction stage at low equivalence ratio (0.5-1.0), while the contribution from the pyrolysis reaction increases significantly as the equivalence ratio increases to 2.0. The apparent activation energies, E(a), for combustion of toluene extracted from ReaxFF MD simulations are consistent with experimental results.
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The reaction mechanism of the gas-phase Pt atom with C(3)H(8) has been systematically investigated on the singlet and triplet potential energy surfaces at CCSD(T)//BPW91/6-311++G(d, p), Lanl2dz level. Pt atom prefers the attack of primary over secondary C-H bonds in propane. For the Pt + C(3)H(8) reaction, the major and minor reaction channels lead to PtC(3)H(6) + H(2) and PtCH(2) + C(2)H(6), respectively, whereas the possibility to form products PtC(2)H(4) + CH(4) is so small that it can be neglected. The minimal energy reaction pathway for the formation of PtC(3)H(6) + H(2), involving one spin inversion, prefers to start at the triplet state and afterward proceed along the singlet state. The optimal C-C bond cleavages are assigned to C-H bond activation as the first step, followed by cleavage of a C-C bond. The C-H insertion intermediates are kinetically favored over the C-C insertion intermediates. From C-C to C-H oxidative insertion, the lowering of activation barrier is mainly caused by the more stabilizing transition state interaction ΔE(≠) (int), which is the actual interaction energy between the deformed reactants in the transition state.
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Modelos Químicos , Propano/químicaRESUMO
According to our recent studies on the nonequilibrium solvation, the solvent reorganization energy is found to be the cost of maintaining the residual polarization P', which equilibrates with the extra electric field E(ex). On the basis of this solvent reorganization energy and the well-established equilibrium solvation energy, a novel and reasonable expression for the spectral shift of the electronic absorption spectra is proposed in this work. Furthermore, the two lowest transitions of uracil in aqueous solution are investigated as test cases with the TDDFT/6-311++G** method. The obtained spectral shift is 0.48 eV for n â π* transition and -0.14 eV for π â π* transition, agreeing well with available experimental results. The contributions to the shift are discussed and the electrostatic plus polarization components are found to be crucial for the electronic absorption spectra of uracil in aqueous solution.
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Solventes/química , Uracila/química , Elétrons , Modelos Moleculares , Teoria Quântica , Termodinâmica , Água/químicaRESUMO
Using an intensified spectroscopic detector CCD and a heated shock tube, transient emission spectra of n-decane in the combustion reaction were measured in a spectral range of 200-850 nm. Experiments were conducted at temperatures of 1100-1600 K, a pressure of 2.0 atm, an initial fuel mole fraction of 1.0% and an equivalence ratio of 1.0. Results show that the main emission bands are attributed to OH, CH and C2 radicals produced during the combustion process of n-decane. Emission intensities of the three radicals reached their maximums only after 5 micros from the onset of their ignitions. After about 30 micros had passed, the band of OH radical was still observed, but the bands of CH and C2 radicals almost disappeared. Time histories of spectral emission intensities represent the time histories of concentrations of the three radicals during the process of combustion The emission peak ratio of OH (306.4 nm)/CH(431.4 nm) is approximately 27/100 in the combustion of n-decane, which is much greater than the corresponding ratio of about 7/100 in the combustion of n-heptane. This result reveals that the two fuels have different reaction mechanisms. High resolution characteristic spectra of CH and C2 were also acquired in the present experiment, the spectra show the rotational structures of the bands clearly. Current results are valuable for understanding the property and validating the mechanism of n-decane combustion reaction
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Using an intensified spectroscopic detector CCD and a chemical shock tube, transient emission spectra of n-heptane during the reaction process of combustion were measured, with exposure time of 6 micros and a spectral range of 200 - 850 nm Experiments were conducted at an ignition temperature of 1 408 K and pressure of 2.0 atmos, with an initial fuel mole fraction of 1.0% and an equivalence ratio of 1.0. Measured emission bands were determined to be produced by OH, CH and C2 free radicals, which reveals that small OH, CH and C2 radicals are important intermediate products in the combustion process of n-heptane. Time-resolved spectra indicate that radical concentrations of OH, CH and C2 reached their peaks sharply; however, CH and C2 reduced and disappeared rapidly while the duration of OH was much longer in the reaction. This work provides experimental data for understanding the microscopic process and validating the mechanism of n-heptane combustion reaction.
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In this work, the solvent reorganization energy is formulated within the framework of classical thermodynamics, by adding some external charges to construct a constrained equilibrium state. The derivation clearly shows that the reorganization energy is exactly the polarization cost for the inertial part of the polarization. We perform our derivation just within the framework of the first law of thermodynamics, and the final form of the reorganization energy is completely the same as that we gave in our recent work by defining a nonequilibrium solvation free energy. With the two-sphere model approximation, our solvent reorganization energy is derived as λ(0) = Δq(2)/2[1/r(D) + 1/r(A) - 2/d][(ε(-1)(op) - ε(-1)(s))/(1 - ε(-1)(s))]. This amends Marcus' model by a factor of (ε(-1)(op) - ε(-1)(s))/(1 - ε(-1)(s)), which is coupled with the solvent polarity. Making use of the modified expression of solvent reorganization energy, two recently reported electron transfer processes are investigated in representative solvents. The results show that our formula can well reproduce the experimental observations.