Au-chin Tang

Theoretical study on mechanisms of the high-temperature reactions C2H3 + H2O and C2H4 + OH

The potential energy surface of the radical-molecule reaction C2H3 + H2O in the gas phase is explored at the 6-31G(d,p) and 6-311G(d,p) B3LYP and single-point QCISD(T)/6-311G(2df,p) levels. The most favorable channel is the direct H-abstraction from H2O to C2H3 leading to product P1 C2H4 + OH, whereas the other channels leading to the products P2 CH3 + CH2O, P3 CH3CHO + H, P4cis-CH2CHOH + H and P4′ trans-CH2CHOH + H are kinetically much less competitive. For the direct H-abstraction channel, high-level energetic calculations at the QCISD(T)/6-311G(2df,p), QCISD(T)/6-311+G(2df,2p) and G2 levels using the B3LYP/6-31G(d,p) and QCISD/6-31G(d,p) optimized geometries are further performed to estimate the thermal rate constants over a wide temperature range 200–5000 K for comparison with future laboratory measurements. The calculated barrier heights at the QCISD(T)/6-311+G(2df,2p) and G2 levels based on the QCISD/6-31G(d,p) geometries with zero-point vibrational energy (ZPVE) correction are 12.6 and 13.0 kcal mol−1, respectively. The results indicate that the C2H3 + H2O reaction might play an important role at high temperatures (T > 1800 K) in the presence of gaseous water and should be incorporated in the C2H3-modeling of hydrocarbon-fuel combustion processes. Discussions are also made in comparison with the analogous reactions C2H3 + H2 and C2H + H2O. While the addition-elimination mechanism of another important radical-molecule reaction C2H4 + OH has been the subject of extensive theoretical and experimental studies, its H-abstraction process leading to C2H3 + H2O has received little attention. For the C2H4 + OH → C2H3 + H2O channel, our calculations predict ZPVE-corrected barriers, 5.6 and 5.4 kcal mol−1, respectively, at the QCISD(T)/6-311+G(2df,2p)//QCISD/6-31G(d,p) and G2//QCISD/6-31G(d,p) levels, and reveal its importance at high temperatures (T > 560 K). In the range 720–1173 K, the calculated high-level rate constants are quantitatively in good agreement with the measured values. However, our calculated activation energy, 9.5 and 9.3 kcal mol−1 at the QCISD(T)/6-311+G(2df,2p)//QCISD/6-31G(d,p) and G2//QCISD/6-31G(d,p) levels with ZPVE correction, respectively, suggests that the experimentally determined value 4–5 kcal mol−1 may be underestimated and future rate constant measurements over a wide temperature range including T > 1200 K may be desirable.

Curing Theory and Scaling Study: Crosslinking Reaction of the Aa Type

Abstract The process of the Aa-crosslinking reaction is considered as a whole to approach the threshold of the sol-gel transition. By a rational way, without Stirlings approximation, the asymptopic form of the Flory-Stockmayer distribution near the gel point is obtained to reach a generalized scaling law.

An analytic method for the accurate calculation of energy eigenvalues of a double-well anharmonic oscillator

Abstract A simple analytic procedure is presented to calculate accurate energy eigenvalues and eigenfunctions of the double-well anharmonic oscillator by incorporating the harmonic oscillator eigenfunctions and Manneback formulas into the variational method. Fast convergence of the method is demonstrated by comparison of some eigenvalues in model calculations.

Crosslinking reaction of type Aa involving intramolecular cyclization

Abstract An alternative way is proposed to approach crosslinking reactions of Type A a by taking into consideration intramolecular cyclization. The sol fraction for postgelation is investigated to deduce the equilibrium number distribution of n-mer, with the Flory-Stockmayer distribution as a criterion. Furthermore, scaling study leads directly to a generalized scaling law.