Decomposition reaction rate of BCl₃–CH₄–H₂ in the gas phase

The decomposition reaction rate of the BCl₃+CH₄+H₂ gas-phase reaction system in preparing boron carbide or boron was investigated based on the most favorable reaction pathways proposed in Liu et al. (Struct Chem 23:1677, 2012). The rate constants of all the elementary reactions were evaluated with the variational transition-state theory in which the necessary vibrational frequencies for the stationary points as well as the selected points along the minimum energy paths (MEPs) were calculated with density functional theory B3PW91/6-311G(d,p) and the energies were refined with the accurate model chemistry method G3(MP2). For the elementary reaction associated with a transition state, the MEP was obtained with the intrinsic reaction coordinates, while for that without a transition state, the relaxed potential energy surface scan was employed to obtain the MEP. The rate constants were calculated for temperatures within 200–2000 K and fitted into three-parameter Arrhenius expressions. The reaction rate was investigated by using the COMSOL software to solve numerically the coupled differential rate equations. The results show that reactants are consumed with a fast process and the consumption rate increases with increasing temperature. The concentration, consistent with the thermodynamics computations, of the reactants achieves a constant of consuming completely with the extension of time. The concentrations of precuts BC and C also increase with increasing temperature, and the concentration of B is always larger than BC in the temperature range of 1200–1600 K. Thus, the rich boron product is easy to form and to deposit at higher temperatures. However, the difference in concentrations (logarithm values) between BC and B becomes smaller with the increasing temperature. This result is also consistent with the experimental conclusion of Ye et al. (Mater Rev 24:108, 2010). The logarithm of the decreasing rate for CH₄ and the reciprocal temperature have excellent linear relationship at 700–2000 K with a correlation coefficient of 0.9999. The slope of the line corresponds to an apparent activation energy 208.4 kJ mol⁻¹, which is comparable with the energy barrier (238.6 kJ mol⁻¹) of the rate control reaction. The logarithm of the decreasing rate for BCl₃ and the reciprocal temperature also have an excellent linear relationship in two temperature ranges 700–1600 and 1700–2000 K, predicting that the reaction follows obviously two different kinetics mechanisms. The correspondence apparent activation energies are 201.7 and 378.3 kJ mol⁻¹, respectively.