Extended first-principles thermochemistry for the oxidation of titanium tetrachloride

A detailed first-principles investigation of the gas-phase precursor chemistry of titanium tetrachloride (TiCl4) in an O2 environment is used to identify the thermodynamically most stable oxidation products. Candidate species are systematically proposed based on twelve manually defined base moieties in combination with possible functional groups attached to each moiety. The ground state geometry and vibrational frequencies for each candidate species are calculated using density functional theory at the B97-1/6-311+G(d,p) level of theory. A set of 2; 328 unique candidate species are found to be physically reasonable. Their thermochemical data are calculated by applying statistical thermodynamics. Standard enthalpies of formation are estimated, if unknown, by using a set of error-cancelling balanced reactions. An equilibrium composition analysis of a mixture of TiCl4/O2 (50 mol%) at 3 bar is performed to identify the thermodynamically stable products. At low temperatures, below approximately 700 K, trimer species are dominant. This is followed by a mid-temperature range of 700 to 1975 K where Ti2OCl6 is the most abundant species, before its thermodynamic stability decreases. Between 1200 and 1825 K TiCl4 is the most stable monomer. At temperatures above 1975 K TiOCl2 becomes the dominant species. This species has been measured experimentally. A structural analysis is used to suggest further potentially stable higher polymers and defines a starting point to investigate the mechanisms leading to the formation of titanium dioxide (TiO2) particles

Numerical simulation and parametric sensitivity study of titanium dioxide particles synthesised in a stagnation flame

A detailed population balance model is used to simulate titanium dioxide nanoparticles synthesised in a stagnation flame from titanium tetraisopropoxide (TTIP) precursor. A two-step simulation methodology is employed to apply the detailed particle model as a post-process to flame profiles obtained from a fully coupled simulation with detailed gas-phase chemistry, flow dynamics and a simple particle model. The detailed particle model tracks the size and coordinates of each primary in an aggregate, and is able to resolve the particle morphology, permitting direct comparison with experimental measurements through simulated TEM-style images. New sintering parameters, informed by molecular dynamics simulations in the literature, are introduced into the model to account for the sintering behaviour of sub-10 nm particles. Simulated primary and aggregate particle size distributions were in excellent agreement with experimental measurements. A parametric sensitivity study found particle morphology to be sensitive to the sintering parameters, demonstrating the need to apply careful consideration to the sintering behaviour of nano-sized particles in modelling studies. The final particle morphology was not found to be sensitive to other model parameters

A unified evaluation of iterative projection algorithms for phase retrieval

Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free diffraction-limited imaging and the possibility of using radiation for which no lenses exist. The challenge of this imaging technique is transfered from the lenses to the algorithms. We evaluate these new computational ``instruments'' developed for the phase retrieval problem, and discuss acceleration strategies.Comment: 12 pages, 9 figures, revte

A systematic method to estimate and validate enthalpies of formation using error-cancelling balanced reactions

The Combustion Institute This paper presents an automated framework that uses overlapping subsets of reference data to systematically derive an informed estimate of the standard enthalpy of formation of chemical species and assess the consistency of the reference data. The theory of error-cancelling balanced reactions (EBRs) is used to calculate estimates of the standard enthalpy of formation. Individual EBRs are identified using linear programming. The first part of the framework recursively identifies multiple EBRs for specified target species. A distribution of estimates can then be determined for each species from which an informed estimate of the enthalpy is derived. The second part of the framework iteratively isolates inconsistent reference data and improves the prediction accuracy by excluding such data. The application of the framework is demonstrated for test cases from organic and inorganic chemistry, including transition metal complexes. Its application to a set of 920 carbon, hydrogen and oxygen containing species resulted in a rapid decrease of the mean absolute error for estimates of the enthalpy of formation of each species due to the identification and exclusion of inconsistent reference data. Its application to titanium-containing species identified that the available reference values of TiOCl and TiO(OH) 2 are inconsistent and need further attention. Revised values are calculated for both species. A comparison with popular high-level quantum chemistry methods shows that the framework is able to use affordable density functional theory (DFT) calculations to deliver highly accurate estimates of the standard enthalpy of formation, comparable to high-level quantum chemistry methods for both hydrocarbons and transition metal complexes

A kinetic mechanism for the thermal decomposition of titanium tetraisopropoxide

This work presents the first systematically derived and thermodynamically consistent mechanism to describe the thermal decomposition of titanium tetraisopropoxide (TTIP). The mechanism is based on an analogy between the decomposition of the isopropoxide branches and the decomposition of isopropanol. Flux and sensitivity analyses were used to identify the main reaction pathways in the proposed mechanism as the step-wise release of C3H6 via four-member ring transition states, the successive abstraction of CH3 radicals via C–C bond cleavage followed by hydrogen abstraction to form C = C double bonds, and hydrogen abstraction from the isopropoxide methyl groups followed by the release of C3H6. The final decomposition product was titanium hydroxide, Ti(OH)4. Rate constants were calculated using conventional and variational transition state theories for reactions in the first two pathways. The calculated rates are similar to the rates calculated for the corresponding isopropanol reactions, providing support for the analogy with isopropanol. The mechanism was used to simulate the ignition delay of isopropanol and TTIP. Excellent agreement was observed with experimental data for isopropanol. However, the mechanism over predicted the ignition delay for TTIP. The discrepancy was shown to be unlikely to be caused by the modest difference between the true reaction rates for the TTIP system and those assumed based on the analogy with isopropanol. It was found that the sensitivity of the TTIP decomposition to the presence of water must be caused by additional chemical pathways than the ones given by isopropanol analogy.This project is partly funded by the National Research Foundation (NRF), Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme. The authors thank Huntsman Pigments for financial support

A big data framework to validate thermodynamic data for chemical species

The advent of large sets of chemical and thermodynamic data has enabled the rapid investigation of increasingly complex systems. The challenge, however, is how to validate such large databases. We propose an automated framework to solve this problem by identifying which data are consistent and recommending what future experiments or calculations are required. The framework is applied to validate data for the standard enthalpy of formation for 920 gas-phase species containing carbon, oxygen and hydrogen retrieved from the NIST Chemistry WebBook. The concept of error-cancelling balanced reactions is used to calculate a distribution of possible values for the standard enthalpy of formation of each species. The method automates the identification and exclusion of inconsistent data. We find that this enables the rapid convergence of the calculations towards chemical accuracy. The method can exploit knowledge of the structural similarities between species and the consistency of the data to identify which species introduce the most error and recommend what future experiments and calculations should be considered.This project is partly funded by the National Research Foundation (NRF), Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme. The authors thank Huntsman Pigments and Additives for financial support