Simultaneous spectrophotometric determination of Co (II) and Co (III) in acidic medium with partial least squares regression and artificial neural networks

This study aims at the application of two chemometric techniques to visible spectra of acetic acid solutions of Co (II) and Co (III) for simultaneous determination thereof. Spectral data of 145 samples in the range of 400-700 nm were used to build the models. Partial least squares regression models were developed for which latent variables were determined using internal cross-validation with a leave-one-out strategy and 3 and 2 latent variables were selected for Co(II) and Co(III) based on root mean square error of cross-validation. For these models, root mean square errors of prediction were 1.16 and 0.536 mM and coefficients of determination were 0.975 and 0.892 for Co (II) and Co (III). As an alternate method, artificial neural networks consisting of three layers, with 10 neurons in hidden layer, were trained to model spectra and concentrations of cobalt species. Levenberg-Marquardt algorithm with feed-forward back-propagation learning resulted root mean square errors of prediction of 0.316 and 0.346 mM for Co (II) and Co (III) respectively and coefficients of determination were 0.996 and 0.988.

Iterative multiscale and multi-physics computations for operando catalyst nanostructure elucidation and kinetic modeling

Modern heterogeneous catalysis has benefitted immensely from computational predictions of catalyst structure and its evolution under reaction conditions, first-principles mechanistic investigations, and detailed kinetic modeling, which are rungs on a multiscale workflow. Establishing connections across these rungs and integration with experiments have been challenging. Here, operando catalyst structure prediction techniques using density functional theory simulations and ab initio thermodynamics calculations, molecular dynamics, and machine learning techniques are presented. Surface structure characterization by computational spectroscopic and machine learning techniques is then discussed. Hierarchical approaches in kinetic parameter estimation involving semi-empirical, data-driven, and first-principles calculations and detailed kinetic modeling via mean-field microkinetic modeling and kinetic Monte Carlo simulations are discussed along with methods and the need for uncertainty quantification. With these as the background, this article proposes a bottom-up hierarchical and closed loop modeling framework incorporating consistency checks and iterative refinements at each level and across levels.

Structure-Preserving Joint Non-negative Tensor Factorization to Identify Reaction Pathways Using Bayesian Networks

Extracting meaningful information from spectroscopic data is key to species identification as a first step to monitoring chemical reactions in unknown complex mixtures. Spectroscopic data obtained over multiple process modes (temperature, residence time) from different sensors [Fourier transform infrared (FTIR), proton nuclear magnetic resonance (¹H NMR)] comprise hidden complementary information of the underlying chemical system. This work proposes an approach to jointly capture these hidden patterns in a structure-preserving and interpretable manner using coupled non-negative tensor factorization to achieve uniqueness in decomposition. Projections onto the modes of spectral channels, specific to each sensor, are interpreted as pseudo-component spectra, while projections onto the shared process modes are interpreted as the corresponding pseudo-component concentrations across temperature and residence times. Causal structure inference among these pseudo-component spectra (using Bayesian networks) is then used to identify plausible reaction pathways among the identified species representing each pseudo-component. Tensor decomposition of the FTIR data enables the development of reaction sequences based on the identified functional groups, while that of ¹H NMR by itself is lacking in mechanism development as it solely reveals the proton environments in a pseudo-component. However, jointly parsing spectra from both the sensors is seen to capture complementary information, wherein insights into the proton environment from ¹H NMR disambiguate pseudo-components that have similar FTIR peaks. A scalable method of parallelizing tensor decomposition to handle high-dimensional modes in process data by using grid tensor factorization, while being robust to process data artifacts like outliers, noise, and missing data, has been developed.

Kinetic Study of Product Distribution Using Various Data-Driven and Statistical Models for Fischer-Tropsch Synthesis

Three modeling techniques, namely, a radial basis function neural network (RBFNN), a comprehensive kinetic with genetic algorithm (CKGA), and a response surface methodology (RSM), were used to study the kinetics of Fischer-Tropsch (FT) synthesis. Using a 29 × 37 (4 independent process parameters as inputs and corresponding 36 responses as outputs) matrix with total 1073 data sets for data training through RBFNN, the established model is capable of predicting hydrocarbon product distribution i.e., the paraffin formation rate (C₂-C₁₅) and the olefin to paraffin ratio (OPR) within acceptable uncertainties. With additional validation data sets (15 × 36 matrix with total 540 data sets), the uncertainties of using three different models were compared and the outcomes were: RBFNN (±5% uncertainties), RSM (±10% uncertainties), and CKGA (±30% uncertainties), respectively. A new effective strategy for kinetic study of the complex FT synthesis is proposed: RBFNN is used for data matrix generation with a limited number of experimental data sets (due to its fast converge and less computation time), CKGA is used for mechanism selections by the Langmuir-Hinshelwood-Hougen-Watson (LHHW) approach using a genetic algorithm to find out potential reaction pathways, and RSM is used for statistical analysis of the investigated data matrix (generated from RBFNN through central composite design) upon responses and subsequent singular/multiple optimizations. The proposed strategy is a very useful and practical tool in process engineering design and practice for the product distribution during FT synthesis.