Effect of Caustic Addition in Epoxy Polymerization Process: A Single and Multi‐Objective Evolutionary Approach

Summary: An epoxy polymerization process is studied in semi‐batch mode. Caustic has a very critical influence on epoxy polymerization process, which is modeled as a set of highly nonlinear coupled ODE's (ordinary differential equations). Owing to the highly complicated, nonlinear domain of analysis, “Differential Evolution (DE)” and “Genetic Algorithm (GA)” are used as optimization tools to identify the ‐PDI Pareto set and study the best operating strategy with respect to NaOH addition. The moment of various oligomeric components during the semi‐batch polymerization is also presented for a better understanding of the process. This study demonstrates the potential of evolutionary optimization algorithm to identify various operating philosophies of a semi‐batch epoxy reactor for a targeted product quality.

Pareto plot for epoxy polymerization process with intermediate NaOH addition varying from 0.0 to 1.0 kmol · m⁻³.     

Modeling of Current Distribution on Smooth and Columnar Platinum Structures

Studying the growth and stability of anisotropic or isotropic disordered surfaces in electrodeposition is of importance in catalytic electrochemistry. In some cases, the metallic nature of the electrode defines the topography and roughness, which are also controlled by the experimental time and applied external potential. Because of the experimental restrictions in conventional electrochemical techniques and ex situ electron microscopies, a theoretical model of the surface geometry could aid in understanding the electrodeposition process and current distributions. In spite of applying a complex theory such as dynamic scaling method or perturbation theories, the resolution of mixed mass‐/charge‐transfer equations (tertiary distribution) for the electrodeposition process would give reliable information. One of the main problems with this type of distribution is the mathematics when solving the spatial n‐dimensional differential equations. Use of a primary current distribution is proposed here to simplify the differential equations; however it limits wide application of the first assumption. Distributions of concentration profile, current density, and electrode potential are presented here as a function of the distance normal to the surface for the cases of smooth and rough platinum growth. In the particular case of columnar surfaces, cycloid curves are used to model the electrode, from which the concentration profile is presented in a parameterized form after solving a first‐type curvilinear integral. The concentration contour results in a combination of a trigonometric inverse function and a linear distribution leading to a negative concavity curve. The calculation of the current density and electrode potential contours also show trigonometric shapes exhibiting forbidden imaginary values only at the minimal values of the trochoid curve.     

Globally convergent trust-region methods for self-consistent field electronic structure calculations

As far as more complex systems are being accessible for quantum chemical calculations, the reliability of the algorithms used becomes increasingly important. Trust-region strategies comprise a large family of optimization algorithms that incorporates both robustness and applicability for a great variety of problems. The objective of this work is to provide a basic algorithm and an adequate theoretical framework for the application of globally convergent trust-region methods to electronic structure calculations. Closed shell restricted Hartree-Fock calculations are addressed as finite-dimensional nonlinear programming problems with weighted orthogonality constraints. A Levenberg-Marquardt-like modification of a trust-region algorithm for constrained optimization is developed for solving this problem. It is proved that this algorithm is globally convergent. The subproblems that ensure global convergence are easy-to-compute projections and are dependent only on the structure of the constraints, thus being extendable to other problems. Numerical experiments are presented, which confirm the theoretical predictions. The structure of the algorithm is such that accelerations can be easily associated without affecting the convergence properties.     

Strategies for Substrate-Regulated P450 Catalysis: From Substrate Engineering to Co-catalysis

Cytochrome P450 enzymes (P450s) catalyze the monooxygenation of various organic substrates. These enzymes are fascinating and promising biocatalysts for synthetic applications. Despite the impressive abilities of P450s in the oxidation of C−H bonds, their practical applications are restricted by intrinsic drawbacks, such as poor stability, low turnover rates, the need for expensive cofactors (e.g., NAD(P)H), and the narrow scope of useful non-native substrates. These issues may be overcome through the general strategy of protein engineering, which focuses on the improvement of the catalysts themselves. Alternatively, several emerging strategies have been developed that regulate the P450 catalytic process from the viewpoint of the substrate. These strategies include substrate engineering, decoy molecule, and dual-functional small-molecule co-catalysis. Substrate engineering focuses on improving the substrate acceptance and reaction selectivity by means of an anchoring group. The latter two strategies utilize co-substrate-like small molecules that either are proposed to reform the active site, thereby switching the substrate specificity, or directly participate in the catalytic process, thereby creating new catalytic peroxygenation capabilities towards non-native substrates. For at least 10 years, these approaches have played unique roles in solving the problems highlighted above, either alone or in conjunction with protein engineering. Herein, we review three strategies for substrate regulation in the P450-catalyzed oxidation of non-native substrates. Furthermore, we address remaining challenges and potential solutions associated with these approaches.     

Modeling and simulation of stationary catalytic processes

Generalized models for steady state catalytic processes are presented in matrix form. Multistep reaction rate control is assumed. Numerical algorithms for solving of the created linear and nonlinear equation systems are developed and tested. Four examples are considered: an Eley–Rideal-mechanism, a Langmuir–Hinshelwood mechanism, a dual route, dual site mechanism, and a monomolecular decomposition with steady state multiplicity. The overall reaction rates are simulated as a function of the reactant concentrations. A maximum reaction rate is obtained in the case of a Langmuir–Hinshelwood mechanism (example 2), the location of the rate maximum in the concentration domain is shifted towards the concentration of the reactant with the lowest adsorption constants. An Eley–Rideal mechanism (example 1) has always monotonously increasing rate curves. In the case of steady state multiplicity (example 4) all steady states could be simulated with the proposed algorithm. The computation of reaction rate surfaces is important in investigating the behavior of complicated catalytic systems (e.g., systems with multistep rate control and/or steady state multiplicity), in planning of experiments and in chemical reactor simulation.     

A family of parametric schemes of arbitrary even order for solving nonlinear models: CMMSE2016

Many problems related to gas dynamics, heat transfer or chemical reactions are modeled by means of partial differential equations that usually are solved by using approximation techniques. When they are transformed in nonlinear systems of equations via a discretization process, this system is big-sized and high-order iterative methods are specially useful. In this paper, we construct a new family of parametric iterative methods with arbitrary even order, based on the extension of Ostrowski’ and Chun’s methods for solving nonlinear systems. Some elements of the proposed class are known methods meanwhile others are new schemes with good properties. Some numerical tests confirm the theoretical results and allow us to compare the numerical results obtained by applying new methods and known ones on academical examples. In addition, we apply one of our methods for approximating the solution of a heat conduction problem described by a parabolic partial differential equation.     

A study of one dimensional nonlinear diffusion equations by Bernstein polynomial based differential quadrature method

The purpose of this work is to study numerical solutions of nonlinear diffusion equations such as Fisher’s equation, Burgers’ equation and modified Burgers’ equation by applying Bernstein differential quadrature method (BDQM). These nonlinear diffusion equations occur in many applications of theoretical, engineering and environmental sciences. Therefore, finding numerical solutions of these equations is very important. In BDQM, Bernstein polynomials are used as base functions to find weighting coefficients of differential quadrature method. We have applied BDQM on eleven different test problems taken from the literature and the computed results confirm that BDQM is an efficient method for finding solution of nonlinear partial differential equations. It is found that BDQM produces very good results even at small number of grid points.     

The Area method for pure fluids and an analysis of the two-phase region

The Area method, developed recently for solving multicomponent phase equilibrium problems, has been extended to pure fluids. The method is based on maximizing a single objective function in the Helmholtz-volume surface along any given isotherm, which reduces the number of independent variables to only two: the saturated liquid and vapour volumes. Two techniques are employed to find the maximum of the objective function, the integral and iterative. The integral always finds the thermodynamically stable solution without any prior assumptions about the values of the molar volumes. This factor distinguishes the integral from the iterative technique and also from methods based on the Maxwell equal-area principle. The method has been applied to a group of high accuracy non-cubic equations of state and some of the thermodynamic inconsistencies which occur inside the two-phase region are explored. A new inequality constraint which eliminates these inconsistencies during the development of new equations of state is proposed, and initial results with fitting a preliminary Helmholtz equation of state for benzene are encouraging.     

一种新的化学计量学方法——蚁群虎法

蚁群算法是一种全新的仿生算法，具有智能搜索，全局优化，稳健笥强，分布式计算，易与其它方法结合等优点，是求解复杂的组合优化问题的有力工具。本文对蚁群算法的基本原理，数学模型，应用领域以及进展情况进行了介绍。     

Continuous optimization methods for ground-state searches of spin clusters

Computational methods were developed for ground-state searches of Heisenberg model spin clusters in which spin sites were represented by classical spin vectors. Simulated annealing, continuous genetic algorithm, and particle swarm optimization methods were applied for solving the problems. Because the results of these calculations were influenced by the settings of optimization parameters, effective parameter settings were also investigated. The results indicated that a continuous genetic algorithm is the most effective method for ground-state searches of Heisenberg model spin clusters, and that a mutation operator plays an important role in this genetic algorithm. These results provide useful information for solving physically or chemically important continuous optimization problems.     

Complex heterogeneous catalytic reactions. Some aspects of simulation

Heterogeneous catalytic reactions take place by stage mechanisms. The existence of reactants and products (at reactor input and output) and intermediates (not included in final equations of reactions) enables to derive a series of linear algebraic equations observed in stationary conditions in each point of reactor and in each point of catalyst grain. This “theory of stationary complex reactions” was developed first in the works of J. Horiuti and M.I. Temkin. Accounting some relationships of this theory enables to derive the first integrals for the set of the differential equations describing the zero-gradient reactors, flow reactors, and fluidized-bed reactors. Their consideration in the internal diffusion processes results in the relationships of diffusion stoichiometry and similar relationships for the grain surface concentrations and temperature. All the said relationships should be taken into account for calculation of the relevant reactors. Accounting the given relationships provides the correct solution of the relevant problem and reduces the order of the set of the differential equations to be solved. Some calculation features and restrictions in solution of inverse kinetic problems arise also if the mechanism of reactions involves reversible and equilibrium routes. This study systematizes the aforesaid issues and indicates to applicability and importance of the features of complex heterogeneous catalytic reactions for simulation of catalytic processes.     

Efficient newton–raphson/singular value decomposition-based optimization scheme with dynamically updated critical condition number for rapid convergence of weighted histogram analysis method equations

Selection of the successful optimization strategy is an essential part of solving numerous practical problems yet often is a nontrivial task, especially when a function to be optimized is multidimensional and involves statistical data. Here we propose a robust optimization scheme, referred to as NR/SVD-Cdyn, which is based on a combination of the Newton–Raphson (NR) method along with singular value decomposition (SVD), and demonstrate its performance by numerically solving a system of the weighted histogram analysis method equations. Our results show significant improvement over the direct iteration and conventional NR optimization methods. The proposed scheme is universal and could be used for solving various optimization problems in the field of computational chemistry such as parameter fitting for the methods of molecular mechanics and semiempirical quantum-mechanical methods. © 2019 Wiley Periodicals, Inc.     

Simulation of nonisothermal reactive liquid chromatography using two-dimensional lumped kinetic model

A nonisothermal two-dimensional lumped kinetic model of reactive liquid chromatography is formulated and applied to simulate the separation of multicomponent mixtures in a fixed-bed cylindrical column operating under nonisothermal condition. The axial and radial variations of concentration and temperature as well as reversibility of the chemical reactions are incorporated in the model equations. The model comprises a system of convection-diffusion-reaction partial differential equations coupled with algebraic and differential equations. Due to the nonlinearity of adsorption and reaction kinetics, it is required to apply an accurate numerical scheme for solving the model equations. In this study, an efficient and accurate high-resolution flux-limiting finite-volume scheme is proposed to solve the model equations. A number of stoichiometrical reactions are numerically simulated to determine the level of coupling between the temperature and concentration profiles. Moreover, the effects of various critical parameters on the process performance are examined. The results obtained are beneficial for understanding reaction and separation processes inside a liquid chromatographic reactor and to improve its performance.     

First Principle Based Computation:Applications to Applied Chemistry and Engineering

Computer simulation on the basis of the first principle approaches has increasingly emerged in both fundamental chemistry and engineering fields. In the development of widely used catalytic processes, the science and engineering aspects in chemical related subjects are the good examples in projecting the demands for the continuously growing computational technologies. The presentation will take two examples from our recent effort in both quantum mechanics applications to the analysis of MoS₂ catalyst (HDS) and the CFD calculation of the flow field in a packed bed catalytic reactor to explore the phenomena induced by flow. The main points of our topic are on the crucial demands for both theoretical and technical improvements in the applications of first principle methods to chemistry and chemical engineering.     

Correlations between two sets of angular relation equations

It is shown here that the angular relation equations between direct and reciprocal vectors are very similar to the angular relation equations in Euler’s theorem. These two sets of equations are usually treated separately as unrelated equations in different fields. In this careful study, the connection between the two sets of angular equations is revealed by considering the cosine rule for the spherical triangle. It is found that understanding of the correlation is hindered by the facts that the same variables are defined differently and different symbols are used to represent them in the two fields. Understanding the connection between different concepts is not only stimulating and beneficial, but also a fundamental tool in innovation and research, and has historical significance. The background of the work presented here contains elements of many scientific disciplines. This work illustrates the common ground of two theories usually considered separately and is therefore of benefit not only for its own sake but also to illustrate a general principle that a theory relevant to one discipline can often be used in another. The paper works with chemistry related concepts using mathematical methodologies unfamiliar to the usual audience of mainstream experimental and theoretical chemists.     

Rheology of double emulsions

New equations for the viscosity of concentrated double emulsions of core-shell droplets are developed using a differential scheme. The equations developed in the paper predict the relative viscosity (eta(r)) of double emulsions to be a function of five variables: a/b (ratio of core drop radius to shell outer radius), lambda(21) (ratio of shell liquid viscosity to external continuous phase viscosity), lambda(32) (ratio of core liquid viscosity to shell liquid viscosity), phi(DE) (volume fraction of core-shell droplets in double emulsion), and phi(m)(DE) (the maximum packing volume fraction of un-deformed core-shell droplets in double emulsion). Two sets of experimental data are obtained on the rheology of O/W/O (oil-in-water-in-oil) double emulsions. The data are compared with the predictions of the proposed equations. The proposed equations describe the experimental viscosity data of double emulsions reasonably well.     

Analysis of the informativity of kinetic measurements in solving inverse problems of chemical kinetics for multi-route reactions

Inverse problems of chemical kinetics that are solved in terms of a set of nonlinear ordinary differential, algebraic-differential, and algebraic equations corresponding to unsteady-state, steady-state, and equilibrium experimental conditions have been investigated. An algorithm has been devised for the analysis of the informativity of kinetic measurements in solving inverse problems of chemical kinetics for multi-route reactions.     

Radial basis function network calibration model for near-infrared spectra in wavelet domain using a genetic algorithm

Near-infrared (NIR) spectrometry is now widely used in various fields and great attention is paid to the application of it to addressing complex problems, which brings about the need for the calibration of systems that fail to exhibit satisfactional linear relationship between input-output data. In this work we present a novel method to build a multivariate calibration model for NIR spectra, i.e. genetic algorithm-radial basis function network in wavelet domain (WT-GA-RBFN), which combines the advantages of wavelet transform and genetic algorithm. The variable selection is accomplished in two stages in wavelet domain: at the first stage, the variables are pre-selected (compressed) by variance and at the second stage the variables are further reduced by a special designed GA. The proposed method is illustrated through presenting its application to three NIR data sets in different fields and the comparison to PLS model.     

A Matrix Based Indexing HDMR method for multivariate data modelling

Modelling multivariate data of real life problems from engineering, chemistry, physics, mathematics or other related sciences, in which function values are known only at arbitrarily distributed points of the problem domain, is an important and complicated issue since there exist mathematical and computational complexities in the analytical structure construction process coming from the multivariance. The Plain High Dimensional Model Representation (HDMR) method expresses a multivariate problem in terms of less-variate problems. In this work, a Matrix Based Indexing HDMR method is developed to make the Plain HDMR philosophy employable for the multivariate data partitioning process. This new method will have the ability of dealing with less-variate data sets by partitioning the given data set into univariate, bivariate and trivariate data sets. Interpolating these partitioned data sets will construct an approximate analytical structure as the model of the given multivariate data modelling problem.     

Optimization of a wet chemical continuous flow analysis method exemplified by the determinations of kjeldahl nitrogen and total phosphorus

The optimization of a rather complex wet chemical analysis method, such as the measurement of Kjeldahl nitrogen or total phosphorus with the Technicon AutoAnalyzer, is extremely tedious when purely empirical approaches are used. A mathematical model of the different stages of the measuring method (digestion, neutralization and color reaction) is described. The system can then be optimized for maximum measuring sensitivity. Optimization is done by solving numerically the non-linear optimization problem with constraints. The starting values for the optimization algorithm were found by varying these values systematically within the tolerated range, with checks that none of the constraints were violated. The theoretical results predict an increase in sensitivity by a factor of 15 compared to the method used previously. In practice, the sensitivity was increased by a factor of 10 for the total phosphorus method. For the simultaneous low-level determinations of Kjeldahl nitrogen and total phosphorus some problems of stability remain.