Experimental design and batch experiments for optimization of Cr(VI) removal from aqueous solutions by hydrous cerium oxide nanoparticles

Hydrous cerium oxide (HCO) was synthesized by intercalation of solutions of cerium(III) nitrate and sodium hydroxide and evaluated as an adsorbent for the removal of hexavalent chromium from aqueous solutions. Simple batch experiments and a 2⁵ factorial experimental design were employed to screen the variables affecting Cr(VI) removal efficiency. The effects of the process variables; solution pH, initial Cr(VI) concentration, temperature, adsorbent dose and ionic strength were examined. Using the experimental results, a linear mathematical model representing the influence of the different variables and their interactions was obtained. Analysis of variance (ANOVA) demonstrated that Cr(VI) adsorption significantly increases with decreased solution pH, initial concentration and amount of adsorbent used (dose), but slightly decreased with an increase in temperature and ionic strength. The optimization study indicates 99% as the maximum removal at pH 2, 20 °C, 1.923 mM of metal concentration and a sorbent dose of 4 g/dm³. At these optimal conditions, Langmuir, Freundlich and Redlich–Peterson isotherm models were obtained. The maximum adsorption capacity of Cr(VI) adsorbed by HCO was 0.828 mmol/g, calculated by the Langmuir isotherm model. Desorption of chromium indicated that the HCO adsorbent can be regenerated using NaOH solution 0.1 M (up to 85%). The adsorption interactions between the surface sites of HCO and the Cr(VI) ions were found to be a combined effect of both anion exchange and surface complexation with the formation of an inner-sphere complex.

A biogeography-based optimization algorithm with mutation strategies for model parameter estimation of solar and fuel cells

Mathematical models are useful tools for simulation, evaluation, optimal operation and control of solar cells and proton exchange membrane fuel cells (PEMFCs). To identify the model parameters of these two type of cells efficiently, a biogeography-based optimization algorithm with mutation strategies (BBO-M) is proposed. The BBO-M uses the structure of biogeography-based optimization algorithm (BBO), and both the mutation motivated from the differential evolution (DE) algorithm and the chaos theory are incorporated into the BBO structure for improving the global searching capability of the algorithm. Numerical experiments have been conducted on ten benchmark functions with 50 dimensions, and the results show that BBO-M can produce solutions of high quality and has fast convergence rate. Then, the proposed BBO-M is applied to the model parameter estimation of the two type of cells. The experimental results clearly demonstrate the power of the proposed BBO-M in estimating model parameters of both solar and fuel cells.

Towards rational catalyst design: a general optimization framework

Rational catalyst design is one of the most fundamental goals in heterogeneous catalysis. Herein, we briefly review our previous design work, and then introduce a general optimization framework, which converts catalyst design into an optimization problem. Furthermore, an example is given using the gradient ascent method to show how this framework can be used for rational catalyst design. This framework may be applied to other design schemes.

New Method Based on the UNIFAC–VISCO Model for the Estimation of Ionic Liquids Viscosity Using the Experimental Data Recommended by Mathematical Gnostics

The viscosity of ionic liquids (ILs) has been modeled as a function of temperature and at atmospheric pressure using a new method based on the UNIFAC–VISCO method. This model extends the calculations previously reported by our group (see Zhao et al. J. Chem. Eng. Data 2016, 61, 2160–2169) which used 154 experimental viscosity data points of 25 ionic liquids for regression of a set of binary interaction parameters and ion Vogel–Fulcher–Tammann (VFT) parameters. Discrepancies in the experimental data of the same IL affect the quality of the correlation and thus the development of the predictive method. In this work, mathematical gnostics was used to analyze the experimental data from different sources and recommend one set of reliable data for each IL. These recommended data (totally 819 data points) for 70 ILs were correlated using this model to obtain an extended set of binary interaction parameters and ion VFT parameters, with a regression accuracy of 1.4%. In addition, 966 experimental viscosity data points for 11 binary mixtures of ILs were collected from literature to establish this model. All the binary data consist of 128 training data points used for the optimization of binary interaction parameters and 838 test data points used for the comparison of the pure evaluated values. The relative average absolute deviation (RAAD) for training and test is 2.9% and 3.9%, respectively.