Purpose: To use the L25 Taguchi orthogonal array for optimizing the three main solvothermal parameters that affect the synthesis of metal-organic frameworks-5 (MOF-5). Methods: The L25 Taguchi methodology was used to study various parameters that affect the degree of crystallinity (DOC) of MOF-5. The parameters comprised temperature of synthesis, duration of synthesis, and ratio of the solvent, N,N-dimethyl formamide (DMF) to reactants. For each parameter, the volume of DMF was varied while keeping the weight of reactants constant. The weights of 1,4-benzodicarboxylate (BDC) and Zn(NO3)2.6H2O used were 0.390 g and 2.166 g, respectively. For each parameter investigated, five different levels were used. The MOF-5 samples were synthesized using the solvothermal reaction method, and successful synthesis was confirmed with x-ray diffraction (XRD), microscopy, Fourier transform infrared spectroscopy (FTIR) and energy-dispersive x-ray spectroscopy (EDS). The DOC obtained via XRD served as a parameter of objective quality. Results: The optimum conditions that gave the highest DOC were synthesis temperature of 130 °C, duration of 60 h, and a vehicle volume of 50 mL, with optimum Brunauer-Emmett-Teller surface area (BET -SA) of 800 m2/g. All the three synthesis parameters significantly influenced the DOC of the synthesized MOF-5 (p < 0.05). Sub-optimal conditions resulted in distorted MOFs, products that deviated from MOF-5 specifications, or MOF-5 with low DOC. Conclusion: Based on DOC and BET-SA, the best conditions for synthesis of MOF-5 when using Taguchi OA, were temperature of 130 °C, duration of 60 h, and a DMF volume of 50 mL.
This paper deals with testing a numerical solution for the discrete classical optimal control problem governed by a linear hyperbolic boundary value problem with variable coefficients. When the discrete classical control is fixed, the proof of the existence and uniqueness theorem for the discrete solution of the discrete weak form is achieved. The existence theorem for the discrete classical optimal control and the necessary conditions for optimality of the problem are proved under suitable assumptions. The discrete classical optimal control problem (DCOCP) is solved by using the mixed Galerkin finite element method to find the solution of the discrete weak form (discrete state). Also, it is used to find the solution for the discrete adj
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