Carbon nanotubes (CNTs) are one of the most exciting discoveries in nanoscale sciences because they have superior properties with respect to other materialsdue to their superior properties for use in several range of applications in materials science, electronics, energy management and many other fields. CNTs can be manipulated chemically and physically in very useful ways and their final properties and dimensions strongly depend on the parameters and the nature of the method used for their synthesis, this is why many methods of synthesis have been reported. Controlling the size of a nanomaterial is critical for its application because the characteristic length of a material significantly affects its mechanical, thermal, chemical, and particularly electronic properties. Several key parameters and operating conditions have to be manipulated to produce CNTs with suitable properties for future applications and it is evident that all these methods of synthesis need to be optimized.
This paper presents an optimization approach for determining the best synthesis method and their corresponding operating conditions for synthesizing carbon nanotubes accounting for technical and economic issues as objective functions for a desired application. Proper correlations for the interaction between the considered variables are proposed, and these correlations are based on experimental data taken of the literature reports. The optimization formulation is a mixed-integer nonlinear programming problem. A case study considering three synthesis methods of carbon nanotubes (arc discharge, laser ablation and chemical vapor deposition) is presented. The results show that the proposed model can be useful to determine the best method and operating conditions with the maximum efficiency, quality and safety at the minimum cost. The results provide that at ~100% the cost per gram of carbon nanotubes obtained for arc discharge is 18.645 USD, for laser ablation is 14.438 USD and chemical vapor deposition of 3.419 USD using camphor as carbon source and 0.374 USD using turpentine.