A drawback in the synthesis of copper dioxide nanoparticles is that because it operates at a control nanoscale morphology and size is difficult to handle, as for example a small increase or decrease in temperature or concentration; It generates big changes. Therefore, a mathematical model from the reaction kinetics taking place in the synthesis is proposed. This mathematical model is from type reaction-diffusion. The control parameters give an idea of model parameters to be varied to obtain a morphology and specific particle size. These control parameters are given by the pH and the initial concentration of the reactants employed in the synthesis copper dioxide nanoparticles. The analysis of linear stability of reaction-diffusion model is realized and fullfil the diffusion-driven instability.
Mathematical model, Turing instability, nonlinear chemical, copper nanoparticles
1. Luo C., Zhang Y., Zeng X., Zeng Y., Wang Y. The Role of poly(ethylene glycol) in the Formation of Silver Nanoparticles. Journal of Colloid and Interface Science, 2005, vol. 288, pp. 444-448.
2. Biswas A.K., Davenport W.G. El cobre:metalurgia extractiva. México: Limusa, 1993.
3. Ball P. Nature´s Patterns. Editorial Oxford University, 2009.
4. Baker R.E., Gaffney E.A., Maini P.K. Partial differential equations for self-organization in cellular and developmental biology. Non linearity, 2008, vol. 21, pp. 251-290.
5. Grzybowski B.A. Chemistry in Motion: Reaction-Diffusion Systems for Micro- and Nanotechnology. Editorial Wiley, 1996.
6. Yakui Bai, Tengfei Yang, Qing Gu, Guoan Cheng, Ruiting Zheng. Shape control mechanism of cuprous oxide nanoparticles in aqueous colloidal solutions. Powder Technology ELSEVIER., 2012, vol. 227, pp. 35-42.
7. Cross M., Hohenberg P. Pattern Formation Outside of Equilibrium. Rev. Mod. Phys., 1993, pp. 851-1112.
8. Murray J. Mathematical Biology: I. An Introduction. Springer Verlag Berlin Heidelberg, 2002.
9. Morales M.A. [et al.] A new mechanochemical model: Coupled Ginzburg-Landau and Swift-Hohenberg equations in biological patterns of marine animals. J. Theor. Biol., 2015, vol. 308, pp. 37-54.
10. Mazin W., Rasmussen K.E., Mosekilde E., Borckmans P., Dewel G. Pattern formation in the bistable Gray-Scott model. Mathematics and Computers in Simulations, 1996, vol. 40, pp. 371-396.
11. Turing A.M. The Chemical Basis of Morphogenesis. Philos. Trans. Royal Soc. B, 1952, vol. 237, p. 641.