A Mathematical Investigation of the Turkevich Organizer Theory in the Citrate Method for the Synthesis of Gold Nanoparticles
Gold nanoparticles are commonly synthesized by reducing chloroauric acid with sodium citrate. This method, referred to as the citrate method, can produce spherical gold nanoparticles (NPs) in the size range 10-150 nm. Gold NPs of this size are useful in many applications. However, the NPs are usually polydisperse and irreproducible. A better understanding of the synthesis mechanisms is thus required. This work thoroughly investigated the only model that describes the synthesis. This model combines mass and population balance equations, describing the NPs synthesis through a sequence of chemical reactions. Chloroauric acid reacts with sodium citrate to form aurous chloride and dicarboxy acetone. The latter organizes aurous chloride in a nucleation step and concurrently degrades into acetone. The unconsumed precursor then grows the formed nuclei. However, depending on the pH, both the precursor and the reducing agent react differently thus affecting the synthesis. In this work, we investigated the model for different conditions of pH, temperature and initial reactant concentrations. To solve the model, we used Parsival, a commercial numerical code, whilst to test it, we considered various conditions studied experimentally by different researchers, for which results are available in the literature. The model poorly predicted the experimental data. We believe that this is because the model does not account for the acid-base properties of both chloroauric acid and sodium citrate.
 Liveri, V. T., Controlled Synthesis of Nanoparticles in Microheterogeneous Systems, Nanostructure Science and Technology, Springer Science, 2006.
 Tamar Dreifuss, Oshra Betzer, Malka Shilo, Aron Popovtzer, Menachem Motieia and Rachela Popovtzer A challenge for theranostics: is the optimal particle for therapy also optimal for diagnostics? Nanoscale, 2015, 7, 15175.
 Turkevich, J.; Stevenson, P.; Hillier, J. A Study of the Nucleation and Growth Process in the Synthesis of Colloidal Gold. Discuss. Faraday Soc. 1951, 11, 55.
 Frens, G. Controlled Nucleation for the Regulation of the Particle Size in Monodisperse Gold Suspensions. Nature 1973, 241, 20.
 Freund, P.; Spiro, M. Colloidal Catalysis: The Effect of Sol Sizeand concentration. J. Phys. Chem. 1985, 89, 1074.
 Chow, M.; Zukoski, C. Gold Sol Formation Mechanisms: Role of Colloidal Stability. J. Colloid Interface Sci. 1994, 165, 97.
 Kumar, S.; Kumar, R.; Gandhi, K. S. Modeling of Formation of Gold Nanoparticles by Citrate Method. Ind. Eng. Chem. Res. 2007, 46, 3128-313.
 Ji, X. H.; Song, X. N.; Li, J.; Bai, Y. B.; Yang, W. S.; Peng, X. G. J. Am. Chem. Soc. 2007, 129, 13939.
 Polte, J.; Erler, R.; Thü nemann, A. F.; Sokolov, S.; Ahner, T. T.; Rademann, K.; Emmerling, F.; Kraehnert, R. Nucleation and Growth of Gold Nanoparticles Studied via in situ Small Angle X-ray Scattering at Millisecond Time Resolution. ACS Nano 2010, 4, 1076−1082.
 Kettemann, F.; Birnbaum, A.; Witte, S.; Wuithschick, M.; Pinna, N.; Kraehnert, R.; Rademann, K.; Polte, J. Chem. Mater. 2016, 28 (11), 4072-4081.
 Wulkow, M., Gerstlauer, A., Nieken, U., 2001. Modeling and simulation of crystallization processes using parsival. Chem. Eng. Sci. 56, 2575–2588. http://dx.doi.org/10.1016/S0009-2509(00)00432-2.
 Takiyama, K. Formation and Aging of Precipitates. VIII. Formation of Monodisperse Particles (1) Gold Sol Particles by Sodium Citrate Method. Bull. Chem. Soc. Jpn. 1958, 31, 944–950.
 M. Wuithschick, S. Witte, F. Kettemann, K. Rademann, J. Polte Phys. Chem. Chem. Phys. 2015, 17, 19895-19900.
 Chunfang Li, Dongxiang Li, Ganggiang Wan, Jie Xu and Wanguo Hou, “Facile synthesis of concentrated gold nanoparticles with low size-distribution in water: temperature and pH control”, Nanoscale Research Letters, vol. 6, p.440, 2011.
 Ojea-Jiménez, I.; Campanera, J. M. Molecular Modeling of the Reduction mechanism in the Citrate-Mediated Synthesis of Gold Nanoparticles. J. Phys. Chem. C 2012, 116, 23682–23691.
 Wiig, E. O. J. Phys. Chem. 1928, 32, 961.
 Wei Wang , Ning Li , and Stan Speaker External Factors Affecting Protein Aggregation, Hoboken, NJ, USA: John Wiley & Sons, Inc. 2010.