Two-factor, Three-level Factorial Experiments for Optimizing Size of Thiol Stabilized Gold Nanoparticles (AuNPs)

When several variables influence a particular output characteristic of a process or principle, the experiment(s) must be designed to ensure that valid, reliable, and sound conclusions can be drawn effectively, efficiently, and economically.Statistical Design of Experiments (SDoE) has been effective and efficient for general problem-solving, as well as for improving or optimizing product design and industrial manufacturing processes.SDoE is a methodology in which multiple variables can be varied and tested in parallel, and the impact of each variable can be resolved and quantified independently of other variables using quantitative statistical tools [1][2][3].Researchers often struggle to compare and reproduce published research results.That has prompted the primary federal funding agencies, e.g., NIH [4], NSF, scientific journals, press and ethic integrity forums to discuss scientific experiments' rigor and reproducibility as the key factors in credibility of research.Previously, we have proposed the use of SDoE to address the issues related to rigor and reproducibility in imaging sciences [5].We now propose the use of SDoE to optimize size and coefficient of variation of AuNPs stabilized with multidentate thiol ligands.AuNPs have been employed in the construction of high-Z probes, biosensors, drug delivery systems, solar cells and catalysts, and their shape, size and polydispersity must be tailored for a desired end application.We have initiated an effort to produce thermally stable, kinetically inert, reduced-sized (smaller hydrodynamic radius) ligand stabilized AuNPs.For this purpose, we design multidentate thiol-/amine-functionalized geodesic/bowl-shaped (Buckyball fragments) ligands that wrap around the gold core [6].Herein, we report 2-factor, 3-level factorial experiments (3 2 ) to predict size, and coefficient of variation (CV) of AuNPs stabilized with corannulene-based polythioether ligands (Fig. 1-Left).AuNPs were synthesized using Brust-Schiffrin's one-phase method [7] and analyzed for size distribution by transmission electron microscopy.Diameter of the ligand (D) or maximum distance between the sulfur atoms (D ∼1.4 nm, ∼2.1 nm and ∼2.8 nm; -S-bonds are flexible) and sulfur-to-gold ratio (Au:S) or Au mol-to-S mol (Au:S = 2:1, 5:1, and 8:1), were used as input parameters (central composite design; CCD); and particle size as the output parameter.All other conditions: temperature, gold-to-reducer ratio, solvent et cetera, were kept constant.Output or NP sizes from the experiments were analyzed using second order multiple regression and analysis of variation (ANOVA) at 5% confidence level (p <0.05).AuNP sizes (output) from each experiment were further correlated to the input variables D and Au:S using a second order/quadratic polynomial equation using Minitab® software.The two-factor, three-level experimental plan and corresponding responses for AuNP synthesis are given Fig. 1-Center.ANOVA with Fisher's statistical analysis was carried out to the best fit for the model (Fig. 1-Right).The ANOVA of both S-to-S distance (D), and Au-to-S ratio (Au:S), are significantly related to AuNP diameter with a significance level of 0.05.Further, the predicted coefficient of determination R 2 = 0.9971 for AuNP diameter agrees with the adjusted R 2 = 0.9923 confirming that the model can be used to produce AuNPs of desired diameter using the corannulene-based polythioether ligands.SDoE (3 2 / CCD) was developed to: i) understand the response surface topology or effect of ligand structure and gold-to-ligand ratio on AuNP size and ii) find the region of optimum response or finding optimum synthetic conditions that yield AuNPs of desired size.SDoE is commonly utilized for optimizing the process variables and developing the quadratic models that describe statistical relationships among the involved parameters.The relationship between AuNP size and the experimental factors can be given as ŶAuNP dia .= 2.95-1.24*D-0.05*Au:S + 0.31 D 2 + 0.071*D*Au:S.SDoE was utilized to identify variables and interactions that affect the AuNP synthesis (p <0.05) and understand potential optimizations for the desired end application (wide infra).The normal plot of the standardized effects (Fig. 2-Left) summarizes the influence of S-to-S distance and Au:S ratio on AuNP size.The contour plot (Fig. 2-Center), and surface plot (Fig. 2-Right) show that increase in both S-to-S distance and Au-to-S ratio leads to increase in the diameter of the AuNPs.While this work was in progress a SDoE for optimizing full width at half maxima (FWHM) of AuNP surface plasmon was reported [8].We are developing AuNP based X-ray contrast agents for kidney imaging and their optimal hydrodynamic diameter for renal clearance is <5-6 nm.Therefore, we are aiming for AuNP core around 2 nm that do not exhibit surface plasmon.The new AuNPs are being screened for their serum stability to determine their suitability as X-ray contrast agents for renal imaging.