Revisiting El-Sayed Synthesis: Bayesian Optimization for Revealing New Insights during the Growth of Gold Nanorods

In diverse fields, machine learning (ML) has sparked transformative changes, primarily driven by the wealth of big data. However, an alternative approach seeks to mine insights from “precious data”, offering the possibility to reveal missed knowledge and escape potential knowledge traps. In this context, Bayesian optimization (BO) protocols have emerged as crucial tools for optimizing the synthesis and discovery of a broad spectrum of compounds including nanoparticles. In our work, we aimed to go beyond the commonly explored experimental conditions and showcase a workflow capable of unearthing fresh insights, even in well-studied research domains. The growth of AuNRs is a nonequilibrium process that remains poorly understood despite the presence of well-established seeded growth protocols. Traditional research aimed at understanding the mechanism of AuNR growth has primarily relied on altering one reaction condition at a time. While these studies are undeniably valuable, they often fail to capture the synergies between different reaction conditions, thus constraining the depth of insights they can offer. In the present study, we exploit BO, to identify diverse experimental conditions yielding AuNRs with similar spectroscopic characteristics. Notably, we identify viable and accelerated synthesis conditions involving elevated temperatures (36–40 °C) as well as high ascorbic acid concentrations. More importantly, we note that ascorbic acid and temperature can modulate each other’s undesirable influences on the growth of AuNRs. Finally, by harnessing the power of interpretable ML algorithms, complemented by our deep chemical understanding, we revisited the established hierarchical relationships among reaction conditions that impact the El-Sayed-based growth of AuNRs.


S1.2 Data and Code
All data and the code used to obtain the figures shown in the main text and the supporting information is available at https://github.com/anishrao/Pr-AuNR-opt. The code was written in Jupyter Notebook and the environment used during the course of the study is also provided in the project folder.The dataset produced during the course of the study is shared as a separate supporting information file (Dataset-all-data.csv).
We used PyCaret (version 3.1.0)to train and compare twenty machine-learning models on our dataset.All models were evaluated using a ten-fold cross-validation protocol.For training the model, 70 % of the data was used to train the model, while the performance of the models was tested on 30% of the remaining data.

S1.3 Transmission Electron Microscopy (TEM) Studies
We performed TEM experiments in order to characterize the dimesnsions of AuNRs formed.Samples for TEM were prepared using 200 µL of as-prepared AuNRs (in 100 mM CTAB) that was centrifuged and redispersed in 200 µL of Milli-Q water.This purification step was repeated twice, and after the last centrifugation cycle, the AuNRs were dispersed in 20 µL of H 2 O. Finally, 5 µL of drop was placed on formvar coated Copper grid.The drop was allowed to slowly evaporate overnight at room temperature before imaging.

S1.4 Modeling of Optical Properties
Simulations of optical spectra were conducted using the boundary element method (BEM). 1,2r simulations, we chose AuNR (in water) with a length of 56 nm and a width of 16 nm.
The dielectric data for Au were taken from Johnson and Christy. 3

S2 Calculate Loss
One of the challenges in the optimization of NPs originates from the necessity to target multiple spectroscopic properties (like peak position, reduction of Au 0 , presence of impurities, full-width half maxima, etc.) at the same time.In the present study, we define a parameter loss that combines all targeted into a single merit.We calculate the value of loss in the following way:- • Normalize the objective (UV calc. ) and experimental (UV exp. ) UV-Vis-NIR spectra.
• Calculate the difference between the two spectra i.e. ∆UV = UV exp.-UV calc. .

• Calculate the L-2 norm of ∆UV
The L-2 norm of a vector is defined as follows:- (1)

S3 Calculate the Experimental Parameter Space
The limits allowed for different reaction conditions are mentioned in Table 1.In order to get a rough estimate of the total number of possible experiments that need to be performed, we performed the following calculation.For instance, imagine A.A., Ag + and HCl can be screened in discrete increments of 50µL.The seeds are screened in discrete amounts of 10µL, and temperature in increments of 2.5 • C.This discretization gives us a choice of 9 A.A., 7 Ag + , 5 seed, 19 HCl and 7 temperature values.These values give rise to 41,895 possible combinations of experiments that need to be performed.It should be noted that the more resolved the search space, the higher the number of experiments that need to be performed.
The discretization followed in the above estimate gives a lower bound to the possible number of experiments that need to be performed.El-Sayed conditions.The length and width of optimized AuNRs are 48.9 ± 9.2, and 19.9 ± 4.4 nm respectively, while the length and width AuNRs grown under El-Sayed conitions are 57.0 ± 6.3, and 16.7 ± 2.7 nm respectively.

Figure S1 :
Figure S1: Schematic showing the complete experimental workflow.Here, optimizing the growth of AuNRs with minimal spectroscopic differences to the calculated UV-Vis-NIR spectra was chosen as the objective.Next, 5 experimental conditions were varied in a continuous fashion, to perform the optimization experiments.

Figure S2 :
Figure S2: UV-Vis-NIR spectrum of all the experiments performed during the first iteration towards optimization of AuNRs.

Figure S3 :
Figure S3: TEM image and accompanying size distribution histogram showing the length (shown in blue) and width (shown in red) of AuNRs synthesized using a) optimized and b)El-Sayed conditions.The length and width of optimized AuNRs are 48.9 ± 9.2, and 19.9 ± 4.4 nm respectively, while the length and width AuNRs grown under El-Sayed conitions are 57.0 ± 6.3, and 16.7 ± 2.7 nm respectively.

Figure S4 :
Figure S4: UV-Vis-NIR spectrum of all the experiments performed during the successful iteration towards optimization of AuNRs.

Figure S5 :
Figure S5: Parallel coordinate graph showing the different experimental conditions that resulted in the growth of similar quality AuNRs.Here, similar values of loss are referred to as similar quality of AuNRs.

Figure S6 :
Figure S6: UV-Vis-NIR spectrum of all the experiments performed during the unsuccessful iteration towards optimization of AuNRs.

Figure S7 :
Figure S7: UV-Vis-NIR spectrum of all the experiments performed during the multi-objective optimization of AuNRs.

Figure S8 :
Figure S8: Figure demonstrating the residuals obtained for training and testing data.

Figure S9 :
Figure S9: Shapley additive explanations (SHAP) analysis of the Random Forest Regressor model for the synthesis of AuNRs.The figure shows the impact of each reaction condition on loss.

Figure S11 :
Figure S11: Partial dependence plots showing the collective effect of different reaction conditions on the predicted loss values.

Figure S12 :
Figure S12: The collective effect between temperature and a) A.A., b) Ag + , c) seeds, and d) HCl on the loss values of obtained AuNRs.Here, dots with large sizes indicate the formation of AuNRs with low loss values (loss less than 8).The pink circles denote the conditions used during El-Sayed synthesis.