# AuNR-SMA: Automated Gold Nanorod Spectral Morphology Analysis Pipeline

Samuel P. Gleason  Department of Chemistry, University of California,
Berkeley, California 94720, United States<EMAIL_ADDRESS><EMAIL_ADDRESS>Jakob C. Dahl  Department of Chemistry,
University of California, Berkeley, California 94720, United States  Mahmoud
Elzouka  Lawrence Berkeley National Laboratory, Berkeley, CA, United States
Xingzhi Wang  Department of Chemistry, University of California, Berkeley,
California 94720, United States  Dana O. Byrne  Department of Chemistry,
University of California, Berkeley, California 94720, United States  Mumtaz
Gababa  Department of Chemistry, University of California, Berkeley,
California 94720, United States  Hannah Cho  Department of Chemistry,
University of California, Berkeley, California 94720, United States  Ravi
Prasher  Lawrence Berkeley National Laboratory, Berkeley, CA, United States
Sean Lubner  Lawrence Berkeley National Laboratory, Berkeley, CA, United
States  Emory Chan  Molecular Foundry, Lawrence Berkeley National Laboratory,
Berkeley, California 94720, United States  A. Paul Alivisatos  Department of
Chemistry, University of California, Berkeley, California 94720, United States

###### Abstract

The development of a colloidal synthesis procedure to produce nanomaterials of
a specific size with high shape and size purity is often a time consuming,
iterative process. This is often due to the time, resource and expertise
intensive characterization methods required for quantitative determination of
nanomaterial size and shape. Absorption spectroscopy is often the easiest
method of colloidal nanomaterial characterization, however, due to the lack of
a reliable method to extract nanoparticle shapes from absorption spectroscopy,
it is generally treated as a more qualitative measure for metal nanoparticles.
This work demonstrates a gold nanorod (AuNR) spectral morphology analysis
(SMA) tool, AuNR-SMA, which is a fast and accurate method to extract
quantitative information about an AuNR sample’s structural parameters from its
absorption spectra. We apply AuNR-SMA in three distinct applications. First,
we demonstrate its utility as an automated analysis tool in a high throughput
AuNR synthesis procedure by generating quantitative size information from
optical spectra. Second, we use the predictions generated by this model to
train a machine learning model capable of predicting the resulting AuNR size
distributions from the reaction conditions used to synthesize them. Third, we
turn this model to spectra extracted from the literature where no size
distributions are reported to impute unreported quantitative information of
AuNR synthesis. This approach can potentially be extended to any other
nanocrystal system where the absorption spectra are size dependent and
accurate numerical simulation of the absorption spectra is possible. In
addition, this pipeline could be integrated into automated synthesis
apparatuses to provide interpretable data from simple measurements and help
explore the synthesis science of nanoparticles in a rational manner or
facilitate closed-loop workflows.

###### keywords:

Automated Analysis, High Throughput, Gold Nanorods, Machine LearningLaTeX

Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley,
California 94720, United States Materials Sciences Division, Lawrence Berkeley
National Laboratory, Berkeley, California 94720, United States Molecular
Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720,
United States Materials Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States Materials Sciences
Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720,
United States Department of Materials Science and Engineering, University of
California, Berkeley, California 94720, United States Materials Sciences
Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720,
United States Kavli Energy NanoScience Institute, Berkeley, California 94720,
United States Current Affiliation: Department of Chemistry, University of
Chicago, Chicago, Illinois 60637, United States UV-VIS,AuNR,AuNRs

##  1 Introduction

Gold nanorods (AuNRs) have drawn significant research efforts due to their
applications in cancer cell imaging and treatment, particularly in the
development of photothermal therapies, 1, 2, 3, 4, 5, 6, 7, 8, 9 Surface
Enhanced Raman Spectroscopy (SERS),9, 10, 11, 12 and photovoltaic devices .9,
13, 14 These applications rely on the localized surface plasmon resonance
(LSPR) of AuNRs, which is highly dependent on the shapes and sizes of these
nanoparticles,9, 15, 16, 17 . The LSPR of AuNRs is tuned primarily by changing
the ratio of length to width, or aspect ratio (AR), of the nanorods15, 16, 17.
Applications of AuNRs thus require the synthesis of these particles with high
shape yield and narrow size distributions. However, it remains a challenge to
quantitatively understand the impact of AuNR synthesis parameters on the
resulting AuNRs.18 Quantitatively determining the size and shape distributions
of AuNRs requires direct measurement using electron microscopy, which is a
time, resource and knowledge intensive task,19, 20 limiting the amount of data
that can be gathered to train models to predict synthesis outcomes.21 Although
progress has been made automating the size measurement of metal nanoparticles
from transmission electron microscopy (TEM) images,20, 22, 23 the hardware
required for the automation of TEM image collection is not widely available.24
Therefore, we have built an automated analysis model which can extract
population level size information from absorption spectroscopy as a tool for
more scalable analysis of AuNRs.

Recent work has found success predicting the sizes of individual AuNRs from
single particle absorption spectra25 and has found limited success at matching
individual simulated single particle absorption spectra to samples with very
narrow size distributions.26 However, it remains a challenge to provide
accurate population level size information for experimental spectra from a
sample with a wide size distribution of AuNRs or where spherical AuNPs (AuNS)
are also present. An analytical method that can determine AuNR size and shape
distributions from absorption spectra and overcome issues related to impure
samples 27, 28 creates new opportunities for developing interpretable models
of AuNR synthesis.

Here we overcome these challenges by focusing on the regions of the spectrum
where degeneracies from AuNS and left over unreacted growth solution are
minimized and selecting spectra according to a series of internal uncertainty
metrics. We also enable the prediction of population-level statistics by
fitting a 2D gaussian ensemble of simulated AuNR spectra directly to the
measured spectrum. This is done using an optimization model which minimizes
the difference between an ensemble simulated spectrum and the experimental
spectrum. This approach provides much more information on the AuNR sample than
existing techniques, which focus on matching single particle simulated spectra
to an experimental spectrum.

We showcase the utility of our automated spectral AuNR morphology analysis in
three applications:

  1. 1.

automating the analysis of one-pot seedless high throughput AuNR synthesis,

  2. 2.

training machine learning models to predict AuNR synthesis outcomes,

  3. 3.

imputing quantitative synthesis data from literature spectra for which
population level size data was not reported.

The first two applications comprise a highly active field of research, and
AuNP synthesis has already been developed to include prediction of absorption
spectrum from synthesis condition, and to rationally design conditions for a
specified spectrum.29, 30, 31, 32 However, these procedures focus on relating
the conditions to the resulting spectrum29, 30, 31 or on AuNS synthesis and
analysis.32 This limits the abilities of these procedures to produce
fundamental synthesis knowledge about how synthesis conditions lead to changes
in AuNP morphology, particularly under new reaction conditions. More broadly,
there is very limited quantitative information regarding how AuNR synthesis
conditions change the resulting AuNR sizes. In recent years, a few studies18,
29 have attempted to fill in this gap, but these have focused on the seed-
mediated synthesis method for AuNRs. Therefore, we focus on the one pot, or
seedless33, synthesis procedure, and combine the AuNR spectral analysis method
we developed with liquid handling synthesis and characterization robots to
build an automated synthesis and analysis pipeline. We then utilize this
pipeline to build quantitative understanding of the seedless AuNR synthesis
procedure and train machine learning models capable of predicting sizes and
aspect ratios from initial concentrations of reagents. Using this model, we
demonstrate the rich quantitative information that can be extracted from
simple measurements and how this information can be applied to nanomaterials
discovery.

Figure 1: An outline of the spectral morphology analysis, showing how single
particle spectra are simulated for a wide range of AuNR sizes, and how these
are combined using an inputted distribution to build a simulated mixture
spectrum. More details on this process can be found in the SI, section
"Spectral Morphology Analysis Outline".

##  2 Results and Discussion

###  2.1 Automated AuNR Size Distribution Analysis

UV/Vis/NIR absorption spectroscopy was selected as the analytical method for
size distribution inference due to the ease of high throughput
characterization and the ability of absorption spectroscopy to simultaneously
measure the absorption of every particle in the colloid. Additionally,
absorption spectroscopy can be used without sample purification, which can
significantly alter the sample’s size distribution. Our spectral morphology
analysis model uses numerically simulated absorption spectra of single AuNRs
to determine the length, diameter and aspect ratio distributions of simulated
AuNRs that most accurately reproduce the experimental spectrum. As such, this
model can provide not only the mean lengths and aspect ratios of the sample,
but also ensemble level information. A full schematic of this model is shown
in Figure 1.

The predictions of this model were validated by TEM analysis of 20 samples
from a high throughput synthesis experiment and 21 spectra extracted from
literature. Using AutoDetect-mNP 20, we determined the size and shape
distributions of AuNRs in each sample and compared them to the predictions
generated from our model. The predictions of the literature spectra were
compared to the size distributions reported in the paper. The accuracy of the
predictions on our 41 validation spectra are shown in Figure 2.

Figure 2 shows an example set of outputs provided by this model and their
validation against known measurements in 1D. Figure 2a-d shows a sample AuNR
spectrum (a) and the predicted length (b) diameter (c) and aspect ratio (d)
distributions plotted over histograms produced by manually measuring AuNRs
taken from TEM images. The model outputs each of these 1D predictions, as well
as the 2D prediction in length and diameter space shown in Figure 1c. Using
the size parameters produced by the model, mean and standard deviation of
lengths, diameters and aspect ratios, we can determine the accuracy of this
model by comparing to measured TEM images taken in this work or presented in
the literature. Figure 2e-h shows these comparisons for length mean (e),
length standard deviation (f), aspect ratio mean (g) and aspect ratio standard
deviation (h).

As the distributions shown in Figure 2b-d are challenging to use as a model
accuracy metric over an ensemble validation set, in this work we express the
accuracy as a comparison between the predicted 2D distribution of lengths and
diameters and the measured distribution. We do this by calculating an overlap
coefficient34 between the predicted size distribution and the true
distribution in length and diameter space (Figure S9). In the case of our high
throughput samples, where manual TEM measurements are available, the true
distribution was projected onto a normal distribution to ensure accurate
comparison with literature distributions, where only means and standard
deviations are reported. For literature spectra, where the individually
measured TEM particles are not available, the overlap was determined by
calculating a distribution based on the reported AuNR means and standard
deviations for length and diameter. Using this validation, this model has been
shown to produce a predicted distribution which has a high degree of overlap.
The average overlap across all the validation spectra is shown to be around
0.3 in Figure 2, showing that, on average, this model is able to reasonably
reproduce the population distribution of AuNRs present in the colloid (Figure
S7, S9).

Figure 2: Accuracy of the spectral morphology analysis. (a-d) shows a sample
AuNR spectrum (a) and an example of the model output in 1D (b-d). The
predicted length distribution (b) is shown in red, the predicted diameter
distribution (c) is shown in blue and the predicted aspect ratio distribution
(d) is shown in purple. The predicted distributions are plotted over
histograms produced by manually measuring AuNRs taken from TEM images. For our
41 validation samples, the accuracy of their size parameters is shown in
(e-h). The predictions are colored by whether they came from our high
throughput samples (blue) or literature spectra (orange). $\mu_{Length}$ (e)
and $\sigma_{Length}$ (f) are the length mean and standard deviation,
respectively. $\mu_{AR}$ (g) and $\sigma_{AR}$ (h) are the aspect ratio mean
and standard deviation, respectively. (i) shows a histogram of the overlap
between the predicted 2D distribution in length and diameter space and the
true distribution, with the mean overlap indicated with a dashed red line.

###  2.2 Application 1 - High Throughput Synthesis Size Mapping

By systematically varying concentrations of AgNO3, hydroquinone, initial NaBH4
and total NaBH4 (See Methods Section - High-Throughput Synthesis), and
utilizing our automated spectral morphology analysis on the spectra of the
resulting samples, we were able to determine trends in sizes and size
distributions of the AuNRs. This high throughput synthesis reaction produced
48 samples where rods were successfully synthesized. Of these 48 samples, 6
spectra could not be processed by our spectral morphology analysis due to high
prediction uncertainty or a longitudinal peak at too high energy (Figure 4).
Using the successfully fit samples, a synthesis map of the size parameters
predicted from their absorption spectra is shown in Figure 3a-d. The x axes
shows the ratio of hydroquinone to the first addition of NaBH4, which was
chosen due to the combination of these two conditions controlling the growth
kinetics, which has been shown to be responsible for changing morphology in
AuNR synthesis35. Additionally, interactions with the weak and strong reducing
agents have also been shown to impact the sizes and yield of AuNRs18. AgNO3
concentration was visualized on the y axes due to myriad observations that
AgNO3 concentration is essential to controlling AuNR morphology 18, 36, 37.

The predicted lengths show that at low AgNO3 concentration the maximum length
produced with any combination of hydroquinone and NaBH4 produces AuNR lengths
from 30-50nm. However, at higher concentrations of AgNO3, lengths of 70-90nm
can be produced for specific hydroquinone and NaBH4 ratios. As these resulting
sizes are much less common for this synthesis procedure, one may be inclined
to attribute this less common result to an error in the spectral morphology
analysis. However, one of the two sets of conditions resulting in longer AuNRs
contains two samples with the same ratio of reaction conditions, and those
produced mean length predictions that were less than 10 nm apart, making it
unlikely that a simple large error in the model is responsible for this
result. Overall, we demonstrate that our model can be integrated into high
throughput experiments as an automated size and size distribution prediction
tool, generating detailed quantitative information on the fly. This allows for
rapid detailed analysis and enables the possibility of closed loop workflows
for robotic AuNR synthesis.

Figure 3: Application 1 - 2D representations of the impact of changing
synthesis conditions on the produced length mean (a), length standard
deviation (b) aspect ratio mean (c) and aspect ratio standard deviation (d)
generated using our model. The contour plots show how each of the four size
parameters change with the ratio of hydroquinone to initial NaBH4 (x axis) and
the AgNO3 concentration (y axis). The black dots show where experiments have
been conducted that produced spectra of sufficient quality to yield a
prediction. Application 2 - Accuracy of the ML model trained on the spectra
labeled with sizes generated by our high-throughput experiments and size
analysis model. (e) length mean (f) length standard deviation (g) mean aspect
ratio (h) aspect ratio standard deviation. Training accuracy is shown in blue
while accuracy on test data is shown in orange. Application 3 - Distributions
of size parameters from the 64 unlabeled literature spectra predicted in this
work. (i) length means (j) length standard deviations (k) mean aspect ratios
(l) aspect ratio standard deviations.

###  2.3 Application 2 - ML Prediction of Sizes From Reaction Conditions

Besides enabling more quantitative understanding of AuNR synthesis, the
ability to predict synthesis outcomes is an important goal to enhance
synthetic exploration and optimization. By combining our synthesis and
analysis pipeline with machine learning, we predict the averages and standard
deviations of lengths and aspect ratios of AuNRs synthesized with our one-pot
procedure from their synthetic parameters. We use a dataset containing 73
samples, where their reaction conditions were labeled by their resulting AuNR
sizes predicted from our model. We use the following algorithms, as
implemented in scikit-learn38, to attempt to predict the output parameters
from synthetic inputs: Elastic Net, Bayesian Ridge Regression, Kernel Ridge
Regression, Support Vector Regression, Random Forest Regression and Gradient
Boosting Regression. Generally, random forest regression models outperformed
k-nearest neighbor, support vector regression, kernel ridge regression and
bayesian ridge regression and elastic nets for most of this dataset. Gradient
boosting regression delivered similar results, though support vector
regression performed better for predicting lengths and k-nearest neighbor
models performed best for aspect ratio standard deviations (See Table S2). The
models were reasonably well predictive for aspect ratio and standard
deviations of aspect ratios, with test R2 values of around 0.7 and
$\tilde{}$10% errors (Figure 3e-h). While length and length standard
deviations were less well predicted, error ranges were similar to those of the
spectral morphology analysis. Previous work using machine learning has shown
the ability to predict spectral alignment of AuNRs in seeded growth synthesis
29, 30. We show here that it is possible to integrate the information gained
from spectral morphology analysis with machine learning methods to directly
predict the size and aspect ratios of AuNRs from their synthesis conditions in
a one-pot, seedless growth procedure. In principle, this analysis routine
could also be used in tandem with kinetic models to produce scientific machine
learning models of particle growth.39

###  2.4 Application 3 - Extraction of Size Information From Literature AuNR
Spectra

In addition to this model’s utility as an automated analysis tool for AuNR
synthesis and our ability to generate predictions of resulting AuNR morphology
from reaction conditions, we also turn this model to the AuNR synthesis
literature to impute size information from published spectra without direct
size measurements. Our extraction produced 64 unlabeled literature spectra
that were successfully fit by our model (Figure 3i-l). The most common aspect
ratios reported in the literature were observed between 4 and 5, with a non
negligible spread higher into ARs of 5-6, although very few are seen greater
than 7. Similarly, AuNR lengths of 30-70 nm are far more commonly seen in the
literature than longer lengths, although rods greater than 100 nm have been
successfully synthesized. Looking in detail at three synthetically interesting
outliers that are predicted to have lengths > 100 nm and where we found TEM
images of similar synthesis outcomes in the same report40, 41, 42, the first
comes from a publication reporting syntheses that result in rods with length >
100 nm 40, the second most likely has a length of roughly 90 nm42 and the
third has TEM images showing rods with roughly 50 nm length 41. A further
detailed comparison and discussion of potential external factors that can
induce errors in predictions can be found in the SI. Overall, we demonstrate
that our model can be used to impute missing size and size distribution
information from previous literature reports, contributing to a richer data
ecosystem, allowing more in-depth analysis, and enabling machine learning
based on previous literature results.

##  3 Conclusion

In this work, we have developed a physics based automated spectral morphology
analysis tool for colloidal AuNR samples. This model is able to predict the
AuNR’s length and aspect ratio mean and standard deviation with a high degree
of accuracy, producing population level information on the produced AuNR
sample from its absorption spectrum. We validated this model by comparing its
predictions to measured AuNR size distributions extracted from transmission
electron microscopy images of the predicted AuNR samples and spectra labeled
with size distributions extracted from the literature. We show the wide range
of applications this model can be used for by utilizing it as an automated
analysis tool in high throughput AuNR synthesis, to generate data for training
machine learning models to predict synthesis results based on reaction
conditions, and as a literature mining tool to increase the volume of
quantitative knowledge available on AuNR synthesis. Through these
applications, we elucidate quantitative information about seedless AuNR
synthesis using hydroquinone and the relationships between the reaction
conditions and the size outcomes. In principle, this approach can be extended
to any other nanocrystal system where the absorption spectra are size
dependent and accurate numerical simulation of the absorption spectra is
possible.

##  4 Methods

###  4.1 Materials

Hexadecyltrimethylammonium bromide (CTAB, 98.0%) was purchased from TCI
America. Hydrogen tetrachloroaurate trihydrate (HAuCl4·3H2O, 99.9%), silver
nitrate (AgNO3, 99.0%), and sodium borohydride (NaBH4, 99.99%) were obtained
from Sigma-Aldrich. Diglycol methyl ether (diglyme 99.5%) was used to dissolve
NaBH4 and was purchased from Sigma-Aldrich. Hydroquinone (99%) was purchased
from Sigma-Aldrich. NaBH4 powder was stored in a nitrogen glovebox.
HAuCl4·3H2O, hydroquinone, and AgNO3 were stored in a vacuum desiccator at
room temperature. Deionized water was used for all aqueous solutions. All
chemicals were used without further purification.

Figure 4: The steps the overall spectral morphology analysis uses to determine
how, or if, an input spectrum is fit and whether the results of that fit are
expected to be accurate. Briefly, the model first determines whether the
inputted spectrum is complete (a-b) discarding incomplete spectra. The model
then determines if the longitudinal peak is before or after 795 nm (c-d)
discarding spectra with peak wavelengths shorter than 795 nm. Finally, the
model determines whether the spectra has been measured out to the baseline
(e-f) and uses a different fitting procedure in each of these cases (g-h). The
model then outputs a 2D distribution of the AuNRs fitted to the sample (i).
The rational for selecting the 795 nm cutoff is shown in (j) and the validity
of the differing methods for the measured baseline and the discarding of
uncertain spectra are shown in (k-l). The overlap metric used in (j-l) is the
overlap of the predicted AuNR population and the measured AuNR population
using TEM, and a full description of this metric can be found in Figure S9. A
detailed description of the full model workflow can be found in the SI,
section "Spectral Morphology Analysis Details".

###  4.2 Automated Size Prediction from Absorption Spectra

AuNR morphology prediction from the absorption spectrum of a colloidal sample
is based on basic optical properties of colloidal samples of AuNRs. First, the
overall spectrum can be approximated as a sum of the absorption of each
particle in the colloid, provided nothing else is absorbing and/or scattering
in the energy range of the spectrum. It then becomes possible to determine the
sizes of AuNRs present in a sample by fitting the relative contribution of
AuNRs of different sizes and finding the distribution which best rebuilds the
sample’s spectrum. These assumptions serve as the basis of our spectral
morphology analysis.

The basis set for spectral fitting in our model consists of numerically
simulated single particle spectra of AuNRs from the scuff-em simulation
procedure, which simulates absorption spectra using boundary-element methods,
as shown in Figure 1a and b.43 The accuracy of these simulations, and their
ability to accurately reproduce a full experimental absorption spectrum, has
been shown by comparison with TEM measurements (Figure S3). The spectral
morphology analysis uses these single particle spectra to reproduce a
colloid’s absorption spectrum by generating a size distribution based on AuNR
mean length/standard deviation, mean diameter/standard deviation and the
correlation between the length and diameter distributions. This distribution
is then applied to the basis set, building a spectrum of a sample with that
underlying size distribution, as shown in Figure 1c and d. This procedure then
returns the values of the 5 parameters that build the best fit, indicating the
predicted population of AuNRs in this sample, as well as the chi square
between the fitted and experimental spectrum as a measure of how well the fit
has replicated the experimental spectrum. In cases where there are multiple
stable fits, unless specified otherwise, the prediction is the fit that has
the lowest chi square value between the two spectra. The accuracy of this
model at predicting size distributions across a broad range of size parameters
has been validated by manual TEM analysis by our group and extracted spectra
from literature results on AuNR synthesis.44, 45, 46, 47, 48, 49, 50, 51, 52,
41, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63

###  4.3 Automated Size Prediction Model Validation

The accuracy of our size prediction model was validated using samples
generated from a high thorughput AuNR synthesis run and spectra extracted from
the literature. Our high throughput synthesis procedure produced 20 samples
deemed suitable for validation. This required at least moderate shape purity,
as many reaction conditions in our high throughput experiment produced a
significant number of AuNS. This was determined by setting a threshold that
the ratio between the transverse plasmon peak at roughly 520 nm, where AuNS
absorption occurs, and the longitudinal peak intensity had to be less than
one. Additionally, only samples following the filtering criteria set out in
Figure 4 were fit. All of the high throughput samples fitting the selection
criteria were fit successfully. At least 500 particles were measured for each
high throughput synthesis sample by taking between 50 and 100 TEM images. The
particles were then measured using AutoDetect-mNP, an automated size and shape
detection algorithm for TEM images of metal nanoparticles.20

In the case of literature spectra, 86 spectra were extracted with reported
size information. Of these, 19 were discarded due to either highly irregular
synthesis conditions deemed likely to impact the spectra (ie large volumes of
biological additives) or noted systematic errors in spectral processing
(spectra that didn’t baseline subtract the H2O peak in the NIR, etc). 12 were
discarded due to the spectra being incomplete, determined by the longitudinal
peak ending before the FWHM of the peak. 10 were discarded due to the reported
size parameters being outside the range of the lower bound of our diameters,
denoted by a threshold set 1 nm higher than our lowest diameter value, 5 nm.
This threshold was chosen due to observations that fitted populations with the
mean diameter lower than 6 nm often had appreciable density in regions where
there were no simulated spectra. 4 additional spectra were discarded due to
their longitudinal peak being too high in energy(see Figure 4)c-d. 17 were
returned as too uncertain to be fit (see Figure 4)g and an additional 3 failed
due to the values hitting the bounds of the prediction space. This resulted in
21 literature spectra that were added to our validation set of labeled
spectra. The full validation set contained 41 labeled spectra, which comprise
Figure 2.

###  4.4 Manual AuNR Synthesis

AuNRs were prepared using a modified version of the procedure described by
Vigderman et al.40 In a general synthesis, aqueous solutions of CTAB, HAuCl4,
and AgNO3, in that order, were added to a 1 mL glass vial with a stir bar.
Then, an aqueous solution of hydroquinone was added to the reaction mixture to
reduce Au(III) to Au(I), inducing a color change from yellow to clear. After
waiting 10 minutes, a solution of NaBH4 dissolved in diglyme and sonicated for
10 minutes was added to the solution under rapid stirring to induce the
formation of AuNRs. Stirring was then stopped after half an hour, and the
solutions were allowed to grow overnight to ensure the reaction had completed.
Then, each solution was centrifuged at 10000 rpm for 30 minutes and re-
suspended in DI water under gentle sonication to disperse the pellet.

###  4.5 Absorbance Spectroscopy

UV–vis absorption spectroscopy of the synthesized AuNRs was conducted using a
Shimadzu UV-3600 double beam spectrometer. Samples were prepared by re-
suspending the centrifuged sample in 1 mL of DI water and then diluting 300 uL
of this sample with 2.7 mL DI water. Before measurements, a background
spectrum was recorded and subtracted using a cuvette filled with 3 mL of DI
water.

###  4.6 Transmission electron microscopy (TEM)

Images of the AuNR samples were taken with a FEI Tecnai T20 transmission
electron microscope equipped with a Gatan RIO16IS camera and a LaB6 filament.
All images were recorded under 200 kV accelerating voltage. Samples were
prepared for TEM by drop casting from the 3 mL sample used for absorption
spectral analysis, which was found to have the appropriate concentration, onto
a carbon support with 400 copper mesh. Samples were dried overnight by placing
them under vacuum.

###  4.7 High-Throughput Synthesis

High throughput synthesis of AuNRs was performed using a Hamilton Microlab
NIMBUS4 liquid handling robot. For high-throughput synthesis, new aqueous
solutions of CTAB (100 mM), Hydroquinone (60 mM), HAuCl4 (4 mM) AgNO3 (5 mM)
and NaBH4 (0.3 mM) were prepared for each run. These solutions were then added
to single use 1 mL glass vials in the order DI H2O, CTAB, HAuCl4, AgNO3,
Hydroquinone, NaBH4 while the entire plate was heated to 30 °C and shaken at
300 rpm. Shaking continued for half an hour after the final addition was
completed, and the plate was then left undisturbed for 4 hours. The samples
were then removed from the plate and placed in a dark cabinet and wrapped in
aluminum foil to continue reacting overnight.

Several components of the typical hydroquinone seedless synthesis procedure40
were changed to produce a reaction that was compatible with our liquid
handling synthesis robot setup. The overall scale of the reaction was
significantly decreased to ensure a 96 well plate could be used for high-
throughput synthesis, optimizing the number of reactions achieved with each
run. This necessitated the use of 1 mL vials, producing 0.5 mL of sample,
which is roughly a factor of 20 below the volume produced by the previously
reported procedures. Additionally, to maximize the liquid handling precision
of the NIMBUS robot, the minimum volumes for each reagent are maintained at 5
$\mu$L, necessitating a lower concentration of stock solutions such as NaBH4.
Diglyme was chosen as a polar, aprotic solvent to eliminate background
reactions of NaBH4 with H2O. This work found NaBH4 to be stable in diglyme for
over 24 hours (Figure S8). The enhanced stability also allows for more
flexibility with the reaction procedure, allowing reactions to be performed
with multiple addition of NaBH4 and potentially allowing options for more
advanced procedures such as AuNR synthesis with a syringe pump. Finally, the
stability of the stock solution allows for improved reproducibility of the
synthesis procedure, potentially overcoming a chronic problem in the field
(Figures S4, S8).

Work at the Molecular Foundry was supported by the Office of Science, Office
of Basic Energy Sciences, of the U.S. Department of Energy under Contract No.
DE-AC02-05CH11231. Other work reported here was supported by the U.S.
Department of Energy, Office of Science, Office of Basic Energy Sciences,
Materials Sciences and Engineering Division, under Contract No. DE-
AC02-05-CH11231 within the Data Science for Data-Driven Synthesis Science
grant (KCD2S2). Computational resources for simulations of AuNR spectra were
provided by the Lawrencium computational cluster resource provided by the IT
Division at the Lawrence Berkeley National Laboratory with funding by the
Director, Office of Science, Office of Basic Energy Sciences, of the U.S.
Department of Energy under Contract No. DE-AC02-05CH11231. J.C.D acknowledges
funding through the NSF-GRFP program under DGE 1752814 and the Kavli
NanoScience Institute, University of California, Berkeley through the
Philomathia Graduate Student Fellowship.

## Data and Code Availability

The dataset of simulated AuNR spectra, the high throughput synthesis reaction
conditions, resulting spectra, size predictions and TEM images used for
analysis, literature spectra, size predictions, true sizes and reaction
conditions (when applicable) and the code generating the size prediction model
will be shared upon request.

## Author Contributions

SPG developed, validated and applied the automated size prediction model,
developed the high throughput synthesis procedure, conducted the high
throughput experiments and wrote the manuscript. JCD provided training,
expertise, and conducted high throughput synthesis experiments, advising on
the automated size prediction model construction and developed the machine
learning models discussed in Application 2. ME generated the simulated AuNR
spectra. XW provided automated size prediction modeling for the TEM images
taken in this work. DOB took the validation TEM images necessary to validate
the size prediction model. MG and HC extracted and labeled literature spectra.
RP and SL provided advising and expertise related to the simulated AuNR
spectra generation. EC provided advising, expertise and training for the high
throughput AuNR synthesis experiments. APA provided experimental AuNR
synthesis knowledge, project planning, led the collaboration and designed the
scope of this work. All authors read, edited and approved the final
manuscript.

## References

  * Tong et al. 2009 Tong, L.; Wei, Q.; Wei, A.; Cheng, J.-X. Gold nanorods as contrast agents for biological imaging: optical properties, surface conjugation and photothermal effects. _Photochem Photobiol_ 2009, _85_ , 21–32
  * Jain et al. 2008 Jain, P. K.; Huang, X.; El-Sayed, I. H.; El-Sayed, M. A. Noble Metals on the Nanoscale: Optical and Photothermal Properties and Some Applications in Imaging, Sensing, Biology, and Medicine. _Acc. Chem. Res._ 2008, _41_ , 1578–1586
  * Kang et al. 2017 Kang, X.; Guo, X.; Niu, X.; An, W.; Li, S.; Liu, Z.; Yang, Y.; Wang, N.; Jiang, Q.; Yan, C.; Wang, H.; Zhang, Q. Photothermal therapeutic application of gold nanorods-porphyrin-trastuzumab complexes in HER2-positive breast cancer. _Scientific Reports_ 2017, _7_
  * Mallick et al. 2013 Mallick, S.; Sun, I.-C.; Kim, K.; Yil, D. K. Silica coated gold nanorods for imaging and photo-thermal therapy of cancer cells. _J Nanosci Nanotechno_ 2013, _13_ , 3223–3229
  * Choi et al. 2012 Choi, W. I.; Sahu, A.; Kim, Y. H.; Tae, G. Photothermal cancer therapy and imaging based on gold nanorods. _Ann Biomed Eng_ 2012, _40_ , 534–546
  * Mbalaha et al. 2019 Mbalaha, Z. S.; Edwards, P. R.; Birch, D. J.; ; Chen, Y. Synthesis of Small Gold Nanorods and Their Subsequent Functionalization with Hairpin Single Stranded DNA. _ACS Omega_ 2019, _4_ , 13740–13746
  * Sebastián et al. 2012 Sebastián, V.; Lee, S.-K.; Zhou, C.; Kraus, M. F.; Fujimoto, J. G.; Jensen, K. F. One-step continuous synthesis of biocompatible gold nanorods for optical coherence tomography. _Chem. Commun._ 2012, _48_ , 6654–6656
  * Zhu et al. 2010 Zhu, J.; Yong, K.-T.; Roy, I.; Hu, R.; Ding, H.; Zhao, L.; Swihart, M. T.; He, G. S.; Cui, Y.; Prasad, P. N. Additive controlled synthesis of gold nanorods (GNRs) for two-photon luminescence imaging of cancer cells. _Nanotechnology_ 2010, _21_
  * Amendola et al. 2017 Amendola, V.; Pilot, R.; Frasconi, M.; Maragò, O. M.; Iatì, M. A. Surface plasmon resonance in gold nanoparticles: a review. _J Phys Condens Matter_ 2017, _29_
  * Ou et al. 2018 Ou, Y.; Wang, X.; Lai, K.; Huang, Y.; Rasco, B. A.; Fan, Y. Gold Nanorods as Surface-Enhanced Raman Spectroscopy Substrates for Rapid and Sensitive Analysis of Allura Red and Sunset Yellow in Beverages. _J Agric Food Chem_ 2018, _66_ , 2954–2961
  * de Barros et al. 2020 de Barros, A.; Shimizu, F. M.; de Oliveira, C. S.; Sigoli, F. A.; dos Santos, D. P.; ; Mazali, I. O. Dynamic Behavior of Surface-Enhanced Raman Spectra for Rhodamine 6G Interacting with Gold Nanorods: Implication for Analyses under Wet versus Dry Conditions. _ACS Appl. Nano Mater._ 2020, _3_ , 8138–8147
  * Alvarez-Puebla et al. 2011 Alvarez-Puebla, R. A.; Agarwal, A.; Manna, P.; Liz-Marzán, L. M. Gold nanorods 3D-supercrystals as surface enhanced Raman scattering spectroscopy substrates for the rapid detection of scrambled prions. _PNAS_ 2011, _108_ , 8157–8161
  * Karg et al. 2015 Karg, M.; König, T. A.; Retsch, M.; Stelling, C.; Reichstein, P. M.; Honold, T.; Thelakkat, M.; Fery, A. Colloidal self-assembly concepts for light management in photovoltaics. _Materials Today_ 2015, _18_ , 185–205
  * Mubeen et al. 2014 Mubeen, S.; Lee, J.; ram Lee, W.; Singh, N.; Stucky, G. D.; Moskovits, M. On the Plasmonic Photovoltaic. _ACS Nano_ 2014, _8_ , 6066–6073
  * Link et al. 1999 Link, S.; Mohamed, M. B.; El-Sayed, M. A. Simulation of the Optical Absorption Spectra of Gold Nanorods as a Function of Their Aspect Ratio and the Effect of the Medium Dielectric Constant. _J. Phys. Chem. B_ 1999, _103_ , 3073–3077
  * Eustis and El-Sayed 2005 Eustis, S.; El-Sayed, M. Aspect Ratio Dependence of the Enhanced Flourescense Intensity of Gold Nanorods: Experimental and Simulation Study. _J. Phys. Chem. B_ 2005, _109_ , 16350–16356
  * Ringe et al. 2012 Ringe, E.; Langille, M. R.; Sohn, K.; Zhang, J.; Huang, J.; Mirkin, C. A.; Duyne, R. P. V.; Marks, L. D. Plasmon Length: A Universal Parameter to Describe Size Effects in Gold Nanoparticles. _J. Phys. Chem. Lett._ 2012, _3_ , 1479–1483
  * Burrows et al. 2017 Burrows, N. D.; Harvey, S.; Idesis, F. A.; Murphy, C. J. Understanding the Seed-Mediated Growth of Gold Nanorods through a Fractional Factorial Design of Experiments. _Langmuir_ 2017, _33_ , 1891–1907
  * Lee et al. 2020 Lee, B.; Yoon, S.; Lee, J. W.; Kim, Y.; Chang, J.; Yun, J.; Ro, J. C.; Lee, J.-S.; Lee, J. H. Statistical Characterization of the Morphologies of Nanoparticles through Machine Learning Based Electron Microscopy Image Analysis. _ACS Nano_ 2020, _14_ , 17125–17133
  * Wang et al. 2021 Wang, X.; Li, J.; Ha, H. D.; Dahl, J. C.; Ondry, J. C.; Moreno-Hernandez, I.; Head-Gordon, T.; Alivisatos, A. P. AutoDetect-mNP: An Unsupervised Machine Learning Algorithm for Automated Analysis of Transmission Electron Microscope Images of Metal Nanoparticles. _JACS Au_ 2021, _1_ , 316–327
  * Dahl et al. 2020 Dahl, J. C.; Wang, X.; Huang, X.; Chan, E. M.; Alivisatos, A. P. Elucidating the Weakly Reversible Cs–Pb–Br Perovskite Nanocrystal Reaction Network with High-Throughput Maps and Transformations. _J. Am. Chem. Soc._ 2020, _142_ , 11915–11926
  * Lee et al. 2020 Lee, B.; Yoon, S.; Lee, J. W.; Kim, Y.; Chang, J.; Yun, J.; Ro, J. C.; Lee, J.-S.; Lee, J. H. Statistical Characterization of the Morphologies of Nanoparticles through Machine Learning Based Electron Microscopy Image Analysis. _ACS Nano_ 2020, _14_ , 17125–17133, PMID: 33231065
  * Laramy et al. 2015 Laramy, C. R.; Brown, K. A.; O’Brien, M. N.; Mirkin, C. A. High-Throughput, Algorithmic Determination of Nanoparticle Structure from Electron Microscopy Images. _ACS Nano_ 2015, _9_ , 12488–12495, PMID: 26588107
  * Mulligan et al. 2015 Mulligan, S. K.; Speir, J. A.; Razinkov, I.; Cheng, A.; Crum, J.; Jain, T.; Duggan, E.; Liu, E.; Nolan, J. P.; Carragher, B.; Potter, C. S. Multiplexed TEM Specimen Preparation and Analysis of Plasmonic Nanoparticles. _Microsc Microanal_ 2015, _21_ , 1017–1025
  * Shiratori et al. 2021 Shiratori, K.; Bishop, L. D. C.; Ostovar, B.; Baiyasi, R.; Cai, Y.-Y.; Rossky, P. J.; Landes, C. F.; ; Link, S. Machine-Learned Decision Trees for Predicting Gold Nanorod Sizes from Spectra. _J. Phys. Chem. C_ 2021, _125_ , 19353–19361
  * Pashkov et al. 2021 Pashkov, D. M.; Guda, A. A.; Kirichkov, M. V.; Guda, S. A.; Martini, A.; Soldatov, S. A.; Soldatov, A. V. Quantitative Analysis of the UV–Vis Spectra for Gold Nanoparticles Powered by Supervised Machine Learning. _J. Phys. Chem. C_ 2021, _125_ , 8656–8666
  * Slaughter et al. 2010 Slaughter, L. S.; Chang, W.-S.; Swanglap, P.; Tcherniak, A.; Khanal, B. P.; Zubarev, E. R.; ; Link, S. Single-Particle Spectroscopy of Gold Nanorods beyond the Quasi-Static Limit: Varying the Width at Constant Aspect Ratio. _J. Phys. Chem. C_ 2010, _114_ , 4934–4938
  * Encina and Coronado 2007 Encina, E. R.; Coronado, E. A. Resonance Conditions for Multipole Plasmon Excitations in Noble Metal Nanorods. _J. Phys. Chem. C_ 2007, _111_ , 16796–16801
  * Salley et al. 2020 Salley, D.; Keenan, G.; Grizou, J.; Sharma, A.; Martín, S.; Cronin, L. A nanomaterials discovery robot for the Darwinian evolution of shape programmable gold nanoparticles. _Nature Communications_ 2020, _11_
  * Jiang et al. 2022 Jiang, Y.; Salley, D.; Sharma, A.; Keenan, G.; Mullin, M.; Cronin, L. An artificial intelligence enabled chemical synthesis robot for exploration and optimization of nanomaterials. _Science Advances_ 2022, _8_
  * Vaddi et al. 2022 Vaddi, K.; Chiang, H. T.; Pozzo, L. D. Autonomous retrosynthesis of gold nanoparticles via spectral shape matching. _Digital Discovery_ 2022, _1_ , 502–510
  * Yazdani et al. 2021 Yazdani, S.; Daneshkhah, A.; Diwate, A.; Patel, H.; Smith, J.; Reul, O.; Cheng, R.; Izadian, A.; Hajrasouliha, A. R. Model for Gold Nanoparticle Synthesis: Effect of pH and Reaction Time. _ACS Omega_ 2021, _6_ , 16847–16853
  * Jana 2005 Jana, N. R. Gram-scale synthesis of soluble, near-monodisperse gold nanorods and other anisotropic nanoparticles. _Small_ 2005, _1_ , 875–882
  * Mulekar and Mishra 1994 Mulekar, M. S.; Mishra, S. N. Overlap Coefficients of Two Normal Densities: Equal Means Case. _Journal of the Japanese Statistical Society_ 1994, _24_ , 169–180
  * Liu et al. 2017 Liu, K.; Bu, Y.; Zheng, Y.; Jiang, X.; Yu, A.; Wang, H. Seedless Synthesis of Monodispersed Gold Nanorods with Remarkably High Yield: Synergistic Effect of Template Modification and Growth Kinetics Regulation. _Chemistry Europe_ 2017, _23_ , 3291–3299
  * Nikoobakht and El-Sayed 2003 Nikoobakht, B.; El-Sayed, M. A. Preparation and Growth Mechanism of Gold Nanorods (NRs) Using Seed-Mediated Growth Method. _Chem. Mater._ 2003, _15_ , 1957–1962
  * Jackson et al. 2014 Jackson, S. R.; McBride, J. R.; Rosenthal, S. J.; Wright, D. W. Where’s the Silver? Imaging Trace Silver Coverage on the Surface of Gold Nanorods. _J. Am. Chem. Soc._ 2014, _136_ , 5261–5263
  * Pedregosa et al. 2011 Pedregosa, F. et al. Scikit-learn: Machine Learning in Python. _Journal of Machine Learning Research_ 2011, _12_ , 2825–2830
  * Dahl et al. 2023 Dahl, J. C.; Niblett, S.; Cho, Y.; Wang, X.; Zhang, Y.; Chan, E. M.; Alivisatos, A. P. Scientific Machine Learning of 2D Perovskite Nanosheet Formation. _Journal of the American Chemical Society_ 2023, _145_ , 23076–23087, PMID: 37847242
  * Vigderman and Zubarev 2013 Vigderman, L.; Zubarev, E. R. High-Yield Synthesis of Gold Nanorods with Longitudinal SPR Peak Greater than 1200 nm Using Hydroquinone as a Reducing Agent. _Chem. Mater._ 2013, _25_ , 1450–1457
  * Zhang et al. 2014 Zhang, L.; Xia, K.; Lu, Z.; Li, G.; Chen, J.; Deng, Y.; Li, S.; Zhou, F.; He, N. Efficient and Facile Synthesis of Gold Nanorods with Finely Tunable Plasmonic Peaks from Visible to Near-IR Range. _Chem. Mater._ 2014, _26_ , 1794–1798
  * Wang et al. 2016 Wang, W.; Li, J.; Lan, S.; Rong, L.; Liu, Y.; Sheng, Y.; Zhang, H.; Yang, B. Seedless synthesis of gold nanorods using resveratrol as a reductant. _Nanotechnology_ 2016, _27_
  * Elzouka et al. 2020 Elzouka, M.; Yang, C.; Albert, A.; Prasher, R. S.; Lubner, S. D. Interpretable Forward and Inverse Design of Particle Spectral Emissivity Using Common Machine-Learning Models. _Cell Reports Physical Science_ 2020, _1_
  * Requejo et al. 2017 Requejo, K. I.; Liopo, A. V.; Derry, P. J.; Zubarev, E. R. Accelerating Gold Nanorod Synthesis with Nanomolar Concentrations of Poly(vinylpyrrolidone). _Langmuir_ 2017, _22_ , 12681–12688
  * Zhang et al. 2016 Zhang, Q.; Han, L.; Jing, H.; Blom, D. A.; Lin, Y.; Xin, H. L.; Wang, H. Facet Control of Gold Nanorods. _ACS Nano_ 2016, _10_ , 2960–2974
  * Scarabelli et al. 2013 Scarabelli, L.; Grzelczak, M.; Liz-Marzán, L. M. Tuning Gold Nanorod Synthesis through Prereduction with Salicylic Acid. _Chem. Mater._ 2013, _25_ , 4232–4238
  * del Caño et al. 2020 del Caño, R.; Gisbert-González, J. M.; González-Rodríguez, J.; Sánchez-Obrero, G.; Madueño, R.; Blázquez, M.; Pineda, T. Effective replacement of cetyltrimethylammonium bromide (CTAB) by mercaptoalkanoic acids on gold nanorod (AuNR) surfaces in aqueous solutions. _Nanoscale_ 2020, _12_
  * Requejo et al. 2018 Requejo, K. I.; Liopo, A. V.; Zubarev, E. R. Synthesis of Gold Nanorods Using Poly(vinylpyrrolidone) of Different Molecular Weights as an Additive. _Chemistry Europe_ 2018, _3_ , 12192–12197
  * Requejo et al. 2020 Requejo, K. I.; Liopo, A. V.; Zubarev, E. R. Gold Nanorod Synthesis with Small Thiolated Molecules. _Langmuir_ 2020, _36_ , 3758–3769
  * Wei et al. 2021 Wei, M.-Z.; Deng, T.-S.; Zhang, Q.; Cheng, Z.; Li, S. Seed-Mediated Synthesis of Gold Nanorods at Low Concentrations of CTAB. _ACS Omega_ 2021, _6_ , 9188–9195
  * Lai et al. 2014 Lai, J.; Zhang, L.; Niu, W.; Qi, W.; Zhao, J.; Liu, Z.; Zhang, W.; Xu, G. One-pot synthesis of gold nanorods using binary surfactant systems with improved monodispersity, dimensional tunability and plasmon resonance scattering properties. _Nanotechnology_ 2014, _25_
  * Ye et al. 2013 Ye, X.; Zheng, C.; Chen, J.; Gao, Y.; Murray, C. B. Using Binary Surfactant Mixtures To Simultaneously Improve the Dimensional Tunability and Monodispersity in the Seeded Growth of Gold Nanorods. _Nano Lett._ 2013, _13_ , 765–771
  * Gallagher et al. 2021 Gallagher, R.; Zhang, X.; Altomare, A.; Jr., D. L.; Shawver, N.; Tran, N.; Beazley, M.; Chen, G. pH-mediated synthesis of monodisperse gold nanorods with quantitative yield and molecular level insight. _Nano Res._ 2021, _14_ , 1167–1174
  * Link and El-Sayed 1999 Link, S.; El-Sayed, M. A. Spectral Properties and Relaxation Dynamics of Surface Plasmon Electronic Oscillations in Gold and Silver Nanodots and Nanorods. _J. Phys. Chem. B_ 1999, _103_ , 8410–8426
  * Xu et al. 2014 Xu, X.; Zhao, Y.; Xue, X.; Huo, S.; Chen, F.; Zou, G.; Liang, X.-J. Seedless synthesis of high aspect ratio gold nanorods with high yield. _J. Mater. Chem. A_ 2014, _2_ , 3528–3535
  * Salavatov et al. 2018 Salavatov, N. A.; Dement’eva, O. V.; Mikhailichenko, A. I.; Rudoy, V. M. Some Aspects of Seedless Synthesis of Gold Nanorods. _Colloid J_ 2018, _80_ , 541–549
  * Ye et al. 2012 Ye, X.; Jin, L.; Caglayan, H.; Chen, J.; Xing, G.; Zheng, C.; Doan-Nguyen, V.; Kang, Y.; Engheta, N.; Kagan, C. R.; Murray, C. B. Improved Size-Tunable Synthesis of Monodisperse Gold Nanorods through the Use of Aromatic Additives. _ACS Nano_ 2012, _6_ , 2804–2817
  * Ye et al. 2013 Ye, X.; Gao, Y.; Chen, J.; Reifsnyder, D. C.; Zheng, C.; Murray, C. B. Seeded Growth of Monodisperse Gold Nanorods Using Bromide-Free Surfactant Mixtures. _Nano Lett._ 2013, _13_ , 2163–2171
  * Roach et al. 2018 Roach, L.; Ye, S.; Moorcroft, S. C. T.; Critchley, K.; Coletta, P. L.; Evans, S. D. Morphological control of seedlessly-synthesized gold nanorods using binary surfactants. _Nanotechnology_ 2018, _29_ , 135601
  * Huang et al. 2018 Huang, H.; Li, H.; Wang, H.; Li, J.; Li, P.; Chen, Q.; Chen, Y.; Chu, P. K.; Li, B.; Yu, X.-F. Morphological control of gold nanorods via thermally driven bi-surfactant growth and application for detection of heavy metal ions. _Nanotechnology_ 2018, _29_ , 334001
  * Tong et al. 2017 Tong, W.; Walsh, M. J.; Mulvaney, P.; Etheridge, J.; Funston, A. M. Control of Symmetry Breaking Size and Aspect Ratio in Gold Nanorods: Underlying Role of Silver Nitrate. _J. Phys. Chem. C_ 2017, _121_ , 3549–3559
  * Liopo et al. 2015 Liopo, A.; Wang, S.; Derry, P. J.; Oraevsky, A. A.; Zubarev, E. R. Seedless synthesis of gold nanorods using dopamine as a reducing agent. _RSC Adv._ 2015, _5_ , 91587–91593
  * Li et al. 2019 Li, M.; Zhou, R.; Liu, X.; Tao, Q. Seedless synthesis of gold nanorods by using hydrogen peroxide as a weak reducing agent. _Spectroscopy Letters_ 2019, _52_ , 239–245
  * Jain and El-Sayed 2010 Jain, P. K.; El-Sayed, M. A. Plasmonic coupling in noble metal nanostructures. _Chemical Physics Letters_ 2010, _487_ , 153–164
  * Rohatgi 2024 Rohatgi, A. WebPlotDigitizer. 2024; https://automeris.io/WebPlotDigitizer.html
  * Samal et al. 2010 Samal, A. K.; Sreeprasad, T. S.; Pradeep, T. Investigation of the role of NaBH4 in the chemical synthesis of gold nanorods. _J Nanopart Res_ 2010, _12_ , 1777–1786

##  5 Supporting Information

###  5.1 Spectral Morphology Analysis Outline

Our basis set for the spectral morphology analysis contains particles set on a
1nm scale for ease of interpretability (Figure 1a). Using the Scuff-em
simulation package 43, the single particle absorption spectra of each of these
AuNRs is simulated and stored in a matrix of identical dimensions to the one
with the size information labels (Figure 1b). When an individual spectrum is
predicted, a population distribution is generated based on predicted size
parameters (Figure 1c). The fitted size parameters are the length mean and
standard deviation, the diameter mean and standard deviation, and the
correlation between the two. This generates a two dimensional probability
distribution which is set on the same scale as the previous two matrices and
normalized. Each entry in this distribution can then be treated as the weight
that each individual single particle spectrum contributes to the simulated
mixture spectrum. By multiplying each weight by its corresponding single
particle spectrum and summing the resulting spectra, a simulated mixture
spectrum is developed and compared to an unknown sample (Figure 1d). This
process is then repeated until the size parameters have been found which
generate a mixture spectrum that most closely matches the unknown sample
spectrum. This iterative process changes the parameters which build the
simulated mixture spectrum, AuNR length mean and standard deviation, AuNR
diameter mean and standard deviation, and the correlation between these two,
until it finds a set of values for these 5 parameters that minimizes the
differences between the simulated mixture spectrum and the sample spectrum. To
ensure that the returned sets of size parameters reflect the global minimum
and not simply a local minimum, mean lengths of 50, 100, and 150 nm and
standard deviations from 10 to 20 percent are seeded as initial guesses. The
diameter is set by setting the initial aspect ratio as predicted by the
equation from40 that gives the aspect ratio from the spectrum as LSPR Peak =
420 + 95AR. Although plasmon coupling could undermine the accuracy of the
additive model, its effect is negligible in most synthesized colloidal
systems, and is therefore safely assumed to be not present64. If the fit hits
one of the imposed bounds, which are set to prevent illogical values being
predicted (i.e. distributions that would result in negative sizes), the fit is
labeled as a failed fit.

###  5.2 Spectra Processing and Smoothing

Spectra are smoothed using a savitzky-golay filter implemented using scipy’s
signal module. The smoothing parameters are based on whether the spectrum came
from the NIRVANA instrument, from our individual shimadzu, or extracted from
literature. As the NIRVANA instrument has essentially no noise, the smoothing
parameters use a window size of 5 and a polynomial order of 3. literature
extraction spectra are also less noisy on average, resulting in a set of
smoothing parameters using a window size of 51 and a polynomial order of 3.
Our manually taken spectra have higher noise due to the lower concentration of
AuNRs in our samples when they are diluted to the volume needed for our
instrument, so in this case the window size is increased to 101. All sample
spectra are baseline subtracted and normalized to one post smoothing.

###  5.3 Spectral Morphology Analysis Details

This procedure filters out spectra where the longitudinal peak is lower in
intensity than the transverse peak, which indicates a high volume of spherical
impurities, spectra where less than the FWHM of the spectrum is recorded on
the red edge and also spectra where the longitudinal peak is redder than 795
nm. This ensures that no absorption from spherical particles or any unreacted
growth solution still in the sample convolutes the spectrum. As seen in Figure
S5, the presence of these quantities can change the spectrum and confuse the
automated spectral morphology analysis, which assumes that all the intensity
in the spectrum is originating only from AuNRs of different sizes. Attempts to
include spheres and growth solution into the fitting produced a series of
inaccurate results, and therefore such procedures were discarded in favor of
only utilizing the section of the spectrum that can be confidently assumed to
be only AuNR absorption. The threshold of 795 nm was chosen by examining the
model’s accuracy on a set of validation spectra where the sizes were known at
cutoffs ranging from 700-850 nm and weighing this against the number of
spectra the model is able to predict at that cutoff, since further red
shifting the cutoff will decrease the number of spectra the model is able to
predict. 795 nm was found to have the third highest accuracy and predict
nearly 75% more of our validation spectra than the two higher cutoffs, 825 and
835. This is shown in Figure 4j. After this filtering step, the model
classifies spectra into those where the red edge goes to the baseline, as
determined by the minimum point being on the red edge of the spectrum, and
those where the baseline is the region in between peaks, as determined by the
minimum point being between the two peaks. If the spectrum runs to the red
edge enough for the baseline to be established on the red edge, and therefore
we can assume it is the true baseline of the spectrum, the model is run
without further amendments and the prediction which produces the lowest chi
square and avoids hitting any bounds is taken as the final fit. If, however,
the baseline is found to be between the two peaks, the minimum of the region
between the transverse and longitudinal in the simulated spectrum is
subtracted off of the spectrum as a whole to make this region the baseline of
the simulated spectrum. Additionally, the blue edge of the spectrum is cut off
at 650 nm rather than 795, to ensure that the model has one edge of the
baseline of the extracted longitudinal peak. This has been observed to be
necessary for an accurate prediction. Then the model is fit using a less
flexible model, where only 4 parameters are fit independently: Length mean,
diameter mean, a relative standard deviation parameter that is the same for
length and diameter, and the 2d correlation. This forces length and diameter
to have the same relative standard deviation, rather than fitting them both
independently. If this model returns a prediction with only one stable fit, as
demonstrated in Figure 4h, that is accepted as the prediction. If, however,
there are multiple or zero stable fits, as demonstrated in 4g then the fit is
run again with a more flexible model, the original 5 parameter length/diameter
standard deviation correlation model, and then if this model returns a
prediction with only one stable fit, that is accepted as the prediction. If,
however, there are multiple or zero stable fits, the spectrum is discarded as
a failed fit. At each step of this multilayered procedure, the accuracy, as
determined by the average overlap between the predicted size distribution and
the true size distribution, was compared to the accuracy of omitting that
individual step, as shown by Figure 4k-l, to justify this approach.

The predicted mean aspect ratio, shown in Figure 2g, shows a distinct
difference in the level of accuracy for the high throughput synthesis samples
and samples extracted from literature. This difference can be explained by the
use of hydroquinone as the weak reducing agent in the high throughput
procedure, which has been known to make AuNRs with flattened tips, rather than
the nearly perfectly hemispherical tips made by the more common procedure
using ascorbic acid as the weak reducing agent40. This flattening of the
AuNR’s tip causes a red shift in the longitudinal peak, leading the spectral
morphology analysis to overestimate the sample’s aspect ratio, as shown in
literature40 and the simulations created here (Figure S1). The ascorbic acid
procedure is much more common across the samples extracted from the
literature, explaining why the aspect ratio is much more accurately predicted
with our literature validation samples. 44, 45, 46, 47, 48, 49, 50, 51, 52,
41, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63 However, despite synthetic
differences that change the rod’s refractive index, the spectral morphology
analysis can still attain a reasonable overlap. The predictions of the mean
length, shown in Figure 2e, are more consistent between high throughput and
literature samples, and shows the vast majority of the predictions are within
20% error, a metric beyond the existing state of the art for AuNR size
prediction.25, 26 The predicted aspect ratio standard deviation, shown in
Figure 2h, is quite accurate overall, showing less than 25% of the validation
set samples have an error greater than 20%. It should also be noted that each
of the true values for the aspect ratio and length standard deviations carry
inherent uncertainty due to the large number of particles required to build an
accurate measured distribution. Qualitative estimates have been made showing
that shape identifications in AuNRs can have be incorrect in as much as 10% of
identified particles, implying that absolute size may carry an even larger
uncertainty20 This may explain some of the errors shown in the length standard
deviation prediction, shown in the Figure 2f, such as the samples with
improbably high standard deviations that are underestimated by the model.

###  5.4 Literature Spectral Extraction and Prediction

Literature spectra were extracted by utilizing webplotdigitizer’s x step with
interpolation function 65. High resolution images of each plot were downloaded
from each paper.

Figure 3i shows a few higher length predictions greater than 100 nm. To probe
the outliers in this distribution in some detail, the higher length rods
predicted by this model were examined - as they are both outliers and
synthetically most interesting. Errors in prediction occur most often when
unusual reaction conditions are used, which can change the refractive index of
the colloid solution or the AuNRs themselves. Of the 4 samples predicted to be
over 100 nm in length, one shows TEMs which qualitatively appear to match its
prediction quite well. This procedure is capable of producing rods greater
than 100 nm in length,40 and one of the spectra without size information
extracted from this paper is predicted to be 113.1 nm. Of the remaining 3, one
is inconclusive as only 1 TEM image is included in the paper,63 so its
prediction of 161.7 nm length is impossible to confirm. Although this length
seems improbably long based on the bulk of other documented and predicted
results, this procedure used hydrogen peroxide as a weak reducing agent, which
is a relatively unexplored procedure and its morphology bounds are not well
understood. One is a mild overestimate, returning prediction of 139.6 nm when
the TEMs shown in the paper appear to be roughly 90nm 42. The final appears to
be a larger miss by the model, as TEMs shown in the paper are roughly 50 nm
while the prediction is 127 nm 41. However, this procedure was conducted at
higher temperature, making it possible that the morphology of the resulting
AuNRs have a different refractive index than those this model was trained and
validated on, potentially explaining this error. The remaining distribution
falls within the space of lengths common in AuNR synthesis, making a miss of
this magnitude unlikely for the remainder of the samples.

###  5.5 Overlap Metric

Direct comparison of the distributions of length, diameter and aspect ratio,
as shown in Figure 2b-d, is a challenging way to visualize accuracy for
multiple samples. Therefore the overlap metric was developed to allow the
accuracy of the predictions to be distilled into a single quantity. To
calculate the overlap between a predicted size distribution and the measured
size distribution from TEM analysis, every point in the two distributions,
which are both on a 1 nm scale, are compared, and the point that is lower in
value is assigned to that point in the overlap matrix (Figure S9 f-g). Upon
construction of the overlap matrix, every point is summed together to produce
the overlap coefficient (Figure S9). This coefficient will be between zero and
one, with a higher overlap indicating a more accurate prediction.

###  5.6 High Throughput Synthesis of AuNRs

The utility of the spectral morphology analysis routine is demonstrated by
predicting size distributions of samples generated by high throughput
synthesis. In this procedure, NaBH4 is added directly to the growth solution,
rather than first synthesizing gold seeds in a separate step and adding these
to the reaction. The NaBH4 creates seeds in situ, which then serve to grow
into AuNRs66

Two complete 96 well plates of AuNR synthesis reactions are reported in this
work. The first was used to build and calibrate the high throughput synthesis
model and the second was used to illustrate its utility. In the first
experiment, only the amounts of hydroquinone and CTAB were varied (Figure S2).
Figure S1 shows there appears to be an inflection point between 14 and 20 mM
CTAB where the samples transition from making virtually no AuNRs to a
moderately successful reaction, as shown by the increased intensity of the
longitudinal peak relative to the transverse peak between the 14 and 20 mM
spectra. Additionally, further increasing the CTAB concentration increases the
shape purity and aspect ratios of the samples, although increasing the
concentration to 58 mM appears to broaden the aspect ratio distribution
significantly (Figure S2), as evidenced by the broadening of the longitudinal
peak. For hydroquinone, increasing the concentration to 10.8 mM steadily
increases AuNR yield and slightly blue shifts the longitudinal peak, but an
increase past this concentration appears to begin to decrease yield, as the
ratio of intensities of the longitudinal and transverse peaks decreases past
this concentration. The second set of high throughput synthesis results were
analyzed by spectral morphology analysis to produce detailed quantitative
information regarding the impact of the synthetic condition on AuNR structural
properties (see Figure 3a-d).

###  5.7 Machine Learning

Chemical input data and predicted morphology parameters from the spectra for
all the high-throughput synthesis were merged, and any unsuccessful analyses
were dropped, resulting in a small dataset of 73 samples. Chemical inputs were
designated as the amounts of water, gold chloride, silver nitrate,
cetyltrimethylammonium bromide, hydroquinone and sodium borohydride added to
the reaction solution. For each of the output parameters ($\mu_{Length}$,
$\sigma_{Length}$, $\mu_{Diameter}$, $\sigma_{Diameter}$, Aspect Ratio
($\mu_{AR}$), $\sigma_{AR}$), the following algorithms as implemented in
scikit-learn38 were used to attempt to predict the output parameters from
synthetic inputs: Elastic Net, Bayesian Ridge Regression, Kernel Ridge
Regression, Support Vector Regression, Random Forest Regression and Gradient
Boosting Regression. For each algorithm, a grid search cross validation was
performed using the parameters and values specified in Table S1 below, all
other parameters remained at preset default values.

| Parameter 1 | Values | Parameter 2 | Values | Parameter 3 | Values | Parameter 4 | Values |
---|---|---|---|---|---|---|---|---|---
Elastic Net | ’alpha’ | [0.0001, 0.001, 0.01, 0.1, 1.0, 10.0] | l1_ratio’ | [0.0, 0.1, 0.25, 0.5, 0.75, 0.9, 1.0] |
Bayesian Ridge | ’alpha_init’ | [1e-09, 0.0001, 1.0, 1000.0] | lambda_init’ | [1e-09, 0.0001, 1.0, 1000.0] |
Kernel Ridge | ’kernel’ | [’linear’, ’rbf’, ’sigmoid’] | alpha’ | [0.001, 0.1, 1.0] | ’gamma’ | [1e-06, 0.001, 1.0, 1000.0] |
K-Neighbors | ’n_neighbors’ | [3, 5, 8, 13] | ’p’ | [1.5, 2.0, 3.0, 5.0] |  |  |  |
Support Vector | ’kernel’ | [’linear’, ’rbf’, ’sigmoid’] | ’epsilon’ | [0.1, 1.0] | ’C’ | [1e-06, 0.001, 1.0, 1000.0] | gamma’ | [1e-06, 0.001, 1.0]
Random Forest | ’n_estimators’ | [30, 100, 200, 500] | ’min_samples_leaf’ | [1, 2, 3, 5] | ’max_features’ | [0.3, 0.6, 1.0] |  |
Gradient Boosting | ’n_estimators’ | [30, 100, 200, 500] | ’min_samples_leaf’ | [1, 2, 3, 5] | ’learning_rate’ | [0.01, 0.03, 0.1, 0.3] | ’alpha’ | [0.01, 0.1, 0.5, 0.9]

Table S1: Parameters optimized through cross-validated gridsearch | Length |  $\sigma$Length | Diameter |  $\sigma$Diameter | AR |  $\sigma$AR
---|---|---|---|---|---|---
Elastic Net | 21.1% | 39.5% | 26.1% | 56.5% | 17.2% | 16.3%
Bayesian Ridge | 22.2% | 41.0% | 26.4% | 58.8% | 17.6% | 16.6%
Kernel Ridge | 20.6% | 37.9% | 25.4% | 51.3% | 16.5% | 16.3%
K-Neighbors | 22.0% | 33.2% | 21.6% | 39.5% | 12.4% | 13.6%
Support Vector | 18.5% | 35.5% | 19.3% | 43.0% | 14.2% | 15.0%
Random Forest | 21.0% | 31.9% | 22.4% | 38.6% | 11.1% | 14.0%
Gradient Boosting | 21.2% | 32.2% | 24.0% | 36.2% | 10.2% | 14.1%
Table S2: Mean Absolute Percentage Validation Error for different regression
algorithms fitting different parts of the dataset. All algorithms were
optimized using gridsearchCV using the parameters and values given in table
S1, results reported here are the errors from 5-fold cross validation of the
best algorithm. Figure S1: An illustration of the red shift caused by flat
tipped AuNRs vs hemispherically capped AuNRs. The two spectra shown here are
for rods of identical size, with the only differene being the tip geometry.
Figure S2: A visualization of a slice of the absorption spectra of the high-
throughput synthesis dataset. All concentration values are given in mM. The
left plot shows spectra of samples synthesized using varying concentrations of
the surfactant, CTAB. The shadowed lines around the spectra show the standard
deviations of the spectra, as these samples are averaged from 12 experiments
using the same concentration of CTAB but different concentrations of the other
reagents. This plot shows that there appears to be an inflection point between
14 and 20 mM where the samples go from making virtually no AuNRs to a
moderately successful reaction (as shown by the increased intensity of the
longitudinal peak relative to the transverse peak between the 14 and 20 mM
spectra). Additionally, further increasing the CTAB concentration increases
the yield and aspect ratios of the samples, although increasing the
concentration to 58 mM appears to broaden the aspect ratio distribution
significantly, as evidenced by the broadening of the longitudinal peak. The
right plot shows a similar analysis of samples synthesized using varying
concentrations of the weak reducing agent, hydroquinone (HQ). Increasing the
concentration of HQ to 10.8 mM steadily increases AuNR yield and slightly blue
shifts the longitudinal peak, but an increase past this concentration appears
to begin to decrease yield, as the ratio of intensities of the longitudinal
and transverse peaks decreases past this concentration. Figure S3: A
comparison of an experimental spectrum and a simulated mixture spectrum
recreated using the size distribution determined for this sample by directly
measuring AuNRs from TEM images, showing a high degree of similarity between
the experimental spectrum and the simulated mixture spectrum. Figure S4: An
illustration of the significant impact the NaBH4 stock solution has on the
resulting product. All 4 spectra have identical reaction conditions, the only
difference being the NaBH4 stock solution used. All four stock solutions are
prepared to nominally identical concentration and purity. However, large
differences appear to exist across the batches, with only two of the four
(green and orange curves) successfully producing AuNRs. Figure S5: A
recreation of a sample spectrum containing AuNS and unreacted growth solution
using simulated AuNRs, AuNS, and a generated growth solution. This was
validated by manual measurements of the AuNRs using TEMs to create the black
curve, and then fitting the AuNS and growth solution fractions which produced
the sample specturm. This shows how growth solution and spheres are needed to
replicate the spectrum and how the growth solution especially influences the
spectrum up to the NIR region. Figure S6: A few examples illustrating the
projection of measured TEMs onto a normal distribution. Figure S7: A few
examples of samples with overlaps around the mean overlap, 0.3. Figure S8: An
example of repeat trials using the same synthesis condition with a stock
solution of NaBH4 in diglyme fresh and aged for 24 hours. The two conditions
produce virtually identical spectra illustrating NaBH4’s stability in diglyme.
Figure S9: An illustration of how the accuracy of the spectral morphology
analysis is represented with the overlap metric. The top row shows an AuNR
spectrum (a) and the predicted length, diameter and aspect ratio distributions
(b-d) on top of the corresponding measurements from TEM (gray histogram). To
calculate the overlap between a predicted size distribution and the measured
size distribution from TEM analysis (f,g), every point in the two
distributions are compared to produce the overlap matrix (e), which is then
summed to produce the overlap coefficient. This coefficient will be between
zero and one, with a higher overlap indicating a more accurate prediction.
More details on the overlap metric can be found in the SI, section "Overlap
Metric"