UV–Vis for Nanoparticles

Chemistry

Nanotechnology

Published

July 4, 2025

Today I am reading “Quantitative Analysis of the UV–Vis Spectra for Gold Nanoparticles Powered by Supervised Machine Learning” (Pashkov et al. 2021)

Decoding SPR spectra

The authors use machine learning to “decode” SPR spectra - to go backwards from the optical spectrum to determine:

What size are the particles?
What shape are they?
For rods, what is their length and diameter?

This is challenging because the relationship between particle geometry and SPR spectra is complex and non-linear, making machine learning an attractive approach for this inverse problem.

The authors trained machine learning models on simulated SPR spectra to predict the $\sqrt{L}$ and $\frac{L}{D}$ ratios, where $L$ is the length and $D$ is the diameter of gold nanorods.

Given a spectrum, the authors can now infer the $\sqrt{L}$ and $\frac{L}{D}$ ratios, which are key parameters for characterizing the nanorods.

This is now the workflow looks like:

Experimental spectrum → ML Algorithm → Best fit parameters (L,D)
                                ↓
                    Generate theoretical spectrum
                    with these parameters
                                ↓
                    "Theory best fit" curve

In figure Figure 1, we see the experimental spectrum, and the spectrum theory best fit. This is a theoretical spectrum based on the parameters predicted by the ML algorithm. The third line, theory for TEM size gives the theoretical spectrum for the size measured by TEM, which is the gold standard for nanoparticle size measurement.

Figure 1: Figre from Pashkov et al. (2021)

Data and simulations

The authors generated theoretical SPR spectra for gold nanoparticles to train their ML models.

Machine Learning Performance

The authors evaluated the prefromance training on different amounts of simulated spectra. Given the small numbers, it is not surprising that the performance improves with more data.

Dataset Size	Without Normalization	Normalizing by Max Value	Normalizing by Area	Normalizing by Value at 400 nm
35	0.0386	0.398	1.05	2.3
75	0.0558	0.244	0.571	0.932
150	0.013	0.0873	0.235	0.44
260	0.022	0.0381	0.0929	0.184

The authors also tested various machine learning models.

ML Method	Normalizing by Max Value	Normalizing by Area	Normalizing by Value at 400 nm
RBF	0.0381	0.0929	0.184
Extra Trees	0.0327	0.046	0.0869
Ridge	0.325	0.581	0.815
Ridge Quadric	0.207	0.428	0.738
LightGBM	0.174	0.358	0.531

The error function is 1 - R² score (lower is better).

Findings

The authors show that particle-particle interactions effect the spectrum the average separation of the particles is 2 nm or less.

References

Pashkov, D. M., A. A. Guda, M. V. Kirichkov, S. A. Guda, A. Martini, S. A. Soldatov, and A. V. Soldatov. 2021. “Quantitative Analysis of the UV–Vis Spectra for Gold Nanoparticles Powered by Supervised Machine Learning.” The Journal of Physical Chemistry C 125 (16): 8656–66. https://doi.org/10.1021/acs.jpcc.0c10680.

--- title: "UV–Vis for Nanoparticles" date: 2025-07-04 categories: ["Chemistry", "Nanotechnology"] draft: false bibliography: references.bib --- Today I am reading "Quantitative Analysis of the UV–Vis Spectra for Gold Nanoparticles Powered by Supervised Machine Learning" [@pashkovQuantitativeAnalysisUV2021] ## Decoding SPR spectra The authors use machine learning to "decode" SPR spectra - to go backwards from the optical spectrum to determine: - What size are the particles? - What shape are they? - For rods, what is their length and diameter? This is challenging because the relationship between particle geometry and SPR spectra is complex and non-linear, making machine learning an attractive approach for this inverse problem. The authors trained machine learning models on simulated SPR spectra to predict the $\sqrt{L}$ and $\frac{L}{D}$ ratios, where $L$ is the length and $D$ is the diameter of gold nanorods. Given a spectrum, the authors can now infer the $\sqrt{L}$ and $\frac{L}{D}$ ratios, which are key parameters for characterizing the nanorods. This is now the workflow looks like: ``` Experimental spectrum → ML Algorithm → Best fit parameters (L,D) ↓ Generate theoretical spectrum with these parameters ↓ "Theory best fit" curve ``` In figure @fig-spectra-comparison, we see the experimental spectrum, and the spectrum theory best fit. This is a theoretical spectrum based on the parameters predicted by the ML algorithm. The third line, theory for TEM size gives the theoretical spectrum for the size measured by TEM, which is the gold standard for nanoparticle size measurement. ![Figre from @pashkovQuantitativeAnalysisUV2021](spectra-comparison.png){#fig-spectra-comparison} ![](parameter-exploration.png) ## Data and simulations The authors generated theoretical SPR spectra for gold nanoparticles to train their ML models. ## Machine Learning Performance The authors evaluated the prefromance training on different amounts of simulated spectra. Given the small numbers, it is not surprising that the performance improves with more data. | Dataset Size | Without Normalization | Normalizing by Max Value | Normalizing by Area | Normalizing by Value at 400 nm | |-------------:|----------------------:|-------------------------:|--------------------:|--------------------------------:| | 35 | 0.0386 | 0.398 | 1.05 | 2.3 | | 75 | 0.0558 | 0.244 | 0.571 | 0.932 | | 150 | 0.013 | 0.0873 | 0.235 | 0.44 | | 260 | 0.022 | **0.0381** | 0.0929 | 0.184 | The authors also tested various machine learning models. | ML Method | Normalizing by Max Value | Normalizing by Area | Normalizing by Value at 400 nm | |-----------|-------------------------:|--------------------:|--------------------------------:| | RBF | 0.0381 | 0.0929 | 0.184 | | Extra Trees | **0.0327** | 0.046 | 0.0869 | | Ridge | 0.325 | 0.581 | 0.815 | | Ridge Quadric | 0.207 | 0.428 | 0.738 | | LightGBM | 0.174 | 0.358 | 0.531 | The error function is 1 - R² score (lower is better). ## Findings The authors show that particle-particle interactions effect the spectrum the average separation of the particles is 2 nm or less.