# Parameter-Free Determination of Au Nanorod Dimensions Using Depolarized DLS and Genetic Optimization

## TL;DR

This paper introduces a new method using depolarized dynamic light scattering and genetic algorithms to accurately determine the dimensions of gold nanorods in solution without prior assumptions.

## Contribution

A novel genetic algorithm approach for parameter-free determination of Au nanorod dimensions from DDLS data is introduced.

## Key findings

- Genetic algorithm analysis of DDLS data provided AuNR length estimates consistent with TEM/SEM measurements.
- The genetic algorithm outperformed analytical methods when DDLS data was noisy.
- The method captures AuNR dimensions from relaxation rates alone, without needing a priori information like aspect ratio.

## Abstract

Gold nanorods (AuNRs) have received considerable attention
for
their distinctive optical properties and well-defined, low-polydispersity
dimensions. These characteristics position them as promising candidates
for diverse applications in imaging, sensing, and treating diseases.
However, accurate characterization of AuNRs in their native solution
state, which is crucial to many applications, presents many challengesespecially
if AuNRs are coated with surface layers (e.g., surfactants or grafted
polymers). When applied to AuNRs with functionalized surfaces, common
techniques such as transmission electron microscopy (TEM), small-angle
scattering, and dynamic light scattering (DLS) can present limitations
such as small sample sizes, the inability to detect light elements,
a lack of a comprehensive analytical framework, and/or a dependence
on a priori information about the particle dimensions.
In this work, we focus on multiangle depolarized DLS (DDLS) measurements
of three distinct, surfactant-coated AuNRs samples in solution. DDLS
data was analyzed using two analytical approaches and compared with
a genetic algorithm analysis that optimizes the dimensions of the
particles to best match relaxation rates obtained from DDLS. For samples
that produced high-quality DDLS data, all three approaches yielded
length estimates that were highly consistent (within 10–20%)
with dimensions obtained from TEM/SEM. In contrast, noisy DDLS data
posed challenges for direct analysis, and the genetic algorithm approach
emerged as particularly advantageous, providing dimensions that more
closely aligned with TEM/SEM values than the analytical methods. Our
results suggest that the genetic algorithm can accurately capture
the dimensions of the AuNRs from their rotational and translational
relaxation rates alone, without the need for additional information
(e.g., aspect ratio). Looking to the future, this approach to analyzing
DDLS measurements will allow the technique to capture important structural
information on more complex, anisotropic nanoparticle systems to enable
their use in a wide range of applications.