Nanoantennae allow to beat Abbe’s diffraction limit: They can focus light to spot sizes far below the wavelength of light. The resulting enormous field enhancement and ultra-strong light intensities can be used for basic science, but also allows disruptive applications such as plasmonic water splitting. While advanced and, most importantly, expensive process steps are required to fabricate such artificial nanoantennae, modern materials science allows a cheap, and thus highly attractive alternative.

Gold nanosponges

Porous gold nanoparticles, so-called gold nanosponges, have recently emerged as a new material and possess fascinating optical properties. One of these is the ability to focus light deep below the wavelength, leading to the appearance of characteristic hotspots: Nanosponges are de-facto ensembles of random nanoantennae. Each individual nanosponge has its own internal structure, which is intimately linked to its optical properties and leads to its own set of resonance frequencies and hotspots.

Research challenges

One of the ongoing areas of study is this link between microscopic structure and macroscopic properties, however the required knowledge about the nanosponges’ structure has been notoriously difficult to acquire. In our newest work, we have carried out detailed measurements of the chaotic nanometer-sized internal structure of several nanosponges and, based on these measurements, created a model to automatically produce similar sponge geometries on the computer, allowing for much deeper research into the connection between structure and properties. We look very much forward to see the transfer of the developed model to other nanoporous materials.

The project was an interdisciplinary work between material scientists and theoretical physicists of the TU Ilmenau and experimental physicists of the University of Oldenburg as part of a larger cooperation on disordered materials for photonic applications sponsored by the German Research Foundation DFG.

Focused-ion-beam tomography

The experimental work was carried out by the group of Peter Schaaf, Dong Wang and Hauke Honig in the clean room facilities of the Centre for Micro- and Nanotechnologies of the TU Ilmenau, Germany. They used a technique called focused-ion-beam tomography (FIB tomography), in which an individual sponge is cut into many slices, each only a few nanometers thick. These slices are then scanned using electron microscopy and the captured images are processed and assembled into a 3D structure. This allowed us to get a detailed look into a nanosponge for the first time, something that has been a major hindrance to everybody’s research for several years. However, the acquisition process must be carried out by trained
specialists and is not the simplest of procedures.

Computer modelling

As each nanosponge is unique, any reliable structure-property theory is of a statistical nature, requiring the recording of dozens of sponges. Previous theoretical work used simple models to represent the nanosponge geometry, but it was not clear how applicable the results were to real nanosponges. Thus, the main idea of our work came about: Can we develop a more sophisticated geometry creation algorithm tuned around the experimental results? Ideally, this would allow us to generate a whole library of hundreds of sponges on the computer and perform our simulations on these to gain statistical certainty.

Nanoporous gold is created through a process called “spinodal demixing”. Spinodal demixing in other systems has been successfully modeled using the so-called phase-field method in the past. It was only natural to test this physics-inspired method on our sponges. Surprisingly, even the first basic attempts already yielded “spongy-looking” particles, motivating us to keep refining our method. For each algorithm iteration, we calculated the optical properties and compared them to the experiment. After all, if our goal is to produce similar sponge geometries, the optical properties should be similar as well.

More challenges

It seemed that with every challenge we solved, a new one appeared. One of the most critical aspects was the generation of an accurate surface, which is extremely important for the optical properties of the nanosponges.  However, eventually, we succeeded in finding a reliable and simple, yet powerful geometry creation algorithm, which is now described in our paper. The method is in principle transferable to other nanoporous particles.

With this done, we returned to our initial question: Can we discover any relation between the structure of our sponges and their exciting optical properties? Equipped with our new tool, it turns out that in fact, we can. We identified a set of global morphological properties, such as the number of holes and the fraction of gold in our sponges. If sponges generated from our algorithm agree in these properties with those of the experimentally measured sponges, similar optical properties result (of course, taking into account that each sponge is still somewhat unique).

Finally, through the FIB measurements we discovered that the nanosponges are actually anisotropic, that is, not uniformly “thick”. Instead, they are thicker at the bottom, an effect we attribute to the substrate they are lying on during formation. We succeeded in implementing this uneven thickness in our geometry creation algorithm as well, in a way that even allows for any imaginable structural anisotropy. Effects like this are suspected to play an important role in, e.g., (photo-)catalysis using gold nanosponges, an area of research that is still in its infancy.

All's well that ends well

In summary, in our newly published work, we carry out state-of-the-art measurements to uncover the previously mysterious inner structure of gold nanosponges and use these results to develop a novel algorithm for creating similar nanosponge geometries on the computer. Using this powerful tool, we are now beginning to uncover the relation between the sponges’ disordered structure and their fascinating properties. The developed algorithm will likely be a powerful method to investigate additional properties of gold nanosponges, for example nonlinear optical effects and photocatalysis. Furthermore, we believe our tools can be useful for workers in related fields investigating other porous materials and have accordingly made our developed algorithms and codebase publicly available.

Read our paper, now published in Nature Communications Materials, under this link: https://www.nature.com/articles/s43246-023-00346-7