Structural order in plasmonic superlattices

This contribution intends to provide some accessible "behind the paper" background to the publication: Structural order in plasmonic superlattices. It starts with a short introduction to plasmons and plasmonic coupling that can be skipped by readers familiar with these concepts.

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Behind the paper: Structural order in plasmonic superlattices

Plasmons and plasmonic coupling

Nanoparticles in close vicinity can interact in various ways, and these interactions could lead to new or tailored properties. In the case of gold nanoparticles (AuNP) the plasmons of individual AuNPs can interact, and this interaction is called plasmonic coupling. A plasmon is the collective and coherent oscillation of the conduction band electrons driven by an external electric field. In the case of most AuNP, the frequency of this external field is in the visible range, so in simpler terms we can say the electron gas, or plasma, is periodically dislocated by light and the plasmon is the quantum of this plasma oscillation. When the frequency of the driving field (light) matches the frequency of the plasmon, the interaction becomes very strong: the coupled oscillations are resonant. Because in nanoparticles the plasmon is localized, the term localized surface plasmon resonance (LSPR) is often found in literature. The consequence of this resonant coupling is that the energy of the light is effectively absorbed by the AuNP and in the optical spectrum a sharp maximum is observed. Any change in the frequency of the plasmon thus can be directly observed by optical spectroscopy. This brings us back to plasmonic coupling that indeed can strongly affect the frequency of the involved plasmons.

When the electron gas is moved, it leaves positive metal ions in the atomic lattice, so the plasmon can also be considered a fluctuating dipole and to some extent plasmonic coupling can be described as an interaction of dipoles. As one would expect, plasmonic coupling therefore sensitively depends on the separation distance of the AuNP, their size and shape, the number of involved AuNP and their arrangement. If AuNP are closely packed but in a rather disordered manner, like in aggregates, all kind of dipolar interactions occur with a resulting broad range of frequencies. Consequently, a very broad absorption spectrum is observed. The color of an aggregated AuNP solution turns from red to blue-violet. This effect can be very useful for analytical assays, but even more interesting is the other case. When AuNP are closely packed in a well-ordered manner, the plasmonic coupling becomes very defined and new, defined resonances can occur. For a crystal formed of AuNP it is possible to calculate a plasmonic band structure in analogy to band structures in semiconductors. Such calculations can help to understand and predict the fascinating interactions of light with such AuNP crystals. To avoid confusion (AuNP itself are atomic crystals) the crystals formed of AuNP are often called superlattices or supercrystals and because of their plasmonic properties we call them plasmonic supercrystals. Acknowledging the interesting physical properties we expect from plasmonic supercrystals the big question arises: how can we obtain such supercrystals?

Synthesis of plasmonic supercrystals

We had been cooperating with the group of Prof. Stephanie Reich from the Freie Universität Berlin for some time and organized a small workshop to discuss and share ideas. The Reich group is working on plasmonics theoretically and experimentally, whereas our group (Prof. Holger Lange, University of Hamburg) has expertise in colloidal synthesis and self-assembly of nanoparticles as well as ultrafast spectroscopy e.g. to study plasmon dynamics. They asked us if it would be possible to synthesize plasmonic supercrystals consisting of AuNP with diameters in the range 25-60 nm with very close spacing of the AuNPs (< 10 nm edge-to-edge distance = gaps). An abundance of literature exists on the self-assembly of all kind of nanoparticles, so in principle protocols were available. At that point we also already had gathered some experience with the self-assembly of AuNP in the desired diameter range ourselves and found interesting plasmonic features in the resulting supercrystals. However, achieving large homogeneous supercrystal areas with a low number of defects in a reproducible manner had been a persistent challenge for us and others. Our idea to tackle this challenge was to synthesize AuNPs with the highest quality we could achieve, meaning a very narrow size distribution and high uniformity by adapting literature protocols. To facilitate crystallization of these AuNPs by self-assembly we needed to coat them with a polymer shell consisting of polystyrene- (PS-) based ligands and phase transfer them from water into an organic solvent (toluene). These ligands were known to be a good choice for the self-assembly of all kind of nanoparticles, but again, the crystalline quality and areas we were looking for had not been achieved at that time. After some struggle with the syntheses and surface chemistry we finally succeeded in developing a robust protocol that provides very large areas of well ordered nanoparticles (Figure 1).

     Figure 1. Large monolayer of self-assembled AuNPs with 25 nm diameter (Transmission electron microscopy (TEM) measurement).

Interestingly, we not only observed extended well-defined monolayers, but also bi-, tri-, tetralayers and so on, up to multilayers > 30. Starting from 2 layers, with each layer additional polariton-modes evolve (the coupling of a plasmon with a photon results in a polariton in the material). By varying the AuNP diameters, the molecular weight of the PS-ligands and the details of the self-assembly protocol, the geometry of the plasmonic supercrystals can be tuned. Because the protocol itself is quite straightforward and the optical properties of the supercrystals sensitively depend on the geometry, these constitute an exciting class of materials for studying the regime of strong light-matter interactions. A detailed discussion of these interactions can be found in a related recent publication (Mueller, N.S., Okamura, Y., Vieira, B.G.M. et al. Deep strong light–matter coupling in plasmonic nanoparticle crystals. Nature 583, 780–784 (2020)). 

To characterize plasmonic supercrystals, small-angle X-ray scattering (SAXS) is an excellent complementary method to electron microscopy, that is usually statistically limited. In cooperation with experts from the German Electron Synchrotron in Hamburg (DESY), namely Dr. Felix Lehmkühler from the group of Prof. Gerhard Grübel and Dr. Fabian Westermeier from the beamline P10 at Petra III we performed extensive thin-film scanning SAXS experiments to map the plasmonic supercrystal samples. This way we obtained tens of thousands SAXS-measurements that allowed us to extract statistically robust geometry data, especially the lattice constants a of the hexagonally ordered supercrystals. Notably, the standard deviation of the lattice constants was below 1 % for all studied samples. In a related study we succeeded in directly comparing SAXS and electron microscopy measurements of the exact same microscopic region of interest on plasmonic supercrystals. There, we discuss in more detail the information provided by the combination of these methods and an additional so-called X-ray cross-correlation analysis (Schulz, F., Westermeier, F., Dallari, F., Markmann, V., Lange, H., Grübel, G., Lehmkühler, F., Plasmonic Supercrystals with a Layered Structure Studied by a Combined TEM‐SAXS‐XCCA Approach. Adv. Mater. Interfaces 2020, 2000919).

 In our paper we describe and discuss the synthesis of the plasmonic supercrystals and their characterization with electron microscopy, SAXS and optical microscopy combined with spectroscopy. The number of layers can be clearly distinguished with optical microscopy and the crystalline areas are large enough to obtain spectra from defined areas. The focus of the laser used for collecting optical spectra was in the range of roughly 1 µm2 (the focus size is quite similar for the X-ray beam in the SAXS mapping experiments) and the crystalline areas we obtained were in the range of many up to many thousands of square microns. We confirm well-defined polaritonic modes and show how the energies of these modes depend on the geometry. Most importantly we show that order indeed plays a role by comparing a well-ordered plasmonic superlattice synthesized with our new protocol with a less-ordered one, synthesized by an older protocol. Except the quality of the superlattice (standard deviation of the lattice constant and number of defects) and constituent AuNP (size distribution and uniformity) the geometry of the two samples (AuNP diameter and interparticle spacing) was similar. The more ordered sample featured polaritonic modes that were not observable in the less ordered sample. This demonstrates that for tailored light-matter interactions and studies thereof the periodic order of the plasmonic supercrystals is more than a nice feature but essential. The polaritonic modes are an emergent collective property of the material that is directly related to its crystalline order. The well ordered plasmonic supercrystals are not only interesting for fundamental studies of light-matter interactions, but have also potential in the field of optical metamaterials and surface-enhanced spectroscopies. Additionally, order can also affect other properties than optical ones, e.g. mechanical and electrical. With our straightforward protocol it is now possible to synthesize a wide range of geometries for according studies.

What now? 

The achieved quality of plasmonic supercrystals is a huge and exciting step forward, but there is still plenty of room to play. In the future we want to try to perfectly control the number of layers in the supercrystals, achieve even larger single crystalline domains, improve the stability, synthesize new crystalline structures including binary ones (consisting of two constituent AuNPs with different diameters), vary the materials of the nanoparticles and incorporate certain types of molecules. In cooperative efforts we will continue to study the structure and properties of these fascinating materials.                    

Florian Schulz

PostDoc, University of Hamburg

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