Fractal graphene trimers widen multiband protein-sensing potential in simulation

A computational study suggests that chains of graphene-coated spherical particles can serve as multi-frequency surface-enhanced Raman scattering substrates for detecting proteins in mixtures. The design consists of three graphene shells arranged inline, with two nanoscale gaps capable of producing intense localized electric fields. By reducing the radii and gap distances according to a shared scaling rule, the researchers increased the number of usable optical bands while retaining the field-amplitude criterion associated with single-molecule detection in the model. The results provide a route to matching multiple operating frequencies to proteins of different sizes, but the findings come from electromagnetic simulation rather than an experiment performed with real protein mixtures.

The work focuses on a known size problem in surface-enhanced Raman scattering, or SERS. In this technique, electromagnetic hotspots between particles can amplify the Raman signal of molecules near their surfaces, but the location, strength and excitation frequency of that enhancement depend strongly on particle size. Proteins themselves span approximate geometric dimensions of 5 to 50 nm, meaning that a substrate optimized for one molecular scale may not provide the same enhancement for another. The graphene trimers were therefore designed to provide several resonance bands rather than relying on a single operating frequency. Their two interparticle gaps also offer separate binding regions in which molecules of different physical and chemical properties might be concentrated.

Graphene was chosen for the modeled particles because it can support strongly confined plasmons with low intrinsic loss in the mid-infrared and terahertz regimes, and because its resonance can be tuned through its chemical potential. Its two-dimensional carbon lattice can also adsorb molecules through π–π interactions, making the platform relevant to refractive-index sensing. Unlike conventional gold or silver structures, graphene-based sensors may reduce interference from intense fluorescence and may be better suited to repeated washing, although the present study did not test chemical durability or regeneration. The authors modeled graphene with a chemical potential of 0.4 electronvolt and a relaxation time of 10 picoseconds, values intended to represent high-quality graphene and produce sufficiently narrow resonances for clear visualization of multiple modes.

Initial simulations examined symmetric, or “homo,” trimers made from graphene shells with radii of 25 and 12.5 nanometers, separated by 2-nanometer gaps. The particles were illuminated by a normally incident, linearly polarized plane wave with its electric field aligned along the chain. Their absorption cross-sections contained three clear peaks associated with hybridized, higher-order modified Mie-type resonances, with an additional resonance visible beyond the three-particle mode set. The electric field was concentrated at the centers of the two gaps and decayed away from the particle surfaces. For the first three bands, the field magnitudes exceeded 1,000 volts per meter under an incident field of 1 volt per meter, meeting the criterion used by the authors to assess potential single-molecule detection.

Particle size nevertheless changed the fourth resonance. For the 25-nanometer trimer, that band also reached the field-amplitude requirement for single-molecule detection in the model, whereas the 12.5-nanometer version was suitable only for conventional SERS according to the same criterion. The study authors note that producing graphene with a long relaxation time on curved surfaces at room temperature remains experimentally difficult, so the 10-picosecond value represents an optimistic condition for resolving higher-order modes. They also restricted the smaller radius at 12.5 nanometers to remain within graphene’s conventional plasmonic region rather than approaching its effective plasma-frequency limit.

To broaden the spectral response, the researchers next scaled the particle radii while beginning with a largest sphere of 100 nanometers. A ratio of 0.7 produced four intense resonances, a ratio of 0.6 produced six, and a ratio of 0.5 produced five. Resonance amplitudes did not vary monotonically with the scaling factor because the differently sized particles hybridize through modes with distinct damping characteristics. These simulations indicate that geometric asymmetry can couple additional multipolar modes into the response, but the number of peaks alone does not establish practical sensitivity: some modes produce weak or spatially uneven fields even when they appear in an absorption spectrum.

The design was then modified so that both radii and gaps followed the same factor, with the relationship Ri+1 = kRi and gi+1 = kgi. At a joint scaling factor of 0.6, the starting radius was 100 nanometers and the first gap was 2 nanometers, reducing the later gaps to 1.2 nanometers. This structure showed five intense visible resonances and several weaker ones, more spectral peaks than the corresponding arrangement with evenly spaced gaps. The additional degrees of freedom allowed constructive or destructive interactions among plasmonic modes to alter both their amplitudes and the localization of their fields. The authors identify gap tuning as a means of making some low-amplitude resonances more useful for sensing.

Across the ten reported frequencies of that fractal design, from 23.69 to 53.70 terahertz, the near-field distribution varied substantially. Five of the bands met the model’s dual-hotspot criterion for single-molecule detection, including four intense resonances and the final band at 53.70 terahertz. At some frequencies, enhancement was concentrated in the gap between the two smaller particles; at others, it appeared between the larger particles. Three bands, at 39.24, 41.34 and 42.37 terahertz, did not produce sufficient field amplitude under the authors’ criterion and would require further geometric adjustment. The field patterns also revealed the participation of higher-order modes: most had an azimuthal index of zero, while the two larger particles in the 39.24-terahertz mode had an index of one, and the 42.37-terahertz mode included indices of zero, one and two from the smallest to largest particle.

These modeled hot spots are the central attraction of the fractal architecture. A conventional trimer already supplies two enhanced regions, but a self-similar chain can create different resonance conditions across those regions and across its operating spectrum. In principle, a protein’s geometry and binding behavior could be used to construct lookup tables connecting particular analytes to particular bands and hotspots. The authors suggest extending the idea to larger fractal assemblies, which could add more hot spots for binding different analytes. Such an extension remains a design direction rather than a demonstrated sensing platform, and protein-specific binding, spectral interference in mixtures and measurable Raman responses would all require direct testing.

The analysis used CST’s frequency-domain optical solver with adaptive meshing, a dispersive surface-impedance model for graphene and perfectly matched boundaries. The electric field was aligned with the array axis, and the simulations extracted absorption cross-sections as well as total and normal electric-field distributions. The authors acknowledge that the modeled spectrum was limited, that additional resonances may occur beyond the reported range and that the simulation box could not be enlarged further because of the required computational time. Accordingly, the study demonstrates a design strategy rather than a completed biosensor: unequal graphene shells and proportionally shrinking gaps can generate additional multiband hotspots, while the quality of the underlying graphene, the geometry of each target protein and the behavior of real samples will determine whether the modeled enhancement translates into practical protein detection.

Subject of Research: Simulated multiband SERS sensing with self-similar graphene nanoparticle trimers

Article Title: Self-similar graphene shells as a multi-frequency pumped SERS substrate for detection of proteins in mixtures

Article References: Raad, S. H., & Afshari-Bavil, M. (2026). Self-similar graphene shells as a multi-frequency pumped SERS substrate for detection of proteins in mixtures. Results in Physics, Article 108770. https://doi.org/10.1016/j.rinp.2026.108770

Image Credits: AI Generated

DOI: 10.1016/j.rinp.2026.108770

Keywords: graphene, SERS, protein detection, plasmonics, fractal nanostructures, electromagnetic simulation, localized hotspots, multiband sensing, surface plasmons, Self-similar, shells, multi-frequency