Optimized thermal response of Au nanoframes in NIR-II window: a numerical study

Abstract

Au nanoframes are promising tools for photothermal drug delivery and cancer treatment because their red-shifted localized surface plasmon resonance (LSPR) can be effectively excited in the near-infrared (NIR) region. Photothermal therapy using Au nanoframes is favorable due to its affordability, nontoxicity, and minimal effect on healthy cells. However, the nanoparticles currently used in this field are affected by various problems, such as thermal deformation and the risk of the LSPR deviating from the NIR range. Here, we present the double-torus (DT) nanoframe design, where two tori are oriented perpendicularly to each other, for enhanced optical and thermal responses. We compare the photothermal properties of DT and several standard nanoparticles in the second NIR (NIR-II) window (1000–1400 nm), simulate their optical and thermal behavior and optimize their size to achieve the desired therapeutic temperature range of 40–49 °C within the NIR-II window, demonstrate how their shape and symmetry influence their thermal efficiency, and investigate their thermal responses across different sizes. Our findings indicate that controlling heat generation within the therapeutic range highly depends on nanoparticle shape, symmetry, and metallic volume. Regarding the sensitivity of nanoparticle heat generation to nanoparticle volume, the DT structure is the most effective for heat regulation. Moreover, the curved design of the toroidal nanoframe minimizes the risk of the LSPR shifting beyond the NIR-II range. Having robust optical and thermal properties, the DT structure is an excellent candidate for use as a colloidal nanoparticle in biomedicine.

Introduction

Localized surface plasmon resonance (LSPR) is a significant characteristic of metallic nanoparticles (sized 1–100 nm). When these metallic nanoparticles are exposed to incident light at a designated wavelength, λ_LSPR, the conduction electrons on their surface undergo coherent oscillations. This collective oscillation of electrons creates a surface plasmon wave akin to that in a plasma state, where electrons are displaced from their respective atomic nuclei. This phenomenon, termed plasmon, was introduced by Pine¹. Nanoparticles that can exploit this unique capability to harness light energy are classified as plasmonic nanoparticles.

Numerous parameters influence the LSPR of nanoparticles, including their size, shape, and composition and the properties of the surrounding medium. Among metallic nanoparticles, Au is particularly advantageous for biomedical applications due to its exceptional mechanical properties, cost-effectiveness, and biocompatibility, which facilitates its integration into physiological environments^2–4. Additionally, Au nanoparticles exhibit favorable dielectric properties, allowing them to display LSPR at wavelengths exceeding 600 nm. This characteristic is paramount for laser-mediated therapy, as the incident laser light must be absorbed effectively by the skin to activate the nanoparticles within the body. The relevant absorption wavelengths are in the near-infrared (NIR) spectrum, which is subdivided into two distinct windows: the first NIR (NIR-I) window spans from 700 to 1000 nm, and the second NIR (NIR-II) window ranges from 1000 to 1400 nm. The NIR-II window enables superior deep-tumor therapy by providing enhanced tissue penetration due to reduced absorption and scattering compared to visible and NIR-I light. This facilitates delivery of therapeutic energy to tumors several centimeters below the surface while minimizing photodamage to healthy tissue and reducing autofluorescence, thereby improving imaging contrast and precision for image-guided treatments. These characteristics make NIR-II highly advantageous for safe and effective photothermal and photodynamic therapies in deep-seated tumors⁵.

Photothermal therapy is a critical biomedical application that leverages the heat generated by Au nanoparticles when subjected to pulsed laser irradiation⁶. The unique optical properties of Au nanoparticles, particularly their LSPR, enable resonant interaction with light of specific wavelengths. This interaction induces oscillations in the surface electrons of the nanoparticles, resulting in localized thermal energy release in the surrounding medium. This mechanism has significant implications for medical applications, particularly in the targeted ablation of malignant tissues^7,8 and the enhancement of drug delivery systems^9,10. Pulsed laser parameters can be controlled to optimize energy deposition and achieve lethal temperatures in cancer cells while preserving adjacent healthy tissues¹¹.

Effective management of the heat generated via LSPR in nanoparticles is critical for therapeutic applications. Thermal therapy usually targets a temperature range of 41–49 °C in tumors. Exceeding 49 °C for extended periods can lead to irreversible cellular damage. At approximately 60 °C, proteins denature almost instantaneously and irreversibly. Beyond 80 °C, thermal damage leads to substantial tissue necrosis, primarily due to the vaporization of intracellular water¹².

Therefore, temperature control is crucial during photothermal treatment. Excessive heating can induce nonselective damage to surrounding tissues. Moreover, even with complete localization within tumors, the heat generated under laser irradiation can spread beyond the tumor boundaries and negatively affect healthy tissues¹³. This emphasizes the need for precise temperature regulation to ensure treatment effectiveness while minimizing harm to adjacent healthy cells. Ideally, the utilized nanoparticles should be less than 100 nm in diameter to optimize their circulation time in the bloodstream and enhance their cellular uptake. Their dispersibility in biocompatible solvents further facilitates their injection into biological systems, making them suitable for effective thermal treatment of tumors. Several Au nanoparticles have been recommended for biomedical applications. However, the λ_LSPR of solid ones, such as nanospheres¹⁴ and nanocubes¹⁵, does not extend to the required NIR-II¹⁶. Solid nanorods have attracted considerable attention due to their large number of synthesis methods and the rational control over their aspect ratio, which can be controlled to shift their LSPR to NIR windows^17–19. Nanorods exhibit superior absorption efficiency at smaller volumes compared with other nanoparticle types²⁰. This heightened absorption capability is crucial for generating sufficient heat, but heat generation should be regulated to maintain cellular integrity and the optical properties of nanoparticles. Prolonged irradiation can produce excessive thermal effects, causing Au nanorods to become spherical²¹. Moreover, the smaller volumes of these nanorods may limit their interactions with larger tumors, potentially necessitating higher concentrations in biological solutions. However, solutions with increased nanoparticle concentrations can elevate toxicity levels and lead to saturation effects in cellular uptake efficiency²². In addition, the limited volume constraint of nanorods hinders their application as effective multitask photothermal nanoparticles that can be used concurrently for thermal treatment and temperature monitoring, primarily due to their reduced scattering cross section¹². The geometrical characteristics of nanorods also mean that their absorption highly depends on their orientation in relation to the incident light polarization, which significantly influences their absorption properties. Their absorption efficacy can be enhanced by using radially polarized lasers instead of the conventional linearly polarized lasers²³.

Porous nanoparticles have emerged as a pivotal tool in targeted drug delivery systems due to their capacity to function as drug reservoirs. Furthermore, they can achieve sufficient temperature levels to ablate cancer cells effectively. Among these nanoparticles, cubic nanoframes (CFs) are gaining traction, as even a minor reduction in frame thickness can result in a pronounced red shift of the LSPR, effectively aligning it with the advantageous NIR-II window^9,24,25. This spectral positioning is highly beneficial for various biomedical applications. Furthermore, the sharp geometries of CFs create plasmonic hotspots that are instrumental in photothermal therapy, significantly enhancing therapeutic efficacy by facilitating localized heat generation at the site of interest. Nevertheless, the deformation of these nanoframes may present challenges stemming from fabrication problems or significant heat buildup^9,26. Similar to nanorods becoming spherical under excessive heat, CFs can undergo structural changes when subjected to high temperatures. High thermal energy can soften the material, rounding the sharp edges of CFs. This alteration compromises nanostructural integrity and functionality, similar to nanorods losing their distinct morphology, potentially affecting the optical properties and stability of CFs^27,28.

Spherical nanoframes (SpFs) were created to study the effects of edge deformation on their optical properties in CFs²⁹. Numerical research indicates that SpFs are more sensitive to porosity variations than CFs. The rounded edges of SpFs help reduce thermal activity, as opposed to the localized hotspots generated at the sharp corners of CFs. In scenarios involving deformed CFs, the transition from sharp to smoothly contoured edges heightens this sensitivity, causing LSPR shifts that may exceed the desired thresholds, thereby diminishing thermal efficiency. This phenomenon poses significant challenges for CF use in targeted drug delivery and related fields.

Nanotorus particles are promising curved porous structures for various biomedical applications^30–32. Their optical properties have been extensively studied theoretically and experimentally, demonstrating that their LSPR can be finely tuned within the NIR spectrum by varying their toroidal aspect ratio, expressed as = /, where is the major radius and is the minor radius of the torus^33–35. However, the asymmetric geometry of the torus, characterized by its two principal axes, significantly influences the absorption characteristics of nanotorus particles based on orientation, leading to potential discrepancies in performance and hindering their use in colloidal nanoparticle systems. Moreover, unlike nanorods, nanotori have inadequate thermal efficiency for effective photothermal applications, primarily due to the circular electron path inherent in their toroidal geometry. By contrast, the linear electron trajectory in nanorods results in more pronounced dipolar moment excitation—a key contributor to LSPR absorption. To mitigate these limitations, we propose enhancing nanoframe symmetry by configuring multiple tori within a single nanoframe arrangement. We present the double-torus (DT) nanoframe design, where two tori are oriented perpendicularly to each other. The DT architecture combines the plasmonic tunability of nanotorus structures with enhanced thermal stability, overcoming limitations of conventional tori and nanoframes. Its high symmetry and increased metallic volume enable strong, stable heat generation, while curved edges ensure controlled thermal response. Additionally, DT extends LSPR tunability into the NIR-II region for photothermal and biomedical applications and provides dual functionality for simultaneous heating and temperature sensing.

We numerically analyze the resonance absorption and the associated temperature elevation of this nanoparticle using COMSOL Multiphysics to optimize its performance characteristics.

The use of numerical methods is crucial for examining the optical characteristics of nanoparticles with complex geometries. Although Mie theory offers a reliable analytical approach for light scattering in smaller spherical particles, it is inadequate for more intricate shapes³⁶. Here, we analyze the thermal response of selected nanoparticles, specifically a CF, an SpF, a nanorod, a nanotorus, and the proposed DT nanoparticle. We assess the temperature elevation of each nanoparticle upon LSPR excitation within the NIR-II region, optimizing its dimensions to keep the generated heat within the target hyperthermia range of 41–49 °C.

Our analysis indicates that the proposed DT structure offers the advantage of symmetry, which reduces polarization sensitivity, and exhibits enhanced thermal efficiency compared with the conventional nanotorus. This improvement is attributed to the increased metallic volume and the formation of hotspots at the junctions of the DT geometry³⁷. Unlike conventional nanoframe configurations, such as those of the CF and SpF, the DT structure does not require porosity adjustments; instead, the primary parameter for optimizing the LSPR is thickness. Furthermore, the unique edge curvature of the DT geometry enhances structural resilience to deformation, outperforming the traditional nanorods and CFs. Therefore, our design is expected to achieve a more stable and robust LSPR response and thermal performance, particularly within the NIR-II window.

Computational method

We compute the absorption spectra of the nanoparticles using COMSOL Multiphysics with the Wave Optics module, which uses the finite element method for numerical analysis. The computational model is established within a three-dimensional rectangular domain structured as a parallelepiped (Fig. 1a). We orient the model such that the incident electromagnetic field approaches from the top of the domain, oriented along the z axis. At the center of this domain, a singular colloidal particle is subjected to a uniform plane wave characterized by a time-harmonic electric field (E) polarized along the x axis. To mitigate unwanted scattering effects from the domain boundaries, we implement perfectly matched layers at the upper and lower boundaries. Furthermore, we establish perfect electric and perfect magnetic conditions at the lateral boundaries perpendicular to the electric field (E) and magnetic field (H). These boundary conditions are selected to replicate an array of repetitive particles in the x and y axes while focusing on the interactions experienced by a single nanoparticle. To restrict the analysis to this particle, we set the dimensions of the xy plane to 225 nm away from the particle, thereby minimizing its potential coupling with neighboring particles. We execute full-field analysis where the electric field (E) within the domain complies with the governing equation of electromagnetic wave propagation.

Fig. 1.

3D schematic illustration of computational domain of colloidal Au nanotorus immersed in water: (a) optical analysis (n = 1.333 for water) and cross-sectional representation of linearly polarized electric field (E_x) along x axis; (b) thermodynamic analysis with Au nanoparticle as heat source under illumination at λ_LSPR and cross-sectional representation of heat distribution.

1

where µ_r and ε_r are the relative permeability and permittivity of the surrounding media, respectively. The optical properties utilized in this study are primarily sourced from the COMSOL material library. The particle is modeled as being submerged in water, which has a refractive index of n = 1.333, closely resembling the optical characteristics of biological fluids, including blood. The dielectric function of the Au particle is defined using the critical point model³⁸, as outlined in the COMSOL material library. The colloidal particles are excited via a time-harmonic surface current applied to the xy plane, positioned above the nanoparticle. We set the maximum mesh element size to one-tenth of the incident wavelength throughout the domain for sufficient computational accuracy. We further refine the mesh in the proximity of the nanoparticle to enhance precision. We also implement higher-order cubic discretization in place of the default quadratic setting to improve calculation accuracy. The absorption characteristics of the nanoparticle are assessed by analyzing the predefined resistive loss variable (Q_h W/m³) within the Wave Optics module. For thermodynamic numerical analysis, we integrate the Wave Optics and Heat Transfer modules. We conduct a time-dependent study to evaluate the temperature rise within the metallic nanoparticle volume under illumination at its λ_LSPR. The absorbed optical power density, Q_h, which quantifies the heat generated per unit volume, is calculated from the frequency domain (time-harmonic) solution of the wave optics model. This value is subsequently used as the heat source in the thermal model. The temperature distribution (T) across the computational domain was governed by

2

where Q is the thermal energy produced per unit volume. In this case, Q is equivalent to Q_h within the Au matrix and is zero in all lossless materials. The thermal properties were from the COMSOL material library, including density (ρ), specific heat capacity (C_p), and thermal conductivity (k). The thermodynamic model had the same computational domain as the wave optics one except that all boundaries were subject to a thermal insulation condition. The model was initialized at 20 °C (Fig. 1b). To achieve controlled heat generation within the hyperthermia range (40–49 °C), we employed an incident irradiance of 56.5 kW/cm², substantially exceeding the maximum permissible exposure (MPE) for skin (0.2–0.3 W/cm²) and typical photothermal therapy levels (0.5–2 W/cm²). This elevated irradiance was intentionally selected to enable precise characterization of thermal behavior and performance at the single-nanostructure level. In practical applications, however, the effective irradiance per particle is markedly lower due to light scattering, absorption, and beam attenuation in multi-particle or high-concentration systems. Prior studies confirm that increasing nanoparticle concentration induces exponential attenuation of laser intensity, further reducing per-particle exposure⁵.

Results and discussion

Nanorods and CFs are widely used geometries in photothermal therapy. In our investigation, we incorporate an SpF as an extreme case of cubic deformation. Furthermore, we systematically evaluate the thermal characteristics of the proposed DT nanoframe geometry in comparison with those of the conventional nanotorus. Figure 2 depicts each particle and its principal dimensional parameters. The maximum dimensions of the CF, SpF, and nanorod are denoted as (a), (d), and (L), respectively. For both the nanotorus and the DT nanoparticle, the maximum dimension is D_out. The LSPR is adjusted for each morphology by modifying the aspect ratio, linking the nanoparticle’s maximum dimension to its thickness (t). Porosity (p) is presented for the CF and SpF, as it substantially affects the LSPR characteristics of these nanostructures.

Fig. 2.

Studied nanoparticles with principal dimensional parameters; top, left to right: CF, SpF, and nanorod; bottom, left to right: nanotorus and DT.

We initiate our study by establishing a maximum dimension of 50 nm for each nanoparticle while fine-tuning their aspect ratios by adjusting their thickness (t = 4–7 nm) to optimize the LSPR within the NIR-II spectral window. The absorption resonance of all examined nanoparticle configurations can be effectively tuned to the target range of 1000–1400 nm (Fig. 3a). The plots in Fig. 3a are normalized to the absorption peak of each nanoparticle shape, which accounts for uniform peak heights despite variations in nanoparticle volume and optical characteristics, which typically lead to disparate peak amplitudes. The illumination is modeled as a plane wave polarized along the major axis of the nanoparticles, aligned with the x axis. However, this modeling does not accurately capture the dynamics of colloidal systems, as it assumes fixed nanoparticle positioning during illumination. Our model constrains the nanoparticles at specific spherical coordinates, at a polar angle (θ) of 0° and an azimuthal angle (φ) of 0°. To account for the random nanoparticle orientation in colloidal settings, we maintain φ at 0° while systematically varying θ. Fixing φ at 0° is considered acceptable because, given the inherent symmetry of the nanoparticles under investigation, variations in φ for a specified θ do not result in any appreciable changes in the computed outcomes.

Fig. 3.

(a) Normalized absorption spectra for Au nanoparticles with maximum dimension of 50 nm and tuned thickness to proximity of λ_LSPR = 1250 nm; (b) normalized absorption peaks for Au nanoparticles with corresponding λ_LSPR in (a), with x-axis-polarized field excitation and varying θ at φ = 0°.

This modification simulates the floating behavior of the nanoparticles, enabling the evaluation of their LSPR characteristics. We illuminate each particle at its designated λ_LSPR (Fig. 3a) and document the behavior of the absorption peaks across various θ. Figure 3b presents the normalized absorption peak values at different θ in relation to the nanoparticle exhibiting the highest absorption peak, which is the CF nanoparticle. The CF exhibits the maximum absorption intensity due to its geometric symmetry, sharp corners (which facilitate hotspot formation), and linear edges (which enhance the dipole moment). Notably, the symmetry inherent in the CF, SpF, and DT configurations contributes to their consistent absorption performance within a colloidal matrix³⁷. By contrast, for the nanorod and nanotorus configurations, the absorption peaks diminish to negligible levels as θ approaches 90°, highlighting their sensitivity to orientation changes^30,39.

The Au nanostructures can be effectively tailored to operate in the NIR-II region (Fig. 3). However, the thermal efficiency of colloidal particles when exposed to linearly polarized lasers necessitates further exploration. In Fig. 4, we outline the therapeutic hyperthermia range of 40–49 °C and illustrate the temperature increase of each Au nanoparticle illuminated at its corresponding λ_LSPR within 50 ns. This duration aligns well with the commonly used pulse lengths in this field⁴⁰.

Fig. 4.

Thermodynamic analysis for Au nanoparticles with maximum dimension of 50 nm over 50 ns: (a) temperature rise of Au nanoparticles aligned along x-axis polarization at spherical coordinates θ = φ = 0°; (b) average temperature for random orientations (φ = 0°, θ = 0°–90°) of Au nanoparticles.

In Fig. 4a, the major axis of the particle is oriented parallel to the linearly polarized incident field, with the nanoparticle positioned at spherical coordinates θ = φ = 0°. To assess the influence of colloidal characteristics on thermal efficiency, we present the average temperatures at θ = 0°–90° over time in Fig. 4b and compare them with those in Fig. 4a. The data suggest that the nanoparticles exhibiting symmetry across all three principal axes—specifically the CF, SpF, and DT—exhibit a consistent thermal response as colloidal nanoparticles. Conversely, the nanorod and nanotorus display marked reductions in thermal efficiency. The thermal results align well with the optical responses in Fig. 3b, indicating the importance of structural symmetry in sustaining thermal performance within colloidal systems. The different nanoparticles exhibit variations in thermal responses (Fig. 4b) despite having comparable optical characteristics, particularly the ability to tune λ_LSPR to the NIR-II range. The CF nanoparticle stands out by achieving a substantial temperature increase, surpassing the desired hyperthermia range, which is attributable to the high degree of deformation of CFs⁹. By contrast, the SpF demonstrates steadier heat generation and may thus be more suitable than the CF for certain applications. However, the LSPR of the SpF is more sensitive to porosity-related deformations than that of the CF, and tuning the LSPR to the NIR-II region entails a reduction in nanoparticle thickness, subsequently lowering particle tolerance for thermal deformation²⁹. Consequently, the SpF may be less desirable for photothermal applications due to its high susceptibility to shape deformation and the challenges associated with LSPR tuning. The conventionally preferred nanorod demonstrates substantial heat production when its major axis aligns with the incident polarization (Fig. 4a) but exhibits a significant decrease in thermal efficiency when averaged over random orientations (Fig. 4b). This variability is likely due to its heightened sensitivity to linearly polarized light³⁹. Such fluctuations in heat generation may cause challenges, including nanorod deformation into spheres and the need for solutions with higher concentrations of nanorod particles¹². The thermal response of the nanotorus is analogous to that of the nanorod, showing adequate heat generation at the specific orientation of θ = φ = 0 (Fig. 4a) but struggling to maintain the hyperthermic temperature range at other orientations relative to the incident field polarization (Fig. 4b). In general, nanorods yield higher heat outputs than nanotori, although the latter’s moderate thermal response and circular geometry provide greater tolerance for heat deformation and enhance LSPR tuning within the limited NIR-II window. To capitalize on these advantages, we propose the DT design, whose toroidal geometry exhibits robust optical properties³⁷. Because of the added symmetry in the DT structure, the thermal response of the DT nanoparticle is stable across various orientations, unlike in the case of the traditional nanotorus. However, as seen in the DT plots in Fig. 4, the heat generation of the DT nanoparticle with D_out = 50 nm cannot reach the therapeutic temperature range of 40–49 °C.

In analyzing the thermal behavior of Au nanoparticles with identical dimensions and corresponding λ_LSPR (Fig. 3), we present the thermal profiles for three specific orientations (θ = 0°, 30°, 90°) and a fixed φ = 0° in Fig. 5. These orientations highlight the extreme variations in the volumetric heating of the particles. We use a consistent scale across all Au nanoparticles for a comparative assessment of their thermal responses. The CF configuration exhibits superior thermal energy absorption regardless of orientation (Fig. 4). The nanorod generates a comparable thermal output exclusively at θ = 0° due to the alignment of its major axis with the polarization of the incident electric field. Indeed, polarization-sensitive particles, such as nanorods and nanotori, display pronounced variations in temperature. The CF, SpF, and DT maintain consistent thermal responses across all orientations, underscoring their uniform heat distribution characteristics.

Fig. 5.

Thermal profiles of Au nanoparticles at orientations of θ = 0°, 30°, 90° at fixed φ = 0°.

The thermal response in Fig. 4 corresponds to the case of a Au nanoparticle with a maximum dimension of 50 nm, where temperatures can increase or drop below the target thermal range. To refine the thermal response and maintain it within the desired limits, we optimize the particle size to regulate heat generation. This is achieved by fixing the aspect ratio of each Au nanoparticle to keep λ_LSPR within the NIR-II window (Fig. 3a) while systematically varying the maximum dimension and the corresponding thickness to adjust the output temperature within the target range of 40–49 °C. Figure 6 presents the thermal response of each Au particle across varying maximum dimensions at a step size of 10 nm. Reducing the CF size diminishes heat generation, with the optimal thermal output occurring at a = 40 nm (Fig. 6a). A 10 nm increase or decrease in the maximum dimension causes temperatures to fall outside the desired thermal range. For the SpF configuration, we use the dimensional matrix used for the CF, as the SpF is a deformed variant of the CF. The results in Fig. 6b suggest that the SpF requires at least d = 50 nm to generate sufficient heat for hyperthermia applications. This introduces complexities in establishing CF deformation criteria, given the ambiguity of whether to use dimensions of below or above 50 nm for CF or SpF contexts. The data indicate that the thermal regulation of the CF within the hyperthermia range is highly sensitive to structural deformations, similar to its optical response, which complicates the management and optimization of CFs for sensitive photothermal applications. The thermal outputs of the nanorods with L = 70 nm and L = 80 nm reveal effective heat generation (Fig. 6c). These nanorods exhibit reduced thermal sensitivity compared with the CF, achieving peak thermal outputs more rapidly than the CF and other Au nanoparticles. This prompt attainment of the maximum thermal output can be attributed to their superior heat transduction but also raises concerns regarding their stability under prolonged exposure to high temperatures, given their relatively small volumes and corresponding susceptibility to heat-induced structural changes. The nanotorus struggles to reach the desired thermal output, even when D_out is increased to 90 nm (Fig. 6d). Unlike in the case of the nanorod, increasing the nanoparticle size fails to mitigate the symmetry disadvantages of the nanotorus, consequently undermining its thermal efficiency under linearly polarized illumination. Thus, the nanotorus may not be optimal for photothermal applications, particularly within the hyperthermia range. Nevertheless, altering the nanotorus geometry into the DT design addresses its symmetry deficiencies while enhancing its thermal efficiency due to the increased metallic volume; hence, the DT variant is a more promising candidate for applications requiring effective thermal performance. The thermal response of the DT nanoparticle shows marked resilience to size increases compared with the CF, SpF, and nanorod profiles (Fig. 6e). A 10 nm variation in D_out does not elicit the considerable heat response spike seen in the CF case. Furthermore, unlike the thermal exposure of the nanorod, that of the DT nanoparticle adapts according to D_out, offering greater flexibility in choosing the appropriate DT dimensions relative to the laser parameters. This capability enables the optimization of the thermal exposure duration, mitigating the risk of excessive heat accumulation.

Fig. 6.

Average temperatures of colloidal Au nanoparticles at random orientations and fixed aspect ratio corresponding to λ_LSPR in Fig. 3a at varying (a) a for CF, (b) d for SpF, (c) L for nanorod, (d) D_out for nanotorus, and (e) D_out for DT.

Based on the results presented in the figures above, achieving a tunable LSPR in Au nanoparticles for effective photothermal therapy requires more than merely optimizing particle dimensions and thermal efficiency. The optical and thermal properties of Au nanoparticles are intricately linked and influence each other substantially. The ultimate objective is to engineer Au nanoparticles with geometric attributes that enable the deliberate tuning of their LSPR within the NIR-II window, specifically targeting temperatures conducive to hyperthermia. The LSPR can be tailored effectively by precisely defining the dimensions of the Au nanoparticles to generate sufficient thermal energy to achieve hyperthermic conditions. The structural integrity of these nanoparticles should be maintained under heat generation, as any deformation can shift the LSPR, thereby compromising thermal efficiency. In Fig. 7a, we demonstrate the impact of thickness (t) on the tuning of the LSPR of the Au nanoparticles with a maximum dimension of 50 nm. Thickness is readily controlled during Au nanoparticle synthesis^3,5,7. For the NIR-II window (1000–1400 nm), our observations indicate that the optimal thickness of the nanorods is 5–8 nm. In comparison, the nanotorus and DT nanoparticles require slightly thicker shells (6–9 nm), whereas the CF and SpF can be utilized at thicknesses of 7–10 nm. Notably, the LSPR shows consistent sensitivity to thickness variations of approximately 3 nm across all nanoparticle types.

Fig. 7.

(a) Variation in thickness vs. λ_LSPR for Au nanoparticles with maximum dimension of 50 nm; (b) variation in porosity vs. λ_LSPR for CF and SpF with a = d = 50 nm and t = 5, 7 nm.

However, porosity in CFs and SpFs significantly influences LSPR tuning²⁹. The LSPR of the CF and SpF is particularly sensitive to porosity variations at fixed thicknesses of 5 and 7 nm, rendering their LSPR susceptible to thermal deformation (Fig. 7b).

The thermal response in Fig. 8 correlates with the volume variations of the Au nanoparticles; their maximum dimensions are from Fig. 6. Notably, the nanorod demonstrates the highest sensitivity to thermal generation per unit volume; even a minimal volume increase of 5800 nm³ can trigger a temperature rise of 10 °C, causing the temperature to exceed the targeted hyperthermia range. By contrast, despite the lower thermal sensitivity of the CF, its operational volume range within the desired temperature threshold is limited, 7000–20,000 nm³. The thermal sensitivity of the SpF to volume fluctuations is comparable to that of the nanorod but higher than that of the CF. Conversely, the nanotorus displays more volume resilience but, as illustrated in Fig. 6d, lacks adequate thermal capacity to reach the hyperthermia threshold. However, the DT nanoparticle presents a distinct advantage due to its reduced sensitivity to volume changes, enabling a wider range of volumes to be effectively utilized within the hyperthermia margin compared with the other Au nanoparticles. This may position the DT nanoparticle as a versatile multitasking nanoparticle, facilitating the incorporation of larger metallic volumes. This feature is advantageous for imaging and temperature recording, as it enhances scattering cross sections, thereby improving signal quality and sensitivity. All volumetric data depicted in Fig. 8 pertain to maximum dimensions of below 100 nm. For the CF and its deformed variant, the SpF, dimensions exceeding 50 nm are avoided, as they will cause the generated heat to breach the hyperthermia upper limit of 49 °C. In the cases of the nanorod, nanotorus, and DT, a maximum dimension of 90 nm is applied.

Fig. 8.

Average temperatures of colloidal Au nanoparticles at random orientations vs. volumes.

Conclusion

In our study, we systematically examined the thermal characteristics of specific Au nanoparticle morphologies, namely, the CF, SpF, nanorod, nanotorus, and DT, to evaluate their efficacy in generating heat within the hyperthermia range of 40–49 °C. Heat generation at λ_LSPR was assessed per particle type, emphasizing LSPR tuning by changing the aspect ratio to align with the NIR-II window, which provides enhanced safety profiles compared with NIR-I. Certain geometries are highly sensitive to LSPR shifts due to structural variations, particularly the porosity effects in the CF and SpF. LSPR excitation and thermal generation are interdependent; excessive heating can induce morphological changes in the nanoparticles, shifting their LSPR beyond the optimal spectral range of 1000–1400 nm (NIR-II). This effect is pronounced in nanorods and CFs, whose thermal efficiency can be disrupted by alterations in geometry. To mitigate these challenges, we shifted our focus toward alternative Au nanoparticle designs that exhibit stable heat generation within the desired thermal range while preserving LSPR tunability in the NIR-II spectrum. Compared to nanotorus, the proposed DT architecture’s highly symmetrical shape and larger metallic volume enable efficient heat generation that is independent of irradiance polarization, while maintaining plasmonic tunability in the NIR-II region. This symmetry and increased volume also ensure a stable and robust thermal response as size scales up—unlike conventional nanoframes, where even slight size increases can push heat levels beyond the therapeutic range. Additionally, DT’s curved edges provide greater tolerance to thermal deformation than the sharp edges of conventional nanoframes, enhancing structural stability under high-temperature conditions. Collectively, these features position DT as an optimized platform for advanced photothermal performance and multifunctionality, combining efficient heating with reliable temperature sensing However, we acknowledge potential fabrication challenges, as most synthesized polyhedral nanoframes typically possess sharp edges, which may lead to dimensional deformation during manufacturing. Therefore, further research is warranted to address these deformations in toroidal nanoframe structures. Nonetheless, our toroidal nanoframe exhibits robust LSPR and thermal properties and thus holds significant promise for use as colloidal nanoparticles in various biomedical contexts.

Author contributions

Material preparation, data collection, and analysis were performed by Fatema Alali. Fatema Ali wrote the first draft of the manuscript. Previous versions of the manuscript were reviewed and commented on by Fatema Alali. The author read and approved the final manuscript.

Data availability

All data generated or analyzed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.