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Abstract
The use of highly sensitive thermometric methods is essential for the evaluation of nanoplatforms for photothermal therapy. In this study, the thermal lens technique was introduced to assess the optically induced temperature changes in colloidal samples of gold nanoparticles. Thermal lens measurements also allowed the acquisition of the nanoparticle absorption cross-section value, regardless of knowing the nanostructure scattering properties. The developed thermometric system exhibited 0.2 °C−1 sensitivity and was capable of measuring temperature variations of metallic colloidal samples with a resolution of 0.01 °C. Measuring colloidal temperature changes allows for the estimation of the localized temperature variation reached by each nanoheater, before thermalization of the excitation volume. Our results establish a practical and effective method to evaluate optically induced temperature changes on metallic colloids.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photothermal processes have been widely used on therapeutic procedures in several areas of medicine [1–3]. Photothermal therapy (PTT), for instance, is based on the induction of cellular damage by light absorption in a target tissue, where localized heating can be accomplished exploring metallic nanostructures as photothermal nanoagents [4–9]. The temperature evaluation of optically heated colloids is essential on the development of efficient materials and procedures for laser-based thermal therapy. Devices such as thermocouples and thermal cameras are widely used on temperature evaluation. For instance, Richardson et al. explored thermocouples to measure the laser heating of a colloidal droplet containing 20 nm gold nanospheres with concentration of 7 $\times$ 10$^{16}$ m$^{-3}$ [10]. The droplet was retained at the tip of a thermocouple, and a temperature increase up to 7 °C was measured under 70 s of 280 mW laser irradiation at 532 nm. Varela et al. shows the use of thermal cameras to sense laser induced temperature variations in a skin-equivalent sample with gold nanoparticles (NPs) [11]. The laser irradiation induced localized temperature variations of 4.5 °C in the sample. However, thermocouples and thermal cameras have limited performance due to low accuracy, not better than 0.1 °C, and slow response time assessing temperature dynamics.
An alternative method to analyze temperature variations around a nanostructure is accomplished exploring luminescent probes [12,13]. For instance, Quintanilla et al. appraised the heating of a single gold nanostar by combining it with $CaF_2:Y^{3+}$ and $CaF_2:Nd^{3+}$ luminescent nanothermometers [14], and measured temperature variations of 80 °C, with 4 °C of resolution. The use of hybrid probes combining plasmonic nanostructures with luminescent nanothermometers is a well-conceived approach for theranostics. However, thermometric systems based on luminescent nanothermometers presents resolutions no better than 1 °C and sensitivity of about $10^{-2}$ °C$^{-1}$ [15]. Alternatively, Carlson et al. evaluated the optical heating of gold NPs by placing the nanostructure on a fluorescent substrate [16], obtaining resolutions limited to a few degrees. Microscopic thermal imaging with 1 °C resolution have also been demonstrated as an important tool for thermoplasmonic studies [17,18].
The light excitation heating dynamics of a colloidal sample of metallic NPs can be described as a two-step process [19]. The first process comprises of heating each dispersed NP until its temperature variation, $\Delta T_{np}$, reaches an intermediate steady-state. For instance, the heating process of a single gold NP with 100 nm diameter presents a characteristic time in the order of 100 ns to reach the intermediate steady-state [19]. The second step on heating a metallic colloid starts when the thermal fronts from neighboring particles starts to overlap, raising the colloid temperature as a whole, until the global steady-state temperature is reached. For this process, the global thermalization time is about dozens of ms or longer. Thus, the colloid temperature can be described as the superposition of the temperature fields of each individual NP. Therefore, the global temperature variation of the colloid in the steady-state ($\Delta T_{global}$) is given by [19–21]:
The shape of a nanostructure plays an important role in how heat is exchanged with its surroundings. The NP propensity to lose heat is related to its surface area, and thus, nanostructures with a higher surface area allows for a more efficient outward heat flux. In Eq. (1), $\beta$ is the shape correction factor [21]. For instance, for nanospheres, $\beta$ is equal to 1.
In the assessment of optically heated metallic colloids, for excitation times longer than the global thermalization time, the contribution of all individual NPs can be described by a homogeneous heat source distributed throughout the entire heated volume, converting Eq. (1) into a volume integral [19]. For a vessel with optical path $\ell$ containing colloidal NPs, the laser beam illuminates a macroscopic cylindrical volume of length $\ell$ and radius $w_0$ ($\ell \gg w_0$). Therefore, for a heated cylindrical volume of length $\ell$ and radius $w_0$ (and $\ell \gg w_0$), the ratio of temperature variations between the global steady-state and a single NP in the intermediate steady-state is given by (see Supplement 1):
An effective way to study the thermal characteristics of transparent samples is by exploring the thermal lens (TL) effect [23]. Briefly, when a laser beam propagates in an absorbing medium, the temperature distribution in the material is modified due to non-radiative relaxation processes, leading to a refractive index gradient that produces a lens effect. The thermally induced lens effect can be exploited to measure optical and thermal properties of transparent liquids and solids. For instance, thermal lens spectroscopy has been applied on the evaluation of thermal diffusivity in liquids and glasses [24–26], chromatographic analysis [27] and fluorescence/quantum-yield measurements [28,29]. It has also been used in thermally controlled reconfigurable lenses [30] and in the measurements of nonlinear refractive index by thermally managed z-scan technique [31–33]. High sensitivity interferometric TL techniques allows for the appraisal of thermally-induced refractive-index changes in the order of $10^{-8}$ at 633 nm in a 10 cm thick sample, which is associated to temperature variations of $10^{-5}$ °C [34]. Furthermore, improvements on the sensitivity of TL measurements can be obtained exploring pump-probe configurations [35,36], and may enable the detection of ultratrace amounts of absorbing molecules in liquid samples [37]. Although temperature evaluation employing TL effect was suggested by Sheldon et al. in 1982 [38], the effective use of the technique has never been performed assessing temperature measurements.
In this work, we appraised laser-induced temperature changes of colloidal nanoheaters by exploiting the thermal lens technique. Moreover, regardless of knowing the NP scattering properties, TL measurements allowed the acquisition of the absorption cross-section value of a metallic nanoparticle, a fundamental parameter to characterize a nanoheater and engineer an efficient photothermal therapy procedure.
2. Materials and methods
2.1 Thermal lens technique
Temperature analysis of the laser-heated colloid was based on the thermal lens technique. The TL measurement is a time-resolved spectroscopy technique [38,39], that is grounded on the analysis of the wave-front temporal evolution of a Gaussian laser beam transmitted through a sample. In our experiment, the TL technique explored a chopped laser beam with wavelength $\lambda$, in resonance with the colloid absorption band. The chopped laser beam is then focused by converging lens in a thin absorptive sample of thickness $\ell$, smaller than the beam Rayleigh length ($z_R$). The sample is placed in the position z, within the focal region, as depicted in Fig. 1. The absorbed light energy leads to a time-dependent transverse profile of the temperature, $\Delta T(r,t)$, in the sample. Therefore, a transient lens-like refractive index structure is established in the colloid. After interacting with the sample, the laser beam reaches a small aperture in the far-field, as shown in Fig. 1.
Fig. 1. TL system configuration; $z$ and $\ell$ are the the position and the thickness of the sample, respectively. $z_R$ is the Rayleigh length and $w_0$ is the beam waist.
The time-dependent light intensity transmitted through the pinhole, $I(V,t)$, is then measured by a photodetector. Thus, the normalized TL signal variation, $TL_{\textrm{sig}}$, can be expressed as [40]:
The time-dependent TL signal in Eq. (3), models the sample heating dynamics. Equation (3) also neglects the contribution from higher-order $\theta$ terms, thus, limiting $\theta$ values to 1.6 and constraining the maximum absorbed power to 6.0 mW ($P_{abs} < 1.6 \kappa _m \lambda /(dn/dT)$) [34]. Sheldon et al. developed a theoretical model describing the spatial-temporal dependence of the temperature change induced in a TL system as [38]:
On the evaluation of the heating dynamics of the colloidal sample, we define the global temperature variation of the heated region as the volumetric average temperature of the cylindrical region of radius $w_{0}$ (beam waist) and length $\ell$ (sample length). By applying the mean value theorem on the temperature distribution of the heated region, the averaged time-dependent global temperature change becomes:
2.2 Experimental setup and materials
The experimental setup explored a laser (Coherent Compass 215M-20, 20 mW CW $@$ 532 nm), chopped at 5 Hz with 50% duty cycle, establishing a pumping window of 100 ms. The laser beam was expanded by a telescope ($f_{L1}$ = 35 mm and $f_{L2}$ = 100 mm), and focused in the sample by a converging lens ($f_{L3}$ = 150 mm). The normalized sample position was $V = -0.8$, in all measurements. After interacting with the sample, the laser beam was partially blocked by a pinhole before reaching the photodiode detector (Vishay BPW21R). The TL setup explored different pumping powers, ranging from 3.5 to 14.0 mW. The spatial resolution of the system is limited by the laser spot size, that is 20.3 $\mu$m in our setup. Higher spatial resolutions can be achieved employing a TL microscopy (TLM) setup [41]. The experimental setup is depicted in Fig. 2.
The measured TL signal was fitted using Eq. (3), which allowed the identification of the thermal lens strength, $\theta$ and the characteristic time, $t_c$. The obtained TL parameters and Eq. (6) were explored to infer global temperature variation in the sample. All measurements were performed using 500 $\mu$L aqueous solutions of 50 nm diameter gold nanospheres, acquired from NanoComposix and placed in a cuvette with 2 mm length. Nanoparticle concentration ranged from 0.5 $\times 10^{16}$ m$^{-3}$ to 2.1 $\times 10^{16}$ m$^{-3}$. The maximum experimental $\theta$ value of 1.4 (obtained with 14.0 mW and 2.1 $\times$ 10$^{16}$ m$^{-3}$) ensures the validity of Eq. (3). The absorption spectrum of all samples were measured before and after running the experiments to assure that the temperature assessment did not modified the colloid. Sample spectra were obtained using the Ocean Optics USB2000 spectrometer.
3. Results and discussion
Figure 3(a) depicts the measured normalized extinction spectrum of the colloidal sample, indicating the plasmonic peak at 529 nm. Figure 3(a) also shows (solid lines) the optical extinction, absorption and scattering cross-sections spectra of a single 50 nm diameter gold nanosphere in water, obtained by Mie theory [42]. As expected, for small particles the extinction cross-section is mainly determined by the absorption properties of the NP. The scatter plot of Fig. 3(b) shows the TL signal for the colloidal sample with concentration of 2.1 $\times 10^{16}$ m$^{-3}$ under 14 mW excitation and the solid line represents the best fit obtained using Eq. (3), which led to $\theta$ = 0.53 and $t_c$ = 3.5 ms.
Fig. 3. (a) Normalized experimental extinction spectrum (red dots). The solid red, dark blue and light blue lines depicts respectively the extinction, absorption and scattering cross-sections spectra of a single 50 nm diameter gold nanosphere in water, calculated by Mie theory. (b) TL experimental data (scatter plot) for $C_{np}=$ 2.1 $\times 10^{16}$ m$^{-3}$ and $P_{exc}=$ 14 mW. The solid line depicts the best fit to the experimental data.
Absorption cross-section values were estimated exploring different sample concentrations and excitation powers. By measuring the TL strength and using Eq. (4), it was possible to estimate the absorption cross-section of the NPs present in the colloid. Figure 4 shows the absorption cross-section values obtained from the TL experiments. The dotted line in Fig. 4 indicates the average value for the NP absorption cross-section, $\sigma _{abs}\approx (8.8 \pm 0.3) \times 10^{-15}$ m$^2$. This result shows a good agreement with the absorption cross-section of 50 nm gold NPs in water obtained by Mie theory ($\sigma _{abs} \approx 6.9 \times 10^{-15}$ m$^2$).
The literature describes the use of integrating spheres on the evaluation of absorption-cross section of colloidal materials [43,44]. The integrating sphere technique has been developed to such a degree that it allows microscopic measurements of absorption and scattering of single nanostructures [45]. Nevertheless, besides rendering information with high precision, it requires the use of a reference sample for calibration. Since TL strength is intrinsically associated to the absorption process, Eq. (4) provides a new strategy to appraise the absorption cross-section of nanoheaters, regardless knowing the NP scattering cross-section ($\sigma _{sca}$) and without the need for reference samples. By knowing the absorption cross-section of the NP, the extinction cross-section ($\sigma _{ext}$) may be obtained by Beer-Lambert law and, thus, scattering cross-section emerges from $\sigma _{sca} = \sigma _{ext} - \sigma _{abs}$ [44].
Using the obtained $\theta$ and $t_{c}$ values on Eq. (6), one can find the averaged time dependent global temperature variation of the colloidal sample. Figure 5(a) shows the experimental behavior of the global temperature variation for sample concentration of 2.1 $\times 10^{16}$ m$^{-3}$ and various pumping powers. Figure 5(b) shows the experimental steady-state ($t = 100$ ms) global temperature variation obtained for different pumping powers and several NP concentrations. As expected, higher temperatures are obtained increasing excitation power. Global temperature variations up to 1.28 °C were observed. Also, the assessment of the TL technique shows that the temperature variation of the colloidal sample and excitation power are linearly dependent, in accordance with theoretical expectations. The dashed lines portray the theoretical values of the averaged global temperature variation obtained from Eq. (6), for $t = 100$ ms. The experimental values shows good agreement with the theory. The measurement error associated to temperature variation was $\pm$ 0.04 °C for sample concentration of 2.1 $\times$ 10$^{16}$ m$^{-3}$ and $\pm$ 0.01 °C for sample concentrations of 1.2 $\times$ 10$^{16}$ m$^{-3}$ and 0.8 $\times$ 10$^{16}$ m$^{-3}$. The temperatures values obtained with the 0.5 $\times$ 10$^{16}$ m$^{-3}$ NP concentration sample showed an error of $\pm$ 0.03 °C. Figure 5(c) is a colormap depicting the theoretical global temperature variation expected from Eq. (6) and the experimental values obtained from TL evaluation (circles) for $t = 100$ ms. The circles are filled with the color representing its experimental temperature variation (see colorbar), which indicates a good agreement between the experimental and theoretical values.
Fig. 5. (a) Temporal behavior of the averaged global temperature variation for the 2.1 $\times 10^{16}$ m$^{-3}$ colloidal sample concentration at various laser excitation powers. (b) Averaged temperature variation as function of pumping power for several NP concentrations, at 100 ms. The solid lines in (b) indicates the theoretical values obtained from Eq. (6). (c) Theoretical averaged global temperature variation colormap, at 100 ms. The experimental data are denoted by the scattered circles.
Figure 6(a) illustrates the temporal evolution of the TL signal for sample concentration of 2.1 $\times$ 10$^{16}$ m$^{-3}$ and several excitation powers. Figure 6(a) also indicates the $TL_{sig}$ amplitude dependence with the steady-state ($t = 100$ ms) average global temperature variations. Therefore, in the steady-state condition, variations in TL signal excursion can be associated to variations in $\Delta T_{global}$. This is shown in Fig. 6(b) for different sample concentrations. According to Eq. (7), the thermometric system sensitivity becomes the ratio of the TL signal difference to the $\Delta T_{global}$ difference between two consecutive measurements. Therefore, the experimental system sensitivity was evaluated in the steady-state ($t = 100$ ms) by measuring the slope of the solid lines in Fig. 6(b). The average experimental sensitivity was 0.2 °C$^{-1}$. TL sensitivity can also be evaluated exploring Eq. (8). Assuming $t = 100$ ms, $V = -0.8$, and considering the same NP concentrations and excitation powers explored in the experimental analysis, the system exhibit 0.3 °C$^{-1}$ average sensitivity, indicating a good agreement with the experimental $S$ value. The TL sensitivity could be optimized by locating the sample at $V = \pm \sqrt {3}$, leading to a higher sensitivity value of 0.4 °C$^{-1}$ under 20 mW of laser excitation, which is at least ten times better than luminescent methods [15].
Fig. 6. (a) Temporal behavior of normalized TL intensity for the 2.1 $\times 10^{16}$ m$^{-3}$ colloidal sample at various excitation powers. The final steady-state temperature variations measured at t = 100 ms are highlighted. (b) TL signal amplitude as function of the averaged global temperature variation, at 100 ms.
Ideally, the sensitivity of the TL system is limited by intensity fluctuations from the laser source as reported by Hu et al. [34]. However, the detection system can be a fundamental contributor to the TL signal noise. Hence, the smaller temperature variation that can be sensed by the thermal lens system, $\delta (\Delta T)$, is limited by the noise of the TL signal. Therefore, the resolution of the thermometric TL system is given by:
where $\delta (TL_{sig})_{_{RMS}}$ is the root mean square value of the noise fluctuation present in the TL signal. Noise analysis reveals that throughout all samples and excitation powers, the RMS noise present in the TL signal fluctuates around 10$^{-3}$ (see Supplement 1), rendering the capability to detect temperature variations as low as 0.01 °C (for $S = 0.2$ °C$^{-1}$). However, based on Eq. (8), if the sample is placed in the optimal position, the system may achieve resolutions as low as 2 $\times$ 10$^{-3}$ °C.As described in Eq. (1), the steady-state global temperature variation ($\Delta T_{global}$) is established by the contribution of each individual nanoheater. The intermediate steady-state temperature variation of each NP ($\Delta T_{np}$) can be estimated knowing NP properties (absorption cross-section, equivalent radius and shape factor) and experimental parameters (laser intensity and solvent thermal conductivity). Nevertheless, the intermediate steady-state temperature variation of each individual NP can also be inferred using the obtained experimental value of $\Delta T_{global}$, according to Eq. (2). Figure 7 depicts the average NP temperature variation values, $\langle \Delta T_{np}\rangle$, obtained experimentally for different excitation powers. Since the intermediate steady-state temperature variation is independent of NP concentration (see Eq. (1)), the $\Delta T_{np}$ values were averaged for the different colloidal sample concentrations available. As expected, the nanoparticle temperature rises linearly as excitation power increases. The dashed line in Fig. 7 corresponds to theoretical $\Delta T_{np}$ results, and demonstrates accordance with experimental findings.
Fig. 7. Average intermediate steady-state temperature variation of individual NPs (before collective heating) for various excitation powers. The faint stripe indicates the error, considering the experimental $\Delta T_{global}$ values obtained with different NP sample concentrations.
As discussed in the introduction, despite presenting high dynamic range on temperature measurements, the luminescent nanothermometric methodologies present low resolution ($\sim 1$ °C) in temperature assessments [14,16]. Our alternative approach employing TL measurements introduce a new thermometric technique capable of obtaining the localized temperature variation of nanoheaters with resolution of $\sim 10^{-2}$ °C.
4. Conclusion
By applying TL measurements as a thermometric method to evaluate temperature changes on optically-heated metallic colloids, we establish a highly sensitive procedure to evaluate the global temperature variations in optically transparent samples. The TL technique allowed the detection of temperature variations as low as 10$^{-2}$ °C, with 0.2 °C$^{-1}$ sensitivity. Moreover, the global temperature variation obtained by this approach allows to estimate the localized temperature variation reached by single nanostructures in its intermediate heating steady-state, before thermalization of the illuminated region. Furthermore, it was also possible to indirectly appraise the absorption cross-section of 50 nm gold nanospheres, regardless of knowing the NP scattering cross-section. Additionally, the technique bestow the capacity to undergo refinements, allowing its applications on a larger variety of samples and optical regimes of excitation.
Funding
Office of Naval Research Global (N62909-18-1-2099); Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001; Conselho Nacional de Desenvolvimento Científico e Tecnológico; Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco.
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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