Why not use the thermal radiation for nanothermometry?
WWhy not use the thermal radiation for nanothermometry?
Liselotte Jauffred a The measurement of temperature with nanoscale spatial resolution is an emerging new technology and it has important impactin various fields. An ideal nanothermometer should not only be accurate, but also applicable over a wide temperature range andunder diverse conditions. Furthermore, the measurement time should be short enough to follow the evolution of the system.However, many of the existing techniques are limited by drawbacks such as low sensitivity and fluctuations of fluorescence.Therefore, Plank’s law offers an appealing relation between the absolute temperature of the system under interrogation and thethermal spectrum. Despite this, thermal radiation spectroscopy is unsuitable for far-field nanothermometry, primarily because ofthe power loss in the near surroundings and a poor spatial resolution.In 2015, stable aerosol trapping of individual metallicnanoparticles (80-200 nm) under atmospheric pressure was re-ported . As the thermal conductance of air is much lower thanthe conductance of water, the heating associated with laserirradiation of airborne metallic nanoparticles is expected tobe tunable in the range from room temperature to the melt-ing point of gold (1,337 K). Currently, there exists no methodto measure the temperature of aerosols of gold nanoparticles.Therefore, I looked into the possibility of accessing the tem-perature through a spectral analysis of thermal radiation.Thermal (blackbody) radiation has a spectrum that dependsentirely on the temperature of the particle. The emission inten-sity for a specific wavelength can be calculated from Planck’slaw and by balancing the absorbed power with the emissionpower and the heat dissipation, the particle temperature canbe extracted.To my knowledge, the first attempts to probe a tempera-ture field at small scales were based on the use of local nan-otips used as a nanoscale thermocoupler. This is the so calledSThM (scanning thermal microscopy) technique and it was in-troduced in 2014 by the group of Levy . The authors shovedthat they, with the nanotip, were able to measure tempera-ture rises of 15 K. In 2016, the group of S¨uzer reported onanother near-field technique to map the temperature of plas-monic nanoantennas . The experiments were conducted inthe context of heat-assisted magnetic recording and the tech-nique was termed Polymer Imprint Thermal Mapping (PITM).The technique explores thermosensitive polymers that perma-nently cross-links upon heating, which causes a thickeningthat can be subsequently mapped with AFM. However, thesenear-field techniques are very invasive and thus has limitedapplication particularly, for nanoparticle aerosols. In the fol-lowing, I will evaluate the possibility of measuring thermalradiation of gold nanoparticles in the far-field, instead of thenear-field. a The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Den-mark.; E-mail: [email protected]. diameter (nm)
50 100 150 200 O p t i c a l c r o ss s e c t i o n s ( n m ) -2 absorption airscattering airextinction airextinction water Fig. 1
Absorption, scattering, and extinction cross sections as afunction of particle diameter calculated in air by Mie theory , forcomparison the extinction cross section for gold in water is alsoshown.
Emission by nanoparticles under laser excitation
For the system described in Ref. , gold nanoparticles are in-dividually trapped with a NIR laser beam (1064 nm) underatmospheric pressure. However, for simplicity, imagine an en-semble of very small gold particles in vacuum irradiated witha laser beam. In this case, the gravity is negligible compared tothe interparticle electrostatic interactions in this colloidal sys-tem. Its apparent density is very small, which indicates thatparticles only seldom are in direct contact. Consequently, thethermal conductivity of the system is very low. Thus, whenirradiated, the absorbed power causes an increase in tempera-ture and a corresponding heat flux. Hence, the energy balanceequation of a single gold nanoparticle can be written as : P abs ( I L ) = P em ( T ) + c p dTdt (1)where I L is the laser intensity, P abs and P em are the power ab-sorbed from the laser and dissipated by the particles, respec- | a r X i v : . [ c ond - m a t . m e s - h a ll ] N ov ively. T is the temperature of the particles and c p the heatcapacity. The absorbed power will be proportional to the laserintensity, according to P abs = AI L , (2)where A depends on geometrical factors like the shape and sizeof the particles and on optical parameters like the absorptionand scattering cross sections given in Fig. 1. As the particleare in low numbers, the heat conduction from particle to par-ticle is neglected. Therefore, in vacuum the only mechanismable to dissipate heat from the particles is blackbody thermalradiation and the emitted power will follow Stefan-Boltzmannlaw : P em = B σ B ( T − T R ) , (3) Wavelength ( m) S p e c t r a l r a d i a n c e ( W s / s r / m )
50 C200 C100 C
Fig. 2
Spectral radiance over the NIR spectrum for 50 ◦ C, 100 ◦ C,and 200 ◦ C. where σ B is Stefan-Boltzmann’s constant, T R the room tem-perature and B a constant that depends on the emissivity andgeometry of particles. This blackbody emission can be de-tected by integrating over all emitted wavelengths. Alterna-tively, the emission in a narrow spectral range around a givenwavelength, λ , can be collected through a monochromator. Inthis case, the measured intensity will follow Planck’s spectralradiance: I em ( λ ) = ε π hc λ ( e hc λ k B T − ) , (4)where ε is the emissivity, h is Planck’s constant, c , the speedof light and k B , Boltzmann’s constant. For nanoparticles irra-diated and heated to a few hundred degrees (Fig. 2), the peakemission is in the NIR spectrum with a tail into the visibleregime. time (ms) E m i ss i on i n t en s i t y / A b s o r bed i n t en s i t y T e m pe r a t u r e ( C ) laser on -5 Fig. 3
Evolution of temperature for gold nanoparticles (200 nm) invacuum (red dashed curve) irradiated with a 1064 nm NIR laserbeam and the corresponding emitted thermal radiation at 470 nmwavelength (blue solid curve)
Following the train of thought of Ref. I used this set ofequations to calculate the radiation emitted by spherical goldnanoparticles ( R =
100 nm). In order to simplify the prob-lem, I considered every particle to absorb and emit radiationindependently, i.e., neglecting shadowing effects. Under theseideal conditions, the constants A and B are simply: A = π R ( − e − α R ) (5)and B = π R ( − e − α R ) , (6)where R is the radius of the particles, α the mean optical ab-sorption and the quantity in parentheses corresponds to theemissivity of an infinite layer of thickness R . The heating ofthe particles under irradiation with a NIR 1,064 nm laser wascalculated, with parameters detailed in table 1. The tempera-ture evolution has been plotted in Fig. 3 (red curve). Initially,when the laser is turned on, the temperature increases at con-stant rate, as the emitted power is small. Hence, the heatingrate is proportional to the intensity of the laser. This behaviorcontinues up to ∼ ◦ C as thermal emission is only impor-tant at high temperatures. When the laser is turned off, theaerosol cools proportional to the emitted power, i.e., T − T R .Once the temperature evolution versus time is known, it ispossible to calculate the intensity of radiation emitted at anywavelength by simply introducing T in Planck’s distributionEq. (4). The emitted intensity at a wavelength of 470 nm(blue) has been calculated and the result is shown in Fig. 3(solid blue curve). Interestingly, the emitted intensity onlyraises when temperatures has reached ∼ ◦ , because of thenon-linear dependence on T given by the Planck distribution.In contrast, the emission decays rapidly when the laser isturned off.According to this analysis, the laser beam is able to heatthe particles because of the lack of dissipation mechanisms. able 1 Parameters
Laser intensity I L =
146 mW/mm Room temperature T R =
293 KParticle radius R =
100 nmParticle mass m = . · − gHeat capacity per particle c p = . · − J/K a Emissivity ε = ( − exp ( − α R )) Absorption coefficient α = . · m − b Reflectivity r = a c p = m · .
129 J/gK at room temperature from Ref. ? . b for λ =1064 nm . This is why in vacuum; only radiative thermal emission is sig-nificant. However, at atmospheric pressure, heat conductionthrough the surroundings would be so efficient that no emittedradiation at all would be detected. This means that at interme-diate pressures one would detect a progressive diminution ofthe emitted radiation. This can be easily calculated. At steadystate, the energy balance equation will be: P abs ( I L ) = P em ( T ) + P gas ( T ) , (7)where P gas ( T ) is the power dissipated through the gas. Ata low enough pressure, it is approximately the product of thenumber of gas collisions on the particle surface times the meanenergy exchanged in one collision ? : P gas ≈ π R p √ π mk B T R k B ( T − T R ) , (8)where p and T R are the gas pressure and temperature, respec-tively, m is the atomic mass and the factor 3/2 arises from theassumption of a monoatomic gas. Eq. (7) and Eq. (8) allowus to calculate the dependence of the steady state emissionintensity versus gas pressure. The result is an exponential de-pendence: I em = I e − p / p , (9)with a very conservative choice of p to be 100 Pascals . Withthis and the parameters listed in table 1, the emission intensityfor atmospheric pressure ( ∼
100 kPa) is less than 10 − of theemitted intensity in vacuum (Fig. 4). pressure (kPa) E m i ss i on i n t en s i t y no r m . -300 -200 -100 Fig. 4
The dependence of the steady state emission intensity on thesurrounding gas pressure.
Concluding remarks
Thermal (blackbody) radiation has a spectrum that dependsentirely on the temperature of the particle and the emissionintensity for a specific wavelength can be calculated fromPlanck’s law. Therefore, by balancing the absorbed powerwith the emission power and the heat dissipation, the parti-cle temperature can be extracted. However, at atmosphericpressure most of the absorbed power is dissipated in the sur-rounding gas. Furthermore, standard thermal imaging, whichis often used to measure heating of nanoparticles in suspen-sion does not apply for nanothermometry. The reason isthat the wavelength of several microns of the peak intensity,given by Planck’ law, would lead to a very poor spatial resolu-tion. Furthermore, as the emission only becomes pronouncedfor temperatures of several hundreds of degrees, the measur-able temperature range is limited to temperatures far above100 ◦ C. Thus, this method is not appropriate to measure am-bient temperature changes of single nanoparticles.Thermal spectroscopy for nanothermometry is further chal-lenged by the fact that most optical components does not trans-mit/reflect light with the same probability over a wavelengthrange that is large enough for spectroscopy, e.g. visible light.For these reasons, thermal spectroscopy for nanothermometryshould not be the first option if the goal is to measure the tem-perature of gold nanoparticle aerosols that are both opticallytrapped and heated by a single laser.
References
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