Nano-Structures & Nano-Objects 12 (2017) 57–67
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Characterization of plasmonic and thermo-optical parameters of spherical metallic nanoparticles Liudmila G. Astafyeva a , Victor K. Pustovalov b, *, Wolfgang Fritzsche c a b c
B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Nezavisimosti pr. 68, 220072, Minsk, Belarus Belarusian National Technical University, Nezavisimosti pr. 65, Minsk, 220013, Belarus Leibniz Institute of Photonic Technology, A.-Einstein-Str. 9, 07745 Jena, Germany
article
info
Article history: Received 15 March 2017 Received in revised form 16 August 2017 Accepted 29 August 2017
Keywords: Nanoparticle Metallic Properties Laser Nanotechnology
a b s t r a c t The metallic nanoparticles are widely applied recent years as photothermal agents in laser and optical nanotechnology for light-to-heat conversion, treatment of materials containing NPs, laser nanomedicine, radiation chemistry and catalysis due to their plasmonic and thermo-optical properties. The influence of nanoparticle (NP) parameters - type of NP metal (aurum, silver, platinum, cobalt, zinc, nickel, titanium, cuprum, aluminum, molybdenum, vanadium, palladium), NP radius, optical indexes of NP metal, characteristics of radiation (wavelength, pulse duration) on plasmonic and thermo-optical properties has been investigated. The dependencies of efficiency factors of absorption Kabs , scattering Ksca and extinction Kext and thermo-optical parameter for pulse durations of 1 ps, 10 ns have been investigated on wavelength in the spectral interval 200–1000 nm. The indicatrixes of scattered radiation in the spectral interval 350–570 nm by NPs with the radii in the range 10–100 nm were analyzed. It is established that maximal value of thermo-optical parameter (maximal NP temperature) can be achieved with the use of the value of Kabs smaller than its maximal value on the dependence of radiation pulse duration and NP radius. This paper presents a platform for the characterization and the selection of the plasmonic and thermooptical properties of metallic NPs for their photonic and photothermal applications. © 2017 Published by Elsevier B.V.
1. Introduction In recent years research efforts have been focused on the investigation of unique size-dependent physical and chemical properties of the metallic nanoparticles (NPs) caused by NP–radiation interaction [1–46]. The properties of metallic NPs that NPs exhibit during their interaction with radiation can create prospects for their wide applications. Optical or laser radiation interacts, first of all, with electrons in metallic NPs [30,31]. The light-metallic NP interaction is determined by localized surface plasmon resonances (LSPRs) with charge-density oscillations on the NP surfaces [1–8]. The position in the wavelength spectrum and amplitude strength of the SPR in a nanosphere determines the optical properties of plasmonic NPs including absorption, scattering and extinction of radiation by NPs [1–8,41–46]. Metallic NPs have the ability to strongly scatter and absorb light at LSPR wavelengths. The absorption of radiation energy by electrons in metallic NPs, electron–phonon coupling and NP heating, heat dissipation
* Corresponding author.
E-mail addresses:
[email protected] (L.G. Astafyeva),
[email protected] (V.K. Pustovalov). http://dx.doi.org/10.1016/j.nanoso.2017.08.014 2352-507X/© 2017 Published by Elsevier B.V.
and exchange with an ambience, and the following thermal and accompanied phenomena induced by the radiation–NP interaction have become increasingly important topics in optical and laser nanotechnology [9–35]. The advances in photo-thermal (PT) nanotechnology, mainly based on the thermal effects, NPs heating and the processes induced by the laser–nanoparticle interaction, have demonstrated their immense potential. There are numerous reasons for the PT applications of NPs in different fields. The conversion of absorbed energy into NP thermal energy, heating of both NP itself as well as the ambient medium [9–15] and following PT phenomena [16–35] is determined by high absorption of radiation by NPs. The PT use of NPs and optical (laser) radiation demonstrated their great potential for laser nanobiomedicine [16–21], radiation chemistry [22,23], laser processing of metallic NPs in nanotechnology [24–29], in nanoscale opto-electronics [30,31], etc. The absorption and the scattering of radiation by NPs is used for optical diagnostics and imaging applications [8,32–35]. The characterization and the selection of appropriate plasmonic and thermo-optical properties of various NPs determines the efficiency of the successful NP applications in photonics and PT nanotechnology depends on a range of NP parameters, and its
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optimization needs. The attempts to search for novel and better plasmonic NPs on the base of NP parameter optimization, the improvement of NPs design for the achievement of ‘‘ideal’’ optical characteristics have been carried out in recent years [36–40]. The possibilities of NP applications are based on their plasmonic effects and nonlinear optical properties. The optical properties of metallic NPs, that are mostly interesting for different nanotechnologies among other NPs, have been investigated [1–8,36–46] including gold [1,5–8] and silver [2,4,41–43,46] NPs. The optical properties of metallic NPs are governed primarily by coherent oscillations of conduction-band electrons. But other metallic NPs (for example, Mo, Ti, Zn, Co, Cu, etc.) have not been sufficiently investigated in [1–8,41–46]. A comparative analysis of optimal parameters and characterization of various metallic NPs for using them as active agents in PT and laser nanotechnology is still missing. The characterization of plasmonic and thermo-optical properties and parameters of spherical metallic NPs of aurum, silver, platinum, cobalt, zinc, nickel, titanium, cuprum, aluminum, molybdenum, vanadium and palladium were theoretically investigated and analyzed on the base of computer modeling. The influence of the NP and radiation parameters on the thermo-optical characteristics of NPs was investigated. 2. Plasmonic and thermo-optical parameters of nanoparticles Next characteristics of NP, solar radiation and ambient medium are of special interest for the light–NP interaction: (1) laser (optical) radiation—(a) pulse duration tP , (b) wavelength λ, (c) radiation exposure (fluence) E0 , intensity I0 = E0 /tP ; (2) spherical nanoparticle—(a) type of NP metal (material) with its thermophysical (density ρ0 , heat capacity c0 ) and optical indexes of refraction n0λ and absorption ~0λ , (b) NP radius r0 ; (3) surrounding medium— (a) coefficient of thermal conductivity k∞ , (b) optical index of refraction nλ. Optical properties of a single NP are determined by the efficiency factors of absorption Kabs , scattering Ksca and extinction Kext of radiation by NP [1]. The parameter determines P1 = Kabs /Ksca
(1)
the correlation between absorption and scattering of radiation by NP. In the cases of predominant role of absorption P1 is greater than 1, P1 > 1 (or P1 ≫ 1) and the factor of absorption Kabs is greater (or much greater in favorable cases) than the scattering factor Ksca . This situation allows to achieve maximal absorption and minimal scattering of radiation by NP and maximal efficiency of solar radiation interaction with NP for its heating [13,15]. Thermo-optical properties of NPs can be determined by the parameter ∆T0 /E0 [13,15]
∆T 0 E0
τ0 =
=
Kabs r0 4k∞ tP
[
(
1 − exp −
tP
τ0
)] (2)
ρ0 c0 r02
–characteristic time for heating and cooling of NP. This 3k∞ parameter determines the maximal increase of NP temperature ∆T0 = Tmax − T∞ under action of radiation fluence with value E0 = 1 J/cm2 , Tmax —maximal temperature of NP at t = tP , T∞ — initial NP temperature. For tP < τ0 and tP > τ0 the parameter ∆T0/ E0 will be approximately determined by (see (2)): tP < τ0 tP > τ0
∆T0 E0 ∆T0 E0
≈ ≈
3Kabs 4ρ0 c0 r0 Kabs r0 4k∞ tP
(3a) (3b)
Combinations Kabs (r 0 )/r 0 and Kabs (r0 )r0 in (3) determine the range of radii r 0 appropriate for the achievement of the maximal value of ∆T0 under fixed values of λ, Kabs (λ). The parameter of ∆T0 /E0 does
not depend on parameters of radiation (tP ) and ambience (K∞ ) in Eq. (3a) and on the NP parameters c 0 , ρ 0 in (3b). The selection of mentioned parameters of NP and radiation in (3, 4) can provide maximal values ∆T0 for concrete values of E 0 . Main characteristics of radiation scattering by NP are efficiency factor of scattering Ksca and angular distribution of scattered radiation in space Isca (Θ ) (so called indicatrix, is angle of observation), that determine the application of scattering in various fields [8,32–35]. Extinction of optical radiation by NP is determined by factor Kext , which is used in optical investigations and applications [41–46]. Comparative analysis of plasmonic and thermo-optical properties of metallic NPs includes the following set of characteristics of the laser–NP interaction processes: efficiency factors of absorption Kabs , scattering Ksca , and extinction Kext of radiation by spherical NP, parameter P1 (1), parameter ∆T0 /E0 (2), angular distribution of scattered radiation in space Isca (θ ). 3. Calculation of NP plasmonic and thermo-optical parameters and their characterization The efficiency factors for absorption Kabs , scattering Ksca and extinction Kext of radiation with wavelength λ in the spectral interval λ = 200–1000 nm by spherical homogeneous metallic NP have been numerically calculated on the base of generalized Mie theory [1]. Values of optical indexes of refraction and absorption of metals and surrounding medium (water) were used from [47,48]. The considered surrounding water is temperature insensitive in terms of refractive index. Presented theoretical model can be extended to temperature sensitive media in terms of refractive index taking into account the temperature dependence of refractive index for the calculation of efficiency factors by Mie theory. The preparation of metallic nanoparticles with the perfect spherical nanostructure and precise radius is widely realized and used [39,40,44]. The calculation and investigation of the dependencies of Kabs , Ksca , Kext , P1 and ∆T0 /E0 on λ for selected fixed values of r0 , tP and metallic NP were carried out as a first step. The investigation of the dependencies of Kabs , Ksca , Kext , P1 and ∆T0 /E0 on r0 for selected values of λ, tP and NP metallic was carried out as a second one. This attitude allows to present clear dependencies of Kabs , Ksca , Kext , P1 and ∆T0 /E0 on one parameter when other parameters are constant. Figs. 1–5 present the dependencies of Kabs , Ksca , Kext , P1 and ∆T0 /E0 on λ, r 0 , tP for metallic NPs. The range of pulse duration tP = 10 ns–1 ps is of great interest for laser applications in nanotechnology and we used two values of tP = 100 ps and tP = 1 ps. The calculations showed that the dependence ∆T0 /E0 (λ) for intermediate value of tP ∼ 100 ps practically coincide with this one for tP = 1 ps and the dependence ∆T0 /E0 (λ) for tP = 100 ps has not been presented in Figs. 1–5. The values of ∆T0 /E0 for tP ∼ 1 ps can be used as upper boundaries of NP heating for concrete value of E0 without NP heat exchange. We used three values of r0 = 10, 25, 50 nm, which are widely used in investigations [9–46]. max The positions of maximal values of efficiency factors of Kabs , max max Ksca , Kext on λ axis are denoted in Figs. 1–5 by different vertical max lines—locations λmax abs of maximal value of absorption factor Kabs max on axis λ are denoted by solid lines, Ksca —dashed lines at λmax sca , max Kext —dashed–dotted lines at λmax ext in the case of different values max max max max of λmax abs , λsca , and λext . In the case of equal values of λabs , λsca , max max max and λmax the location of coincident values of K , K , K ext sca ext are abs denoted by solid lines. In some cases additional solid lines mark the formation of new maxima of efficiency factors. Horizontal dashed lines in Figs. 1–4(d, h, l) denote the value of P1 = 1. Fig. 1 presents the dependencies of efficiency factors of Kabs , Ksca and Kext , parameters ∆T0 /E0 for tP = 10 ns, 1 ps and P1 for homogeneous metallic Au, Ag and Pt NPs with the radii r0 = 10, 25, 50 nm on wavelength λ.
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Fig. 1. Dependencies of factors Kabs (solid), Ksca (dashed) and Kext (dashed–dotted), parameter ∆T0 /E0 (dotted) for tP = 10 ns, 1 ps for the radii r0 = 10 (a, e, i), 25 (b, f, j), 50 (c, g, k) nm, and dependencies of parameter P1 (d, h, l) for the radii r0 = 10, 25, 50 nm for Au (a, b, c, d), Ag (e, f, g, h), Pt (i, j, k, l) NPs on wavelengths λ.
The dependencies of efficiency factors of Kabs , Ksca and Kext on
λ for fixed values of r0 have complicated forms for mentioned max metallic NPs. Values of Kabs are placed at λmax ∼ 510–530 nm abs max for Au NPs and λabs ∼ 380–410 nm for Ag NPs with r0 = 10, 25, 50 nm. Consequently the absorption of radiation is determined by plasmon resonances of silver and gold NPs in the field of electromagnetic (laser) radiation [1–8]. Values of Kabs are decreased in UV and NIR spectral intervals out of plasmon wavelengths and these values undergo sharp decrease up to 102 –103 times especially for Ag NPs. The values of Kabs for Au NPs undergo a slight decrease in the UV spectral interval in comparison with NIR spectral interval. The behavior of the dependencies of Ksca on wavelength λ is mainly analogous for the dependencies of Kabs (λ). Factor Ksca for Ag NPs max achieves the maximal value of about Ksca ∼ 11.7 for λ ∼ 413 nm,
r0 = 25 nm. The dependence of Kext on λ presents itself the sum of max max the dependencies of Kabs (λ) and Ksca (λ). Values of Kabs and Kext for Au, Ag NPs with r0 = 10 nm practically coincide with each other (see Fig. 1), when Kabs > Ksca . The values of Ksca are greater than Kabs for r0 = 50 nm. An increase of r0 may lead to an increase in max max the maximal values of Ksca and Kext . max max max The placements of maximal values of Kabs , Ksca and Kext on axis λ can be different in some cases (Fig. 1 c, g, k). The formation of additional maxima of Kabs , Ksca and Kext on axis λ can be connected with possible manifestation of higher order resonances (Fig. 1g, k for Ag and Pt NPs). The increase of NP radii to r0 = 50 nm shifts max max max the maximal values of Kabs , Ksca and Kext in the region of greater values of λ and this shift achieves the values of about ∆λmax ∼ 50 nm for Au NPs and of about ∆λmax ∼ 100 nm for Ag NPs.
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Fig. 2. Dependencies of factors Kabs (solid), Ksca (dashed) and Kext (dashed–dotted), parameter ∆T0 /E0 (dotted) for tP = 10 ns, 1 ps for the radii r0 = 10 (a, e, i), 25 (b, f, j), 50 (c, g, k) nm, and dependencies of parameter P1 (d, h, l) for the radii r0 = 10, 25, 50 nm for Pd (a, b, c, d), Mo (e, f, g, h), Cu (i, j, k, l) NPs on wavelengths λ.
The dependencies of Kabs , Ksca , Kext for Pt NPs with r0 = 10, 25, 50 nm more slowly decrease with increase of λ after achievement their maximal values in comparison with Au and Ag NPs. Factor Kabs > Ksca for r0 = 10, 25 nm and for whole spectral interval and as a result Kabs ∼ Kext and their dependencies practically coincide. Only for r0 = 50 nm, Ksca > Kabs in the narrow spectral interval of max max max 350–500 nm. First maxima of Kabs , Ksca , Kext has been observed for r0 = 25 nm at λ ∼ 270–290 nm. The formation of the light max second maximal of Kabs has been observed. Figs. 1–4 present spectral dependencies of the parameter ∆T0 /E0 (3) for pulse duration tP = 10 ns, 1 ps for NPs with radii r0 = 10, 25, 50 nm. The spectral dependence of ∆T0 /E0 (λ) is determined by the dependence of Kabs (λ) for all values of r0 because of dependence ∆T0 /E0 ∼ Kabs (λ) in Eqs. (2) and (3) The influence
of NP radius r0 on ∆T0 /E0 is directly determined by the dependence of Kabs (r0 ) and the value of r0 in (2), (3). The values of ∆T0 /E0 for tP = 10 ns are, as a rule, smaller in comparison with other ones for tP = 1 ps. It is determined by the influence of heat exchange of NP with surrounding medium during radiation pulse action with tP = 10 ns and larger. Maximal values of about (∆T0 /E0 )max ∼ 1.7 × 106 K cm2 J−1 for Ag NPs are observed for r0 = 10 nm, tP = 1 ps and NP heating can reach ∆T0 = 100 K under action of laser pulse with λ = 382 nm, tP = 1 ps, and E0 = 5.6 × 10−5 J cm−2 . It is connected with the max achievement of maximal values of Kabs for Ag NPs in comparison with the other studied NPs. The dependencies of P1 on λ are determined by the dependencies of Kabs and Ksca on λ. For Au NPs, the increase of r0 from
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Fig. 3. Dependencies of factors Kabs (solid), Ksca (dashed) and Kext (dashed–dotted), parameter ∆T0 /E0 (dotted) for tP = 10 ns, 1 ps for the radii r0 = 10 (a, e, i), 25 (b, f, j), 50 (c, g, k) nm, and dependencies of parameter P1 (d, h, l) for the radii r0 = 10, 25, 50 nm for Ni (a, b, c, d), V (e, f, g, h), Ti (i, j, k, l) NPs on wavelengths λ.
r0 = 10 nm to r0 = 50 nm leads to the decrease of the parameter P1 from the values of about P1 ∼ 20–300 for λ ∼ 300–1000 nm to values of about P1 ∼ 0.1–0.3 for λ ∼ 600–1000 nm. It means a sharp increase of radiation scattering by NPs with an increase of NP r0 . For Ag NPs, a sharp decrease of P1 with increasing of λ in the spectral interval λ ∼ 300–400 nm is observed, and P1 stays approximately constant in the interval λ ∼ 450–1000 nm. The dependencies of P1 on λ for Pt NPs increase with ascending λ for r0 = 10, 25 nm, and achieve values of P1 ∼ 3–200 for the whole spectral interval because of a sharp decrease of Ksca with increase of λ (see Fig. 1). A general feature for all presented dependencies of P1 (λ, r0 ) is the decrease of P1 with increasing of r0 for the whole spectral interval λ ∼ 200–1000 nm. Fig. 2 presents the dependencies of Kabs , Ksca and Kext , parameters ∆T0 /E0 for tP = 1·10−8 , 1·10−12 s, tp = 10 ns, 1 ps and P1 for Pd, Mo, and Cu NPs with the radii r0 = 10, 25, 50 nm on wavelength λ.
The spectral dependencies of Kabs , Ksca and Kext for Pd and Mo NPs have common features. The dependencies of Kabs and Kext are smooth enough, but the dependence of Ksca sharply decreases for all values of r0 . For Pd and Mo NPs (Fig. 2) maxima of max max max Kabs , Ksca , Kext are realized in the spectral regions 200–230 nm and 180–200 nm accordingly for r0 = 10 nm. These maxima of max max max Kabs , Ksca , Kext are shifted from the position at r0 = 10 nm to larger values of λ with increasing r0 and with formation of two max max max max weakly defined maxima of Kabs (Pd) and Kabs , Ksca , Kext (Mo) for r0 = 50 nm. For Mo and Pd NPs parameter P1 increases up to values of P1 ∼ 10–100 for r0 = 10, 25, 50 nm with increasing of λ in whole spectral range. But for the spectral intervals λ ≈ 300–600 nm (Pd) and λ ≈ 200–500 nm (Mo) the value of P1 is smaller than 1, P1 < 1 for r0 = 50 nm. Two maximal values of about (∆T0 /E0 )max = 1.105 K cm2 J−1 are realized in Fig. 2 for Mo and Pd NPs because of two max maxima of Kabs for r0 = 50 nm.
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Fig. 4. Dependencies of factors Kabs (solid), Ksca (dashed) and Kext (dashed–dotted), parameter ∆T0 /E0 (dotted) for tP = 10 ns, 1 ps for the radii r0 = 10 (a, e, i), 25 (b, f, j), 50 (c, g, k) nm, and dependencies of parameter P1 (d, h, l) for the radii r0 = 10, 25, 50 nm for Co (a, b, c, d), Zn (e, f, g, h), Al (i, j, k, l) NPs on wavelengths λ.
An interesting feature of the dependencies of Kabs , Kext on λ for Cu NPs with r0 = 10, 25 nm is a steep drop, with a weak dependence of Kabs , Kext on λ for the spectral interval of λ ≈ 300– 560 nm followed by a sharp fall of the dependencies of Kabs , Kext on λ for λ > 560 nm. The scattering factor Ksca monotonously decreases with growing λ for r0 = 10, 25 nm. For r0 = 10, 25 nm values of Kabs ≫ Ksca and dependencies of Kext and Kabs on λ are close to each other. There is one weakly defined maximal in these curves at 310 nm (r0 = 10 nm) and at 390 nm (r0 = 25 nm). More over the maxima of Kabs , Ksca and Kext have been observed at λ ∼ 560–590 nm with a sharp decrease of these factors with increase of λ. The parameter P1 for Cu NPs has the values of P1 ∼ 10–100 for r0 = 10, 25 nm and a complex behavior for increasing λ. For spectral intervals λ ≈ 600–1000 nm the value of P1 is less than 1,
max max max P1 < 1 for r0 = 50 nm. The positions of Kabs , Ksca and Kext for Pd, Mo, and Cu NPs differ for r0 = 25, 50 nm slightly (Fig. 2). Fig. 3 presents the spectral dependencies of Kabs , Ksca and Kext , parameters ∆T0 /E0 for tP = 10 ns, 1 ps and P1 for Ni, V and Ti NPs with radii r0 = 10, 25, 50 nm. The spectral dependencies of efficiency factors of Kabs , Ksca and Kext for Ni, V and Ti NPs for the radii r0 = 10 nm and 25 nm are smooth curves with maxima in the UV region. All factors slowly decrease with increasing wavelength till 1000 nm after achievement of small maxima. max max max A first feature is the shift of the values of Kabs , Ksca and Kext to larger values of λ, a second one is the shift between the placements max max max max max of λmax abs , λsca and λext of Kabs , Ksca and Kext on λ with increasing NP radius. A third feature is the formation of a weakly defined max second maximal of Kabs (V) at λ ≈ 480 nm for r0 = 50 nm.
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Fig. 5. Dependencies of Kabs (solid), Ksca (dashed) and Kext (dashed–dotted) – all these lines refer to the left axis – and thermo-optical parameter ∆T0 /E0 (dotted lines refer to the right axis) for tP = 10 ns, 1 ps for NPs—Au, λ = 532 nm (a), Ag, λ = 400 nm (b), Pt, λ = 500 nm (c), Cu, λ = 570 nm (d), Pd, λ = 470 nm (e), Ti, λ = 500 nm (f), Ni, λ = 470 nm (g), Zn, λ = 350 nm (h) on r0 .
The parameters P1 for Ni, V, Ti NPs for the radiation spectral interval λ ≈ 150–1000 nm are larger than 1, P1 > 1, r0 = 10, 25, 50 nm, instead of narrow interval λ ≈ 200–480 nm for V NPs with r0 = 50 nm. More over, for r0 = 10, 25 nm parameters P1 achieve the values of P1 ≈ 10–500 with increasing λ in IR interval. Maximal values of (∆T0 /E0 )max = 4.105 K cm2 J−1 are realized for Ni, V, Ti NPs with r0 = 10 nm and a little bit smaller for NPs with r0 = 25, 50 nm. It means that Ni, Ti, V NPs are good absorbers of radiation in wide range of ultraviolet, visible and infrared optical spectrum and can be used for light-to-heat conversion and thermooptical applications.
Fig. 4 presents the spectral dependencies of Kabs , Ksca and Kext , parameters ∆T0 /E0 for tP = 10 ns, 1 ps and P1 for Co, Zn and Al NPs with the radii r0 = 10, 25, 50 nm. The spectral dependencies of Kabs , Ksca and Kext have common features for Zn and Al NPs with significant differences for Co NPs. Spectral dependencies of efficiency factors of Kabs , Ksca and Kext for Co nanoparticles are smooth and have defined maximal located in UV region of spectra for r0 = 10, 25 nm at λ ≈ 230–300 nm. For r0 = 50 nm Co NPs with r0 = 10, 25, 50 nm are good absorbers and inefficient scatterers for all spectral interval of λ ≈ 200–1000 nm, instead of a small interval for r0 = 50 nm. The maximum of absorption is positioned in the UV region of spectra at λ ≈ 300 nm,
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and the maxima of scattering and extinction have been shifted to the visible region of spectrum to λ ≈ 450 nm. For Zn and Al NPs the spectral dependencies of Kabs , Ksca and Kext show strongly defined maxima located mainly in the UV. We max max note the shifting of Ksca , Kext to larger values of λ in comparison max with positionKabs for Zn and Al NPs with simultaneous formation of oscillation structure of the Kabs dependence on λ with increase of r0 till r0 = 50 nm. Maximal values of absorption and scattering Al NPs are close for r0 = 10 nm, then for r0 = 25 and 50 nm maximal values of scattering are essentially higher than absorption. We have to note the sharp decrease of Ksca for Co, Zn and Al NPs with increasing of the radii r0 = 10, 25, 50 nm. Zn NPs with r0 = 10, 25 nm are good absorbers and bad scatterers for whole spectral interval of λ ≈ 200–1000 nm. The parameter P1 for Al NPs is smaller than one (P1 < 1) in the interval of λ ≈ 200–500 nm and larger than 1 (P1 > 1) in the range of λ ≈ 500–1000 nm for r0 = 25 nm. It means that Al NPs are good scatterers in one interval and good absorber in other one. The parameter P1 for Al NPs is smaller than one (P1 < 1) for r0 = 50 nm in the whole interval of considered wavelengths. The value of thermo-optical parameter achieves the maximal value (∆T0 /E0 )max ≈ 1.5 × 106 K cm2 J−1 at λmax abs ≈ 190 nm for Al NPs with r0 = 10 nm. Fig. 5 presents the dependencies of efficiency factors Kabs , Ksca , Kext , and thermo-optical parameter ∆T0 /E0 for tP = 10 ns, 1 ps on r0 for metallic NPs and fixed values of λ – Au, λ = 532 nm; Ag, λ = 400 nm; Pt, λ = 500 nm; Cu, λ = 570 nm; Ti, λ = 500 nm; Pd, λ = 470 nm; Ni, λ = 470 nm; Zn, λ = 350 nm. The locations of max maximal values of Kabs (r0 ) and (∆T0 /E0 )max (tP , r 0 ) on r0 axis are denoted by vertical lines (solid and dotted accordingly). The choice of mentioned wavelengths has been determined by their location close to plasmon wavelengths for these NPs (see Figs. 1–4) with r0 = 50 nm. The characteristic time τ0 (see (2)) is equal τ0 ∼ 1.2 · 10−10 − 1.2 · 10−8 s for the range of r0 = 10–100 nm and for ambient water with k∞ = 6 · 10−3 W/cm K [49], for example, τ 0 ∼ 0.9 ns for r0 = 25 nm. The separate dependencies of ∆T0 /E0 only on r0 are the next one from Eqs. (3): tP < τ0
∆T 0 E0
∼
Kabs (r0 ) r0
tP > τ0
∆T 0 E0
∼ Kabs (r0 ) r0
(4)
We consider the results for Au (Fig. 5a) and Ag (Fig. 5b) NPs more closely. The condition of ‘‘short’’ pulses tp < τ0 is applicable for tP = 1 ps for all values of r0 : 5 < r0 < 100 nm presented in Fig. 5. Under condition of ‘‘short’’ pulses tP < τ0 , the parameter ∆T0 /E0 depends on the combination Kabs /r0 according Eq. (4). The value of ∆T0 /E0 slowly increases with increasing of Kabs and in spite of increase of r0. It achieves maximal value and - after that - decreases because of decreasing of Kabs and increasing of r0 (see Fig. 5a). The condition of ‘‘long’’ pulses with tP = 10 ns is fulfilled for the interval r0 = 5–90 nm. In this case the value of ∆T0 /E0 sharply increases (∼Kabs (r0 ) r0 ), achieves maximal value and after that slowly decreases because of decrease of Kabs in spite of increase of r0 . The oscillations of the dependence of Kabs (r0 ) influence on the behavior of ∆T0 /E0 (r0 ) for the Ag and Zn NPs. The use of ‘‘long’’ pulses with tP = 10 ns leads to a significant decrease of the value of ∆T0 /E0 by up to 1–2 orders in comparison with the values of ∆T0 /E0 for tP = 1 ps. It is determined by heat conduction losses from NP during irradiation with the value of tP = 10 ns and because of the dependence ∆T0 /E0 ∼ 1/tP (see (3)). The difference between the values of ∆T0 /E0 for tP = 10 ns and tP = 1 ps significantly decreases from ∼102 –101 times for r0 = 10 nm to ∼2–3 times for r0 = 100 nm. It can be additionally explained by a sharp increase of τ0 ∼ r02 , approaching of τ0 to tP = 10 ns and approximate fulfillment of short pulse condition (without heat loss) for r0 ≈ 90–100 nm and tP ≤ τ0 .
max max The maximal value of Kabs is equal Kabs ≈ 3.97 for r0 = 33 nm (Au, λ = 532 nm). The maximal values of (∆T0 /E0 )max ≈ 4.1 × 105 K cm2 J−1 are realized for tP = 1 ps at r0 ≈ 23 nm, Kabs ≈ 3.1, and (∆T0 /E0 )max ≈ 6 × 104 K cm2 J−1 for tP = 10 ns at r0 ≈ 39 nm, Kabs ≈ 3.7, (see Fig. 5a) for λ = 532 nm. The maximal values of max Kabs (r0 ) and (∆T0 /E0 )max (r0 ) have different locations on r0 axis for λ = 532 nm in Fig. 5a. The maximal values of (∆T0 /E0 )max have been shifted to smaller values of r0 for tP = 1 ps and to larger values of r0 for tP = 10 ns in comparison with the location of max Kabs (r0 ) in Fig. 5a. It means that for achieving of maximal values of (∆T0 /E0 )max under minimal values of E0 we have to use the values max of Kabs , which are smaller than Kabs mentioned above. The values of Ksca are smaller than the values of Kabs , Ksca < Kabs , P1 > 1 for r0 ≈ 0–50 nm and Ksca > Kabs , P1 < 1 for r0 ≈ 50– 100 nm. It means that gold NPs can be used as absorbers and scatterers in mentioned ranges of r0 accordingly. The values of Kext , Kabs are approximately equal, Kext ∼ Kabs , for the range of r0 ≈ 5– 20 nm and Kext > Kabs for r0 ≈ 20–100 nm. Fig. 5b presents the dependencies of Kabs , Ksca , Kext , ∆T0 /E0 (r0 , tP ) (3) for the pulse durations tP = 10 ns, 1 ps for Ag NPs and max λ = 400 nm on r0 . There are three maxima of Kabs with their decreasing values for an increase of r0 and correspondingly three maximal values of (∆T0 /E0 )max for tP = 1 ps in the range of r0 = 5–100 nm, placed at r0 ≈ 20, 58, 94 nm. These maxima can be possibly connected with the formation of quadrupole and octupolar plasmon resonances. The values of Ksca are larger than the values of Kabs , Ksca > Kabs , P1 < 1 for the range r0 ≈ 15–100 nm. It means that silver NPs can be used first of all as scatterers in the mentioned range of r0 . Maximal values of (∆T0 /E0 )max for Ag NPs are equal (∆T0 /E0 )max ≈ 9.2 × 105 K cm2 J−1 , tP = 1 ps, r0 ∼ 20 nm and (∆T0 /E0 )max ≈ 5.3 × 104 K cm2 J−1 , tP = 10 ns at r0 ∼ 21 nm in the range 5–30 nm (see Fig. 5b). Another two maxima of (∆T0 /E0 )max are placed in the range 30–100 nm. Oscillated dependencies of ∆T0 /E0 behave in an analogous manner to the dependencies of Kabs on r0 for the presented values of λ (see Fig. 5b). Values of ∆T0 /E0 for tP = 10 ns are smaller than the ones for tP = 1 ps for the whole range of max r0 = 5–100 nm. The values of shift between the locations of Kabs and (∆T0 /E0 )max for Ag NPs are smaller than in the case of Au NPs because of sharp dependencies of Kabs on r0 , for λ = 400 nm (see Fig. 5b), but in any case these shifts exist and noticeable. In general, the dependencies of Kabs , Ksca , Kext , ∆T0 /E0 on r0 for presented values of λ, tP for Pt, Cu, Pd, Ti, Ni NPs are analogous to the dependencies of Au NPs. It should be noted that Pt, Cu, Pd, Ni NPs are good absorbers for r0 ∼ 5–50 nm and good scatterers for r0 ∼ 50–100 nm. Ti NPs are good absorbers for the range r0 ∼ 5– 70 nm and only for r0 ∼ 70–100 nm Ti NPs absorb and scatter radiation equally. The dependencies of Zn NP parameters on r0 are analogous to the dependencies of Ag NPs. The formation of three plasmon resonance maxima of Kabs is observed—first a strong resonance at r0 ≈ 19 nm, and two more weaker resonances at r0 ≈ 52 and 83 nm. Zn NPs are bad absorbers and good scatterers for the practically important range r0 ≈ 30–100 nm and P1 τT . This observation represents a significant result for the thermo-optical applications of NPs in laser and photonics nanotechnology. Fig. 6 presents the angular distributions (optical indicatrixes) of radiation intensity Isca (θ ) scattered by metallic NPs with radii r0 = 10, 25, 50, 100 nm and for NPs—Au, λ = 532 nm; Ag, λ = 400 nm; Pt, λ = 500 nm; Cu, λ = 570 nm; Ti, λ = 500 nm; Pd, λ = 470 nm; Ni, λ = 470 nm; Zn, λ = 350 nm. The direction of laser radiation propagation is from left to right (from 180o to
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Fig. 6. Angular distributions (optical indicatrixes) of radiation intensity Isca scattered by metallic NPs with radii r0 = 10 (solid), 25 (dashed), 50 (dotted), 100 (dashed–dotted) nm and for the following combination of metals and radiation wavelengths: Au, λ = 532 nm (a), Ag, λ = 400 nm (b), Pt, λ = 500 nm (c), Cu, λ = 570 nm (d), Pd, λ = 470 nm (e), Ti, λ = 500 nm (f), Ni, λ = 470 nm (g), Zn, λ = 350 nm (h). The direction of laser radiation propagation is from left to right (from 180o to 0o ). Polar coordinates show angles for scattered radiation in the range 0o –360o .
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0o ). Polar coordinates show angles of observation θ for scattered radiation in the range of 0o –360o , NP is placed in the center of the each figure. The optical indicatrix of radiation scattered by NP shows the distribution of scattered radiation in outward space around NP depending on the angle of observation θ . The optical indicatrix depends on the diffraction parameter ρ = 2π r0 /λ and optical indexes of refraction and absorption of NP metallic (material). Diffraction parameter ρ for the NP radii in the range r0 = 5–100 nm are in the limits ρ = 0.06–1.18 for wavelength λ = 532 nm. For λ = 532 nm and for the size range of 5 < r0 < 80 nm, the diffraction parameter ρ < 1. The angular intensity function of scattered radiation by gold spherical NP appears symmetrical for both (forward and backward) hemispheres under the condition ρ 1. These results mean that gold NPs can be used as effective scatterers for optical diagnostics with λ = 532 nm, r0 = 50–100 nm. The amount of scattered radiation from NP sharply increases with an increase of NP radius r0 by up to 3–4 orders of value. The value of scattered radiation by various NP in direction of angle θ can be applied for the purposes of dark-field microscopy. The value of scattered intensity by NPs will be measured by an optical detector and so it can be used for a diagnostic assessment of the distribution and concentration of NPs. The results for Al, Co, V, Mo NPs do not present in Figs. 5 and 6 because these ones are analogous the presented results for other eight metallic NPs. 4. Discussion The investigations and analysis of plasmonic (Kabs , Ksca , Kext ) and thermo-optical (∆T0 /E0 ) characteristics of 12 metallic (Au, Ag, Cu, Pt, Co, Zn, Al, Ni, Ti, V, Pd, Mo) NPs for radiation wavelengths in the spectral interval 200–1000 nm and in the range of NP radii r0 = 10–50 nm have been conducted on the base of computer and analytical modeling (Figs. 1–4). Water was used as surrounding medium. Maximal values of Kabs were achieved for Au, Ag, Zn, max max Cu. The positions λmax abs , λsca and λext of the maximal values of max max max Kabs , Ksca and Kext on the wavelength axis λ do not coincide in some cases. Transformation of plasmonic (Kabs , Ksca , Kext ) and thermooptical (∆T0 /E0 ) properties in dependence on r0 in the range r0 = 10–50 nm for Au, Ag, Pt, Cu, Pd, Ti, Ni, Zn NPs and for some fixed radiation wavelengths is presented in Fig. 5. It was established that maximal values of ∆T0 /E0 and accordingly of NP temperature ∆T0 can be achieved when the value of absorption efficiency factor max Kabs is smaller than its maximal value of Kabs taking into account irradiation duration, characteristics of NPs and their cooling. The main goal of light-to-thermal energy conversion is to achieve maximal value of efficiency parameter of ∆T0 /E0 for NPs at minimal values of E0 . The influence of the parameters of radiation – tP , λ, E0 , NP – ρ0 , c0 , r0 , Kabs and surrounding medium—k∞ , nλ on maximal value of ∆T0 /E0 has been investigated on the base of an analytical model. It is possible to achieve the maximal values of about ∆T0 /E0 ∼ 1 · 106 K cm2 J−1 for tP ≤ 1 · 10−10 s under radiation energy density E0 = 1 · 10−3 J/cm2 and the heating of such NP could achieve 1 · 103 K. All presented metallic NPs exhibit high absorbance and parameter P1 reaches P1 ≥ 100 for all metallic NPs with r0 = 10 nm and in part P1 > 1 for some spectral intervals (Figs. 1–4). Increasing of r0 leads to an increase in scattering and decrease in absorbance for all presented metallic NPs. The values of P1 are smaller than 1 for Co, Mo, Pd, Zn NPs with r0 = 50 nm instead of spectral interval 600 < λ < 1000 nm. But for Ni and Ti NPs the parameter P1
is larger than 1, P1 > 1, for whole interval 200–1000 nm. It is interesting to note that Zn and Al NPs with r0 = 25 nm can be used as absorbers in the wavelength interval 600 < λ < 1100 nm and as scatterers in the wavelength interval 200 < λ < 600 nm. The value P1 ∼ 1 means approximately equal possibility of use NP as absorber and scatterer simultaneously. The indicatrixes (Fig. 6) describe the distribution of scattered by NP radiation in the space and can be used in optical diagnostics. 5. Conclusions The strongly enhanced absorption and scattering of radiation by spherical metallic NPs makes them a novel and highly effective class of contrast agents for PT applications and thermoplasmonics. The efficiency factors of absorption Kabs , scattering Ksca and extinction Kext of radiation by NP, parameters of P1 and ∆T0 /E0 , indicatrix of scattered radiation should be selected and optimized for the success in mentioned fields. Our results allow estimate optimal characteristics of radiation absorption and scattering by metallic NPs and light-to-heat conversion into photothermal phenomena by selection of the NP and radiation parameters and ambience properties. We present a platform for the characterization and selection of the appropriate plasmonic and thermo-optical properties of a wide range of metallic NPs for their photonic and thermo-plasmonic applications. Acknowledgment This article is partially supported by BMBF project WTZ-BASE (FKZ 01DK15012). References [1] C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, New York, 1983. [2] U. Kreibig, M. Vollmer, Optical Properties of Metallic Clusters, in: Springer Series in Material Science, vol. 25, Springer, Heidelberg, 1995. [3] M. Quinten, Optical Properties of Nanoparticle Systems: Mie and Beyond, Wiley-VCH Verlag GmbH & Co, New York, 2011. [4] I. Mayergoyz, Plasmon Resonances in Nanoparticles, World Scientific Publishing, Singapore, 2013. [5] V.K. Pustovalov, V.A. Babenko, Optical properties of gold nanoparticles at laser radiation wavelengths for laser applications in nanotechnology and medicine, Laser Phys. Lett. 1 (2004) 516–520. [6] E.A. Coronado, E.R. Encina, F.D. Stefani, Optical properties of metallic nanoparticles: manipulating light, heat and forces at the nanoscale, Nanoscale 3 (2011) 4042–4054. [7] Y. Sonnefraud, A. Koh, D. McComb, S. Maier, Nanoplasmonics: Engineering and observation of localized plasmon modes, Laser Photonics Rev. 6 (2012) 277– 295. [8] A. Crut, P. Maioli, N. Del Fatti, F. Vallée, Optical absorption and scattering spectroscopies of single nano-objects, Chem. Soc. Rev. 43 (2014) 3921–3956. [9] S. Joseph, S. Mathew, G. Sharma, M. Hari, A. Kurian, P. Radhakrishnan, V.P.N. Nampoori, Phototermal characterization of nanogold under conditions of resonant excitation and energy transfer, Plasmonics 5 (2010) 63–68. [10] H. Chen, L. Shao, T. Ming, Z. Sun, C. Zhao, B. Yang, J. Wang, Understanding the photothermal conversion efficiency of gold nanocrystals, Small 6 (2010) 2272– 2280. [11] K. Jiang, D.A. Smith, A. Pinchuk, Size-dependent photothermal conversion efficiencies of plasmonically heated gold nanoparticles, J. Phys. Chem. C 117 (2013) 27073–27078. [12] H. Zhang, H.-J. Chen, X. Du, D. Wen, Photothermal conversion characteristics of gold nanoparticle dispersions, Sol. Energy 100 (2014) 141–147. [13] V.K. Pustovalov, Light-to-heat conversion and heating of single nanoparticles, their assemblies, and surrounding medium under laser pulses, Review, RSC Adv. 6 (2016) 81266–81289. [14] G. Baffou, R. Quidant, Thermo-plasmonics: using metallic nanostructures as nano-sources of heat, Laser Photonics Rev. 7 (2013) 171–187. [15] V. Pustovalov, L. Astafyeva, W. Fritzsche, Selection of thermo-optical parameter of nanoparticles for achievement of their maximum thermal energy under optical irradiation, Nano Energy 2 (2013) 1137–1141. [16] L. Kennedy, L. Bickford, N. Lewinsky, A. Coughlin, Y. Hu, J. West, R. Drezek, A new era for cancer therapy: gold nanoparticle-mediated thermal therapies, Small 7 (2010) 169–183.
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