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The optical properties of the cobalt nanoparticles in the transparent condensed matrices
M. V. Ananyeva1, A. V. Kalenskii1, A. A. Zvekov2, A. P. Nikitin2, I. Yu. Zykov1
1Kemerovo state University, Kemerovo, 650043, Russia, 2Institute of Coal Chemistry and Material Science SB RAS, Kemerovo, 650000, Russia
kriger@kemsu.ru
PACS 61.46.+w, 82.33.Vx DOI 10.17586/2220-8054-2015-6-5-628-636
The absorption and scattering efficiency factors for cobalt nanoparticles over wavelengths ranging from 400 -1200 nm were calculated. The maximum values and corresponding radii of the absorption efficiency were shown to be dependent upon the incident light wavelength. The highest scattering factor values in the studied spectral range were between 2.2 and 2.4. If the absorptivity of the matrix increases, absorption of the light by cobalt nanoparticles begins to dominate over scattering process. The obtained results allow us to predict the optical properties for composite materials based on a transparent matrix with cobalt nanoparticles, which is essential for the accurate modeling of such systems' behavior under laser irradiation.
Keywords: optical properties, Mie theory, nanoparticles, cobalt, composite materials, laser irradiation. Received: 5 July 2015 Revised: 27 September 2015
1. Introduction
Nanoparticles have unique thermochemical, physical and optical properties. Their inclusion into condensed matrices significantly changes the properties of the obtained composite materials. The composites, based on metal nanoparticles and transparent matrix, are of the great interest for the optical physics and optoelectronics [1]. Both experimental and theoretical investigations of such composites' optical properties are presented in [2-4]. The problem is important today because of the possible practical use of the absorption and scattering of light by nanoparticles in timing devices of nonlinear optical equipment [5], application to the thermal cancer therapy, and optical detonators [6,7].
It is known that iron-group element nanoparticles may be used in the high-speed optical devices [7, 8]. Aluminium nanoparticles in pentaerythritol tetranitrate (PETN) reduce the explosive decomposition threshold by more than 100-fold in case of initiation by the first and second harmonics of the Nd:YAG laser [6,9,10]. The possibility of using cobalt nanoparticle-based composites in secondary explosives as an optical detonator cup was mentioned in [3,11,12]. Methods for synthesizing cobalt nanoparticles with definite sizes have been previously described [13]. In order to calculate the illumination intensity in the composite's volume, it is necessary to take into account multiple scattering of light by the metal nanoparticles [14,15]. This point was verified experimentally for the pressed PETN-aluminium pellets [4]. In order to find the optimal material for an optical detonator cup and compositions for the nonlinear optical equipment, it is necessary to calculate the relationships of the absorption and scattering efficiency factors by varying particle size and the wavelength of the incident light [16].
2. Calculation procedure and Results
The interaction of metal nanoparticles and electromagnetic radiation is traditionally described by using the absorption efficiency (Qabs) and scattering efficiency factors (Qsca). These dimensionless parameters are equal to the ratio of the particle's cross-section and its geometrical cross-section Q = a/ag. The Qabs was calculated in terms of Mie theory as the difference of the absorption efficiency (Qext) and scattering efficiency factors (Qsca) [16-18].
The main parameters of the theory are the complex refractive index (m) of cobalt, which depends on the wavelength of the incident light (A), and the refractive index of the medium (m0) [19]. These data over the range 400 - 1210 nm with increments of ~ 100 nm are presented in [20]. In order to calculate the absorption and scattering efficiency factors for the wavelengths, which were not presented in [19], work we used the spline interpolation with 1 nm increments, obtaining a smooth dependence m^(A) in this manner [18,19]. The range of nanoparticle radii studied is dictated by their potential use in optic initiation systems where values of 20 < R < 200 nm are utilized.
Figures 1 and 2 show the dependences of the absorption efficiency (Qabs) and scattering efficiency factors (Qsca) respectively on the cobalt particle's radius in a transparent medium with mo equal to 1.54 calculated for the light wavelengths of 400, 600, 800, 1000, and 1200 nm.
Fig. 1. The dependence of the absorption efficiency factor of the cobalt nanoparticles in the PETN matrix on their radius for the wavelengths in nm presented in the legend.
This refractive index was chosen as a typical value for dielectric media and is equal to the refractive index of pentaerythritol tetranitrate (PETN), which is one of the most important compounds among secondary explosives. As seen, Qabs values increase for small particle radii values and tend to steady-state value with oscillations in the R ^ ro limit [21,22]. The dependence has a well-marked maximum which tends to shift to larger radii when the wavelength increases. At the same time, the maximum's amplitude decreases significantly. The dependence Qsca vs. R increases for the small radii, then it achieves constant value and remains close to that value with minor fluctuations. The curve Qsca(R) has several local maxima. One can see the shift of the principal maximum position in Fig. 3. Enumerating the maxima from
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............I.............. ---- 600
/ / / J jt* - 800 ...... 1000
j _y<Ê ■ffiUll-"^! • 1200
50
100
150
R, nm
200
Fig. 2. The dependence of the scattering efficiency factor of the cobalt nanopar-ticles in the PETN matrix on their radius for the wavelengths in nm presented in the legend.
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i ■• ; / .............UlL - 1 — 1.25 —■ 1.5 1.75 2
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0 50 100 150 200
R, nm
Fig. 3. The dependence of the scattering efficiency factor of the cobalt nanopar-ticles for of the second harmonics of Nd:YAG laser irradiation. The refractive indexes of the media are 1, 1.25, 1.5, 1.75, and 2
small to higher R values it is seen that for A > 463 nm, the principal maximum is the first one, while in the spectral range A < 463 nm the highest maximum is the second one.
Figures 3 and 4 show the dependences of the absorption and scattering efficiency factors of the cobalt nanoparticles upon their radii for 532 nm light and for different refractive indices. This value of A coincides with the second harmonics wavelength for the Nd:YAG laser, which is widely used in many applications [6-8]. The displays show that increasing the medium's refractive index results in an increase of the maximum amplitude for Qabs(R) and a shift to smaller radii values. The increasing of the refraction index of the media results in the shift
3
1
2.5
1.25 1.5 1.75
2
2
1.5
1
0.5
0
0
50
100
150
200
R, nm
Fig. 4. The dependence of the cobalt nanoparticle absorption factor in case of irradiation of the second harmonic of Nd:YAG laser, refractive indexes of the media are 1, 1.25, 1.5, 1.75, and 2
of the initial ascending part of the Qsca(R) curve to the smaller radii values. Additionally, the oscillations' amplitude decreases for larger particle radius values and one can see a small decrease for the Qsca stationary value when R ^ œ.
Based on the data presented above, the maximum values of absorption (Qabs max) and scattering efficiency factors (Qscamax) were calculated for cobalt nanoparticles for different wavelengths. These calculations for the positions of the maxima were done assuming a refractive index 1.54 for the medium. The results are presented in Table 1. These data show that the absorption exceeds the scattering for shorter wavelength values. The maximum values of absorption and scattering efficiency factor coincide for cobalt nanoparticles at a wavelength of 482.5 nm. Increasing of wavelength from 400 up to 1200 nm results in monotonic Qabsmax(A) decreasing in ~ 2.2 fold, from 2.6589 to 1.2065. If the wavelength increases, the radius of the particles with the largest absorption efficiency factor (Rabs max) increases linearly from 27.7 nm for A = 400 nm up to 111.5 nm for A = 1200 nm. For Qscamax(A), this dependence is dissimilar. Qsca max is almost independent of the wavelength and shows small oscillations in the vicinity of the stationary value. For all wavelengths, the values of Qscamax(A) are 2.1992 - 2.3371, and the minimum is observed at A = 471 nm. The radius of the nanoparticles having the greatest scattering efficiency factor for a given wavelength (Rsca max) increases from 73.3 nm to 105.3 nm in the 400 < A < 550 nm range and from 63.2 nm to 136.3 nm in the 575 < A < 1200 nm range. In the 550 - 575 nm wavelength range, a two fold decreasing of Rscamax values was observed. This might be explained by the fact that in the 400 < A < 550 nm range, the second maximum dominates for the Qsca(R) dependence, and if the wavelength is longer than 550 nm, the first one dominates.
The contributions of the harmonics to the scattering efficiency factor were calculated for a wavelength of 532 nm and m0 = 1.54 in an attempt to explain the shift of the maximum (Fig. 5). Letters c denotes the electric-type oscillations of the electron density on the surface of the metal, letters b - magnetic-type oscillations. The figures show the harmonics index: 1 -dipole, 2 - quadrupole, 3 - octopole, etc. One can readily see that when the radius of the cobalt nanoparticles is less than 70 nm, the first electric oscillation predominates. When the radius
Table 1. Spectral regularities for maximum absorption and scattering factor values for cobalt nanoparticles
Л, nm mi Qabs max Rabs max, nm Qsca max Rsca max, nm
400 1.2000 - 3.0000i 2.6589 27.7 2.3371 73.3
450 1.5070 - 3.1721i 2.3400 33.5 2.2070 85.0
500 1.7000 - 3.4000i 2.1355 38.9 2.2079 95.3
532 1.7932 - 3.5609i 2.0249 42.2 2.2286 101.7
550 1.8430 - 3.6529i 1.9662 44.1 2.2402 105.3
600 2.0000 - 3.9000i 1.8172 49.4 2.2777 66.0
650 2.2148 - 4.1164i 1.6973 54.9 2.2787 71.8
700 2.4500 - 4.3000i 1.6086 60.3 2.2613 77.8
750 2.6628 - 4.4567i 1.5434 65.6 2.2469 83.7
800 2.8700 - 4.6000i 1.4907 70.9 2.2333 89.6
850 3.0914 - 4.7444i 1.4432 76.2 2.2196 95.6
900 3.3000 - 4.9000i 1.3978 81.4 2.2134 101.4
950 3.4667 - 5.0719i 1.3528 86.5 2.2191 107.2
1000 3.6000 - 5.2500i 1.3096 91.6 2.2304 112.9
1050 3.7178 - 5.4203i 1.2708 96.5 2.2411 118.7
1064 3.7505 - 5.4647i 1.2611 97.9 2.2433 120.3
1100 3.8381 - 5.5688i 1.2391 101.5 2.2463 124.5
1150 3.9789 - 5.6816i 1.2170 106.5 2.2421 130.4
1200 4.1580 - 5.7446i 1.2065 111.5 2.2255 136.3
increases, the contribution of the second electric and the first magnetic oscillations become noticeable, these oscillations become dominant when R > 100 nm. Competition between the electric and magnetic oscillations results in two different effects:
i) the maximum on the dependence Qabs(R) shifts with increasing wavelength;
ii) local maxima for the dependence Qsca (R) have almost the same amplitude and for large cobalt nanoparticle radii; there is almost no dependence on R. Since there are several oscillations of comparable intensity, their sum changes only slightly.
Figures 6 and 7 present spectral dependencies of the absorption and scattering efficiency factors for cobalt nanoparticles of different radii in a PETN matrix. The line descriptions and radii values are represented on the legend. For 30 nm nanoparticles, Qabs decreases monoton-ically. For the 50 nm nanoparticles, a maximum for Qabs occurs at 553 nm and that of the scattering efficiency factor at 400 nm. Increasing the nanoparticle radius causes the appearance of a second maximum. It is worth pointing out the difference between our results and those obtained for gold nanoparticles [16]. Spectral regularities of the latter have a narrow band (half-width ~ tens nm) due to plasmon resonance. In the case of cobalt, there are wide bands in the absorption spectra and scattering efficiency factor, as for other iron-group elements [7,8,15].
In the visible region of the spectrum and for larger cobalt nanoparticles, the standard deviation of the absorption and scattering factors is about 10-20 %. The weak dependence
2.5 I bsca
1.5
0.5
i
% h
b 1 I
b
h 4
/K
/ [ \ -
50 100 150
R, nm
Fig. 5. Dependences of electric (c) and magnetic (b) oscillations of the scattering factor upon the cobalt nanoparticle radius at 532 nm
Fig. 6. Spectral dependencies of the absorption efficiency factors for cobalt nanoparticles with 30, 50, 70, and 100 nm radii
of the mentioned parameters upon the wavelength proves that the composite materials, based on the transparent media and cobalt nanoparticles with radius of ~ 100 nm, are neutral-density filters. So, this differs from the gold or silver colloidal solutions, which are colored and are used as a band-pass filter. Thus, it appears that a light filter with cobalt nanoparticles decreases the light's intensity primarily by scattering but not because of the absorption.
Figure 8 displays the calculated spectral regularities for the absorptivity of 1.5 nm cobalt nanoparticles and the experimental values of the molar absorptivity e presented in [23]. The figure shows that the absorption predominates considerably over the scattering and the comparison of the extinction and the absorption is incorrect. As it follows from Fig. 8, in both cases, decreasing the wavelength results in increased absorptive properties. The region of
Fig. 7. Spectral dependencies of the scattering efficiency factors for cobalt nanoparticles with radii of 30, 50, 70, and 100 nm
Fig. 8. Experimental spectral regularities for the molar absorptivity of 2 - 4 nm radii cobalt nanoparticles (1) [23]; calculated spectral regularities of the absorption factor for 1.5 nm radii cobalt nanoparticles (2)
the increase coincides, but the quantitative results do not coincide because of the three reasons. First, cobalt is partially lost during the synthesis (yield is always less than 100 %), this makes the calculated molar absorptivity larger than that which is observed. Second, cobalt nanoparticles are covered by a mixed oxide-hydroxide film [13]. Third, the existing size distribution of the particles can distort the spectrum. When these considerations are taken into account, the calculated values and the experimental results are in good agreement.
3. Conclusion
The absorption and scattering of light by cobalt nanoparticles with variation of wavelength and radius values was studied in terms of Mie theory. The optimal nanoparticles' radii performing maximal absorption and scattering efficiency factors, which are of practical interest in different applications including light filters and optic detonators, were determined for different wavelengths. The spectral dependencies of cobalt nanoparticles' scattering and absorption efficiency factors show wide bands or continuum spectrum, thus exhibiting a vast difference relative to gold or silver nanoparticles.
Acknowledgments
This work was supported by Ministry of Education and Science of the Russian Federation (governmental project No. 2014/64), grant of the Russian President (MK-4331.2015.2) and Russian Foundation for Basic Research for the financial support (grant 14-03-31648).
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