Calculation Of The Optical Characteristics Of Cuo Nanocomposite By Single

Calculation of the optical characteristics of CuO nanocomposite by single scattering approximation Igor V. Zabenkov, Vyacheslav I. Kochubey∗, Dmitry A. Zimnyakov Saratov State University, Astrakhanskaya Str., 83, 410012, Saratov, Russia ABSTRACT The program which calculate the process of light scattering by particles with the Gaussian size distribution by single scattering approximation was written. This program was used to calculate the optical characteristics of light scattering by an optically thin layer of the polystyrene spheres in water. These data were applied to compare two optical schemes, which are used for spectroscopy of the scattering samples. First method uses a wide-angle photodetector and second – uses an integral sphere. It was shown that in spectrophotometric experiments with such samples we must use an integral sphere to obtain a true spectrum. This program was used to calculation the optical characteristics of CuO nanocomposite to investigate Keywords: nanocomposite, scattering, spectroscopy

INTRODUCTION The physics of nanoparticles is one of the most important topics in modern science. One of the specialties in this area is a study of the metal-containing nanocomposites in a polymer matrix on calculated refractive index and absorption factor. High scattering is an integral property of such media, that's why these coefficients are defined by a classical fashion, using an integral sphere. Integral sphere guarantees elimination of the spatial garbling of the transmitted and reflected light and allows obtaining a true spectrum. But sometimes in spectroscopy of such scattering media seems possible instead of an integral sphere to use a wide-angle photodetector, allowing registering most of the scattered light. In this case it is expected that received spectrum don't have a qualitative distinctions from true, but its distortion, caused by angular dependency of the scattering it is enough small. The problem of this work is study of the possibility of removing a true spectrum of the scattering media, without using an integral sphere, but only wide-angle photodetector. To this end we used the mathematical modeling of light scattering by optically thin layer of the polystyrene spheres in water, with a normal size distribution.

TWO MEASURING SCHEMES The measuring scheme, which traditionally is used to obtain the spectral characteristics of the scattering media, is shown in Fig. 1. Use an integral sphere allows to collect all scattered light or in the backward hemisphere (reflection spectrum) or in the forward hemisphere. So, we can observe a true spectrum. The measuring schemes in which is used a wide-angle photodetector are shown in Fig.2-3. These schemes are often used for weak scattering samples, so most of it is registered within a wide aperture of the photodetector. But without using an integral sphere before, impossible know how many of the scattered light was register. It means we can't know the difference between a true spectrum and spectrum which was obtain with use a wide-angle photodetector.

THE MIE PROGRAM AND RESULTS OF CALCULATIONS It is necessary to study the spectral dependence of the most important characteristics to solve a putted problem. These characteristics: phase function ρ (θ ) - which describes an angular distribution of the scattering, efficiencies for total

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scattering Qsca (λ ) and extinction Qext (λ ) - which describes amount of the scattered ant scattered + absorbed light by particle correspond.

Fig. 1. The registration of the scattered light with use an integral sphere.

Fig. 2. The registration of the transmission spectrum with use a wide-angle photodetector.

Fig. 3. The registration of the reflection spectrum with use a wide-angle photodetector.

To determine these parameters we created a MIE program. This program calculates a scattering field by an optically thin layer (single scattering approximation) of spherical particles which have a normal size distribution. As input parameters this program uses the dependence of reflection and refraction indexes of particles on wavelength (loading from *.dat file) and their parameters of the normal size distribution. The ability to calculate scattering field using both

Mie scattering theory (the bigness of particle more then wavelength а ≥ λ) and Reley theory (the bigness of particle noticeably less then wavelength а << λ) is one of particularity of this program. After computations the MIE returns data to the screen in the manner of graphs ρ (θ ) , Qext (λ ) and Qsca (λ ) . To solve the task which was formulated in introduction we used the mathematical modeling of light scattering by optically thin layer of the polystyrene spheres in water, with a normal size distribution. Parameters of this medium which are used as input arguments of MIE program: Average size of the scattering particles a0=1.35 μm, standard deviation of a normal size distribution Δa=20 nm, minimal and maximal size of particles amin=1.31 μm and amax=1.39 μm correspondingly. Moreover, it’s well known that a relative refraction index of polystyrene in water are about n=1.19. For our model medium we used a value of relative refraction index n=1.19 and absorption index K=0 in spectral band from 400 to1200 nm.

lg(Int)

Consider the results of calculations. In Fig. 5 are shown three scattering indicatrixes of our model medium ρ (θ ) corresponds a wavelength 1) - 400 nm, 2) - 800 nm and 3) - 1200 nm. We use a logarithmic scale to present these results lg( ρ (θ ) ) because of back scattering is weakly than forward scattering by a few order. This graph shows that a angular bigness of scattering cone decreasing with increasing of wavelength, for example 200 correspond to 400 nm, 400 - 800 nm and 500 - 1200 nm. 5,0 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 -0,5 -1,0 -1,5

1 2

3 0

20

40

60

80 100 120 140 160 180

0

θ,

Fig. 5. The scattering indicatrixes of the optically thin polydisperse layer of spherical polystyrene particles in water. Scattering at a wavelength of 400 nm (1); Scattering at a wavelength of 800 nm (2); Scattering at a wavelength of 1200 nm (3).

In Fig. 6 are shown dependences of 1) efficiency for extinction Qext (λ ) and 2) efficiency for backscattering Qback (λ ) on wavelength. Note, that in our case the absorption coefficient K=0 over the spectral diapason 400 – 1200 nm and that is why characteristic Qext (λ ) coincide with Qsca (λ ) within. As we can see in Qext (λ ) the light scattering have a maximum at a wavelength of 780 nm called a diffraction resonance. The characteristic Qback (λ ) describe the spectral dependence of backscattering on wavelength. The oscillations in this graph describes a sequential increasing and decreasing of backscattering corresponding to appearance of a new scattering modes. The results of computations, presented as dependences of ρ (θ ) and Qext (λ ) on wavelength permit comparison of two measuring schemes. First scheme uses an integral sphere Fig. 1, and second – a wide-angle photodetector Fig. 2-3. The graph (1) in Fig. 7 corresponds to experiment with an integral sphere. This curve shows that for our model medium in the wavelength range from 400 to 1200 nm the primary is scattering to the front hemisphere ≥ 98% relative to whole scattered light. The graph (2) in Fig. 7 corresponds to experiment with wide-angle (Δθ=300) photodetector. This graph shows a strong spectral dependency of the light fraction registered within a wide aperture of the photodetector. In experiment, this fact means that we obtain an invalid, distorted data. The results of similar comparison for reflection spectra are shown below. Graphs (1) and (2) in Fig. 8 shows a spectral dependence of the scattered light fraction registered in back hemisphere and at an angle θ=1650 within body angle

Δθ=300 correspondly. Since in these graphs is seen only quantitative difference, we consider difference graph Fig. 9. The oscillations in this graph points out that spectrum obtained without an integral sphere is invalid and distort.

Q,a.u. 3.5

1

3.0 2.5 2.0 1.5 1.0

2

0.5 0.0 400

600

800

1000

1200

λ ,nm

Fig. 6. Efficiency for extinction of the optically thin polydisperse layer of spherical polystyrene particles in water. Total scattering Qext (λ ) (1); Backscattering Qback (λ ) (2).

So, comparison of the calculated data (1), (2) in Fig. 7 and (1), (2) in Fig. 8 to carry inference that using of a wideangle photodetector for scattering media, instead of an integral sphere to lead up to distortion of spectra.

I,a.u. 1 1.0

0.9

2 0.8

0.7

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400

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1200 λ ,nm

Fig. 7. The scattering power of the optically thin polydisperse layer of spherical polystyrene particles in water at an angle of θ=00 with an internal beam direction in body angle 1800 (1); The scattering power at an angle of θ=00 and recorded within aperture of photodetector Δθ=300 (2). The power measured relatively to all scattered light.

I,a.u. 0.018 0.016 0.014 0.012 0.010 0.008

1

0.006 0.004

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0.002 0.000

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λ ,nm

Fig. 8. The scattering power of the optically thin polydisperse layer of spherical polystyrene particles in water at an angle of θ=1800 with an internal beam direction in body angle 1800 (1); The scattering power at an angle of θ=1650 and registered within aperture of photodetector Δθ=300. The power measured relatively to all scattered light.

I,a.u. 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06

400

600

800

1000

1200λ ,nm

Fig. 9. The scattering power of the optically thin polydisperse layer of spherical polystyrene particles in water at an angle of θ=1650 with an internal beam direction in body angle 300. The power measured relatively to light detected at an angle of θ=1800 within a body angle 1800.

THE OPTICAL CARACTERISTICS OF CuO NANO-COMPOSITE The last section described some of perhaps consequences of using in spectroscopy of scattering media a wide-angular photodetectors instead of an integral sphere (quantitative and qualitative distortions of the reflection and transmission spectra). Given section presents an analogical investigation for CuO nanocomposite which was synthesized by our scientific group.

The parameters of this media which we will use in MIE program are presented bellow. Absorption factor K(λ) calculated from the transmission and reflection spectra of CuO nanocomposite is shown in Fig. 10. The relative refraction index of this media in the wavelength range from 350 to 1650 nm let n=1.5.

K 0,07 0,06 0,05 0,04 0,03 0,02 400

600

800

1000 1200 1400 1600

λ ,nm

Fig. 10. Absorption factor calculated from the transmission and reflection spectrum of the metal-containing polymer CuO nanocomposite

The CuO nanoparticles of our medium have a Gaussian size distribution. The parameters of this distribution: average size of the nanoparticles a0=9.75 nm, standard deviation Δa=2.25 nm, minimal and maximal size of particles amin=5.25 nm and amax=14.25 nm correspondingly. The calculated extinction Qext (λ ) and scattering Qsca (λ ) spectra are presented in Fig. 11. High extinction in the spectral band 350-530 correspond to fundamental absorption of CuO. The pseudo noise splashes from 800 to 1650 nm caused by the noise of the photodetector in the IR diapason.

Q,a.u. 0.010 0.009 0.008 0.007

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0.006 0.005 0.004 0.003

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0.002 0.001 0.000 400

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1000 1200 1400 1600

λ ,nm

Fig. 11. Efficiency for extinction of the optically thin layer of CuO nanocomposite. Total extinction Qext (λ ) (1); Total scattering Qsca (λ ) (2).

An angular dependence of a decimal logarithm of the phase function lg( ρ (θ ) ) at a wavelength 1) - 350, 2) - 1000 and 3) - 1650 nm is shown in Fig. 12. It is known that light scattering by nanoparticles (size of particle less than wavelength) describes by Rayleigh law. In this case the scattering field has only one scattering mode. Tree graphs in Fig. 12 mirrors this fact. The quantitative dependence of light scattering on wavelength is well seen as in graph 2 in Fig. 11, as in Fig. 12. Since the scattering indicatrix of the nanoparticles is conserved under concerned spectral band it is naturally assumption that the both methods: uses an integral sphere and uses a wide-angular photodetector give a qualitatively equivalent spectra. Moreover, as anisotropy factor in the case of nanoparticles g=0, as amount of light scattered at forward and backward direction are equal. Both last facts are shown in Fig. 13 and Fig. 14.

1

-5,0 -5,5

lg(Int)

-6,0 -6,5 -7,0

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-7,5 -8,0 -8,5

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-9,0 -9,5 0

20 40 60 80 100 120 140 160 180

0

θ,

Fig. 12. The decimal logarithm of the scattering indicatrixes of the optically thin layer of CuO nanocomposite. Scattering at a wavelength of 350 nm (1); 1000 nm (2); 1650 nm (3).

I,a.u.

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0.50 0.45 0.40 0.35 0.30 0.25 0.20

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0.15 0.10 0.05 0.00

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λ ,nm

Fig. 13. The scattering power of of the optically thin layer of CuO nanocomposit at an angle of θ=00 with an internal beam direction in body angle 1800 (1); The scattering power at an angle of θ=00 and recorded within aperture of photodetector Δθ=300 (2). The power measured relatively to all scattered light.

I,a.u.

1

0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15

2

0.10 0.05 0.00

400

600

800 1000 1200 1400 1600 λ ,nm

Fig. 14. The scattering power of of the optically thin layer of CuO nanocomposit at an angle of θ=1800 with an internal beam direction in body angle 1800 (1); The scattering power at an angle of θ=1650 and recorded within aperture of photodetector Δθ=300 (2). The power measured relatively to all scattered light.

CONCLUSION Comparative analysis of two schemes uses an integral sphere and uses a wide-angular photodetector allow to conclude that generally for scattering samples we must use first.

REFERENCES 1.

Bohren C.F., Huffman D.R. Absorbing and scattering of light by small particles. N.Y.: John Willey & Sons 1983.