Infrared diffuse reflection spectroscopy of vibration states in nanocarbons

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Diamond & Related Materials 16 (2007) 2093 – 2097 www.elsevier.com/locate/diamond

Infrared diffuse reflection spectroscopy of vibration states in nanocarbons A.N. Bekhterev a,b,⁎, V.M. Zolotarev a a

St.-Petersburg State University of Information Technologies, Mechanics and Optics, Russia b Magnitogorsk State University, Physics Department, Russia Available online 23 August 2007

Abstract In this work the method of infrared diffuse reflection spectroscopy is applied to quantitative analysis of the vibration states in nanocrystaline carbon. The formula received on the basis of Kubelka–Munk relation is offered. According to the formula the influence of initial parameters of the sample (concentration, degree of the sample dispersion, index of dispersion) on selectivity of infrared diffuse reflection spectra are investigated. The interpretation of the absorption bands in diffuse reflection spectra of the glassy carbon samples is made. © 2007 Elsevier B.V. All rights reserved. Keywords: Diffuse reflection spectroscopy; Glassy carbon; Vibration states

Optical properties of crystalline and amorphous modifications of condensed carbon were investigated in considerable detail by Raman scattering (RS) [1], IR specular reflection (IR ) [1,2], and also absorption in thin layers and films [1,3,4]. Most of the above works included investigation of the spectral region above 0.5 ev and the results were interpreted in terms of electronic transitions near the Fermi level according to the energy band models of twoand three-dimensional graphite [5,6]. The 0.5–0.1 ev optical interval where the vibrational states of condensed carbon should be active is less studied. The available works deal practically with studies of the RS and inelastic slow-neutron scattering of crystalline and amorphous modifications of condensed carbon [1,7]. Because of the alternative exclusion rule, however, not all of the vibrational modes are active simultaneously in the RS and IR spectra. While inelastic neutron scattering receives information on the density of any symmetry phonon states, this method features low spectral resolution [1]. IR transmittance spectra of carbon-based materials in powdered form received by the traditional KBr-technique are insufficiently informative to be used in quantitative analysis because of significant scattering from absorbing particles of the powder samples and of background absorption by free charge carriers. The intense scattering originates from the large dif⁎ Corresponding author. St.-Petersburg State University of Information Technologies, Mechanics and Optics, Russia. E-mail address: [email protected] (A.N. Bekhterev). 0925-9635/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2007.08.012

ferences between the refractive indices of condensed carbon and of KBr (NaCl) immersion optical media [8]. We are reporting here on a study into the possibility of quantitatively probing the vibrational states of condensed nanocarbon of hexagonal symmetry by diffuse reflection (DR) spectroscopy with special optical attachment [8] in the wavelength domain where the in-plane and out-of-plane vibrations of carbon atoms (E1u, A2u) in graphite unit are active. 1. Structure and properties nanocrystaline carbons We studied samples of nanocrystaline glassy carbons (GC), prepared by the standard technique involving thermal pyrolysis of phenol pitches with slow rise of temperature up to 1500 °C in argon atmosphere [9]. Thereafter, GC samples were subjected to standard thermal treatment at the temperature up to 3000 °C in a chemically pure argon environment. This heat treatment has brought to monotonous growth of the crystal sizes in GC samples and to the reduction of in-plane distance in the crystal lattice, to the increase of free-carrier concentration. By its physical properties, GC samples belong to semimetals with a fairly high free-carriers concentration (n ≈ 4.3⁎1019 cm− 3, GC-30) and low impurity contents (≤10− 3 wt.%) [2,9]. By its structures, GC can be classed among typical materials with nanocrystaline hexagonal 4 structure of D6h symmetry with statistically averaged crystals sizes: Lc = 2.5 nm and La = 3.5 nm in the crystal lattice along the hexagonal c axis and a axis perpendicular to it, respectively, and

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out-of-plane distance d002 = 3.510 nm (GC-15); Lc = 4.2 nm, La = 5.4 nm, d002 = 3.425 nm (GC-30). However, the GC structure greatly differs from the structure of ideal graphite even at high heat treatment temperatures and refers to the “turbostratic” structure [9]. It is expected that in GC structure, the graphite, carbine, fullerenes, and tubular fragments of structures are present. The main vibration modes of graphite should be active in the IR range 3000–50 cm− 1. Group theoretical analysis of the hexagonal graphite lattice, suggests the following four optically active vibration modes relative to the Г central point of the Brillouin zone [7,10]: D46h : Cvibr ¼ A2u þ E1u þ 2⁎ E2g ;

ð1Þ

one of which (A2u), is derived from nondegenerate out-of-plane antisymmetric vibrations of carbon atoms in the graphite cell, and the other three modes are twofold degenerate. The modes E1u and E2g describe in-plane carbon atom vibrations. According to the selection rules, the A2u and E1u vibrations should manifest in IR spectra, while the modes of E2g symmetry should be active in Raman spectra of graphite [1]. An analysis of experimental data [1,7,10] relating to the optical properties of the structures of graphite and materials based on condensed nanocarbon suggests that the vibrational modes of E1u and E2g symmetries characterize primarily the two-dimensional structural order, while the A2u mode is associated with three-dimensional order in carbon atom arrangement over the graphite lattice. Deviations from ideal structural order in the samples bring about a corresponding lowering of symmetry of individual lattice fragments and, as consequence, possible violation of the selection rules and manifestations of these factors in the IR and Raman spectra [7,10]. Among lattice distortions of the hexagonal graphite are, in particular, formation, in addition to the three-dimensional of two-dimensional graphene structures; deformation of graphene sheets and the ensuing deviation of the valence angles from 120°; breakdown of translational symmetry caused by finite sizes of the nanocrystals; formation of fragments similar to the nanotubes and fullerenes carbon structures; and the presence of adsorbed atoms and molecular groups (oxygen, hydrogen, and hydroxyl groups). This may give rise to the appearance in an IR spectrum of absorption bands corresponding to the symmetry of one-dimensional tubular (Dnh, Dnd, Cn) and two-dimensional fullerenes (Ih) nanocarbons and adsorbed molecules. In this case the vibration modes of the condensed carbon will in addition correspond to the following irreducible representations [10]: Dnh : Cvibr ¼ 4A1g þ 2A1u þ 4A2g þ 2A2u þ 2B1g þ 4B1u þ 2B2g þ 4B2u þ 4E1g þ 8E1u þ 8E2g þ 4E2u þ N þ 8Eðn=21Þg þ 4Eðn=21Þu :

ð2Þ

Cn : Cvibr ¼ 6A þ 6B þ þ6E1 þ 6E2 þ N þ 6Eðn=21Þ ;

ð3Þ

Ih : Cvibr ¼ 2Ag þ 3T 1g þ 4T2g þ 6Gg þ 8Hg þ Au þ 4T1u þ 5T2u þ 6Gu þ 7Hu :

ð4Þ

Here modes A1, A1u, A2u, E1, E1u, T1u, are derived from antisymmetric vibrations, and modes A1, A1g, E1, E1g, E2g, E2,

Hg are derived from symmetric vibrations of carbon atoms in crystal cell of GC. An analysis of theory group irreducible representations (2–4) suggests that the lowering of the lattice symmetry of condensed carbon gives rise to an increase of the number of IR and Raman active modes, with some of them being observed, as a result of the violation of the selection rules, simultaneously in the Raman and IR spectra. The 13C-carbon isomer and other impurities in the GC samples lead to removing the vibrational states degeneration and to increasing the number of the absorption bands in GC optical spectra [10]. The second order vibration spectra of condensed carbon can be mediated by phonons with practically any value of the wave vector, while second order phonon spectra should be determined by the three-dimensional structure of the crystal lattice samples [7]. Recent experimental and theoretical researches of carbon nanotubes and fullerenes structures have shown more than ten vibration bands [11]. This modes were carried out to the carbon vibration modes of the first, second order, and combined frequencies in tubular and fullerenes structures. 2. Experimental techniques The vibrational states of nanocrystaline carbon were probed by IR diffuse reflection method. In the work the strongly absorbing GC disperse component diluted optimally with the NaCl component which being likewise disperse, was transparent in the spectral region of interest here. We assumed, as this is done in most of the fundamental studies dealing with the spectroscopy of light-scattering media, that the chosen experimental conditions provide a persistent diffuse structure of the light inside the scattering medium along the beam path [12,13]. To bring the conditions of the experiment as close as possible to be accepted in the theory and providing constant beam structure in the light medium, the GC samples and chemically pure NaCl powder were dispersed and mixed in a standard ball mill with GC contents of up to 5 wt.%. We also envisaged a possibility of performing measurements at DR coefficients optimal for photometry. One should not also disregard the dispersion-induced distortion of the crystal lattice and change of the GC crystallite parameters. We have conducted X-ray structural studies of the time milling samples influence on its structure. Experiments showed times below 10 min to be optimal for the preparation of homogeneous, well reflecting media. Structural parameters of GC (La, Lc, d002) at within the above milling time practically do not change within measurement error (5–7%). Using compounds (NaCl, LiF, KBr) optically transparent in the IR region as immersion scattering media makes it possible for the probing IR radiation to penetrate large enough depths of a disperse sample and, participating in multiple absorptionscattering events, to accumulate information on the absorptivity of the subject under study. A transparent scattering medium (NaCl) dispersed to the same extent as a sample served as a reference. The decrease in radiation intensity in the reference sample originates from multiple scattering effect only. The low

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enough GC concentration (1–3%) in the sample, the scattered light field structure in the sample and in the reference may be considered the same. In this way one can eliminate the effect of scattering on the spectroscopic characteristics of the GC IR absorption bands in DR spectra. In transmission spectrophotometry the spectral dependence of the absorptance of a substance (æ) is related to the variation of the transmittance T of a system and the beam path length d in the medium through the Bouguer law: æ(ν) = −1/d⁎ln T(ν). In scattering media, the diffuse reflection coefficient (R∞) is a complex function not only æ, but a number of other parameters as well scattering coefficient – s, the average sizes of particles – l, light field wave structures etc. This problem allows exact solution only in the frame of a rigorous theory of radiative transfer [14]. Analysis of an absorption spectrum of a substance by its DR spectrum requires frequently the knowledge not of the absolute values of the absorptance (æ) but rather of its spectral dependence, i.e., the shape of the absorption curve. In this case, one should choose a function which would reproduce as closely as possible the pattern of the æ(ν) variation. This aspect has been treated in great detail in more than one publication [12,13]. Among the functions tried as possible candidates to fit the absorption spectrum were −log R∞ , (1 − R∞ ), 1 / R∞, (1 − R∞ )2 / R∞ . After a thorough experimental and theoretical testing we choose for this purpose the Kubelka–Munk relation [15,16]: f ðRl Þ ¼

ð1  R l Þ2 k ¼ s 2Rl

ð5Þ

where R∞ – is the DR coefficient from infinitely thick layer (depth regime), and k and s are, respectively, the coefficients of absorption and scattering for a disperse layer of unit thickness. This relation provides the best description of the spectral behavior of the absorptance of a substance within a fairly broad range of absorptance, concentration, and extents of dispersion. In some cases, Kubelka–Munk relation practically coincides with the spectral dependence of the absorptance of substance æ(ν) [12,13]. In [17] where a diffusely reflecting medium was modeled by a system of plain-parallel plates with a thickness equal to the average diameter of scattering particles, it was shown, that for weakly scattering media, the constants k and s can be represented in the form k¼

1  ro 2ro ; &; s ¼ 1 þ ro ð1 þ ro Þl

ð6Þ

where ro, æ, l are, respectively, the coefficient of normal reflection, absorptance, and the average particle diameter of the scattering medium. If the scattering medium is a mixture of two components with concentration c1 and c2, then the coefficient s of absorption and scattering considered in linear approximation take is on the form j ¼ c1 k1 þ c2 k2 ; k ¼ c1 s1 þ c2 s2 ;

ð7Þ

where k1, s1, k2, and s2 are respectively, the coefficients of absorption and scattering for the starting components taken at

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the unit concentration. Substituting k and s in the formula (5), allowing for the fact that one medium is absorbing and scattering (1-GC), and the second medium, transparent and scattering (2-NaCl), and that one can accept k2 = 0 (NaCl), c1 b b c2 (the GC concentration ≈1%, NaCl concentration≈ 99%), s1 bb s2 (for the GC–NaCl system), introducing c = c1 / c2, and neglecting small terms, we arrive at ð1  Rl Þ2 ck1 ¼ : 2Rl s2

ð8Þ

Substituting constants k1 and s2 from Eq. (6) and neglecting r02 compared with unity we come to f ðRl Þ ¼

ð1  Rl Þ2 ð1  r01 Þ ¼ & l2 c: 2Rl ð1 þ r01 Þ2r02

ð9Þ

Because r01(ν) and r02(ν) spectra do not have strong bands, one would expect from Eq. (9) a linear dependence between the Kubelka–Munk function and the absorber concentration c, appearance in the f(R∞) spectrum of selective absorption band æ(ν) and dependence of this function on the extent of dispersion of the immersion scattering medium (l2). As long as the l and c parameters are kept constant in experiment, a DR spectrum should reveal primarily absorption æ(ν) and reflection/scattering r(ν) effects. For low sample concentration (below 1–3%), the reflection and scattering effects in the sample and in the reference may be considered to be the same, and, thus, they are taken properly into account in DR spectral measurements. In this case, micro particles of the sample will be more transparent for the radiation, and the spectral behavior of the DR coefficient, according to Eq. (9), will follow the pattern of that of absorptance æ(ν) of the sample. The method of IR DR spectroscopy has two basic particularities for the absorbing objects. The first one is connected with the light absorption by adsorbed water on the surface of the fine powder samples, and the second one is caused by the microscopic sizes of the GC particles comparable to the IR wavelength. The first factor can cause the breaching of the light flux balance in the sample channel and reference channel in the region of water absorption (3400 cm− 1 и 1640 cm− 1). The second factor can lead to the increasing of dispersion coefficient with rising of the IR wavelength radiation. It's necessary to take into account both factors at the analysis of IR DR spectrum of the GC samples. 3. The analysis of the results The spectral dependence of f(R∞) for GC samples (1 wt.%) is presented in 4000 ÷ 700 cm− 1 spectral region, Fig. 1a. One can see the low absorption regions in DR spectrum of GC (∼3390, ∼ 1640 cm− 1) that are close to the frequencies of polisorbed H2O on NaCl powder grains. This is apparently closely connected with the DR depth regimes in the sample and the reference being different because in the sample radiation penetrates smaller depths. The band at 2200 cm− 1 relates to atmospheric CO2. The other bands in the ranges 3250 ÷ 2700, 1700 ÷ 1100 cm− 1,

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Fig. 1.

1050÷ 800 cm− 1 can be attributed to the GC which correlates well enough with features in the phonons density of states function and Raman spectra of condensed carbons structures [7,10]. The features below 1600 cm− 1 basically are caused by the normal vibration, and in the 4000÷ 1700 cm− 1 region are connected with the overtones of vibrations and the combined frequencies of the carbon atoms in the GC samples. The calculated phonon spectra of graphite suggest manifestation of out-of-plane carbon atom vibrations (A2u) in the IR absorption spectrum in the region at 850 cm− 1 [10]. The wide bands with the several resolved maxima at 1245, 1065, 1015, 948, 858, 750–650 cm− 1 (GC-30) and at 1255, 1060, 1008, 862, 650 cm− 1 (GC-15) are observed in the IR DR spectra of the GC samples, Fig. 1a. The in-plane carbon atom vibration of symmetry E1u, is active near 1580 cm− 1. The DR spectrum of GC in this region shows the following bands: absorption maxima at 1510 and 1320 сm− 1 (GC-30), and at 1515 cm− 1, 1330 cm− 1 (GC-15). The features in the form of

absorption shoulders lie at 1550 and 1400 cm− 1 for both samples, accuracy of the measurement spectrum formed 5 cm− 1. According to [7], the IR bands in the region at 1550 cm− 1 and 1510 cm− 1 should be assigned to in-plane (E1u) vibrations of carbon atoms of in the graphite lattice. The second maximum is attributed to the vibrations of carbon atoms residing in strained graphite sheets, with the angles in hexagonal structures deviated from 120° [18]. The maximum at 1310 cm− 1 derives from the breakdown of translation symmetry of the sheets in their finite sizes in real structures [10]. The feature near 1400 cm− 1 reflects maximum in the phonons density at Г and M points of the graphite Brillouin zone [7,10]. The absorption bands in the regions of 1250–900, and 750–650 cm− 1 can be attributed to the vibration of carbon atoms in small carbon clusters or in fullerenes motives which can be present in the GC structure [3,10]. The absorption bands at 3100 cm− 1, 2960 cm− 1, 2700 cm− 1, 2450 cm− 1 in spectrum of the GC samples should be assigned

Table 1 Vibration states in optical spectra of glassy carbons according to various methods Vibration mode, cm− 1

2E2, 2E1

E2 + A1

2A1g, 2A1

Defects

E2g, E1u

Defects

A1g, A1

A2u

3230

2940 2950

2710 2717

1610 1620

1597 1585

3220 3230

2950 w 2950 w

2740 2760

1640 w 1630 w

1570 1580

1510 1485

1340 1355

780 815

3100 w 3250 w

3050 w 2950 w

2750 w 2750

1600 w 1600 w

1560 w 1570

1515 1510

865 858

3250

2975

2760 2680

1595

1530

1330 1320 1370 1380

The methods of research RS, λ = 488.0 нм GC-15 GC-30 IR-reflection. (Kr.-Kr. anal.), æ(ν) GC-15 GC-30 Diffuse reflec. R∞(ν) GC-15 GC-30 Density of phonon states in graphite, G(ν)

Notes: RS – [19], IR – Kramers–Kronig analysis of IR reflection data [2,3], DR – this work, G(ν) – [7,10], w – weak.

1355 1358

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to overtones of the carbon atoms vibration and, probably, to the adsorbed hydrogen atoms. Fig. 1b displays the concentration dependence of the intensity of 1510 cm− 1 band for GC concentrations in the sample up to 5 wt.%. Our experimental data suggest that at concentration of dispersed carbon in a sample of less then 2.5–3 wt.% the band intensity f(R∞), in accordance with Eq. (9), varies linearly with concentration. This relation holds for other absorption bands in DR spectrum of GC as well. Because the material used to prepare samples was not monodisperse, we carried out only a qualitative check of the effect sample dispersion exerts on the DR coefficient. It has been established that the DR coefficient (R∞) decreases with the increase of the largest size of sample particles (sieve mesh greater than 30 μm). As the degree of GC dispersion (varied by properly adjusting the grinding time) grew ever finer with the weight concentration of the sample kept constant, the IR absorption band intensity of the sample increased, in full accordance with Eq. (9). To estimate the effect of specular reflection from absorbing particles at the interface with air, a model experiment involving measurement of the DR spectrum from dispersed GC, which was coated with a thin transparent layer of finely dispersed NaCl powder, was performed. A NaCl powder dispersed to the same level served as reference. The model experiment reveals the features of some selective absorption which were observed earlier in DR spectra of this sample obtained in the depth regime of absorption/scattering. These results suggest that the selective absorption bands in the DR spectra originate primarily from the passage of radiation through the smallest particles of dispersed GC under depth regime conditions of the absorption/scattering of the IR radiation. Because the radiation wavelength was larger than the sample nanocrystal size, which in the course of grinding practically did not change, one is led to the conclusion that the above selective absorption bands in the DR spectra are due primarily to the specific features of the vibrational spectrum of carbon atoms present in GC nanocrystals. Table 1 compares information on the IR absorption bands observed in the GC samples according to various methods [2,3,19] with available data on the phonon density of states function of the condensed carbon G(ν) [7,10]. The spectroscopic obtained data correlate well with the positions of the optically active vibrational states of carbon atoms in the GC structure.

structure and chemisorbed atoms (–CHn, C_O). We discovered the absorption bands in the region of 1250–650 cm− 1 which can be attributed to the vibrational states of carbon atoms in small carbon clusters or in fullerenes motives which can be present in the GC structure. The applicability of the equation derived from the Kubelka– Munk relation and the equations from the theory of radiative transfer in a disperse medium to assignment of the DR spectra of GC have been analyzed. The effect of the absorber concentration in a sample, its dispersion, scattering factors on the intensity and position of the IR selective absorption bands have been experimentally studied. The absorption bands measured in GC DR spectra have been assigned and collated with the features observed in the IR and Raman spectra of the GC samples under study and of the other samples of nanocrystaline carbon structure [19,20]. This study was supported by Russian Foundation for Basic Research, project no. 06-08-00340a. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

4. The basic conclusions We have used for the first time a diffuse reflection method to detect selective bands which can be assigned to in-plane and out-of-plane vibrational states of carbon atoms in the GC

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[19] [20]

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