The IR Spectra , Molar Absorptivity , and Integrated Molar Absorptivity of the C 76-D 2 and C 84-D 2 : 22 Isomers

The FT-IR spectra of the stable C76 and C84 isomers of D2 symmetry, isolated by the new, advanced extraction and chromatographic methods and processes, were recorded by the KBr technique, over the relevant region from 400 to 2000 cm, at room temperature. All the observed infrared bands are in excellent agreement with the semiempirical QCFF/PI, DFT, and TB potential calculations for these fullerenes, which is presented in this article, as the evidence of their validity. The molar absorptivity ε and the integrated molar absorptivity ψ of their IR absorption bands were determined and reported together with the relative intensities. Excellent agreement is found between the relative intensities of the main and characteristic absorption maxima calculated from ελ and from theψλ values in adequate integration ranges.These results are significant for the identification and quantitative determination of the C76-D2 and C84-D2:22 fullerenes, either in natural resources on Earth and in space or in artificially synthesized and biomaterials, electronic, optical, and biomedical devices, sensors, polymers, optical limiters, solar cells, organic field effect transistors, special lenses, diagnostic and therapeutic agents, pharmaceutical substances in biomedical engineering, and so forth.

It is expected that also higher fullerenes can be found in space, besides C 60 and C 70 .Calculations [27] suggest that, on a per carbon atom basis [1], higher fullerenes are thermodynamically even more stable than C 60 , C 70 [28], and from the hydrogenated derivatives fulleranes [17,18,[29][30][31].Their formation through coalescence of smaller fullerenes [32] and by laser ablation of carbon [17-19, 33, 34] also leads to the conclusion about their possible presence in nature.
For the qualitative detection of C 76 and C 84 fullerenes, the knowledge of the infrared band position and band widths, as well as the evolution of these parameters with temperature, is necessary.This need was fulfilled, for instance, by the previous works [1,[35][36][37][38][39][40][41][42] in the infrared spectroscopy of C 76 and C 84 , whereas quantitative assessment of these fullerenes requires knowledge about intensities of their IR absorption bands, which is provided in the current work.
A comparison of the experimentally observed vibrational frequencies in the IR absorption spectra of the isolated C 76 -D 2 and C 84 -D 2 :22 samples [35,38] with the semiempirical QCFF/PI, DFT, as well as TB potential theoretical calculations for these fullerenes [44,45,[48][49][50], is presented in this article, indicating their validity.
In this work also, the molar extinction coefficients and the integrated molar extinction coefficients of their main and characteristic IR absorption bands were determined.
These data are important for the qualitative and quantitative determination of the C 76 -D 2 and C 84 -D 2 :22 isomers, either in natural resources on Earth and in space or in artificially synthesized materials, electronic and optical devices, diagnostic and therapeutic agents for the applications in biomedical engineering, and so forth.

Experimental Methods
In the first phase of this research, C 60 , C 70 [24][25][26], and the higher fullerenes, mainly C 76 and C 84 [35][36][37][38][39][40][41][42], were Soxhlet-extracted with a series of different and previously unapplied solvents or combinations of solvents from the samples of carbon soot, produced by electric arc (MER Corporation, Tucson, USA).The extraction procedures were performed until the complete disappearance of color in a Soxhlet extraction thimble.Solvents used were n-heptane, toluene, chlorobenzene, p-xylene, a mixture of o/m/p-xylene, and pyridine, as well as the successive use of toluene and chlorobenzene and p-xylene and pyridine.The yields, as well as the compositions of all the extracts, were determined by spectroscopic and chromatographic methods.The procedures for increases of fullerenes yields, as well as for additional selective extraction of higher order fullerenes, were found [24][25][26][35][36][37][38][39][40][41][42].
In the second phase, C 60 , C 70 , and the higher fullerenes C 76 and C 84 (the only stable C 60 -Ih, C 70 -D 5h , and C 76 -D 2 isomers of the first three mentioned fullerenes and the most abundant, stable C 84 isomer of D 2 symmetry) were chromatographically separated from the obtained soot extracts on the activated Al 2 O 3 columns, by new and advanced methods [35][36][37][38][39][40][41][42].
The main difference and advancement of these methods [35][36][37][38][39][40][41][42], in comparison to previous methods under pressure [55][56][57][58][59][60][61][62][63], is the isolation of the purified stable isomers of the higher fullerenes C 76 and C 84 (the C 76 -D 2 and C 84 -D 2 :22 isomers), successively after the basic fullerenes, in one phase of each of the processes, under atmospheric pressure and smaller flow of 1.5 mL/min, in increased milligrams yields.The other advantages of the developed methods [35,42] are the use of significantly smaller amounts of the initial materials, as well as less expensive laboratory equipment.In these methods [35,42], the entire materials and energy expense, the time spent on the purification processes, and environmental pollution were decreased, using smaller amounts of less toxic solvents.The yields and the purities of the isolated fullerenes were increased or maximized [35,36,39].
For comparison, using flash chromatography to separate fullerenes [55], on alumina, with hexane or 5% toluene in hexane as eluent, required about 50 times larger quantities of the initial materials, such as 500 mg of crude fullerenes extract, 2500 mg of alumina, and about 12.5 L of solvent for one chromatographic fraction, C 60 , or 75 L for six chromatographic fullerene fractions, per one chromatography and the large size of columns.The entire time of this purification process, including repeated chromatographies, was 66 hours and purified higher fullerenes were obtained in lower yields.From the total amount of 2500 mg of toluene soluble soot extract, 12 mg of C 76 and 2 mg of C 84 were isolated.
From these data, it follows [36,39] that 21 times larger amounts of the initial materials (extract, stationary phase, and solvent) and 2 times longer time are needed for obtaining 1 g of purified C 76 , and 125 times larger amounts of the initial materials and 10 times longer time are required for obtaining 1 g of purified C 84 by the mentioned flash chromatography process [54], in comparison to our protocols [35][36][37][38][39][40][41][42].
The IR spectra of all the chromatographically purified fractions of the basic and the higher fullerenes from this research, as well as of the obtained soot extracts, were previously recorded on a Perkin Elmer FT-IR 1725 X spectrometer by the KBr pellet technique, from 400 to 4000 cm −1 , at a resolution of 1 cm −1 , in the transparence mode [24-26, 36, 37, 39-42].
The IR spectra of the C 76 -D 2 and C 84 -D 2 :22 samples, isolated by the new and advanced chromatographic methods [35][36][37][38][39][40][41][42], were also recorded on a Thermo Scientific FT-IR spectrometer Nicolet IR-6700, by the KB disk technique, in the range of 400-2000 cm −1 , at a resolution of 1 cm −1 , in the transparence mode [35,38], as well as in the absorption mode in this article.The resulting pellets were placed in the FT-IR spectrometer.Measurements of the intensities (heights) of the absorption bands, as well as of the integrated band intensities of C 76 -D 2 and C 84 -D 2 :22, with automatic subtraction of the baseline, were made possible through the OMNIC software from Thermo Scientific, dedicated to the FT-IR spectrometer.This software has also been recently used for the measurement of relative intensities of IR absorption bands of C 60 and C 70 [4].

Measurement of the Molar Absorptivity and Integrated Molar Absorptivity of C
The masses of the resulting pellets were 71.0 mg and 78.1 mg, and the percentages of carbon determined by the elemental analysis were 0.351 and 0.346.Their measured thicknesses () were 0.67 mm∼0.07 cm and 0.74 mm∼0.07 cm, the diameters () were 0.7 cm, and the half diameters () were 0.35 cm.
The volumes of the pellets () were determined from the abovementioned  and  parameters, by the equation  =  2 .The obtained values of the volumes, as well as the thicknesses of pellets, were also confirmed using KBr density (2.753 g/cm 3 ) [4] and the masses of pellets.
Concentrations () of fullerenes C 76 and C 84 in the pellets, as the number of moles per unit of volume, were calculated using the masses of C 76 and C 84 in the pellets, their molar masses of 912.76 g/mol and 1008.84 g/mol, and the volumes of pellets.

Results and Discussion
In the recent works [1,[35][36][37][38][39][40][41][42], the IR spectra of the higher fullerenes C 76 and C 84 and their stable isomers of D 2 symmetry have been studied.The dependence on temperature of the position and width of their infrared absorption bands has been determined [1,35].The molar extinction coefficients and integrated molar absorptivity of the infrared absorption spectra of C 60 and C 70 , as well as of related hydrogenated derivatives, fulleranes, have also been recently determined [2][3][4][5].However, neither the molar absorptivity nor the integrated band intensity of C 76 -D 2 and C 84 -D 2 :22 has been reported.
Determination of molar absorptivity of the isolated higher fullerenes, in L⋅cm −1 ⋅mol −1 , at a given wavenumber,   , was achieved through (1), previously applied for C 60 and C 70 , as well as for hydrogenated fullerenes [2-6, 64], according to Lambert and Beer law, using the absorbance   read at a given wavenumber: ( The determined values of () −1 for both the C 76 -D 2 and the C 84 -D 2 :22 samples are reported in the Experimental Methods.
It was found that the peak height measurements that correspond to the absorbance  are sensitive to changes in the resolution of the spectrometers used [2][3][4][5][6]64].The measurement of the integrated intensity that corresponds to the total area below a given absorption band is much less sensitive to instrumental resolution than the peak height measurement [2][3][4][5][6]64].
Thus, the absorbance and the integrated band intensities in the obtained original IR spectra of the isolated C 76 -D 2 and C 84 -D 2 :22 samples were determined using the OMNIC software of our spectrometer, in both cases subtracting automatically the baseline.
The integrated molar absorptivity of the C 76 -D 2 and C 84 -D 2 :22 fullerenes, expressed in cm mol −1 or 10 −5 km mol −1 , was determined by (2), previously applied for the basic fullerenes, as well as for fulleranes [2][3][4][5][6]64]: In this equation,  is the wavelength and   is the molar absorptivity measured with a spectrometer with unlimited resolution, integrated over the whole band.In practice, by substituting (1) into (2), we get [2][3][4][5][6]64] Ψ = () −1 ∫   . ( The original, characteristic, representative IR spectrum of the isolated sample of the C 76 -D 2 isomer is obtained in this article in the absorption mode, Figure 1, for determination of the molar absorptivity and integrated molar absorptivity of its absorption bands, which is important for the quantitative assessment of this fullerene and represents the main work of this article.It was previously provided in transparence mode, in supplemental material of our article [35], for the qualitative determination.
The main three, most intense, dominant C 76 maxima, registered in this research [35][36][37][38][39][40][41][42], appear at 967, 1082, and 1187 cm −1 , with some weak, distinct shoulders.Characteristic, sharp absorption bands unique to C 76 occur in the first relevant part at 893 and 823 cm −1 , with a neighboring shoulder at 792 cm −1 .Several other bands are present at 703 cm −1 with a shoulder at 742 cm −1 , at 605 cm −1 with the shoulders at 647 and 665 cm −1 , and at 484 cm −1 with the shoulders at 538, 462, 456, and 426 cm −1 .Pronounced and intense bands are present in the higher frequency region at 1386 cm −1 with the shoulders at 1397 and 1364 cm −1 , at 1493 cm −1 with a neighboring shoulder band at 1462 cm −1 , as a doublet, and at 1735 cm −1 .Maximum at 1312 cm −1 appears with the neighboring shoulders at 1273 and 1248 cm −1 , as a triplet.Complete absorption in this spectrum [35]   agreement with the theoretical calculations for C 76 -D 2 , as well as for its dianion [44,45].
There is also a good agreement between the absorption bands in our infrared spectra at room temperature [35][36][37][38][39][40][41][42] and the recent spectra of C 76 -D 2 at three different temperatures [1].Only some smaller shifts, as well as some changes of their relative intensities with the temperature, were observed [1,35].
From the IR spectrum of C 76 -D 2 in a mode, presented in Figure 1, the absorbance values   , as well as the integrated absorbance values of the absorption bands, were determined using the OMNIC software.
The molar absorptivity   , calculated according to (1), the integrated molar absorptivity Ψ  , calculated according to (3), and the integration ranges of absorption bands of this fullerene are reported in Table 2.
It can also be seen from Table 2 that excellent agreement is found between the relative intensities of the main and characteristic absorption maxima of C 76 -D 2 computed from   and from the Ψ values, in adequate integration ranges, taking as 100 the most intense vibration mode of C 76 -D 2 at the frequency of 967 cm −1 .
The original, characteristic, representative IR absorption spectrum of the isolated sample of the isomer C 84 -D 2 :22 is obtained in this article in the absorption mode, Figure 2, for determination of the molar absorptivity and integrated molar absorptivity of its absorption bands, which is important for its quantitative determination, as the main work of this article.It was previously provided in transparence mode [35], for qualitative determination.A group of sharp, characteristic absorption bands is present between ca.700 and 840 cm −1 [35][36][37][38][39][40][41][42], at 711, 746, 779, and 843 cm −1 , followed by the bands at 635 and 473 cm −1 in the first relevant part.Dominant and pronounced C 84 -D 2 :22 maxima appear in the higher frequency region, between ca.1390 and 1120 cm −1 , as well as a group around 1600 cm −1 .The main, most intense band is present at 1385 cm −1 , followed by the bands at 1263 cm −1 and 1122 cm −1 .Intense bands also appear at 1456-1465 cm −1 , 1599-1616 cm −1 , and 1731 cm −1 .The entire absorption in this spectrum [35] corresponds to the theoretical predictions for C 84 -D 2 :22 [48][49][50].
In the previous article [35], a comparison of the experimentally observed absorption frequencies in the IR spectra of the chromatographically isolated C 84 -D 2 :22 samples, recorded on a Thermo Scientific FT-IR spectrometer Nicolet IR-6700 at room temperature [35,38], with the semiempirical QCFF/PI theoretical calculations for this fullerene [48], as well as with the IR spectra of C 84 (mixture of isomers), recorded on three different temperatures between −180 ∘ C and +250 ∘ C [1,35], was presented.On the basis of the obtained excellent agreement [35,38,48], the validity of both the experimental results [35,38] and the mentioned theoretical calculations [48] was indicated [35].
From the IR spectrum of C 84 -D 2 :22 in a mode, presented in Figure 2, the absorbance values   , as well as the integrated absorbance values of the absorption bands, were determined using the OMNIC software.
The molar absorptivity   , as well as the integrated molar absorptivity Ψ  , calculated according to (1) and (3), and the integration ranges of the absorption bands of this fullerene are presented in Table 4.
Also in this case, as can be seen from Table 4, excellent agreement is found between the relative intensities of the main and characteristic absorption maxima of C 84 -D 2 :22 calculated from   and from the Ψ values, in adequate integration ranges, taking as 100 the most intense vibration mode of C 84 -D 2 :22 at the frequency of 1385 cm −1 .

Conclusion
In this research, the stable C 76 and C 84 isomers of D 2 symmetry were isolated from carbon soot, by new and advanced chromatographic methods and processes [35][36][37][38][39][40][41][42].The IR-KBr spectra of the isolated fullerenes were obtained over the entire fullerenes fingerprint region, 400-2000 cm −1 , on a Thermo Scientific FT-IR spectrometer, in transparence mode [35,38], as well as in the absorption mode in this article.
The molar extinction coefficients and the integrated molar extinction coefficients of the IR absorption bands of the C 76 -D 2 and C 84 -D 2 :22 isomers were determined at room temperature in KBr matrix.Excellent agreement is found between the relative intensities of the main and characteristic absorption maxima of these fullerenes calculated from the   values and from the   values in adequate integration ranges.These results can be used for their quantitative determination.
All the obtained data are important for the identification and quantitative assessment of the C 76 -D 2 and C 84 -D 2 :22 isomers, either in natural resources on Earth and in space or in artificially synthesized materials, electronic and optical devices, such as polymers, composites, nanophotonic and biocompatible materials, optical limiters, sensors, special lenses with optical absorption properties closer to human eye light sensitivity, diagnostic and therapeutic agents, pharmaceutical substances, and biomaterials.[35,38] and theoretically calculated values between 400 and 2000 cm −1 [48][49][50].

Figure 1 :
Figure 1: The IR spectrum of C 76 -D 2 in a mode. 401

Figure 2 :
Figure 2: The IR spectrum of C 84 -D 2 :22 in a mode.
is in

Table 2 :
The relative intensities of the absorption bands of C 76 -D 2 computed from   and from the Ψ values in adequate integration ranges.