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UDC 535.338.42+539.196
PHYSICS
I. F. KOVALEV, V. A. ARBUZOV, L. A. OZOLIN,
M. G. VORONKOV
INTEGRAL INTENSITIES
IN INFRARED VIBRATIONAL ABSORPTION SPECTRA
OF CYCLIC POLYDIMETHYLSILOXANES
(Presented by Academician I. V. Obreimov, February 2, 1968)
This paper presents the results of an experimental study of the principal parameters of vibrational absorption bands in the infrared spectra of cyclic polydimethylsiloxanes \([(\mathrm{CH}_3)_2\mathrm{SiO}]_n\) \((n = 4—7)\), for which previously only the positions of the bands and their qualitative intensities had been measured \((^{1-6})\). In the region \(400—3000\ \mathrm{cm}^{-1}\), using an IKS-14 spectrophotometer, the frequencies, integral intensities, absorption coefficients at the maximum, and half-widths were measured. For the frequency interval \(400—670\ \mathrm{cm}^{-1}\), samples of the pure liquid were studied; for \(700—860\ \mathrm{cm}^{-1}\) and \(860—3000\ \mathrm{cm}^{-1}\), solutions of different concentrations in \(\mathrm{CS}_2\) and \(\mathrm{CCl}_4\), respectively, were used. The spectrograms were processed mainly according to Johansen \((^7)\). The obtained values of the spectral characteristics and the interpretation of the vibrational spectra are given in Table 1.
The infrared absorption spectrum of \([(\mathrm{CH}_3)_2\mathrm{SiO}]_n\) molecules has clearly expressed features. Owing to the character of the symmetry, the stretching vibrations of the Si—O—Si bridges in these molecules are split into a number of bands. The symmetric stretching bridge vibrations of the ring lie in the region \(480—550\ \mathrm{cm}^{-1}\) and are rather weak. For one of these vibrations in each compound \((480—495\ \mathrm{cm}^{-1})\), a very strong polarized line is observed in the Raman spectrum. The opposite picture is characteristic of the antisymmetric vibrations \(\nu_{as}(\mathrm{Si—O—Si})\), which appear in the region \(1060—1100\ \mathrm{cm}^{-1}\).
The distribution of intensities in the absorption spectra of the compounds under consideration shows that, with very high probability, levels corresponding to ring vibrations are excited in them. The antisymmetric vibrations \(\nu_{as}(\mathrm{Si—O})\) account for \(50—60\%\) of the total absorption, excluding the unstudied region \(150—450\ \mathrm{cm}^{-1}\). In the liquid phase, for each compound, two vibrations \(\nu_{as}(\mathrm{Si—O—Si})\) are recorded. In the spectra of \(D_6\) and \(D_7\) \([D = (\mathrm{CH}_3)_2\mathrm{SiO}]\), the bands corresponding to these vibrations can be separated (although only with a rather large approximation). In \(D_5\) they overlap more closely. In the spectrum of \(D_4\), the vibrations are recorded as a single band. The anomalously large value of the half-width of \(\nu_{as}(\mathrm{Si—O—Si})\), in calculations for \(D_4\) and \(D_5\) in the representation of a single band, indicates the superposition of two bands in this region. The most intense band \(\nu_{as}(\mathrm{Si—O—Si})\) may reasonably be assigned to a degenerate type of vibrations. In the spectra of \(D_6\) and \(D_7\) it is 3–4 times more intense than the observed second band. The position of the intense band changes within \(30\ \mathrm{cm}^{-1}\) as the ring increases. In compounds with an even number of Si—O—Si bridges it lies in the region \(1075—1080\ \mathrm{cm}^{-1}\).
Comparison of the total intensities for the \(\nu_{as}(\mathrm{Si—O—Si})\) bands shows a systematic and fairly linear increase of this sum with increasing number of Si—O—Si bridges in the ring. The deviation from linearity lies within \(10\%\). In hexamethyldisiloxane, the antisymmet-
Table 1
Principal parameters of the vibrational infrared absorption bands
| Interpretation | Frequency $\nu$, cm$^{-1}$, $[(\mathrm{CH}_3)_2\mathrm{SiO}]_4$ | Integral intensity $A\cdot10^9$, cm$^2$/molecule·sec, $[(\mathrm{CH}_3)_2\mathrm{SiO}]_4$ | Absorption coefficient at maximum $K_{\max}$, cm$^{-1}$, $[(\mathrm{CH}_3)_2\mathrm{SiO}]_4$ | Half-width $\gamma$, cm$^{-1}$, $[(\mathrm{CH}_3)_2\mathrm{SiO}]_4$ | Frequency $\nu$, cm$^{-1}$, $[(\mathrm{CH}_3)_2\mathrm{SiO}]_6$ | Integral intensity $A\cdot10^9$, cm$^2$/molecule·sec, $[(\mathrm{CH}_3)_2\mathrm{SiO}]_6$ | Absorption coefficient at maximum $K_{\max}$, cm$^{-1}$, $[(\mathrm{CH}_3)_2\mathrm{SiO}]_6$ | Half-width $\gamma$, cm$^{-1}$, $[(\mathrm{CH}_3)_2\mathrm{SiO}]_6$ |
|---|---|---|---|---|---|---|---|---|
| $\nu_s(\mathrm{Si}-\mathrm{O})$ | 478 551 |
— 250 |
— 500 |
— 20.0 |
495 516 |
90 260 |
90 200 |
24.7 36.0 |
| $\nu+\delta_\perp$ | 629 | v. wk. | — | — | 587 634 |
200 v. wk. |
180 — |
35.0 — |
| $\nu_s(\mathrm{Si}-\mathrm{C})$ | 658 | 60 | 270 | 7.9 | 657 667 682 |
(80) med. med. |
— — sh. |
— — — |
| $\rho(\mathrm{CH}_3),\ \nu_s(\mathrm{Si}-\mathrm{C})$ $\nu_{as}(\mathrm{Si}-\mathrm{C}),\ \rho(\mathrm{CH}_3)$ |
694 795 |
460 v. wk. |
1500 — |
12.1 — |
699 781 |
1030 v. wk. |
2350 sh. |
12.8 — |
| $\rho(\mathrm{CH}_3),\ \nu_{as}(\mathrm{Si}-\mathrm{C})$ | 807 | 6400; total 5960 | 15 800 | 9.7 | 806 818 |
8090; total 6990 (770) |
19 400 (2000) sh. |
10.7 (11) |
| $\rho(\mathrm{CH}_3)$ | 856 877 |
total (380) | — — |
— — |
856 871 |
total (620) | — sh. |
— — |
| $\nu_{as}(\mathrm{Si}-\mathrm{O})$ | 1076 | 16 000; total 15 060 | 19 900 | 44 | 1078 1098 |
22 660; total 21 940 (5300) |
17 200 (4700) |
35 31 |
| $\delta_s(\mathrm{CH}_3)$ | 1264 | 2170 | 25 500 | 2.8 | 1263 | 3420 | 23 700 | 4.9 |
| $\delta_{as}(\mathrm{CH}_3)$ | 1405 1412 1448 |
— (240); total 390 — |
— (380) — |
— — — |
1406 1413 1448 |
— (440); total 800 — |
— (490) — |
— — — |
| $\nu_s(\mathrm{C}-\mathrm{H})$ | 2909 | 190 | 300 | 24 | 2909 | 330 | 340 | 23 |
| $\nu_{as}(\mathrm{C}-\mathrm{H})$ | 2966 | 1100 | 2500 | 18.4 | 2967 | 1560 | 2450 | 19.2 |
Table 1 (continued)
| Interpretation | Frequency $\nu$, cm$^{-1}$ | Integral intensity $A\cdot10^9$, cm$^2$/(molec. sec.) | Absorption coefficient at maximum $K_{\max}$, cm$^{-1}$ | Half-width $\gamma$, cm$^{-1}$ | Frequency $\nu$, cm$^{-1}$ | Integral intensity $A\cdot10^9$, cm$^2$/(molec. sec.) | Absorption coefficient at maximum $K_{\max}$, cm$^{-1}$ | Half-width $\gamma$, cm$^{-1}$ |
|---|---|---|---|---|---|---|---|---|
| \multicolumn{4}{c}{\([(CH_3)_2SiO]_5\)} | \multicolumn{4}{c}{\([(CH_3)_2SiO]_7\)} | |||||||
| $\nu_s(\mathrm{Si—O})$ | 482 | 40 | 60 | 24.9 | 490 | — | — | — |
| $\nu_s(\mathrm{Si—O})$ | 529 | 110 | 150 | 25.0 | 518 | (300) | (150) | (44) |
| $\nu+\delta_\perp$ | 615 | 60 | 90 | 21.4 | 569 | 85 | 90 | 22.0 |
| $\nu+\delta_\perp$ | 626 | 160 | 110 | 26.7 | ||||
| $\nu_s(\mathrm{Si—C})$ | 671 | (40) | — | — | 672 | weak | — | — |
| $\nu_s(\mathrm{Si—C})$ | 678 | weak | — | — | ||||
| $\rho(\mathrm{CH}_3),\ \nu_s(\mathrm{Si—C})$ | 698 | 680 | 1970 | 10.7 | 700 | 1240 | 2180 | 12.6 |
| $\nu_{as}(\mathrm{Si—C}),\ \rho(\mathrm{CH}_3)$ | 790 | very weak | sh. | — | 802 | 8950 } 7980 | 17 640 | 11.2 |
| $\nu_{as}(\mathrm{Si—C}),\ \rho(\mathrm{CH}_3)$ | 801 | (8070) } 6800 | — | 13.0 | 820 | (1120) } 7980 | (2150) | (11) |
| $\nu_{as}(\mathrm{Si—C}),\ \rho(\mathrm{CH}_3)$ | 815 | weak | sh. | — | ||||
| $\rho(\mathrm{CH}_3)$ | 856 | } (550) | — | — | 859 | (1120) | — | — |
| $\rho(\mathrm{CH}_3)$ | 870 | } (550) | sh. | — | 876 | very weak | sh. | — |
| $\nu_{as}(\mathrm{Si—O})$ | 1070 | } 20 500 | — | — | 1057 | (21 850) } 24 200 | (17 000) | (32) |
| $\nu_{as}(\mathrm{Si—O})$ | 1087 | 28 200 } 20 500 | 16 000 | 62 | 1085 | 8200 } 24 200 | 5800 | 36 |
| $\delta_s(\mathrm{CH}_3)$ | 1262 | 2550 | 25 900 | 3.5 | 1263 | 4520 | (20 000) | 5.4 |
| $\delta_{as}(\mathrm{CH}_3)$ | 1405 | } 750 | — | — | 1405 | } 1160 | — | — |
| $\delta_{as}(\mathrm{CH}_3)$ | 1412 | (380) } 750 | (440) | — | 1413 | (510) } 1160 | (490) | — |
| $\delta_{as}(\mathrm{CH}_3)$ | 1448 | } 750 | — | — | 1445 | } 1160 | — | — |
| $\nu_s(\mathrm{C—H})$ | 2909 | 220 | 320 | 25 | 2910 | 320 | 300 | 24 |
| $\nu_{as}(\mathrm{C—H})$ | 2966 | 1450 | 2670 | 18.4 | 2966 | 1860 | 2250 | 19.3 |
Notes. 1. The summed intensities were determined independently and without taking into account the correction for wings. The parameters for the $\nu_{as}(\mathrm{Si—O})$ vibrations in $D_4$ and $D_5$ were calculated by representing them as a single band. 2. The reproducibility of the results in calculations of the parameters $A$ and $\gamma$ was generally within 5–10%. The coefficient $K_{\max}$ is usually calculated with a larger error. Less accurate values of the parameters, obtained for strongly overlapping bands, are given in parentheses. 3. Notation: $\nu$ — stretching vibration, $\delta$ — deformation, $\rho$ — rocking, $\delta_\perp$ — “nonplanar” vibration of the ring, $s$ — symmetric band, $as$ — antisymmetric, av. — average intensity, weak — weak, very weak — very weak, sh. — shoulder.
band \(\nu_{as}(\mathrm{Si—O—Si})\) is observed in the region of 1050 cm\(^{-1}\). Its intensity \((1800\cdot10^{-9}\ \mathrm{cm}^2/\mathrm{molecule}\cdot\mathrm{s})\) is several times smaller than the average value falling on each \(\mathrm{Si—O—Si}\) unit in the cycles. A considerable value of the intensity is also characteristic of one of the antisymmetric stretching vibrations of the \(\mathrm{Si—C}\) bond, with a frequency of 800–810 cm\(^{-1}\). Although in this region there is superposition of closely spaced bands, and in separating them the introduction of a significant error is not excluded, here too the additivity factor is manifested. Of course, one cannot proceed from the assumption of an obligatory linear dependence of the intensity of the band under consideration on the number of identical bonds or groups corresponding to it in the molecule. In the general case this is a complex function (\(^8\)).
For methyl groups, the intensity of the antisymmetric stretching vibration \(\nu_{as}(\mathrm{C—H})\) increases linearly with increasing ring size. The bands of the methyl groups are characteristic in intensity and polarization. These groups have rather closed electron shells.
Table 2
Physical constants of compounds \([(\mathrm{CH}_3)_2\mathrm{SiO}]_n\)
| \(n\) | B.p., °C (pressure, mm) | M.p., °C | \(d_4^{20}\) | \(n_D^{20}\) |
|---|---|---|---|---|
| 4 | 175.8 (760) | 17.6 | 0.9561 | 1.3968 |
| 5 | 101 (20) | −43.5 | 0.9597 | 1.3982 |
| 6 | 128 (20) | −3.0 | 0.9672 | 1.4015 |
| 7 | 151 (20) | −31.5 | 0.9728 | 1.4040 |
Thus, analysis of the integral intensities shows that the change in dipole moments in cyclic polydimethylsiloxanes occurs primarily in normal vibrations belonging to antisymmetric stretching vibrations of the \(\mathrm{Si—O—Si}\) bridges and the \(\mathrm{Si—C}\) bonds. The probabilities of transitions in symmetric deformation and antisymmetric stretching vibrations in methyl groups are also significant. In the molecules considered, the additive character of the integral intensities of infrared vibrational absorption bands is clearly manifested.
It is of interest to estimate the magnitude of the cross sections of spontaneous combination scattering for the polarized lines \(\nu_s(\mathrm{Si—O})\). As an example, let us carry out calculations for the molecules \([(\mathrm{CH}_3)_2\mathrm{SiO}]_n\) (\(n=5, 6\)), in whose spectra the frequencies 488 and 493 cm\(^{-1}\), respectively, are identified with symmetric stretching vibrations of the \(\mathrm{Si—O}\) bond. The scattering coefficients \(S\) of these vibrations (on the cyclohexane scale) are equal to 2.77 and 3.21. Proceeding from the local-field correction (\(^3\)), on the basis of formulas (1), (2) (\(^9\)), the complete absolute cross sections of combination scattering per molecule per unit solid angle \(d\sigma/d\Omega\) for the Stokes wave 4358 Å are obtained as follows: in \([(\mathrm{CH}_3)_2\mathrm{SiO}]_5\), \(41\cdot10^{-30}\ \mathrm{cm}^2\); in \([(\mathrm{CH}_3)_2\mathrm{SiO}]_6\), \(47\cdot10^{-30}\ \mathrm{cm}^2\). In the case considered they will be the same for linearly polarized and for natural incident light. In the calculations of \(d\sigma/d\Omega\), conversion was made to the standard line 459 cm\(^{-1}\) of \(\mathrm{CCl}_4\), for which the value \(5b^{\prime 2}+7g^{\prime 2}\) was taken as \(13\cdot10^{-8}\ \mathrm{cm}^4\mathrm{g}^{-1}\) (\(^10\)).
The investigated cyclic polydimethylsiloxanes were synthesized and purified by the previously described method (\(^{11,12}\)) (see Table 2).
Saratov State Pedagogical Institute
Institute of Organic Synthesis
Academy of Sciences of the Latvian SSR
Received
1 II 1968
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