Theory of Normal Vibrations of Chain Molecules with Finite Length

Matsuda, Hirotsugu; Okada, Kenkichi; Takase, Toshiro; Yamamoto, Takaya

doi:10.1063/1.1726118

Cited by 50 publications

(23 citation statements)

References 20 publications

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“…For the CCC bending mode, N is equal to m . A series of infrared (and Raman) bands observed for n ‐alkanes of a planar zigzag conformation showed smooth curves when the vibrational frequencies were plotted against the phase angle δ 9–12, 14. These curves are called vibrational frequency/phase difference dispersion curves, and they can be reproduced theoretically by the calculation of the normal‐mode frequencies of an infinitely long polymethylene chain as functions of δ 17–20.…”

Section: Resultsmentioning

confidence: 98%

“…In these analyses, a vibrational mode of the methylene unit is replaced with an oscillator, and in this way the coupling between serially arrayed oscillators is considered. This concept is called a simply coupled oscillator model and has been used well for the analysis of progression bands observed for a series of n ‐alkane compounds 9–15. When this concept is applied to the progression bands of nylons, however, the interpretation is more complicated 1–5.…”

Section: Introductionmentioning

confidence: 99%

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New interpretation of progression bands observed in infrared spectra of nylon‐m/n

Yoshioka

Tashiro

Ramesh

2003

J Polym Sci B Polym Phys

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A series of progression bands observed in the infrared spectra of nylon-m/n and their model compounds have been interpreted in a new manner on the basis of simply coupled oscillator models of zigzag alkyl chains. Nylon-m/n possesses the methylene sequences of (CH 2 ) m and (CH 2 ) nϪ2 , and so the effective models of m and n Ϫ 2 coupled oscillators, respectively, had previously been assumed for the methylene rocking-twisting mode, for example. However, the spectral patterns of progression bands predicted by this previously proposed model have been found to be inconsistent with those observed for many kinds of nylon samples with various m and n values. It is rather reasonable to assume that the effective numbers of oscillators should be m Ϫ 2 and n Ϫ 4 for the methylene rocking, twisting, and wagging modes of the (CH 2 ) m and (CH 2 ) nϪ2 sequences, respectively. In other words, the infrared progression bands observed for methylene local modes of nylon-m/n may be interpreted reasonably with the data of n-alkane molecules with the chemical formulae CH 3 (CH 2 ) mϪ2 CH 3 and CH 3 (CH 2 ) nϪ4 CH 3 . For the C™C stretching modes, the equivalent n-alkanes are CH 3 (CH 2 ) mϪ1 CH 3 and CH 3 (CH 2 ) nϪ3 CH 3 , respectively. In the simply coupled oscillator model, the vibrational mode of one methylene group is represented by an oscillator, for example. Our new concept is to isolate the terminal oscillator adjacent to the amide group from the other oscillators in the inner parts of the methylene zigzag sequence. This corresponds to a physical situation in which the methylene group adjacent to the amide group shows a different vibrational behavior of larger amplitude than those of the inner methylene sequence, as supported by broad-line NMR data and molecular dynamics calculations reported in the literature. Another possibility is a difference in the electron structure of the methylene unit adjacent to the amide group from that of the inner methylene sequence, resulting in a difference in the force constant and giving a vibrational decoupling between these two types of methylene units.

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Section: Resultsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

New interpretation of progression bands observed in infrared spectra of nylon‐m/n

Yoshioka

Tashiro

Ramesh

2003

J Polym Sci B Polym Phys

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“…37 The measurement of amorphous and NCCT conformers via Raman spectroscopy is based on CH 2 twist peaks in the (1290 to 1310) cm −1 region of the spectrum. Peaks in this region do not appear to follow simple coupled oscillator theory, 37, 38 but the Raman scattering intensities of alkane chains with different amounts of gauche bonds have been calculated by Meier et al . 18, 39 using ab initio methods.…”

Section: Resultsmentioning

confidence: 99%

Raman analysis of bond conformations in the rotator state and premelting of normal alkanes

2016

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We perform Raman spectroscopic measurements on normal alkanes (CnH2n+2) to quantify the n dependence of the conformational disorder that occurs below the melt temperature. We employ a three-state spectral analysis method originally developed for semi-crystalline polyethylene that posits crystalline, amorphous, and non-crystalline consecutive trans (NCCT) conformations to extract their respective mass fractions. For the alkanes studied that melt via a rotator phase (21 ≤ n ≤ 37), we find that conformational disorder can be quantified by the loss of NCCT mass fraction, which systematically decreases with increasing chain length. For those that melt directly via the crystal phase (n ≥ 40), we observe NCCT conformational mass fractions that are independent of chain length but whose disordered mass fraction increases with length. These complement prior IR measurements which measure disorder via gauche conformations, but have not been able to measure the mass fraction of this disorder as a function of n. An interesting feature of the three-state analysis when applied to alkanes is that the measured fraction of disordered chain conformations in the rotator phase of (10 to 30) % greatly exceeds the mass fraction of gauche bonds (1 to 7) % as measured from IR; we reconcile this difference through DFT calculations.

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“…For this, an analytical form for the vibrational states depending on system size is needed, especially for obtaining the selection rules. Unfortunately, the eigenvalue problems of vibrational states for finite systems are more complicated (because of the end effect) than those of electronic states as well as those of vibrational states for infinite systems, so that little has been published [9].…”

Section: Introductionmentioning

confidence: 99%

Application of molecular orbital graph theory to vibrational problems of finite chain systems

Lü

Tachibana

Yamabe

1990

Int J of Quantum Chemistry

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A generating function approach based on molecular orbital graph theory is presented that provides a straightforward way of obtaining the secular polynomials and energy bands for repeated unit systems from polynomial recurrence expressions. The possibility of obtaining the analytical energy-level spectrum of the system can also be predicted. These results are then used to discuss the vibrational problems of finite chain systems with single-and double-component lattices. It seems to be the first report describing the vibrational states of an (AB)N chain. *On leave from the Changchun

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Theory of Normal Vibrations of Chain Molecules with Finite Length

Cited by 50 publications

References 20 publications

New interpretation of progression bands observed in infrared spectra of nylon‐m/n

New interpretation of progression bands observed in infrared spectra of nylon‐m/n

Raman analysis of bond conformations in the rotator state and premelting of normal alkanes

Application of molecular orbital graph theory to vibrational problems of finite chain systems

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