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2014 | OriginalPaper | Chapter

4. Unbranched n-Alkanes

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Abstract

In this chapter, Raman jet spectra are presented and compared with quantum chemical calculations. Raman bands are assigned and \({n_{c}} = 17\) is identified as the critical chain length beyond which n-alkanes prefer a folded “hairpin” conformation over an extended all-trans conformation.

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Footnotes
1
The shown example is intended to serve an illustrative purpose; more recent calculations of the pentane PES are available (for example Refs. [24]).
 
2
A hydrocarbon chain with \(n\) carbon atoms involves \(n-3\) C–C–C–C segments leading to torsional isomerism.
 
3
A prominent example is the case of pentane: The g\(^\pm \)g\(^\pm \) conformer is found to have an enthalpy of \(\approx \)3.9 \({{\text {kJ}}}\,{\text {mol}}^{-1}\) relative to tt—less then twice the enthalpy difference of the single gauche conformer (\(\approx \)2.6\(~{{\text {kJ}}}\,{\text {mol}}^{-1}\)) [19].
 
4
Snyder reported this value based on the agreement between simulated and observed Raman spectra of liquid alkanes. The deviation between the energy value used by Snyder and the one used here might stem from different structural preferences of liquid and gaseous alkanes [25] (intermolecular interactions outweigh intramolecular interactions).
 
5
The number of vibrational degrees of freedom \(f_\mathrm{vib}\) may be calculated by \(f_\mathrm{vib}=3N-6\), using the overall number of atoms \(N\), or, more conveniently, by \(f_\mathrm{vib}=9n\), using the chain length \(n\) (\(N=3n+2\)).
 
6
In the double harmonic approximation, the force pulling the molecule back to its equilibrium geometry is proportional to the displacement along the normal coordinates, yielding a parabolic potential. On top of this, the polarizability is treated as depending linearly on the displacement along the normal coordinates. Terms of higher order in the displacement are neglected for both, the force and the polarizability.
 
7
For the all-trans conformer of the shortest alkane considered, tridecane (\(n=13\)), the largest rotational constant is \(\approx \)0.21 \(\mathrm{~cm}^{-1}\). Calculating for a linear rigid rotator, this would translate to a characteristic rotational temperature \(\theta _\mathrm{rot}<0.5\) K. The classical approximation holds for \(T \gg \theta _\mathrm{rot}\), and thus in this case even at low rotational temperatures in jet expansions.
 
8
This is also apparent from the fact that vibrational partition function approaches infinity, in case a wavenumber approaches zero (see Eq. 4.7).
 
9
This is close to important all-trans accordion vibrations and hairpin vibrations, see later in the text.
 
10
Pentane: \(1.77 \times 10^{-34}\) \({{\text {m}}^2\,{\text {sr}}^{-1}}\) (at 396 \({\text {cm}^{-1}}\)); hexane: \(1.74 \times 10^{-34}\) \({{\text {m}}^2\,{\text {sr}}^{-1}}\) (at 366 \({\text {cm}^{-1}}\)).
 
11
A general discussion of this aspect will be given in more detail in Sect. 6.​1.
 
12
Snyder uses the opposite phase description for the methylene twisting-rocking modes, because of a different coordinate definition [29].
 
13
Unscaled harmonic wavenumbers.
 
14
The weak dependence of the CH-stretching band on the carrier gas supports this assumption, see Fig. 3.​10 in Sect. 3.​2.
 
15
That is, a high amount of air in the expansion, sucked in by the brass saturator. If so, this would invite for further measurements with helium mixed with a substantial amount of nitrogen.
 
16
Based on a linear extrapolation of the published energies for \(n=14,22,\) and \(30\).
 
17
MM2: Ref. [21], MM3: Ref. [45], AMBER energy calculated with Gaussian 09 [96].
 
18
Applies to the x\(^\pm \)g\(^\mp \) pentane conformer with the highest energy relative to tt pentane.
 
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Metadata
Title
Unbranched n-Alkanes
Author
Nils Olaf Bernd Lüttschwager
Copyright Year
2014
DOI
https://doi.org/10.1007/978-3-319-08566-1_4

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