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J. Phys. Chem. A 2010, 114, 1118–1122
Helical C2 Structure of Perfluoropentane and the C2W Structure of Perfluoropropane Joseph A. Fournier,† Robert K. Bohn,*,† John A. Montgomery, Jr.,‡ and Masao Onda§ Departments of Chemistry and Physics, UniVersity of Connecticut, Storrs, Connecticut 06269-3060, and Department of Chemistry, Faculty of Science and Technology, Sophia UniVersity, Kioicho 7-1, Chiyoda-ku, Tokyo 102-8554, Japan ReceiVed: September 28, 2009
Saturated hydrocarbons have structures with completely staggered bonds and dihedral angles of 180°. Substituting hydrogen by fluorine results in a slight shift from 180°, giving rise to a helical structure. X-ray diffraction studies on fibers and computational studies on perfluoroalkanes estimate a dihedral angle of about 17° from the trans position. The rotational spectra of perfluoropentane and its three 13C isotopomers have been observed and assigned using a pulsed-jet Fourier transform microwave spectrometer. The rotational constants for the parent species are A 990.6394(3) MHz, B 314.0002(1) MHz, and C 304.3703(1) MHz, respectively. The determination of an exact dihedral angle has been challenging, as the helical twist has proven to be quite sensitive to the structural inputs and constraints. A series of r0 structures incorporating various model constraints and a Kraitchman analysis gives a range of 13-19° for the torsional angle. An objective approach, which only assumes overall C2 symmetry, is to scale the principal coordinates from ab initio models by the square root of the ratio of the observed second moments to the computed second moments. The scaled structures of computed models at various levels of theory reproduce the parent second moments exactly and the 13C second moments very well, giving a dihedral angle of 17 ( 1° from trans. The microwave spectrum of perfluoropropane has also been observed and assigned. The rotational constants are A 1678.5982(9) MHz, B 900.1968(10) MHz, and C 955.3216(11) MHz, respectively. Unlike longer perfluoroalkanes, perfluoropropane has a nonhelical, C2V structure. Computations are in excellent agreement with experimental results. I. Introduction The helical structure of polytetrafluoroethylene (PTFE) is well established.1 The structure can be characterized in two manners, by a helical perspective or a molecular perspective. The helical perspective,2 used by X-ray crystallographers, describes the structure in terms of the following three parameters: the distance from each atom to the helical axis (helical radius), F; the helical angle made about the helical axis, θ; and the translation (pitch) about the helical axis, d. The molecular perspective defines the structure by the C-C bond lengths, r; CCC bonds angles, φ; and CCCC dihedral angles, τ. Visualized representations of the two perspectives can be seen in Figure 1. The mathematical relationships for converting from one set of parameters to the other are known and are displayed in eqs 1 and 2.2,3 Equation 1: Helical parameters as functions of molecular parameters.
r2 ) d2 + 4F2 sin2(θ/2) cos(φ/2) ) (1 - d2 /r2)1/2 sin(θ/2) tan(τ/2) ) (d/r) tan(θ/2)
(2)
X-ray crystal structure studies reveal that PTFE undergoes several phase changes.4 Below 19 °C (phase II) the chain twists 180° per 13 carbon atoms, a helical angle of 13.8°. This is equivalent to ∼163° dihedral angle, or about 17° away from trans. Between 19 and 30 °C (phase IV) the chain untwists slightly, giving a 180° turn per 15 carbon atoms. This corresponds to a helical angle of 12.0°. Above 30 °C (phase I) further disorder enters the structure but the helical angle does not change. All of these phases are disordered to various degrees so few molecular structure details are revealed. Attempts to prepare single crystals of specific perfluorocarbon compounds without significant defects have not succeeded. An electron
1 cos θ ) [-cos φ + cos τ - cos φ cos τ - 1] 2 d2 ) r2(1 - cos τ)(1 - cos φ)/(3 + cos φ - cos τ + cos φ cos τ) F2 ) 2r2(1 + cos φ)/(3 + cos φ - cos τ + cos φ cos τ)2
(1) Equation 2: Molecular parameters as functions of helical parameters. †
Department of Chemistry, University of Connecticut. Department of Physics, University of Connecticut. § Sophia University. ‡
Figure 1. Helical (left) and molecular (right) perspectives for describing a helix. The dashed line represents the helical axis and the blue circles represent CF2 groups.
10.1021/jp9093035 2010 American Chemical Society Published on Web 12/16/2009
Structures of Perfluoropentane and Perfluoropropane
Figure 2. Top view of perfluoropentane (left) and perfluoropropane (right) along the b-axis.
Figure 3. Staggered structure of pentane, C5H12 (left), with dihedral angles of 180°, the helical structure of perfluoropentane, C5F12 (center), with a twist of 17° away from 180°, and the nonhelical C2V structure of perfluoropropane, C3F8 (right).
J. Phys. Chem. A, Vol. 114, No. 2, 2010 1119 and reasonable signals were observed throughout the concentration range. The sample mixture flowed at 1.5 atm into the nozzle of the pulsed-jet Fourier transform microwave spectrometer16 of the Southern New England Microwave Consortium,17 and gas pulses were admitted at 5 Hz. The nozzle was mounted in one of the cavity mirrors, five microwave pulses were observed per gas pulse, and rotational transitions were observed in the range between 9 and 18 GHz, although the complete range was not scanned. Transitions were observed as Doppler doublets and line widths in the power spectrum range 10-20 kHz with uncertainties estimated to be about 2 kHz. The rotational temperature of the expanded gas was estimated to be about 5 K. The perfluoropropane measurements were carried out at Sophia University using a pulsed-jet Fourier transform microwave spectrometer.16,18,19 The sample was purchased from Synquest Laboratories and used directly. The sample was mixed with argon to a concentration of about 2%. Rotational transitions were observed in the 6-16 GHz range. III. Results
diffraction study of thin films of n-C24F50 revealed unit cell information but not molecular structural details.5 The helicity of PTFE has been attributed to steric and dipole repulsions due to the overcrowding between F atoms on alternate carbons. A slight twist in the carbon chain away from trans alleviates these repulsions (Figures 2 and 3). Much computational work has been devoted to PTFE and its smaller perfluoroalkane oligomers.6–8,10–15 Perfluorobutane (C4F10), as the simplest model for PTFE, was first investigated by Dixon6 with a modest basis set and was shown to have a helical structure with a dihedral angle ∼15° from trans and a higher energy gauche form. Smith and co-workers,7 using a larger basis set, predicted a third stable minimum with a torsion of ∼90°, called the ortho form. A nitrogen matrix-isolation IR spectrum of perfluorobutane was obtained by Albinsson and Michl8 and each form was assigned by comparison to ab initio predictions with only small quantities of the ortho form observed. A microwave study of perfluorobutane was later performed9 with only the gauche form observed. The dihedral angle of the gauche conformer was determined to be 54.9 ( 2.4°. The helical trans form apparently has too small a dipole moment to observe a spectrum. The dihedral angle in perfluoropentane (C5F12) has been calculated to be ∼16-17° away from trans using a variety of computational methods.7,10–15 Most of these studies considered ways to model PTFE and how to computationally reproduce the structural characteristics of PTFE through force fields,11,12 density functional theory,10,14 and other methods.7 To complement the computational studies, we thought it was important to experimentally determine the structure of the lowest energy helical form of perfluoropentane, particularly the value of the CCCC dihedral angle. The microwave spectra of perfluoropentane and its three 13C isotopomers have been observed and assigned and the molecular geometry determined using several methods. The spectrum of perfluoropropane (C3F8) has also been observed and assigned. II. Methods Perfluoropentane was purchased from Synquest Laboratories and studied directly. Vapor of the sample was transferred into a 7 L stainless steel bulb to a pressure of 0.09, and 4.5 atm He was added to produce a 2% sample mixture. During the course of experiments, the sample was diluted up to 10 times with He
C5F12 Parent Isotopomer. An automatic overnight scan in the 11-11.7 GHz region displayed a beautiful b-type Q-branch with a band head near 11 584 MHz. For a nearly prolate rotor with b-type transitions, similar Q-branches should be observed at spacings of twice A-C. Another beautiful Q-branch was observed near 10 220 MHz so that A-C ∼ 680 MHz. The 10 220 MHz branch corresponds to ∆Kp of 8 r 7 and ∆Kp is 9 r 8 for the 11 584 branch. All of those Q-branch lines are doubly degenerate so they do not distinguish B and C. Lower Kp R-branch transitions were needed to be measured to avoid degeneracies and distinguish B from C. A pair of lines separated by 0.3 MHz was observed at 10 335 MHz near estimated frequencies and splitting of the 946-835 and 945-836 transitions. This assignment was made and new lines were predicted that were measured, confirming and refining the assignment. Rotational quantum numbers of transitions were observed up to J ) 40 and Kp ) 9. The full array of assigned transitions is listed in Supplementary Table 1 and the fitted spectroscopic parameters are given in Table 1. The S/N ratio for many of the transitions was >100 allowing the opportunity to search for 13C isotopomers in natural abundance. C5F12 13C Isotopomers. The initial parent model was adjusted to fit the observed rotational constants by simultaneously fitting three parameters: the C-C bond length, CCC bond angle, and CCCC dihedral angle. The rotational constants for the three possible 13C isotopomers were predicted from this model. The Pickett suite of programs20 was used to predict the most intense transitions. Since the natural abundance of 13C is about 1%, the intensities of 13C transitions are about 0.01 that of the parent species. The 13C1 and 13C2 positions in perfluoropentane are doubly degenerate, assuming C2 symmetry, allowing intensities of about 2% of that of the parent. Since C5F12 is nearly a symmetric top, there are many pairs of high K transitions that are degenerate. This additional degeneracy allows for relatively intense lines for the 13C1 and 13C2 isotopomers. The observed intensities for the 13C1 and 13C2 isotopomers are twice that of the 13C3 species, consistent with C2 symmetry. Sixteen of the degenerate transitions were observed for 13C1, five for 13C2, and seven for 13C3. The slightly split (
