Fundamental Torsional Mode Research Articles

Far infrared spectrum, conformational stability, barriers to internal rotation, vibrational assignment, and ab initio calculations of 2-chloro-3-fluoropropene

The far infrared spectrum (375 to 30 cm−1) of gaseous 2-chloro-3-fluoropropene, CH2=C(CH2F)CI, has been recorded at a resolution of 0.10 cm−1. The fundamental asymmetric torsional mode is observed at 117.5 cm−1 with ten excited states falling to low frequency for thes-cis (fluorine atom eclipsing the double bond) conformer. For the higher energy gauche conformer, the asymmetric torsion is estimated to be at 94 cm−1. From these data the asymmetric torsional potential function has been calculated. The potential function coefficients are calculated to be in cm−1):V1=803±21,V2=−94±21,V3= 1025±10,V4=95±10, andV6=2±1, with an enthalpy difference between the more stables-cis and gauche conformera of 550±100 cm−1 (1.57±0.29 kcal/mol). This function gives values of 1227±50cm−1(3.51±0.14kcal/mol), 1266±200 cm−1 (3.62±0.57 kcal/mol), and 665±100 cm−1 (1.90±0.29 kcal/mol), for thes-cis to gauche, gauche to gauche, and gauche tos-cis barriers, respectively. From the relative intensities of the Raman lines of the gas at 652 cm−1 (gauche) and 731 cm−1 (s-cis) as a function temperature, the enthalpy difference is found to be 565±96 cm−1 (1.62±0.27 kcal/mol). However, the more polar gauche conformer remains in the crystalline solid. The Raman spectrum of the gas has been recorded from 3500 to 70 cm−1 and, utilizing these data and the previously reported infrared data, a complete vibrational analysis is proposed for both conformers. The conformational stability, barriers to internal rotation, fundamental vibrational frequencies, and structural parameters that have been determined experimentally are compared to those obtained from ab initio Hartree-Fock gradient calculations employing both the 3–21 G* and 6–31G* basis sets and to the corresponding quantities for some similar molecules.

Conformational stability, barrier to internal rotation, structural parameters, ab initio calculations, and vibrational assignment of cyclopropylcarbonyl chloride

The fundamental asymmetric torsional mode of cyclopropylcarbonyl chloride, c-C 3H 5-CClO, for the more stable cis conformer (carbonyl group oriented cis to the ring) is observed at about 54 cm −1. The corresponding mode for the high energy trans form is assigned to a Q-branch series with stronger intensity beginning at 87.4 cm −1, decreasing in frequency with successive excited states. From a study of the Raman spectra of the vapor at variable temperatures, it has been determined that the cis is more stable than the trans form by 171 ± 35 cm −1 (489 ± 100 cal mol −1) and that the cis conformer remains in the solid. From a similar study of the spectrum of the liquid, it is found that the trans form is slightly more stable than the cis form by 93 ± 27 cm −1 (266 ± 77 calmol −1). From these data, the potential function for internal rotation of the asymmetric top has been determined and the potential coefficients are: V 1 = 528 ± 14, V 2 = 1769 ± 27 and V 3 = −371 ± 15 cm −1. This potential is consistent with cis to trans and trans to cis barriers of 1934 and 1779 cm −1, respectively, and a conformational energy difference of 155 ± 56 cm −1 (443 ± 160 cal mol −1). The r 0 structural parameters have been obtained for the cis conformer from a combination of ab initio calculated parameters with appropriate off-set values and the fit of the previously reported microwave rotational constants for the two naturally occurring chlorine isotopes. The conformational stability, barriers to internal rotation and fundamental vibrational frequencies, which have been determined from experimental data, are compared with those obtained from ab initio Hartree—Fock gradient calculations with the 3-21G * and 6-31G * basis sets and results obtained for some similar molecules.

Raman and far‐infrared spectra, conformational stability, barriers to internal rotation, vibrational assignment and ab initio calculations of 2,3‐dicholoropropene

AbstractThe far‐infrared spectrum (375 to 30 cm−1) of gaseous 2,3‐dichloropropene, CH2C(CH2Cl)Cl, was recorded at a resolution of 0.06 cm−1. The fundamental asymmetric torsional mode is observed at 91.9 cm−1 with eight excited states falling to low frequency for the s‐cis (chlorine atom eclipsing the double bond) conformer. For the higher energy gauche conformer, the asymmetric torsion is estimated to be near 85 cm−1. Utilizing the s‐cis torsional frequency, the gauche dihedral angle and the enthalpy difference between conformers, the potential function governing the interconversion of the rotamers was calculated. The determined potential function coefficients are V1 = 1047 ± 96, V2 = −619 ± 68, V3 = 1216 ± 50 and V4 = 26 ± 22 cm−1, with an enthalpy difference between the more stable s‐cis and gauche conformers of 245 ± 30 cm−1 (0.70 ± 0.09 kcal mol−1). This function gives values of 1035 ± 10 cm−1 (2.96 ± 0.03 kcal mol−1), 2015 ± 150 cm−1 (5.76 ± 0.43 kcal mol−1) and 787 ± 10 cm−1 (2.25 ± 0.03 kcal mol−1) for the s‐cis to gauche, gauche to gauche and gauche to s‐cis barriers, respectively. From the relative intensities of the Raman lines of the liquid at 1633 cm−1 (gauche) and 1649 cm−1 (s‐cis) as a function of temperature, the enthalpy difference is found to be 334 ± 39 cm−1 (0.95 ± 0.11 kcal mol−1), but now with the gauche conformer more stable. Also, the more polar gauche conformer remains in the crystalline solid. The Raman spectrum of the gas was recorded from 3500 to 70 cm−1 and, utilizing these data and the previously reported infrared data, a complete vibrational analysis is proposed for both conformers. The conformational stability, barriers to internal rotation, fundamental vibrational frequencies and structural parameters which were determined experimentally are compared to those obtained from ab initio Hartree—Fock gradient calculations employing both the 3‐21G* and 6‐31G* basis sets and to the corresponding quantities for some similar molecules.

Far-infrared spectrum, barriers to internal rotation, structural parameters, and vibrational assignment of cyclopropylcarbonyl fluoride

The far-infrared (400 to 50 cm −1) spectrum of gaseous cyclopropylcarbonyl fluoride, c-C 3H 5CFO, was recorded at 0.1 cm −1 resolution. The fundamental asymmetric torsion for the most stable conformer, which has the carbonyl group oriented cis to the ring, is observed at 83.51 cm −1 with five torsionally excited-state transitions proceeding to lower frequencies. For the high energy trans conformer the fundamental asymmetric torsional mode was assigned to a series of C-type Q branches in the region of 94 to 85 cm −1. From these data the potential function for internal rotation of the asymmetric top was determined and the potential coefficients are: V 1 =459±10, V 2=2131±47, V 3 = −320±18, V 4 = 16 ± 15 cm −1 and V 5 = 57±9. The cis to trans and trans to cis barriers were determined to be 2307 ± 28 and 2111 ± 26 cm −1, respectively, with an enthalpy difference between the conformers of 196 ± 75 cm −1 (560 ± 214 cal mol −1). The conformational stability, barriers to internal rotation, and fundamental vibrational frequencies are compared with those obtained from ab initio Hartree-Fock gradient calculations at the 3-21G and 6-31G* basis set levels. The structural parameters were determined for c-C 3H 5CFO from the ab initio values, with adjustments, and the microwave data. The results obtained are compared with the corresponding results for some similar molecules.

Coupled lateral‐torsional behaviour of frame structures under earthquake loading

AbstractA series of parametrically defined experimental model structures has been tested under earthquake base loading using the SERC national U.K. earthquake simulator. The models have been designed with variable ratios of torsional to lateral stiffness, and with both symmetric and asymmetric mass distributions. This paper first describes the tests carried out to determine the basic dynamic model properties and the establishment of idealized analytical models which give accurate predictions of model behaviour under steady‐state loading and free‐vibration conditions. Secondly, a detailed discussion is made of the two highly coupled structural models having uncoupled torsional to lateral frequency ratio Rf = 1.2, commenting on the ability of the modal analysis procedures to predict accurately the maximum recorded responses. It is concluded that the theory underestimates the significance of the fundamental torsional mode of vibration in the combined structural response, and overestimates the contribution of the first lateral mode. These effects compensate each other on the side of the structure which is most severely affected by torsional response, but produce large inaccuracies on the side of the building which is commonly assumed to be affected beneficially by torsional coupling.

Tuning fork resonator

A piezoelectric coupled mode turning fork using the fundamental vibration of a flexural mode coupled with the fundamental mode of torsion. The fundamental frequency of the torsional mode is adjusted by masses near the side edges of the tine tips, and the fundamental frequency of the flexural mode being adjusted by masses near the center of the tine tips which are nodes of the fundamental torsional mode.

Far infrared spectra of methyl nitrate and methyl-d 3 nitrate

The far infrared spectra from 300 to 50 cm −1 of methyl nitrate, CH 3ONO 2, and methyl-d 3 nitrate, CD 3NO 2, have been recorded at a resolution of 0.12 cm −1. The fundamental methyl torsional mode has been observed at 204.5 cm −1 (154.2 cm −1 for CD 3ONO 2) with two excited states falling to lower frequencies which gives a V 3 barrier of 980 ± 40 cm −1 (2.80 ± 0.11 kcal/mol). The NO 2 torsion (methoxy) has been observed with the 1 ← 0 transition being at 133.7 cm −1 (119.5 cm −1 for CD 3ONO 2) and eight successive excited states falling to lower frequencies. From these data the twofold barrier to internal rotation has been calculated to be 2650 ± 75 cm −1 (7.69 ± 0.21 kcal/mol).

Torsional-mode losses at contacts between homogeneous fiber waveguides and supporting structures

A fundamental torsional mode, transmitted through a homogeneous fused silica fiber of circular cross section, is used to probe the acoustic contact losses at the fiber supports. Losses introduced by clamping-bar supports are measured over one to two decades of clamping force for clamping materials spanning a wide range of elastic properties. The data are found to agree approximately with an analysis proceeding from one basic assumption, that the power loss caused by an element of contact area is proportional to the area. Development of this concept leads to a loss exponent proportional to F2/3 and s2/3, where F is applied force and s is a mean compliance parameter for the fiber and support bars. Measurements also show that the frequency dependence of the loss exponent is either weak or nonexistent. The F2/3 law plus a calculated dependence of loss on the fiber and support-bar diameters are used to extrapolate the data to smaller loads and thinner supports to estimate losses for several types of supporting structures.

Ramanspektren von Se 2Cl 2 und Se 2Br 2 erregt mit einem quasikontinuierlichen Rubinlaser

The Raman spectra of pure Se 2Cl 2 and Se 2Br 2 and of solutions in CS 2, CCl 4 and benzene have been recorded using a quasicontinuous ruby laser as light source. The depolarization ratios of all Raman lines were determined. Assignments are proposed (Se 2Cl 2 : C 2 symmetry; Se 2Br 2:C 2 v symmetry). In the case of Se 2Br 2 the assignment is not in agreement with those reported by previous authors (C 2). The lowest frequency Raman line is assigned to the fundamental torsional mode.

Viscoelastic Properties of Polystyrene Solutions

Quartz crystals resonant in the fundamental torsional mode at frequencies of 40 and 73 kc/sec have been used to measure the viscoelastic properties of solutions of polystyrene in toluene, methylethylketone, and cyclohexane. A monodisperse polystyrene sample of molecular weight 2.39×105 was employed. The results have been compared with those of Harrison, Lamb, and Matheson (1964) for dilute solutions in toluene of a number of polystyrene samples of different molecular weight. In toluene, it is found that 25% of the contribution of the polymer to the viscosity of the solution is not able to take part in viscoelastic relaxation, and that the dynamic viscosity at high frequencies (the “Einstein viscosity”) is greater than the solvent viscosity. Under these conditions, the viscoelastic behavior of all time solutions of toluene of polystyrene samples of different molecular weights agrees with the predictions of the Rouse theory. From time value obtained for the Einstein viscosity of the solutions, it is shown that the radius of time equivalent hydrodynamic sphere is approximately proportional to the square root of the molecular weight of the polymer molecule. The viscoelastic behavior of the solution in methylethylketone is intermediate between the predictions of the Zimm and Rouse theories.

The viscoelastic properties of polystyrene solutions

Quartz crystals resonant in the fundamental torsional mode at frequencies of 40 and 73 kc/s have been used to measure the viscoelastic properties of solutions of polystyrene in toluene, methylethyl ketone and cyclohexane. A monodisperse polystyrene sample of molecular weight 2.39 x 10 5 was employed. The results have been compared with those of Harrison, Lamb & Matheson (1964) for dilute solutions in toluene of a number of polystyrene samples of different molecular weights. In toluene it is found that 25 % of the contribution of the polymer to the viscosity of the solution is not able to take part in viscoelastic relaxation, and that the dynamic viscosity at high frequencies (the ‘Einstein viscosity’) is greater than the solvent viscosity. Under these conditions the viscoelastic behaviour of all the solutions in toluene of polystyrene samples of different molecular weights agrees with the predictions of the Rouse theory. From the value obtained for the Einstein viscosity of the solutions, it is shown that the radius of the equivalent hydrodynamic sphere is approximately proportional to the square root of the molecular weight of the polymer molecule. If one assumes that the radius of the equivalent hydrodynamic sphere of a given polymer molecule is the same in all solvents, then the viscoelastic behaviour of the solution in methylethyl ketone is intermediate between the predictions of the Zimm and Rouse theories. The solution in cyclohexane seems to show behaviour close to that predicted by the Zimm theory. The possibility of using such measurements to determine molecular weight distributions is discussed.

The viscosity of liquid helium 3

Abstract Measurements have been made of the viscosity of liquid 3He under its saturated vapour pressure in the temperature range 0•14—2•1°K. In the experiments, a polished cylinder of quartz oscillates in the liquid in its fundamental elastic torsional mode, the viscosity being obtained by observing the logarithmic decrement of the system. The resulting values of the viscosity are in agreement with those of Osborne et al. (1949) and of Taylor and Dash (1957), but are appreciably higher than those of Zinov'eva (1958). At lower temperatures the present results appear to extrapolate towards values consistent with the coefficients of the absorption of sound observed by Abel et al. (1961), and are not inconsistent with the 1/T 2 dependence predicted by Landau's theory of a Fermi liquid.