Compliance Constants Research Articles

The determination of Poisson's ratio compliances for polyethylene terephthalate sheets using a Michelson interferometer

Two of the Poisson's ratio compliances have been determined for oriented polyethylene terephthalate (PET) sheet. The method adopted was to determine the fringe shift under load when the specimens were placed in one arm of a Michelson interferometer operating in a vertical fringe mode. Data obtained for the specimens in air and in a water bath, with two polarization directions, can be used to provide two independent measurements of each compliance. Good agreement was shown between these measurements, and the values for the compliance constants are reasonable on physical grounds, as well as being consistent with previous work on PET fibres.

Near-infrared spectra of formamide and its anharmonic potential

Abstract The near-infrared spectra of formamide and its N- and C-deuterated compounds in chloroform solutions were investigated and a perturbation calculation of the vibrational levels of these isotopic formamides was carried out. The trans -interaction constant and the cubic cross-term constants between the NH stretching and the CNH bending coordinates were found to be necessary to reproduce observed frequencies. The stretching potentials of the trans - and the cis -NH bonds show close correspondence with those of the free and the bonded NH bonds of o -bromoaniline. The correlation between the compliance constants and the change of the CH, CO, and NH bond lengths on the dissociation of the CN bond is discussed.

Spectroscopic studies of lewis acid—base complexes: IV. An infrared study of oriented single crystals and normal coordinate analyses of trimethylamine—boron halide adducts

A total of 19 isotopic species of various (CH 3) 3NBX 3 complexes have been prepared and their IR spectra studied in the solid state in the region 40–4000 cm −1. The isotopes involved are deuterium, boron-10, boron-11, and nitrogen-15 with X = F, CI, Br and I. C 3v symmetry has been preserved in all cases. Symmetry classifications of the fundamental molecular frequencies have been derived from polarized IR measurements on oriented single crystals in the range 250–4000 cm −1. Errors and inconsistencies in previous studies have been resolved and revised vibrational assignments are proposed on the basis of the new data. Normal coordinate analyses have been carried out utilizing symmetry compliance constants without the assumption of point mass methyl groups. A common potential function containing 22 parameters for the A 1 class and 26 for the E class was utilized. The results support the proposed frequency assignments. B-N force constants obtained by inversion of the compliance matrices vary systematically from the chloro to the iodo complex. However, the B-N force constant for the fluoro complex falls between that for the chloro and bromo species; no systematic trend appears for the B-N compliance constants.

Molecular vibrational constants of some simple polyatomic molecules: trihalogenomethanes, CHX3 and trihalogenosilanes, SiHX3 (X = F, Cl, Br)

Force constants and compliance constants for the CHX 3 and SiHX 3 molecules have been obtained, using the vibrational frequencies of CHX 3 and CDX 3 (SiHX 3 and SiDX 3 ) molecules only. The reliability of the resulting force field has been checked by calculation of Coriolis coupling constants, centrifugal distortion constants and mean amplitudes of vibration and by comparison with the available experimental data.

ChemInform Abstract: MOLECULAR FORCE AND COMPLIANCE CONSTANTS FOR SOME METAL‐HALOGEN BONDS IN COMPLEXES

Abstract The force and compliance constants of some metal-halogen coordinated bonds of MX 2 , MX 3 − and MX 4 2− (M = Zn, Cd, Hg; X = Cl, Br, I) for their free state and for solutions in anhydrous tri- n -butyl phosphate (TBP) are evaluated and the effect of complexing with TBP on the compliance of the bonds is studied.

Molecular force and compliance constants for some metal-halogen bonds in complexes

The force and compliance constants of some metal-halogen coordinated bonds of MX 2, MX 3 − and MX 4 2− (M = Zn, Cd, Hg; X = Cl, Br, I) for their free state and for solutions in anhydrous tri- n-butyl phosphate (TBP) are evaluated and the effect of complexing with TBP on the compliance of the bonds is studied.

Deformation of oriented polyethylene

AbstractThe deformation of polyethylene in terms of structural processes has been investigated by low‐and wide‐angle x‐ray diffraction in the case of low‐density and, to a lesser extent, high‐density polyethylene. The samples possessed a range of simple textures which enabled the deformation processes to be identified. The results are interpreted in terms of a model of stacks of lamellae which have axes along the original draw direction and which deform by lamellar slip, chain slip, and lamellar separation. In most cases these processes accounted for the macroscopic strain but in some cases discrepancies were observed which could be accounted for by inhomogeneous deformation or by the effects of a distribution of lamellar thicknesses. Attempts were made to identify fibrillar slip, without success. The relative contributions of the various deformation processes are examined as a function of temperature and sample treatment by defining a compliance constant for each process. Below room temperature, the results are consistent with expectations based on the α and β mechanical relaxations, whereas the unusual effects at high temperatures are attributed to gradual melting. The compliance constants are also found to depend on the annealing temperature of the sample, and are used to predict the mechanical anisotropy. The volume changes accompanying lamellar separation are examined. They were less than expected in low‐density polyethylene, but satisfactory agreement was obtained in high‐density polyethylene. A general relation is suggested between volume changes and the lateral development of the lamellae. Hence in narrow lamellae the interlamellar layer can contract laterally whereas the greater constraints imposed by wide lamellae lead to void formation. Other effects examined include the reversibility of the processes which is most marked in the case of chain slip and which is explained by the presence of restoring forces in the amorphous regions including the fold surface. Finally, the differences between low‐ and highdensity polyethylene are highlighted, emphasizing the part played in the deformation by the amorphous component.

Anharmonic force field of ethylene

A simple anharmonic force field of ethylene is proposed. It includes the principal cubic and quartic stretching constants derived from appropriate Morse functions for individual bonds and two other higher-order constants. The quadratic part consists of general valence type constants that show the characteristics of the Pulay-Meyer Set II force field. The perturbation method including a general treatment of the first- and the second-order resonances has been used, and about 190 vibrational frequencies of ethylene and six deuterated ethylenes have been calculated to agree fairly well with the experimental values. The proposed potential gives also reasonable values of the Coriolis coupling constants, the centrifugal distortion constants, and the 13C-isotope shifts. The signs of the compliance constants are consistent with the assumption of monotone changes of internal coordinates on the dehydrogenation into acetylene and on the dissociation into two methylene radicals.

Measurement of the Elastic Compliance Constants of Antiferroelectric Copper Formate Single Crystals

The temperature dependence of the components of the elastic compliance constants of copper formate tetrahydrate crystals, s 11 , s 22 , s 33 , s 15 , s 35 , ( s 44 +2 s 23 ), ( s 55 +2 s 13 ), and ( s 66 +2 s 12 ), have been measured at 100 kHz by the composite bar method. ( s 44 +2 s 23 ) and ( s 66 +2 s 12 ) have been found to show sharp and high peaks at the antiferroelectric phase transition temperature T 0 . All absolute values of s 's show stepwise decreases when the crystal enters the antiferroelectric phase.

On the Definitions of Characteristic Molecular Vibrations and the Distribution of Vibrational Energy

Abstract The relationship of the definition of a completely characteristic normal vibration to the stationary properties of force and compliance constants is examined. The corresponding properties of various distributions of potential, kinetic, and total vibrational energy are described.

Green's function analysis of molecular compliance constants: linear and non-linear triatomic molecules

Green's function analysis of molecular compliance constants: linear and non-linear triatomic molecules

Force field of cyanogen from vibrational spectra of isotopic species

The Raman spectra of ( 12C 14N) 2, ( 13C 14N) 2, and ( 12C 15N) 2 in the vapor phase have been studied. From the isotope shifts of several levels the Fermi resonance constant, W 01000-0002 00 = 41 cm −1, has been determined. The observed data, together with earlier infrared data, allow a determination of all the first order anharmonic corrections and thus of the fundamental harmonic frequencies. From these results, force constants and compliance constants of a general quadratic force field are calculated and discussed.

Compliance constants for thiophene calculated by an iterative consistency method

Compliance constant matrix C of the thiophene molecule has been determined on the basis of the experimental frequencies of C 4H 4S and C 4D 4S by the iterative consistency method.

Elasticity in Polymers. II. The Directional Properties of the Compliance Constants in Uniaxially and Biaxially Drawn Polymers

The theoretical analysis of elasticity in oriented polymers in terms of the spherical components of the compliance tensor presented earlier has been extended to include biaxial orientation and also the case of a segment cut at an arbitrary angle in a drawn polymer. The significance of the results is discussed.

The Young's modulus and Poisson's ratio of arsenic, antimony and bismuth

The orientational dependences of the Young's modulus and Poisson's ratio of the A7 structure elements arsenic, antimony, and bismuth are investigated, using available experimental data of the six elastic compliance constants. The behaviour of these technical elastic constants in antimony and bismuth is shown to differ not only in degree but also in kind from that of arsenic, which exhibits the characteristics expected of a layer-like crystal; arsenic is elastically a very anisotropic material, its Young's modulus varies by a factor as large as 11.3: the largest anisotropy ratio reported for a metallic element.

On the evaluation of molecular compliance constants: nonlinear XY 2 molecules

An attempt is made to calculate the compliance constants, first introduced by Decius for a number of nonlinear XY 2 type molecules. The results obtained by independent methods are found to be in good agreement.

Piezoelectric and Elastic Properties of Single Crystalline Se-Te Alloys

The piezoelectric constants, the electromechanical coupling factors and the elastic compliance constants of Se-Te alloys are studied by the transmission circuit method and/or the mechanical resonance method. The piezoelectric constants d11 and d14 decrease rapidly when the Te concentration increases within the range of 0∼25 at.% and then increase with the Te concentration up to 80 at.%. The values of d11 and d14 are 2.76·10-6 and 1.95·10-6 C.G.S. for pure Se and 3.1·10-6 (±10%) and 1.9·10-6 (±15%) C.G.S. for the alloy of 80 at.%, respectively. A similar tendency is observed in the electro mechanical coupling factors k11 and k14, which are 0.250 and 0.156 for pure Se and 0.25 (±10%) and 0.17 (±15%) for the alloy of 80 at.%, respectively. All elastic compliance constants do not change linearly with the Te concentration within the range of 0∼30 at.%, but at higher Te concentration they change almost linearly with the concentration.

Redundant forces and compliance constants

Expressions are obtained for the derivatives of (i) “inverse” frequency parameters λ i −1, (ii) coriolis coupling constants ζ ij α , (iii) centrifugal sretching constants τ αβ, γδ , (iv) “inverse” isotopic shifts Δ ii −1 and (v) vibrational mean square amplitudes 〈 r i 2 〉 with respect to an arbitrary compliance constant c in a vibrating rotating molecule when the internal coordinates and hence the generalized forces form a redundant set. It is shown that except the last one, to derive which anyway an approximate expression is assumed for 〈 r i 2 〉, all other derivatives are invariant under the removal of redundancy.

Anisotropic behaviour of the compliance and stiffness coefficients for cubic materials

By the use of Eulerian angles, expressions are given for the directionality of the sets of eighty-one compliance and stiffness constants in cubic materials. These expressions are trigonometric series in nθ (n=1, 2, 4), where θ is the angle of rotation in a given plane. Coefficients of the series are listed for planes in the standard triangle and a procedure is presented to extend the analysis to all planes of the same form.

Vibration of fluid-filled fiber-reinforced spherical shells

The extensional vibrations of fluid-filled fiber-reinforced spherical shells were studied. The shells' materials are made of filament wound glass fiber in epoxy matrix. By evaluation of the equivalent elastic orthotropic compliance constants, the natural frequencies and their corresponding mode shapes are obtained. The problem has also been solved for an equivalent isotropic spherical shell and the results were compared.