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  • Atomic, Molecular and Optical Physics  (3)
  • Physics  (2)
  • 1975-1979  (5)
  • 1965-1969
  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 189-211 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The theory of pth-order singular differential equations is adaptable to the study of the system of recurrence relations occurring in the problem of a one-dimensional chain with pth-neighbor interactions. By using Green's formula, a mapping is defined between the space Vn of eigenvectors to the dynamical matrix and the symplectic space V2p of boundary conditions for the recurrence equations. The properties of the resolvent are obtained from an analysis of the solutions of a system of inhomogeneous equations and Green's matrix is constructed for the case of standard Sturm-Liouvilletype boundary conditions. The Weyl surface is discussed and its properties used for the construction of square summable sequences which in turn can be employed in expansion formulas. The generalization of Weyl's m-function in the second-order case (p = 1) becomes for p ≥ 2 a p × p matrix M(λ), where λ is a complex parameter. The imaginary part Im {M(λ)} is related to the spectral properties and serves as basis for the discussion of different concepts of spectral density for the normal modes of lattice dynamical problems. An important practical result is the equation M = -Ψa-1Φa valid in the limit point case, generalizing the corresponding second-order formula.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 415-425 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The transferability of bonds in a set of small molecules has been explored. The molecular wave-functions have been calculated from the group (or loge) function method, via a construction based on Gaussian functions. The transferability is very good and the effect of lone pairs on adjacent bonds has been analysed. Furthermore, a very simple procedure has been proposed to estimate the frontiers of the bonds.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 10 (1976), S. 191-216 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A satisfactory definition of spectral density for the normal modes of lattice dynamics problems requires the study of singular recurrence relations which is carried out in detail for one-dimensional chains with pth neighbor interactions. The relationship of transfer matrices to the dynamical matrix is explored in order to obtain Green's formula. By using Green's formula, a mapping is defined between Vn, whose basis is formed from the normal modes of vibration of an n-particle chain, and V2p, which is the space of boundary conditions for the recurrsion equations. Most of the properties of this mapping may be deduced from a symplectic bilinear form in V2p which is associated with the Hermitean inner product in Vn. This symplectic form defines a geometry which is invariant under the recursion relation, as well as canonical initial and boundary conditions, and a maximal isotropic subspace which may be used to determine square summability of the normal modes and the spectral density in the limit as the number of particles becomes infinite.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 13 (1975), S. 1991-2029 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A theory for amorphous orientation in spherulitic polymers is presented based upon a consideration of conformational changes in the chains, loops, and cilia located between crystalline lamellae within a spherulite which is assumed to undergo an affine deformation. Chain statistics are worked out on the basis of (a) an analytical method involving random walks on a cubic lattice between barriers following a technique proposed by DiMarzio and Rubin and (b) a Monte Carlo computer simulation on a tetrahedral lattice. The latter method is considered more appropriate in view of the chain constraints such that lattice geometry becomes important. Values of the amorphous orientation are calculated as a function of the degree of crystallinity, initial lamellar separation, mole fraction of bonds in amorphous chains of each type, and chain lengths of each type of amorphous chain. It is found that tie chains are the principal contributor to amorphous orientation and the amount increases with increasing fraction and decreasing length of these. Results are compared with measurements of amorphous orientation by the birefringence x-ray and the infrared dichroism technique. It is concluded that the tie chains must be initially quite highly elongated and that the assumed affineness of spherulite deformation is not closely obeyed.
    Additional Material: 24 Ill.
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  • 5
    ISSN: 0360-6376
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Poly(N-aryl maleimide)s of characteristic structures have been synthesized and some of their physical properties studied. These include N-(2-fluoro phenyl), N-(3-fluoro phenyl), N-(4-fluoro phenyl), N-(2,4-difluoro phenyl), N-(2,5-difluoro phenyl), N-(2,3,5,6-tetrafluoro phenyl), and N-(pentafluoro phenyl). The polymerization of N-(fluoro phenyl) maleimides by free-radical initiation in bulk or in solution and by anionic catalyst have been studied to compare the characteristics of polymerization by γ-ray irradiation with that by free-radical initiation. The polymers were characterized by elemental analysis, intrinsic viscosity, spectroscopy (IR and NMR), programmed thermogravimetric analysis, and x-ray diffraction. Spectra of polymers prepared by radiation and anionic polymerization were nearly identical with those of polymers prepared by free-radical polymerization initiated by AIBN in bulk or in solution and by the self-initiated thermal polymerization. A variety of reaction conditions were tried, but all attempts to change the molecular structure of the polymers were unsuccessful. Rates of thermal degradation for poly[N-(fluoro phenyl) maleimide]s have been analyzed by using a multiple-heating-rate procedure. Overall activation energy, order of reaction, and frequency factor have been evaluated. On the basis of the comparison between the overall activation energy of the thermal degradation of poly[N-(fluoro phenyl) maleimide]s and NMR spectra of their corresponding monomers, it can be concluded that the 1H shifts due to ethylenic protons are so characteristic in sign and magnitude as to be useful in thermal stability elucidation. Some qualitative explanations were given on the stability of these polymers as affected by the type and size of the substituent. The x-ray diffractograms of all samples show two rather broad peaks indicative of noncrystalline structures. The location of the peaks does not depend upon preparation conditions and temperature. Poly(N-maleimide)s of fluoroanilines have not been hitherto described.
    Additional Material: 6 Ill.
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