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  • 1
    Electronic Resource
    Electronic Resource
    Improved expression of mean-square radius of gyration. I. Vinyl polymers (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 4792-4800 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Taking account of the effect of large side groups, the mean-square radius of gyration of vinyl polymer chains has been deduced by the method of matrix algebra. According to previous approaches to the computation of conformational energy, every substituent of vinyl polymer is confined to an orientation in which the conformational energy is minimum, i.e., its plane is approximately perpendicular to the one defined by the skeletal bonds flanking the Cα atom. This model facilitates the derivation of mean-square radius of gyration. Neglecting the effect of side groups, the expression for mean-square radius of gyration given in this work reduces to be that reported by Flory. Numerical calculations indicate that for tactic polypropylene, polystyrene, poly(methyl acrylate), and poly-1,2-butadiene the dependence of mean-square radius of gyration on molecular weight can be expressed as 〈S2〉=aMb, which is in agreement with the experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462765
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  • 2
    Electronic Resource
    Electronic Resource
    Kinetic model of star-branched polycondensation (1998)
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 7 (1998), S. 13-18 
    Details
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A kinetic model was developed for the whole process of star-branched polycondensation of AB type monomers with a multifunctional core, RAf. The evolution of molecular weight distribution and other molecular parameters during reaction were estimated in terms of the derived expressions. The molecular weight distribution first becomes broader with increasing reaction extent of B groups and the functionality of RAf, but suddenly turns to be markedly narrower than the Schulz-Flory distribution when the polycondensation approaches completion.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Improved expression of the mean-square radius of gyration, 2Part 1: cf. ref.3. Poly(1,1-disubstituted ethylene)s (1995)
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 4 (1995), S. 155-164 
    Details
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The mean-square radius of gyration of poly(1,1-disubstituted ethylene)s is calculated according to a method already developed for poly(methyl methacrylate), poly(α-methylstyrene) and polyitaconate. During the derivation both the effect of side groups and the masses of skeletal atoms were taken into account. A hypothetical polymer chain was introduced, in which the mass of the substituents on every Cα was considered to be concentrated in their center of mass, and the virtual side bond vector runs from Cα to this center. The mean-square radius of gyration of poly(1,1-disubstituted ethylene)s consists of two parts, one of which is the mean-square radius of gyration of the hypothetical molecule described before and the other is related to the geometrical characteristics of the side groups. Numerical calculations indicated that the dependence of the mean-square radius of gyration of poly(1,1-disubstituted ethylene)s on the molecular weight is analogous to that of vinyl polymers, 〈S2〉 = aMb, where a and b are constants characteristic of the polymer.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mats.1995.040040111
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  • 4
    Electronic Resource
    Electronic Resource
    Mean-square radius of gyration of polymer chains (1997)
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 6 (1997), S. 597-611 
    Details
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The calculations of the mean-square radius of gyration for more than thirty sorts of polymer chains are reviewed on the basis of a unified approach. A general expression of the mean-square radius of gyration was developed for polymer chains with side groups and/or heteroatoms. It consists of two parts. The first part is the mean-square radius of gyration of a model chain, in which every side group, R, was considered to be located in the centroid of the substituent flanking the related skeletal atom, and the second one is the total contribution of the square radius of gyration of every substituent around its centroid. Numerical calculations showed that the logarithmic relationship between the mean-square radius of gyration and the degree of polymerization becomes linear when x is greater than 100, and the dependence of the mean-square radius of gyration on the molecular weight can be expressed by the general formula 〈S2〉 = aMb, which was supported by a number of experimental measurements. A comparison of our expression for the mean-square radius of gyration with that reported by Flory was made. The difference is obvious in the range of lower molecular weight, and gradually declines with increasing degree of polymerization.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mats.1997.040060302
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  • 5
    Electronic Resource
    Electronic Resource
    Characteristic ratio of the mean-square end-to-end distance of poly(vinylidene fluoride) with microstructural defects (1995)
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 4 (1995), S. 471-479 
    Details
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The segment length distribution of isoregic head-to-head and tail-to-tail sequences in poly-(vinylidene fluoride) (PVF2)System. name: poly(1,1-difluoroethylene). chains is calculated from 19F NMR literature data. It is found that the average length of inverse segments is very close to one unit; therefore almost all head-to-head defects are immediately repaired by an adjacent tail-to-tail addition. The role of microstructure on the characteristic ratio of the end-to-end distance is then investigated. Results obtained by two different methods indicate that, in agreement with previous Monte Carlo calculations, defects play a minor role for the conformational characteristics of PVF2. However, a slight contraction of about 4% is expected for very defective chains.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mats.1995.040040306
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  • 6
    Electronic Resource
    Electronic Resource
    Configurational-conformational statistics of stereoirregular polystyrene (1996)
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 5 (1996), S. 939-945 
    Details
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The dependence of the configurational-conformational characteristics, such as the mean-square end-to-end distance, the mean-square radius of gyration, and the temperature coefficient of the stereoirregular polystyrene chains on the fraction of meso dyads, Pm was investigated, using the periodic condition method. The calculation shows that polystyrene has the most compact chain when Pm = 0.7, and the temperature coefficient of the characteristic ratio of the mean-square end-to-end distance reaches the minimum, -0.89 × 10-3 K-1, at Pm = 0.5. The theoretical result of the mean-square radius of gyration for atactic polystyrene, 〈S2〉1/2 = 0.2245 M0.5106 shows good agreement with the experimental measurement in both bulk amorphous state and θ-solvent.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mats.1996.040050510
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  • 7
    Electronic Resource
    Electronic Resource
    Mean-square radius of gyration of polysiloxanes (1997)
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 6 (1997), S. 161-168 
    Details
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The mean-square radius of gyration for polysiloxanes has been derived according to the exact definition. Taking account of the examples of symmetrically substituted poly(dimethylsiloxane) and unsymmetrically substituted poly(methylphenylsiloxane), we find that the dependence of 〈S2〉 on the molecular weight follows the general formula 〈S2〉 = aMb with b = 1 ± 0.016, which is analogous to the theoretical outcomes for vinyl or vinylidene polymers even though the skeletal bone of polysiloxanes consists of alternating heteroatoms. A numerical comparison of the rigorous expression of the mean-square radius of gyration given in this paper with that reported by Flory shows that the difference is obvious for low-molecular-weight polymer and it gradually declines with increasing degree of polymerization.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mats.1997.040060111
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  • 8
    Electronic Resource
    Electronic Resource
    Third-order interaction approximation for linear polymer chains (1991)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 29 (1991), S. 877-882 
    Details
    ISSN: 0887-6266
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Third-order interactions imposed by a pair of atoms separated by five bonds are taken into account in computations of the mean-square end-to-end distance and the mean-square radius of gyration for linear polymer chains. The statistical weight matrices are established on the basis of the rotational isomeric state model. The conformational energy of n-hexane is calculated as a function of the C—C bond rotation angles. The third-order interaction energy is obtained by comparison with that of n-pentane. The characteristic ratio of polymethylene is 6.6 in the third-order interaction approximation, which is in agreement with experimental data.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/polb.1991.090290712
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  • 9
    Electronic Resource
    Electronic Resource
    Improved expression of the mean-square radius of gyration, 3Part 2: cf. ref.10. 1,4-polydienes (1995)
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 4 (1995), S. 459-470 
    Details
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The mean-square radii of gyration of cis- and trans-1,4-polybutadiene and corresponding 1,4-polyisoprene were derived using Abe's and Flory's rotational isomeric scheme. Calculations performed using available experimental data showed that the dependence of the mean-square radius of gyration on the molecular weight for these stereoregular polydienes can be expressed as \documentclass{article}\pagestyle{empty}\begin{document}$ \langle S^2 \rangle = aM^b $\end{document} where a and b are constants characteristic of the polymer. This behaviour is analogous to that of vinyl polymers and poly-1,1-disubstituted ethylenes discussed in the preceding papers of the present series. The mean-square radius of gyration of 1,4-polyisoprene with predominantly trans units is more sensitive to stereoirregularity than with predominantly cis units. However, 1,4-polybutadiene chains are comparatively insensitive to the stereochemical composition.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mats.1995.040040305
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  • 10
    Electronic Resource
    Electronic Resource
    Theoretical study on the linking process of divinyl compounds with living precursors, 1. Uniform precursor chains (1997)
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 6 (1997), S. 1211-1235 
    Details
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The theoretical aspect of the linking reaction between divinyl compounds and uniform living precursors has been studied by using the model of threads going through the holes of buttons. The expressions of various molecular parameters of the clusters formed during the linking process, such as the number- and the weight-average molecular weights, the average degree of branching, the branch distribution function, and the molecular weight distribution function, were rigorously derived. The critical condition of gelation is given as well. The theoretical results obtained are appropriate to the core formation process for the core-first preparation procedure of star-shaped polymers, and to the arm-first approach using a uniform living precursor with low or moderate molecular size.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mats.1997.040060611
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