Premium
Chain Connectivity and Conformational Variability of Polymers: Clues to an Adequate Thermodynamic Description of Their Solutions, 2
Author(s) -
Wolf Bernhard A.
Publication year - 2003
Publication title -
macromolecular chemistry and physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.57
H-Index - 112
eISSN - 1521-3935
pISSN - 1022-1352
DOI - 10.1002/macp.200350002
Subject(s) - chain (unit) , composition (language) , maxima and minima , polymer , limiting , macromolecule , thermodynamics , function (biology) , statistical physics , range (aeronautics) , chemistry , yield (engineering) , flory–huggins solution theory , product (mathematics) , additive function , physics , materials science , mathematics , organic chemistry , mathematical analysis , quantum mechanics , mechanical engineering , philosophy , linguistics , biochemistry , geometry , evolutionary biology , engineering , composite material , biology
In Part 1 of this contribution we have reported how the Flory‐Huggins interaction parameter χ can be modeled as a function of chain length within the composition range of pair interaction between the macromolecules by means of the three parameters α , ζ , and λ . This contribution presents the extension of the approach to arbitrary volume fractions, φ , of the polymer and its application to published data on χ ( φ ). The resulting equation reads χ = α (1 − νφ ) −2 − ζ ( λ + 2(1 − λ ) φ ) and requires only the additional parameter ν to incorporate the composition dependence. Its employment to experimental data is very much facilitated by substituting for χ o (limiting value for φ → 0); furthermore, the expression can in good approximation be simplified to χ ≈ ( χ 0 + ζλ )(1 − ν φ ) −2 − ζλ (1 + 2 φ ). That is: only two parameters, ν and the product of ζ and λ , need to be adjusted. This relation is capable of describing all types of composition dependencies reported in the literature, including the hitherto incomprehensible occurrence of pronounced minima in χ ( φ ). For a given system the evaluation of the chain length dependence of χ o , reported in Part 1, and the present evaluation of the composition dependence of χ yield the same data for the conformational response ζ . Similarly both types of measurements generate the same interdependence between ζ and α . The physical meaning of the different parameters and the reason for the observed correlations are discussed.Interrelation between ζλ and α for the evaluated systems.