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Application of an extended Porod law to the study of the ionic aggregates in telechelic ionomers
Author(s) -
Sobry R.,
Ledent J.,
Fontaine F.
Publication year - 1991
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s002188989100328x
Subject(s) - small angle x ray scattering , scattering , small angle scattering , ionic bonding , phase (matter) , interphase , parallelepiped , measure (data warehouse) , chemistry , materials science , ion , physics , geometry , optics , mathematics , organic chemistry , database , biology , computer science , genetics
Porod's law extended to the sixth‐order term can be written I = ( K p / s 4 + K 6 / s 6 ) U 2 ( s,σ ) where I is the scattered intensity, s = 2(sin θ )/ λ , θ being half the scattering angle and λ the wavelength used; U 2 ( s, σ ) describes the interphase profile and σ is a measure of the width of the interphase transition zone. K p and K 6 are two constants. In the same way as K p can be related to the specific area, K 6 is related to a pure number θ called here `angulosity'. For an angulous body, θ always is negative and can easily be calculated when its geometry is simple. It does not depend on the dimensions of the body. It is shown in the present paper that K 6 / K p = θ /2 π 2 S so that, in a two‐phase system, the ratio K 6 / K p represents the angulosity per unit area S of the interface between the phases. A least‐squares analysis of the experimental small‐angle X‐ray scattering (SAXS) curve gives the values of K p , K 6 and σ . The method was successfully applied in the case of telechelic ionomers to characterize their ionic aggregates. These aggregates present a larger angulosity than that of a parallelepiped. Their volume is relatively small and only contains a small number of ions. The results agree with the results obtained by other techniques. It can be concluded from this that the introduction of the s −6 term into Porod's law is judicious and allows the structure of the phases to be better characterized.