Application of an extended Porod law to the study of the ionic aggregates in telechelic ionomers

Sobry, R.; Ledent, J.; Fontaine, F.

doi:10.1107/s002188989100328x

Cited by 18 publications

(20 citation statements)

References 17 publications

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“…of (1.6) to be equal to the right-hand side (r.h.s.). Sobry et al (1991) remarked that for right prisms the correct '~(3)(0+) value (Mrring & Tchoubar, 1968) is simply obtained by assigning to each vertex a contribution that was explicitly determined (see also Sobry, Fontaine & Ledent, 1994) for vertices with three entering edges and such that two of the three angles formed by the entering edges are equal to rr/2. In this way, Sobry, Fontaine & Ledent essentially conjectured that the exact ~3)(0+) value can be obtained by adding to the Kirste-Porod value the contributions arising from the singularities of the interfaces.…”

Section: I(h) = [I(h)/47rv( R12)]mentioning

confidence: 99%

The vertex contribution to the Kirste–Porod term

Ciccariello¹,

Sobry²

1995

Acta Cryst Sect A

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It is shown that, close to the origin, the correlation function [y(r)] of any N-component sample with interfaces made up of planar facets is always a third-degree polynomial in r. Hence, the only monotonically decreasing terms present in the asymptotic expansion of the relevant small-angle scattered intensity are the Porod [-2y'(0+)/h 4] and the KirstePorod [4')(3)(0 +)/h 6] contributions. The latter contribution is non-zero owing to the contributions arising from each vertex of the interphase surfaces. The general vertex contribution is evaluated in closed form and the )'(3)(0+) values relevant to the regular polyhedra are reported.

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Section: I(h) = [I(h)/47rv( R12)]mentioning

confidence: 99%

The vertex contribution to the Kirste–Porod term

Ciccariello¹,

Sobry²

1995

Acta Cryst Sect A

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“…Its expression is where (HZ)s and (x)s denote, respectively, the averages of the squared mean curvature and the Gaussian curvature of the interface throughout the latter. The corrections to the value of Era,, arising from the presence of vertices and sharp curvilinear edges, have been discussed recently by Sobry et al (1991) and Ciccariello & Sobry (1995). For smooth interfaces also, the contributions monotonously decreasing as h -s and h -1° have been explicitly evaluated by Wu & Schmidt (1971) and Ciccariello (1995), respectively.…”

Section: Id Lat(h ) = ~ H4mentioning

confidence: 99%

Diffuse Interfaces and Small-Angle Scattering Intensity Behaviour

Ciccariello¹,

Sobry²

1997

J Appl Cryst

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The contributions corresponding to the Porod, the oscillatory O(h -4) and the Kirste-Porod O(h -6) terms, present in the asymptotic expansion of the small-angle scattering (SAS) intensities, are numerically evaluated, in the presence of diffuse interfaces generated by different smoothing functions (Gaussian, spherical or HelfandTagami). It is shown that SAS experiments are generally unable to distinguish among different profiles, because any smoothing can be made to coincide with another type by scaling its thickness parameter. The oscillatory deviations are observable in the Porod plot of the intensities when the typical distance between parallel diffuse interfaces is greater than 50 A and the ratio of the thickness to this distance is less than 1/4. The same conclusion applies to the infinite-slit intensities.

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“…An increase in φ PGA results in an improved phase homogeneity. Desmearing of the Kratky camera scattering has been performed by the Vonk method [6] and an original method by Sobry et al [7]. As expected, the pinhole intensity, I, does not show characteristic features and all the scattering curves are very similar.…”

Section: Resultsmentioning

confidence: 90%

SAXS analysis of the morphology of biocompatible and biodegradable poly(ε-caprolactone-b-glycolide) copolymers

Sobry

Bossche

Fontaine

et al. 1996

Journal of Molecular Structure

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Poly(ε-caprolacrone-b-glycolide) diblock copolyesters have been synthesized by the sequential polymerization of ε-caprolactone and glycolide as initiated by aluminium alkoxides. Copolymerization is typically "living" and yields copolyesters of perfectly controlled molecular weight and composition. Diblock molecular weight (Mn PGA +Mn PCL ) ranges from 5700 to 42 000 and the ρ = Mn PCL /Mn PGA ratio varies from 1.5 to 13.1. Due to the inherent insolubility of the polyglycolide (PGA) segment in common organic solvent, the diblock copolyesters form stable non-aqueous colloidal dispersions e.g. in toluene, the stability of which results from the soluble poly(ε-caprolactone) (PCL) block. Combining all the experimental observations (PCS, TEM, WAXS, SAXS, AFM), a micelle model has been proposed which consists of a polyglycolide core surrounded with a corona of polycaprolactone (PCL). Both constituents are semi crystalline. From SAXS observations, the PGA core is better described by two concentric spheres. The internal sphere of a 5-6.7 nm diameter would essentially contain crystalline PGA. The diameter of the external sphere, D PGA , is in the range from 6.2 to 9.6 nm, at least for the investigated diblock copolymers. As a rule, this diameter increases as ρ decreases at constant molecular weight and as the diblock molecular weight increases at constant ρ. A scattering peak (weak) is observed in the range from 10.8 to 15.5 nm and the Bragg distance is close ΜD PGA > where µ is equal to (l+3ρ/2) 1/3 . From steric considerations, µ is the ratio between the diameter of the micelle and the diameter of the PGA core, so that this peak has been assigned to the characteristic intermicellar distance. At very small angles, several additional peaks are the signature of a hyperstructure which is possibly lamellar.

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Application of an extended Porod law to the study of the ionic aggregates in telechelic ionomers

Cited by 18 publications

References 17 publications

The vertex contribution to the Kirste–Porod term

The vertex contribution to the Kirste–Porod term

Diffuse Interfaces and Small-Angle Scattering Intensity Behaviour

SAXS analysis of the morphology of biocompatible and biodegradable poly(ε-caprolactone-b-glycolide) copolymers

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