On the Porod law

Ciccariello, S.; Goodisman, Jerry; Brumberger, H.

doi:10.1107/s0021889887010409

Cited by 85 publications

(67 citation statements)

References 22 publications

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“…However, even in Ruland's (1987) most recent analysis devoted to the case of fluctuating interfaces, the discussion has been confined to the Porod contribution. Ruland's procedure will be briefly reviewed now and slightly reformulated by using some considerations reported by Ciccariello et al (1988). In general, a sample's electron-density fluctuation can be written as r/(r) = r/o(r ) + vo(r ).…”

Section: Smoothing Functionsmentioning

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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Section: Smoothing Functionsmentioning

confidence: 99%

Diffuse Interfaces and Small-Angle Scattering Intensity Behaviour

Ciccariello¹,

Sobry²

1997

J Appl Cryst

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“…Thus, the dominating correction to the first order scaling p∝φ 3 is logarithmic, following from the logarithmic rescaling of bending rigidity and saddle-splay modulus. We have also demonstrated that the simulations reproduce the Porod laws for bulk 12,52 and film 53 scattering qualitatively. Finally, we have shown that the low-q behavior of the scattering intensity in film scattering matches theoretical predictions of a q −1 behavior.…”

Section: Discussionmentioning

confidence: 67%

Scattering intensity of bicontinuous microemulsions and sponge phases

Peltomäki

Gompper

Kroll

2012

The Journal of Chemical Physics

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Monte Carlo simulations of dynamically triangulated surfaces of variable topology are used to investigate the scattering intensities of bicontinuous microemulsions. The bulk scattering intensity is shown to follow the Teubner-Strey expression. The domain size and the correlation length are extracted from the scattering peaks as a function of the bending rigidity, saddle-splay modulus, and surfactant density. The results are compared to earlier theories based on Ginzburg-Landau and Gaussian random field models. The ratio of the two length scales is shown to be well described by a linear combination of logarithmically renormalized bending rigidity and saddle-splay modulus with universal prefactors. This is in contrast to earlier theoretical predictions in which the scattering intensity is independent of the saddle-splay modulus. The equation of state, and the asymptotics of the bulk and film scattering intensities for high and low wave vectors are determined from simulations and compared with theoretical results.

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“…In a strict sense, the observation of a Porod plateau depends on the existence of sharp discontinuities in the electronic density from one phase to another. In other respects, Ciccariello, Goodisman & Brumberger (1988)-henceforth referred to as CGB -showed that Porod's law can only be verified, strictly speaking, over a confined domain when a real system is dealt with. As a result, it is possible to observe more than one plateau in a SAS curve.…”

Section: Introductionmentioning

confidence: 99%

Extension of Kirste–Porod's law in the case of angulous interfaces

Sobry¹,

Fontaine²,

Ledent³

1994

J Appl Cryst

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A preceding paper handled, by way of application, the usefulness of Porod's law extended to the second nonoscillating term. The h-6 term allows the structure of the phases to be better characterized. This paper is mainly concerned with the setting up of the main equations used in this preceding paper. The h-6 term is analysed from the correlation function 7(r) and related to the 'stick probability function'. It can be positive or negative. The positive case appears in smooth phases and has been previously analysed by Kirste & Porod. The negative case occurs in the presence of linear edges resulting from the meeting of surfaces that are planar in the vicinity of their intersection. More precisely, it is shown that the h-6 negative term results from the finite length of the edge. Its magnitude depends on the dihedral angles at the vertex defined by the limited sharp edges. The smaller the dihedral angles, the greater the h -6 term amplitude. The new concept of angulosity, 0, a pure number characterizing the geometry of the phase, is introduced. In this way, it is possible to develop similar equations for a specific surface, angularity and angulosity. Some simple-geometry examples are developed. The region where the extended Kirste-Porod law is useful in analysing small-angle scattering curves is discussed.

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On the Porod law

Cited by 85 publications

References 22 publications

Diffuse Interfaces and Small-Angle Scattering Intensity Behaviour

Diffuse Interfaces and Small-Angle Scattering Intensity Behaviour

Scattering intensity of bicontinuous microemulsions and sponge phases

Extension of Kirste–Porod's law in the case of angulous interfaces

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