Fractal S(q)


Calculates the structure factor term ONLY from the Fractal model.

The Teixeira & Chen fractal structure factor.

Calculates the structure factor for mass fractal aggregates of monodisperse spherical particles of effective radius $R_p$ according to

S(q) = 1 + \frac{D_m\Gamma(D_m - 1)}{(qR_p)^{D_m}
[1+(q\xi)^{-2}]^{(D_m-1)/2}} sin[(D_m - 1) tan^{-1}(q\xi)]

where $D_m$ is the mass fractal dimension, $R_p$ is assumed to be equivalent to the lower fractal cutoff length, and $\xi$ is the upper fractal cutoff length (the distance above which the mass distribution of the fractal no longer scales as $size^{D^m}$).

The returned value is a dimensionless structure factor, $S(q)$.

The radius-of-gyration for the mass fractal is given by

R_g = \frac{D_m(D_m + 1)\xi^{2}}{2}

Unlike most other structure factor models, this $S(q)$ does not explicitly include the particle volume fraction and so the $volfraction$ parameter that SasView adds by default has no effect. If combining this model with a particulate form factor, use the $scale$ parameter to adjust the effective volume fraction.

Combining this structure factor model with either the Sphere model or the Core_Shell_Sphere model replicates the Fractal model or the Fractal_Core_Shell model, respectively. In the latter case, make $radius$_$effective$ = $radius$ + $thickness$.

The mass fractal dimension, which can be fractional, is only valid in the range $1 <= D_m <= 3$. The S(q) function here goes negative if $D_m$ is too large, and the Gamma function diverges at $D_m$ = 0 and $D_m$ = 1.

J Teixeira, J. Appl. Cryst., 21 (1988) 781-785

Chapter 6, Equation 6.51 in
Small-Angle Scattering from Confined and Interfacial Fluids
Yuri B. Melnichenko
Springer, 2016

Authorship and Verification
Author: Ziggy Attala Date: 10/09/2019
Last Modified by: Steve King Date: 19/09/2019
Last Reviewed by: Date:


Created By smk78
Uploaded Sept. 19, 2019, 11:10 a.m.
Category Structure Factor
Score 0
Verified This model has not been verified by a member of the SasView team
In Library This model is not currently included in the SasView library. You must download the files and install it yourself.


Thu 19 Sep 2019 at 11:12
Confirmed that sphere * fractal_sq = fractal and that core_shell_sphere * fractal_sq = fractal_core_shell

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