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A set of material balance equations is derived in order to account for the content of each sample and its scattering length density.
5) Scattering length density difference between the micelles and the solvent
The discrepancy between [[PHI]] and [[PHI].sub.mix] as well as the fitted scattering length density difference between the micelle core and the solvent '[DELTA][rho] are used as inputs in order to back out the SDS fraction participating in micelle formation.
A scattering length density model was then fit to the experimental data by the same procedure used for X-ray reflectivity.
The X-ray parameters listed in Table I are used to construct an electron density model, and the neutron parameters are used to construct a neutron scattering length density model.
Thus, the scattering length density difference between the components is 0.95 X [10.sup.10] [cm.sup.-2].
The nuclear and magnetic scattering length density distributions [[rho].sub.N](r) and [[rho].sub.M](r) then equal [4,8] half the sum and difference respectively between [[rho].sub.u](r) and [[rho].sub.d](r) (Fig.
It should be noted that in a layer system the material with highest scattering length density [approximately] (1-n) is responsible for the position of the total reflection angle.
Glassy materials (such as the amorphous silica particles used in this research) can be characterized by random fluctuations in scattering length density. Particles in dispersion thus demonstrate random fluctuations in contrast.
where b is a parameter with units of length that is a measure of the average distance between neighboring maxima and minima in the fluctuating scattering length density.
2) The measure of the intensity of the fluctuation in scattering length density, [epsilon], should be a relatively small number; 20% variations above and below [[rho].sub.s] would give values of [epsilon] of the order of 0.15.