lamellar

Lyotropic lamellar phase with uniform SLD and random distribution

Parameter Description Units Default value
scale Source intensity None 1
background Source background cm-1 0.001
thickness total layer thickness 50
sld Layer scattering length density 10-6-2 1
sld_solvent Solvent scattering length density 10-6-2 6

The returned value is scaled to units of cm-1 sr-1, absolute scale.

Polydispersity in the bilayer thickness can be applied from the GUI.

Definition

The scattering intensity I(q) for dilute, randomly oriented, “infinitely large” sheets or lamellae is

I(q)=scale2πP(q)q2δ+background

The form factor is

P(q)=2Δρ2q2(1cos(qδ))=4Δρ2q2sin2(qδ2)

where δ is the total layer thickness and Δρ is the scattering length density difference.

This is the limiting form for a spherical shell of infinitely large radius. Note that the division by δ means that scale in sasview is the volume fraction of sheet, ϕ=Sδ where S is the area of sheet per unit volume. S is half the Porod surface area per unit volume of a thicker layer (as that would include both faces of the sheet).

The 2D scattering intensity is calculated in the same way as 1D, where the q vector is defined as

q=q2x+q2y
../../_images/lamellar_autogenfig.png

Fig. 46 1D plot corresponding to the default parameters of the model.

References

F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502

also in J. Phys. Chem. B, 105, (2001) 11081-11088