lamellar

Lyotropic lamellar phase with uniform SLD and random distribution

Parameter	Description	Units	Default value
scale	Scale factor or Volume fraction	None	1
background	Source background	cm-1	0.001
thickness	total layer thickness	Å	50
sld	Layer scattering length density	10-6Å-2	1
sld_solvent	Solvent scattering length density	10-6Å-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

$$I(q) = \text{scale}\frac{2\pi P(q)}{q^2\delta} + \text{background}$$

The form factor is

$$P(q) = \frac{2\Delta\rho^2}{q^2}(1-\cos(q\delta)) = \frac{4\Delta\rho^2}{q^2}\sin^2\left(\frac{q\delta}{2}\right)$$

where $\delta$ is the total layer thickness and $\Delta\rho$ is the scattering length density difference.

This is the limiting form for a spherical shell of infinitely large radius. Note that the division by $\delta$ means that $scale$ in sasview is the volume fraction of sheet, $\phi = S\delta$ 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

$$q = \sqrt{q_x^2 + q_y^2}$$

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

Source

lamellar.py

References

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

2. J Berghausen, J Zipfel, P Lindner, W Richtering, J. Phys. Chem. B, 105, (2001) 11081-11088

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