# 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 |
0.001 |

thickness |
total layer thickness |
Å |
50 |

sld |
Layer scattering length density |
10 |
1 |

sld_solvent |
Solvent scattering length density |
10 |
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

The form factor is

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

**Source**

**References**

F Nallet, R Laversanne, and D Roux,

*J. Phys. II France*, 3, (1993) 487-502J Berghausen, J Zipfel, P Lindner, W Richtering,

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

**Authorship and Verification**

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