# lamellar_hg¶

Random lamellar phase with Head and Tail Groups

Parameter |
Description |
Units |
Default value |
---|---|---|---|

scale |
Scale factor or Volume fraction |
None |
1 |

background |
Source background |
cm |
0.001 |

length_tail |
Tail thickness ( total = H+T+T+H) |
Å |
15 |

length_head |
Head thickness |
Å |
10 |

sld |
Tail scattering length density |
10 |
0.4 |

sld_head |
Head scattering length density |
10 |
3 |

sld_solvent |
Solvent scattering length density |
10 |
6 |

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

This model provides the scattering intensity, \(I(q)\), for a lyotropic lamellar phase where a random distribution in solution are assumed. The SLD of the head region is taken to be different from the SLD of the tail region.

**Definition**

The scattering intensity \(I(q)\) is

The form factor \(P(q)\) is

where \(\delta_T\) is *length_tail*, \(\delta_H\) is *length_head*,
\(\Delta\rho_H\) is the head contrast (*sld_head* \(-\) *sld_solvent*),
and \(\Delta\rho_T\) is tail contrast (*sld* \(-\) *sld_solvent*).

The total thickness of the lamellar sheet is a_H + delta_T + delta_T + delta_H$. Note that in a non aqueous solvent the chemical “head” group may be the “Tail region” and vice-versa.

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**

**Author:****Last Modified by:****Last Reviewed by:**S King and P Butler**Date**April 17, 2014