# lamellar_hg

Random lamellar phase with Head and Tail Groups

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

scale | Source intensity | None | 1 |

background | Source background | cm^{-1} |
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^{-6}Å^{-2} |
0.4 |

sld_head | Head scattering length density | 10^{-6}Å^{-2} |
3 |

sld_solvent | Solvent scattering length density | 10^{-6}Å^{-2} |
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 \(\delta_H + \delta_T + \delta_T + \delta_H\). 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

**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

*2014/04/17 - Description reviewed by S King and P Butler.*