Lamellar Hg

# Note: model title and parameter table are inserted automatically 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

$$ I(q) = 2\pi\frac{\text{scale}}{2(\delta_H + \delta_T)} P(q) \frac{1}{q^2}
$$
The form factor $P(q)$ is

$$ P(q) = \frac{4}{q^2} \left\lbrace \Delta \rho_H \left[\sin[q(\delta_H + \delta_T)\ - \sin(q\delta_T)\right] + \Delta\rho_T\sin(q\delta_T) \right\rbrace^2
$$
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

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

References

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