.. _lamellar-hg: 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^-1| 0.001 length_tail Tail thickness ( total = H+T+T+H) |Ang| 15 length_head Head thickness |Ang| 10 sld Tail scattering length density |1e-6Ang^-2| 0.4 sld_head Head scattering length density |1e-6Ang^-2| 3 sld_solvent Solvent scattering length density |1e-6Ang^-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 .. math:: I(q) = 2\pi\frac{\text{scale}}{2(\delta_H + \delta_T)} P(q) \frac{1}{q^2} The form factor $P(q)$ is .. math:: 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 .. math:: q = \sqrt{q_x^2 + q_y^2} .. figure:: img/lamellar_hg_autogenfig.png 1D plot corresponding to the default parameters of the model. **Source** :download:`lamellar_hg.py ` **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