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) Å 15
length_head Head thickness Å 10
sld Tail scattering length density 10-6Å-2 0.4
sld_head Head scattering length density 10-6Å-2 3
sld_solvent Solvent scattering length density 10-6Å-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

\[I(q) = 2\pi\frac{\text{scale}}{2(\delta_H + \delta_T)} P(q) \frac{1}{q^2}\]

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

\[q = \sqrt{q_x^2 + q_y^2}\]
../../_images/lamellar_hg_autogenfig.png

Fig. 47 1D plot corresponding to the default parameters of the model.

Source

lamellar_hg.py

References

  1. F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502
  2. 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