source: sasmodels/_sources/model/lamellar.txt @ 68532f3

.. _lamellar:

Lamellar
=======================================================

Lyotropic lamellar phase with uniform SLD and random distribution

=========== ================================= ============ =============
Parameter   Description                       Units        Default value
=========== ================================= ============ =============
scale       Source intensity                  None                     1
background  Source background                 |cm^-1|                  0
sld         Layer scattering length density   |1e-6Ang^-2|             1
solvent_sld Solvent scattering length density |1e-6Ang^-2|             6
thickness   Bilayer thickness                 |Ang|                   50
=========== ================================= ============ =============

The returned value is scaled to units of |cm^-1|.


Polydispersity in the bilayer thickness can be applied from the GUI.

Definition
----------

The scattering intensity *I(Q)* is

.. math::

    I(Q) = 2\pi{P(Q) \over \delta Q^2}


The form factor is

.. math::

    P(Q) = {2\Delta\rho^2 \over Q^2}(1-cos(Q\delta))


where |delta| = bilayer thickness.

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}



Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research
(Kline, 2006).

.. figure:: img/lamellar_1d.jpg

    1D plot using the default values (w/1000 data point).


Reference
---------

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