2.1.3.5. Lamellarpc¶
Random lamellar sheet with paracrystal structure factor
| Parameter | Description | Units | Default value |
|---|---|---|---|
| scale | Source intensity | None | 1 |
| background | Source background | cm-1 | 0 |
| thickness | sheet thickness | Å | 33 |
| Nlayers | Number of layers | None | 20 |
| spacing | d-spacing of paracrystal stack | Å | 250 |
| spacing_polydisp | d-spacing of paracrystal stack | Å | 0 |
| sld | layer scattering length density | 10-6Å-2 | 1 |
| solvent_sld | Solvent scattering length density | 10-6Å-2 | 6.34 |
The returned value is scaled to units of cm-1.
This model calculates the scattering from a stack of repeating lamellar structures. The stacks of lamellae (infinite in lateral dimension) are treated as a paracrystal to account for the repeating spacing. The repeat distance is further characterized by a Gaussian polydispersity. This model can be used for large multilamellar vesicles.
2.1.33.1. Definition
The scattering intensity I(q) is calculated as
The form factor of the bilayer is approximated as the cross section of an infinite, planar bilayer of thickness t
Here, the scale factor is used instead of the mass per area of the bilayer (G). The scale factor is the volume fraction of the material in the bilayer, not the total excluded volume of the paracrystal. ZN(q) describes the interference effects for aggregates consisting of more than one bilayer. The equations used are (3-5) from the Bergstrom reference below.
Non-integer numbers of stacks are calculated as a linear combination of the lower and higher values
The 2D scattering intensity is the same as 1D, regardless of the orientation of the q vector which is defined as
The parameters of the model are Nlayers = no. of layers, and pd_spacing = polydispersity of spacing.
| Parameter name | Units | Default value |
|---|---|---|
| background | cm-1 | 0 |
| scale | None | 1 |
| Nlayers | None | 20 |
| pd_spacing | None | 0.2 |
| sld_layer | Å-2 | 1e-6 |
| sld_solvent | Å-2 | 6.34e-6 |
| spacing | Å | 250 |
| thickness | Å | 33 |
Figure. 1D plot using the default values above (w/20000 data point).
Our model uses the form factor calculations implemented in a C library provided by the NIST Center for Neutron Research (Kline, 2006).
REFERENCE
M Bergstrom, J S Pedersen, P Schurtenberger, S U Egelhaaf, J. Phys. Chem. B, 103 (1999) 9888-9897