[68532f3] | 1 | .. _lamellar: |
---|
| 2 | |
---|
| 3 | Lamellar |
---|
| 4 | ======================================================= |
---|
| 5 | |
---|
| 6 | Lyotropic lamellar phase with uniform SLD and random distribution |
---|
| 7 | |
---|
| 8 | =========== ================================= ============ ============= |
---|
| 9 | Parameter Description Units Default value |
---|
| 10 | =========== ================================= ============ ============= |
---|
| 11 | scale Source intensity None 1 |
---|
| 12 | background Source background |cm^-1| 0 |
---|
| 13 | sld Layer scattering length density |1e-6Ang^-2| 1 |
---|
| 14 | solvent_sld Solvent scattering length density |1e-6Ang^-2| 6 |
---|
| 15 | thickness Bilayer thickness |Ang| 50 |
---|
| 16 | =========== ================================= ============ ============= |
---|
| 17 | |
---|
| 18 | The returned value is scaled to units of |cm^-1|. |
---|
| 19 | |
---|
| 20 | |
---|
| 21 | Polydispersity in the bilayer thickness can be applied from the GUI. |
---|
| 22 | |
---|
| 23 | Definition |
---|
| 24 | ---------- |
---|
| 25 | |
---|
| 26 | The scattering intensity *I(Q)* is |
---|
| 27 | |
---|
| 28 | .. math:: |
---|
| 29 | |
---|
| 30 | I(Q) = 2\pi{P(Q) \over \delta Q^2} |
---|
| 31 | |
---|
| 32 | |
---|
| 33 | The form factor is |
---|
| 34 | |
---|
| 35 | .. math:: |
---|
| 36 | |
---|
| 37 | P(Q) = {2\Delta\rho^2 \over Q^2}(1-cos(Q\delta)) |
---|
| 38 | |
---|
| 39 | |
---|
| 40 | where |delta| = bilayer thickness. |
---|
| 41 | |
---|
| 42 | The 2D scattering intensity is calculated in the same way as 1D, where the $Q$ vector is defined as |
---|
| 43 | |
---|
| 44 | .. math:: |
---|
| 45 | |
---|
| 46 | Q = \sqrt{Q_x^2 + Q_y^2} |
---|
| 47 | |
---|
| 48 | |
---|
| 49 | |
---|
| 50 | Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research |
---|
| 51 | (Kline, 2006). |
---|
| 52 | |
---|
| 53 | .. figure:: img/lamellar_1d.jpg |
---|
| 54 | |
---|
| 55 | 1D plot using the default values (w/1000 data point). |
---|
| 56 | |
---|
| 57 | |
---|
| 58 | Reference |
---|
| 59 | --------- |
---|
| 60 | |
---|
| 61 | F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502 |
---|
| 62 | |
---|
| 63 | also in J. Phys. Chem. B, 105, (2001) 11081-11088 |
---|
| 64 | |
---|
| 65 | |
---|
| 66 | |
---|