- Timestamp:
- Apr 27, 2014 8:34:06 PM (11 years ago)
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src/sans/models/media/model_functions.html (modified) (1 diff)
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src/sans/models/media/model_functions.html
ra27b3df r29b6cbd 4545 4545 <p style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.35.</span></b><b><span style="font-size: 7pt;"> </span></b><a name="LamellarFFHGModel"></a><b><span style="font-size: 14pt;">LamellarFFHGModel</span></b></p> 4546 4546 <p>This model calculates the form factor from a lyotropic lamellar phase. The intensity calculated is for lamellae of two-layer scattering length density that are randomly distributed in solution (a powder average). The scattering length density of the tail region, headgroup region, and solvent are taken to be different. 4547 No inter-lamellar structure factor is calculated. Other models are available where S(q) is calculated. I(<em>q</em>)</p>4548 <p>The returned value is scale*I(q) + background, and is in units of [cm<sup>-1</sup>]:</p>4547 No inter-lamellar structure factor is calculated. Other models are available where S(q) is calculated.</p> 4548 <p>The returned value is scale*I(q) + background, and is in units of [cm<sup>-1</sup>]:</p> 4549 4549 <p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image136.PNG" alt="" /></span></p> 4550 <p>where the form factor is given by ,</p>4550 <p>where the form factor is given by:</p> 4551 4551 <p style="text-align: center;" align="center"><img src="img/image137.jpg" alt="" width="432" height="46" /></p> 4552 <p>where δ<sub>T</sub> = tail length (or t_length), δ<sub>H</sub> = head thickness (or h_thickness) 4552 <p>where δ<sub>T</sub> = tail length (or t_length), δ<sub>H</sub> = head thickness (or h_thickness), Δρ<sub>H</sub> = SLD (headgroup) - SLD(solvent), and Δρ<sub>T</sub> = SLD (tail) - SLD(solvent). 4553 4553 <br>(sld_tail = SLD of the tail group, and sld_head = SLD of the head group)</p> 4554 <p>The 2D scattering intensity is calculated in the same way as 1D, where the <em>q</em> vector is defined as<span style="font-size: 12pt; font-family: 'Times New Roman','serif'; position: relative; top: 4.5pt;"><img src="img/image040.gif" alt="" width="111" height="23" /></span><span style="font-size: 14pt;">.</span></p> 4555 <p><span style="font-size: 14pt;"> </span></p> 4554 <p>The 2D scattering intensity is calculated in the same way as 1D, where the q vector is defined as:</br> 4555 <img src="img/image040.gif" alt="" width="111" height="23" /></p> 4556 <!-- <p><span style="font-size: 14pt;"> </span></p> --> 4556 4557 <p>NOTE: The total bilayer thickness = 2(δ<sub>H</sub> + δ<sub>T</sub>)</p> 4557 4558 <p>The meaning of the multiplicative scale factor is not well-defined, but should be on the order of the volume fraction of solution occupied by the lamellar crystallites. Please see the original references for clarification.</p>
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