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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
r9611dd6 ra27b3df 4544 4544 <p> also in J. Phys. Chem. B, 105, (2001) 11081-11088.</p> 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 <p>This model provides the scattering intensity, I(<em>q</em>), 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.</p> 4547 <p>The scattering intensity I(q) is:</p> 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> 4548 4549 <p style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="img/image136.PNG" alt="" /></span></p> 4549 <p> The form factor is,</p>4550 <p>where the form factor is given by,</p> 4550 4551 <p style="text-align: center;" align="center"><img src="img/image137.jpg" alt="" width="432" height="46" /></p> 4551 <p>where <span style="font-family: Symbol;">dT</span> = tail length (or t_length), <span style="font-family: Symbol;">dH</span> = heasd thickness (or h_thickness) , <span style="font-family: Symbol;">Dr</span>H = SLD (headgroup) - SLD(solvent), and <span style="font-family: Symbol;">Dr</span>T = SLD (tail) - SLD(headgroup).</p> 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 <br>(sld_tail = SLD of the tail group, and sld_head = SLD of the head group)</p> 4552 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> 4553 4555 <p><span style="font-size: 14pt;"> </span></p> 4554 <p>The returned value is in units of [cm-1], on absolute scale. In the parameters, sld_tail = SLD of the tail group, and sld_head = SLD of the head group.</p> 4556 <p>NOTE: The total bilayer thickness = 2(δ<sub>H</sub> + δ<sub>T</sub>)</p> 4557 <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> 4555 4558 <p> </p> 4556 4559 <div align="center">
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