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| 33 | <div class="header"><h1 class="heading"><a href="../index.html"> |
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| 34 | <span>Home</span></a></h1> |
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| 35 | <h2 class="heading"><span>2.1.3.5. Lamellarpc</span></h2> |
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| 36 | </div> |
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| 37 | <div class="topnav"> |
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| 38 | |
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| 39 | <p> |
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| 40 | «  <a href="lamellarFFHG.html">2.1.3.4. Lamellar ffhg</a> |
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| 41 |   ::   |
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| 42 | <a class="uplink" href="../index.html">Contents</a> |
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| 43 |   ::   |
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| 44 | <a href="../ref/models/shape-paracrystal.html">2.1.4. Paracrystal Functions</a>  Â» |
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| 45 | </p> |
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| 46 | |
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| 47 | </div> |
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| 48 | <div class="content"> |
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| 49 | |
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| 50 | |
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| 51 | <div class="section" id="lamellarpc"> |
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| 52 | <span id="id1"></span><h1>2.1.3.5. Lamellarpc<a class="headerlink" href="#lamellarpc" title="Permalink to this headline">¶</a></h1> |
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| 53 | <p>Random lamellar sheet with paracrystal structure factor</p> |
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| 54 | <table border="1" class="docutils"> |
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| 55 | <colgroup> |
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| 56 | <col width="22%" /> |
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| 57 | <col width="45%" /> |
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| 58 | <col width="16%" /> |
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| 59 | <col width="18%" /> |
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| 60 | </colgroup> |
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| 61 | <thead valign="bottom"> |
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| 62 | <tr class="row-odd"><th class="head">Parameter</th> |
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| 63 | <th class="head">Description</th> |
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| 64 | <th class="head">Units</th> |
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| 65 | <th class="head">Default value</th> |
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| 66 | </tr> |
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| 67 | </thead> |
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| 68 | <tbody valign="top"> |
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| 69 | <tr class="row-even"><td>scale</td> |
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| 70 | <td>Source intensity</td> |
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| 71 | <td>None</td> |
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| 72 | <td>1</td> |
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| 73 | </tr> |
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| 74 | <tr class="row-odd"><td>background</td> |
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| 75 | <td>Source background</td> |
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| 76 | <td>cm<sup>-1</sup></td> |
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| 77 | <td>0</td> |
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| 78 | </tr> |
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| 79 | <tr class="row-even"><td>thickness</td> |
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| 80 | <td>sheet thickness</td> |
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| 81 | <td>â«</td> |
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| 82 | <td>33</td> |
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| 83 | </tr> |
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| 84 | <tr class="row-odd"><td>Nlayers</td> |
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| 85 | <td>Number of layers</td> |
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| 86 | <td>None</td> |
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| 87 | <td>20</td> |
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| 88 | </tr> |
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| 89 | <tr class="row-even"><td>spacing</td> |
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| 90 | <td>d-spacing of paracrystal stack</td> |
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| 91 | <td>â«</td> |
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| 92 | <td>250</td> |
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| 93 | </tr> |
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| 94 | <tr class="row-odd"><td>spacing_polydisp</td> |
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| 95 | <td>d-spacing of paracrystal stack</td> |
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| 96 | <td>â«</td> |
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| 97 | <td>0</td> |
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| 98 | </tr> |
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| 99 | <tr class="row-even"><td>sld</td> |
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| 100 | <td>layer scattering length density</td> |
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| 101 | <td>10<sup>-6</sup>â«<sup>-2</sup></td> |
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| 102 | <td>1</td> |
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| 103 | </tr> |
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| 104 | <tr class="row-odd"><td>solvent_sld</td> |
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| 105 | <td>Solvent scattering length density</td> |
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| 106 | <td>10<sup>-6</sup>â«<sup>-2</sup></td> |
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| 107 | <td>6.34</td> |
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| 108 | </tr> |
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| 109 | </tbody> |
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| 110 | </table> |
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| 111 | <p>The returned value is scaled to units of cm<sup>-1</sup>.</p> |
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| 112 | <p>This model calculates the scattering from a stack of repeating lamellar |
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| 113 | structures. The stacks of lamellae (infinite in lateral dimension) are |
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| 114 | treated as a paracrystal to account for the repeating spacing. The repeat |
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| 115 | distance is further characterized by a Gaussian polydispersity. <strong>This model |
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| 116 | can be used for large multilamellar vesicles.</strong></p> |
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| 117 | <p><em>2.1.33.1. Definition</em></p> |
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| 118 | <p>The scattering intensity <em>I(q)</em> is calculated as</p> |
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| 119 | <img alt="model/img/image145.jpg" src="model/img/image145.jpg" /> |
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| 120 | <p>The form factor of the bilayer is approximated as the cross section of an |
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| 121 | infinite, planar bilayer of thickness <em>t</em></p> |
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| 122 | <img alt="model/img/image146.jpg" src="model/img/image146.jpg" /> |
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| 123 | <p>Here, the scale factor is used instead of the mass per area of the |
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| 124 | bilayer (<em>G</em>). The scale factor is the volume fraction of the material in |
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| 125 | the bilayer, <em>not</em> the total excluded volume of the paracrystal. |
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| 126 | <em>Z</em><sub>N</sub><em>(q)</em> describes the interference effects for aggregates |
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| 127 | consisting of more than one bilayer. The equations used are (3-5) |
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| 128 | from the Bergstrom reference below.</p> |
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| 129 | <p>Non-integer numbers of stacks are calculated as a linear combination of |
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| 130 | the lower and higher values</p> |
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| 131 | <img alt="model/img/image147.jpg" src="model/img/image147.jpg" /> |
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| 132 | <p>The 2D scattering intensity is the same as 1D, regardless of the orientation |
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| 133 | of the <em>q</em> vector which is defined as</p> |
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| 134 | <div class="math"> |
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| 135 | \[Q = \sqrt{Q_x^2 + Q_y^2}\]</div> |
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| 136 | <p>The parameters of the model are <em>Nlayers</em> = no. of layers, and |
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| 137 | <em>pd_spacing</em> = polydispersity of spacing.</p> |
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| 138 | <table border="1" class="docutils"> |
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| 139 | <colgroup> |
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| 140 | <col width="40%" /> |
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| 141 | <col width="23%" /> |
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| 142 | <col width="37%" /> |
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| 143 | </colgroup> |
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| 144 | <thead valign="bottom"> |
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| 145 | <tr class="row-odd"><th class="head">Parameter name</th> |
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| 146 | <th class="head">Units</th> |
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| 147 | <th class="head">Default value</th> |
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| 148 | </tr> |
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| 149 | </thead> |
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| 150 | <tbody valign="top"> |
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| 151 | <tr class="row-even"><td>background</td> |
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| 152 | <td>cm<sup>-1</sup></td> |
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| 153 | <td>0</td> |
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| 154 | </tr> |
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| 155 | <tr class="row-odd"><td>scale</td> |
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| 156 | <td>None</td> |
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| 157 | <td>1</td> |
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| 158 | </tr> |
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| 159 | <tr class="row-even"><td>Nlayers</td> |
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| 160 | <td>None</td> |
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| 161 | <td>20</td> |
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| 162 | </tr> |
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| 163 | <tr class="row-odd"><td>pd_spacing</td> |
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| 164 | <td>None</td> |
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| 165 | <td>0.2</td> |
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| 166 | </tr> |
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| 167 | <tr class="row-even"><td>sld_layer</td> |
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| 168 | <td>â«<sup>-2</sup></td> |
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| 169 | <td>1e-6</td> |
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| 170 | </tr> |
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| 171 | <tr class="row-odd"><td>sld_solvent</td> |
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| 172 | <td>â«<sup>-2</sup></td> |
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| 173 | <td>6.34e-6</td> |
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| 174 | </tr> |
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| 175 | <tr class="row-even"><td>spacing</td> |
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| 176 | <td>â«</td> |
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| 177 | <td>250</td> |
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| 178 | </tr> |
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| 179 | <tr class="row-odd"><td>thickness</td> |
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| 180 | <td>â«</td> |
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| 181 | <td>33</td> |
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| 182 | </tr> |
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| 183 | </tbody> |
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| 184 | </table> |
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| 185 | <img alt="model/img/image148.jpg" src="model/img/image148.jpg" /> |
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| 186 | <p><em>Figure. 1D plot using the default values above (w/20000 data point).</em></p> |
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| 187 | <p>Our model uses the form factor calculations implemented in a C library |
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| 188 | provided by the NIST Center for Neutron Research (Kline, 2006).</p> |
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| 189 | <p>REFERENCE</p> |
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| 190 | <p>M Bergstrom, J S Pedersen, P Schurtenberger, S U Egelhaaf, |
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| 191 | <em>J. Phys. Chem. B</em>, 103 (1999) 9888-9897</p> |
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| 192 | </div> |
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| 193 | |
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| 194 | |
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| 195 | </div> |
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| 196 | <div class="bottomnav"> |
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| 197 | |
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| 198 | <p> |
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| 199 | «  <a href="lamellarFFHG.html">2.1.3.4. Lamellar ffhg</a> |
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| 200 |   ::   |
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| 201 | <a class="uplink" href="../index.html">Contents</a> |
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| 202 |   ::   |
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| 203 | <a href="../ref/models/shape-paracrystal.html">2.1.4. Paracrystal Functions</a>  Â» |
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| 204 | </p> |
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| 205 | |
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