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