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34          <span>Home</span></a></h1>
35        <h2 class="heading"><span>2.1.3.4. Lamellar ffhg</span></h2>
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39        <p>
40        «&#160;&#160;<a href="lamellarCailleHG.html">2.1.3.3. Lamellarcaillehg</a>
41        &#160;&#160;::&#160;&#160;
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51  <div class="section" id="lamellar-ffhg">
52<span id="id1"></span><h1>2.1.3.4. Lamellar ffhg<a class="headerlink" href="#lamellar-ffhg" title="Permalink to this headline">¶</a></h1>
53<p>Random lamellar phase with Head Groups</p>
54<table border="1" class="docutils">
55<colgroup>
56<col width="16%" />
57<col width="48%" />
58<col width="17%" />
59<col width="19%" />
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>tail_length</td>
80<td>Tail thickness</td>
81<td>Å</td>
82<td>15</td>
83</tr>
84<tr class="row-odd"><td>head_length</td>
85<td>head thickness</td>
86<td>Å</td>
87<td>10</td>
88</tr>
89<tr class="row-even"><td>sld</td>
90<td>Tail scattering length density</td>
91<td>10<sup>-6</sup>Å<sup>-2</sup></td>
92<td>0.4</td>
93</tr>
94<tr class="row-odd"><td>head_sld</td>
95<td>Head scattering length density</td>
96<td>10<sup>-6</sup>Å<sup>-2</sup></td>
97<td>3</td>
98</tr>
99<tr class="row-even"><td>solvent_sld</td>
100<td>Solvent scattering length density</td>
101<td>10<sup>-6</sup>Å<sup>-2</sup></td>
102<td>6</td>
103</tr>
104</tbody>
105</table>
106<p>The returned value is scaled to units of cm<sup>-1</sup>.</p>
107<p>This model provides the scattering intensity, <em>I(q)</em>, for a lyotropic lamellar
108phase where a random distribution in solution are assumed. The SLD of the head
109region is taken to be different from the SLD of the tail region.</p>
110<p><em>2.1.31.1. Definition</em></p>
111<p>The scattering intensity <em>I(q)</em> is</p>
112<div class="math">
113\[I(Q) = 2\pi{P(Q) \over (2(|delta|\ H +|delta|\ T) Q^2)\]</div>
114<p>The form factor is</p>
115<img alt="model/img/lamellarFFHG_.jpg" src="model/img/lamellarFFHG_.jpg" />
116<p>where ÎŽT = tail length (or <em>tail_length</em>), ÎŽH = head thickness
117(or <em>h_thickness</em>), ΔρH = SLD(headgroup) - SLD(solvent),
118and ΔρT = SLD(tail) - SLD(solvent).</p>
119<p>The 2D scattering intensity is calculated in the same way as 1D, where
120the <em>q</em> vector is defined as</p>
121<div class="math">
122\[Q = \sqrt{Q_x^2 + Q_y^2}\]</div>
123<p>The returned value is in units of cm<sup>-1</sup>, on absolute scale. In the
124parameters, <em>sld_tail</em> = SLD of the tail group, and <em>sld_head</em> = SLD
125of the head group.</p>
126<img alt="../_images/lamellarFFHG_138.jpg" src="../_images/lamellarFFHG_138.jpg" />
127<p><em>Figure. 1D plot using the default values (w/1000 data point).</em></p>
128<p>Our model uses the form factor calculations implemented in a C library
129provided by the NIST Center for Neutron Research (Kline, 2006).</p>
130<p>REFERENCE</p>
131<p>F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502</p>
132<p>also in J. Phys. Chem. B, 105, (2001) 11081-11088</p>
133<p><em>2014/04/17 - Description reviewed by S King and P Butler.</em></p>
134</div>
135
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