Ignore:
Timestamp:
Jul 16, 2012 8:43:43 AM (12 years ago)
Author:
Robert Whitley <robert.whitley@…>
Branches:
master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
Children:
f518eef
Parents:
325bc4a
Message:

Refs #84. Add model function help.

File:
1 edited

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  • sansmodels/src/sans/models/media/model_functions.html

    re0405592 rdc9660d  
    473473<a href="#DAB_Model">DAB_Model</a>, <a href="#Debye">Debye</a>, <a href="#Number_Density_Fractal">FractalModel</a>, <a href="#FractalCoreShell">FractalCoreShell</a>, <a href="#GaussLorentzGel">GaussLorentzGel</a>, <a href="#Guinier">Guinier</a>, <a href="#GuinierPorod">GuinierPorod</a>, <a href="#Lorentz">Lorentz</a>, <a href="#Mass_Fractal">MassFractalModel</a>, <a href="#MassSurface_Fractal">MassSurfaceFractal</a>, <a href="#Peak%20Gauss%20Model">PeakGaussModel</a>, <a href="#Peak%20Lorentz%20Model">PeakLorentzModel</a>, <a href="#Poly_GaussCoil">Poly_GaussCoil</a>, <a href="#PolymerExclVolume">PolyExclVolume</a>, <a href="#PorodModel">PorodModel</a>, <a href="#RPA10Model">RPA10Model</a><a href="model_functions.html#ReflectivityIIModel">, </a><a href="#Surface_Fractal">SurfaceFractalModel</a>, 
    474474<a href="#Teubner%20Strey">Teubner Strey</a>, <a href="#TwoLorentzian">TwoLorentzian</a>, <a href="#TwoPowerLaw">TwoPowerLaw</a>, <a href="#UnifiedPowerRg">UnifiedPowerRg</a>, <a href="#LineModel">LineModel</a>, <a href="#ReflectivityModel">ReflectivityModel</a>, 
    475 <a href="#ReflectivityIIModel">ReflectivityIIModel</a>.</li> 
     475<a href="#ReflectivityIIModel">ReflectivityIIModel</a>, <a href="#GelFitModel">GelFitModel</a>.</li> 
    476476<li class="MsoNormal" style="line-height: 115%;"><a href="#Model"><b>Customized Models</b></a>: 
    477477<a href="#testmodel">testmodel</a>, <a href="#testmodel_2">testmodel_2</a>, <a href="#sum_p1_p2">sum_p1_p2</a>, <a href="#sum_Ap1_1_Ap2">sum_Ap1_1_Ap2</a>, <a href="#polynomial5">polynomial5</a>, <a href="#sph_bessel_jn">sph_bessel_jn</a>.</li> 
    … …  
    1093310933This 
    1093410934model was implemented by an interested user. </p> 
     10935 
     10936 
     10937 
     10938 
     10939 
     10940 
     10941<p>&nbsp;</p> 
     10942<p>&nbsp;</p> 
     10943<p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"></p> 
     10944<p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;">&nbsp;</p> 
     10945<p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">3.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     10946</span></b><a name="GelFitModel"><b><span style="font-size: 14pt;">GelFitModel</span></b></a></p> 
     10947<p class="MsoListParagraph" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">&nbsp;</span></b></p> 
     10948<p class="MsoNormal">&nbsp;&nbsp;&nbsp; Unlike a concentrated polymer solution, the fine-scale polymer distribution in a gel involves  
     10949at least two characteristic length scales, a shorter correlation length (a1) to describe the rapid fluctuations in the position of the  
     10950polymer chains that ensure thermodynamic equilibrium, and a longer distance (denoted here as a2) needed to account for the static  
     10951accumulations of polymer pinned down by junction points or clusters of such points. The letter is derived from a simple Guinier function.</p> 
     10952<p>&nbsp;</p> 
     10953<p class="MsoListParagraph" style="margin-left: 0.55in;"> 
     10954The scattered intensity I(Q) is then calculated as: </p> 
     10955<p> <img src="image233.gif"></p> 
     10956<p class="MsoListParagraph" style="margin-left: 0.55in;"> 
     10957Where: </p> 
     10958<p> <span><img src="image234.gif"></span></p> 
     10959<p> </p> 
     10960<p> </p> 
     10961<p class="MsoNormal">&nbsp;&nbsp;&nbsp; Note the first term reduces to the Ornstein-Zernicke equation when D=2; ie, when the Flory exponent is 0.5 (theta conditions). 
     10962&nbsp; 
     10963In gels with significant hydrogen bonding D has been reported to be ~2.6 to 2.8. 
     10964</p> 
     10965<p>&nbsp;</p> 
     10966<p class="MsoNormal">&nbsp;&nbsp;&nbsp; Note: 
     10967This 
     10968model was implemented by an interested user. </p> 
     10969 
     10970<p class="MsoNormal" style="margin-left: 0.25in;">&nbsp;</p> 
     10971<p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><b>Default 
     10972input parameter values</b></p> 
     10973<div align="center"> 
     10974<table class="MsoNormalTable" style="border-collapse: collapse;" border="2" cellpadding="0" cellspacing="0"> 
     10975<tbody> 
     10976<tr style="height: 19.25pt;"> 
     10977<td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     10978<p class="MsoBodyText">Parameter name</p> 
     10979</td> 
     10980<td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     10981<p class="MsoBodyText">Units</p> 
     10982</td> 
     10983<td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     10984<p class="MsoBodyText">Default value</p> 
     10985</td> 
     10986</tr> 
     10987<tr style="height: 19.25pt;"> 
     10988<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     10989<p class="MsoBodyText">Background</p> 
     10990</td> 
     10991<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     10992<p class="MsoBodyText">cm<sup>-1</sup></p> 
     10993</td> 
     10994<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     10995<p class="MsoBodyText">0.01</p> 
     10996</td> 
     10997</tr> 
     10998<tr style="height: 19.25pt;"> 
     10999<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; vertical-align: top; width: 107pt; height: 19.25pt;"> 
     11000<p class="MsoBodyText">Guinier scale</p> 
     11001</td> 
     11002<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11003<p class="MsoBodyText">cm<sup>-1</sup></p> 
     11004</td> 
     11005<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11006<p class="MsoBodyText">1.7</p> 
     11007</td> 
     11008</tr> 
     11009<tr style="height: 19.25pt;"> 
     11010<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11011<p class="MsoBodyText">Lorentzian scale</p> 
     11012</td> 
     11013<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11014<p class="MsoBodyText">cm<sup>-1</sup></p> 
     11015</td> 
     11016<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11017<p class="MsoBodyText">3.5</p> 
     11018</td> 
     11019</tr> 
     11020<tr style="height: 19.25pt;"> 
     11021<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11022<p class="MsoBodyText">Radius of gyration</p> 
     11023</td> 
     11024<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11025<p class="MsoBodyText">Å</p> 
     11026</td> 
     11027<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11028<p class="MsoBodyText">104</p> 
     11029</td> 
     11030</tr> 
     11031<tr style="height: 19.25pt;"> 
     11032<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11033<p class="MsoBodyText">Fractal exponent</p> 
     11034</td> 
     11035<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"></td> 
     11036<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11037<p class="MsoBodyText">2</p> 
     11038</td> 
     11039</tr> 
     11040<tr style="height: 19.25pt;"> 
     11041<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11042<p class="MsoBodyText">Correlation length</p> 
     11043</td> 
     11044<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11045<p class="MsoBodyText">Å</p> 
     11046</td> 
     11047<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 19.25pt;" valign="top" width="143"> 
     11048<p class="MsoBodyText">16</p> 
     11049</td> 
     11050</tr> 
     11051</tbody> 
     11052</table> 
     11053</div> 
     11054<p class="MsoNormal" style="margin-left: 0.5in;">&nbsp;</p> 
     11055<p class="MsoNormal" style="margin-left: 0.5in;">&nbsp;</p> 
     11056<p class="MsoNormal" style="margin-left: 0.5in; text-align: center;" align="center"><img id="Picture 11" src="image235.gif" height="336" width="470"></p> 
     11057<p class="MsoNormal" style="text-align: center;" align="center"><b>Figure. 
     110581D plot using the default values (w/300 data points, qmin=0.001, and qmax=0.3).</b></p> 
     11059<p class="MsoNormal" style="margin-left: 0.5in; text-align: center;" align="center">&nbsp;</p> 
     11060<p class="MsoNormal" style="margin-left: 0.25in;">&nbsp;</p> 
     11061<p class="MsoNormal" style="margin-left: 0.25in;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
     11062REFERENCES</p> 
     11063<p class="MsoNormal" style="margin-left: 0.25in;"> 
     11064Mitsuhiro Shibayama, Toyoichi Tanaka, Charles C. Han, J. Chem. Phys. 1992, 97 (9), 6829-6841.</p> 
     11065<p class="MsoNormal" style="margin-left: 0.25in;"> 
     11066Simon Mallam, Ferenc Horkay, Anne-Marie Hecht, Adrian R. Rennie, Erik Geissler, Macromolecules 1991, 24, 543-548.</p> 
     11067 
     11068 
     11069 
     11070 
    1093511071<p class="MsoNormal"><b><span style="font-size: 14pt;">&nbsp;</span></b></p> 
    1093611072<p class="MsoNormal"><b><span style="font-size: 14pt;"></span></b></p> 
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