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	<id>http://gisaxs.com/index.php?action=history&amp;feed=atom&amp;title=Example%3AVirial_coefficient</id>
	<title>Example:Virial coefficient - Revision history</title>
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	<updated>2026-04-08T17:45:50Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>http://gisaxs.com/index.php?title=Example:Virial_coefficient&amp;diff=5073&amp;oldid=prev</id>
		<title>KevinYager at 13:38, 25 July 2015</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Example:Virial_coefficient&amp;diff=5073&amp;oldid=prev"/>
		<updated>2015-07-25T13:38:43Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 13:38, 25 July 2015&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Interparticle interactions can be probed by measuring [[SAXS]] as a function of concentration (&amp;#039;&amp;#039;c&amp;#039;&amp;#039;). At low concentration, the particles do not interact. The scattering in this case is dominated by the [[form factor]] (&amp;lt;math&amp;gt;\scriptstyle P(q)&amp;lt;/math&amp;gt;), which simply encodes the particle size/shape (because the structure factor is eliminated: &amp;lt;math&amp;gt;\scriptstyle S(c=0,q)=1&amp;lt;/math&amp;gt;). On the other hand, at high concentrations, particles interact strongly, leading to a non-trivial structure factor.&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Interparticle interactions can be probed by measuring [[SAXS]] as a function of concentration (&amp;#039;&amp;#039;c&amp;#039;&amp;#039;). At low concentration, the particles do not interact. The &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[[&lt;/ins&gt;scattering&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;]] &lt;/ins&gt;in this case is dominated by the [[form factor]] (&amp;lt;math&amp;gt;\scriptstyle P(q)&amp;lt;/math&amp;gt;), which simply encodes the particle size/shape (because the &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[[&lt;/ins&gt;structure factor&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;]] &lt;/ins&gt;is eliminated: &amp;lt;math&amp;gt;\scriptstyle S(c=0,q)=1&amp;lt;/math&amp;gt;). On the other hand, at high concentrations, particles interact strongly, leading to a non-trivial structure factor.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;lt;math&amp;gt;I(c,q) = I(c=0,q) \times S(c,q)&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;lt;math&amp;gt;I(c,q) = I(c=0,q) \times S(c,q)&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>KevinYager</name></author>
		
	</entry>
	<entry>
		<id>http://gisaxs.com/index.php?title=Example:Virial_coefficient&amp;diff=5072&amp;oldid=prev</id>
		<title>KevinYager: Created page with &quot;Interparticle interactions can be probed by measuring SAXS as a function of concentration (&#039;&#039;c&#039;&#039;). At low concentration, the particles do not interact. The scattering in t...&quot;</title>
		<link rel="alternate" type="text/html" href="http://gisaxs.com/index.php?title=Example:Virial_coefficient&amp;diff=5072&amp;oldid=prev"/>
		<updated>2015-07-25T13:37:00Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;Interparticle interactions can be probed by measuring &lt;a href=&quot;/index.php/SAXS&quot; title=&quot;SAXS&quot;&gt;SAXS&lt;/a&gt; as a function of concentration (&amp;#039;&amp;#039;c&amp;#039;&amp;#039;). At low concentration, the particles do not interact. The scattering in t...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;Interparticle interactions can be probed by measuring [[SAXS]] as a function of concentration (&amp;#039;&amp;#039;c&amp;#039;&amp;#039;). At low concentration, the particles do not interact. The scattering in this case is dominated by the [[form factor]] (&amp;lt;math&amp;gt;\scriptstyle P(q)&amp;lt;/math&amp;gt;), which simply encodes the particle size/shape (because the structure factor is eliminated: &amp;lt;math&amp;gt;\scriptstyle S(c=0,q)=1&amp;lt;/math&amp;gt;). On the other hand, at high concentrations, particles interact strongly, leading to a non-trivial structure factor.&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;I(c,q) = I(c=0,q) \times S(c,q)&amp;lt;/math&amp;gt;&lt;br /&gt;
:&amp;lt;math&amp;gt;S(c,q) = \frac{ I(c,q) }{  I(0,q) }&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
From the solution [[structure factor]] (&amp;lt;math&amp;gt;\scriptstyle S(q)&amp;lt;/math&amp;gt;), one can calculate the second virial coefficient (&amp;#039;&amp;#039;A&amp;#039;&amp;#039;&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;):&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{1}{S(c,q=0)} = 1 + 2 M A_2 c&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
* &amp;#039;&amp;#039;Journal of Crystal Growth&amp;#039;&amp;#039; &amp;#039;&amp;#039;&amp;#039;2001&amp;#039;&amp;#039;&amp;#039;, 232, 1-9.&lt;br /&gt;
* &amp;#039;&amp;#039;Methods in Enzymology&amp;#039;&amp;#039; &amp;#039;&amp;#039;&amp;#039;1997&amp;#039;&amp;#039;&amp;#039;, Vol. 276, 100-110.&lt;/div&gt;</summary>
		<author><name>KevinYager</name></author>
		
	</entry>
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