http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&feed=atom&action=history
Frenkel line - Revision history
2024-03-28T23:56:41Z
Revision history for this page on the wiki
MediaWiki 1.41.0
http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&diff=14606&oldid=prev
Carl McBride: Reinstated CO2 references and mention of CH4
2015-03-16T18:19:09Z
<p>Reinstated CO2 references and mention of CH4</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:19, 16 March 2015</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[hydrogen]] <ref> [http://dx.doi.org/10.1103/PhysRevE.89.032126 K. Trachenko, V. V. Brazhkin, and D. Bolmatov, "Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants", Physical Review E '''89''' 032126 (2014)]</ref>, </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[hydrogen]] <ref> [http://dx.doi.org/10.1103/PhysRevE.89.032126 K. Trachenko, V. V. Brazhkin, and D. Bolmatov, "Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants", Physical Review E '''89''' 032126 (2014)]</ref>, </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[water]] <ref name="kostya3"> [http://dx.doi.org/10.1103/PhysRevE.91.012112 C. Yang, V. V. Brazhkin, M. T. Dove, and K. Trachenko "Frenkel line and solubility maximum in supercritical fluids", Physical Review E '''91''' 012112 (2015)]</ref>, </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[water]] <ref name="kostya3"> [http://dx.doi.org/10.1103/PhysRevE.91.012112 C. Yang, V. V. Brazhkin, M. T. Dove, and K. Trachenko "Frenkel line and solubility maximum in supercritical fluids", Physical Review E '''91''' 012112 (2015)]</ref>, </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>[[carbon dioxide]] <ref name="StructuralEvolutionJPCL" ></ref><ref> <del style="font-weight: bold; text-decoration: none;">[http:</del>/<del style="font-weight: bold; text-decoration: none;">/pubs.acs.org/doi/abs/10.1021/jz5012127 Dima Bolmatov, D. Zav’yalov, M. Gao</del>, and <del style="font-weight: bold; text-decoration: none;">Mikhail Zhernenkov </del>"<del style="font-weight: bold; text-decoration: none;">Evidence for structural crossover in the supercritical state</del>"<del style="font-weight: bold; text-decoration: none;">, Journal of Physical Chemistry '''5''' pp 2785-2790 (2014)]</del></ref></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>[[carbon dioxide]] <ref name="StructuralEvolutionJPCL" ></ref><ref <ins style="font-weight: bold; text-decoration: none;">name="kostya3"</ins>> <ins style="font-weight: bold; text-decoration: none;"><</ins>/<ins style="font-weight: bold; text-decoration: none;">ref></ins>,</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>and <ins style="font-weight: bold; text-decoration: none;">[[methane]] <ref name=</ins>"<ins style="font-weight: bold; text-decoration: none;">kostya3</ins>"<ins style="font-weight: bold; text-decoration: none;">> </ins></ref></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>have been reported in the literature.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>have been reported in the literature.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>==Related Lines==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>==Related Lines==</div></td></tr>
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Carl McBride
http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&diff=14605&oldid=prev
Carl McBride: Corrected article title
2015-03-16T18:15:40Z
<p>Corrected article title</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:15, 16 March 2015</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Crossing the Frenkel line leads also to some structural crossovers in fluids </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Crossing the Frenkel line leads also to some structural crossovers in fluids </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div><ref>[http://dx.doi.org/10.1063/1.4844135 Dima Bolmatov, V. V. Brazhkin, Yu. D. Fomin, V. N. Ryzhov, and K. Trachenko "Evidence for structural crossover in the supercritical state", Journal of Chemical Physics '''139''' 234501 (2013)]</ref></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div><ref>[http://dx.doi.org/10.1063/1.4844135 Dima Bolmatov, V. V. Brazhkin, Yu. D. Fomin, V. N. Ryzhov, and K. Trachenko "Evidence for structural crossover in the supercritical state", Journal of Chemical Physics '''139''' 234501 (2013)]</ref></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div><ref>[http://dx.doi.org/10.1021/jz5012127 Dima Bolmatov, D. Zav’yalov, M. Gao, and Mikhail Zhernenkov "Structural Evolution of Supercritical CO2 across the Frenkel Line", Journal of Physical Chemistry Letters '''5''' pp 2785-2790 (2014)]</ref>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div><ref <ins style="font-weight: bold; text-decoration: none;">name="StructuralEvolutionJPCL" </ins>>[http://dx.doi.org/10.1021/jz5012127 Dima Bolmatov, D. Zav’yalov, M. Gao, and Mikhail Zhernenkov "Structural Evolution of Supercritical CO2 across the Frenkel Line", Journal of Physical Chemistry Letters '''5''' pp 2785-2790 (2014)]</ref>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Currently Frenkel lines of several [[Idealised models|idealised liquids]], such as [[Lennard-Jones model|Lennard-Jones]] and [[Soft sphere potential|soft spheres]] </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Currently Frenkel lines of several [[Idealised models|idealised liquids]], such as [[Lennard-Jones model|Lennard-Jones]] and [[Soft sphere potential|soft spheres]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div><ref name="ufn"> </ref>, <ref name="frpre"> </ref>, <ref name="frprl"> </ref> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div><ref name="ufn"> </ref>, <ref name="frpre"> </ref>, <ref name="frprl"> </ref> </div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l77">Line 77:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[hydrogen]] <ref> [http://dx.doi.org/10.1103/PhysRevE.89.032126 K. Trachenko, V. V. Brazhkin, and D. Bolmatov, "Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants", Physical Review E '''89''' 032126 (2014)]</ref>, </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[hydrogen]] <ref> [http://dx.doi.org/10.1103/PhysRevE.89.032126 K. Trachenko, V. V. Brazhkin, and D. Bolmatov, "Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants", Physical Review E '''89''' 032126 (2014)]</ref>, </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[water]] <ref name="kostya3"> [http://dx.doi.org/10.1103/PhysRevE.91.012112 C. Yang, V. V. Brazhkin, M. T. Dove, and K. Trachenko "Frenkel line and solubility maximum in supercritical fluids", Physical Review E '''91''' 012112 (2015)]</ref>, </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[water]] <ref name="kostya3"> [http://dx.doi.org/10.1103/PhysRevE.91.012112 C. Yang, V. V. Brazhkin, M. T. Dove, and K. Trachenko "Frenkel line and solubility maximum in supercritical fluids", Physical Review E '''91''' 012112 (2015)]</ref>, </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>[[carbon dioxide]] <ref> [http://pubs.acs.org/doi/abs/10.1021/jz5012127 Dima Bolmatov, D. Zav’yalov, M. Gao, and Mikhail Zhernenkov "Evidence for structural crossover in the supercritical state", Journal of Physical Chemistry '''5''' pp 2785-2790 (2014)]</ref></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>[[carbon dioxide]] <ins style="font-weight: bold; text-decoration: none;"><ref name="StructuralEvolutionJPCL" ></ref></ins><ref> [http://pubs.acs.org/doi/abs/10.1021/jz5012127 Dima Bolmatov, D. Zav’yalov, M. Gao, and Mikhail Zhernenkov "Evidence for structural crossover in the supercritical state", Journal of Physical Chemistry '''5''' pp 2785-2790 (2014)]</ref></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>have been reported in the literature.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>have been reported in the literature.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>==Related Lines==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>==Related Lines==</div></td></tr>
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Carl McBride
http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&diff=14604&oldid=prev
Carl McBride: Corrected journal title
2015-03-16T18:13:22Z
<p>Corrected journal title</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:13, 16 March 2015</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Crossing the Frenkel line leads also to some structural crossovers in fluids </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Crossing the Frenkel line leads also to some structural crossovers in fluids </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div><ref> [http://dx.doi.org/10.1063/1.4844135 Dima Bolmatov, V. V. Brazhkin, Yu. D. Fomin, V. N. Ryzhov, and K. Trachenko "Evidence for structural crossover in the supercritical state", Journal of Chemical Physics '''139''' 234501 (2013)]</ref></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div><ref>[http://dx.doi.org/10.1063/1.4844135 Dima Bolmatov, V. V. Brazhkin, Yu. D. Fomin, V. N. Ryzhov, and K. Trachenko "Evidence for structural crossover in the supercritical state", Journal of Chemical Physics '''139''' 234501 (2013)]</ref></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div><ref> [http://dx.doi.org/10.1021/jz5012127 Dima Bolmatov, D. Zav’yalov, M. Gao, and Mikhail Zhernenkov "Structural Evolution of Supercritical CO2 across the Frenkel Line", Journal of Physical Chemistry '''5''' pp 2785-2790 (2014)]</ref>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div><ref>[http://dx.doi.org/10.1021/jz5012127 Dima Bolmatov, D. Zav’yalov, M. Gao, and Mikhail Zhernenkov "Structural Evolution of Supercritical CO2 across the Frenkel Line", Journal of Physical Chemistry <ins style="font-weight: bold; text-decoration: none;">Letters </ins>'''5''' pp 2785-2790 (2014)]</ref>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Currently Frenkel lines of several [[Idealised models|idealised liquids]], such as [[Lennard-Jones model|Lennard-Jones]] and [[Soft sphere potential|soft spheres]] </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Currently Frenkel lines of several [[Idealised models|idealised liquids]], such as [[Lennard-Jones model|Lennard-Jones]] and [[Soft sphere potential|soft spheres]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div><ref name="ufn"> </ref>, <ref name="frpre"> </ref>, <ref name="frprl"> </ref> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div><ref name="ufn"> </ref>, <ref name="frpre"> </ref>, <ref name="frprl"> </ref> </div></td></tr>
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Carl McBride
http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&diff=14603&oldid=prev
Carl McBride: Replaced link with DOI
2015-03-16T18:06:24Z
<p>Replaced link with DOI</p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Crossing the Frenkel line leads also to some structural crossovers in fluids </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Crossing the Frenkel line leads also to some structural crossovers in fluids </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div><ref> [http://dx.doi.org/10.1063/1.4844135 Dima Bolmatov, V. V. Brazhkin, Yu. D. Fomin, V. N. Ryzhov, and K. Trachenko "Evidence for structural crossover in the supercritical state", Journal of Chemical Physics '''139''' 234501 (2013)]</ref><del style="font-weight: bold; text-decoration: none;">, </del><ref> [http://<del style="font-weight: bold; text-decoration: none;">pubs</del>.<del style="font-weight: bold; text-decoration: none;">acs</del>.org<del style="font-weight: bold; text-decoration: none;">/doi/abs</del>/10.1021/jz5012127 <del style="font-weight: bold; text-decoration: none;"> </del>Dima Bolmatov, D. Zav’yalov, M. Gao, and Mikhail Zhernenkov "Structural Evolution of Supercritical CO2 across the Frenkel Line", Journal of Physical Chemistry '''5''' pp 2785-2790 (2014)]</ref>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div><ref> [http://dx.doi.org/10.1063/1.4844135 Dima Bolmatov, V. V. Brazhkin, Yu. D. Fomin, V. N. Ryzhov, and K. Trachenko "Evidence for structural crossover in the supercritical state", Journal of Chemical Physics '''139''' 234501 (2013)]</ref></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div><ref> [http://<ins style="font-weight: bold; text-decoration: none;">dx</ins>.<ins style="font-weight: bold; text-decoration: none;">doi</ins>.org/10.1021/jz5012127 Dima Bolmatov, D. Zav’yalov, M. Gao, and Mikhail Zhernenkov "Structural Evolution of Supercritical CO2 across the Frenkel Line", Journal of Physical Chemistry '''5''' pp 2785-2790 (2014)]</ref>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Currently Frenkel lines of several [[Idealised models|idealised liquids]], such as [[Lennard-Jones model|Lennard-Jones]] and [[Soft sphere potential|soft spheres]] </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Currently Frenkel lines of several [[Idealised models|idealised liquids]], such as [[Lennard-Jones model|Lennard-Jones]] and [[Soft sphere potential|soft spheres]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div><ref name="ufn"> </ref>, <ref name="frpre"> </ref>, <ref name="frprl"> </ref> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div><ref name="ufn"> </ref>, <ref name="frpre"> </ref>, <ref name="frprl"> </ref> </div></td></tr>
</table>
Carl McBride
http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&diff=14602&oldid=prev
Carl McBride: Added DOI and corrected a journal name
2015-03-16T17:59:24Z
<p>Added DOI and corrected a journal name</p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:59, 16 March 2015</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l63">Line 63:</td>
<td colspan="2" class="diff-lineno">Line 63:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>of transverse excitations is <math> 1 k_B </math>. Therefore at the Frenkel</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>of transverse excitations is <math> 1 k_B </math>. Therefore at the Frenkel</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>line, where transverse excitations vanish, the isochoric heat</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>line, where transverse excitations vanish, the isochoric heat</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>capacity per particle should be <math> c_V=2 k_B </math>, a direct prediction from the phonon theory of liquid thermodynamics <ref> [http://<del style="font-weight: bold; text-decoration: none;">www</del>.<del style="font-weight: bold; text-decoration: none;">nature</del>.<del style="font-weight: bold; text-decoration: none;">com</del>/<del style="font-weight: bold; text-decoration: none;">srep/2012/120524</del>/srep00421<del style="font-weight: bold; text-decoration: none;">/full/srep00421.html </del>D. Bolmatov, V. V. Brazhkin, and K. Trachenko "The phonon theory of liquid thermodynamics", Scientific Reports '''2''' 421 (2012)]</ref><del style="font-weight: bold; text-decoration: none;">, </del><ref> [http://<del style="font-weight: bold; text-decoration: none;">www</del>.<del style="font-weight: bold; text-decoration: none;">nature</del>.com/<del style="font-weight: bold; text-decoration: none;">ncomms</del>/<del style="font-weight: bold; text-decoration: none;">2013</del>/<del style="font-weight: bold; text-decoration: none;">130816</del>/<del style="font-weight: bold; text-decoration: none;">ncomms3331/full</del>/ncomms3331<del style="font-weight: bold; text-decoration: none;">.html </del>Dima Bolmatov, V. V. Brazhkin, and K. Trachenko "Thermodynamic behaviour of supercritical matter", <del style="font-weight: bold; text-decoration: none;">Scientific Reports </del>'''4''' 2331 (2013)<del style="font-weight: bold; text-decoration: none;">]</ref>, <ref> [http://physicsworld.com/cws/article/news/2012/jun/13/phonon-theory-sheds-light-on-liquid-thermodynamics "Phonon theory sheds light on liquid thermodynamics", PhysicsWorld, 2012</del>]</ref>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>capacity per particle should be <math> c_V=2 k_B </math>, a direct prediction from the phonon theory of liquid thermodynamics </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div><ref> [http://<ins style="font-weight: bold; text-decoration: none;">dx</ins>.<ins style="font-weight: bold; text-decoration: none;">doi</ins>.<ins style="font-weight: bold; text-decoration: none;">org</ins>/<ins style="font-weight: bold; text-decoration: none;">10.1038</ins>/srep00421 D. Bolmatov, V. V. Brazhkin, and K. Trachenko "The phonon theory of liquid thermodynamics", Scientific Reports '''2''' 421 (2012)]</ref> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div><ref> [http://<ins style="font-weight: bold; text-decoration: none;">physicsworld</ins>.<ins style="font-weight: bold; text-decoration: none;">com/cws/article/news/2012/jun/13/phonon-theory-sheds-light-on-liquid-thermodynamics Hamish Johnston "Phonon theory sheds light on liquid thermodynamics", PhysicsWorld</ins>.com <ins style="font-weight: bold; text-decoration: none;"> June 13 (2012)]<</ins>/<ins style="font-weight: bold; text-decoration: none;">ref></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div><ins style="font-weight: bold; text-decoration: none;"><ref> [http:</ins>//<ins style="font-weight: bold; text-decoration: none;">dx.doi.org</ins>/<ins style="font-weight: bold; text-decoration: none;">10.1038</ins>/ncomms3331 Dima Bolmatov, V. V. Brazhkin, and K. Trachenko "Thermodynamic behaviour of supercritical matter", <ins style="font-weight: bold; text-decoration: none;">Nature Communications </ins>'''4''' 2331 (2013)]</ref>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Crossing the Frenkel line leads also to some structural crossovers in fluids </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Crossing the Frenkel line leads also to some structural crossovers in fluids </div></td></tr>
</table>
Carl McBride
http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&diff=14599&oldid=prev
Davidcohen at 23:36, 15 March 2015
2015-03-15T23:36:06Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:36, 16 March 2015</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>The '''Frenkel line''' is a line of change of <del style="font-weight: bold; text-decoration: none;">microscopic </del>dynamics of</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>The '''Frenkel line''' is a line of change of <ins style="font-weight: bold; text-decoration: none;">thermodynamics, </ins>dynamics <ins style="font-weight: bold; text-decoration: none;">and structure </ins>of</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>fluids. Below the Frenkel line the fluids are "rigid" and</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>fluids. Below the Frenkel line the fluids are "rigid" and</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>"solid-like" while above it fluids are "soft" and "gas-like".</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>"solid-like" while above it fluids are "soft" and "gas-like".</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>of transverse excitations is <math> 1 k_B </math>. Therefore at the Frenkel</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>of transverse excitations is <math> 1 k_B </math>. Therefore at the Frenkel</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>line, where transverse excitations vanish, the isochoric heat</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>line, where transverse excitations vanish, the isochoric heat</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>capacity per particle should be <math> c_V=2 k_B </math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>capacity per particle should be <math> c_V=2 k_B </math<ins style="font-weight: bold; text-decoration: none;">>, a direct prediction from the phonon theory of liquid thermodynamics <ref> [http://www.nature.com/srep/2012/120524/srep00421/full/srep00421.html D. Bolmatov, V. V. Brazhkin, and K. Trachenko "The phonon theory of liquid thermodynamics", Scientific Reports '''2''' 421 (2012)]</ref>, <ref> [http://www.nature.com/ncomms/2013/130816/ncomms3331/full/ncomms3331.html Dima Bolmatov, V. V. Brazhkin, and K. Trachenko "Thermodynamic behaviour of supercritical matter", Scientific Reports '''4''' 2331 (2013)]</ref>, <ref> [http://physicsworld.com/cws/article/news/2012/jun/13/phonon-theory-sheds-light-on-liquid-thermodynamics "Phonon theory sheds light on liquid thermodynamics", PhysicsWorld, 2012]</ref</ins>>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>Crossing the Frenkel line leads also to some structural <del style="font-weight: bold; text-decoration: none;">changes </del>in fluids </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>Crossing the Frenkel line leads also to some structural <ins style="font-weight: bold; text-decoration: none;">crossovers </ins>in fluids </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div><ref> [http://dx.doi.org/10.1063/1.4844135 Dima Bolmatov, V. V. Brazhkin, Yu. D. Fomin, V. N. Ryzhov, and K. Trachenko "Evidence for structural crossover in the supercritical state", Journal of Chemical Physics '''139''' 234501 (2013)]</ref>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div><ref> [http://dx.doi.org/10.1063/1.4844135 Dima Bolmatov, V. V. Brazhkin, Yu. D. Fomin, V. N. Ryzhov, and K. Trachenko "Evidence for structural crossover in the supercritical state", Journal of Chemical Physics '''139''' 234501 (2013<ins style="font-weight: bold; text-decoration: none;">)]</ref>, <ref> [http://pubs.acs.org/doi/abs/10.1021/jz5012127 Dima Bolmatov, D. Zav’yalov, M. Gao, and Mikhail Zhernenkov "Structural Evolution of Supercritical CO2 across the Frenkel Line", Journal of Physical Chemistry '''5''' pp 2785-2790 (2014</ins>)]</ref>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Currently Frenkel lines of several [[Idealised models|idealised liquids]], such as [[Lennard-Jones model|Lennard-Jones]] and [[Soft sphere potential|soft spheres]] </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>Currently Frenkel lines of several [[Idealised models|idealised liquids]], such as [[Lennard-Jones model|Lennard-Jones]] and [[Soft sphere potential|soft spheres]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div><ref name="ufn"> </ref>, <ref name="frpre"> </ref>, <ref name="frprl"> </ref> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div><ref name="ufn"> </ref>, <ref name="frpre"> </ref>, <ref name="frprl"> </ref> </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>as well as [[realistic models]] such as</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>as well as [[realistic models]] such as</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[iron|liquid iron]] <ref>[http://dx.doi.org/10.1038/srep07194 Yu. D. Fomin, V. N. Ryzhov, E. N. Tsiok, V. V. Brazhkin, and K. Trachenko "Dynamic transition in supercritical iron", Scientific Reports '''4''' 7194 (2014)]</ref>,</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[iron|liquid iron]] <ref>[http://dx.doi.org/10.1038/srep07194 Yu. D. Fomin, V. N. Ryzhov, E. N. Tsiok, V. V. Brazhkin, and K. Trachenko "Dynamic transition in supercritical iron", Scientific Reports '''4''' 7194 (2014)]</ref>,</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>[[hydrogen]] <ref> [http://dx.doi.org/10.1103/PhysRevE.89.032126 K. Trachenko, V. V. Brazhkin, and D.Bolmatov, "Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants", Physical Review E '''89''' 032126 (2014)]</ref>, </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>[[hydrogen]] <ref> [http://dx.doi.org/10.1103/PhysRevE.89.032126 K. Trachenko, V. V. Brazhkin, and D. Bolmatov, "Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants", Physical Review E '''89''' 032126 (2014)]</ref>, </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[water]] <ref name="kostya3"> [http://dx.doi.org/10.1103/PhysRevE.91.012112 C. Yang, V. V. Brazhkin, M. T. Dove, and K. Trachenko "Frenkel line and solubility maximum in supercritical fluids", Physical Review E '''91''' 012112 (2015)]</ref>, </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>[[water]] <ref name="kostya3"> [http://dx.doi.org/10.1103/PhysRevE.91.012112 C. Yang, V. V. Brazhkin, M. T. Dove, and K. Trachenko "Frenkel line and solubility maximum in supercritical fluids", Physical Review E '''91''' 012112 (2015)]</ref>, </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>[[carbon dioxide]] <ref <del style="font-weight: bold; text-decoration: none;">name="kostya3"</del>> <del style="font-weight: bold; text-decoration: none;"><</del>/<del style="font-weight: bold; text-decoration: none;">ref></del>, </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>[[carbon dioxide]] <ref> <ins style="font-weight: bold; text-decoration: none;">[http:</ins>/<ins style="font-weight: bold; text-decoration: none;">/pubs.acs.org/doi/abs/10.1021/jz5012127 Dima Bolmatov, D. Zav’yalov, M. Gao</ins>, and <ins style="font-weight: bold; text-decoration: none;">Mikhail Zhernenkov </ins>"<ins style="font-weight: bold; text-decoration: none;">Evidence for structural crossover in the supercritical state</ins>"<ins style="font-weight: bold; text-decoration: none;">, Journal of Physical Chemistry '''5''' pp 2785-2790 (2014)]</ins></ref></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>and <del style="font-weight: bold; text-decoration: none;">[[methane]] <ref name=</del>"<del style="font-weight: bold; text-decoration: none;">kostya3</del>"<del style="font-weight: bold; text-decoration: none;">> </del></ref> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>have been reported in the literature.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>have been reported in the literature.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>==Related Lines==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>==Related Lines==</div></td></tr>
</table>
Davidcohen
http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&diff=14567&oldid=prev
Carl McBride: Slight tidy + added internal links
2015-02-26T16:24:25Z
<p>Slight tidy + added internal links</p>
<a href="http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&diff=14567&oldid=14566">Show changes</a>
Carl McBride
http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&diff=14566&oldid=prev
Fomin314 at 16:15, 25 February 2015
2015-02-25T16:15:58Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:15, 25 February 2015</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>'''Frenkel line''' is a line of change of microscopic dynamics of</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><div>'''Frenkel line''' is a line of change of microscopic dynamics of</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>fluids. Below the Frenkel line the <del style="font-weight: bold; text-decoration: none;">fluid </del>are "rigid" and</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>fluids. Below the Frenkel line the <ins style="font-weight: bold; text-decoration: none;">fluids </ins>are "rigid" and</div></td></tr>
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Fomin314
http://www.sklogwiki.org/SklogWiki/index.php?title=Frenkel_line&diff=14564&oldid=prev
Fomin314: Created page with "'''Frenkel line''' is a line of change of microscopic dynamics of fluids. Below the Frenkel line the fluid are "rigid" and "solid-like" while above it fluids are "soft" and "g..."
2015-02-25T15:56:33Z
<p>Created page with "'''Frenkel line''' is a line of change of microscopic dynamics of fluids. Below the Frenkel line the fluid are "rigid" and "solid-like" while above it fluids are "soft" and "g..."</p>
<p><b>New page</b></p><div>'''Frenkel line''' is a line of change of microscopic dynamics of<br />
fluids. Below the Frenkel line the fluid are "rigid" and<br />
"solid-like" while above it fluids are "soft" and "gas-like".<br />
<br />
<br />
Two types of approaches to the behavior of liquids present in the<br />
literature. The most common one is due to van der Waals. It treats<br />
the liquids as dense structureless gases. Although this approach<br />
allows to explain many principle features of fluids, in<br />
particular, the liquid-gas phase transition, it fails in<br />
explanation of other important issues, such as, for example,<br />
existence in liquids of transverse collective excitations such as<br />
phonons.<br />
<br />
Another approach to fluid properties was proposed by J. Frenkel<br />
<ref>[J. Frenkel, Kinetic Theory of Liquids (Oxford University Press, London, 1947]</ref>. It is based on an assumption that at moderate<br />
temperatures the particles of liquid behave similar to the case of<br />
crystal, i.e. the particles demonstrate oscillatory motions.<br />
However, while in crystal they oscillate around theirs nodes, in<br />
liquids after several periods the particles change the nodes. This<br />
approach based on postulation of some similarity between crystals<br />
and liquids allows to explain many important properties of the<br />
later: transverse collective excitations, large hear capacity and<br />
so on.<br />
<br />
From the discussion above one can see that the microscopic<br />
behavior of particles of moderate and high temperature fluids is<br />
qualitatively different. If one heats up a fluid from a<br />
temperature close to the melting one up to some high temperature a<br />
crossover from the solid-like to gas-like regime appears. The line<br />
of this crossover was named Frenkel line after J. Frenkel.<br />
<br />
Several methods to locate the Frenkel line were proposed in the<br />
literature. The most detailed reviews of the methods are given in<br />
Refs. <ref name="ufn"> [http://iopscience.iop.org/1063-7869/55/11/R01/ V.V. Brazhkin, A.G. Lyapin, V.N. Ryzhov, K. Trachenko, Yu.D. Fomin, E.N. Tsiok, Phys. Usp. 55, 1061 (2012) ]</ref>, <ref name="frpre"> [http://journals.aps.org/pre/abstract/10.1103/PhysRevE.85.031203 V. V. Brazhkin, Yu. D. Fomin, A. G. Lyapin, V. N. Ryzhov, and K. Trachenko, Phys. Rev. E 85, 031203 (2012)]</ref>. The exact criterion of Frenkel line is the one based on comparison of characteristic times in fluids. One can<br />
define a 'jump time' via :<math> \tau_0=\frac{a^2}{6D} </math>, where <math> a </math> is the particles size and :<math> D </math> - diffusion coefficient. This is the time necessary for a particle to move to it's own size. The second characteristic time is the shortest period of transverse oscillations of particles of fluid: <math> \tau^* </math>. When these two time<br />
scales become comparable one cannot distinguish the oscillations of the particles and theirs jumps to another position. Therefore<br />
the criterion for Frenkel line is given by <math> \tau_0 \approx \tau^* </math>.<br />
<br />
There are several approximate criteria to locate the Frenkel line<br />
in <math> (P,T) </math> Refs. <ref name="ufn"> </ref>, <ref name="frpre"> </ref>, <ref name="frprl"> [http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.145901 V. V. Brazhkin, Yu. D. Fomin, A. G. Lyapin, V. N. Ryzhov, E. N. Tsiok, and Kostya Trachenko, Phys. Rev. Lett. 111, 145901 (2013)]</ref>. One of these criteria is based<br />
on velocity autocorrelation function (vacf): below the Frenkel<br />
line vacf demonstrate oscillation behavior while above it vacfs<br />
monotonically decay to zero. The second criterion is based on the<br />
fact that at moderate temperature liquids can sustain transverse<br />
excitations which disappear on heating the liquid up. One more<br />
criterion is based on isochoric heat capacities measurements. The<br />
isochoric heat capacity per particle of a monatomic liquid close<br />
to the melting line is close to <math> 3 k_B </math> ( <math> k_B </math> is Boltzmann<br />
constant). The contribution to the heat capacity of potential part<br />
of transverse excitations is <math> 1 k_B </math>. Therefore at the Frenkel<br />
line where transverse excitations vanish the isochoric heat<br />
capacity per particle should be <math> c_V=2 k_B </math>.<br />
<br />
Crossing the Frenkel line leads also to some structural changes in<br />
fluids <ref> [http://scitation.aip.org/content/aip/journal/jcp/139/23/10.1063/1.4844135 D. Bolmatov, V. V. Brazhkin, Yu. D. Fomin, V. N. Ryzhov and K. Trachenko, J. Chem. Phys. 139, 234501 (2013)] </ref>.<br />
<br />
<br />
<br />
<br />
Currently Frenkel lines of several model liquids (Lennard-Jones<br />
and soft spheres <ref name="ufn"> </ref>, <ref name="frpre"> </ref>, <ref name="frprl"> </ref> and real ones (liquid<br />
iron <ref> [http://www.nature.com/srep/2014/141126/srep07194/fig_tab/srep07194_F1.html Yu. D. Fomin, V. N. Ryzhov, E. N. Tsiok, V. V. Brazhkin and K. Trachenko, Scientific Reports, 4, 7194 (2014)] </ref>, hydrogen <ref> [http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032126 K. Trachenko, V. V. Brazhkin, and D.Bolmatov, Phys. Rev. E 89, 032126 (2014)] </ref>, water<br />
<ref name="kostya3"> [http://journals.aps.org/pre/abstract/10.1103/PhysRevE.91.012112 C. Yang, V. V. Brazhkin, M. T. Dove, and K. Trachenko, Phys. Rev. E, 91, 012112 (2015)] </ref>, <math> CO_2 </math> <ref name="kostya3"> </ref>, <math> CH_4 </math> <ref name="kostya3"> </ref> were reported in the literature.<br />
<br />
<br />
<br />
==Related Lines==<br />
*[[Widom line]]<br />
*[[Fisher-Widom line]]<br />
<br />
==References==<br />
<references /><br />
[[Category:statistical mechanics]]</div>
Fomin314