http://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&feed=atom&action=historyLattice simulations (Polymers) - Revision history2024-03-28T14:24:07ZRevision history for this page on the wikiMediaWiki 1.41.0http://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&diff=10347&oldid=prevCarl McBride: Corrected figure numbering2010-05-19T11:20:27Z<p>Corrected figure numbering</p>
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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>[[Image:End_rotation.png|thumb|right|Fig. <del style="font-weight: bold; text-decoration: none;">2</del>. Example of an end rotation move]]</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>[[Image:End_rotation.png|thumb|right|Fig. <ins style="font-weight: bold; text-decoration: none;">1</ins>. Example of an end rotation move]]</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>[[Image:Bend_move.png|thumb|right|Fig. 2. Example of a "bend" move]]</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>[[Image:Bend_move.png|thumb|right|Fig. 2. Example of a "bend" move]]</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>[[Image:Crankshaft_move.png|thumb|right|Fig. 3. Example of a "crankshaft" move]]</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>[[Image:Crankshaft_move.png|thumb|right|Fig. 3. Example of a "crankshaft" move]]</div></td></tr>
</table>Carl McBridehttp://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&diff=10345&oldid=prevCarl McBride: Added another figure2010-05-19T11:19:01Z<p>Added another figure</p>
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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>[[Image:Bend_move.png|thumb|right|Fig. <del style="font-weight: bold; text-decoration: none;">1</del>. Example of a "bend" move]]</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><ins style="font-weight: bold; text-decoration: none;">[[Image:End_rotation.png|thumb|right|Fig. 2. Example of an end rotation move]]</ins></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>[[Image:Crankshaft_move.png|thumb|right|Fig. <del style="font-weight: bold; text-decoration: none;">2</del>. Example of a "crankshaft" move]]</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>[[Image:Bend_move.png|thumb|right|Fig. <ins style="font-weight: bold; text-decoration: none;">2</ins>. Example of a "bend" move]]</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>[[Image:Crankshaft_move.png|thumb|right|Fig. <ins style="font-weight: bold; text-decoration: none;">3</ins>. Example of a "crankshaft" move]]</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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[Idealised models#Lattice models| Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[Idealised models#Lattice models| Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics <ref>[http://dx.doi.org/10.1063/1.1732301 P. H. Verdier and W. H. Stockmayer "Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution", Journal of Chemical Physics '''36''' pp. 227-235 (1962)]</ref>. Combinations of bend (<del style="font-weight: bold; text-decoration: none;">Fig. 1</del>) and crankshaft (<del style="font-weight: bold; text-decoration: none;">Fig. 2</del>) moves <del style="font-weight: bold; text-decoration: none;">was </del>shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic lattice <ref>[http://dx.doi.org/10.1063/1.431297 H. J. Hilhorst and J. M. Deutch "Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume", Journal of Chemical Physics '''63''' pp. 5153-5161 (1975)]</ref>. More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains <ref>[http://dx.doi.org/10.1007/BF01022990 Neal Madras and Alan D. Sokal "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk", Journal of Statistical Physics '''50''' pp. 109-186 (1988)]</ref>. Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems <ref>[http://dx.doi.org/10.1021/ma00169a036 T. Pakula and S. Geyler "Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation", Macromolecules '''20''' pp. 679-682 (1987)]</ref>. Also, specific algorithms to perform [[isothermal-isobaric ensemble]] (''NpT'') simulations have been designed <ref>[http://dx.doi.org/10.1063/1.469450 A. D. Mackie, A. Z. Panagiotopoulos, S. K. Kumar "Monte Carlo simulations of phase equilibria for a lattice homopolymer model", Journal of Chemical Physics '''102''' pp. 1014-1023 (1995)]</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>Algorithms useful for lattice models may have special difficulties to comply with the <ins style="font-weight: bold; text-decoration: none;">[[Ergodic hypothesis |</ins>ergodicity<ins style="font-weight: bold; text-decoration: none;">]] </ins>and [[<ins style="font-weight: bold; text-decoration: none;">Detailed balance |</ins>microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics <ref>[http://dx.doi.org/10.1063/1.1732301 P. H. Verdier and W. H. Stockmayer "Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution", Journal of Chemical Physics '''36''' pp. 227-235 (1962)]</ref>. Combinations of <ins style="font-weight: bold; text-decoration: none;">end rotations (figure 1), </ins>bend (<ins style="font-weight: bold; text-decoration: none;">or "kink") (figure 2</ins>) and crankshaft (<ins style="font-weight: bold; text-decoration: none;">figure 3</ins>) moves <ins style="font-weight: bold; text-decoration: none;">has been </ins>shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic lattice <ref>[http://dx.doi.org/10.1063/1.431297 H. J. Hilhorst and J. M. Deutch "Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume", Journal of Chemical Physics '''63''' pp. 5153-5161 (1975)]</ref>. More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains <ref>[http://dx.doi.org/10.1007/BF01022990 Neal Madras and Alan D. Sokal "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk", Journal of Statistical Physics '''50''' pp. 109-186 (1988)]</ref>. Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems <ref>[http://dx.doi.org/10.1021/ma00169a036 T. Pakula and S. Geyler "Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation", Macromolecules '''20''' pp. 679-682 (1987)]</ref>. Also, specific algorithms to perform [[isothermal-isobaric ensemble]] (''NpT'') simulations have been designed <ref>[http://dx.doi.org/10.1063/1.469450 A. D. Mackie, A. Z. Panagiotopoulos, S. K. Kumar "Monte Carlo simulations of phase equilibria for a lattice homopolymer model", Journal of Chemical Physics '''102''' pp. 1014-1023 (1995)]</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>The [[bond fluctuation model]] has been proposed to combine the advantages of lattice and off-lattice models.</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>The [[bond fluctuation model]] has been proposed to combine the advantages of lattice and off-lattice models.</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>==See also==</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>==See also==</div></td></tr>
</table>Carl McBridehttp://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&diff=10324&oldid=prevCarl McBride: Added figure numbers2010-05-18T11:05:41Z<p>Added figure numbers</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;">Revision as of 12:05, 18 May 2010</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>[[Image:Bend_move.png|thumb|right|Example of a "bend" move]]</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>[[Image:Bend_move.png|thumb|right|<ins style="font-weight: bold; text-decoration: none;">Fig. 1. </ins>Example of a "bend" move]]</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>[[Image:Crankshaft_move.png|thumb|right|Example of a "crankshaft" move]]</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>[[Image:Crankshaft_move.png|thumb|right|<ins style="font-weight: bold; text-decoration: none;">Fig. 2. </ins>Example of a "crankshaft" move]]</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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[Idealised models#Lattice models| Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[Idealised models#Lattice models| Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics <ref>[http://dx.doi.org/10.1063/1.1732301 P. H. Verdier and W. H. Stockmayer "Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution", Journal of Chemical Physics '''36''' pp. 227-235 (1962)]</ref>. <del style="font-weight: bold; text-decoration: none;">A combinations </del>of <del style="font-weight: bold; text-decoration: none;">bends </del>and crankshaft was shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic lattice <ref>[http://dx.doi.org/10.1063/1.431297 H. J. Hilhorst and J. M. Deutch "Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume", Journal of Chemical Physics '''63''' pp. 5153-5161 (1975)]</ref>. More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains <ref>[http://dx.doi.org/10.1007/BF01022990 Neal Madras and Alan D. Sokal "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk", Journal of Statistical Physics '''50''' pp. 109-186 (1988)]</ref>. Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems <ref>[http://dx.doi.org/10.1021/ma00169a036 T. Pakula and S. Geyler "Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation", Macromolecules '''20''' pp. 679-682 (1987)]</ref>. Also, specific algorithms to perform [[isothermal-isobaric ensemble]] (''NpT'') simulations have been designed <ref>[http://dx.doi.org/10.1063/1.469450 A. D. Mackie, A. Z. Panagiotopoulos, S. K. Kumar "Monte Carlo simulations of phase equilibria for a lattice homopolymer model", Journal of Chemical Physics '''102''' pp. 1014-1023 (1995)]</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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics <ref>[http://dx.doi.org/10.1063/1.1732301 P. H. Verdier and W. H. Stockmayer "Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution", Journal of Chemical Physics '''36''' pp. 227-235 (1962)]</ref>. <ins style="font-weight: bold; text-decoration: none;">Combinations </ins>of <ins style="font-weight: bold; text-decoration: none;">bend (Fig. 1) </ins>and crankshaft <ins style="font-weight: bold; text-decoration: none;">(Fig. 2) moves </ins>was shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic lattice <ref>[http://dx.doi.org/10.1063/1.431297 H. J. Hilhorst and J. M. Deutch "Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume", Journal of Chemical Physics '''63''' pp. 5153-5161 (1975)]</ref>. More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains <ref>[http://dx.doi.org/10.1007/BF01022990 Neal Madras and Alan D. Sokal "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk", Journal of Statistical Physics '''50''' pp. 109-186 (1988)]</ref>. Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems <ref>[http://dx.doi.org/10.1021/ma00169a036 T. Pakula and S. Geyler "Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation", Macromolecules '''20''' pp. 679-682 (1987)]</ref>. Also, specific algorithms to perform [[isothermal-isobaric ensemble]] (''NpT'') simulations have been designed <ref>[http://dx.doi.org/10.1063/1.469450 A. D. Mackie, A. Z. Panagiotopoulos, S. K. Kumar "Monte Carlo simulations of phase equilibria for a lattice homopolymer model", Journal of Chemical Physics '''102''' pp. 1014-1023 (1995)]</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>The [[bond fluctuation model]] has been proposed to combine the advantages of lattice and off-lattice models.</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>The [[bond fluctuation model]] has been proposed to combine the advantages of lattice and off-lattice models.</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>==See also==</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>==See also==</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>*[[Monte Carlo reptation moves]]</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>*[[Monte Carlo reptation moves]] </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>==References==</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>==References==</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><references/></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><references/></div></td></tr>
</table>Carl McBridehttp://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&diff=10318&oldid=prevCarl McBride: Added a see also section2010-05-17T15:01:39Z<p>Added a see also section</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:01, 17 May 2010</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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics <ref>[http://dx.doi.org/10.1063/1.1732301 P. H. Verdier and W. H. Stockmayer "Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution", Journal of Chemical Physics '''36''' pp. 227-235 (1962)]</ref>. A combinations of bends and crankshaft was shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic lattice <ref>[http://dx.doi.org/10.1063/1.431297 H. J. Hilhorst and J. M. Deutch "Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume", Journal of Chemical Physics '''63''' pp. 5153-5161 (1975)]</ref>. More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains <ref>[http://dx.doi.org/10.1007/BF01022990 Neal Madras and Alan D. Sokal "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk", Journal of Statistical Physics '''50''' pp. 109-186 (1988)]</ref>. Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems <ref>[http://dx.doi.org/10.1021/ma00169a036 T. Pakula and S. Geyler "Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation", Macromolecules '''20''' pp. 679-682 (1987)]</ref>. Also, specific algorithms to perform [[isothermal-isobaric ensemble]] (''NpT'') simulations have been designed <ref>[http://dx.doi.org/10.1063/1.469450 A. D. Mackie, A. Z. Panagiotopoulos, S. K. Kumar "Monte Carlo simulations of phase equilibria for a lattice homopolymer model", Journal of Chemical Physics '''102''' pp. 1014-1023 (1995)]</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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics <ref>[http://dx.doi.org/10.1063/1.1732301 P. H. Verdier and W. H. Stockmayer "Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution", Journal of Chemical Physics '''36''' pp. 227-235 (1962)]</ref>. A combinations of bends and crankshaft was shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic lattice <ref>[http://dx.doi.org/10.1063/1.431297 H. J. Hilhorst and J. M. Deutch "Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume", Journal of Chemical Physics '''63''' pp. 5153-5161 (1975)]</ref>. More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains <ref>[http://dx.doi.org/10.1007/BF01022990 Neal Madras and Alan D. Sokal "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk", Journal of Statistical Physics '''50''' pp. 109-186 (1988)]</ref>. Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems <ref>[http://dx.doi.org/10.1021/ma00169a036 T. Pakula and S. Geyler "Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation", Macromolecules '''20''' pp. 679-682 (1987)]</ref>. Also, specific algorithms to perform [[isothermal-isobaric ensemble]] (''NpT'') simulations have been designed <ref>[http://dx.doi.org/10.1063/1.469450 A. D. Mackie, A. Z. Panagiotopoulos, S. K. Kumar "Monte Carlo simulations of phase equilibria for a lattice homopolymer model", Journal of Chemical Physics '''102''' pp. 1014-1023 (1995)]</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>The [[bond fluctuation model]] has been proposed to combine the advantages of lattice and off-lattice models.</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>The [[bond fluctuation model]] has been proposed to combine the advantages of lattice and off-lattice models.</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;">==See also==</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;">*[[Monte Carlo reptation moves]]</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;"><div>==References==</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>==References==</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><references/></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><references/></div></td></tr>
</table>Carl McBridehttp://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&diff=10315&oldid=prevCarl McBride: Added a couple of illustrative images2010-05-17T14:53:17Z<p>Added a couple of illustrative images</p>
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<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;">[[Image:Bend_move.png|thumb|right|Example of a "bend" move]]</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;">[[Image:Crankshaft_move.png|thumb|right|Example of a "crankshaft" move]]</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;"><div>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[Idealised models#Lattice models| Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[Idealised models#Lattice models| Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </div></td></tr>
</table>Carl McBridehttp://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&diff=10314&oldid=prevCarl McBride: Changed references to cite format2010-05-17T14:43:28Z<p>Changed references to cite format</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:43, 17 May 2010</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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[Idealised models#Lattice models| Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[Idealised models#Lattice models| Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics <del style="font-weight: bold; text-decoration: none;">(Ref</del>. 1). A combinations of bends and crankshaft was shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic <del style="font-weight: bold; text-decoration: none;">latice </del>(<del style="font-weight: bold; text-decoration: none;">Ref. 2</del>). More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains (<del style="font-weight: bold; text-decoration: none;">Ref. 3</del>). Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems (<del style="font-weight: bold; text-decoration: none;">Ref. 4</del>). Also, specific algorithms to perform ''NpT'' simulations have been designed (<del style="font-weight: bold; text-decoration: none;">Ref. 5</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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics <ins style="font-weight: bold; text-decoration: none;"><ref>[http://dx.doi.org/10</ins>.<ins style="font-weight: bold; text-decoration: none;">1063/</ins>1<ins style="font-weight: bold; text-decoration: none;">.1732301 P. H. Verdier and W. H. Stockmayer "Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution", Journal of Chemical Physics '''36''' pp. 227-235 (1962</ins>)<ins style="font-weight: bold; text-decoration: none;">]</ref></ins>. A combinations of bends and crankshaft was shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic <ins style="font-weight: bold; text-decoration: none;">lattice <ref>[http://dx.doi.org/10.1063/1.431297 H. J. Hilhorst and J. M. Deutch "Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume", Journal of Chemical Physics '''63''' pp. 5153-5161 </ins>(<ins style="font-weight: bold; text-decoration: none;">1975</ins>)<ins style="font-weight: bold; text-decoration: none;">]</ref></ins>. More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains <ins style="font-weight: bold; text-decoration: none;"><ref>[http://dx.doi.org/10.1007/BF01022990 Neal Madras and Alan D. Sokal "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk", Journal of Statistical Physics '''50''' pp. 109-186 </ins>(<ins style="font-weight: bold; text-decoration: none;">1988</ins>)<ins style="font-weight: bold; text-decoration: none;">]</ref></ins>. Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems <ins style="font-weight: bold; text-decoration: none;"><ref>[http://dx.doi.org/10.1021/ma00169a036 T. Pakula and S. Geyler "Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation", Macromolecules '''20''' pp. 679-682 </ins>(<ins style="font-weight: bold; text-decoration: none;">1987</ins>)<ins style="font-weight: bold; text-decoration: none;">]</ref></ins>. Also, specific algorithms to perform <ins style="font-weight: bold; text-decoration: none;">[[isothermal-isobaric ensemble]] (</ins>''NpT''<ins style="font-weight: bold; text-decoration: none;">) </ins>simulations have been designed <ins style="font-weight: bold; text-decoration: none;"><ref>[http://dx.doi.org/10.1063/1.469450 A. D. Mackie, A. Z. Panagiotopoulos, S. K. Kumar "Monte Carlo simulations of phase equilibria for a lattice homopolymer model", Journal of Chemical Physics '''102''' pp. 1014-1023 </ins>(<ins style="font-weight: bold; text-decoration: none;">1995</ins>)<ins style="font-weight: bold; text-decoration: none;">]</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;"><div>The [[bond fluctuation model]] has been proposed to combine the advantages of lattice and off-lattice models.</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>The [[bond fluctuation model]] has been proposed to combine the advantages of lattice and off-lattice models.</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>==References==</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>==References==</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><del style="font-weight: bold; text-decoration: none;">#[http:</del>/<del style="font-weight: bold; text-decoration: none;">/dx.doi.org/10.1063/1.1732301 P. H. Verdier and W. H. Stockmayer "Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution", Journal of Chemical Physics '''36''' pp. 227-235 (1962)]</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><ins style="font-weight: bold; text-decoration: none;"><references</ins>/<ins style="font-weight: bold; text-decoration: none;">></ins></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><del style="font-weight: bold; text-decoration: none;">#[http://dx.doi.org/10.1063/1.431297 H. J. Hilhorst and J. M. Deutch "Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume", Journal of Chemical Physics '''63''' pp. 5153-5161 (1975)]</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> </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><del style="font-weight: bold; text-decoration: none;">#[http://dx.doi.org/10.1007/BF01022990 Neal Madras and Alan D. Sokal "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk", Journal of Statistical Physics '''50''' pp. 109-186 (1988)]</del></div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">#[http://dx.doi.org/10.1021/ma00169a036 T. Pakula and S. Geyler "Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation", Macromolecules '''20''' pp. 679 - 682 (1987)]</del></div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">#[http://dx.doi.org/10.1063/1.469450 A. D. Mackie, A. Z. Panagiotopoulos, S. K. Kumar "Monte Carlo simulations of phase equilibria for a lattice homopolymer model", Journal of Chemical Physics '''102''' pp. 1014-1023 (1995)]</del></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>[[category: Computer simulation techniques]]</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>[[category: Computer simulation techniques]]</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>[[category: Monte Carlo]]</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>[[category: Monte Carlo]]</div></td></tr>
</table>Carl McBridehttp://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&diff=7986&oldid=prevNoe: Lattice simulations moved to Lattice simulations (Polymers): Previous title is too general2009-03-20T10:25:38Z<p><a href="/SklogWiki/index.php/Lattice_simulations" class="mw-redirect" title="Lattice simulations">Lattice simulations</a> moved to <a href="/SklogWiki/index.php/Lattice_simulations_(Polymers)" title="Lattice simulations (Polymers)">Lattice simulations (Polymers)</a>: Previous title is too general</p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:25, 20 March 2009</td>
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</td></tr></table>Noehttp://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&diff=5898&oldid=prevCarl McBride: Updated internal link2008-02-18T14:22:44Z<p>Updated internal link</p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
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<col class="diff-content" />
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:22, 18 February 2008</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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[<del style="font-weight: bold; text-decoration: none;">Models </del>| Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[<ins style="font-weight: bold; text-decoration: none;">Idealised models#Lattice models</ins>| Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics (Ref. 1). A combinations of bends and crankshaft was shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic latice (Ref. 2). More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains (Ref. 3). Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems (Ref. 4). Also, specific algorithms to perform ''NpT'' simulations have been designed (Ref. 5). </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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics (Ref. 1). A combinations of bends and crankshaft was shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic latice (Ref. 2). More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains (Ref. 3). Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems (Ref. 4). Also, specific algorithms to perform ''NpT'' simulations have been designed (Ref. 5). </div></td></tr>
</table>Carl McBridehttp://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&diff=3137&oldid=prev62.204.202.244 at 10:59, 27 June 20072007-06-27T10:59:31Z<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 11:59, 27 June 2007</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"></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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[Models | Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>[[Polymers]] have many interesting mesoscopic properties that can adequately represented through [[Coarse graining | coarse-grained]] models. [[Models | Lattice models]] are particularly useful since they employ integer coordinates that can be quickly processed. Another advantage is the possibility of checking the occupancy of the discrete number of sites and store it in an array. Therefore, overlapping between beads can be easily avoided. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Earlier simulations were performed with the [[Building up a simple cubic lattice | simple cubic]] or [[tetrahedral lattices]], employing different algorithms. Tetrahedral lattice models are mainly used because of their closer similarity of their bond angles with those of the [[aliphatic chains]]. </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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics. A combinations of bends and crankshaft was shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic latice (Ref. <del style="font-weight: bold; text-decoration: none;">1</del>). More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains (Ref. <del style="font-weight: bold; text-decoration: none;">2</del>). Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems (Ref. <del style="font-weight: bold; text-decoration: none;">3</del>). Also, specific algorithms to perform ''NpT'' simulations have been designed (Ref. <del style="font-weight: bold; text-decoration: none;">4</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>Algorithms useful for lattice models may have special difficulties to comply with the ergodicity and [[microscopic reversibility]] conditions. Elementary bead jumps are commonly used to try to mimic dynamics <ins style="font-weight: bold; text-decoration: none;">(Ref. 1)</ins>. A combinations of bends and crankshaft was shown to be nearly ergodic and reproduce adequately the [[Rouse dynamics]] of single chain systems in a cubic latice (Ref. <ins style="font-weight: bold; text-decoration: none;">2</ins>). More efficient pivot moves have been devised to explore the equilibrium properties of very long single chains (Ref. <ins style="font-weight: bold; text-decoration: none;">3</ins>). Although the lattice simulations can effectively represent melts, most algorithms employ a certain amount of voids to allow specific local motions. An exception is the cooperative motion algorithm that considers totally occupied systems (Ref. <ins style="font-weight: bold; text-decoration: none;">4</ins>). Also, specific algorithms to perform ''NpT'' simulations have been designed (Ref. <ins style="font-weight: bold; text-decoration: none;">5</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;"><div>The [[bond fluctuation model]] has been proposed to combine the advantages of lattice and off-lattice models.</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>The [[bond fluctuation model]] has been proposed to combine the advantages of lattice and off-lattice models.</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>==References==</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>==References==</div></td></tr>
</table>62.204.202.244http://www.sklogwiki.org/SklogWiki/index.php?title=Lattice_simulations_(Polymers)&diff=3136&oldid=prev62.204.202.244: /* References */2007-06-27T10:56:31Z<p><span dir="auto"><span class="autocomment">References</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:56, 27 June 2007</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>==References==</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>==References==</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>#[http://dx.doi.org/10.1063/1.1732301 P. H. Verdier and W. H. Stockmayer "Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution", Journal of Chemical Physics '''36''' pp. 227-235 (1962)]</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>#[http://dx.doi.org/10.1063/1.1732301 P. H. Verdier and W. H. Stockmayer "Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution", Journal of Chemical Physics '''36''' pp. 227-235 (1962)]</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;">#[http://dx.doi.org/10.1063/1.431297 H. J. Hilhorst and J. M. Deutch "Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume", Journal of Chemical Physics '''63''' pp. 5153-5161 (1975)]</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;"><div>#[http://dx.doi.org/10.1007/BF01022990 Neal Madras and Alan D. Sokal "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk", Journal of Statistical Physics '''50''' pp. 109-186 (1988)]</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>#[http://dx.doi.org/10.1007/BF01022990 Neal Madras and Alan D. Sokal "The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk", Journal of Statistical Physics '''50''' pp. 109-186 (1988)]</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>#[http://dx.doi.org/10.1021/ma00169a036 T. Pakula and S. Geyler "Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation", Macromolecules '''20''' pp. 679 - 682 (1987)]</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>#[http://dx.doi.org/10.1021/ma00169a036 T. Pakula and S. Geyler "Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation", Macromolecules '''20''' pp. 679 - 682 (1987)]</div></td></tr>
</table>62.204.202.244