forked from lijiext/lammps
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307 lines
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<a href="Manual.html" class="icon icon-home"> LAMMPS
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<li>fix rx command</li>
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<a href="Section_commands.html#comm">Commands</a>
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<div itemprop="articleBody">
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<div class="section" id="fix-rx-command">
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<span id="index-0"></span><h1>fix rx command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">rx</span> <span class="n">file</span> <span class="n">localTemp</span> <span class="n">solver</span> <span class="o">...</span>
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</pre></div>
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</div>
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<ul class="simple">
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<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><span class="doc">fix</span></a> command</li>
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<li>rx = style name of this fix command</li>
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<li>file = filename containing the reaction kinetic equations and Arrhenius parameters</li>
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<li>localTemp = <em>none,lucy</em> = no local temperature averaging or local temperature defined through Lucy weighting function</li>
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<li>solver = <em>lammps_rk4</em> = Explicit 4th order Runge-Kutta method</li>
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<li>minSteps = # of steps for rk4 solver</li>
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</ul>
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</div>
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<div class="section" id="examples">
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<h2>Examples</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">none</span> <span class="n">lammps_rk4</span>
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<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">none</span> <span class="n">lammps_rk4</span> <span class="mi">1</span>
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<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">rx</span> <span class="n">kinetics</span><span class="o">.</span><span class="n">rx</span> <span class="n">lucy</span> <span class="n">lammps_rk4</span> <span class="mi">10</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description</h2>
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<p>Fix <em>rx</em> solves the reaction kinetic ODEs for a given reaction set that is
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defined within the file associated with this command.</p>
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<p>For a general reaction such that</p>
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<img alt="Eqs/fix_rx_reaction.jpg" class="align-center" src="Eqs/fix_rx_reaction.jpg" />
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<p>the reaction rate equation is defined to be of the form</p>
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<img alt="Eqs/fix_rx_reactionRate.jpg" class="align-center" src="Eqs/fix_rx_reactionRate.jpg" />
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<p>In the current implementation, the exponents are defined to be equal to the
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stoichiometric coefficients. A given reaction set consisting of <em>n</em> reaction
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equations will contain a total of <em>m</em> species. A set of <em>m</em> ordinary
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differential equations (ODEs) that describe the change in concentration of a
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given species as a function of time are then constructed based on the <em>n</em>
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reaction rate equations.</p>
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<p>The ODE systems are solved over the full DPD timestep <em>dt</em> using a 4th order
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Runge-Kutta <em>rk4</em> method with a fixed step-size <em>h</em>, specified by the
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<em>lammps_rk4</em> keyword. The number of ODE steps per DPD timestep for the rk4 method
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is optionally specified immediately after the rk4 keyword. The ODE step-size is set as
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<em>dt/num_steps</em>. Smaller step-sizes tend to yield more accurate results but there
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is not control on the error.</p>
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<hr class="docutils" />
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<p>The filename specifies a file that contains the entire set of reaction
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kinetic equations and corresponding Arrhenius parameters. The format of
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this file is described below.</p>
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<p>There is no restriction on the total number or reaction equations that are
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specified. The species names are arbitrary string names that are associated
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with the species concentrations.
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Each species in a given reaction must be preceded by it’s stoichiometric
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coefficient. The only delimiters that are recognized between the species are
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either a <em>+</em> or <em>=</em> character. The <em>=</em> character corresponds to an
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irreversible reaction. After specifying the reaction, the reaction rate
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constant is determined through the temperature dependent Arrhenius equation:</p>
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<img alt="Eqs/fix_rx.jpg" class="align-center" src="Eqs/fix_rx.jpg" />
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<p>where <em>A</em> is the Arrhenius factor in time units or concentration/time units,
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<em>n</em> is the unitless exponent of the temperature dependence, and <em>E_a</em> is the
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activation energy in energy units. The temperature dependence can be removed
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by specifying the exponent as zero.</p>
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<p>The internal temperature of the coarse-grained particles can be used in constructing the
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reaction rate constants at every DPD timestep by specifying the keyword <em>none</em>.
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Alternatively, the keyword <em>lucy</em> can be specified to compute a local-average particle
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internal temperature for use in the reaction rate constant expressions.
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The local-average particle internal temperature is defined as:</p>
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<img alt="Eqs/fix_rx_localTemp.jpg" class="align-center" src="Eqs/fix_rx_localTemp.jpg" />
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<p>where the Lucy function is expressed as:</p>
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<img alt="Eqs/fix_rx_localTemp2.jpg" class="align-center" src="Eqs/fix_rx_localTemp2.jpg" />
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<p>The self-particle interaction is included in the above equation.</p>
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<hr class="docutils" />
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<p>The format of a tabulated file is as follows (without the parenthesized comments):</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Rxn equations and parameters (one or more comment or blank lines)</span>
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</pre></div>
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</div>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mf">1.0</span> <span class="n">hcn</span> <span class="o">+</span> <span class="mf">1.0</span> <span class="n">no2</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="n">no</span> <span class="o">+</span> <span class="mf">0.5</span> <span class="n">n2</span> <span class="o">+</span> <span class="mf">0.5</span> <span class="n">h2</span> <span class="o">+</span> <span class="mf">1.0</span> <span class="n">co</span> <span class="mf">2.49E+01</span> <span class="mf">0.0</span> <span class="mf">1.34</span> <span class="p">(</span><span class="n">rxn</span> <span class="n">equation</span><span class="p">,</span> <span class="n">A</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">Ea</span><span class="p">)</span>
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<span class="mf">1.0</span> <span class="n">hcn</span> <span class="o">+</span> <span class="mf">1.0</span> <span class="n">no</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="n">co</span> <span class="o">+</span> <span class="mf">1.0</span> <span class="n">n2</span> <span class="o">+</span> <span class="mf">0.5</span> <span class="n">h2</span> <span class="mf">2.16E+00</span> <span class="mf">0.0</span> <span class="mf">1.52</span>
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<span class="o">...</span>
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<span class="mf">1.0</span> <span class="n">no</span> <span class="o">+</span> <span class="mf">1.0</span> <span class="n">co</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="n">n2</span> <span class="o">+</span> <span class="mf">1.0</span> <span class="n">co2</span> <span class="mf">1.66E+06</span> <span class="mf">0.0</span> <span class="mf">0.69</span>
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</pre></div>
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</div>
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<p>A section begins with a non-blank line whose 1st character is not a
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“#”; blank lines or lines starting with “#” can be used as comments
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between sections.</p>
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<p>Following a blank line, the next N lines list the N reaction equations.
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Each species within the reaction equation is specified through its
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stoichiometric coefficient and a species tag. Reactant species are specified
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on the left-hand side of the equation and product species are specified on the
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right-hand side of the equation. After specifying the reactant and product
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species, the final three arguments of each line represent the Arrhenius
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parameter <em>A</em>, the temperature exponent <em>n</em>, and the activation energy <em>Ea</em>.</p>
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<p>Note that the species tags that are defined in the reaction equations are
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used by the <a class="reference internal" href="fix_eos_table_rx.html"><span class="doc">fix eos/table/rx</span></a> command to define the
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thermodynamic properties of each species. Furthermore, the number of species
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molecules (i.e., concentration) can be specified either with the <a class="reference internal" href="set.html"><span class="doc">set</span></a>
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command using the “<a href="#id1"><span class="problematic" id="id2">d_</span></a>” prefix or by reading directly the concentrations from a
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data file. For the latter case, the <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> command with the
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fix keyword should be specified, where the fix-ID will be the “fix rx`ID with a <SPECIES”>`_ suffix, e.g.</p>
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<p>fix foo all rx reaction.file ...
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read_data data.dpd fix foo_SPECIES NULL Species</p>
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</div>
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<hr class="docutils" />
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<div class="section" id="restrictions">
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<h2>Restrictions</h2>
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<p>The fix <em>rx</em> is only available if LAMMPS is built with the USER-DPD package.</p>
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<p>The fix <em>rx</em> must be used with the <a class="reference internal" href="atom_style.html"><span class="doc">atom_style dpd</span></a> command.</p>
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<p>The fix <em>rx</em> can only be used with a constant energy or constant enthalpy DPD simulation.</p>
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</div>
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<div class="section" id="related-commands">
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<h2>Related commands</h2>
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<p><a class="reference internal" href="fix_eos_table_rx.html"><span class="doc">fix eos/table/rx</span></a>,
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<a class="reference internal" href="fix_shardlow.html"><span class="doc">fix shardlow</span></a>,
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<span class="xref doc">pair dpd/fdt/energy</span></p>
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<p><strong>Default:</strong> none</p>
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<hr class="docutils" />
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</div>
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</div>
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<div role="contentinfo">
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<p>
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© Copyright 2013 Sandia Corporation.
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