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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<H3>pair_style colloid command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>pair_style colloid cutoff
</PRE>
<UL><LI>cutoff = global cutoff for colloidal interactions (distance units)
</UL>
<P><B>Examples:</B>
</P>
<PRE>pair_style colloid 10.0
pair_coeff * * 25 1.0 10.0 10.0
pair_coeff 1 1 144 1.0 0.0 0.0 3.0
pair_coeff 1 2 75.398 1.0 0.0 10.0 9.0
pair_coeff 2 2 39.478 1.0 10.0 10.0 25.0
</PRE>
<P><B>Description:</B>
</P>
<P>Style <I>colloid</I> computes pairwise interactions between large colloidal
particles and small solvent particles using 3 formulas. A colloidal
particle has a size > sigma; a solvent particle is the usual
Lennard-Jones particle of size sigma.
</P>
<P>The colloid-colloid interaction energy is given by
</P>
<CENTER><IMG SRC = "Eqs/pair_colloid_cc.jpg">
</CENTER>
<P>A is the Hamaker constant, a1 and a2 are the radii of the two
colloidal particles, and Rc is the cutoff. This equation results from
describing each colloidal particle as an integrated collection of
Lennard-Jones particles of size sigma and is derived in
<A HREF = "#Everaers">(Everaers)</A>.
</P>
<P>The colloid-solvent interaction energy is given by
</P>
<CENTER><IMG SRC = "Eqs/pair_colloid_cs.jpg">
</CENTER>
<P>A is the Hamaker constant, a is the radius of the colloidal particle,
and Rc is the cutoff. This formula is derived from the
colloid-colloid interaction, letting one of the particle sizes go to
zero.
</P>
<P>The solvent-solvent interaction energy is given by the usual
Lennard-Jones formula
</P>
<CENTER><IMG SRC = "Eqs/pair_colloid_ss.jpg">
</CENTER>
<P>which results from letting both particle sizes go to zero.
</P>
<P>The following coefficients must be defined for each pair of atoms
types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
above, or in the data file or restart files read by the
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
commands:
</P>
<UL><LI>A (energy units)
<LI>sigma (distance units)
<LI>d1 (distance units)
<LI>d2 (distance units)
<LI>cutoff (distance units)
</UL>
<P>A is the energy prefactor and should typically be set as follows:
</P>
<UL><LI>A_cc = colloid/colloid = 4 pi^2 = 39.5
<LI>A_ss = solvent/solvent = 144 (assuming epsilon = 1, so that 144/36 = 4)
<LI>A_cs = colloid/solvent = sqrt(A_cc*A_ss)
</UL>
<P>Sigma is the size of the solvent particle or the constituent particles
integrated over in the colloidal particle and should typically be set
as follows:
</P>
<UL><LI>Sigma_cc = colloid/colloid = 1.0
<LI>Sigma_ss = solvent/solvent = 1.0 or whatever size the solvent particle is
<LI>Sigma_cs = colloid/solvent = arithmetic mixing between colloid sigma and solvent sigma
</UL>
<P>Thus typically Sigma_cs = 1.0, unless the solvent particle's size !=
1.0.
</P>
<P>D1 and d2 are particle diameters, so that d1 = 2*a1 and d2 = 2*a2 in
the formulas above. Both d1 and d2 must be values >= 0. If d1 > 0
and d2 > 0, then the pair interacts via the colloid-colloid formula
above. If d1 = 0 and d2 = 0, then the pair interacts via the
solvent-solvent formula. I.e. a d value of 0 is a Lennard-Jones
particle of size sigma. If either d1 = 0 or d2 = 0 and the other is
larger, then the pair interacts via the colloid-solvent formula.
</P>
<P>Note that the diameter of a particular particle type may appear in
multiple pair_coeff commands, as it interacts with other particle
types. You should insure the particle diameter is specified
consistently each time it appears.
</P>
<P>The last coefficient is optional. If not specified, the global cutoff
specified in the pair_style command is used. However, you typically
want different cutoffs for interactions between different particle
sizes. E.g. if colloidal particles of diameter 10 are used with
solvent particles of diameter 1, then a solvent-solvent cutoff of 2.5
would correspond to a colloid-colloid cutoff of 25. A good
rule-of-thumb is to use a colloid-solvent cutoff that is half the big
diamter + 4 times the small diamter. I.e. 9 = 5 + 4 for the
colloid-solvent cutoff in this case.
</P>
<P>If a pair_coeff command is not specified for I != J, then the
coefficients are mixed according the mixing rules defined by the
<A HREF = "pair_modify.html">pair_modify</A> command. The prefactor A is mixed like
the Lennard-Jones epsilon; sigma,d1,d2 are all mixed like the
Lennard-Jones sigma.
</P>
<P><B>Restrictions:</B>
</P>
<P>The <I>colloid</I> style is part of the "colloid" package. It is only
enabled if LAMMPS was built with that package. See the <A HREF = "Section_start.html#2_3">Making
LAMMPS</A> section for more info.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "pair_coeff.html">pair_coeff</A>
</P>
<P><B>Default:</B> none
</P>
<HR>
<A NAME = "Everaers"></A>
<P><B>(Everaers)</B> Everaers, Ejtehadi, Phys Rev E, 67, 041710 (2003).
</P>
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