git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@1090 f3b2605a-c512-4ea7-a41b-209d697bcdaa
This commit is contained in:
@ -36,7 +36,7 @@ Lennard-Jones particle of size sigma.
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</P>
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</P>
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<CENTER><IMG SRC = "Eqs/pair_colloid_cc.jpg">
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<CENTER><IMG SRC = "Eqs/pair_colloid_cc.jpg">
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</CENTER>
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</CENTER>
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<P>A is the Hamaker constant, a1 and a2 are the radii of the two
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<P>A_cc is the Hamaker constant, a1 and a2 are the radii of the two
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colloidal particles, and Rc is the cutoff. This equation results from
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colloidal particles, and Rc is the cutoff. This equation results from
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describing each colloidal particle as an integrated collection of
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describing each colloidal particle as an integrated collection of
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Lennard-Jones particles of size sigma and is derived in
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Lennard-Jones particles of size sigma and is derived in
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@ -46,8 +46,8 @@ Lennard-Jones particles of size sigma and is derived in
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</P>
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</P>
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<CENTER><IMG SRC = "Eqs/pair_colloid_cs.jpg">
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<CENTER><IMG SRC = "Eqs/pair_colloid_cs.jpg">
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</CENTER>
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</CENTER>
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<P>A is the Hamaker constant, a is the radius of the colloidal particle,
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<P>A_cs is the Hamaker constant, a is the radius of the colloidal
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and Rc is the cutoff. This formula is derived from the
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particle, and Rc is the cutoff. This formula is derived from the
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colloid-colloid interaction, letting one of the particle sizes go to
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colloid-colloid interaction, letting one of the particle sizes go to
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zero.
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zero.
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</P>
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</P>
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@ -56,7 +56,8 @@ Lennard-Jones formula
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</P>
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</P>
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<CENTER><IMG SRC = "Eqs/pair_colloid_ss.jpg">
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<CENTER><IMG SRC = "Eqs/pair_colloid_ss.jpg">
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</CENTER>
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</CENTER>
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<P>which results from letting both particle sizes go to zero.
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<P>with A_ss set appropriately, which results from letting both particle
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sizes go to zero.
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</P>
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</P>
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<P>The following coefficients must be defined for each pair of atoms
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<P>The following coefficients must be defined for each pair of atoms
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types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
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types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
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@ -70,19 +71,20 @@ commands, or by mixing as described below:
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<LI>d2 (distance units)
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<LI>d2 (distance units)
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<LI>cutoff (distance units)
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<LI>cutoff (distance units)
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</UL>
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</UL>
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<P>A is the energy prefactor and should typically be set as follows:
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<P>A is the Hamaker energy prefactor and should typically be set as
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follows:
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</P>
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</P>
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<UL><LI>A_cc = colloid/colloid = 4 pi^2 = 39.5
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<UL><LI>A_cc = colloid/colloid = 4 pi^2 = 39.5
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<LI>A_ss = solvent/solvent = 144 (assuming epsilon = 1, so that 144/36 = 4)
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<LI>A_cs = colloid/solvent = sqrt(A_cc*A_ss)
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<LI>A_cs = colloid/solvent = sqrt(A_cc*A_ss)
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<LI>A_ss = solvent/solvent = 144 (assuming epsilon = 1, so that 144/36 = 4)
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</UL>
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</UL>
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<P>Sigma is the size of the solvent particle or the constituent particles
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<P>Sigma is the size of the solvent particle or the constituent particles
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integrated over in the colloidal particle and should typically be set
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integrated over in the colloidal particle and should typically be set
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as follows:
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as follows:
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</P>
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</P>
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<UL><LI>Sigma_cc = colloid/colloid = 1.0
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<UL><LI>Sigma_cc = colloid/colloid = 1.0
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<LI>Sigma_ss = solvent/solvent = 1.0 or whatever size the solvent particle is
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<LI>Sigma_cs = colloid/solvent = arithmetic mixing between colloid sigma and solvent sigma
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<LI>Sigma_cs = colloid/solvent = arithmetic mixing between colloid sigma and solvent sigma
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<LI>Sigma_ss = solvent/solvent = 1.0 or whatever size the solvent particle is
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</UL>
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</UL>
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<P>Thus typically Sigma_cs = 1.0, unless the solvent particle's size !=
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<P>Thus typically Sigma_cs = 1.0, unless the solvent particle's size !=
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1.0.
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1.0.
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@ -33,7 +33,7 @@ The colloid-colloid interaction energy is given by
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:c,image(Eqs/pair_colloid_cc.jpg)
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:c,image(Eqs/pair_colloid_cc.jpg)
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A is the Hamaker constant, a1 and a2 are the radii of the two
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A_cc is the Hamaker constant, a1 and a2 are the radii of the two
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colloidal particles, and Rc is the cutoff. This equation results from
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colloidal particles, and Rc is the cutoff. This equation results from
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describing each colloidal particle as an integrated collection of
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describing each colloidal particle as an integrated collection of
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Lennard-Jones particles of size sigma and is derived in
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Lennard-Jones particles of size sigma and is derived in
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@ -43,8 +43,8 @@ The colloid-solvent interaction energy is given by
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:c,image(Eqs/pair_colloid_cs.jpg)
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:c,image(Eqs/pair_colloid_cs.jpg)
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A is the Hamaker constant, a is the radius of the colloidal particle,
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A_cs is the Hamaker constant, a is the radius of the colloidal
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and Rc is the cutoff. This formula is derived from the
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particle, and Rc is the cutoff. This formula is derived from the
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colloid-colloid interaction, letting one of the particle sizes go to
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colloid-colloid interaction, letting one of the particle sizes go to
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zero.
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zero.
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@ -53,7 +53,8 @@ Lennard-Jones formula
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:c,image(Eqs/pair_colloid_ss.jpg)
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:c,image(Eqs/pair_colloid_ss.jpg)
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which results from letting both particle sizes go to zero.
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with A_ss set appropriately, which results from letting both particle
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sizes go to zero.
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The following coefficients must be defined for each pair of atoms
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The following coefficients must be defined for each pair of atoms
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types via the "pair_coeff"_pair_coeff.html command as in the examples
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types via the "pair_coeff"_pair_coeff.html command as in the examples
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@ -67,19 +68,20 @@ d1 (distance units)
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d2 (distance units)
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d2 (distance units)
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cutoff (distance units) :ul
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cutoff (distance units) :ul
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A is the energy prefactor and should typically be set as follows:
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A is the Hamaker energy prefactor and should typically be set as
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follows:
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A_cc = colloid/colloid = 4 pi^2 = 39.5
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A_cc = colloid/colloid = 4 pi^2 = 39.5
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A_ss = solvent/solvent = 144 (assuming epsilon = 1, so that 144/36 = 4)
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A_cs = colloid/solvent = sqrt(A_cc*A_ss)
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A_cs = colloid/solvent = sqrt(A_cc*A_ss) :ul
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A_ss = solvent/solvent = 144 (assuming epsilon = 1, so that 144/36 = 4) :ul
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Sigma is the size of the solvent particle or the constituent particles
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Sigma is the size of the solvent particle or the constituent particles
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integrated over in the colloidal particle and should typically be set
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integrated over in the colloidal particle and should typically be set
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as follows:
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as follows:
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Sigma_cc = colloid/colloid = 1.0
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Sigma_cc = colloid/colloid = 1.0
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Sigma_ss = solvent/solvent = 1.0 or whatever size the solvent particle is
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Sigma_cs = colloid/solvent = arithmetic mixing between colloid sigma and solvent sigma
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Sigma_cs = colloid/solvent = arithmetic mixing between colloid sigma and solvent sigma :ul
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Sigma_ss = solvent/solvent = 1.0 or whatever size the solvent particle is :ul
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Thus typically Sigma_cs = 1.0, unless the solvent particle's size !=
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Thus typically Sigma_cs = 1.0, unless the solvent particle's size !=
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1.0.
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1.0.
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