A is the Hamaker constant, a1 and a2 are the radii of the two +
A_cc 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 @@ -46,8 +46,8 @@ Lennard-Jones particles of size sigma and is derived in
A is the Hamaker constant, a is the radius of the colloidal particle, -and Rc is the cutoff. This formula is derived from the +
A_cs 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.
@@ -56,7 +56,8 @@ Lennard-Jones formula
which results from letting both particle sizes go to zero. +
with A_ss set appropriately, which results from letting both particle +sizes go to zero.
The following coefficients must be defined for each pair of atoms types via the pair_coeff command as in the examples @@ -70,19 +71,20 @@ commands, or by mixing as described below:
A is the energy prefactor and should typically be set as follows: +
A is the Hamaker energy prefactor and should typically be set as +follows:
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:
Thus typically Sigma_cs = 1.0, unless the solvent particle's size != 1.0. diff --git a/doc/pair_colloid.txt b/doc/pair_colloid.txt index 27fffe36b8..2699fa5d9e 100644 --- a/doc/pair_colloid.txt +++ b/doc/pair_colloid.txt @@ -33,7 +33,7 @@ The colloid-colloid interaction energy is given by :c,image(Eqs/pair_colloid_cc.jpg) -A is the Hamaker constant, a1 and a2 are the radii of the two +A_cc 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 @@ -43,8 +43,8 @@ The colloid-solvent interaction energy is given by :c,image(Eqs/pair_colloid_cs.jpg) -A is the Hamaker constant, a is the radius of the colloidal particle, -and Rc is the cutoff. This formula is derived from the +A_cs 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. @@ -53,7 +53,8 @@ Lennard-Jones formula :c,image(Eqs/pair_colloid_ss.jpg) -which results from letting both particle sizes go to zero. +with A_ss set appropriately, which results from letting both particle +sizes go to zero. The following coefficients must be defined for each pair of atoms types via the "pair_coeff"_pair_coeff.html command as in the examples @@ -67,19 +68,20 @@ d1 (distance units) d2 (distance units) cutoff (distance units) :ul -A is the energy prefactor and should typically be set as follows: +A is the Hamaker energy prefactor and should typically be set as +follows: A_cc = colloid/colloid = 4 pi^2 = 39.5 -A_ss = solvent/solvent = 144 (assuming epsilon = 1, so that 144/36 = 4) -A_cs = colloid/solvent = sqrt(A_cc*A_ss) :ul +A_cs = colloid/solvent = sqrt(A_cc*A_ss) +A_ss = solvent/solvent = 144 (assuming epsilon = 1, so that 144/36 = 4) :ul 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: Sigma_cc = colloid/colloid = 1.0 -Sigma_ss = solvent/solvent = 1.0 or whatever size the solvent particle is -Sigma_cs = colloid/solvent = arithmetic mixing between colloid sigma and solvent sigma :ul +Sigma_cs = colloid/solvent = arithmetic mixing between colloid sigma and solvent sigma +Sigma_ss = solvent/solvent = 1.0 or whatever size the solvent particle is :ul Thus typically Sigma_cs = 1.0, unless the solvent particle's size != 1.0.