Loading doc/src/pair_colloid.rst +10 −11 Original line number Diff line number Diff line Loading @@ -53,8 +53,7 @@ The colloid-colloid interaction energy is given by \right] \\ & \\ U_R = & \frac{A_{cc}}{37800} \frac{\sigma^6}{r} \left[ \frac{}{} \right. \\ &\qquad \frac{r^2-7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)} \biggl[ \frac{r^2-7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)} {\left(r-a_1-a_2\right)^7} \\ &\qquad +\frac{r^2+7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)} {\left(r+a_1+a_2\right)^7} \\ Loading @@ -66,8 +65,8 @@ The colloid-colloid interaction energy is given by & \\ U = & U_A + U_R, \qquad r < r_c where :math:`A_{cc}` is the Hamaker constant, a\_1 and a\_2 are the radii of the two colloidal particles, and Rc is the cutoff. This where :math:`A_{cc}` is the Hamaker constant, :math:`a_1` and :math:`a_2` are the radii of the two colloidal particles, and :math:`r_c` 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 :ref:`(Everaers) <Everaers1>`. Loading @@ -76,12 +75,12 @@ The colloid-solvent interaction energy is given by .. math:: U = & \frac{2 ~ a^3 ~ \sigma^3 ~ A_{cs}}{9 \left( a^2 - r^2 \right)^3} U = \frac{2 ~ a^3 ~ \sigma^3 ~ A_{cs}}{9 \left( a^2 - r^2 \right)^3} \left[ 1 - \frac{\left(5 ~ a^6+45~a^4~r^2+63~a^2~r^4+15~r^6\right) \sigma^6} {15 \left(a-r\right)^6 \left( a+r \right)^6} \right], \quad r < r_c where :math: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 where :math:A_{cs}` is the Hamaker constant, *a* is the radius of the colloidal particle, and :math:`r_c` is the cutoff. This formula is derived from the colloid-colloid interaction, letting one of the particle sizes go to zero. Loading @@ -90,16 +89,16 @@ Lennard-Jones formula .. math:: U = & \frac{A_{ss}}{36} \left[ \left( \frac{\sigma}{r} U = \frac{A_{ss}}{36} \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{ \sigma}{r} \right)^6 \right], \quad r < r_c with :math:`A_{ss}` set appropriately, which results from letting both particle sizes go to zero. When used in combination with :doc:`pair_style yukawa/colloid <pair_colloid>`, the two terms become the so-called DLVO potential, which combines electrostatic repulsion and van der Waals attraction. When used in combination with :doc:`pair_style yukawa/colloid <pair_colloid>`, the two terms become the so-called DLVO potential, which combines electrostatic repulsion and van der Waals attraction. The following coefficients must be defined for each pair of atoms types via the :doc:`pair_coeff <pair_coeff>` command as in the examples Loading Loading
doc/src/pair_colloid.rst +10 −11 Original line number Diff line number Diff line Loading @@ -53,8 +53,7 @@ The colloid-colloid interaction energy is given by \right] \\ & \\ U_R = & \frac{A_{cc}}{37800} \frac{\sigma^6}{r} \left[ \frac{}{} \right. \\ &\qquad \frac{r^2-7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)} \biggl[ \frac{r^2-7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)} {\left(r-a_1-a_2\right)^7} \\ &\qquad +\frac{r^2+7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)} {\left(r+a_1+a_2\right)^7} \\ Loading @@ -66,8 +65,8 @@ The colloid-colloid interaction energy is given by & \\ U = & U_A + U_R, \qquad r < r_c where :math:`A_{cc}` is the Hamaker constant, a\_1 and a\_2 are the radii of the two colloidal particles, and Rc is the cutoff. This where :math:`A_{cc}` is the Hamaker constant, :math:`a_1` and :math:`a_2` are the radii of the two colloidal particles, and :math:`r_c` 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 :ref:`(Everaers) <Everaers1>`. Loading @@ -76,12 +75,12 @@ The colloid-solvent interaction energy is given by .. math:: U = & \frac{2 ~ a^3 ~ \sigma^3 ~ A_{cs}}{9 \left( a^2 - r^2 \right)^3} U = \frac{2 ~ a^3 ~ \sigma^3 ~ A_{cs}}{9 \left( a^2 - r^2 \right)^3} \left[ 1 - \frac{\left(5 ~ a^6+45~a^4~r^2+63~a^2~r^4+15~r^6\right) \sigma^6} {15 \left(a-r\right)^6 \left( a+r \right)^6} \right], \quad r < r_c where :math: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 where :math:A_{cs}` is the Hamaker constant, *a* is the radius of the colloidal particle, and :math:`r_c` is the cutoff. This formula is derived from the colloid-colloid interaction, letting one of the particle sizes go to zero. Loading @@ -90,16 +89,16 @@ Lennard-Jones formula .. math:: U = & \frac{A_{ss}}{36} \left[ \left( \frac{\sigma}{r} U = \frac{A_{ss}}{36} \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{ \sigma}{r} \right)^6 \right], \quad r < r_c with :math:`A_{ss}` set appropriately, which results from letting both particle sizes go to zero. When used in combination with :doc:`pair_style yukawa/colloid <pair_colloid>`, the two terms become the so-called DLVO potential, which combines electrostatic repulsion and van der Waals attraction. When used in combination with :doc:`pair_style yukawa/colloid <pair_colloid>`, the two terms become the so-called DLVO potential, which combines electrostatic repulsion and van der Waals attraction. The following coefficients must be defined for each pair of atoms types via the :doc:`pair_coeff <pair_coeff>` command as in the examples Loading
