diff --git a/doc/src/bond_quartic.rst b/doc/src/bond_quartic.rst index 1f9f9bf4e9..cda30cfd95 100644 --- a/doc/src/bond_quartic.rst +++ b/doc/src/bond_quartic.rst @@ -28,11 +28,18 @@ The *quartic* bond style uses the potential .. math:: - E = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 + 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon + E & = E_q + E_{LJ} \\ + E_q & = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 \\ + E_{LJ} & = \left\{ \begin{array} {l@{\quad:\quad}l} + 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon & r < 2^{\frac{1}{6}}, \epsilon = 1, \sigma = 1 \\ + 0 & r >= 2^{\frac{1}{6}} + \end{array} \right. to define a bond that can be broken as the simulation proceeds (e.g. -due to a polymer being stretched). The :math:`\sigma` and :math:`\epsilon` used in the -LJ portion of the formula are both set equal to 1.0 by LAMMPS. +due to a polymer being stretched). The :math:`\sigma` and +:math:`\epsilon` used in the LJ portion of the formula are both set +equal to 1.0 by LAMMPS and the LJ portion is cut off at its minimum, +i.e. at :math:`r_c = 2^{\frac{1}{6}}`. The following coefficients must be defined for each bond type via the :doc:`bond_coeff ` command as in the example above, or in @@ -46,9 +53,9 @@ or :doc:`read_restart ` commands: * :math:`U_0` (energy) This potential was constructed to mimic the FENE bond potential for -coarse-grained polymer chains. When monomers with :math:`\sigma = \epsilon = 1.0` -are used, the following choice of parameters gives a quartic potential that -looks nearly like the FENE potential: +coarse-grained polymer chains. When monomers with :math:`\sigma = +\epsilon = 1.0` are used, the following choice of parameters gives a +quartic potential that looks nearly like the FENE potential: .. math::