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clarify LJ energy function component of the quartic bond style

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Axel Kohlmeyer
2022-09-30 19:48:56 -04:00
parent 2538929d76
commit c61b356a71
1 changed files with 13 additions and 6 deletions
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19
doc/src/bond_quartic.rst
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@ -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 <bond_coeff>` command as in the example above, or in
@ -46,9 +53,9 @@ or :doc:`read_restart <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::