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:rename the file name to Two_Yukawa
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Liu committed Jan 24, 2024
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22 changes: 15 additions & 7 deletions sasmodels/models/TY_YukawaSq.py → sasmodels/models/Two_Yukawa.py
Original file line number Diff line number Diff line change
Expand Up @@ -13,12 +13,14 @@
\frac{V(r)}{k_BT} = \begin{cases}
\infty & r < 2R \\
K_1 \frac{e^{-Z_1(r-2R)}}{r} + K_2 \frac{e^{-Z_2(r-2R)}}{r} & r \geq 2R
K_1 \frac{e^{-Z_1(r-1)}}{r} + K_2 \frac{e^{-Z_2(r-1)}}{r} & r \geq 2R
\end{cases}
where $R$ is radius_effective.
$K_1$ ( or $K_2$ ) is positive when there is a repulsion.
$K_1$ ( or $K_2$ ) is negative when there is an attraction.
And $r$ is the normalized inter-particle distance, $\frac{r_{cc}}{2R}$.
$r_{cc}$ is the distance between the center-of-mass of particles.
.. note::
Expand All @@ -45,24 +47,30 @@
The algorithm used in this model was originally proposed and developled by Liu
et al. in 2005 and implemented using MatLab.[1] The algorithm was later
reimplemented using C and Igor. SasView uses the C codes developed by M. Hennig
reimplemented using C and Igor. The codes for a two Yukawa potential in SasView are mostly based on the C codes written by M. Hennig
in 2010.
When the overall attraction is not very strong, this algorithm produces
reasonably accurate results.[2] However, when the net attraction is very strong,
it has been shown that the fitting algorithm tends to underestimate the
it has been shown that the fitting algorithm tends to overestimate the
attraction strength. Accuracy of this algorithm was evaluated by Broccio, et
al.[2]
al.[2] It should be noted that the MSA is not be an accurate closure for
systems with strong attractions. So cares need to be taken when having quantitative
discussions of the fitting results for those systems.
When using the O-Z equation to obtain the structure factor, it assumes that a
system is in a liquid state. However, when the attraction potential is too
strong the system may not be in a liquid state, and the O-Z equation may not
have a solution, or the solution may be unphysical.
have a solution, or the solution may be unphysical. It should be noted that any closure
for a O-Z euqation is an approximation. Thus, the structure factor calculated using a closure
is an approximation of the real structure factor. Its accuracy varies for different parameter ranges.
One should not "blindly" trust the results. This is true too for the MSA closure used here to solve
the O-Z equation for two Yukawa potential.[2]
References
----------
#. Y. Liu, W. Chen, S-H Chen, *J. Chem. Phys.*, 122 (2005) 044507
#. Y. Liu, W. R. Chen, S-H Chen, *J. Chem. Phys.*, 122 (2005) 044507
#. M. Broccio, D. Costa, Y. Liu, S-H Chen, *J. Chem. Phys.*, 124 (2006) 084501
Expand All @@ -79,7 +87,7 @@
"""
from numpy import inf

name = "TY_YukawaSq"
name = "Two_Yukawa"
title = "User model for two Yukawa structure factor (S(q))"
description = """"""

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