# squarewell

Square well structure factor with Mean Spherical Approximation closure

Parameter |
Description |
Units |
Default value |
---|---|---|---|

radius_effective |
effective radius of hard sphere |
Å |
50 |

volfraction |
volume fraction of spheres |
None |
0.04 |

welldepth |
depth of well, epsilon |
kT |
1.5 |

wellwidth |
width of well in diameters (=2R) units, must be > 1 |
diameters |
1.2 |

The returned value is a dimensionless structure factor, \(S(q)\).

Calculates the interparticle structure factor for a hard sphere fluid
with a narrow, attractive, square well potential. **The Mean Spherical
Approximation (MSA) closure relationship is used, but it is not the most
appropriate closure for an attractive interparticle potential.** However,
the solution has been compared to Monte Carlo simulations for a square
well fluid and these show the MSA calculation to be limited to well
depths \(\epsilon < 1.5\) kT and volume fractions \(\phi < 0.08\).

Positive well depths correspond to an attractive potential well. Negative well depths correspond to a potential “shoulder”, which may or may not be physically reasonable. The stickyhardsphere model may be a better choice in some circumstances.

Computed values may behave badly at extremely small \(qR\).

Note

Earlier versions of SasView did not incorporate the so-called \(\beta(q)\) (“beta”) correction [2] for polydispersity and non-sphericity. This is only available in SasView versions 5.0 and higher.

The well width \((\lambda)\) is defined as multiples of the particle diameter \((2 R)\).

The interaction potential is:

where \(r\) is the distance from the center of a sphere of a radius \(R\).

In SasView the effective radius may be calculated from the parameters used in the form factor \(P(q)\) that this \(S(q)\) is combined with.

For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the \(q\) vector is defined as

**Source**

**References**

R V Sharma, K C Sharma,

*Physica*, 89A (1977) 213M Kotlarchyk and S-H Chen,

*J. Chem. Phys.*, 79 (1983) 2461-2469

**Authorship and Verification**

**Author:****Last Modified by:****Last Reviewed by:**Steve King**Date:**March 27, 2019