# Squarewell

## Description:

# Note: model title and parameter table are inserted automatically 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:

$$U(r) = \begin{cases} \infty & r < 2R \\ -\epsilon & 2R \leq r < 2R\lambda \\ 0 & r \geq 2R\lambda \end{cases}$$
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

$$q = \sqrt{q_x^2 + q_y^2}$$
References

R V Sharma, K C Sharma, *Physica*, 89A (1977) 213

M Kotlarchyk and S-H Chen, *J. Chem. Phys.*, 79 (1983) 2461-2469

Authorship and Verification

**Author:**