.. _hayter-msa:
hayter_msa
=======================================================
Hayter-Penfold Rescaled Mean Spherical Approximation (RMSA) structure factor for charged spheres
================== ============================================================================================== ===== =============
Parameter Description Units Default value
================== ============================================================================================== ===== =============
radius_effective effective radius of charged sphere |Ang| 20.75
volfraction volume fraction of spheres None 0.0192
charge charge on sphere (in electrons) e 19
temperature temperature, in Kelvin, for Debye length calculation K 318.16
concentration_salt conc of salt, moles/litre, 1:1 electolyte, for Debye length M 0
dielectconst dielectric constant (relative permittivity) of solvent, kappa, default water, for Debye length None 71.08
================== ============================================================================================== ===== =============
The returned value is a dimensionless structure factor, $S(q)$.
Calculates the interparticle structure factor for a system of charged,
spheroidal, objects in a dielectric medium [1,2]. When combined with an
appropriate form factor $P(q)$, this allows for inclusion of the
interparticle interference effects due to screened Coulombic
repulsion between the charged particles.
.. note::
This routine only works for charged particles! If the charge is set
to zero the routine may self-destruct! For uncharged particles use
the :ref:`hardsphere` $S(q)$ instead. The upper limit for the charge
is limited to 200e to avoid numerical instabilities.
.. note::
Earlier versions of SasView did not incorporate the so-called
$\beta(q)$ ("beta") correction [3] for polydispersity and non-sphericity.
This is only available in SasView versions 5.0 and higher.
The salt concentration is used to compute the ionic strength of the solution
which in turn is used to compute the Debye screening length. There is no
provision for entering the ionic strength directly. **At present the
counterions are assumed to be monovalent**, though it should be possible
to simulate the effect of multivalent counterions by increasing the salt
concentration.
Over the range 0 - 100 C the dielectric constant $\kappa$ of water may be
approximated with a maximum deviation of 0.01 units by the empirical
formula [4]
.. math::
\kappa = 87.740 - 0.40008 T + 9.398x10^{-4} T^2 - 1.410x10^{-6} T^3
where $T$ is the temperature in celsius.
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.
The computation uses a Taylor series expansion at very small rescaled $qR$, to
avoid some serious rounding error issues, this may result in a minor artefact
in the transition region under some circumstances.
For 2D data, the scattering intensity is calculated in the same way as 1D,
where the $q$ vector is defined as
.. math::
q = \sqrt{q_x^2 + q_y^2}
.. figure:: img/hayter_msa_autogenfig.png
1D plot corresponding to the default parameters of the model.
**Source**
:download:`hayter_msa.py `
$\ \star\ $ :download:`hayter_msa.c `
**References**
#. J B Hayter and J Penfold, *Molecular Physics*, 42 (1981) 109-118
#. J P Hansen and J B Hayter, *Molecular Physics*, 46 (1982) 651-656
#. M Kotlarchyk and S-H Chen, *J. Chem. Phys.*, 79 (1983) 2461-2469
#. C G Malmberg and A A Maryott, *J. Res. Nat. Bureau Standards*, 56 (1956) 2641
**Authorship and Verification**
* **Author:**
* **Last Modified by:**
* **Last Reviewed by:** Steve King **Date:** March 28, 2019