MODEL

PolyHardSphere

AUTHOR/MODIFICATION

Steve Kline 06 NOV 1998

Alan Munter 08 JULY 1999, converted to Java.

APPROVED FOR DISTRIBUTION

DESCRIPTION

This function calculates the scattered intensity for a population of polydisperse spheres, including hard sphere interactions between the particles. The calculation is an exact, multicomponent solution, using the Percus-Yevick closure. A Schulz distribution is used to describe the polydispersity of the diameter.

VARIABLES

Input Variables (default values):

Parameter | Variable | Value |
---|---|---|

0 | Radius (Å) | 100.0 |

1 | Polydispersity (0-1) | 0.12 |

2 | Volume Fraction (0-1) | 0.1 |

3 | Contrast (Å^{-2}) | 2.0e-6 |

4 | incoherent Background(cm^{-1}) | 0.000 |

USAGE NOTES

The returned value is the scattered intensity in absolute scale,
units of [cm^{-1}]. Since both the form factor and structure
factor are included in this calculation, any other structure factor
selected in the calculation will not be applied.

Polydispersity, *p* = *s*/R, where *s*^{2}
is the variance of the distribution and R is the mean particle radius,
Parameter[0]. For a more complete description of the Schulz
distribution, see: J. Hayter in "Physics of Amphiphiles - Micelles,
Vesicles and Microemulsions" V. DeGiorgio and M. Corti, Eds. (1983)
p. 69.

Polydispersity, Parameter[1], is constrained during
calculation to remain between its physical limits of 0 <
*p* < 1. If a value larger than this is entered the value is
quietly converted to 1.

Scattering contrast = SLD (sphere) - SLD (solvent).

Volume fraction and scattering contrast are correlated, and one or both should be held fixed during model fitting.

REFERENCE

Griffith, W. L.; Triolo, R.; Compere, A. L. *Phys. Rev. A*,
**1987**, *35*, 2200.

TEST DATASET

This example dataset is produced by calculating the PolyHardSphere
using 256 data points, *q*_{min} = 0.001 Å^{-1},
*q*_{max} = 0.7 Å^{-1} and the above default
parameter values.