PolyHardSphere

Steve Kline 06 NOV 1998

Alan Munter 08 JULY 1999, converted to Java.

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.

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

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 s² 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.

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

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.