Flexible exponential model with a flat background.

DEFINITION

This model calculates a variety of exponential functions.

The scattered intensity $I(q)$ is calculated as

$I(q) = \text{scale} \cdot exp(-\text{prefactor} \cdot q^{\text{exponent}}) + \text{background}$

Note the minus sign in the exponential term. Thus if $prefactor$ is entered

as a positive number during fitting the returned function will decrease

as $q$ increases.

Also note that unlike many other models, $scale$ in this model is NOT

explicitly related to a volume fraction. Be careful if combining this model

with other models.

The value of $exponent$ controls the behaviour of the function. When:

$exponent$=1 : a normal exponential function is returned

0<$exponent$<1 : a so-called stretched exponential (or Kohlrausch-Williams-Watts, KWW) [1,2] function is returned

$exponent$>1 : a compressed exponential is returned

$exponent$=2 : a normal distribution function is returned.

This model probably has limited applicability in the analysis of SAS data but

is of great use in allied fields. For example, the KWW function is used in the

analysis of dielectric spectra data, rheological relaxation data, and dynamic

light scattering (photon correlation spectroscopy) data.

REFERENCES

1. R. Kohlrausch, Annalen der Physik und Chemie, 91(1) (1854) 56-82 & 179-213

2. G. Williams & D.C. Watts,Transactions of the Faraday Society, 66 (1970) 80-85

Created By |
smk78 |

Uploaded |
March 7, 2020, 6:51 p.m. |

Category |
Shape-Independent |

Score |
0 |

Verified |
This model has not been verified by a member of the SasView team |

In Library |
This model is not currently included in the SasView library. You must download the files and install it yourself. |

Files |
exponential.py |

No comments yet.

Please log in to add a comment.