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Minor changes to Porod model docs
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smk78 authored Mar 29, 2020
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24 changes: 12 additions & 12 deletions sasmodels/models/porod.py
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interfaces.
In the special case of a two phase system, the power law constant $C$ derived
from the appropriate $Q$ limit portion of the data is known as the Porod
from the appropriate $q$ limit portion of the data is known as the Porod
Constant and can be written as:
.. math:: C = 2\pi (\Delta\rho)^2 S_v
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analysis panel will also compute the $S_v$ by entering the contrast term
and the Porod Constant obtained here into the appropriate entry boxes.
There are however several caveats regarding obtaining a good experimental
There are, however, several caveats regarding obtaining a good experimental
value of the Porod Constant.
* First, as it is the scale value, the data **must** be on an absolute scale.
* Next of course there must be a sufficiently large $q$ range that is in
the Porod region to be able to fit. Note that this is not always
possible: for example polymer coils in solution will often not reach that
* Next of course, there must be a sufficiently large $q$ range that is in
the Porod region to be able to be fit. But this may not always be
possible: for example, polymer coils in solution will often not reach that
limit within typical SAS ranges, nor even the $q$ ranges where the
continuum approach of using SLD is even valid.
continuum approach of using the SLD is even valid.
* For highly monodisperse systems with limited resolution smearing, the
data will contain large oscillations which will make the estimate from
this fit unreliable. It will vary depending on the exact range to fit
that is chosen. This is because, numerical integration over a finite
number of points cannot properly capture the exact area across these very
sharp dips.
this fit unreliable. It will vary depending on the exact range of the fit
that is chosen. This is because numerical integration using a finite
number of points cannot properly capture the exact area under the data
across these very sharp dips.
* Ironically, large resolution smearing, and/or polydispersity smearing
* Ironically, large resolution smearing, and/or polydispersity smearing,
will make the value obtained much more consistant and reliable. Thus the
problem is less severe for typical real data than for simulated data that
does not simulate any resolution smearing.
* If in any doubt, using several values of $q_{min}$ in the fitting, and
comparing with the value obtained in a different manner, is advisable.
comparing with the value obtained in a different manner, is highly advisable.
One such method uses the Porod plot ($I(q)* q^4$ vs. $q^4$).
Fitting the highest $q$ (strictly speaking $q^4$) data to a straight line
using as much of the high $q$ as fits well to a straight line, yields a
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