PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheorySingleExp_Nonerg_DDM

PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheorySingleExp_Nonerg_DDM#

dTheorySingleExp_Nonerg_DDM(lagtime, amplitude, tau, bg, s, C)#

Theoretical model for the DDM matrix with an exponential term for the intermediate scatting function. Also contains a non-ergodicity parameter. With this, the ISF will decay to the non-ergodicity paramter (C), instead of to zero as is the case with ergodic systems.

Parameters:

  • lagtime (array) – 1D array of the lagtimes

  • amplitude (float) – Amplitude, “A” in equation below

  • tau (float) – The characteristic decay time

  • bg (float) – Background term, “B” in equation below

  • s (float) – Stretching exponent

  • C (float) – The non-ergodicity parameter

Returns:

ddm_matrix – DDM matrix as shown in equation below

Return type:

array

Notes

\[\begin{split}f(q, \Delta t) = e^{\left( \frac{-\Delta t}{\tau}\right)^{s}} + C \\ D(q, \Delta t) = A \times (1 - f(q, \Delta t)) + B\end{split}\]

A non-ergodic model was used in the paper below. [1]

References

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