PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheorySingleExp_Nonerg_DDM
PyDDM.ISF_and_DDMmatrix_theoretical_models.dTheorySingleExp_Nonerg_DDM¶
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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
- 1
Cho, J. H., Cerbino, R. & Bischofberger, I. Emergence of Multiscale Dynamics in Colloidal Gels. Phys. Rev. Lett. 124, 088005 (2020).