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The heterogeneity of the viscoelasticity of a lamellar gel network based oncetyl-trimethylammonium chloride (CTAC) and ceto-stearyl alcohol was studiedusing particle tracking microrheology. A recurrent neural network (RNN)architecture was used for estimating the Hurst exponent, $H$, on small sectionsof tracks of probe spheres moving with fractional Brownian motion. Thus dynamicsegmentation of tracks via neural networks was used in microrheology for thefirst time and it is significantly more accurate than using mean squaredisplacements. An ensemble of 414 particles produces a mean squareddisplacement (MSD) that is subdiffusive in time, $t$, with a power law of theform $t^{0.74\pm0.02}$, indicating power law viscoelasticity. RNN analysis ofthe probability distributions of $H$, combined with detailed analysis of thetime-averaged MSDs of individual tracks, revealed diverse diffusion processesbelied by the simple scaling of the ensemble MSD, such as caging phenomena,which give rise to the complex viscoelasticity of lamellar gels.

Extreme heterogeneity in the microrheology of lamellar surfactant gels analyzed with neural networks