# Anomalous surfactant diffusion in a living polymer system

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**Anomalous surfactant diffusion in a living polymer system.** / Angelico, Ruggero; Ceglie, Andrea; Olsson, Ulf; Palazzo, Gerardo; Ambrosone, Luigi.

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift

### Harvard

*Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)*, vol. 74, nr. 3. https://doi.org/10.1103/PhysRevE.74.031403

### APA

*Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)*,

*74*(3). https://doi.org/10.1103/PhysRevE.74.031403

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*Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)*. 2006. 74(3). https://doi.org/10.1103/PhysRevE.74.031403

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TY - JOUR

T1 - Anomalous surfactant diffusion in a living polymer system

AU - Angelico, Ruggero

AU - Ceglie, Andrea

AU - Olsson, Ulf

AU - Palazzo, Gerardo

AU - Ambrosone, Luigi

PY - 2006

Y1 - 2006

N2 - Random processes are generally described by Gaussian statistics as formulated by the central limit theorem. However, there exists a large number of exceptions to this rule that can be found in a variety of fields. Diffusion processes are often analyzed by the scaling law < r(2)>similar to t(2 beta), where the second moment of the diffusion propagator or molecular mean square displacement, < r(2)>, in the case of Gaussian diffusion is proportional to t, i.e., beta=1/2. A deviation from Gaussian behavior may be either superdiffusion (beta > 1/2) or subdiffusion (beta < 1/2). In this paper we demonstrate that all three diffusion regimes may be observed for the surfactant self-diffusion, on the length scale of 10(-6) m and the time scale of 0.02-0.8 s. in a system of wormlike micelles, depending on small variations in the sample composition. The self-diffusion is followed by pulsed gradient NMR where one not only measures the second moment of the diffusion propagator, but actually measures the Fourier transform of the full diffusion propagator itself. A generalized diffusion equation in terms of fractional time derivatives provides a general description of all the different diffusion regimes, and where 1/beta can be interpreted as a dynamic fractal dimension. Experimentally, we find beta=1/4 and 3/4, in the regimes of sub- and superdiffusion, respectively. The physical interpretation of the subdiffusion behavior is that the dominating diffusion mechanism corresponds to a lateral diffusion along the contour of the wormlike micelles. Superdiffusion is obtained near the overlap concentration where the average micellar size is smaller so that the center of mass diffusion of the micelles contributes to the transport of surfactant molecules.

AB - Random processes are generally described by Gaussian statistics as formulated by the central limit theorem. However, there exists a large number of exceptions to this rule that can be found in a variety of fields. Diffusion processes are often analyzed by the scaling law < r(2)>similar to t(2 beta), where the second moment of the diffusion propagator or molecular mean square displacement, < r(2)>, in the case of Gaussian diffusion is proportional to t, i.e., beta=1/2. A deviation from Gaussian behavior may be either superdiffusion (beta > 1/2) or subdiffusion (beta < 1/2). In this paper we demonstrate that all three diffusion regimes may be observed for the surfactant self-diffusion, on the length scale of 10(-6) m and the time scale of 0.02-0.8 s. in a system of wormlike micelles, depending on small variations in the sample composition. The self-diffusion is followed by pulsed gradient NMR where one not only measures the second moment of the diffusion propagator, but actually measures the Fourier transform of the full diffusion propagator itself. A generalized diffusion equation in terms of fractional time derivatives provides a general description of all the different diffusion regimes, and where 1/beta can be interpreted as a dynamic fractal dimension. Experimentally, we find beta=1/4 and 3/4, in the regimes of sub- and superdiffusion, respectively. The physical interpretation of the subdiffusion behavior is that the dominating diffusion mechanism corresponds to a lateral diffusion along the contour of the wormlike micelles. Superdiffusion is obtained near the overlap concentration where the average micellar size is smaller so that the center of mass diffusion of the micelles contributes to the transport of surfactant molecules.

U2 - 10.1103/PhysRevE.74.031403

DO - 10.1103/PhysRevE.74.031403

M3 - Article

VL - 74

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 2470-0045

IS - 3

ER -