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Anomalous surfactant diffusion in a living polymer system

Angelico, Ruggero; Ceglie, Andrea; Olsson, Ulf LU ; Palazzo, Gerardo and Ambrosone, Luigi (2006) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 74(3).
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
volume
74
issue
3
publisher
American Physical Society
external identifiers
  • wos:000240870100056
  • scopus:33748955334
ISSN
1539-3755
DOI
10.1103/PhysRevE.74.031403
language
English
LU publication?
yes
id
21f14cfd-b245-46a7-be4a-b6603f90a674 (old id 388834)
date added to LUP
2007-09-25 10:30:50
date last changed
2019-06-25 01:44:00
@article{21f14cfd-b245-46a7-be4a-b6603f90a674,
  abstract     = {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 &lt; r(2)&gt;similar to t(2 beta), where the second moment of the diffusion propagator or molecular mean square displacement, &lt; r(2)&gt;, 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 &gt; 1/2) or subdiffusion (beta &lt; 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.},
  author       = {Angelico, Ruggero and Ceglie, Andrea and Olsson, Ulf and Palazzo, Gerardo and Ambrosone, Luigi},
  issn         = {1539-3755},
  language     = {eng},
  number       = {3},
  publisher    = {American Physical Society},
  series       = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)},
  title        = {Anomalous surfactant diffusion in a living polymer system},
  url          = {http://dx.doi.org/10.1103/PhysRevE.74.031403},
  volume       = {74},
  year         = {2006},
}