Anomalous surfactant diffusion in a living polymer system
(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 selfdiffusion, 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 selfdiffusion, on the length scale of 10(6) m and the time scale of 0.020.8 s. in a system of wormlike micelles, depending on small variations in the sample composition. The selfdiffusion 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:
https://lup.lub.lu.se/record/388834
 author
 Angelico, Ruggero ; Ceglie, Andrea ; Olsson, Ulf ^{LU} ; Palazzo, Gerardo and Ambrosone, Luigi
 organization
 publishing date
 2006
 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
 pmid:17025631
 ISSN
 15393755
 DOI
 10.1103/PhysRevE.74.031403
 language
 English
 LU publication?
 yes
 id
 21f14cfdb24546a7be4ab6603f90a674 (old id 388834)
 date added to LUP
 20160401 12:33:00
 date last changed
 20201122 06:31:05
@article{21f14cfdb24546a7be4ab6603f90a674, 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 selfdiffusion, on the length scale of 10(6) m and the time scale of 0.020.8 s. in a system of wormlike micelles, depending on small variations in the sample composition. The selfdiffusion 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 = {15393755}, 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}, doi = {10.1103/PhysRevE.74.031403}, volume = {74}, year = {2006}, }