Non-Gaussian polymers described by alpha-stable chain statistics: Model, effective interactions in binary mixtures, and application to on-surface separation. Majka, M. and Góra, P. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2015.
Non-Gaussian polymers described by alpha-stable chain statistics: Model, effective interactions in binary mixtures, and application to on-surface separation [link]Paper  doi  abstract   bibtex   
The Gaussian chain model is the classical description of a polymeric chain, which provides analytical results regarding end-to-end distance, the distribution of segments around the mass center of a chain, coarse-grained interactions between two chains and effective interactions in binary mixtures. This hierarchy of results can be calculated thanks to the α stability of the Gaussian distribution. In this paper we show that it is possible to generalize the model of Gaussian chain to the entire class of α-stable distributions, obtaining the analogous hierarchy of results expressed by the analytical closed-form formulas in the Fourier space. This allows us to establish the α-stable chain model. We begin with reviewing the applications of Levy flights in the context of polymer sciences, which include: chains described by the heavy-tailed distributions of persistence length; polymers adsorbed to the surface; and the chains driven by a noise with power-law spatial correlations. Further, we derive the distribution of segments around the mass center of the α-stable chain and construct the coarse-grained interaction potential between two chains. These results are employed to discuss the model of binary mixture consisting of the α-stable chains. In what follows, we establish the spinodal decomposition condition generalized to the mixtures of the α-stable polymers. This condition is further applied to compare the on-surface phase separation of adsorbed polymers (which are known to be described with heavy-tailed statistics) with the phase separation condition in the bulk. Finally, we predict the four different scenarios of simultaneous mixing and demixing in the two- and three-dimensional systems. © 2015 American Physical Society.
@ARTICLE{Majka2015,
author={Majka, M. and Góra, P.F.},
title={Non-Gaussian polymers described by alpha-stable chain statistics: Model, effective interactions in binary mixtures, and application to on-surface separation},
journal={Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},
year={2015},
volume={91},
number={5},
doi={10.1103/PhysRevE.91.052602},
art_number={052602},
url={https://www2.scopus.com/inward/record.uri?eid=2-s2.0-84929191293&doi=10.1103%2fPhysRevE.91.052602&partnerID=40&md5=ad16d5492d886360e6bc39b3c4bf6d27},
abstract={The Gaussian chain model is the classical description of a polymeric chain, which provides analytical results regarding end-to-end distance, the distribution of segments around the mass center of a chain, coarse-grained interactions between two chains and effective interactions in binary mixtures. This hierarchy of results can be calculated thanks to the α stability of the Gaussian distribution. In this paper we show that it is possible to generalize the model of Gaussian chain to the entire class of α-stable distributions, obtaining the analogous hierarchy of results expressed by the analytical closed-form formulas in the Fourier space. This allows us to establish the α-stable chain model. We begin with reviewing the applications of Levy flights in the context of polymer sciences, which include: chains described by the heavy-tailed distributions of persistence length; polymers adsorbed to the surface; and the chains driven by a noise with power-law spatial correlations. Further, we derive the distribution of segments around the mass center of the α-stable chain and construct the coarse-grained interaction potential between two chains. These results are employed to discuss the model of binary mixture consisting of the α-stable chains. In what follows, we establish the spinodal decomposition condition generalized to the mixtures of the α-stable polymers. This condition is further applied to compare the on-surface phase separation of adsorbed polymers (which are known to be described with heavy-tailed statistics) with the phase separation condition in the bulk. Finally, we predict the four different scenarios of simultaneous mixing and demixing in the two- and three-dimensional systems. © 2015 American Physical Society.},
keywords={Chains;  Gaussian distribution;  Mixtures;  Phase separation;  Polymers;  Spinodal decomposition, Alpha-stable distribution;  Effective interactions;  Gaussian chain models;  Heavy-tailed distribution;  Interaction potentials;  Separation condition;  Spatial correlations;  Three dimensional systems, Binary mixtures},
document_type={Article},
source={Scopus},
}
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