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Non-Gaussian polymers described by alpha-stable chain statistics : model, effective interactions in binary mixtures, and application to on-surface separation
Non-Gaussian polymers described by alpha-stable chain statistics : model, effective interactions in binary mixtures, and application to on-surface separation
Non-Gaussian polymers described by alpha-stable chain statistics : model, effective interactions in binary mixtures, and application to on-surface separation
autor:
Majka Maciej , Góra Paweł
tytuł czasopisma:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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.
liczba arkuszy wydawniczych:
0,7
wydział: instytut / zakład / katedra:
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
typ:
artykuł w czasopiśmie
podtyp:
artykuł
punktacja MEiN [2015 A]: 35
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