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Shapes of macromolecules in good solvents: field theoretical renormalization group approach

Shapes of macromolecules in good solvents: field theoretical renormalization group approach

In this paper, we show how the method of field theoretical reno rmalization group may be used to analyze universal shape properties of long polymer chains in porous environment. So far such analytical calculations were primarily focussed on the scaling exponents that govern conformational properties...

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Main Authors: Blavatska, V., von Ferber, C., Holovatch, Yu.
Format: Article
Language:English
Published: Інститут фізики конденсованих систем НАН України 2011
Series:Condensed Matter Physics
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/120035
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spelling irk-123456789-1200352017-06-11T03:04:05Z Shapes of macromolecules in good solvents: field theoretical renormalization group approach Blavatska, V. von Ferber, C. Holovatch, Yu. In this paper, we show how the method of field theoretical reno rmalization group may be used to analyze universal shape properties of long polymer chains in porous environment. So far such analytical calculations were primarily focussed on the scaling exponents that govern conformational properties of polymer macromolecules. However, there are other observables that along with the scaling exponents are universal (i.e. independent of the chemical structure of macromolecules and of the solvent) and may be analyzed within the renormalization group approach. Here, we address the question of shape which is acquired by the long flexible polymer macromolecule when it is immersed in a solve nt in the presence of a porous environment. This question is of relevance for understanding of the behavior of macromolecules in colloidal solutions, near microporous membranes, and in cellular environment. To this end, we consider a previously suggested model of polymers in d-dimensions [V. Blavats’ka, C. von Ferber, Yu. Holovatch, Phys. Rev. E, 2001, 64, 041102] in an environment with structural obstacles, characterized by a pair correlation function h(r), that decays with distance r according to a power law: h(r) ∼ r−a. We apply the field-theoretical renormalization group ap-proach and estimate the size ratio hR²ei/hR²Gi and the asphericity ratio Aˆd up to the first order of a double ε = 4−d, δ = 4−a expansion. У статтi ми показуємо, яким чином можна застосувати метод теоретико-польової ренормалiзацiйної групи для аналiзу унiверсальних властивостей форм довгих гнучких полiмерних ланцюгiв у пористому середовищi. До цього часу такi аналiтичнi розрахунки в основному торкались показникiв скей-лiнгу, що визначають конформацiйнi властивостi полiмерних макромолекул. Проте, iснують й iншi спостережуванi величини, що, як i показники скейлiнгу, є унiверсальними (тобто незалежними вiд хiмiчної структури як макромолекул, так i розчинника), а отже можуть бути проаналiзованi в межах пiдходу ренормалiзацiйної групи. Ми цiкавимось питанням, якої форми набуває довга гнучка полiмерна макромолекула у розчинi в присутностi пористого середовища. Це питання є суттєвим для розумiння поведiнки макромолекул у колоїдних розчинах, поблизу мiкропористих мембран, а також у клiтинному середовищi. Ми розглядаємо запропоновану ранiше модель полiмера у d-вимiрному просторi [V. Blavats’ka, C. von Ferber, Yu. Holovatch, Phys. Rev. E, 2001, 64, 041102] у середовищi iз структурними неоднорiдностями, що характеризуються парною кореляцiйною функцiєю h(r), яка спадає iз вiдстанню r згiдно степеневого закону: h(r) ∼ r−a. Застосовуємо пiдхiд теоретико-польової ре-нормалiзацiйної групи i оцiнюємо вiдношення розмiрiв hR²ei/hR²Gi та асферичнiсть Aˆd до першого порядку ε = 4−d, δ = 4−a-розкладу. 2011 Article Shapes of macromolecules in good solvents: field theoretical renormalization group approach/ V. Blavatska, C. von Ferber, Yu. Holovatch // Condensed Matter Physics. — 2011. — Т. 14, № 3. — С. 33701: 1-20. — Бібліогр.: 45 назв. — англ. 1607-324X PACS: 75.10.Hk, 11.10.Hi, 12.38.Cy DOI:10.5488/CMP.14.33701 arXiv:1106.2042 http://dspace.nbuv.gov.ua/handle/123456789/120035 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description In this paper, we show how the method of field theoretical reno rmalization group may be used to analyze universal shape properties of long polymer chains in porous environment. So far such analytical calculations were primarily focussed on the scaling exponents that govern conformational properties of polymer macromolecules. However, there are other observables that along with the scaling exponents are universal (i.e. independent of the chemical structure of macromolecules and of the solvent) and may be analyzed within the renormalization group approach. Here, we address the question of shape which is acquired by the long flexible polymer macromolecule when it is immersed in a solve nt in the presence of a porous environment. This question is of relevance for understanding of the behavior of macromolecules in colloidal solutions, near microporous membranes, and in cellular environment. To this end, we consider a previously suggested model of polymers in d-dimensions [V. Blavats’ka, C. von Ferber, Yu. Holovatch, Phys. Rev. E, 2001, 64, 041102] in an environment with structural obstacles, characterized by a pair correlation function h(r), that decays with distance r according to a power law: h(r) ∼ r−a. We apply the field-theoretical renormalization group ap-proach and estimate the size ratio hR²ei/hR²Gi and the asphericity ratio Aˆd up to the first order of a double ε = 4−d, δ = 4−a expansion.
format Article
author Blavatska, V.
von Ferber, C.
Holovatch, Yu.
spellingShingle Blavatska, V.
von Ferber, C.
Holovatch, Yu.
Shapes of macromolecules in good solvents: field theoretical renormalization group approach
Condensed Matter Physics
author_facet Blavatska, V.
von Ferber, C.
Holovatch, Yu.
author_sort Blavatska, V.
title Shapes of macromolecules in good solvents: field theoretical renormalization group approach
title_short Shapes of macromolecules in good solvents: field theoretical renormalization group approach
title_full Shapes of macromolecules in good solvents: field theoretical renormalization group approach
title_fullStr Shapes of macromolecules in good solvents: field theoretical renormalization group approach
title_full_unstemmed Shapes of macromolecules in good solvents: field theoretical renormalization group approach
title_sort shapes of macromolecules in good solvents: field theoretical renormalization group approach
publisher Інститут фізики конденсованих систем НАН України
publishDate 2011
url http://dspace.nbuv.gov.ua/handle/123456789/120035
citation_txt Shapes of macromolecules in good solvents: field theoretical renormalization group approach/ V. Blavatska, C. von Ferber, Yu. Holovatch // Condensed Matter Physics. — 2011. — Т. 14, № 3. — С. 33701: 1-20. — Бібліогр.: 45 назв. — англ.
series Condensed Matter Physics
work_keys_str_mv AT blavatskav shapesofmacromoleculesingoodsolventsfieldtheoreticalrenormalizationgroupapproach
AT vonferberc shapesofmacromoleculesingoodsolventsfieldtheoreticalrenormalizationgroupapproach
AT holovatchyu shapesofmacromoleculesingoodsolventsfieldtheoreticalrenormalizationgroupapproach
first_indexed 2023-10-18T20:36:04Z
last_indexed 2023-10-18T20:36:04Z
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