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Haydukivska K, Blavatska V. Probability of loops formation in star polymers in long range correlated disorder. J Chem Phys 2017. [DOI: 10.1063/1.4983127] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
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Haydukivska K, Blavatska V. Loop statistics in polymers in crowded environment. J Chem Phys 2016; 144:084901. [PMID: 26931720 DOI: 10.1063/1.4941980] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
We analyze the probability to find a single loop in a long flexible polymer chain in disordered environment in d dimensions. The structural defects are considered to be correlated on large distances r according to a power law ∼r(-a). Working within the frames of continuous chain model and applying the direct polymer renormalization scheme, we obtain the values of critical exponents governing the scaling of probabilities to find the loops of various positions along the chain as function of loops' length. Our results quantitatively reveal that the presence of structural defects in environment decreases the probability of loop formation in polymer macromolecules.
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Affiliation(s)
- K Haydukivska
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine
| | - V Blavatska
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine
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Fricke N, Janke W. Asymptotic scaling behavior of self-avoiding walks on critical percolation clusters. PHYSICAL REVIEW LETTERS 2014; 113:255701. [PMID: 25554895 DOI: 10.1103/physrevlett.113.255701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2014] [Indexed: 06/04/2023]
Abstract
We study self-avoiding walks on three-dimensional critical percolation clusters using a new exact enumeration method. It overcomes the exponential increase in computation time by exploiting the clusters' fractal nature. We enumerate walks of over 10^{4} steps, far more than has ever been possible. The scaling exponent ν for the end-to-end distance turns out to be smaller than previously thought and appears to be the same on the backbones as on full clusters. We find strong evidence against the widely assumed scaling law for the number of conformations and propose an alternative, which perfectly fits our data.
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Affiliation(s)
- Niklas Fricke
- Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig, Postfach 100920, D-04009 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig, Postfach 100920, D-04009 Leipzig, Germany
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Blavatska V. Equivalence of quenched and annealed averaging in models of disordered polymers. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:505101. [PMID: 24219876 DOI: 10.1088/0953-8984/25/50/505101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
The equivalence of the influence of quenched and annealed disorder on the scaling properties of long flexible polymer chains is proved by analyzing the O(m)-symmetric field theory in the polymer (de Gennes) limit m → 0. Additional symmetry properties of the model in this limit are discussed.
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Affiliation(s)
- V Blavatska
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine
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Blavatska V, von Ferber C, Holovatch Y. Star copolymers in porous environments: scaling and its manifestations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:011803. [PMID: 21405706 DOI: 10.1103/physreve.83.011803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2010] [Indexed: 05/30/2023]
Abstract
We consider star polymers, consisting of two different polymer species, in a solvent subject to quenched correlated structural obstacles. We assume that the disorder is correlated with a power-law decay of the pair-correlation function g(x)~x(-a). Applying the field-theoretical renormalization group approach in d dimensions, we analyze different scenarios of scaling behavior working to first order of a double ɛ=4-d, δ=4-a expansion. We discuss the influence of the correlated disorder on the resulting scaling laws and possible manifestations such as diffusion-controlled reactions in the vicinity of absorbing traps placed on polymers as well as the effective short-distance interaction between star copolymers.
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Affiliation(s)
- V Blavatska
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lviv, Ukraine.
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Blavatska V, Janke W. Multifractality of self-avoiding walks on percolation clusters. PHYSICAL REVIEW LETTERS 2008; 101:125701. [PMID: 18851389 DOI: 10.1103/physrevlett.101.125701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2008] [Revised: 07/28/2008] [Indexed: 05/26/2023]
Abstract
We consider self-avoiding walks on the backbone of percolation clusters in space dimensions d=2,3,4. Applying numerical simulations, we show that the whole multifractal spectrum of singularities emerges in exploring the peculiarities of the model. We obtain estimates for the set of critical exponents that govern scaling laws of higher moments of the distribution of percolation cluster sites visited by self-avoiding walks, in a good correspondence with an appropriately summed field-theoretical epsilon=6-d expansion [H.-K. Janssen and O. Stenull, Phys. Rev. E 75, 020801(R) (2007)10.1103/PhysRevE.75.020801].
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Affiliation(s)
- Viktoria Blavatska
- Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig, Postfach 100 920, Leipzig, Germany.
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Blavats'ka V, von Ferber C, Holovatch Y. Entropy-induced separation of star polymers in porous media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031801. [PMID: 17025657 DOI: 10.1103/physreve.74.031801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2006] [Indexed: 05/12/2023]
Abstract
We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of f-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the pair correlation function g(r) approximately r-a. Applying the field-theoretical renormalization group approach we show in a double expansion in epsilon=4-d and delta=4-a that there is a range of correlation strengths delta for which the disorder changes the scaling behavior of star polymers. In a second approach we calculate for fixed space dimension d=3 and different values of the correlation parameter a the corresponding scaling exponents gammaf that govern entropic effects. We find that gammaf-1, the deviation of gammaf from its mean field value is amplified by the disorder once we increase delta beyond a threshold. The consequences for a solution of diluted chain and star polymers of equal molecular weight inside a porous medium are that star polymers exert a higher osmotic pressure than chain polymers and in general higher branched star polymers are expelled more strongly from the correlated porous medium. Surprisingly, polymer chains will prefer a stronger correlated medium to a less or uncorrelated medium of the same density while the opposite is the case for star polymers.
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Affiliation(s)
- V Blavats'ka
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine.
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Usatenko Z, Ciach A. Critical adsorption of polymers in a medium with long-range correlated quenched disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:051801. [PMID: 15600640 DOI: 10.1103/physreve.70.051801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2004] [Indexed: 05/24/2023]
Abstract
The process of adsorption on a planar wall of long flexible polymer chains in a medium with quenched long-range correlated disorder is investigated. We focus on the case of correlations between defects or impurities that decay according to the power law x(-a) for large distances x , where x= (r,z) . A field theoretical approach in d=4-epsilon and directly in d=3 dimensions up to one-loop order for the semi-infinite |phi|(4) m-vector model (in the limit m-->0 ) with a planar boundary is used. The whole set of surface critical exponents at the adsorption threshold T= T(a) , which separates the nonadsorbed region from the adsorbed one, is obtained. Moreover, we calculate the crossover critical exponent Phi and the set of exponents associated with it. We perform calculations in a double epsilon=4-d and delta=4-a expansion and also for a fixed dimension d=3 , up to one-loop order for different values of the correlation parameter 2< a < or =3 . The obtained results indicate that for systems with long-range correlated quenched disorder a different set of surface critical exponents arises. All the surface critical exponents depend on a . Hence, the presence of long-range correlated disorder influences the process of adsorption of long flexible polymer chains on a wall in a significant way.
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Affiliation(s)
- Z Usatenko
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, UA-79011 Lviv, Ukraine.
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von Ferber C, Blavats'ka V, Folk R, Holovatch Y. Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:035104. [PMID: 15524568 DOI: 10.1103/physreve.70.035104] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2003] [Indexed: 05/24/2023]
Abstract
The scaling properties of self-avoiding walks on a d -dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Phys. Rev. Lett. 63, 2819 (1989)] and argue that via renormalization its multifractal properties are directly accessible. While the former first order perturbation did not agree with the results of other methods our analytic result gives an accurate description of the available MC and exact enumeration data in a wide range of dimensions 2</=d</=6 .
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Affiliation(s)
- C von Ferber
- Theoretische Polymerphysik, Universität Freiburg, D-79104 Freiburg, Germany.
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Blavats'ka V, von Ferber C, Holovatch Y. Polymers in long-range-correlated disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:041102. [PMID: 11690005 DOI: 10.1103/physreve.64.041102] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2001] [Indexed: 05/23/2023]
Abstract
We study the scaling properties of polymers in a d-dimensional medium with quenched defects that have power law correlations approximately r(-a) for large separations r. This type of disorder is known to be relevant for magnetic phase transitions. We find strong evidence that this is true also for the polymer case. Applying the field-theoretical renormalization group approach we perform calculations both in a double expansion in epsilon=4-d and delta=4-a up to the one-loop order and second in a fixed dimension (d=3) approach up to the two-loop approximation for different fixed values of the correlation parameter, 2<or=a<or=3. In the latter case the numerical results need appropriate resummation. We find that the asymptotic behavior of self-avoiding walks in three dimensions and long-range-correlated disorder is governed by a set of separate exponents. In particular, we give estimates for the nu and gamma exponents as well as for the correction-to-scaling exponent omega. The latter exponent is also calculated for the general m-vector model with m=1,2,3.
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Affiliation(s)
- V Blavats'ka
- Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine
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Blavats'ka V, von Ferber C, Holovatch Y. Polymers in media with long-range-correlated quenched disorder. J Mol Liq 2001. [DOI: 10.1016/s0167-7322(01)00179-9] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Nakanishi H, Lee SB. Exact enumeration study of self-avoiding walks on two-dimensional percolation clusters. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/24/6/026] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Roy AK, Chakrabarti BK. Scaling theory for the statistics of self-avoiding walks on random lattices. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/20/1/029] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Rajasekaran JJ, Muthukumar M. Tricritical theory of dilute polymer solutions with quenched disorder. J Chem Phys 1993. [DOI: 10.1063/1.465911] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kim Y. Flory approximants and self-avoiding walks on critical percolation clusters. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:6103-6106. [PMID: 9907710 DOI: 10.1103/physreva.45.6103] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Woo KY, Lee SB. Monte Carlo study of self-avoiding walks on a percolation cluster. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:999-1007. [PMID: 9906049 DOI: 10.1103/physreva.44.999] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Machta J, Kirkpatrick TR. Self-avoiding walks and manifolds in random environments. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:5345-5356. [PMID: 9902921 DOI: 10.1103/physreva.41.5345] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kim Y. Universality of self-avoiding walks on critical percolation clusters. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:4554-4557. [PMID: 9903666 DOI: 10.1103/physreva.41.4554] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Meir Y, Harris AB. Self-avoiding walks on diluted networks. PHYSICAL REVIEW LETTERS 1989; 63:2819-2822. [PMID: 10041001 DOI: 10.1103/physrevlett.63.2819] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Lee SB, Nakanishi H, Kim Y. Monte Carlo study of self-avoiding walks on a critical percolation cluster. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:9561-9572. [PMID: 9947693 DOI: 10.1103/physrevb.39.9561] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kim Y. Growing kinetics for self-avoiding walks on diluted lattices. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:4923-4925. [PMID: 9901859 DOI: 10.1103/physreva.39.4923] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Lee SB, Nakanishi H. Self-avoiding walks on randomly diluted lattices. PHYSICAL REVIEW LETTERS 1988; 61:2022-2025. [PMID: 10038963 DOI: 10.1103/physrevlett.61.2022] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Duplantier B. Tricritical disorder transition of polymers in a cloudy solvent: Annealed randomness. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 38:3647-3663. [PMID: 9900803 DOI: 10.1103/physreva.38.3647] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Roy AK, Manna SS. Statistics of directed self-avoiding walks on percolation clusters at the percolation threshold. ACTA ACUST UNITED AC 1985. [DOI: 10.1007/bf01307777] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Roy AK, Chakrabarti BK. Statistics of self-avoiding walks on random lattices. ACTA ACUST UNITED AC 1984. [DOI: 10.1007/bf01420564] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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