Two-dimensional copolymers and multifractality: Comparing perturbative expansions, Monte Carlo simulations, and exact results

Ferber, Christian von; Holovatch, Yu.

doi:10.1103/physreve.65.042801

Cited by 10 publications

(12 citation statements)

References 30 publications

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“…Previous theoretical predictions of γ f used ǫ = 4 − d -expansions [6,7] and the cone approximation [38,39]. The latter assumes that each branch is confined to a cone of space angle 4π/f , and gives…”

Section: A Partition Sums and γ-Exponentsmentioning

confidence: 99%

Scaling of Star Polymers with 1−80 Arms

2004

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We present large statistics simulations of 3-dimensional star polymers with up to f = 80 arms, and with up to 4000 monomers per arm for small values of f . They were done for the Domb-Joyce model on the simple cubic lattice. This is a model with soft core exclusion which allows multiple occupancy of sites but punishes each same-site pair of monomers with a Boltzmann factor v < 1. We use this to allow all arms to be attached at the central site, and we use the 'magic' value v = 0.6 to minimize corrections to scaling. The simulations are made with a very efficient chain growth algorithm with resampling, PERM, modified to allow simultaneous growth of all arms. This allows us to measure not only the swelling (as observed from the center-to-end distances), but also the partition sum. The latter gives very precise estimates of the critical exponents γ f . For completeness we made also extensive simulations of linear (unbranched) polymers which give the best estimates for the exponent γ.

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Section: A Partition Sums and γ-Exponentsmentioning

confidence: 99%

Scaling of Star Polymers with 1−80 Arms

2004

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“…Moreover, it can be shown, that the scaling behavior of sim-ple star polymers also determines the behavior of general polymer networks of more complicated structure [24,25]. Recently, progress in the synthesis of high quality monodisperse polymer networks [26,27,28,29,30] has stimulated numerous theoretical studies of star polymers, both by computer simulation [31,32,33,34,35,36] and by the renormalization group technique [24,25,37,38,39,40,41,42,43,44,45,46,47,48,49]. Let us note, that polymer stars are hybrids between polymer like entities and colloidal particles, establishing an important link between these different systems [21,22,23,50,51,52].…”

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confidence: 99%

“…The question we are interested in is: how does the presence of long-range-correlated disorder change the values of the critical exponents (2), (4)? Besides the starstar interaction, the exponents govern various phenomena that involve star polymers and polymer networks [44,45,46,47,48,49]. A particular effect that may be observable experimentally for star polymer solutions in a porous medium is an architecture-dependent impact of the medium on the star polymer.…”

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confidence: 99%

Entropy-induced separation of star polymers in porous media

2006

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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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“…In (b), instead, the distinction between solid and dashed lines becomes irrelevant as neighboring lines avoid each other. In the latter case the lines form a vertex of four mutually avoiding walks (MAWs) [16]. A vertex with L outgoing MAWs, has an associated entropic exponent [10,17]:…”

Section: Mutually Avoiding Walksmentioning

confidence: 99%

A simple model of DNA denaturation and mutually avoiding walks statistics

et al. 2002

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Recently Garel, Monthus and Orland (Europhys. Lett. 55, 132 (2001)) considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme they found a first order denaturation. We show that a first order transition for this model follows from exact results for the statistics of two mutually avoiding random walks, whose reunion exponent is c > 2, both in two and three dimensions. Analytical estimates of c due to the interactions with other denaturated loops, as well as numerical calculations, indicate that the transition is even sharper than in models where excluded volume effects are fully incorporated. The probability distribution of distances between homologous base pairs decays as a power law at the transition.

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Two-dimensional copolymers and multifractality: Comparing perturbative expansions, Monte Carlo simulations, and exact results

Cited by 10 publications

References 30 publications

Scaling of Star Polymers with 1−80 Arms

Scaling of Star Polymers with 1−80 Arms

Entropy-induced separation of star polymers in porous media

A simple model of DNA denaturation and mutually avoiding walks statistics

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