Statistics of Multicomponent Polymer Stars

Ferber, von; Holovatch,

doi:10.5488/cmp.10.9

Cited by 8 publications

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“…For the critical exponents that describe the scaling of homogeneous polymer chains and star polymers (or, more generally, homogeneous polymer networks) the perturbative approach [5] is in fair agreement with the exact data for D = 2 [6]. For the heterogeneous case however, only perturbative results [7,8] were available until recently. An exact solution for scaling exponents has been recently proposed that uses methods of conformal invariance on random graphs [9].…”

mentioning

confidence: 64%

“…The field theoretical description of the scaling properties of polymer chains in good solvents has been generalized to the case of multicomponent polymer solutions [4] and linked polymers [5,6]. Recently, the theory was suited to describe polymer networks of different species [7,8]. The simplest nontrivial case of a heterogeneous polymer network -a star-shaped copolymer in D = 2 dimensions -is the subject of the present report.…”

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confidence: 98%

“…A remarkable feature of the scaling spectrum of a copolymer star is that it possesses multifractal properties that can also be analyzed in terms of field theory and the conformal invariance approach. [7,8,9,10,11,12].…”

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confidence: 99%

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

Ferber

Holovatch²

2002

Phys. Rev. E

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We analyze the scaling laws for a set of two different species of long flexible polymer chains joined together at one of their extremities (copolymer stars) in space dimension D=2. We use a formerly constructed field-theoretic description and compare our perturbative results for the scaling exponents with recent conjectures for exact conformal scaling dimensions derived by a conformal invariance technique in the context of D=2 quantum gravity. A simple Monte Carlo simulation brings about reasonable agreement with both approaches. We analyze the remarkable multifractal properties of the spectrum of scaling exponents.

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confidence: 64%

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confidence: 98%

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

Ferber

Holovatch²

2002

Phys. Rev. E

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“…The functions (27), (28) are the standard RG functions of the O(m = 0) symmetric theory. They are known by now in high orders of perturbation theory, whereas the functions (29) have been obtained only up to three loops. In the field theory they are related to the anomalous dimension of composite operators of traceless symmetry [15].…”

Section: Homogeneous Star Polymer In Three Dimensionsmentioning

confidence: 99%

Field-Theoretical Renormalization Group Analysis for the Scaling Exponents of Star Polymers

Ferber¹,

Holovatch²

2002

Condens. Matter Phys.

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We review recent results of the field theoretical renormalization group analysis on the scaling properties of star polymers. We give a brief account of how the numerical values of the exponents governing the scaling of star polymers were obtained as well as provide some examples of the phenomena governed by these exponents. In particular we treat the interaction between star polymers in a good solvent, the Brownian motion near absorbing polymers, and diffusion-controlled reactions involving polymers.

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“…A star-polymer is a a e-mail: benhamou.mabrouk@eudoramail.com typical branched macromolecule, which possesses a central core from which many end-attached linear chains emerge. The physics of star-polymers is the subject of a great deal of attention from theoretical [8][9][10][11][12][13][14][15][16][17][18][19][20] and experimental [21] point of view. Theoretical works pioneered by Daoud and Cotton (DC) [9].…”

Section: Introductionmentioning

confidence: 99%

Interaction force between incompatible star-polymers in dilute solution

Benhamou¹,

Benzouine²

2001

The European Physical Journal E

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We consider a low-density assembly of spherical colloids, such that each is clothed by L endgrafted chemically incompatible polymer chains either of types A or B. These are assumed to be dissolved in a good common solvent. We assume that colloids are of small size to be considered as star-polymers. Two adjacent star-polymers A and B interact through a force F originating from both excluded-volume effects and chemical mismatch between unlike monomers. Using a method developed by Witten and Pincus (Macromolecules 19, 2509(Macromolecules 19, (1986) in the context of star-polymers of the same chemical nature, we determine exactly the force F as a function of the center-to-center distance h. We find that this force is the sum of two contributions F e and Fs. The former, that results from the excluded volume, decays as Fe ∼ ALh −1 , with the L -dependent universal amplitude AL ∼ L 3/2 . While the second, which comes from the chemical mismatch, decays more slowly as Fs ∼ χBLh −1−τ , where τ is a critical exponent whose value is found to be τ ∼ = 0.40, and χ is the standard Flory interaction parameter. We find that the corresponding L-dependent universal amplitude is BL ∼ L (3+τ )/2 . Theses forces are comparable near the cores of two adjacent star-polymers, i.e. for h ∼ hc ∼ aχ 1/τ √ L (a is the monomer size). Finally, for two star-polymers of the same chemical nature (A or B), the force F that simply results from excluded-volume effects coincides exactly with Fe, and then the known result is recovered.

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Statistics of Multicomponent Polymer Stars

Cited by 8 publications

References 0 publications

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

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

Field-Theoretical Renormalization Group Analysis for the Scaling Exponents of Star Polymers

Interaction force between incompatible star-polymers in dilute solution

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