Swelling of an isolated polymer chain in a solvent

Cloizeaux, J. des; Conte, R.; Jannink, G.

doi:10.1051/jphyslet:019850046013059500

Cited by 35 publications

(20 citation statements)

References 7 publications

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“…III B we define the crossover limit for walk models and derive some general results for the universal crossover functions. In particular, we show that they are exactly related to the crossover functions computed in field theory [37][38][39]. Moreover, by using the results of Ref.…”

Section: Introductionsupporting

confidence: 58%

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

et al. 2001

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We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, which corresponds to the limit N-->0 of an N-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed by using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions for the critical crossover functions, finding good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal crossover behavior of our data for any finite range.

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Section: Introductionsupporting

confidence: 58%

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

et al. 2001

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“…45 Recently the estimate ϭ 0.5882 Ϯ 0.0011 was obtained from perturbation theory calculations for the O(N) model for N ϭ 0. 46 Perturbation expansion of the 3D continuum Edwards model produced the estimates Ϸ 0.588, ⌬ 1 Ϸ 0.473, 47 and Ϸ 0.5886, ⌬ 1 Ϸ 0.465. 48 Monte Carlo simulation of the Domb-Joyce model for walks of up to N ϭ 10000 steps on a simple cubic lattice gave the estimate ϭ 0.5867 Ϯ 0.0007.…”

Section: Scaling Relations and Distribution Functionsmentioning

confidence: 98%

Off-lattice Monte Carlo simulation of the discrete Edwards model

Besold

Guo

Zuckermann

2000

J. Polym. Sci. B Polym. Phys.

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“…For this phenomenon we offer the following explanation: For values of N tending to infinity, when the number of accessible end points within each shell becomes very large, it is natural to assume that (n (p) > N is proportional to the EEDF given by some limiting equation, e.g., of the form ofEq. (2). On the other hand, for finite values of N and limited numbers of accessible points, one has…”

Section: Intrinsic (Geometric) Deviations From the Limiting Distrimentioning

confidence: 99%

“…Fisher showed 23 further per = NV roz ) = (roNY) -df(z) = AN -vdz6exp ( -z-S) ( each other. Consequently, des Cloizeaux and Jannink proposed that the whole EEDF be described approximately by the function 28 P(r=N'"p) =AN-,'d p g exp ( -13/» (2) in terms of the reduced variablep = r/N", where again A isa normalization constant and () a mean value, in principle ()" except in the vicinity of p = O. The des Cloizeaux-Jannink distribution differs from the McKenzie-Moore distribution, in that besides 8 and () a third parameter f3 appears in the distribution.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo precise determination of the end-to-end distribution function of self-avoiding walks on the simple-cubic lattice

Dayantis

Palierne

1991

The Journal of Chemical Physics

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Chains have been generated on the simple-cubic lattice to determine, by Monte Carlo simulation, the end-to-end distribution function of self-avoiding walks. The modulus r of the end-to-end distribution vector r, the square of this modulus, and the interactions of all orders were recorded for each chain. The Alexandrowicz dimerization procedure has been used to circumvent attrition and thus obtain statistically significant samples of large chains. This made it possible to obtain samples involving 12 000–16 000 chains, within ‘‘windows’’ of width Δρ=0.2, where ρ=r/Nν, N being the number of steps in the walk and ν the scaling exponent. It was found that the mean value 〈r〉=aNν, with ν=0.5919 and the prefactor a very close (perhaps strictly equal) to unity. The above value of ν is slightly larger than that calculated by Le Guillou and Zinn-Justin, but in accord with the Wilson ε=4−d expansion, where d is the space dimensionality. Also, 〈r 2〉=bN2ν, with b=1.136±0.05. An attempt was made to fit the data to the Fisher–McKenzie–des Cloizeaux distribution, P(r=Nνρ)=N−νdA ρθ exp(−βρδ), where θ, β, and δ are adjustable parameters. Taking δ=(1−ν)−1=2.45, in accordance with the Fisher law, it was found that plots for various N values of ln L(ρ)+βρδ vs ln ρ, where L(ρ) is the number of chains falling within subwindows of width dρ=0.02, were linear (except for the lowest values of ρ), if β was taken equal to 1.07. From the slope of the linear plot it was found that θ=0.27, in accord with theory. Finally, in three dimensions the end-to-end distribution function P(r) can be expressed by the relation P(r=Nνρ)=N−νd 0.2393ρ0.27 exp(−1.07ρ2.45). This relation is in good agreement with that proposed by des Cloizeaux and Jannink. A brief discussion of the two-dimensional case as well as fluctuations of the end-to-end distance is also presented.

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Swelling of an isolated polymer chain in a solvent

Cited by 35 publications

References 7 publications

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

Off-lattice Monte Carlo simulation of the discrete Edwards model

Monte Carlo precise determination of the end-to-end distribution function of self-avoiding walks on the simple-cubic lattice

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