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Critical exponents, hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks (1995)

Li, Bin ; Madras, Neal ; Sokal, Alan D.

Springer

Journal of statistical physics 80 (1995), S. 661-754

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ISSN: 1572-9613

Keywords: Self-avoiding walk ; polymer ; critical exponent ; hyperscaling ; universal amplitude ratio ; second virial coefficient ; interpenetration ratio ; renormalization group ; two-parameter theory ; Monte Carlo ; pivot algorithm ; Karp-Luby algorithm

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2Δ 4 −γ as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2Δ 4 −γ. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios 〈R g 2 〉/〈R e 2 〉=0.14026±0.00007, 〈R m 2 〉/〈R e 2 〉=0.43961±0.00034, and Ψ*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponentΔ 1=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy forΔ 1. Earlier Monte Carlo estimates ofv, which were ≈0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios 〈R g 2 〉/〈R e 2 〉=0.1599±0.0002 and Ψ*=0.2471±0.0003; since Ψ*〉0, hyperscaling holds. The approach to Ψ* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2Δ 4 −γ for two-dimensional SAWs.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02178552

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Study of ion solvation and ion association in polymer gel electrolyte with polyethylene oxide-co-polypropylene oxide as a plasticizer (1996)

Sun, Xiao Guang ; Li, Bin ; Lin, Yun Qing ; [et al.]

New York, NY [u.a.] : Wiley-Blackwell

Polymer International 41 (1996), S. 301-305

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ISSN: 0959-8103

Keywords: gel electrolyte ; polytriethylene glycol dimethacrylate ; ion solvation ; ion association ; molal conductance ; Chemistry ; Polymer and Materials Science

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics

Notes: Using a molal conductance method, ion solvation and ion association in polytriethylene glycol dimethacrylate (PTREGD)-LiClO4 gel electrolytes with amorphous ethylene oxide-co-propylene oxide (EO-co-PO, M̄n = 1750) as the plasticizer were investigated. It was found that the fraction of solute existing as single ions (αi) and ion pairs (αp) decreases, while that of triple ions (αt) increases linearly with increasing salt concentration. The dependence of these fractions on molecular weight of plasticizer was also examined. It was shown that αi and αt increase and αp decreases with increasing molecular weight. The result of temperature dependence of these fractions was very interesting: when the temperature is lower than 55°C, αi increases while αp and αt decrease with increasing temperature; however, when the temperature is higher than 55°C, the reverse is true.

Additional Material: 4 Ill.