Crossover behaviour between Gaussian and self-avoiding limits of a single polymer chain: Conformational space renormalisation for polymers. VI

Yoshitsugu Oono, K. F. Fred

Research output: Contribution to journalArticle

Abstract

The Gell-Mann-Low style conformational space renormalisation method for polymers is generalised to describe the crossover between the random walk and self-avoiding walk limits, i.e. to describe the excluded volume dependence. Explicit calculations are provided to order epsilon =4-d (d the spatial dimensionality) for the full end-to-end vector distribution function, the coherent elastic scattering function, the second virial coefficients and (R 2) and (S2). The crossover functions are required therefore to exhibit the correct asymptotic limits of both the random and self-avoiding walks. The theory demonstrates that the latter choice implies that the expansion factors, alpha 2 and alpha s2, for the mean square end-to-end vector (R2) and radius of gyration (S2), respectively, are not universal functions of the single scaling variable describing the strength of the excluded volume interactions. Nevertheless, much of the available experimental data on long chain polymers appears to involve small renormalised dimensionless excluded volume, and therefore alpha 2 and alpha s2 are approximately universal quantities. Comparisons between our theoretical predictions and experimental data on the second virial coefficient and alpha s2 show good agreement.

Original languageEnglish (US)
Article number032
Pages (from-to)1931-1950
Number of pages20
JournalJournal of Physics A: Mathematical and General
Volume15
Issue number6
DOIs
StatePublished - Dec 1 1982

Fingerprint

Renormalization
Crossover
crossovers
Polymers
Self-avoiding Walk
virial coefficients
polymers
Experimental Data
Coherent scattering
Universal Function
Elastic scattering
coherent scattering
Asymptotic Limit
scattering functions
gyration
Coefficient
random walk
Dimensionless
Mean Square
Distribution functions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Crossover behaviour between Gaussian and self-avoiding limits of a single polymer chain : Conformational space renormalisation for polymers. VI. / Oono, Yoshitsugu; Fred, K. F.

In: Journal of Physics A: Mathematical and General, Vol. 15, No. 6, 032, 01.12.1982, p. 1931-1950.

Research output: Contribution to journalArticle

@article{dd3e5f0c09924a399daaf3775320239c,
title = "Crossover behaviour between Gaussian and self-avoiding limits of a single polymer chain: Conformational space renormalisation for polymers. VI",
abstract = "The Gell-Mann-Low style conformational space renormalisation method for polymers is generalised to describe the crossover between the random walk and self-avoiding walk limits, i.e. to describe the excluded volume dependence. Explicit calculations are provided to order epsilon =4-d (d the spatial dimensionality) for the full end-to-end vector distribution function, the coherent elastic scattering function, the second virial coefficients and (R 2) and (S2). The crossover functions are required therefore to exhibit the correct asymptotic limits of both the random and self-avoiding walks. The theory demonstrates that the latter choice implies that the expansion factors, alpha 2 and alpha s2, for the mean square end-to-end vector (R2) and radius of gyration (S2), respectively, are not universal functions of the single scaling variable describing the strength of the excluded volume interactions. Nevertheless, much of the available experimental data on long chain polymers appears to involve small renormalised dimensionless excluded volume, and therefore alpha 2 and alpha s2 are approximately universal quantities. Comparisons between our theoretical predictions and experimental data on the second virial coefficient and alpha s2 show good agreement.",
author = "Yoshitsugu Oono and Fred, {K. F.}",
year = "1982",
month = "12",
day = "1",
doi = "10.1088/0305-4470/15/6/032",
language = "English (US)",
volume = "15",
pages = "1931--1950",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "6",

}

TY - JOUR

T1 - Crossover behaviour between Gaussian and self-avoiding limits of a single polymer chain

T2 - Conformational space renormalisation for polymers. VI

AU - Oono, Yoshitsugu

AU - Fred, K. F.

PY - 1982/12/1

Y1 - 1982/12/1

N2 - The Gell-Mann-Low style conformational space renormalisation method for polymers is generalised to describe the crossover between the random walk and self-avoiding walk limits, i.e. to describe the excluded volume dependence. Explicit calculations are provided to order epsilon =4-d (d the spatial dimensionality) for the full end-to-end vector distribution function, the coherent elastic scattering function, the second virial coefficients and (R 2) and (S2). The crossover functions are required therefore to exhibit the correct asymptotic limits of both the random and self-avoiding walks. The theory demonstrates that the latter choice implies that the expansion factors, alpha 2 and alpha s2, for the mean square end-to-end vector (R2) and radius of gyration (S2), respectively, are not universal functions of the single scaling variable describing the strength of the excluded volume interactions. Nevertheless, much of the available experimental data on long chain polymers appears to involve small renormalised dimensionless excluded volume, and therefore alpha 2 and alpha s2 are approximately universal quantities. Comparisons between our theoretical predictions and experimental data on the second virial coefficient and alpha s2 show good agreement.

AB - The Gell-Mann-Low style conformational space renormalisation method for polymers is generalised to describe the crossover between the random walk and self-avoiding walk limits, i.e. to describe the excluded volume dependence. Explicit calculations are provided to order epsilon =4-d (d the spatial dimensionality) for the full end-to-end vector distribution function, the coherent elastic scattering function, the second virial coefficients and (R 2) and (S2). The crossover functions are required therefore to exhibit the correct asymptotic limits of both the random and self-avoiding walks. The theory demonstrates that the latter choice implies that the expansion factors, alpha 2 and alpha s2, for the mean square end-to-end vector (R2) and radius of gyration (S2), respectively, are not universal functions of the single scaling variable describing the strength of the excluded volume interactions. Nevertheless, much of the available experimental data on long chain polymers appears to involve small renormalised dimensionless excluded volume, and therefore alpha 2 and alpha s2 are approximately universal quantities. Comparisons between our theoretical predictions and experimental data on the second virial coefficient and alpha s2 show good agreement.

UR - http://www.scopus.com/inward/record.url?scp=0010694791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010694791&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/15/6/032

DO - 10.1088/0305-4470/15/6/032

M3 - Article

AN - SCOPUS:0010694791

VL - 15

SP - 1931

EP - 1950

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 6

M1 - 032

ER -