Crossover approach to scaling behavior in dilute polymer solutions: theory and simulation

L. Lue, S. B. Kiselev

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We develop a crossover theory for dilute polymer solutions, analogous to crossover theories for critical phenomena in simple fluids. In this theory, a critical degree of polymerization N∗ is found, which plays a similar role as the Ginzburg number in second-order phase transitions. To test the predictions of this theory, we perform Monte Carlo simulations of polymer chains composed of rigidly bonded hard spheres of various diameters and chain lengths. Various properties of these chains were analyzed, including the end-to-end distance distribution and mean-square radius of gyration. We find that the approach to the asymptotic scaling regime displays two types of crossover behavior, depending on the value of the model parameter ū, which is a measure of the strength of the monomer-monomer excluded volume interaction: (i) ū<1 and (ii) ū>1. In case (i), the system exhibits crossover from a Gaussian chain to the Kuhnian chain, as the degree of polymerization increases. In case (ii), the system exhibits crossover from the rigid rod to a Kuhnian chain. Our crossover theory is found to work well for polymers with ū>1 only near the asymptotic scaling regime. However, for ū<1, the theory works well in all regimes.
LanguageEnglish
Pages2684-2691
Number of pages7
JournalJournal of Chemical Physics
Volume110
Issue number5
DOIs
Publication statusPublished - 1 Feb 1999

Fingerprint

Polymer solutions
crossovers
Polymers
Monomers
Polymerization
scaling
polymers
Chain length
simulation
Phase transitions
Fluids
polymerization
monomers
gyration
rods
radii
fluids
predictions
Monte Carlo simulation
interactions

Keywords

  • conformational space renormalization
  • self-avoiding walks
  • Monte-Carlo simulation
  • excluded-volume
  • dimensional regularization
  • 2-parameter theory
  • pivot algorithm
  • 3 dimensions
  • chain
  • lattice

Cite this

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title = "Crossover approach to scaling behavior in dilute polymer solutions: theory and simulation",
abstract = "We develop a crossover theory for dilute polymer solutions, analogous to crossover theories for critical phenomena in simple fluids. In this theory, a critical degree of polymerization N∗ is found, which plays a similar role as the Ginzburg number in second-order phase transitions. To test the predictions of this theory, we perform Monte Carlo simulations of polymer chains composed of rigidly bonded hard spheres of various diameters and chain lengths. Various properties of these chains were analyzed, including the end-to-end distance distribution and mean-square radius of gyration. We find that the approach to the asymptotic scaling regime displays two types of crossover behavior, depending on the value of the model parameter ū, which is a measure of the strength of the monomer-monomer excluded volume interaction: (i) ū<1 and (ii) ū>1. In case (i), the system exhibits crossover from a Gaussian chain to the Kuhnian chain, as the degree of polymerization increases. In case (ii), the system exhibits crossover from the rigid rod to a Kuhnian chain. Our crossover theory is found to work well for polymers with ū>1 only near the asymptotic scaling regime. However, for ū<1, the theory works well in all regimes.",
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Crossover approach to scaling behavior in dilute polymer solutions: theory and simulation. / Lue, L.; Kiselev, S. B.

In: Journal of Chemical Physics, Vol. 110, No. 5, 01.02.1999, p. 2684-2691.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Crossover approach to scaling behavior in dilute polymer solutions: theory and simulation

AU - Lue, L.

AU - Kiselev, S. B.

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Y1 - 1999/2/1

N2 - We develop a crossover theory for dilute polymer solutions, analogous to crossover theories for critical phenomena in simple fluids. In this theory, a critical degree of polymerization N∗ is found, which plays a similar role as the Ginzburg number in second-order phase transitions. To test the predictions of this theory, we perform Monte Carlo simulations of polymer chains composed of rigidly bonded hard spheres of various diameters and chain lengths. Various properties of these chains were analyzed, including the end-to-end distance distribution and mean-square radius of gyration. We find that the approach to the asymptotic scaling regime displays two types of crossover behavior, depending on the value of the model parameter ū, which is a measure of the strength of the monomer-monomer excluded volume interaction: (i) ū<1 and (ii) ū>1. In case (i), the system exhibits crossover from a Gaussian chain to the Kuhnian chain, as the degree of polymerization increases. In case (ii), the system exhibits crossover from the rigid rod to a Kuhnian chain. Our crossover theory is found to work well for polymers with ū>1 only near the asymptotic scaling regime. However, for ū<1, the theory works well in all regimes.

AB - We develop a crossover theory for dilute polymer solutions, analogous to crossover theories for critical phenomena in simple fluids. In this theory, a critical degree of polymerization N∗ is found, which plays a similar role as the Ginzburg number in second-order phase transitions. To test the predictions of this theory, we perform Monte Carlo simulations of polymer chains composed of rigidly bonded hard spheres of various diameters and chain lengths. Various properties of these chains were analyzed, including the end-to-end distance distribution and mean-square radius of gyration. We find that the approach to the asymptotic scaling regime displays two types of crossover behavior, depending on the value of the model parameter ū, which is a measure of the strength of the monomer-monomer excluded volume interaction: (i) ū<1 and (ii) ū>1. In case (i), the system exhibits crossover from a Gaussian chain to the Kuhnian chain, as the degree of polymerization increases. In case (ii), the system exhibits crossover from the rigid rod to a Kuhnian chain. Our crossover theory is found to work well for polymers with ū>1 only near the asymptotic scaling regime. However, for ū<1, the theory works well in all regimes.

KW - conformational space renormalization

KW - self-avoiding walks

KW - Monte-Carlo simulation

KW - excluded-volume

KW - dimensional regularization

KW - 2-parameter theory

KW - pivot algorithm

KW - 3 dimensions

KW - chain

KW - lattice

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