Applicability of a particularly simple model to nonlinear elasticity of slide-ring gels with movable cross-links as revealed by unequal biaxial deformation

Yuuki Kondo, Kenji Urayama, Masatoshi Kidowaki, Koichi Mayumi, Toshikazu Takigawa, Kohzo Ito

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (σyx) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.

Original languageEnglish
Article number134906
JournalJournal of Chemical Physics
Volume141
Issue number13
DOIs
Publication statusPublished - 2014 Oct 7

Fingerprint

chutes
Elasticity
elastic properties
Gels
gels
rings
Strain energy
strands
Probability density function
flux density
Elastomers
preparation
shear strain
elastomers
elongation
Stretching
Elongation
Entropy
Elastic moduli
entropy

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

Applicability of a particularly simple model to nonlinear elasticity of slide-ring gels with movable cross-links as revealed by unequal biaxial deformation. / Kondo, Yuuki; Urayama, Kenji; Kidowaki, Masatoshi; Mayumi, Koichi; Takigawa, Toshikazu; Ito, Kohzo.

In: Journal of Chemical Physics, Vol. 141, No. 13, 134906, 07.10.2014.

Research output: Contribution to journalArticle

@article{495a77e374c5433c966bc346fd30462e,
title = "Applicability of a particularly simple model to nonlinear elasticity of slide-ring gels with movable cross-links as revealed by unequal biaxial deformation",
abstract = "The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (σy/σx) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.",
author = "Yuuki Kondo and Kenji Urayama and Masatoshi Kidowaki and Koichi Mayumi and Toshikazu Takigawa and Kohzo Ito",
year = "2014",
month = "10",
day = "7",
doi = "10.1063/1.4897134",
language = "English",
volume = "141",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
publisher = "American Institute of Physics Publising LLC",
number = "13",

}

TY - JOUR

T1 - Applicability of a particularly simple model to nonlinear elasticity of slide-ring gels with movable cross-links as revealed by unequal biaxial deformation

AU - Kondo, Yuuki

AU - Urayama, Kenji

AU - Kidowaki, Masatoshi

AU - Mayumi, Koichi

AU - Takigawa, Toshikazu

AU - Ito, Kohzo

PY - 2014/10/7

Y1 - 2014/10/7

N2 - The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (σy/σx) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.

AB - The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (σy/σx) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.

UR - http://www.scopus.com/inward/record.url?scp=84907882597&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907882597&partnerID=8YFLogxK

U2 - 10.1063/1.4897134

DO - 10.1063/1.4897134

M3 - Article

AN - SCOPUS:84907882597

VL - 141

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 13

M1 - 134906

ER -