attached chain, which may be stretched before the exchange, is relaxed [17]. Bond
exchange can also be considered as a chain detachment and reattachment process,
but the detachment and reattachment occur simultaneously and therefore at the same
rate. The macroscopic viscoelasticity caused by bond exchange can also be modeled
using the MDT [46] or the TNT [32].
Acknowledgment R.L. acknowledges the support from a CAREER award from the National
Science Foundation (CMMI-1752449).
References
1. Rubinstein M, Colby RH (2003) Polymer physics (chemistry). Oxford University Press,
New York
2. Treloar LRG (1943) The elasticity of a network of long-chain molecules I. Trans Faraday Soc
39:36–41
3. Treloar LRG (1973) The elasticity and related properties of rubbers. Rep Prog Phys 36:755–826
4. Boyce MC, Arruda EM (2000) Constitutive models of rubber elasticity: a review. Rubber Chem
Technol 73:504–523
5. Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley,
Chichester
6. Mooney M (1940) A theory of large elastic deformation. J Appl Phys 11:582–592
7. Rivlin RS (1948) Large elastic deformations of isotropic materials. IV. Further developments of
the general theory. Philos Trans R Soc A Math Phys Eng Sci 241:379–397
8. Ogden RW (1972) Large deformation isotropic elasticity - on the correlation of theory and
experiment for incompressible rubberlike solids. Proc R Soc A Math Phys Eng Sci
326:565–584
9. Gent AN (1996) A new constitutive relation for rubber. Rubber Chem Technol 69:59–61
10. Wang MC, Guth E (1952) Statistical theory of networks of non-Gaussian flexible chains.
J Chem Phys 20:1144–1157
11. Flory PJ, Rehner J (1943) Statistical mechanics of cross-linked polymer networks I. Rubberlike
elasticity. J Chem Phys 11:512–520
12. Arruda EM, Boyce MC (1993) A three-dimensional constitutive model for the large stretch
behavior of rubber elastic materials. J Mech Phys Solids 41:389–412
13. Wu PD, Van Der Giessen E (1993) On improved network models for rubber elasticity and their
applications to orientation hardening in glassy polymers. J Mech Phys Solids 41:427–456
14. Wojtecki RJ, Meador MA, Rowan SJ (2011) Using the dynamic bond to access macroscopically responsive structurally dynamic polymers. Nat Mater 10:14–27
15. Narita T, Mayumi K, Ducouret G, Hébraud P (2013) Viscoelastic properties of poly(vinyl
alcohol) hydrogels having permanent and transient cross-links studied by microrheology,
classical rheometry, and dynamic light scattering. Macromolecules 46:4174–4183
16. Chen X et al (2002) A thermally re-mendable cross-linked polymeric material. Science
295:1698–1702
17. Montarnal D, Capelot M, Tournilhac F, Leibler L (2011) Silica-like malleable materials from
permanent organic networks. Science 334:965–968
18. Creton C (2017) 50th anniversary perspective: networks and gels: soft but dynamic and tough.
Macromolecules 50:8297–8316
19. Gong JP, Katsuyama Y, Kurokawa T, Osada Y (2003) Double-network hydrogels with
extremely high mechanical strength. Adv Mater 15:1155–1158
20. Zhao X (2014) Multi-scale multi-mechanism design of tough hydrogels: building dissipation
into stretchy networks. Soft Matter 10:672–687
Mechanics of Polymer Networks with Dynamic Bonds
163
exchange can also be considered as a chain detachment and reattachment process,
but the detachment and reattachment occur simultaneously and therefore at the same
rate. The macroscopic viscoelasticity caused by bond exchange can also be modeled
using the MDT [46] or the TNT [32].
Acknowledgment R.L. acknowledges the support from a CAREER award from the National
Science Foundation (CMMI-1752449).
References
1. Rubinstein M, Colby RH (2003) Polymer physics (chemistry). Oxford University Press,
New York
2. Treloar LRG (1943) The elasticity of a network of long-chain molecules I. Trans Faraday Soc
39:36–41
3. Treloar LRG (1973) The elasticity and related properties of rubbers. Rep Prog Phys 36:755–826
4. Boyce MC, Arruda EM (2000) Constitutive models of rubber elasticity: a review. Rubber Chem
Technol 73:504–523
5. Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley,
Chichester
6. Mooney M (1940) A theory of large elastic deformation. J Appl Phys 11:582–592
7. Rivlin RS (1948) Large elastic deformations of isotropic materials. IV. Further developments of
the general theory. Philos Trans R Soc A Math Phys Eng Sci 241:379–397
8. Ogden RW (1972) Large deformation isotropic elasticity - on the correlation of theory and
experiment for incompressible rubberlike solids. Proc R Soc A Math Phys Eng Sci
326:565–584
9. Gent AN (1996) A new constitutive relation for rubber. Rubber Chem Technol 69:59–61
10. Wang MC, Guth E (1952) Statistical theory of networks of non-Gaussian flexible chains.
J Chem Phys 20:1144–1157
11. Flory PJ, Rehner J (1943) Statistical mechanics of cross-linked polymer networks I. Rubberlike
elasticity. J Chem Phys 11:512–520
12. Arruda EM, Boyce MC (1993) A three-dimensional constitutive model for the large stretch
behavior of rubber elastic materials. J Mech Phys Solids 41:389–412
13. Wu PD, Van Der Giessen E (1993) On improved network models for rubber elasticity and their
applications to orientation hardening in glassy polymers. J Mech Phys Solids 41:427–456
14. Wojtecki RJ, Meador MA, Rowan SJ (2011) Using the dynamic bond to access macroscopically responsive structurally dynamic polymers. Nat Mater 10:14–27
15. Narita T, Mayumi K, Ducouret G, Hébraud P (2013) Viscoelastic properties of poly(vinyl
alcohol) hydrogels having permanent and transient cross-links studied by microrheology,
classical rheometry, and dynamic light scattering. Macromolecules 46:4174–4183
16. Chen X et al (2002) A thermally re-mendable cross-linked polymeric material. Science
295:1698–1702
17. Montarnal D, Capelot M, Tournilhac F, Leibler L (2011) Silica-like malleable materials from
permanent organic networks. Science 334:965–968
18. Creton C (2017) 50th anniversary perspective: networks and gels: soft but dynamic and tough.
Macromolecules 50:8297–8316
19. Gong JP, Katsuyama Y, Kurokawa T, Osada Y (2003) Double-network hydrogels with
extremely high mechanical strength. Adv Mater 15:1155–1158
20. Zhao X (2014) Multi-scale multi-mechanism design of tough hydrogels: building dissipation
into stretchy networks. Soft Matter 10:672–687
Mechanics of Polymer Networks with Dynamic Bonds
163