Rheologica Acta

, 49:1 | Cite as

Planar elongation of soft polymeric networks

  • Mette Krog Jensen
  • Ole Hassager
  • Henrik Koblitz Rasmussen
  • Anne Ladegaard Skov
  • Anders Bach
  • Henning Koldbech
Original Contribution


A new test fixture for the filament stretch rheometer (FSR) has been developed to measure planar elongation of soft polymeric networks with application towards pressure-sensitive adhesives (PSAs). The concept of this new geometry is to elongate a tube-like sample by keeping the perimeter constant. To validate this new technique, soft polymeric networks of poly(propylene oxide) (PPO) were investigated during deformation. Particle tracking and video recording were used to detect to what extent the imposed strain rate and the sample perimeter remained constant. It was observed that, by using an appropriate choice of initial sample height, perimeter, and thickness, the planar stretch ratio will follow \(\lambda(t) = h(t)/h_0= \exp({\dot{\varepsilon}} t)\), with h(t) being the height at time t and \({\dot{\varepsilon}}\) the imposed constant strain rate. The perimeter would decrease by a few percent only, which is found to be negligible. The ideal planar extension in this new fixture was confirmed by finite element simulations. Analysis of the stress difference, σzz − σxx, showed a network response similar to that of the classical neo-Hookean model. As the Deborah number was increased, the stress difference deviated more from the classical prediction due to the dynamic structures in the material. A modified Lodge model using characteristic parameters from linear viscoelastic measurements gave very good stress predictions at all Deborah numbers used in the quasi-linear regime.


Filament stretching Non-linear rheology Planar elongation 


  1. Bach A, Rasmussen HK, Longin P, Hassager O (2002) Growth of non-axisymmetric disturbances of the free surface in the filament stretch rheometer: experiments and simulation. J Non-Newton Fluid Mech 108:163MATHCrossRefGoogle Scholar
  2. Ball R, Doi M, Edwards S, Warner M (1981) Elasticity of entangled networks. Polymer 22(8):1010–1018CrossRefGoogle Scholar
  3. Bernstein EKB, Zapas L (1963) Study of stress relaxation with finite strain. Trans Soc Rheol 7:391–410CrossRefGoogle Scholar
  4. Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, vol 1: fluid dynamics. Whiley Interscience, New YorkGoogle Scholar
  5. Chambon F, Winter HH (1987) Linear viscoelasticity at the gel point of a cross-linking pdms with imbalanced stoichiometry. J Rheol 31(8):683CrossRefADSGoogle Scholar
  6. Currie P (1982) Constitutive equations for polymer melts predicted by the Doi–Edwards and Curtiss–Bird kinetic theory models. J Non-Newton Fluid Mech 11:53–68MATHCrossRefGoogle Scholar
  7. Fetters L, Lohse D, Richter D, Witten T, Zirkel A (1994) Connection between polymer molecular weight, density, chain dimensions, and melt viscoelastic properties. Macromolecules 27(17):4639–4647CrossRefADSGoogle Scholar
  8. Flory P (1941) Molecular size distribution in three dimensional polymers. iii. Tetrafunctional branching units. J Am Chem Soc 63(11):3096–3100CrossRefGoogle Scholar
  9. Gao Z, Nahrup JS, Mark JE, Sakr A (2003) Poly(dimethylsiloxane) coatings for controlled drug release. i. preparation and characterization of pharmaceutically acceptable materials. J Appl Polym Sci 90(3):658–666. http://dx.doi.org/10.1002/app.12700 CrossRefGoogle Scholar
  10. Hansen R, Skov AL, Hassager O (2008) Constitutive equation for polymer networks with phonon fluctuations. Phys Rev E 77(1):011, 802–6. http://link.aps.org/abstract/PRE/v77/e011802 CrossRefGoogle Scholar
  11. Hassager O, Kristensen SB, Larsen JR, Neergaard J (1999) Inflation and instability of a polymeric membrane. J Non-Newton Fluid Mech 88(1–2):185–204MATHCrossRefGoogle Scholar
  12. Jensen M, Bach A, Hassager O, Skov A (2009) Linear rheology of cross-linked polypropylene oxide as a pressure sensitive adhesive. Int J Adhes Adhes 29:687–693CrossRefGoogle Scholar
  13. Kaye A (1962) College of aeronautics. Cranheld Note no 134Google Scholar
  14. Larsen AL, Hansen K, Sommer-Larsen P, Hassager O, Bach A, Ndoni S, Jørgensen M (2003) Elastic properties of nonstoichiometric reacted pdms networks. Macromolecules 36:10063CrossRefADSGoogle Scholar
  15. Larsen AL, Sommer-Larsen P, Hassager O (2004) Some experimental results for the end-linked polydimethylsiloxane network system. e-Polymers 050(050):1–18Google Scholar
  16. Laun HM, Schuch H (1989) Transient elongational viscosities and drawability of polymer melts. J Rheol 33(1):119CrossRefADSGoogle Scholar
  17. Macosko CW, Miller DR (1976) A new derivation of average molecular weights of nonlinear polymers. Macromolecules 9(2):199CrossRefPubMedADSGoogle Scholar
  18. Marcelo A, Villar M, Valles E (1996) Influence of pendant chains on mechanical properties of model poly(dimethylsiloxane) networks. 2. Viscoelastic properties. Macromolecules 29:4081–4089CrossRefADSGoogle Scholar
  19. Marín JMR, Rasmussen HK (2009) Lagrangian finite element method for the simulation of k-bkz fluids with third order accuracy. J Non-Newton Fluid Mech 156:177–188CrossRefGoogle Scholar
  20. Meissner J (1987) Polymer melt elongation, methods, results, and recent developements. Polym Eng Sci 27(8):537CrossRefGoogle Scholar
  21. Miller DR, Macosko CW (1976) A new derivation of post gel properties of network polymers. Macromolecules 9(2):206CrossRefADSGoogle Scholar
  22. Mortensen K (1996) Structural studies of aqueous solutions of PEO-PPO-PEO triblock copolymers, their micellar aggregates and mesophases; a small-angle neutron scattering study. J Phys Condens Matter 8:103–124CrossRefADSGoogle Scholar
  23. Noone R, Goldwyn R, McGrath M, Spear S, Evans G (2007) 50th anniversary plastic surgery research council panel on the future of academic plastic surgery. Plast Reconstr Surg 120(6):1709CrossRefPubMedGoogle Scholar
  24. Rasmussen HK (1999) Time-dependent finite-element method for the simulation of three-dimensional viscoelastic flow with integral models. J Non-Newton Fluid Mech 84:217–232MATHCrossRefMathSciNetGoogle Scholar
  25. Rasmussen HK (2000) Lagrangian viscoelastic flow computations using Rivlin-Sawyers constitutive model. J Non-Newton Fluid Mech 92:227–243MATHCrossRefGoogle Scholar
  26. Rasmussen HK (2002) Lagrangian viscoelastic flow computations using a generalized molecular stress function model. J Non-Newton Fluid Mech 106:107–120MATHCrossRefGoogle Scholar
  27. Rasmussen HK, Christensen JH, Gøttsche S (2000) Inflation of polymer melts into elliptic and circular cylinders. J Non-Newton Fluid Mech 93(2–3):245–263MATHCrossRefGoogle Scholar
  28. Sridhar T, Tirtaatmadja V, Nguyen D, Gupta R (1991) Measurement of extensional viscosity of polymer solutions. J Non-newton Fluid Mech 40(3):271–280CrossRefGoogle Scholar
  29. Urayama K (2008) Network topology–mechanical properties relationships of model elastomers. Polym J(8):669–678Google Scholar
  30. Venkataraman S, Coyne L, Chambon F, Gottlieb M, Winter H (1989) Critical extent of reaction of a Polydimethylsiloxane polymer network. Polymer 30(12):2222–2226CrossRefGoogle Scholar
  31. Villar M, Bibbó M, Valles E (1996) Influence of pendant chains on mechanical properties of model poly(dimethylsiloxane) networks. 1. analysis of the molecular structure of the network. Macromolecules 29:4072–4080CrossRefADSGoogle Scholar
  32. Wagner M, Schaeffer J (1993) Rubbers and polymer melts: Universal aspects of nonlinear stress–strain relations. J Rheol 37:643CrossRefADSGoogle Scholar
  33. Wagner M, Rubio P, Bastian H (2001) The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release. J Rheol 45(6):1387CrossRefADSGoogle Scholar
  34. Wagner MH, Schaeffer J (1994) Assessment of non-linear strain measures for extensional and shearing flows of polymer melts. Rheol Acta 33:506–516CrossRefGoogle Scholar
  35. Wang S, Mark JE (1992) Unimodal and bimodal networks of poly(dimethyl siloxane) in pure shear. J Polymer Science: Part B: Polymer Physics 30:801–807CrossRefGoogle Scholar
  36. Winter HH, Chambon F (1986) Analysis of linear viscoelasticity of a cross-linking polymer at the gel point. J Rheol 30(2):367CrossRefADSGoogle Scholar
  37. Xing X, Goldbart PM, Radzihovsky L (2007) Thermal fluctuations and rubber elasticity. Phys Rev Lett 98(7):075, 502–504CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Mette Krog Jensen
    • 1
  • Ole Hassager
    • 1
  • Henrik Koblitz Rasmussen
    • 2
  • Anne Ladegaard Skov
    • 1
  • Anders Bach
    • 3
  • Henning Koldbech
    • 4
  1. 1.Department of Chemical and Biochemical Engineering, Building 423The Technical University of DenmarkLyngbyDenmark
  2. 2.Department of Mechanical Engineering, Building 423The Technical University of DenmarkLyngbyDenmark
  3. 3.Coloplast A/SGlobal R&D, Holtedam 1HumlebækDenmark
  4. 4.Department of Chemical and Biochemical Engineering, Building 229The Technical University of DenmarkLyngbyDenmark

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