Skip to main content
SpringerLink
Log in

Separating viscoelasticity and poroelasticity of gels with different length and time scales

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Viscoelasticity and poroelasticity commonly coexist as time-dependent behaviors in polymer gels. Engineering applications often require knowledge of both behaviors separated; however, few methods exist to decouple viscoelastic and poroelastic properties of gels. We propose a method capable of separating viscoelasticity and poroelasticity of gels in various mechanical tests. The viscoelastic characteristic time and the poroelastic diffusivity of a gel define an intrinsic material length scale of the gel. The experimental setup gives a sample length scale, over which the solvent migrates in the gel. By setting the sample length to be much larger or smaller than the material length, the viscoelasticity and poroelasticity of the gel will dominate at different time scales in a test. Therefore, the viscoelastic and poroelastic properties of the gel can be probed separately at different time scales of the test. We further validate the method by finite-element models and stress-relaxation experiments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zwieniecki, M.A., Melcher, P.J., Holbrook, N.M.: Hydrogel control of xylem hydraulic resistance in plants. Science 291, 1059–1062 (2001)

    Article  Google Scholar 

  2. Mow, V.C., Kuei, S.C., Lai, W.M., et al.: Biphasic creep and stress-relaxation of articular-cartilage in compression—heory and experiments. J. Biomech. Eng.-Trans. ASME 102, 73–84 (1980)

    Article  Google Scholar 

  3. Liu, Z., Swaddiwudhipong, S., Hong, W.: Pattern formation in plants via instability theory of hydrogels. Soft Matter 9, 577–587 (2013)

    Article  Google Scholar 

  4. Liu, Z., Hong, W., Suo, Z., et al.: Modeling and simulation of buckling of polymeric membrane thin film gel. Computational Materials Science 49, S60–S64 (2010)

    Article  Google Scholar 

  5. Zhao, X., Kim, J., Cezar, C.A., et al.: Active scaffolds for ondemand drug and cell delivery. Proceedings of the National Academy of Sciences of the United States of America 108, 67–72 (2011)

    Article  Google Scholar 

  6. Lee, K.Y., Mooney, D.J.: Hydrogels for tissue engineering. Chemical Reviews 101, 1869–1879 (2001)

    Article  Google Scholar 

  7. Luo, Y., Shoichet, M.S.: A photolabile hydrogel for guided three-dimensional cell growth and migration. Nature materials 3, 249–253 (2004)

    Article  Google Scholar 

  8. Richter, A., Paschew, G., Klatt, S., et al.: Review on hydrogelbased pH sensors and microsensors. Sensors 8, 561–581 (2008)

    Article  Google Scholar 

  9. Gerlach, G., Guenther, M., Sorber, J., et al.: Chemical and pH sensors based on the swelling behavior of hydrogels. Sensors and Actuators B: Chemical 111, 555–561 (2005)

    Article  Google Scholar 

  10. Suo, Z.: Theory of dielectric elastomers. Acta Mechanica Solida Sinica 23, 549–578 (2010)

    Article  Google Scholar 

  11. Beebe, D.J., Moore, J.S., Bauer, J.M., et al.: Functional hydrogel structures for autonomous flow control inside microfluidic channels. Nature 404, 588–590 (2000)

    Article  Google Scholar 

  12. He, T., Li, M., Zhou, J.: Modeling deformation and contacts of pH sensitive hydrogels for microfluidic flow control. Soft Matter 8, 3083–3089 (2012)

    Article  Google Scholar 

  13. Cai, S., Lou, Y., Ganguly, P., et al.: Force generated by a swelling elastomer subject to constraint. Journal of Applied Physics 107, 103535 (2010)

    Article  Google Scholar 

  14. Barbut, S., Foegeding, E.A.: Ca2+-Induced gelation of preheated whey-protein isolate. J. Food Sci. 58, 867–871 (1993)

    Article  Google Scholar 

  15. Hong, W., Zhao, X., Zhou, J., et al.: A theory of coupled diffusion and large deformation in polymeric gels. Journal of the Mechanics and Physics of Solids 56, 1779–1793 (2008)

    Article  MATH  Google Scholar 

  16. Yoon, J., Cai, S., Suo, Z., et al.: Poroelastic swelling kinetics of thin hydrogel layers: Comparison of theory and experiment. Soft Matter 6, 6004–6012 (2010)

    Article  Google Scholar 

  17. Li, Y., Tanaka, T.: Kinetics of swelling and shrinking of gels. The Journal of Chemical Physics 92, 1365–1371 (1990)

    Article  Google Scholar 

  18. Quesada-Péez, M., Maroto-Centeno, J.A., Forcada, J., et al.: Gel swelling theories: The classical formalism and recent approaches. Soft Matter 7, 10536–10547 (2011)

    Article  Google Scholar 

  19. Cai, S., Suo, Z.: Equations of state for ideal elastomeric gels. EPL (Europhysics Letters) 97, 34009 (2012)

    Article  Google Scholar 

  20. Hong, W., Liu, Z., Suo, Z.: Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load. International Journal of Solids and Structures 46, 3282–3289 (2009)

    Article  MATH  Google Scholar 

  21. Kang, M.K., Huang, R.: A variational approach and finite element implementation for swelling of polymeric hydrogels under geometric constraints. Journal of Applied Mechanics 77, 061004 (2010)

    Article  Google Scholar 

  22. Zhang, J., Zhao, X., Suo, Z., et al.: A finite element method for transient analysis of concurrent large deformation and mass transport in gels. Journal of Applied Physics 105, 093522 (2009)

    Article  Google Scholar 

  23. Zhou, J., Huang, G., Li, M., et al.: Stress evolution in a phaseseparating polymeric gel. Modelling and Simulation in Materials Science and Engineering 18, 025002 (2010)

    Article  Google Scholar 

  24. Ferry, J.D.: Viscoelastic Properties of Polymers. John Wiley & Sons, Inc., New York (1980)

    Google Scholar 

  25. Zhao, X., Huebsch, N., Mooney, D.J., et al.: Stress-relaxation behavior in gels with ionic and covalent crosslinks. Journal of Applied Physics 107, 063509 (2010)

    Article  Google Scholar 

  26. Chen, D.T., Wen, Q., Janmey, P.A., et al.: Rheology of soft materials. Annual Review of Condensed Matter Physics 1, 301–322 (2010)

    Article  Google Scholar 

  27. Cai, S., Hu, Y., Zhao, X., et al.: Poroelasticity of a covalently crosslinked alginate hydrogel under compression. Journal of Applied Physics 108, 113514 (2010)

    Article  Google Scholar 

  28. Hu, Y., Chan, E.P., Vlassak, J.J., et al.: Poroelastic relaxation indentation of thin layers of gels. Journal of Applied Physics 110, 086103 (2011)

    Article  Google Scholar 

  29. Hu, Y., You, J.O., Auguste, D.T., et al.: Indentation: A simple, nondestructive method for characterizing the mechanical and transport properties of pH-sensitive hydrogels. J. Mater. Res. 27, 152–160 (2012)

    Article  Google Scholar 

  30. Hu, Y., Chen, X., Whitesides, G.M., et al.: Indentation of polydimethylsiloxane submerged in organic solvents. J.Mater. Res. 26, 785–795 (2011)

    Article  Google Scholar 

  31. Kalcioglu, Z.I., Mahmoodian, R., Hu, Y., et al.: From macro-to microscale poroelastic characterization of polymeric hydrogels via indentation. Soft Matter 8, 3393–3398 (2012)

    Article  Google Scholar 

  32. Strange, D.G., Fletcher, T.L., Tonsomboon, K., et al.: Separating poroviscoelastic deformation mechanisms in hydrogels. Appl. Phys. Lett. 102, 031913 (2013)

    Article  Google Scholar 

  33. Hyland, L.L., Taraban, M.B., Feng, Y., et al.: Viscoelastic properties and nanoscale structures of composite oligopeptidepolysaccharide hydrogels. Biopolymers 97, 177–188 (2012)

    Article  Google Scholar 

  34. Olberding, J.E., Francis Suh, J.: A dual optimization method for the material parameter identification of a biphasic poroviscoelastic hydrogel: Potential application to hypercompliant soft tissues. J. Biomech. 39, 2468–2475 (2006)

    Article  Google Scholar 

  35. Cheng, L., Xia, X., Scriven, L.E., et al.: Spherical-tip indentation of viscoelastic material. Mech. Mater. 37, 213–226 (2005)

    Article  Google Scholar 

  36. Constantinides, G., Kalcioglu, Z.I., McFarland, M., et al.: Probing mechanical properties of fully hydrated gels and biological tissues. J. Biomech. 41, 3285–3289 (2008)

    Article  Google Scholar 

  37. Ebenstein, D.M., Pruitt, L.A.: Nanoindentation of soft hydrated materials for application to vascular tissues. J. Biomed. Mater. Res. Part A 69A, 222–232 (2004)

    Article  Google Scholar 

  38. Galli, M., Oyen, M.L.: Fast identification of poroelastic parameters from indentation tests. CMES-Comp. Model. Eng. Sci. 48, 241–269 (2009)

    MATH  MathSciNet  Google Scholar 

  39. Hui, C.Y., Muralidharan, V.: Gel mechanics: A comparison of the theories of Biot and Tanaka, Hocker, and Benedek. J. Chem. Phys. 123, 154905 (2005)

    Article  Google Scholar 

  40. Kaufman, J.D., Miller, G.J., Morgan, E.F., et al.: Timedependent mechanical characterization of poly(2-hydroxyethyl methacrylate) hydrogels using nanoindentation and unconfined compression. J. Mater. Res. 23, 1472–1481 (2008)

    Article  Google Scholar 

  41. Lin, Y.Y., Hu, B.W.: Load relaxation of a flat rigid circular indenter on a gel half space. J. Non-Cryst. Solids 352, 4034–4040 (2006)

    Article  Google Scholar 

  42. Oyen, M.L.: Poroelastic nanoindentation responses of hydrated bone. J. Mater. Res. 23, 1307–1314 (2008)

    Article  Google Scholar 

  43. Hui, C.Y., Lin, Y.Y., Chuang, F.C., et al.: A contact mechanics method for characterizing the elastic properties and permeability of gels. J. Polym. Sci. Pt. B-Polym. Phys. 44, 359–370 (2006)

    Article  Google Scholar 

  44. Hu, Y.H., Zhao, X.H., Vlassak, J.J., et al.: Using indentation to characterize the poroelasticity of gels. Appl. Phys. Lett. 96, 121904 (2010)

    Article  Google Scholar 

  45. Galli, M., Comley, K.S.C., Shean, T.A.V., et al.: Viscoelastic and poroelastic mechanical characterization of hydrated gels. J. Mater. Res. 24, 973–979 (2009)

    Article  Google Scholar 

  46. Galli, M., Fornasiere, E., Cugnoni, J., et al.: Poroviscoelastic characterization of particle-reinforced gelatin gels using indentation and homogenization. Journal of the Mechanical Behavior of Biomedical Materials 4, 610–617 (2011)

    Article  Google Scholar 

  47. Chiravarambath, S., Simha, N.K., Namani, R., et al.: Poroviscoelastic cartilage properties in the mouse from indentation. Journal of biomechanical engineering 131, 011004 (2009)

    Article  Google Scholar 

  48. Li, J., Hu, Y., Vlassak, J.J., et al.: Experimental determination of equations of state for ideal elastomeric gels. Soft Matter 8, 8121–8128 (2012)

    Article  Google Scholar 

  49. Liu, Y., Chan-Park, M.B.: Hydrogel based on interpenetrating polymer networks of dextran and gelatin for vascular tissue engineering. Biomaterials 30, 196–207 (2009)

    Article  Google Scholar 

  50. Hui, C., Feng, X., Jagota, A.: In situ measurement of the viscoelastic modulus of gels using pure twist-theory. Soft Matter 9, 913–920 (2013)

    Article  Google Scholar 

  51. Wang, X., Hong, W.: A visco-poroelastic theory for polymeric gels. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Science 468, 3824–3841 (2012)

    Article  MathSciNet  Google Scholar 

  52. Hu, Y., Suo, Z.: Viscoelasticity and poroelasticity in elastomeric gels. Acta Mechanica Solida Sinica 25, 441–458 (2012)

    Article  Google Scholar 

  53. Biot, M.: Theory of deformation of a porous viscoelastic anisotropic solid. Journal of Applied Physics 27, 459–467 (1956)

    Article  MathSciNet  Google Scholar 

  54. Weitsman, Y.: Stress assisted diffusion in elastic and viscoelastic materials. Journal of the Mechanics and Physics of Solids 35, 73–94 (1987)

    Article  MATH  Google Scholar 

  55. Weitsman, Y.: A continuum diffusion model for viscoelastic materials. Journal of Physical Chemistry 94, 961–968 (1990)

    Article  Google Scholar 

  56. Govindjee, S., Simo, J.C.: Coupled stress-diffusion: Case II. Journal of the Mechanics and Physics of Solids 41, 863–887 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  57. McBride, A.T., Bargmann, S., Steinmann, P.: Geometrically nonlinear continuum thermomechanics coupled to diffusion: a framework for case II diffusion. Advances in Extended and Multifield Theories for Continua. Springer, 89–107 (2011)

    Chapter  Google Scholar 

  58. Gong, J.P., Katsuyama, Y., Kurokawa, T., et al.: Doublenetwork hydrogels with extremely high mechanical strength. Advanced Materials 15, 1155–1158 (2003)

    Article  Google Scholar 

  59. Zhao, X.H.: A theory for large deformation and damage of interpenetrating polymer networks. Journal of the Mechanics and Physics of Solids 60, 319–332 (2012)

    Article  Google Scholar 

  60. Wang, X., Hong, W.: Pseudo-elasticity of a double network gel. Soft Matter 7, 8576–8581 (2011)

    Article  Google Scholar 

  61. Sun, J.Y., Zhao, X., Illeperuma, W.R., et al.: Highly stretchable and tough hydrogels. Nature 489, 133–136 (2012)

    Article  Google Scholar 

  62. An, Y., Solis, F.J., Jiang, H.: A thermodynamic model of physical gels. Journal of the Mechanics and Physics of Solids 58, 2083–2099 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  63. Henderson, K.J., Zhou, T.C., Otim, K.J., et al.: Ionically cross-linked triblock copolymer hydrogels with high strength. Macromolecules 43, 6193–6201 (2010)

    Article  Google Scholar 

  64. Hui, C.Y., Long, R.: A constitutive model for the large deformation of a self-healing gel. Soft Matter 8, 8209–8216 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Soft Active Materials Laboratory, Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, 27708, USA

    Qi-Ming Wang, Anirudh C. Mohan & Xuan-He Zhao

  2. Cambridge University Engineering Department, Trumpington St., CB2 1PZ, Cambridge, UK

    Michelle L. Oyen

Authors
  1. Qi-Ming Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anirudh C. Mohan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michelle L. Oyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xuan-He Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuan-He Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, QM., Mohan, A.C., Oyen, M.L. et al. Separating viscoelasticity and poroelasticity of gels with different length and time scales. Acta Mech Sin 30, 20–27 (2014). https://doi.org/10.1007/s10409-014-0015-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-014-0015-z

Keywords

Search

Navigation