Skip to main content
SpringerLink
Log in

Mesoscale modeling of microgel mechanics and kinetics through the swelling transition

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The mechanics and swelling kinetics of polymeric microgels are simulated using a mesoscale computational model based on dissipative particle dynamics. Microgels are represented by a random elastic network submerged in an explicit viscous solvent. The model is used to probe the effect of different solvent conditions on the bulk modulus of the microgels. Comparison of the simulation results through the volume phase transition reveals favorable agreement with Flory-Rehner’s theory for polymeric gels. The model is also used to examine the microgel swelling kinetics, and is found to be in good agreement with Tanaka’s theory for spherical gels. The simulations show that, during the swelling process, the microgel maintains a nearly homogeneous structure, whereas deswelling is characterized by the formation of chain bundles and network coarsening.

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. Hoffman, A. S. Hydrogels for biomedical applications. Advanced Drug Delivery Reviews, 64, 18–23 (2012)

    Article  Google Scholar 

  2. Chaudhuri, O., Gu, L., Klumpers, D., Darnell, M., Bencherif, S. A., Weaver, J. C., Huebsch, N., Lee, H. P., Lippens, E., and Duda, G. N. Hydrogels with tunable stress relaxation regulate stem cell fate and activity. Nature Materials, 15, 326 (2016)

    Article  Google Scholar 

  3. Shin, S. R., Bae, H., Cha, J. M., Mun, J. Y., Chen, Y. C., Tekin, H., Shin, H., Farshchi, S., Dokmeci, M. R., and Tang, S. Carbon nanotube reinforced hybrid microgels as scaffold materials for cell encapsulation. ACS Nano, 6, 362–372 (2011)

    Article  Google Scholar 

  4. Kim, M. Y. and Kim, J. Y. Chitosan microgels embedded with catalase nanozyme-loaded mesocellular silica foam for glucose-responsive drug delivery. ACS Biomaterials Science and Engineering, 3, 572–578 (2017)

    Article  Google Scholar 

  5. Utech, S., Prodanovic, R., Mao, A. S., Ostafe, R., Mooney, D. J., and Weitz, D. A. Microfluidic generation of monodisperse, structurally homogeneous alginate microgels for cell encapsulation and 3D cell culture. Advanced Healthcare Materials, 4, 1628–1633 (2015)

    Article  Google Scholar 

  6. Hardin, J. O., Fernandez-Nieves, A., Martinez, C. J., and Milam, V. T. Altering colloidal surface functionalization using DNA encapsulated inside monodisperse gelatin microsphere templates. Langmuir, 29, 5534–5539 (2013)

    Article  Google Scholar 

  7. Brown, A. C., Stabenfeldt, S. E., Ahn, B., Hannan, R. T., Dhada, K. S., Herman, E. S., Stefanelli, V., Guzzetta, N., Alexeev, A., Lam, W. A., Lyon, L. A., and Barker, T. H. Ultrasoft microgels displaying emergent platelet-like behaviours. Nature Materials, 13, 1108–1114 (2014)

    Article  Google Scholar 

  8. Douglas, A. M., Fragkopoulos, A. A., Gaines, M. K., Lyon, L. A., Fernandez-Nieves, A., and Barker, T. H. Dynamic assembly of ultrasoft colloidal networks enables cell invasion within restrictive fibrillar polymers. Proceedings of the National Academy of Sciences, 114, 885–890 (2017)

    Article  Google Scholar 

  9. Wu, S. H., Duan, B., Qin, X. H., and Butcher, J. T. Nanofiber-structured hydrogel yarns with pH-response capacity and cardiomyocyte-drivability for bio-microactuator application. Acta Biomaterialia, 60, 144–153 (2017)

    Article  Google Scholar 

  10. Ye, C. H., Nikolov, S. V., Calabrese, R., Dindar, A., Alexeev, A., Kippelen, B., Kaplan, D. L., and Tsukruk, V. V. Self-(un)rolling biopolymer microstructures: rings, tubules, and helical tubules from the same material. Angewandte Chemie International Edition, 54, 8490–8493 (2015)

    Article  Google Scholar 

  11. Ye, C. H., Nikolov, S. V., Geryak, R. D., Calabrese, R., Ankner, J. F., Alexeev, A., Kaplan, D. L., and Tsukruk, V. V. Bimorph silk microsheets with programmable actuating behavior: experimental analysis and computer simulations. ACS Applied Materials and Interfaces, 8, 17694–17706 (2016)

    Article  Google Scholar 

  12. Vikram, S. A. and Sitti, M. Targeted drug delivery and imaging using mobile milli/microrobots: a promising future towards theranostic pharmaceutical design. Current Pharmaceutical Design, 22, 1418–1428 (2016)

    Article  Google Scholar 

  13. Nikolov, S. V., Yeh, P. D., and Alexeev, A. Self-propelled microswimmer actuated by stimuli- sensitive bilayered hydrogel. ACS Macro Letters, 4, 84–88 (2015)

    Article  Google Scholar 

  14. Masoud, H., Bingham, B. I., and Alexeev, A. Designing maneuverable micro-swimmers actuated by responsive gel. Soft Matter, 8, 8944–8951 (2012)

    Article  Google Scholar 

  15. Du, H. B. and Qian, X. H. Molecular dynamics simulations of PNIPAM-co-PEGMA copolymer hydrophilic to hydrophobic transition in NaCl solution. Journal of Polymer Science Part B: Polymer Physics, 49, 1112–1122 (2011)

    Article  Google Scholar 

  16. Kang, M. K. and 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 

  17. Mills, Z. G., Mao, W. B., and Alexeev, A. Mesoscale modeling: solving complex flows in biology and biotechnology. Trends in Biotechnology, 31, 426–434 (2013)

    Article  Google Scholar 

  18. Yeh, P. D. and Alexeev, A. Mesoscale modelling of environmentally responsive hydrogels: emerg- ing applications. Chemical Communications, 51, 10083–10095 (2015)

    Article  Google Scholar 

  19. Espanol, P. and Warren, P. Perspective: dissipative particle dynamics. The Journal of Chemical Physics, 146, 150901 (2017)

    Article  Google Scholar 

  20. Groot, R. D. and Warren, P. B. Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. Journal of Chemical Physics, 107, 4423–4435 (1997)

    Article  Google Scholar 

  21. Hoogerbrugge, P. J. and Koelman, J. M. V. A. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhysics Letters, 19, 155–160 (1992)

    Article  Google Scholar 

  22. Espanol, P. and Warren, P. Statistical-mechanics of dissipative particle dynamics. Europhysics Letters, 30, 191–196 (1995)

    Article  Google Scholar 

  23. Glotzer, S. C. and Paul, W. Molecular and mesoscale simulation methods for polymer materials. Annual Review of Materials Research, 32, 401–436 (2002)

    Article  Google Scholar 

  24. Groot, R. D. and Rabone, K. L. Mesoscopic simulation of cell membrane damage, morphology change and rupture by nonionic surfactants. Biophysical Journal, 81, 725–736 (2001)

    Article  Google Scholar 

  25. Chen, S., Phan-Thien, N., Fan, X. J., and Khoo, B. C. Dissipative particle dynamics simulation of polymer drops in a periodic shear flow. Journal of Non-Newtonian Fluid Mechanics, 118, 65–81 (2004)

    Article  MATH  Google Scholar 

  26. Fedosov, D. A., Karniadakis, G. E., and Caswell, B. Dissipative particle dynamics simulation of depletion layer and polymer migration in micro and nanochannels for dilute polymer solutions. Journal of Chemical Physics, 128, 144903 (2008)

    Article  Google Scholar 

  27. Spenley, N. A. Scaling laws for polymers in dissipative particle dynamics. Europhysics Letters, 49, 534–540 (2000)

    Article  Google Scholar 

  28. Ripoll, M., Ernst, M. H., and Espanol, P. Large scale and mesoscopic hydrodynamics for dissipative particle dynamics. Journal of Chemical Physics, 115, 7271–7284 (2001)

    Article  Google Scholar 

  29. Lee, M. T., Vishnyakov, A. N., and Alexander, V. Modeling proton dissociation and transfer using dissipative particle dynamics simulation. Journal of Chemical Theory and Computation, 11, 4395–4403 (2015)

    Article  Google Scholar 

  30. Li, N. K., Kuang, H. H., Fuss, W. H., and Yingling, Y. G. Salt responsive morphologies of ssDNA-based triblock polyelectrolytes in semi-dilute regime: effect of volume fractions and polyelectrolyte length. Macromolecular Rapid Communications, 38, 1700422 (2017)

    Article  Google Scholar 

  31. Groot, R. D. Electrostatic interactions in dissipative particle dynamics-simulation of polyelectrolytes and anionic surfactants. Journal of Chemical Physics, 118, 11265–11277 (2003)

    Article  Google Scholar 

  32. Ibergay, C., Malfreyt, P., and Tildesley, D. J. Electrostatic interactions in dissipative particle dynamics: toward a mesoscale modeling of the polyelectrolyte brushes. Journal of Chemical Theory and Computation, 5, 3245–3259 (2009)

    Article  Google Scholar 

  33. Boek, E. S., Coveney, P. V., Lekkerkerker, H. N. W., and van der Schoot, P. Simulating the rheology of dense colloidal suspensions using dissipative particle dynamics. Physical Review E, 55, 3124–3133 (1997)

    Article  Google Scholar 

  34. Symeonidis, V., Karniadakis, G. E., and Caswell, B. Dissipative particle dynamics simulations of polymer chains: scaling laws and shearing response compared to DNA experiments. Physical Review Letters, 95, 076001 (2005)

    Article  Google Scholar 

  35. Ganzenmuller, G. C., Hiermaier, S., and Steinhauser, M. O. Shock-wave induced damage in lipid bilayers: a dissipative particle dynamics simulation study. Soft Matter, 7, 4307–4317 (2011)

    Article  Google Scholar 

  36. Chu, X. L., Aydin, F., and Meenakshi, D. Modeling interactions between multicomponent vesicles and antimicrobial peptide-inspired nanoparticles. ACS Nano, 10, 7351–7361 (2016)

    Article  Google Scholar 

  37. Pivkin, I. V., Peng, Z. L., Karniadakis, G. E., Buffet, P. A., Dao, M., and Suresh, S. A Biomechanics of red blood cells in human spleen and consequences for physiology and disease. Proceedings of the National Academy of Sciences of the United States of America, 114, E4521 (2017)

  38. Masoud, H. and Alexeev, A. Permeability and diffusion through mechanically deformed random polymer networks. Macromolecules, 43, 10117–10122 (2010)

    Article  Google Scholar 

  39. Masoud, H. and Alexeev, A. Controlled release of nanoparticles and macromolecules from re- sponsive microgel capsules. ACS Nano, 6, 212–219 (2012)

    Article  Google Scholar 

  40. Sirk, T. W., Slizoberg, Y. R., Brennan, J. K., Lisal, M., and Andzelm, J. W. An enhanced entangled polymer model for dissipative particle dynamics. Journal of Chemical Physics, 136, 134903 (2012)

    Article  Google Scholar 

  41. Tarjan, R. Depth-first search and linear graph algorithms. SIAM Journal on Computing, 1, 146–160 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  42. Pelaez-Fernandez, M., Souslov, A., Lyon, L. A., Goldbart, P. M., and Fernandez-Nieves, A. Impact of single-particle compressibility on the fluid-solid phase transition for ionic microgel suspensions. Physical Review Letters, 114, 098303 (2015)

    Article  Google Scholar 

  43. Senff, H. and Richtering, W. Influence of cross-link density on rheological properties of temperature-sensitive microgel suspensions. Colloid and Polymer Science, 278, 830–840 (2000)

    Article  Google Scholar 

  44. Fernandez-Nieves, A., Wyss, H., Mattsson, J., and Weitz, D. A. Microgel Suspensions: Fundamentals and Applications, John Wiley and Sons, Singapore (2011)

    Book  Google Scholar 

  45. De Gennes, P. G. Scaling Concepts in Polymer Physics, Cornell University Press, New York (1979)

    Google Scholar 

  46. Annabi, N., Nichol, J. W., Zhong, X., Ji, C. D., Koshy, S., Khademhosseini, A., and Dehghani, F. Controlling the porosity and microarchitecture of hydrogels for tissue engineering. Tissue Engineering Part B: Reviews, 16, 371–383 (2010)

    Article  Google Scholar 

  47. Stukowski, A. Visualization and analysis of atomistic simulation data with OVITO—the open visualization tool. Modelling and Simulation in Materials Science and Engineering, 18, 015012 (2009)

    Article  Google Scholar 

  48. Sierra-Martin, B., Laporte, Y., South, A. B., Lyon, L. A., and Fernandez-Nieves, A. Bulk modulus of poly (N-isopropylacrylamide) microgels through the swelling transition. Physical Review E, 84, 011406 (2011)

    Article  Google Scholar 

  49. Hirotsu, S. Static and time-dependent properties of polymer gels around the volume phase transition. Phase Transitions: A Multinational Journal, 47, 183–240 (1994)

    Article  Google Scholar 

  50. Sliozberg, Y. R., Andzelm, J. W., Brennan, J. K., Vanlandingham, M. R., Pryamitsyn, V., and Ganesan, V. Modeling viscoelastic properties of triblock copolymers: a DPD simulation study. Journal of Polymer Science Part B: Polymer Physics, 48, 15–25 (2010)

    Article  Google Scholar 

  51. Hirotsu, S. Coexistence of phases and the nature of first-order phase transition in poly-N-isopropylacrylamide gels. Responsive Gels: Volume Transitions II, Springer, Berlin, Heidelberg, 1–26 (1993)

    Google Scholar 

  52. Lopez-Leon, T. and Fernandez-Nieves, A. Macroscopically probing the entropic influence of ions: deswelling neutral microgels with salt. Physical Review E, 75, 011801 (2007)

    Article  Google Scholar 

  53. Fernandez-Barbero, A., Fernandez-Nieves, A., Grillo, I., and Lopez-Cabarcos, E. Structural modifications in the swelling of inhomogeneous microgels by light and neutron scattering. Physical Review E, 66, 051803 (2002)

    Article  Google Scholar 

  54. Tanaka, T. and Fillmore, D. J. Kinetics of swelling of gels. The Journal of Chemical Physics, 70, 1214–1218 (1979)

    Article  Google Scholar 

  55. Geissler, E., Bohidar, H. B., and Hecht, A. M. Collective diffusion in semi-dilute gels at the theta temperature. Macromolecules, 18, 949–953 (1985)

    Article  Google Scholar 

  56. Shibayama, M., Morimoto, M., and Nomura, S. J. Phase separation induced mechanical transi- tion of poly (N-isopropylacrylamide) water isochore gels. Macromolecules, 27, 5060–5066 (1994)

    Article  Google Scholar 

  57. Patil, N., Soni, J., Ghosh, N., and De, P. Swelling-induced optical anisotropy of thermoresponsive hydrogels based on poly (2-(2-methoxyethoxy) ethyl methacrylate): deswelling kinetics probed by quantitative Mueller matrix polarimetry. The Journal of Physical Chemistry B, 116, 13913–13921 (2012)

    Article  Google Scholar 

  58. Hirotsu, S. Softening of bulk modulus and negative Poisson’s ratio near the volume phase transition of polymer gels. The Journal of Chemical Physics, 94, 3949–3957 (1991)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    S. Nikolov & A. Alexeev

  2. School of Physics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    A. Fernandez-Nieves

Authors
  1. S. Nikolov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Fernandez-Nieves
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Alexeev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Alexeev.

Additional information

Citation: Nikolov, S., Fernandez-Nieves, A., and Alexeev, A. Mesoscale modeling of microgel mechanics and kinetics through the swelling transition. Applied Mathematics and Mechanics (English Edition), 39(1), 47–62 (2018) https://doi.org/10.1007/s10483-018-2259-6

Project supported by the National Science Foundation of U. S.A. (Nos.DMR-1255288, DMR-1609841, and DGE-1650044)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nikolov, S., Fernandez-Nieves, A. & Alexeev, A. Mesoscale modeling of microgel mechanics and kinetics through the swelling transition. Appl. Math. Mech.-Engl. Ed. 39, 47–62 (2018). https://doi.org/10.1007/s10483-018-2259-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-018-2259-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation