Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Diffusion of rigid nanoparticles in crowded polymer-network hydrogels: dominance of segmental density over crosslinking density

  • 773 Accesses

  • 1 Citations


Swollen polymer-network gels usually exhibit notable spatial inhomogeneity of their crosslinking density. The effect of this inhomogeneity on the permeability of the gel to small particles is of major importance in many applications such as those in analytical separation technology. To systematically address this effect, we mimic inhomogeneous polymer-network gels by dense-packed pastes of sub-micrometer-sized microgel building blocks with two distinctly different crosslinking degrees. The diffusive mobility of rigid nanoparticle tracers within these inhomogeneous pastes that contain purposely imparted densely and loosely cross-linked local domains is studied by spatially resolved dual-focus fluorescence correlation spectroscopy on a sub-micrometer length scale. The outcome of this investigation is that the sub-micrometer-scale tracer diffusivity of the tracers is not affected by the gel-matrix crosslinking density, and hence, also not by its spatial inhomogeneity. Instead, the tracer diffusion is dominantly hindered by the high density of polymer segments in the deswollen gel matrixes.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4


  1. 1.

    Plamper FA, Richtering W (2017) Acc Chem Res 50:131–140. doi:10.1021/acs.accounts.6b00544

  2. 2.

    Hoare TR, Kohane DS (2008) Hydrogels in drug delivery: progress and challenges. Polymer 49(8):1993–2007

  3. 3.

    Sivakumaran D, Maitland D, Hoare T (2011) Injectable microgel-hydrogel composites for prolonged small-molecule drug delivery. Biomacromolecules 12(11):4112–4120

  4. 4.

    Kanazawa H, Sunamoto T, Ayano E, Matsushima Y, Kikuchi A, Okano T (2002) Temperature-responsive chromatography using poly-(N-isopropylacrylamide) hydrogel-modified silica. Anal Sci 18:45–48

  5. 5.

    Wang O, Samitsu S, Ichinose I (2011) Ultrafiltration membranes composed of highly cross-linked cationic polymer gel: the network structure and superior separation performance. Adv Mater 23(17):2004–2008

  6. 6.

    Muhr AH, Blanshard JMV (1982) Diffusion in gels. Polymer 23:1012–1026

  7. 7.

    Bastide J, Leibler L (1988) Large-scale heterogeneities in randomly cross-linked networks. Macromolecules 21(8):2647–2649

  8. 8.

    Nishi K, Asai H, Fujii K, Han YS, Kim TH, Sakai T, Shibayama M (2014) Small-angle neutron scattering study on defect-controlled polymer networks. Macromolecules 47(5):1801–1809

  9. 9.

    Nishio I, Reina JC, Bansil R (1987) Quasielastic light-scattering study of the movement of particles in gels. Phys Rev Lett 59(6):684–687

  10. 10.

    Reina JC, Bansil R, Koňák C (1990) Dynamics of probe particles in polymer solutions and gels. Polymer 31(6):1038–1044

  11. 11.

    Lee CH, Crosby AJ, Emrick T, Hayward RC (2014) Characterization of heterogeneous polyacrylamide hydrogels by tracking of single quantum dots. Macromolecules 47(2):741–749

  12. 12.

    Cai LH, Panyukov S, Rubinstein M (2015) Hopping diffusion of nanoparticles in polymer matrices. Macromolecules 48(3):847–862

  13. 13.

    Kondo S, Sakurai H, Chung U, Sakai T (2013) Mechanical properties of polymer gels with bimodal distribution in strand length. Macromolecules 46(17):7027–7033

  14. 14.

    Di Lorenzo F, Seiffert S (2013) Macro- and Microrheology of heterogeneous microgel packings. Macromolecules 46(5):1962–1972

  15. 15.

    Di Lorenzo F, Seiffert S (2014) Tracer diffusion in heterogeneous polymer networks. Macromol Chem Phys 215:2097–2111

  16. 16.

    Lehmann S, Seiffert S, Richtering W (2012) Spatially resolved tracer diffusion in complex responsive hydrogels. J Am Chem Soc 134(38):15963–15969

  17. 17.

    Lehmann S, Seiffert S, Richtering W (2014) Diffusion of guest molecules within sensitive core–shell microgel carriers. J Colloid Interface Sci 431:204–208

  18. 18.

    Seiffert S, Oppermann W (2008) Diffusion of linear macromolecules and spherical particles in semidilute polymer solutions and polymer networks. Polymer 49:4115–4126

  19. 19.

    Riest J, Eckert T, Richtering W, Nägele G (2015) Dynamics of suspensions of hydrodynamically structured particles: analytic theory and applications to experiments. Soft Matter 11:2821–2843

  20. 20.

    Eckert T, Richtering W (2008) Thermodynamic and hydrodynamic interaction in concentrated microgel suspensions: hard or soft sphere behavior? J Chem Phys 129(12):1249021–1249026

  21. 21.

    Linkhorst J, Beckmann T, Go D, Kuehne AJC, Wessling M (2016) Microfluidic colloid filtration. Sci Rep 6:22376

  22. 22.

    Roa R, Zholkovskiy EK, Nägele G (2015) Ultrafiltration modeling of non-ionic microgels. Soft Matter 11:4106–4122

  23. 23.

    McPhee W, Tam KC, Pelton R (1993) Poly(N-isopropylacrylamide) lattices prepared with sodium dodecyl sulfate. J Colloid Interface Sci 156:24–30

  24. 24.

    Pich A, Richtering W (2010) Microgels by precipitation polymerization: synthesis, characterization, and functionalization. Adv Polym Sci 234:1–37

  25. 25.

    Shimizu H, Wada R, Okabe M (2009) Preparation and characterization of micrometer-sized poly(N-isopropylacrylamide) hydrogel particles. Polym J 41:771–777

  26. 26.

    Senff H, Richtering W (1999) Temperature sensitive microgel suspensions: colloidal phase behavior and rheology of soft spheres. J Chem Phys 111(4):1705–1711

  27. 27.

    Seth JR, Cloitre M, Bonnecaze RT (2006) Elastic properties of soft particle pastes. J Rheol 50(3):353–376

  28. 28.

    Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, Ithaca, NY

  29. 29.

    Cohen Y, Ramon O, Kopelman IJ, Mizrahi S (1992) Characterization of inhomogeneous polyacrylamide hydrogels. J Polym Sci B Polym Phys 30(9):1055–1067

  30. 30.

    Cloitre M, Borrega R, Monti F, Leibler L (2003) Glassy dynamics and flow properties of soft colloidal pastes. Phys Rev Lett 90(6):068303

  31. 31.

    Ma K, Mendoza C, Hanson M, Werner-Zwanziger U, Zwanziger J, Wiesner U (2015) Control of ultrasmall sub-10 nm ligand-functionalized fluorescent core–shell silica nanoparticle growth in water. Chem Mater 27(11):4119–4133

  32. 32.

    Ma K, Zhang D, Cong Y, Wiesner U (2016) Elucidating the mechanism of silica nanoparticle PEGylation processes using fluorescence correlation spectroscopies. Chem Mater 28(5):1537–1545

  33. 33.

    Liétor-Santos JJ, Sierra-Martín B, Gasser U, Fernández-Nieves A (2011) The effect of hydrostatic pressure over the swelling of microgel particles. Soft Matter 7:6370–6374

  34. 34.

    Mohanty PS, Paloli D, Crassous JJ, Zaccarelli E, Schurtenberger P (2014) Effective interactions between soft-repulsive colloids: experiments, theory, and simulations. J Chem Phys 140:094901

  35. 35.

    Gianneli M, Beines PW, Roskamp RF, Koynov K, Fytas G, Knoll W (2007) Local and global dynamics of transient polymer networks and swollen gels anchored on solid surfaces. J Phys Chem C 111(35):13205–13211

  36. 36.

    Wöll D (2014) Fluorescence correlation spectroscopy in polymer science. RSC Adv 4:2447–2465

  37. 37.

    Papadakis CM, Košovan P, Richtering W, Wöll D (2014) Polymers in focus: fluorescence correlation spectroscopy. Colloid Polym Sci 292:2399–2411

  38. 38.

    Enderlein J, Gregor I, Patra D, Dertinger T, Kaupp UB (2005) Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration. Chem Phys Chem 6(11):2324–2336

  39. 39.

    Dertinger T, Pacheco V, von der Hocht I, Hartmann R, Gregor I, Enderlein J (2007) Two-focus fluorescence correlation spectroscopy: a new tool for accurate and absolute diffusion measurements. Chem Phys Chem 8(3):433–443

  40. 40.

    Müller CB, Loman A, Pacheco V, Koberling F, Willbold D, Richtering W, Enderlein J (2008) Precise measurement of diffusion by multi-color dual-focus fluorescence correlation spectroscopy. Europhys Lett 83:46001

  41. 41.

    Müller CB, Richtering W (2008) Sealed and temperature-controlled sample cell for inverted and confocal microscopes and fluorescence correlation spectroscopy. Colloid Polym Sci 286:1215–1222

  42. 42.

    Daoud M, Cotton JP, Farnoux B, Jannink G, Sarma G, Benoit H, Duplessix R, Picot C, de Gennes PG (1975) Solutions of flexible polymers. Neutron experiments and interpretation. Macromolecules 8(6):804–818

  43. 43.

    Flory PJ, Rehner J (1943) Statistical mechanics of cross-linked polymer networks II. Swelling J Chem Phys 11:521–526

  44. 44.

    Vagias A, Raccis R, Koynov K, Jonas U, Butt HJ, Fytas G, Košovan P, Lenz O, Holm C (2013) Complex tracer diffusion dynamics in polymer solutions. Phys Rev Lett 111(8):088301

  45. 45.

    Jönsson B, Wennerström H, Nilsson PG, Linse P (1986) Self-diffusion of small molecules in colloidal systems. Colloid Polym Sci 264:77–88

  46. 46.

    Raccis R, Roskamp R, Hopp I, Menges B, Koynov K, Jonas U, Knoll W, Butt HJ, Fytas G (2011) Probing mobility and structural inhomogeneities in grafted hydrogel films by fluorescence correlation spectroscopy. Soft Matter 7:7042–7053

  47. 47.

    Vagias A, Schultze J, Doroshenko M, Koynov K, Butt HJ, Gauthier M, Fytas G, Vlassopoulos D (2015) Molecular tracer diffusion in nondilute polymer solutions: universal master curve and glass transition effects. Macromolecules 48(24):8907–8912

  48. 48.

    Langevin D, Rondelez F (1978) Sedimentation of large colloidal particles through semidilute polymer solutions. Polymer 19:875–882

  49. 49.

    Cukier RI (1984) Diffusion of Brownian spheres in semidilute polymer solutions. Macromolecules 17(2):252–255

  50. 50.

    Altenberger AR, Tirrell M (1984) On the theory of self-diffusion in a polymer gel. J Chem Phys 80:2208–2213

  51. 51.

    Phillies GDJ, Ullmann GS, Ullmann K, Lin TH (1985) Phenomenological scaling laws for "semidilute" macromolecule solutions from light scattering by optical probe particles. J Chem Phys 82(11):5242–5246

  52. 52.

    Phillies GDJ (1987) Dynamics of polymers in concentrated solutions: the universal scaling equation derived. Macromolecules 20(3):558–564

  53. 53.

    Phillies GDJ (1990) Chain architecture in the hydrodynamic scaling picture for polymer dynamics. Macromolecules 23(10):2742–2748

Download references


K.M. and U.W. acknowledge support by the National Cancer Institute of the National Institutes of Health under Award Number U54CA199081.

Author information

Correspondence to Walter Richtering or Sebastian Seiffert.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Electronic supplementary material


(PDF 1500 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Walta, S., Di Lorenzo, F., Ma, K. et al. Diffusion of rigid nanoparticles in crowded polymer-network hydrogels: dominance of segmental density over crosslinking density. Colloid Polym Sci 295, 1371–1381 (2017). https://doi.org/10.1007/s00396-017-4069-x

Download citation


  • Microgels
  • Hydrogels
  • Tracer diffusion
  • Crowding
  • Fluorescence
  • Fluorescence correlation spectroscopy
  • C-dots