Granular Matter

, 20:9 | Cite as

Granular sphere-chain relaxation dynamics to interpret polymer-nanocomposite glass transition temperatures

Original Paper
  • 71 Downloads

Abstract

Free volume and polymer chain architecture play important roles in controlling the glass transition temperature \(T_g\) of polymer nanocomposites. Various changes in \(T_g\) with respect to nanoparticle (NP) loading have been reported, depending, in part, on whether there are attractive or repulsive interactions between the polymer and NPs. However, even with no enthalpic interaction, there are ostensible changes in \(T_g\) that must be attributed to topological factors, such as chain stiffness and nanoparticle size. Here we adopt a macroscopic granular model to help understand frustrated dynamics in glassy polymer nanocomposites. Mixtures of granular chains with spherical inclusions were prepared with prescribed sphere size, chain length, and mixture composition. We measured the time to reach a close–packed, jammed state when these composites were subjected to controlled mechanical shaking. The compaction dynamics reveal that spherical inclusions profoundly influence the chain relaxation dynamics. In the long-chain limit, increasing the NP loading furnishes a minimum in the chain relaxation time, which may be loosely associated with an intermediate minimum in \(T_g\) with respect to nanoparticle loading for polymer nanocomposites. This minimum occurs for spheres having different sizes, but only at concentrations where the characteristic sphere separation is comparable to the chain loop size. This observation may explain the variety of contrasting trends that have been found in the literature for the dependence of \(T_g\) on nanoparticle loading in polymeric nanocomposites.

Notes

Acknowledgements

Funding was provided by Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN 262785-08).

Funding R.J.H. gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Research Chairs program. A.M. thanks the Faculty of Engineering, McGill University, for support through a McGill Engineering Doctoral Award (MEDA).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Matteucci, S., Yampolskii, Y., Freeman, B.D., Pinnau, I.: Materials Science of Membranes for Gas and Vapor Separation. Wiley, New York (2006)Google Scholar
  2. 2.
    Kasapis, S.: Definition and applications of the network glass transition temperature. Food Hydrocolloid. 20(2–3), 218–228 (2006)CrossRefGoogle Scholar
  3. 3.
    Wilberforce, S.I.J., Best, S.M., Cameron, R.E.: A dynamic mechanical thermal analysis study of the viscoelastic properties and glass transition temperature behaviour of bioresorbable polymer matrix nanocomposites. J. Mater. Sci. 21(12), 3085–3093 (2010)Google Scholar
  4. 4.
    Chandran, S., Basu, J.K., Mukhopadhyay, M.K.: Variation in glass transition temperature of polymer nanocomposite films driven by morphological transitions. J. Chem. Phys. 138(1), 014902–014908 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    Xu, W.B., Zhou, Z.F., Ge, M.L., Pan, W.P.: Polyvinyl chloride/montmorillonite nanocomposites: Glass transition temperature and mechanical properties. J. Therm. Anal. Calorim. 78(1), 91–99 (2004)CrossRefGoogle Scholar
  6. 6.
    Castillo, F.Y., Socher, R., Krause, B., Headrick, R., Grady, B.P., Prada-Silvy, R., Potschke, P.: Electrical, mechanical, and glass transition behavior of polycarbonate-based nanocomposites with different multi-walled carbon nanotubes. Polymer 52(17), 3835–3845 (2011)CrossRefGoogle Scholar
  7. 7.
    Sun, Y., Zhang, Z., Moon, K.S., Wong, C.P.: Glass transition and relaxation behavior of epoxy nanocomposites. J. Polym. Sci. B 42(21), 3849–3858 (2004)CrossRefGoogle Scholar
  8. 8.
    Ash, B.J., Schadler, L.S., Siegel, R.W.: Glass transition behavior of alumina/polymethylmethacrylate nanocomposites. Mater. Lett. 55(1–2), 83–87 (2002)CrossRefGoogle Scholar
  9. 9.
    Ash, B.J., Siegel, R.W., Schadler, L.S.: Glass-transition temperature behavior of alumina/pmma nanocomposites. J. Polym. Sci. B 42(23), 4371–4383 (2004)CrossRefGoogle Scholar
  10. 10.
    Khan, A.N., Hong, P.D., Chuang, W.T., Shih, K.S.: Effect of uniaxial drawing on the structure and glass transition behavior of poly(trimethylene 2,6-naphthalate)/layered clay nanocomposites. Polymer 50(26), 6287–6296 (2009)CrossRefGoogle Scholar
  11. 11.
    Liu, F.K., Hsieh, S.Y., Ko, F.H., Chu, T.C.: Synthesis of gold/poly(methyl methacrylate) hybrid nanocomposites. Colloid Surf. A 231(1–3), 31–38 (2003)CrossRefGoogle Scholar
  12. 12.
    Arrighi, V., McEwen, I.J., Qian, H., Prieto, M.B.S.: The glass transition and interfacial layer in styrene-butadiene rubber containing silica nanofiller. Polymer 44(20), 6259–6266 (2003)CrossRefGoogle Scholar
  13. 13.
    Zhang, X., Loo, L.S.: Study of glass transition and reinforcement mechanism in polymer/layered silicate nanocomposites. Macromolecules 42(14), 5196–5207 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    Pandis, C., Logakis, E., Kyritsis, A., Pissis, P., Vodnik, V.V., Dzunuzovic, E., Nedeljkovic, J.M., Djokovic, V., Hernandez, J.C.R., Ribelles, J.L.G.: Glass transition and polymer dynamics in silver/poly(methyl methacrylate) nanocomposites. Eur. Polym. J. 47(8), 1514–1525 (2011)CrossRefGoogle Scholar
  15. 15.
    Chandran, S., Basu, J.K.: Effect of nanoparticle dispersion on glass transition in thin films of polymer nanocomposites. Eur. Phys. J. E 34(9), 99 (2011)CrossRefGoogle Scholar
  16. 16.
    Pham, J.Q., Mitchell, C.A., Bahr, J.L., Tour, J.M., Krishanamoorti, K., Green, P.F.: Glass transition of polymer/single-walled carbon nanotube composite films. J. Polym. Sci. B 41(24), 3339–3345 (2003)CrossRefGoogle Scholar
  17. 17.
    Awad, S., Chen, H., Chen, G., Gu, X., Lee, J.L., Abdel-Hady, E.E., Jean, Y.C.: Free volumes, glass transitions, and cross-links in zinc oxide/waterborne polyurethane nanocomposites. Macromolecules 44(1), 29–38 (2011)ADSCrossRefGoogle Scholar
  18. 18.
    Chen, L., Zheng, K., Tian, X., Hu, K., Wang, R., Liu, C., Li, Y., Cui, P.: Double glass transitions and interfacial immobilized layer in in-situ-synthesized polyvinyl alcohol/silica nanocomposites. Macromolecules 43(2), 1076–1082 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    Fragiadakis, D., Pissis, P., Bokobza, L.: Glass transition and molecular dynamics in poly(dimethylsiloxane)/silica nanocomposites. Polymer 46(16), 6001–6008 (2005)CrossRefGoogle Scholar
  20. 20.
    Fragiadakis, D., Pissis, P.: Glass transition and segmental dynamics in poly(dimethylsiloxane)/silica nanocomposites studied by various techniques. J. Non-cryst. Solids 353(47–51), 4344–4352 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    Patidar, D., Agrawal, S., Saxena, N.S.: Storage modulus and glass transition behaviour of Cds/PMMA nanocomposites. J. Exp. Nanosci. 6(4), 441–449 (2011)CrossRefGoogle Scholar
  22. 22.
    Comer, A.C., Kalika, D.S., Kusuma, V.A., Freeman, B.D.: Glass-transition and gas-transport characteristics of polymer nanocomposites based on crosslinked poly(ethylene oxide). J. Appl. Polym. Sci. 117(4), 2395–2405 (2010)CrossRefGoogle Scholar
  23. 23.
    Moll, J., Kumar, S.K.: Glass transitions in highly attractive highly filled polymer nanocomposites. Macromolecules 45(2), 1131–1135 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    Ahn, S.I., Ohk, C.W., Kim, J.H., Zin, W.C.: Glass transition temperature of polymer nanocomposites: prediction from the continuous-multilayer model. J. Polym. Sci. B 47(22), 2281–2287 (2009)CrossRefGoogle Scholar
  25. 25.
    Kim, S.H., Chung, J.W., Kang, T.J., Kwak, S.Y., Suzuki, T.: Determination of the glass transition temperature of polymer/layered silicate nanocomposites from positron annihilation lifetime measurements. Polymer 48(14), 4271–4277 (2007)CrossRefGoogle Scholar
  26. 26.
    Wong, M., Tsuji, R., Nutt, S., Sue, H.-J.: Glass transition temperature changes of melt-blended polymer nanocomposites containing finely dispersed ZnO quantum dots. Soft Matter 6(18), 4482–4490 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    Wang, Z., Pang, H., Li, G., Zhang, Z.: Glass transition and free volume of high impact polystyrene/\(TiO_2\) nanocomposites determined by dilatometry. J. Macromol. Sci. B 45(5), 689–697 (2006)CrossRefGoogle Scholar
  28. 28.
    Qiao, R., Deng, H., Putz, K.W., Brinson, L.C.: Effect of particle agglomeration and interphase on the glass transition temperature of polymer nanocomposites. J. Polym. Sci. B 49(10), 740–748 (2011)CrossRefGoogle Scholar
  29. 29.
    Xiong, G., Gu, M., You, B., Wu, L.: Preparation and characterization of poly(styrene butylacrylate) latex/nano-ZnO nanocomposites. J. Appl. Polym. Sci. 90(7), 1923–1931 (2003)CrossRefGoogle Scholar
  30. 30.
    Chatterjee, A., Islam, M.S.: Fabrication and characterization of TiO2-epoxy nanocomposite. Mater. Sci. Eng. A 487(1–2), 574–585 (2008)CrossRefGoogle Scholar
  31. 31.
    Zou, L.N., Cheng, X., Rivers, M.L., Jaeger, H.M., Nagel, S.R.: The packing of granular polymer chains. Science 326(5951), 408–410 (2009)ADSMathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Mohaddespour, A., Hill, R.J.: Granular polymer composites. Soft Matter 8(48), 12060–12065 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    Wang, G., Zheng, N., Wen, P., Li, L., Shi, Q.: Scaling probability distribution of granular chains in two dimensions. Physica A 407, 192–197 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    Brown, E., Nasto, A., Athanassiadis, A.G., Jaeger, H.M.: Strain stiffening in random packings of entangled granular chains. Phys. Rev. Lett. 108(10), 108302 (2012)ADSCrossRefGoogle Scholar
  35. 35.
    Lopatina, L.M., Reichhardt, C.J.O., Reichhardt, C.: Jamming in granular polymers. Phys. Rev. E 84, 011303–011308 (2011)ADSCrossRefGoogle Scholar
  36. 36.
    He, L., Dong, Z., Zhang, L.: Selective adsorption behavior of polymer at the polymer-nanoparticle interface. J. Polym. Sci. Part B Polym. Phys. 54(18), 1829–1837 (2016)ADSCrossRefGoogle Scholar
  37. 37.
    Qiao, R., Brinson, L.C.: Simulation of interphase percolation and gradients in polymer nanocomposites. Compos. Sci. Technol. 69(3–4), 491–499 (2009)CrossRefGoogle Scholar
  38. 38.
    Starr, F.W., Schroder, T.B., Glotzer, S.C.: Molecular dynamics simulation of a polymer melt with a nanoscopic particle. Macromolecules 35(11), 4481–4492 (2002)ADSCrossRefGoogle Scholar
  39. 39.
    Rittigstein, P., Torkelson, J.M.: Polymer-nanoparticle interfacial interactions in polymer nanocomposites: confinement effects on glass transition temperature and suppression of physical aging. J. Polym. Sci. B 44(20), 2935–2943 (2006)CrossRefGoogle Scholar
  40. 40.
    Ramanathan, T., Liu, H., Brinson, L.C.: Functionalized SWNT/polymer nanocomposites for dramatic property improvement. J. Polym. Sci. B 43(17), 2269–2279 (2005)CrossRefGoogle Scholar
  41. 41.
    Tate, R.S., Fryer, D.S., Paqualini, S., Montague, M.F., De Pablo, J.J., Nealey, P.F.: Extraordinary elevation of the glass transition temperature of thin polymer films grafted to silicon oxide substrates. J. Chem. Phys. 115(21), 9982–9990 (2001)ADSCrossRefGoogle Scholar
  42. 42.
    Wei, C., Srivastava, D., Cho, K.: Thermal expansion and diffusion coefficients of carbon nanotube-polymer composites. Nano Lett. 2(6), 647–650 (2002)ADSCrossRefGoogle Scholar
  43. 43.
    Van Zanten, J.H., Wallace, W.E., Wu, W.L.: Effect of strongly favorable substrate interactions on the thermal properties of ultrathin polymer films. Phys. Rev. E 53(3), R2053–R2056 (1996)ADSCrossRefGoogle Scholar
  44. 44.
    Li, Y., Kroger, M., Liu, W.K.: Nanoparticle effect on the dynamics of polymer chains and their entanglement network. Phys. Rev. Lett. 109(11), 118001 (2012)ADSCrossRefGoogle Scholar
  45. 45.
    Cheng, S., Carroll, B., Bocharova, V., Carrillo, J.-M., Sumpter, B.G., Sokolov, A.P.: Focus: Structure and dynamics of the interfacial layer in polymer nanocomposites with attractive interactions. J. Chem. Phys. 146(20), 203201 (2017)ADSCrossRefGoogle Scholar
  46. 46.
    Lee, K.J., Lee, D.K., Kim, Y.W., Choe, W.-S., Kim, J.H.: Theoretical consideration on the glass transition behavior of polymer nanocomposites. J. Polym. Sci. B 45(16), 2232–2238 (2007)CrossRefGoogle Scholar
  47. 47.
    Qin, X., Xia, W., Sinko, R., Keten, S.: Tuning glass transition in polymer nanocomposites with functionalized cellulose nanocrystals through nanoconfinement. Nano Lett. 15(10), 6738–6744 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    Roldughin, V.I., Serenko, O.A., Getmanova, E.V., Novozhilova, N.A., Nikifirova, G.G., Buzin, M.I., Chvalun, S.N., Ozerin, A.N., Muzafarov, A.M.: Effect of hybrid nanoparticles on glass transition temperature of polymer nanocomposites. Polym. Compos. 37(7), 1978–1990 (2016)CrossRefGoogle Scholar
  49. 49.
    Oh, H., Green, P.F.: Polymer chain dynamics and glass transition in athermal polymer/nanoparticle mixtures. Nat. Mater. 8(2), 139–143 (2009)ADSCrossRefGoogle Scholar
  50. 50.
    Xia, W., Song, J., Hsu, D.D., Keten, S.: Side-group size effects on interfaces and glass formation in supported polymer thin films. J. Chem. Phys. 146(20), 203311 (2017)ADSCrossRefGoogle Scholar
  51. 51.
    Philippe, P., Bideau, D.: Compaction dynamics of a granular medium under vertical tapping. Europhys. Lett. 60(5), 677–683 (2002)ADSCrossRefGoogle Scholar
  52. 52.
    Knight, J.B., Fandrich, C.G., Lau, C.N., Jaeger, H.M., Nagel, S.R.: Density relaxation in a vibrated granular material. Phys. Rev. E 51(5), 3957–3963 (1995)ADSCrossRefGoogle Scholar
  53. 53.
    Kumar, N., Luding, S.: Memory of jamming-multiscale models for soft and granular matter. Granular Matter 18(3), 58 (2016)CrossRefGoogle Scholar
  54. 54.
    Lumay, G., Vandewalle, N.: Compaction of anisotropic granular materials: experiments and simulations. Phys. Rev. E 70(5–1), 051314 (2004)ADSCrossRefGoogle Scholar
  55. 55.
    Ribiere, P., Richard, P., Delannay, R., Bideau, D.: Importance of convection in the compaction mechanisms of anisotropic granular media. Phys. Rev. E 71(1), 011304 (2005)ADSCrossRefGoogle Scholar
  56. 56.
    Villarruel, F.X., Lauderdale, B.E., Mueth, D.M., Jaeger, H.M.: Compaction of rods: relaxation and ordering in vibrated, anisotropic granular material. Phys. Rev. E 61(6), 6914–6921 (2000)ADSCrossRefGoogle Scholar
  57. 57.
    Olson, C.J., Reichhardt, C., McCloskey, M., Zieve, R.J.: Effect of grain anisotropy on ordering, stability and dynamics in granular systems. Europhys. Lett. 57(6), 904–910 (2002)ADSCrossRefGoogle Scholar
  58. 58.
    Caglioti, E., Loreto, V., Herrmann, H.J., Nicodemi, M.: A tetris-like model for the compaction of dry granular media. Phys. Rev. Lett. 79(8), 1575–1578 (1997)ADSCrossRefGoogle Scholar
  59. 59.
    Ludewig, F., Dorbolo, S., Vandewalle, N.: Effect of friction in a toy model of granular compaction. Phys. Rev. E 70(5–1), 051304 (2004)ADSCrossRefGoogle Scholar
  60. 60.
    Ben-Naim, E., Knight, J.B., Nowak, E.R., Jaeger, H.M., Nagel, S.R.: Slow relaxation in granular compaction. Physica D 123(1–4), 380–385 (1998)ADSCrossRefGoogle Scholar
  61. 61.
    Mayadunne, A., Bhattacharya, S.N., Kosior, E.: Modelling of packing behaviour of irregularly shaped particles dispersed in a polymer matrix. Powder Technol. 89(2), 115–127 (1996)CrossRefGoogle Scholar
  62. 62.
    Wang, D., Driessen, H.P.C., Tickle, I.J.: Molpack: molecular graphics for studying the packing of protein molecules in the crystallographic unit cell. J. Mol. Graphics 9(1), 50–52 (1991)CrossRefGoogle Scholar
  63. 63.
    Hud, N.V., Allen, M.J., Downing, K.H., Lee, J., Balhorn, R.: Identification of the elemental packing unit of dna in mammalian sperm cells by atomic force microscopy. Biochem. Biophys. Res. Commun. 193(3), 1347–1354 (1993)CrossRefGoogle Scholar
  64. 64.
    Boss, J.M.N., Feneley, R.C.L., Mays, R.G.W.: Modes of chromatin packing in feulgen stained normal and malignant uro epithelial cell nuclei, and in lymphocytes, in relation to dna content. J. Microsc. 108(3), 291–300 (1976)CrossRefGoogle Scholar
  65. 65.
    Palmer, R.G., Stein, D.L., Abrahams, E., Anderson, P.W.: Models of hierarchically constrained dynamics for glassy relaxation. Phys. Rev. Lett. 53, 958–961 (1984)ADSCrossRefGoogle Scholar
  66. 66.
    Bogdanski, N., Wissen, M., Möllenbeck, S., Scheer, H.-C.: Polymers below the critical molecular weight for thermal imprint lithography. Microelectron. Eng. 85(5–6), 825–829 (2008)CrossRefGoogle Scholar
  67. 67.
    Mackay, M.E., Dao, T.T., Tuteja, A., Ho, D.L., van Horn, B., Kim, H.C., Hawker, C.J.: Nanoscale effects leading to non-Einstein-like decrease in viscosity. Nat. Mater. 2(11), 762–766 (2003)ADSCrossRefGoogle Scholar
  68. 68.
    Gardner, M.: Packing Spheres. Simon and Schuster, New York (1966)Google Scholar
  69. 69.
    Allen, G.: A History of the Glassy State. Nottingham University Press, Nottingham (1993)Google Scholar
  70. 70.
    Robinson, D.A., Friedman, S.P.: Electrical conductivity and dielectric permittivity of sphere packings: measurements and modelling of cubic lattices, randomly packed monosize spheres and multi-size mixtures. Phys. A 358(2–4), 447–465 (2005)CrossRefGoogle Scholar
  71. 71.
    Sowa, H., Koch, E., Fischer, W.: Hexagonal and trigonal sphere packings. I. Invariant and univariant lattice complexes. Acta Crystallogr. A 59(4), 317–326 (2003)MathSciNetCrossRefMATHGoogle Scholar
  72. 72.
    Jaeger, H.M., Nagel, S.R.: Physics of the granular state. Science 255(5051), 1523–1531 (1992)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Chemical EngineeringMcGill UniversityMontrealCanada

Personalised recommendations