Diffusion Mode Transition between Gaussian and Non-Gaussian of Nanoparticles in Polymer Solutions

Yi Ye; Han Qin; Ming Tian; Jian-Guo Mi

doi:10.1007/s10118-019-2237-9

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Diffusion Mode Transition between Gaussian and Non-Gaussian of Nanoparticles in Polymer Solutions

ARTICLE | Updated：2021-02-18

- Diffusion Mode Transition between Gaussian and Non-Gaussian of Nanoparticles in Polymer Solutions
- Chinese Journal of Polymer Science Vol. 37, Issue 7, Pages: 719-728(2019)
- Affiliations：
  
  a.State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China
  b.Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology, Beijing 100029, China
- Author bio：
  
  tianm@mail.buct.edu.cn (M.T.)
  mijg@mail.buct.edu.cn (J.G.M.)
- Funds：
- DOI：10.1007/s10118-019-2237-9
  CLC：
- Received：24 December 2018，
  
  Revised：2019-1-27，
  
  Accepted：31 January 2019，
  
  Online First：12 March 2019，
  
  Published：2019-07
- Accepted：
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Citation: Ye, Y.; Qin, H.; Tian, M.; Mi, J. G. Diffusion mode transition between Gaussian and non-Gaussian of nanoparticles in polymer solutions. Chinese J. Polym. Sci. 2019, 37, 719–728

Yi Ye, Han Qin, Ming Tian, et al. Diffusion Mode Transition between Gaussian and Non-Gaussian of Nanoparticles in Polymer Solutions[J]. Chinese Journal of Polymer Science, 2019, 37(7): 719-728.
Citation: Ye, Y.; Qin, H.; Tian, M.; Mi, J. G. Diffusion mode transition between Gaussian and non-Gaussian of nanoparticles in polymer solutions. Chinese J. Polym. Sci. 2019, 37, 719–728 DOI： 10.1007/s10118-019-2237-9.

Yi Ye, Han Qin, Ming Tian, et al. Diffusion Mode Transition between Gaussian and Non-Gaussian of Nanoparticles in Polymer Solutions[J]. Chinese Journal of Polymer Science, 2019, 37(7): 719-728. DOI： 10.1007/s10118-019-2237-9.

摘要

Abstract

The dynamic density functional theory is applied to study the diffusion of nanoparticles in polymer solutions

in which different diffusion modes have been identified by exploiting the density and free energy evolutions. Under the condition of low polymer concentration

diffusion is controlled by particle free motion with a normal Gaussian type. As the concentration increases

the non-Gaussian behavior can be observed when the particle size is comparable to the correlation length of polymer chain. Particles need to penetrate through a cage and overcome an entropic barrier

where the hopping and the model-coupling diffusion coexist. Further increase of polymer concentration can result in complete restriction of the particle by surrounding polymer segments. In this case

the non-Gaussian process fades away

and particle diffusion is controlled by Rouse dynamics of polymer chains with the generalized Gaussian characteristics.

关键词

Keywords

references

Shen, H.; Tauzin, L. J.; Baiyasi, R.; Wang, W.; Moringo, N.; Shuang, B.; Landes, C. F . Single particle tracking: From theory to biophysical applications . Chem. Rev. , 2017 . 117 7331 - 7376 . DOI: 10.1021/acs.chemrev.6b00815 http://doi.org/10.1021/acs.chemrev.6b00815 .

Zimmerman, S. B.; Minton, A. P . Macromolecular crowding: Biochemical, biophysical, and physiological consequences . Annu. Rev. Biophys. Biomol. Struct. , 1993 . 22 27 - 65 . DOI: 10.1146/annurev.bb.22.060193.000331 http://doi.org/10.1146/annurev.bb.22.060193.000331 .

Kessler, M. R . Polymer matrix composites: A perspective for a special issue of polymer reviews . Polym. Rev. , 2012 . 52 229 - 233 . DOI: 10.1080/15583724.2012.708004 http://doi.org/10.1080/15583724.2012.708004 .

Mackay, M. E.; Dao, T. T.; Tuteja, A.; Ho, D. L.; van Horn, B.; Kim, H.; Hawker, C. J . Nanoscale effects leading to non-Einstein-like decrease in viscosity . Nat. Mater. , 2003 . 2 762 - 766 . DOI: 10.1038/nmat999 http://doi.org/10.1038/nmat999 .

Yu, Y. X.; Tian, A. W.; Gao, G. H . Prediction of collective diffusion coefficient of bovine serum albumin in aqueous electrolyte solution with hard-core two-Yukawa potential . Phys. Chem. Chem. Phys. , 2005 . 7 2423 - 2428 . DOI: 10.1039/b500371g http://doi.org/10.1039/b500371g .

Tuteja, A.; Mackay, M. E.; Narayanan, S.; Asokan, S.; Wong. M. S . Breakdown of the continuum Stokes-Einstein relation for nanoparticle diffusion . Nano Lett. , 2007 . 7 1276 - 1281 . DOI: 10.1021/nl070192x http://doi.org/10.1021/nl070192x .

Zhang, X.; Gray-Weale, A. A . Local hydrodynamics of solvent near diffusing dendrimers: A test of the new Stokes-Einstein relation . J. Polym. Sci., Part B: Polym. Phys. , 2017 . 55 1380 - 1392 . DOI: 10.1002/polb.v55.18 http://doi.org/10.1002/polb.v55.18 .

Lungova, M.; Krutyeva, M.; Pyckhout-Hintzen, W.; Wischnewski, A.; Monkenbusch, M.; Allgaier, J.; Ohl, M.; Sharp, M.; Richter. D . Nanoscale motion of soft nanoparticles in unentangled and entangled polymer matrices . Phys. Rev. Lett. , 2016 . 117 147803 DOI: 10.1103/PhysRevLett.117.147803 http://doi.org/10.1103/PhysRevLett.117.147803 .

Cai, L. H.; Panyukov, S.; Rubinstein, M . Hopping diffusion of nanoparticles in polymer matrices . Macromolecules , 2015 . 48 847 - 862 . DOI: 10.1021/ma501608x http://doi.org/10.1021/ma501608x .

Kohli, I.; Mukhopadhyay, A . Diffusion of nanoparticles in semidilute polymer solutions: Effect of different length scales . Macromolecules , 2012 . 45 6143 - 6149 . DOI: 10.1021/ma301237r http://doi.org/10.1021/ma301237r .

Grabowski, C. A.; Mukhopadhyay, A . Size effect of nanoparticle diffusion in a polymer melt . Macromolecules , 2014 . 47 7238 - 7242 . DOI: 10.1021/ma501670u http://doi.org/10.1021/ma501670u .

Griffin, P. J.; Bocharova, V.; Middleton, L. R.; Composto, R. J.; Clarke, N.; Schweizer, K. S.; Winey, K. I . Influence of the bound polymer layer on nanoparticle diffusion in polymer melts . ACS Macro Lett. , 2016 . 5 1141 - 1145 . DOI: 10.1021/acsmacrolett.6b00649 http://doi.org/10.1021/acsmacrolett.6b00649 .

Brown W, Stepanek P . Dynamic light scattering of poly( n -laurylmethacrylate) in the melt and in concentrated ethyl acetate solutions . J. Polym. Sci., Part B: Polym. Phys. , 1997 . 35 1013 - 1024 . .

Ge, T.; Kalathi, J. T.; Halverson, J. D.; Grest, G. S.; Rubinstein, M . Nanoparticle motion in entangled melts of linear and nonconcatenated ring polymers . Macromolecules , 2017 . 50 1749 - 1754 . DOI: 10.1021/acs.macromol.6b02632 http://doi.org/10.1021/acs.macromol.6b02632 .

Petekidis, G.; Fytas, G.; Scherf, U.; Mullen, K.; Fleischer, G . Dynamics of poly( p -phenylene) ladder polymers in solution . J. Polym. Sci., Part B: Polym. Phys. , 1999 . 37 2211 - 2220 . DOI: 10.1002/(ISSN)1099-0488 http://doi.org/10.1002/(ISSN)1099-0488 .

Eslami, H.; Rahimi, M.; Müller-Plathe, F . Molecular dynamics simulation of a silica nanoparticle in oligomeric poly(methyl methacrylate): A model system for studying the interphase thickness in a polymer-nanocomposite via different properties . Macromolecules , 2013 . 46 8680 - 8692 . DOI: 10.1021/ma401443v http://doi.org/10.1021/ma401443v .

Starr, F. W.; Schrøder, T. B.; Glotzer, S. C . Molecular dynamics simulation of a polymer melt with a nanoscopic particle . Macromolecules , 2002 . 35 4481 - 4492 . DOI: 10.1021/ma010626p http://doi.org/10.1021/ma010626p .

Volgin, I. V.; Larin, S. V.; Abad, E.; Lyulin, S. V . Molecular dynamics simulations of fullerene diffusion in polymer melts . Macromolecules , 2017 . 50 2207 - 2218 . DOI: 10.1021/acs.macromol.6b02050 http://doi.org/10.1021/acs.macromol.6b02050 .

de Gennes, P. G. in Scaling concepts in polymer physics , Cornell University Press, Ithaca, NY, 1979 .

Brochard Wyart, F.; de Gennes, P. G . Viscosity at small scales in polymer melts . Eur. Phys. J. E , 2000 . 1 93 - 97 . DOI: 10.1007/s101890050011 http://doi.org/10.1007/s101890050011 .

Phillies, G. D. J.; Clomenil, D . Probe diffusion in polymer solutions under THETA and good conditions . Macromolecules , 1993 . 26 167 - 170 . DOI: 10.1021/ma00053a025 http://doi.org/10.1021/ma00053a025 .

Cukier, R. I . Diffusion of Brownian spheres in semidilute polymer solutions . Macromolecules , 1984 . 17 252 - 255 . DOI: 10.1021/ma00132a023 http://doi.org/10.1021/ma00132a023 .

Cai, L. H.; Panyukov, S.; Rubinstein, M . Mobility of nonsticky nanoparticles in polymer liquids . Macromolecules , 2011 . 44 7853 - 7863 . DOI: 10.1021/ma201583q http://doi.org/10.1021/ma201583q .

Cheng, S.; Xie, S. J.; Carrillo, J. M. Y.; Carroll, B.; Martin, H.; Cao, P. F.; Dadmun, M. D.; Sumpter, B. G.; Novikov, V. N.; Schweizer, K. S.; Sokolov. A. P . Big effect of small nanoparticles: A shift in paradigm for polymer nanocomposites . ACS Nano , 2017 . 11 752 - 759 . DOI: 10.1021/acsnano.6b07172 http://doi.org/10.1021/acsnano.6b07172 .

Fan, T. H.; Dhont, J. K. G.; Tuinier, R . Motion of a sphere through a polymer solution . Phys. Rev. E , 2007 . 75 011803 DOI: 10.1103/PhysRevE.75.011803 http://doi.org/10.1103/PhysRevE.75.011803 .

Liu, J.; Cao, D.; Zhang, L . Molecular dynamics study on nanoparticle diffusion in polymer melts: A test of the Stokes-Einstein law . J. Phys. Chem. C , 2008 . 112 6653 - 6661 . .

Yamamoto, U.; Schweizer, K. S . Theory of nanoparticle diffusion in unentangled and entangled polymer melts . J. Chem. Phys. , 2011 . 135 224902 DOI: 10.1063/1.3664863 http://doi.org/10.1063/1.3664863 .

Yamamoto, U.; Schweizer, K. S . Microscopic theory of the long-time diffusivity and intermediate-time anomalous transport of a nanoparticle in polymer melts . Macromolecules , 2014 . 48 152 - 163 . .

Ye, Y.; Ning, N.; Tian, M.; Zhang, L.; Mi, J . Nucleation and growth of hexagonal ice by dynamical density functional theory . Crys. Grow. Des. , 2016 . 17 100 - 105 . .

Rex, M.; Löwen, H . Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps . Phys. Rev. Lett. , 2008 . 101 148302 DOI: 10.1103/PhysRevLett.101.148302 http://doi.org/10.1103/PhysRevLett.101.148302 .

van Teeffelen, S.; Likos, C. N.; Löwen, H . Colloidal crystal growth at externally imposed nucleation clusters . Phys. Rev. Lett. , 2008 . 100 108302 DOI: 10.1103/PhysRevLett.100.108302 http://doi.org/10.1103/PhysRevLett.100.108302 .

Wittkowski, R.; Löwen, H.; Brand, H. R . Extended dynamical density functional theory for colloidal mixtures with temperature gradients . J. Chem. Phys. , 2012 . 137 224904 DOI: 10.1063/1.4769101 http://doi.org/10.1063/1.4769101 .

Rex, M.; Wensink, H. H.; Löwen, H . Dynamical density functional theory for anisotropic colloidal particles . Phys. Rev. E , 2007 . 76 021403 DOI: 10.1103/PhysRevE.76.021403 http://doi.org/10.1103/PhysRevE.76.021403 .

Archer, A. J . Dynamical density functional theory for molecular and colloidal fluids: A microscopic approach to fluid mechanics . J. Chem. Phys. , 2009 . 130 014509 DOI: 10.1063/1.3054633 http://doi.org/10.1063/1.3054633 .

Ye, Y.; Du, Z.; Tian, M.; Zhang, L.; Mi, J . Diffusive dynamics of polymer chains in an array of nanoposts . Phys. Chem. Chem. Phys. , 2017 . 19 380 - 387 . DOI: 10.1039/C6CP07217H http://doi.org/10.1039/C6CP07217H .

Yu, Y. X.; Wu, J . Extended test-particle method for predicting the inter- and intramolecular correlation functions of polymeric fluid . J. Chem. Phys. , 2003 . 118 3835 - 3842 . DOI: 10.1063/1.1539840 http://doi.org/10.1063/1.1539840 .

Bresme, F.; Quirke. N . Computer simulation study of the wetting behavior and line tensions of nanometer size particulates at a liquid-vapor interface . Phys. Rev. Lett. , 1998 . 80 3791 DOI: 10.1103/PhysRevLett.80.3791 http://doi.org/10.1103/PhysRevLett.80.3791 .

Holian, B. L.; Evans, D. J . Shear viscosities away from the melting line: A comparison of equilibrium and nonequilibrium molecular dynamics . J. Chem. Phys. , 1983 . 78 5147 - 5150 . DOI: 10.1063/1.445384 http://doi.org/10.1063/1.445384 .

Fenwick, N. I. D.; Bresme, F.; Quirke, N . Computer simulation of a Langmuir trough experiment carried out on a nanoparticulate array . J. Chem. Phys. , 2001 . 114 7274 - 7282 . DOI: 10.1063/1.1357795 http://doi.org/10.1063/1.1357795 .

Yamamoto, U.; Schweizer, K. S . Spatially dependent relative diffusion of nanoparticles in polymer melts . J. Chem. Phys. , 2013 . 139 064907 DOI: 10.1063/1.4817593 http://doi.org/10.1063/1.4817593 .

Kim, S.; Karrila, S. J. in Microhydrodynamics: Principles and selected applications , Butterworth-Heinemann, Boston, 1991 .

Rotne, J.; Prager, S . Variational treatment of hydrodynamic interaction in polymers . J. Chem. Phys. , 1969 . 50 4831 - 4837 . DOI: 10.1063/1.1670977 http://doi.org/10.1063/1.1670977 .

Trokhymchuk, A.; Nezbeda, I.; Jirsák, J.; Henderson, D . Hard-sphere radial distribution function again . J. Chem. Phys. , 2005 . 123 024501 DOI: 10.1063/1.1979488 http://doi.org/10.1063/1.1979488 .

Rosenfeld, Y . Free-energy model for the inhomogeneous hard-sphere fluid mixture and density-functional theory of freezing . Phys. Rev. Lett. , 1989 . 63 980 DOI: 10.1103/PhysRevLett.63.980 http://doi.org/10.1103/PhysRevLett.63.980 .

Yu, Y X.; Wu, J. Z . Structures of hard-sphere fluids from a modified fundamental-measure theory . J. Chem. Phys. , 2002 . 117 10156 - 10164 . DOI: 10.1063/1.1520530 http://doi.org/10.1063/1.1520530 .

Davis, H. T. in Statistical mechanics of phases, interfaces, and thin films , Wiley-VCH, New York, 1996 .

Kim, S. C.; Lee, S. H . A density functional perturbative approach for simple fluids: The structure of a nonuniform Lennard-Jones fluid at interfaces . J. Phys.: Condens. Matter , 2004 . 16 6365 DOI: 10.1088/0953-8984/16/36/003 http://doi.org/10.1088/0953-8984/16/36/003 .

Lee, J. K.; Barker, J. A.; Pound, G. M . Surface structure and surface tension: Perturbation theory and Monte Carlo calculation . J. Chem. Phys. , 1974 . 60 1976 - 1980 . DOI: 10.1063/1.1681303 http://doi.org/10.1063/1.1681303 .

Peng, B.; Yu, Y. X . A density functional theory with a mean-field weight function: Applications to surface tension, adsorption, and Phase transition of a Lennard-Jones fluid in a slit-like pore . J. Phys. Chem. B , 2008 . 112 15407 - 15416 . DOI: 10.1021/jp805697p http://doi.org/10.1021/jp805697p .

Peng, B.; Yu, Y. X . A density functional theory for Lennard-Jones fluids in cylindrical pores and its applications to adsorption of nitrogen on MCM-41 materials . Langmuir , 2008 . 24 12431 - 12439 . DOI: 10.1021/la8024099 http://doi.org/10.1021/la8024099 .

Tripathi, S.; Chapman, W. G . Microstructure and thermodynamics of inhomogeneous polymer blends and solutions . Phys. Rev. Lett. , 2005 . 94 087801 DOI: 10.1103/PhysRevLett.94.087801 http://doi.org/10.1103/PhysRevLett.94.087801 .

McGarrity, E. S.; Frischknecht, A. L.; Mackay, M. E . Phase behavior of polymer/nanoparticle blends near a substrate . J. Chem. Phys. , 2008 . 128 154904 DOI: 10.1063/1.2899329 http://doi.org/10.1063/1.2899329 .

Plimpton, S . Fast parallel algorithms for short-range molecular dynamics . J. Comput. Phys. , 1995 . 117 1 - 19 . DOI: 10.1006/jcph.1995.1039 http://doi.org/10.1006/jcph.1995.1039 .

Martin, M. G.; Siepmann, J. I . Transferable potentials for phase equilibria. 1. United-atom description of n -alkanes . J. Phys. Chem. B , 1998 . 102 2569 - 2577 . DOI: 10.1021/jp972543+ http://doi.org/10.1021/jp972543+ .

Curro, J. G.; Frischknecht, A. L . The structure of poly(ethylene oxide) liquids: Comparison of integral equation theory with molecular dynamics simulations and neutron scattering . Polymer , 2005 . 46 6500 - 6506 . DOI: 10.1016/j.polymer.2005.03.123 http://doi.org/10.1016/j.polymer.2005.03.123 .

Hayakawa, H.; Ichiki, K . Statistical theory of sedimentation of disordered suspensions . Phys. Rev. E , 1995 . 51 R3815 DOI: 10.1103/PhysRevE.51.R3815 http://doi.org/10.1103/PhysRevE.51.R3815 .

Charbonneau, P.; Kurchan, J.; Parisi, G.; Urbani, P.; Zamponi, F . Glass and jamming transitions: From exact results to finite-dimensional descriptions . Ann. Rev. Conden. Matt. Phys. , 2017 . 8 265 - 288 . DOI: 10.1146/annurev-conmatphys-031016-025334 http://doi.org/10.1146/annurev-conmatphys-031016-025334 .

Charbonneau, P.; Jin, Y.; Parisi, G.; Zamponi, F . Hopping and the Stokes-Einstein relation breakdown in simple glass formers . Proc. Natl. Acad. Sci. , 2014 . 111 15025 - 15030 . DOI: 10.1073/pnas.1417182111 http://doi.org/10.1073/pnas.1417182111 .

Boshoff, J. H. D.; Lobo, R. F.; Wagner, N. J . Influence of polymer motion, topology and simulation size on penetrant diffusion in amorphous, glassy polymers: Diffusion of helium in polypropylene . Macromolecules , 2001 . 34 6107 - 6116 . DOI: 10.1021/ma010255c http://doi.org/10.1021/ma010255c .

Kim, J.; Kim, C.; Sung, B. J . Simulation study of seemingly Fickian but heterogeneous dynamics of two dimensional colloids . Phys. Rev. Lett. , 2013 . 110 047801 DOI: 10.1103/PhysRevLett.110.047801 http://doi.org/10.1103/PhysRevLett.110.047801 .

Patti, A.; El Masri, D.; van Roij, R.; Dijkstra, M . Stringlike clusters and cooperative interlayer permeation in smectic liquid crystals formed by colloidal rods . Phys. Rev. Lett. , 2009 . 103 248304 DOI: 10.1103/PhysRevLett.103.248304 http://doi.org/10.1103/PhysRevLett.103.248304 .

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