Abstract.
Recent experiments have demonstrated that the dynamics in liquids close to and below the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. We use here a model proposed recently for explaining these features, and show that the heterogeneous nature of the dynamics has important consequences when considering the dynamics of thin films. We show how the dominant relaxation time in a thin film is changed as compared to the bulk, as a function of the thickness, the interaction energy with the substrate, and the temperature. The corresponding time scales cover the so-called VFT (or WLF) regime and vary between 10-8 s to 104 s typically. In the absence of interaction, our model allows for interpreting suspended films experiments, in the case of small polymers for which the data do not depend on the polymer weight. The interaction leads to an increase of \(T_{\rm g}\) for an interaction per monomer of the order of the thermal energy T. This increase saturates at the value corresponding to strongly interacting films for adsorption energies slightly larger and still of order T. In particular, we predict that the \(T_{\rm g}\) shift can be non-monotonous as a function of the film thickness, in the case of intermediate interaction strength.
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References
M.D. Ediger, C.A. Angell, S.R. Nagel, J. Phys. Chem. 100, 13200 (1996).
C.A. Angell, Science 267, 1924 (1995).
J.D. Ferry, Viscoelastic Properties of Polymers (John Wiley and Sons, Inc., 1980).
K. Schmidt-Rohr, H.W. Spiess, Phys. Rev. Lett. 66, 3020 (1991).
U. Tracht, M. Wilhelm, A. Heuer, H. Feng, K. Schmidt-Rohr, H.W. Spiess, Phys. Rev. Lett. 81, 2727 (1998).
S.A. Reinsberg, X.H. Qiu, M. Wilhelm, H.W. Spiess, M.D. Ediger, J. Chem. Phys. 114, 7299 (2001).
M.T. Cicerone, F.R. Blackburn, M.D. Ediger, Macromolecules 28, 8224 (1995).
C.-Y. Wang, M.D. Ediger, Macromolecules 30, 4770 (1997).
M.T. Cicerone, P.A. Wagner, M.D. Ediger, J. Phys. Chem. B 101, 8727 (1997).
C.-Y. Wang, M.D. Ediger, J. Phys. Chem. B 103, 4177 (1999).
C.-Y. Wang, M.D. Ediger, J. Chem. Phys. 112, 6933 (2000).
Y. Hwang, T. Inoue, P.A. Wagner, M.D. Ediger, J. Polym. Sci. 38, 68 (2000).
F. Fujara, B. Geil, H. Sillescu, G. Fleischer, Z. Phys. B. 88, 195 (1992).
I. Chang, F. Fujara, B. Geil, G. Heuberger, T. Mangel, H. Sillescu, J. Non-Cryst. Solids 172-174, 248 (1994).
B. Schiener, Böhmer R., A. Loidl, R.V. Chamberlin, Science 274, 752 (1996).
R. Richert, J. Chem. Phys. 113, 8404 (2000).
H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999).
M.D. Ediger, Annu. Rev. Chem. 51, 99 (2000).
R. Richert, J. Phys. Condens. Matter 14, R703 (2002).
G. Adam, J.H. Gibbs, J. Chem. Phys. 43, 139 (1965).
J.A. Forrest, Eur. Phys. J. E 8, 261 (2002).
J.L. Keddie, R.A.L. Jones, R.A. Cory, Europhys. Lett. 27, 59 (1994).
J.A. Forrest, K. Dalnoki-Veress, J.R. Stevens, J.R. Dutcher, Phys. Rev. Lett. 77, 2002; 4108 (1996).
J.A. Forrest, K. Dalnoki-Veress, J.R. Dutcher, Phys. Rev. E. 56, 5705 (1997).
J.A. Forrest, C. Svanberg, Révész K., M. Rodahl, L.M. Torell, B. Kasemo, Phys. Rev. E 58, R1226 (1998).
K. Dalnoki-Veress, B.G. Nickel, C.B. Roth, J.R. Dutcher, Phys. Rev. E. 59, 2153 (1999).
K. Fukao, Y. Miyamoto, Phys. Rev. E. 61, 1743 (2000).
J.A. Forrest, J. Mattsson, Phys. Rev. E 61, R53 (2000).
J. Mattsson, J.A. Forrest and Börjesson L., Phys. Rev. E. 62, 5187 (2000).
S. Kawana, R.A.L. Jones, Phys. Rev. E. 63, 021501 (2001).
K. Dalnoki-Veress, J.A. Forrest, C. Murray, C. Gigault, J.R. Dutcher, Phys. Rev. E. 63, 031801 (2001).
L. Hartmann, W. Gorbatschow, J. Hauwede, F. Kremer, Eur. Phys. J. E 8, 145 (2002).
J.Q. Pham, P.F. Green, J. Chem. Phys. 116, 5801 (2002).
J.Q. Pham, P.F. Green, Macromolecules 36, 1665 (2003).
C.J. Ellison, J.M. Torkelson, Nature Mater. 2, 695 (2003).
J.S. Sharp, J.A. Forrest, Phys. Rev. E 67, 031805 (2003).
W.E. Wallace, J.H. van Zanten, W.L. Wu, Phys. Rev. E 52, R3329 (1995).
J.H. van Zanten, W.E. Wallace, W.L. Wu, Phys. Rev. E 53, R2053 (1996).
Y. Grohens, M. Brogly, C. Labbe, M.-O. David, J. Schultz, Langmuir 14, 2929 (1998).
P. Carriere, Y. Grohens, J. Spevacek, J. Schultz, Langmuir 16, 5051 (2000).
Y. Grohens, L. Hamon, G. Reiter, A. Soldera, Y. Holl, Eur. Phys. J. E 8, 217 (2002).
D.S. Fryer, E.J. Peters, J.E. Kim, J.E. Tomaszewski, J.J. de Pablo, P.F. Nealey, C.C. White, W. Wu, Macromolecules 34, 5627 (2001).
D.S. Fryer, P.F. Nealey, J.J. de Pablo, Macromolecules 33, 6439 (2000).
O.K.C. Tsui, T.P. Russell, C.J. Hawker, Macromolecules 34, 5535 (2002).
S. Ge, Y. Pu, W. Zhang, M. Rafailovich, J. Sokolov, C. Buenviaje, R. Buckmaster, R.M. Overney, Phys. Rev. Lett. 85, 2340 (2000).
K. Tanaka, A. Takahara, T. Kajiyama, Macromolecules 33, 7588 (2000).
J.A. Hammerschmidt, W.L. Gladfelter, G. Haugstad, Macromolecules 32, 3360 (1999).
J. Berriot, H. Montés, F. Lequeux, D. Long, P. Sotta, Macromolecules 35, 9756 (2002).
J. Berriot, H. Montés, F. Lequeux, D. Long, P. Sotta, Europhys. Lett. 64, 50 (2003).
D. Long, F. Lequeux, Eur. Phys. J. E 4, 371 (2001).
S. Merabia, D. Long, Eur. Phys. J. E 9, 195 (2002).
C.T. Moynihan, J.-H. Wang, Mater. Rec. Soc. Symp. Proc. 455, 133 (1997).
M.D. Ediger, J. Non-Cryst. Solids 235-237, 10 (1998).
G.S. Grest, M.H. Cohen, Adv. Chem. Phys. 48, 455 (1981).
Götze W. and Sjögren L., Rep. Prog. Phys. 55, 241 (1992).
G. Tarjus, D. Kivelson, Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales, edited by S.A. Edwards Liu, S. Nagel (Taylor and Francis, 2001).
R. Yamamoto, A. Onuki, Phys. Rev. Lett. 81, 4915 (1998).
C. Donati, J.F. Douglas, W. Kob, S.J. Plimpton, P.H. Poole, S.C. Glotzer, Phys. Rev. Lett. 80, 2338 (1998).
C. Mischler, J. Baschnagel, K. Binder, Adv. Colloid Interface Sci. 94, 197 (2001).
F. Varnik, J. Baschnagel, K. Binder, Eur. Phys. J. E 8, 175 (2002).
P. Scheidler, W. Kob, K. Binder, Europhys. Lett. 59, 701 (2002).
P. Scheidler, W. Kob, K. Binder, J. Phys. Chem. B 108, 6673 (2004).
S. Herminghaus, Eur. Phys. J. E 8, 237 (2002).
P.-G. De Gennes, Eur. Phys. J. E 2, 201 (2000).
J.E. Mark, Physical Properties of Polymers Handbook (American Institute of Physics, 1996).
T. Inoue, H. Hayashihara, H. Okamoto, K. Osaki, J. Polym. Sci. 30, 409 (1992).
E. Hempel, G. Hempel, A. Hensel, C. Schick, E. Donth, J. Phys. Chem. B 104, 2460 (2000).
G.W. Scherer, Relaxation in Glass and Composites (John Wiley and Sons, New York, 1986).
N.G. McCrum, B.E. Read, G. Williams, Anelastic and Dielectric Effects in Polymeric Solids (Dover Publications, Inc., New York, 1967).
B.J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
A. Brodin, R. Bergman, J. Mattsson, Rössler E.A., Eur. Phys. J. B 36, 349 (2003).
K. Schmidt-Rohr, H.W. Spiess, Multidimensional Solid-State NMR and Polymers (Academic Press London, 1994).
A.M. Puertas, M. Fuchs, M.E. Cates, Phys. Rev. Lett. 88, 098301 (2002); Phys. Rev. E 67, 031406 (2003).
W.C.K. Poon, J. Phys. Condens. Matter 14, R859 (2002).
W.C.K. Poon, M.D. Haw, Adv. Colloid Interface Sci. 73, 71 (1997).
H. Verduin, J.K.G. Dhont, J. Colloid Interface Sci. 172, 425 (1995).
A.P. Gast, W.B. Russel, C.K. Hall, J. Colloid Interface Sci. 109, 161 (1986).
R.H. Colby, J.R. Gillmor, M. Rubinstein, Phys. Rev. E 48, 3712 (1993).
M. Rubinstein, R.H. Colby, Macromolecules 27, 3184 (1994).
M.C. Grant, W.B. Russel, Phys. Rev. E 47, 2606 (1993).
S.K. Kumar, J.F. Douglas, Phys. Rev. Lett. 87, 188301 (2001).
L. Cipelletti, S. Manley, R.C. Ball, D.A. Weitz, Phys. Rev. Lett. 84, 2275 (2000).
K.G. Soga, J.R. Melrose, R.C. Ball, J. Chem. Phys. 108, 6026 (1998).
A.N. Semenov, M. Rubinstein, Macromolecules 31, 1373 (1998).
M. Rubinstein, A.N. Semenov, Macromolecules 31, 1386 (1998).
M.J. Solomon, P. Varadan, Phys. Rev. E 63, 051402 (2001).
P. Sotta, D. Long, Eur. Phys. J. E 11, 375 (2003).
D. Stauffer, A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1994).
L.E. Nielsen, R.F. Landel, Mechanical Properties of Polymers and Composites (Marcel Dekker, New York, 1994).
D.C. Edwards, J. Mater. Sci. 25, 4175 (1990).
J.N. Israelachvili Intermolecular and Surface Forces (Academic Press, London, 1992).
T. Sasaki, A. Shimizu, T.H. Mourey, C.T. Thurau, M.D. Ediger, J. Chem. Phys. 119, 8730 (2003).
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Received: 1 July 2004, Published online: 26 October 2004
PACS:
64.70.Pf Glass transitions - 61.41. + e Polymers, elastomers, and plastics - 68.15. + e Liquid thin films
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Merabia, S., Sotta, P. & Long, D. Heterogeneous nature of the dynamics and glass transition in thin polymer films. Eur. Phys. J. E 15, 189–210 (2004). https://doi.org/10.1140/epje/i2004-10047-7
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DOI: https://doi.org/10.1140/epje/i2004-10047-7