메뉴 건너뛰기




Volumn 66, Issue 6, 2002, Pages 12-

Dewetting of thin-film polymers

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; FUNCTIONS; INTERPOLATION; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; POLYSTYRENES; RHEOLOGY; SILICON WAFERS; ULTRATHIN FILMS; VISCOELASTICITY; VISCOSITY;

EID: 41349116505     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.061607     Document Type: Article
Times cited : (48)

References (44)
  • 2
    • 0032582532 scopus 로고    scopus 로고
    • See e.g., G. Reiter, Science 282, 888 (1998);
    • (1998) Science , vol.282 , pp. 888
    • Reiter, G.1
  • 3
    • 0032582533 scopus 로고    scopus 로고
    • ScienceS. Herminghaus, 282, 916 (1998).
    • (1998) , vol.282 , pp. 916
    • Herminghaus, S.1
  • 9
    • 0000400617 scopus 로고
    • For earlier work on the subject, see, A. Dupré, Ann. Chim. Phys. 11, 194 (1867).
    • (1867) Ann. Chim. Phys. , vol.11 , pp. 194
    • Dupré, A.1
  • 10
    • 0000229521 scopus 로고
    • For a discussion on breaking of nonuniform liquid films and threads, based on a simple equation of motion as Taylor and Culick’s one, see, J.B. Keller, Phys. Fluids 26, 3451 (1983).
    • (1983) Phys. Fluids , vol.26 , pp. 3451
    • Keller, J.B.1
  • 12
    • 36449004142 scopus 로고
    • The precise shape of the rim was later analysed by Keller, et al. who showed that it is a cylindrical cap expanding in time like (Formula presented) see, J.B. Keller, A. King, and L. Ting, Phys. Fluids 7, 226 (1995).
    • (1995) Phys. Fluids , vol.7 , pp. 226
    • Keller, J.B.1    King, A.2    Ting, L.3
  • 15
    • 85036232054 scopus 로고    scopus 로고
    • The driving force of the dewetting process is a difference of interfacial tensions: (Formula presented) (where SL corresponds to the solid/liquid interface, SO to solid/air interface, etc…)
    • The driving force of the dewetting process is a difference of interfacial tensions: (Formula presented) (where SL corresponds to the solid/liquid interface, SO to solid/air interface, etc…).
  • 16
    • 0000258893 scopus 로고    scopus 로고
    • Solving numerically the Navier-Stokes equations for long wavelength modulations of the film surface, Brenner and collaborator consider the shape of the rim of a very viscous film retracting under surface tension, see M.P. Brenner and D. Gueyffier, Phys. Fluids 11, 737 (1999).
    • (1999) Phys. Fluids , vol.11 , pp. 737
    • Brenner, M.P.1    Gueyffier, D.2
  • 17
    • 0000237295 scopus 로고    scopus 로고
    • For molecular simulations on the fluids dynamics of the moving rim, see, J. Koplik and J.R. Banavar, Phys. Rev. Lett. 84, 4401 (2000).
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 4401
    • Koplik, J.1    Banavar, J.R.2
  • 18
    • 0032533101 scopus 로고    scopus 로고
    • Kinetics of growth of dry patches (during the early stages of dewetting process of microscopically thin polymer films cast on a solid surface) are simulated by molecular dynamics in: H. Liu, A. Bhattacharya, and A. Chakrabarti, J. Chem. Phys. 109, 8607 (1998).
    • (1998) J. Chem. Phys. , vol.109 , pp. 8607
    • Liu, H.1    Bhattacharya, A.2    Chakrabarti, A.3
  • 26
    • 0000478261 scopus 로고
    • This Wagner-type constitutive relation can also be obtained from a purely rheological approach, based on the Cox-Merz rule and Eyring’s expression for the nonlinear shear viscosity: see, J.C. Dyre, Rheol. Acta 29, 145 (1990).
    • (1990) Rheol. Acta , vol.29 , pp. 145
    • Dyre, J.C.1
  • 28
    • 85036377028 scopus 로고    scopus 로고
    • H.A. Barnes, J.F. Hutton, and K. Walters, An Introduction to Rheology (Elsevier, New York, 1989), p. 18
    • H.A. Barnes, J.F. Hutton, and K. Walters, An Introduction to Rheology (Elsevier, New York, 1989), p. 18.
  • 29
    • 85036371736 scopus 로고    scopus 로고
    • R.M. Christensen, Theory of Viscoelasticity, an Introduction 2nd ed. (Academic Press, New York, 1982), p. 53
    • R.M. Christensen, Theory of Viscoelasticity, an Introduction 2nd ed. (Academic Press, New York, 1982), p. 53.
  • 30
    • 85036250547 scopus 로고    scopus 로고
    • order to keep the model analytically tractable, we here neglect the pressure discontinuity arising from the interface curvature. Taking this Laplace pressure into account may lead to oscillations of film profile, and may even give rise to a cascade of pinch-off events, as proposed in Ref. 20
    • In order to keep the model analytically tractable, we here neglect the pressure discontinuity arising from the interface curvature. Taking this Laplace pressure into account may lead to oscillations of film profile, and may even give rise to a cascade of pinch-off events, as proposed in Ref. 20.
  • 33
    • 0001012295 scopus 로고
    • A theoretical approach to the spinodal dewetting is proposed in: S.A. Safran and J. Klein, J. Phys. II 3, 749 (1993).
    • (1993) J. Phys. II , vol.3 , pp. 749
    • Safran, S.A.1    Klein, J.2
  • 34
    • 0031075077 scopus 로고    scopus 로고
    • F. Brochard-Wyart, Macromolecules 30, 1211 (1997). This exponential behavior is observed during the initial stage of process, as long as the viscous friction on the liquid/substrate interface remains negligible compared with the dissipation in the plug flow of removing fluid.
    • (1997) Macromolecules , vol.30 , pp. 1211
    • Brochard-Wyart, F.1
  • 35
    • 85036413346 scopus 로고    scopus 로고
    • The development of (Formula presented) at small (Formula presented) shows that F does not admit a Taylor expansion near zero. This is directly due to the fact that the Cross rheological equation (4) itself is not analytical, since the second term of its development near zero is of order (Formula presented)
    • The development of (Formula presented) at small (Formula presented) shows that F does not admit a Taylor expansion near zero. This is directly due to the fact that the Cross rheological equation (4) itself is not analytical, since the second term of its development near zero is of order (Formula presented)
  • 36
    • 85036320646 scopus 로고    scopus 로고
    • It is clear that this exponential law cannot be valid for too thin films. Writing (Formula presented) (where E is an elastic modulus, and (Formula presented) is the reptation time of polymers, the relaxation time of the material), one obtains (Formula presented) with (Formula presented) which leads to a characteristic time (Formula presented) smaller than (Formula presented) if (Formula presented) the relaxation would be too fast
    • It is clear that this exponential law cannot be valid for too thin films. Writing (Formula presented) (where E is an elastic modulus, and (Formula presented) is the reptation time of polymers, the relaxation time of the material), one obtains (Formula presented) with (Formula presented) which leads to a characteristic time (Formula presented) smaller than (Formula presented) if (Formula presented) the relaxation would be too fast.
  • 37
    • 85036342230 scopus 로고    scopus 로고
    • G. Reiter (private communication)
    • G. Reiter (private communication).
  • 38
    • 0040357338 scopus 로고
    • On the wetting and slippage of polymer films on solid surfaces, see, F. Brochard-Wyart, Langmuir 10, 1566 (1994);
    • (1994) Langmuir , vol.10 , pp. 1566
    • Brochard-Wyart, F.1
  • 40
    • 0035797997 scopus 로고    scopus 로고
    • An experimental study of the dewetting of PS from poly (methylmethacrylate) on silicon substrates as a function of film thickness was recently proposed. See, C. Wang, G. Krausch, and M. Geoghegan, Langmuir 17, 6269 (2001).
    • (2001) Langmuir , vol.17 , pp. 6269
    • Wang, C.1    Krausch, G.2    Geoghegan, M.3
  • 44
    • 85036305477 scopus 로고    scopus 로고
    • E. Guyon, J.-P. Hulin, and L. Petit, Hydrodynamique Physique, 2nd ed. (CNRS Eds., Paris, 2001), p. 233
    • E. Guyon, J.-P. Hulin, and L. Petit, Hydrodynamique Physique, 2nd ed. (CNRS Eds., Paris, 2001), p. 233.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.