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Dynamics of Ultrathin Films in the Glassy State J. H. Xavier,* C. Li, M. H. Rafailovich, and J. Sokolov* Department of Materials Science and Engineering, SUNY at Stony Brook, Stony Brook, New York 11794 Received December 27, 2004. In Final Form: March 4, 2005 We report hole growth experiments in free-standing polystyrene (PS) films at temperatures up to 10 °C below the bulk glass transition. The data show an unexpected result: the growth rate of nucleated holes increases with increasing molecular weight, up to a limiting value beyond which the rate is approximately constant. Film thicknesses of 45, 80, and 100 nm were studied, using PS molecular weights ranging from 65K to 11.4 Mg/mol. Hole diameters grew linearly with time, and no growing rims were observed to form around the developing holes. Possible explanations in terms of elasticity, yield, and influence of sample preparation and confinement effects are discussed.
Introduction The issue of stability and structure of polymer thin films has attracted wide interest, both to obtain an understanding of the basic science involved and to further development of various applications in the areas of coatings, adhesives, lithography, and patterning.1-18 Topics of interest include uniformity, film-substrate interactions, rim structures around growing holes, effects of temperature, time, film thickness, and polymer molecular weight, stress in the films (residual, due to the method used to form the film or that generated during dewetting), and orientation of the polymer molecules. Recent theoretical work3,5,15,19 has focused on the dynamics of dewetting and included, within various models, the influence of viscous, elastic, and plastic deformations. The dynamics for experiments performed well above the glass transition temperature, (Tg), are dominated by viscosity, surface, and interfacial tensions and can be said to be reasonably well understood. However, for experiments near Tg, where elasticity and plasticity become important, the situation is far more complex, and the degree of understanding is * Authors to whom correspondence should be addressed. Tel: 631-632-8483. Fax: 631-632-5764. E-mail:
[email protected] (J.H.X.);
[email protected] (J.S.). (1) Geoghegan, M.; Krausch, G. Prog. Polym. Sci. 2003, 28, 261. (2) de Gennes, P.-G. Rev. Mod. Phys. 1985, 57, 827. (3) Brochard-Wyart, F.; Daillant, J. Can. J. Phys. 1990, 68, 1084. (4) Reiter, G. Phys. Rev. Lett. 1992, 68, 75. (5) Debregeas, G.; Martin, P.; Brochard-Wyart, F. Phys. Rev. Lett. 1995, 75, 3886. (6) Yerushalmi-Rosen, R.; Klein, J. Langmuir 1995, 11, 2806. (7) Lambooy, P.; Phelan, K. C.; Haugg, O.; Krausch, G. Phys. Rev. Lett. 1996, 76, 1110. (8) Carre, A.; Gastel, J.-C.; Shanahan, M. E. R. Nature 1996, 379, 432. (9) Jacobs, K.; Herminghaus, S.; Mecke, K. R. Langmuir 1998, 14, 965, and Masson, J.-L.; Green, P. F. Phys. Rev. Lett. 2002, 88, 205504. (10) Jacobs, K.; Seemann, R.; Schatz, G.; Herminghaus, S. Langmuir 1998, 14, 4961. (11) Reiter, G.; Khanna, R. Langmuir 2000, 16, 6351. (12) Seemann, R.; Herminghaus, S.; Jacobs, K. J. Phys.: Condensed Matter 2001, 13, 4925; Phys. Rev. Lett. 2001, 86, 5534. (13) Seemann, R.; Herminghaus, S.; Jacobs, K. Phys. Rev. Lett. 2001, 87, 196101. (14) Reiter, G. Phys. Rev. Lett. 2001, 87, 186101. (15) Shenoy, V.; Sharma, A. Phys. Rev. Lett. 2002, 88, 236101. (16) Reiter, G. Eur. Phys. J. E 2002, 8, 251. (17) Damman, P.; Baudelet, N.; Reiter, G. Phys. Rev. Lett. 2003, 91, 216101. (18) Reiter, G.; Sferrazza, M.; Damman, P. Eur. Phys. J. E 2003, 12, 133. (19) Saulnier, F.; Raphael, E.; deGennes, P.-G. Phys. Rev. E 2002, 66, 061607; Phys. Rev. Lett. 2002, 88, 196101.
less satisfactory. In this paper, we consider the growth of nucleated holes in thin free-standing polystyrene (PS) films well below the bulk glass transition temperature. Free-standing films, though more difficult to make, provide certain simplifications in analysis. The main advantages are that complicated substrate-film interactions are absent and the films are more symmetrical (two polymervacuum interfaces, rather than one polymer-vacuum and one polymer-substrate). Relatively little previous work5,20,21 has appeared on free-standing films, all in the melt. Due to the large driving force, the Laplace pressure, PL ) γ/e, with γ the surface tension and e the film thickness, hole growth may be induced even in the glassy state. Films having thickness 100 nm and surface tension 30 × 10-3 N/m, produce PL ≈ MPa, enough to induce yield, as pointed out by previous authors.8,16,21 Below, we present results for thin PS films, 45-100 nm thick, having molecular weights from 65 Kg/mol up to 11.4 Mg/mol at temperatures of 90-95 °C, i.e., up to 10 °C below the bulk Tg of 100 °C. Experimental Procedure The details of sample preparation and the hole growth experiments are described in ref 21. Briefly, thin films of monodisperse polystyrene (Pressure Chemical) were spun-cast from toluene solutions onto glass slides, floated onto the surface of a distilled water bath, and then deposited on aluminum or silicon substrates having 9 mm diameter holes at their center. Most samples were pre-annealed at 100 °C for 30 min, under vacuum, producing a wrinkle-free surface or for a shorter time if spontaneous holes were formed. A sharp needle was used to nucleate a hole diameter of 0.05-0.1 mm in each film. A temperature-controlled vacuum oven with a base pressure of 1 × 10-6 Torr was used for the hole growth experiments. An Olympus optical microscope and CCD video camera were used to monitor hole growth vs time up to a diameter of 2.5 mm. Some samples developed a larger number of spontaneous secondary holes in addition to the single nucleated hole. Data from these samples were not included. Films of thicknesses 45-100 nm were used, with molecular weights ranging from 65 Kg/mol to 11.4 Mg/mol. Table 1 shows the corresponding radii of gyration (Rg), and polydispersity index (Mw/Mn) for the polymers. Rg shown in Table 1 is given by Rg ) 6.7*(N/6)1/2, where N is the polymerization index. (20) Danolki-Veress, K.; Nickel, B. G.; Roth, C.; Dutcher, J. R. J. R. Phys. Rev. E 1999, 59, 2153. (21) Xavier, J. H.; Pu, Y.; Li, C.; Rafailovich, M. H.; Sokolov, J. Macromolecules 2004, 37, 1470.
10.1021/la046776l CCC: $30.25 © 2005 American Chemical Society Published on Web 04/09/2005
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Table 1. Characteristics of Polystyrene Used for This Studya MW (g/mol)
Rg (Å)
Mw/Mn
MW (g/mol)
Rg (Å)
Mw/Mn
65K 123K 200K 390K 650K
71 97 124 173 224
e1.04 e1.08 e1.06 e1.06 e1.06
2M 3.9M 7.11M 11.4M
393 555 740 937
e1.30 e1.05 e1.09 e1.09
a Cotton, J. P.; Decker, D.; Benoit, H.; Farnoux, B.; Higgings, J.; Jannink, G.; Ober, R.; Picot, C.; desCloizeaux, J. Macromolecules 1974, 7, 863.
Figure 2. Plot of hole diameter as a function of time for PS at T ) 95 °C, thickness e ) 1000 ( 50 Å and MW ranging from 123 Kg/mol to 11.4 Mg/mol.
Figure 1. Plot of hole diameter as a function of time for PS at T ) 95 °C, thickness e ) 800 ( 40 Å and MW ranging from 65 Kg/mol to 11.4 Mg/mol.
Results In Figure 1 are shown plots of hole diameter vs time at T ) 95 °C for 800 ( 40 Å thick PS films having molecular weights ranging from 65K to 11.4M. The striking feature is that the holes in the lower-molecular-weight films grow more slowly than the higher-molecular-weight films. For molecular weights greater than 2M, the growth rates are essentially independent of molecular weight. In all cases, the holes grow linearly with time, as found previously for similar films above, but near to, the glass transition.21 Also, as determined by atomic-force microscopy, no growing rims were observed to form around the growing holes, consistent with previous results on free-standing polymer films.5,20,21 Repeatability of the growth rates for similarly prepared samples are generally within 20%, and a minimum of three runs were made for each molecular weight. The trend of slower dynamics with lower molecular weights is certainly unexpected. The effects of viscosity, elasticity, plasticity, and film structural changes relative to bulk (dependent on Rg/e, where e ) film thickness) all may need to be taken into account. In addition, residual stresses produced by the sample preparation method may be significant.22,23 A set of observations which may be relevant for this work regards thin-film glass transitions. It has been reported,24 though there is not a concensus in the literature,25 that for very-high-molecular-weight PS free-standing films (e e 800 Å, MWs on the order of 1M) that the glass transition temperature (Tg) is reduced for increasing molecular weight. If this is the case, one would (22) Prest, W. M.; Luca, D. J. J. Appl. Phys. 1980, 51, 5170. (23) Richardson, H.; Carelli, C.; Keddie, J. L.; Sferrazza, M. Euro. Phys. J. E 2003, 12, 437. (24) Forrest, J. A.; Danolki-Veress, K.; Stevens, J. R.; Dutcher, J. R. Phys. Rev. Lett. 1996, 77, 2002. (25) Ge, S.; Pu, Y.; Zhang, W.; Rafailovich, M.; Sokolov, J.; Buenviaje, C.; Buckmaster, R.; Overney, R. M. Phys. Rev. Lett. 2000, 85, 2340.
expect faster dynamics, at a fixed temperature, for the larger polymers. To test this, we prepared a series of samples of somewhat greater thickness, 1000 ( 50 Å, for which the reported Tg’s24 are essentially bulklike. The results are shown in Figure 2, where it may be seen that the molecular trend is the same as for the 800 Å data. Therefore, a Tg effect does not appear to offer an explanation here. We next consider the possible influence of residual stress in the film, which has been examined in recent papers by Richardson et al.23 and deGennes et al.26 The spin-coating process (involving high shear rates) and the rapid evaporation (causing stresses to be frozen in as the film vitrifies on top of a rigid substrate) can induce large stresses, estimated to be as high as 100’s of MPa. The procedure of floating the spun-cast films onto a wafer before mounting on the sample frames should reduce this stress,23 as well as the moderate pre-anneal that the samples undergo. To test for possible effects of stress, we prepared samples which were taken from both the center of the spun-cast films (where the shear induced by spinning is lowest) and from the edges of the films (where the shear is larger). In Figure 3, we show the results 800 Å films, molecular weight 123K at 95 °C. The data show modest variations, not larger than what we see typically for other samples. We tentatively conclude that residual stress is not the dominant effect, though more work is needed to clarify the matter. Finally, we show a limited set of data in Figure 4 for T ) 90 °C, i.e., 10 °C below the bulk glass transition. The films were made of thickness 450 ( 15 Å so that experimental times would not be too long. Runs were made for times up to 2500 min. As can be seen from the figure, there is still substantial hole growth, and the same trend with molecular weight is evident. Figure 5 summarizes all the data of velocity of hole growth vs molecular weight. Discussion The hole growth experiment appears to be a creep-type experiment, with the driving force being due to the Laplace stress ()γ/e, γ ) polymer surface tension, e ) film thickness) at the edge of the hole. As discussed in deBregeas et al.,5 the elastic stress is propagated rapidly (at the speed of sound) through the viscoelastic polymer, (26) de Gennes, P.-G. Eur. Phys. J. E 2002, 7, 31.
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Figure 3. Plot of diameter vs time for prepared samples which were taken from both the center of the spun-cast films and from the edges of the films, PS, 123 K, e ) 800 Å ( 40 Å, T ) 95 °C.
Figure 4. Plot of hole diameter as a function of time for PS at T ) 90 °C, thickness e ) 450 ( 15 Å and MW ranging from 650 Kg/mol to 7.1 Mg/mol.
leading to a uniform thickening of the film. We would expect, therefore, that the stress and strain distribution would follow the form found for a thin elastic membrane having a hole at its center and a given stress applied to its inner surface.27 Assuming an incompressible material and radial symmetry, this leads to solutions of the form 27 Ur(r) ) K1r/2 + k2/r, σrr(r) ) k3 (k1 - 2k2/r2), and rr(r) ) ∂Ur/∂r ) k1/2 - k2/r2, where Ur(r) is the radial displacement of an element initially located at radial position r, σrr is the radial stress, rr is the radial component of strain, and k1, k2, and k3 are constants to be determined by the boundary conditions and the Hookean stress-strain relations. In our case, the boundary conditions are σrr (r ) ri) ) -PL, Ur (r ) router) ) 0, with ri the initial hole radius and router the outer radius of the hole (fixed onto substrate). This leads to
Ur(r) ) [3PLri2r(-1 + router2/r2)]/[2E(router2 + 3ri2)] (1) σrr(r) ) [-PLri2(3 + router2/r2)]/[(router2 + 3ri2)] (2) 2
rr(r) ) [-3PLri (1 +
router2/r2)]/[2E(router2
2
+ 3ri )] (3)
where E is the elastic modulus. For the case of viscoelastic polymers,28 we could consider a time-dependent r(t) and elastic modulus E f E(t)29,30 in eqs 1-3, or alternatively 1/E(t) f J(t), where J(t) is some appropriate creep compliance. To make a crude estimate of what J(t) would be, we consider the 123K PS sample, 1000 Å thick at T ) 95 °C. Up to t ) 104 s, the hole diameter grows from approximately 0.2 mm (i.e., ri ) 0.1 mm) to 0.4 mm, the radius therefore growing by 0.1 mm. Taking router ) 4.5 mm and Ur (r ) ri ) 0.1 mm) ) 0.1 mm = (3PL/2)J(t)*(0.1 mm), gives J (t ) 104 s) = 2 × 10-6 m2/N (27) Young, W. C. Roark’s Formulas for Stress and Strain, 6th ed.; McGraw-Hill: New York, 2002; p 638. (28) Ferry, J. Viscoelastic Properties of Polymers, 3rd ed.; Wiley: New York, 1980. (29) Schwarzl, F. R. Polymermechanik; Springer-Verlag: Berlin 1990, quoted in: Strobl, G. The Physics of Polymers; Springer-Verlag: Berlin, 1996; p 218. (30) Shya, G. D.; Isayev, A. I.; Li, C. T. J. Polym. Sci., Part B: Polym. Phys. 2001, 39, 2252.
Figure 5. Plot of hole velocity (V) as a function of Rg/e. PS, 95 °C (thickness e ) 800 ( 40 Å, e ) 1000 ( 50 Å), and 90 °C (e ) 450 ( 15 Å).
for PL ) γ/e = 3 × 105 N/m2 (for γ ) 30 mN/m and e ) 1000 Å). This may be compared with an estimate based on bulk creep data29 of J (t ) 104 s) = 2 × 10-7 m2/N, which is smaller by a factor 10. Of course, for higher molecular weights, the bulk compliance would be lower, contrary to the observed trend. For our experimental times and temperatures, we would mostly be in the glass-to-rubber transition region of the compliance curves. The experiments done at 90 °C, however, would correspond more nearly to the glassy region J ≈ 10-9 m2/N, and the discrepancy would be even larger. We are not able to explain the molecular-weight dependence of the hole growth by bulk viscoelastic behavior. Yield phenomena (for PS, see refs 30-33), as pointed out by Reiter,16 may be important. The maximum stresses induced by the Laplace Pressure are of the order 106 Pa, possibly enough to induce yield. However, this (31) Lach, R.; Grellmann, W.; Schroter, K.; Donth, E. Polymer 1999, 40, 1481. (32) Govaert, L. E.; Van Melick, H. G. H.; Meijer, H. E. H. Polymer 2001, 42, 1271. (33) Van Melick, H. G. H.; Govaert, L. E.; Raas, B.; Nauta, Meijer, H. E. H. Polymer 2003, 44, 1171.
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radial stress is concentrated near the edge of the hole, decreasing to =-4PL(ri2/router2) , PL at the outer radius (see eq 2 above) of the sample and in that region we would not expect yield. Similarly, the local radial strain decreases from ∼-1 near the hole to perhaps 10-3 near r ) router. The absence of a growing rim around the hole and the uniform thickening would favor the picture that the response throughout the film is similar (i.e., not the case that there is yielding near the hole but not far away from it). We also do not observe radial striations on the surface near the hole, as reported by Reiter16 for thin PS on coated substrates at temperatures slightly above Tg. We may conjecture that thin-film effects, either intrinsic or due to the spin-casting process, are dominant. Residual stresses23 and conformational changes22,34 of the polymer chains are present in thin films and should influence the dynamics. PS of molecular weights 2M and 11M has bulk molecular diameters, 2Rg, of 760 and 1780 Å, respectively, so that all of the films in the range where the hole growth velocity is constant have film thicknesses comparable to the PS molecular sizes. Prest and Luca22 observed that birefringence of micrometers-thick solution-cast PS films, indicative of molecular orientation, increased in magnitude with molecular weight up to about 105 g/mol and levels off. Stresses were estimated to be of order 1 MPa, similar to PL of our experiments. It is possible that this same trend of increasing molecular orientation with increasing molecular weight (up to some saturation point) is present to an even higher degree in our samples, which are produced by spin-casting and are an order of magnitude thinner. The increased orientation would cause lower elastic modulus and higher compliances, qualitatively in agreement with the trends of Figure 4. However, recent (34) Brown, H. R.; Russell, T. P. Macromolecules 1996, 29, 798, and references there in. (35) Stafford, C. M.; Harrison, C.; Beers, K. L.; Karim, A.; Amis, E. J.; Vanlandingham, M. R.; Kim, H.-C.; Volksen, W.; Miller, R. D.; Simonyi, E. Nat. Mater. 2004, 3, 545; A. Karim, private communication.
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measurements of Young’s modulus in PS films as thin as 30 nm did not find deviations from bulk values,35 though a sharp drop was observed below about 10 nm. In contrast, Brown and Russell,34 in a paper on entanglement effects at surfaces and interfaces, argue that several types of experiments (surface buffing alignment of polymers, strength of immiscible interfaces reinforced with diblocks, and diffusion near interfaces) are consistent with the hypothesis that chain entanglements are reduced relative to the bulk within a zone of width Rg near an inteface. If this is the case, the fraction of a thin film sample having reduced entanglements would be 2Rg/e or 4Rg/e (assuming either zones of Rg or 2Rg from the two surfaces of our free-standing films). This picture would predict an increase with molecular weight of velocity, due to an increasing fraction of the film having reduced entanglements, as well as a saturation point (when molecular weight is so large that the entire film has reduced entanglements). The crossover should occur roughly between Rg/e ) 1/4 to 1/2. The agreement with the main trends observed in Figure 5 is indeed encouraging. Conclusion Hole growth in thin PS films exhibits highly unusual features in the molecular weight dependence. We believe that an explanation based on modifications of the entanglements in the films offers the best explanation at present. However, more detailed characterization of the stress (optical birefringence experiments are in progress) and polymer conformations are needed, as well as an appropriate theoretical model. Acknowledgment. J.H.X., M.H.R., and J.S. acknowledge the financial support of the NSF-MRSEC program DMR 9632525. We want to thank A. Karim, S. Safran, and R. Colby for useful discussions, as well as the referee who drew our attention to ref 34. LA046776L
