Temperature- and thickness-dependent elastic moduli of polymer thin films
© Ao and Li; licensee Springer. 2011
Received: 24 September 2010
Accepted: 22 March 2011
Published: 22 March 2011
The mechanical properties of polymer ultrathin films are usually different from those of their counterparts in bulk. Understanding the effect of thickness on the mechanical properties of these films is crucial for their applications. However, it is a great challenge to measure their elastic modulus experimentally with in situ heating. In this study, a thermodynamic model for temperature- (T) and thickness (h)-dependent elastic moduli of polymer thin films E f(T,h) is developed with verification by the reported experimental data on polystyrene (PS) thin films. For the PS thin films on a passivated substrate, E f(T,h) decreases with the decreasing film thickness, when h is less than 60 nm at ambient temperature. However, the onset thickness (h*), at which thickness E f(T,h) deviates from the bulk value, can be modulated by T. h* becomes larger at higher T because of the depression of the quenching depth, which determines the thickness of the surface layer δ.
As devices are being developed with a view towards making them smaller, thinner and lighter in dimension, thin polymer films are found to be in more stringent demand in various applications, such as diffusion barriers, dielectric coatings, electronic packing, and so on . Therefore, understanding the elastic modulus in confined geometries, such as in thin films, is critical to the stability of the structures of the actual devices. A growing demand exists for the determination of the mechanical properties of thin films and coatings at a rapid pace. Recent researches primarily focusing on the confinement effect of the glass-transition temperature T g in thin films [2–7], have presented inconsistent results. It is believed that such a phenomenon might be attributed to the surface and interfacial effects. However, despite its technological importance, the corresponding elastic modulus of the confined thin polymer films has yet to be fully characterized to the same extent as T g effects have been done.
Direct experimental measures of the ultrathin material modulus have proven to be difficult since the presence of stiff substrate tends to interfere with the measurements . With regard to the impact of confinement on the elastic modulus of soft materials, there is no agreement. This occurrence was caused by the various measurement strategies , similar to the initial polymer thin film T g measurements [4, 6]. The different trends of the elastic modulus are due to the different interfacial interactions between probe and the polymer surface. Thus, noncontact mechanics measurement, which does not disturb the free surface, appears to be potentially advantageous for determining the modulus of polymer films. Recently, a wrinkle-based metrology was developed to measure the elastic properties of thin polymer films . In surface wrinkling measurements, to determine the modulus of thin polymer films, a wrinkling instability is utilized to induce compression of a stiff film bonded to a compliant substrate. The film modulus E f is determined based on the formula relating the substrate modulus E sub, the film thickness h, and the wrinkling wavelength λ: . At room temperature, the deduced elastic modulus of the films decreases with decreasing film thickness for ultrathin polymer films (thickness less than 30 nm) . In order to understand better the physical nature of the thickness dependence of the deduced elastic modulus in ultrathin films, a bilayer model was proposed to account for the surface effect on the wrinkling associated with the surface of a soft layer .
In the most recent research, the elastic moduli of a series of poly(methacrylate) films with widely varying bulk glass-transition temperature (T gb) as function of thickness at ambient temperature were measured by wrinkle-based metrology. A decrease of the modulus was found in all ultrathin polymers films (< 30 nm) with the onset of confinement effects shifting to larger film thicknesses as the quench depth into glass state (T gb - T) decreases, where T is the measured temperature . In other words, the quench depth affects the extent of the size dependence. To have a better clarification of the quench-depth effect on the elastic modulus of thin polymer films and the nature of the glass transition of polymers, T was considered as a variant to obtain the temperature-dependent elastic modulus of thin films. However, the in situ heating of a polymer-substrate system covering all the processing and characterization steps is impractical . Therefore, in this study, a model will be developed to investigate the temperature- and thickness-dependent elastic moduli of thin polymer films based on both the bilayer and the size-dependent glass-transition temperature thermodynamic models. The results of this new proposed model are then verified with experimental data that were obtained by wrinkle-based metrology for thin polystyrene (PS) films with different molar weights (M w).
where h 0 = 2c ξ, with ξ being the correlation length for the intermolecular cooperative rearrangement; c is a parameter related with the surface and interface: c = 1 for free-standing thin films or supported thin film with strong interaction between the polymer and the substrate, such as hydrogen bonding; and c = 1/2 for a supported thin film with weak interaction between the polymer and the substrate, such as van der Waals force, which is equivalent to the disappearance of the interface. αs = [2ΔC pb/3R]+1, where R is the ideal gas constant, and ΔC pb is the heat-capacity difference between the bulk glass and the bulk liquid at T gb. αi = αs E s/E i with E s and E i being the bond strength at the surface and interface, respectively.
Results and discussion
The theoretical model was applied to the PS thin films to verify the newly developed temperature- and thickness-dependent elastic modulus model. First, E bulk(T) and T g(h) should be determined for the PS films. It is known that the elastic properties decrease almost linearly in the glass state. They present a very strong temperature-dependent behavior near T g [8, 19]. In addition, generally the glass transition occurs from T g-50 K for bulk polymers. Therefore, E bulk(T) for bulk PS at T < T g-50 K is a linear function, which can be deduced from the experimental data obtained from E bulk(T) = -0.00189T + 4.558 . The result is also in agreement with another experimental result where the elastic modulus of bulk PS, E bulk = 4.0 GPa at T = 294 ± 3 K . E sur was considered much smaller than the corresponding E bulk; it is about 0.1 GPa for PS .
A theoretical model for the temperature- and thickness-dependent elastic modulus E f(T,h) was established for amorphous polymer thin films to investigate the dominance of this mechanical property of PS films at nanometer scale. We found that at ambient temperature, E f(T,h) of PS thin films on the passivated substrate decreases as h decreases when h is thinner than 60 nm, while E f(T,h) is nearly independent on h for h > 60 nm. Furthermore, a significant thickness effect can be induced by the temperature. The onset of thickness, at which E f(T,h) deviates from the bulk value, is dependent on temperature and is larger at high temperature. At a certain temperature, E f(T,h) exhibits the same size-dependent trend as T g(h), which is associated with the quench depth of T g(h) - T. Except for the temperature effect, the thickness of the surface layer also depends on h, and it increases as h decreases due to the size-dependent glass-transition temperature T g(h). Therefore, E f(T,h) of the thin films can be determined using the developed model, thus providing references for the applications of polymer thin films.
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This study was supported by the Vice-Chancellor's Postdoctoral Research Fellowship Program of the University of New South Wales (SIR50/PS19184), the ECR grant of the University of New South Wales (SIR30/PS24201), and the Australian Research Council Discovery Programs DP1096769.
- Elshabini-Riad AAR, Barlow FD: Thin Film Technology Handbook. New York: McGraw-Hill; 1997.
- Keddie JE, Jones RAL, Cory RA: Size-dependent depression of the glass transition temperature in polymer films. Europhys Lett 1994, 27: 59–64. 10.1209/0295-5075/27/1/011View Article
- Forrest JA, Dalnoki VK: The glass transition in thin polymer films. Adv Colloid Interface Sci 2001, 94: 167–195. 10.1016/S0001-8686(01)00060-4View Article
- Jiang Q, Lang XY: Glass transition of low-dimensional polystyrene. Macromol Rapid Commun 2004, 25: 825–828. 10.1002/marc.200300274View Article
- Ao ZM, Jiang Q: Size effects on miscibility and glass transition temperature of binary polymer blend films. Langmuir 2006, 22: 1241–1246. 10.1021/la0516779View Article
- Alcoutlabi M, McKenna GB: Effects of confinement on material behavior at the nanometer size scale. J Phys Condens Matter 2005, 17: R461-R524. 10.1088/0953-8984/17/15/R01View Article
- Ellison CJ, Torkelson JM: The distribution of glass-transition temperatures in nanoscopically confined glass formers. Nat Mater 2003, 2: 659–700. 10.1038/nmat980View Article
- Torres JM, Stafford CM, Vogt BD: Elastic modulus of amorphous polymer thin filmes: Relationship to the glass transition temperature. ACS Nano 2009, 3: 2677–2685. 10.1021/nn9006847View Article
- Forrest JA, Dalnoki-Veress K, Dutcher JR: Brillouin light scattering studies of the mechanical properties of thin freely standing polystyrene films. Phys Phys E 1998, 58: 6109–6114.
- Stafford CM, Harrison C, Beers KL, Karim AK, Amis EJ, Vanlandingham MR, Kim H-C, Volksen W, Miller RD, Simonyi EE: A buckling-based metrology for measuring the elastic moduli of polymeric thin films. Nat Mater 2004, 3: 545–550. 10.1038/nmat1175View Article
- Stafford CM, Vogt BD, Harrison C, Julhongpiput D, Huang R: Elastic moduli of ultrathin amorphous polymer films. Macromolecules 2006, 39: 5095–5099. 10.1021/ma060790iView Article
- Huang R, Stafford CM, Vogt BD: Effect of surface properties on wrinkling of ultrathin films. J Aerospace Eng 2007, 20: 38–44. 10.1061/(ASCE)0893-1321(2007)20:1(38)View Article
- Ao ZM, Li S, Jiang Q: The determination of Young's modulus in noble metal nanowires. Appl Phys Lett 2008, 93: 081905. 10.1063/1.2976134View Article
- Sun CQ: Size dependence of nanostructures: impact of bond order deficiency. Prog Solid State Chem 2007, 35: 1–159. 10.1016/j.progsolidstchem.2006.03.001View Article
- Ouyang G, Li XL, Tan X, Yang GW: Size-induced strain and stiffness of nanocrystals. Appl Phys Lett 2006, 89: 031904. 10.1063/1.2221897View Article
- Mansfield KF, Theodorou DN: Molecular dynamics simulation of a glassy polymer surface. Macromolecules 1991, 24: 6283–6294. 10.1021/ma00023a034View Article
- Fakhraai Z, Forrest JA: Measuring the surface dynamics of glassy polymers. Science 2008, 319: 600–604. 10.1126/science.1151205View Article
- Bohme TR, de Pablo JJ: Evidence for size-dependent mechanical properties from simulations of nanoscopic polymeric structures. J Chem Phys 2002, 116: 9939–9951. 10.1063/1.1476315View Article
- Fukuhara M: Temperature dependency of elastic moduli and internal dilational and shear frictions of polyetherimide. J Appl Polym Sci 2003, 90: 759–764. 10.1002/app.12717View Article
- Yoshimoto K, Jain T, Nealey PF, de Pablo JJ: Local dynamic mechanical properties in model free-standing polymer thin films. J Chem Phys 2005, 122: 144712. 10.1063/1.1873732View Article
- Ao ZM, Zheng WT, Jiang Q: Lindemann-like size-independent glass-transition criterion for polymers. Polymer 2008, 49: 3578–3581. 10.1016/j.polymer.2008.05.044View Article
- Tran TA, Saïd S, Grohens Y: Nanoscale characteristic length at the glass transition in confined syndiotactic poly(methyl methacrylate). Macromolecules 2005, 38: 3867–3871. 10.1021/ma0487296View Article
- Ilton M, Qi D, Forrest JA: Using nanoparticle embedding to probe surface rheology and the length scale of surface mobility in glassy polymers. Macromolecules 2009, 42: 6851–6854. 10.1021/ma901057bView Article
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