Macromolecular Rapid Communications
Communication
Molecular Weight Effects on the Glass Transition and Confinement Behavior of Polymer Thin Films Wenjie Xia, David D. Hsu, Sinan Keten*
Nanoscale polymer thin films exhibit strong confinement effects on Tg arising from free surfaces. However, the coupled influence of molecular weight (MW) and surface effects on Tg is not well understood for low MW film systems below the entanglement length. Utilizing atomistically informed coarse-grained molecular dynamics simulations for poly(methyl methacrylate) (PMMA), it is demonstrated that the decrease in free-standing film Tg with respect to bulk is more significant for low MW compared to high MW systems. Investigation of the local interfacial properties reveals that the increase in the local free volume near the free surface is greater for low MW, explaining the MW dependence of Tg-confinement behaviors. These findings corroborate recent experiments on low MW films, and highlight the relationship between nanoconfinement phenomena and local free volume effects arising from free surfaces.
1. Introduction Predicting the glass-transition behavior of polymer films is essential for numerous applications such as nanoelectronics[1] and nanocomposites.[2] The glass transition temperature (Tg) of polymers is often significantly lower than bulk values at small length scales in thin films where free-surface effects dominate over substrate effects on chain dynamics. Tg depression observed in thin films relative to the bulk is mainly attributed to the free-surfaceinduced enhancement of segmental mobility and shift of chain relaxation.[3–6] Previous experiments and molecular simulations have consistently demonstrated that the freesurface effects on thin film Tg are influenced by factors W. Xia, D. D. Hsu, Prof. S. Keten Department of Civil & Environmental Engineering and Department of Mechanical Engineering Northwestern University Evanston, IL 60208, USA E-mail: [email protected]
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relevant to polymer chain relaxation and dynamics, such as film thickness,[5,7,8] chain rigidity,[9,10] cohesive interactions,[11,12] and others.[13] Among these factors, the role of molecular weight (MW) effects on Tg-confinement behavior has been studied experimentally,[14–17] and has also led to theoretical models such as de Gennes’ sliding motion mechanism[18] and the delayed glassification model.[19] Interest in low MW systems is growing, partially due to their prevalence in applications such as lithography where the size of individual molecules impacts surface roughness.[20] However, previous confinement studies mostly focus on the high MW regime, far above the entanglement length, and systems with MW below the entanglement length remain to be fully explored. Several experimental studies have been performed with disparate observations. Ellison et al.[21] observed that polystyrene (PS) thin films over a broad MW range from 5 to 3000 kg mol−1 have no significant MW effect on the thickness dependence of Tg, suggesting that the factors associated with MW, such as chain-end segregation
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DOI: 10.1002/marc.201500194
Molecular Weight Effects on the Glass Transition and Confinement Behavior of Polymer Thin Films
Macromolecular Rapid Communications www.mrc-journal.de
and entanglement density, play an insignificant role in Tg-confinement. Dion et al.[22] observed that addition of low MW components in poly(methyl methacrylate) (PMMA) thin films can lead to a dramatic decrease in film Tg with decreasing thickness. Lan and Torkelson later confirmed this finding,[23] showing that the Tg depression of silica-supported PMMA and poly(1-ethylcyclopentyl methacrylate) (PECPMA) thin films compared to bulk is greater for low MW than high MW. Xue and co-workers[24] used differential alternating current chip calorimetry to quantify the Tg in silica-supported PS and PMMA films, and found a much more pronounced Tg depression for oligomers and star-shaped polymers, compared to their long linear chain analogues. Conversely, Tsui and co-workers[25] observed that there is no thickness dependent Tg depression for low MW (Mn = 1.3 kg mol−1) poly(α-methyl styrene) (PαMS) films supported by silica, but there is significant depression in Tg for high MW. Understanding the mechanisms of these contradictory experimental observations is challenging due to the experimental limitations in measurement resolution and synthesis such as controlling polydispersity.[26] Moreover, experiments on low MW thin films typically require a substrate support, causing free-surface effects to be obscured.[27–30] To provide mechanistic insight into the confinement and glass-transition behavior of low MW thin films, here we present a study of coarse-grained molecular dynamics (CG-MD) simulations. Rather than using generic CG models, we instead use a two-bead per monomer CG model for PMMA, which has been parameterized from all-atomistic simulations to match local structure and thermomechanical properties.[31] This provides the advantage of reflecting chemical specificity for quantitative experimental comparison while maintaining efficiency of length and time scales. Utilizing this CG model, we carry out free-standing thin film simulations with free surfaces to investigate MW effect on Tg confinement behavior. Employing the layermodel approach, both apparent Tg of free-standing films and local Tg of free-surface layers within the films are analyzed and compared for low and high MW. The results indicate that low MW films exhibit a greater Tg reduction than high MW films, which can be attributed to the reduced interfacial density associated with the perturbation in local free volume and chain packing arising from free surfaces.
2. Simulation Methods The multi-scale approach involves a two-bead per monomer model (Figure 1a) optimized towards structural distributions with additional calibrations to reproduce thermomechanical properties of bulk PMMA such as
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Figure 1. a) Chemical structure of PMMA and mapping scheme of the two-bead CG model. The locations of the mass and force centers for the carbon backbone and side-chain group are labeled by A and B, respectively. b) Snapshot of the CG free-standing thin film.
elastic modulus, density, and Tg.[31] Here, we carry out free-standing thin film simulations for MWs ranging from 2 to 20 kg mol−1, corresponding to chain lengths from 20 to 200 monomers per chain. The thin film systems consist of 14 200 to 46 000 beads, resulting in films with thicknesses varying from ≈10 to 40 nm along the z-axis at room temperature. The initial configurations of films are built using a self-avoiding random walk algorithm with a density of 1.18 g cm−3. The center of the film is aligned with the x–y plane at z = 0 nm. Periodic boundary conditions are applied in both x- and y-directions with dimensions of ≈9 × 9 nm2 and nonperiodic boundary conditions are applied in the z-direction, allowing two free surfaces (Figure 1b). During equilibration, two annealing cycles from 210 to 750 K are carried out for 2 ns, and the system is subsequently equilibrated at 510 K for another 2 ns before cooling. The energy, pressure, and film thickness converge to their respective average values at the end of the equilibration. A time step of 4 fs and the canonical ensemble (NVT) are adopted for all thin film simulations. For each MW and film thickness condition, four separate films with different initial configurations are simulated for the purpose of statistical analysis. Polymer segmental relaxation is evaluated from the self-part of the intermediate scattering function Fs ( q , t ) measured at a wavenumber q = 15.19 nm−1 corresponding to the first peak in the static structure factor. The relaxation time τα is defined as the time at which Fs ( q , t ) decays to 0.2. Note that the exact choice of the decay value will not qualitatively change the results presented herein. The temperature dependent τα can be described by the VogelFulcher-Tammann (VFT) equation. Tg is defined as the temperature at which τα reaches 1 ns, which is consistent with the computational convention employed by Simmons et al.[32] Additionally, we also use the methodology described by Tsige and Taylor[33] to validate our bulk Tg calculations from the measurement of mean-squared displacement (MSD) of CG atoms.
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Detailed description of the simulation and analysis protocols are provided in the Supporting Information.
3. Results and Discussion In order to perform thin film comparisons with the bulk, we first characterize the MW-dependent bulk Tg based on the relaxation measurement (Figure S2, Supporting Information). The MW-dependent bulk Tg can be well captured by the Flory–Fox equation: Tgbulk ( Mn ) = Tg∞ − K / Mn , where Tg∞ and K are fitting constants. The obtained values of Tg∞ and K from the fitting are 400 K and 43 380 K g mol−1, respectively. The experimental values of Tg∞ and K varies from 330 to 400 K and 4 × 104 to 3 × 105 K g mol−1, respectively, depending on the experimental technique and polymer tacticity.[34–36] Our simulation result agrees well with previous experimental values. Next, we focus on the molecular weight-dependent depression of thin film Tg. Figure 2a shows the comparison of τα for bulk and 18 nm-thick films for Mn = 2 and 20 kg mol−1 as a function of temperature, where intersections of the dotted line and VFT curves mark the Tg prediction for each case. We find that the relaxation time τα is lower in the thin film compared to the bulk system indicating that the free surfaces induce higher mobility of polymer chains for both low and high MW. Additionally, it can be observed that the polymer film with low MW exhibits a greater deviation of τα from the bulk than for high MW, suggesting that that the free-surface effect on film Tg is greater for low MW. Figure 2b shows how film Tg depends on film thickness H ranging from ≈10 to 40 nm. Here, we define the difference between the film and bulk Tg as ΔTg = Tgfilm − Tgbulk . We find that the ΔTg slowly vanishes to zero as the film thickness increases. This is because the free-surface layer becomes a smaller portion for thicker films, an observation that is common in experiments as well.[3,23] However, regardless of the thickness of the film, the free-surfaceinduced decrease in Tg is more pronounced for low MW. While there is nearly no difference between the film and bulk Tg for the 40 nm thick film for high MW, the Tg difference is still clearly discernible for low MW. A commonly employed concept in describing the physics of free-standing thin films is a bilayer model that consists of a surface region with enhanced mobility and an interior bulk-like region,[37–39] which is illustrated in Figure 2c. To quantify the coupling between MW and freesurface effects on the glass-transition behavior of films, we investigate the local Tg of the free-surface layer within the film. We estimate the size of the surface layer region by measuring the spatial relaxation time across the film at their bulk Tg (Figure S3, Supporting Information). The spatial relaxation profile indicates that there exists a local
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Figure 2. a) Relaxation time for bulk and 18 nm thick films for low and high MW systems. The solid and dashed curves are the VFT fits to the data. b) Tg depression of the film at different thicknesses. c) Tg depression of the entire film (H = 18 nm) compared to the surface layer for different MWs (left). Dashed curves illustrate trends. Schematic of the bilayer model in describing local Tg (right).
relaxation gradient in the surface region with a thickness of about 3.5 nm, which agrees well with previous experiments on PMMA that measured a length scale of ≈3 nm.[40] The MW effects on ΔTg of the entire film with a thickness of 18 nm as well as at the surface layer only
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Molecular Weight Effects on the Glass Transition and Confinement Behavior of Polymer Thin Films
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are shown in Figure 2c. The local ΔTg at the surface layer increases with MW and exhibits a qualitatively similar trend as that of the entire film. However, the magnitude of local ΔTg is significantly lower than the bulk due to reduced intermolecular constraints at the vicinity of the free surface, resulting in an overall reduction in film Tg. Local structure of polymer chains near the free surface provides further insight into the nature of MW-associated free surface effects on film glass transition and relaxation. Figure 3a shows the density profile as a function of film position (z-coordinate) for low and high MW 18 nm thick film. From the density profile, it can be seen that the local density decreases from the bulk value in the core of the film to zero at the surface. The high MW film exhibits a small local density peak near the surface that is absent in low MW films. This difference in the density profile indicates that local structural properties associated with chain packing are characteristically dissimilar for different MW.
Figure 3. a) Density profile and b) order parameter Sz along the height of 18 nm thick free-standing film for Mn = 2 and 20 kg mol−1.
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We further examine the structural ordering of polymer chains in the film by calculating the orientational order parameter Sz as a function of film position along the height: Sz = (3/2)〈cos2 α〉−1/2, where α is the angle between the backbone bond (AA) vector and z-axis. Figure 3b shows the order parameter results for MW = 2 and 20 kg mol−1. From the plot, a negative value of Sz at the vicinity of the free surface indicates that the bonds generally tend to be parallel to the surface in the surface region, while the bonds have no preferential orientations in the interior region of the film. Sz in the surface region for high MW is more highly negative compared to low MW indicating that the free surface influence on local chain orientation in the high MW system is stronger than the low MW system, leading to greater structural anisotropy in the high MW system. This suggests that the increased local density for high MW systems due to structural ordering and chain packing behaviors near the surface, can effectively reduce the free-surface effect on the Tg compared to low MW. From the density profile, the region near the free surface can be characterized as a liquid-like mobile region with reduced density, often called the interfacial layer. On the basis of the Gibbs dividing surface (GDS) concept, the thickness of the interfacial layer, or interfacial thickness hint, can be calculated by the equation: hint = (hmax − heff )/ 2 , where hmax is the maximum film thickness defined by the distance between the maximum and minimum z-coordinates of the film and heff is the effective film thickness between the two GDS boundaries. Figure 4 shows the comparison of hint for low and high MW systems. The magnitude of hint is about 0.5 nm, which is in a similar range as reported by earlier MD studies of polymer thin films.[11,41] Note that the hint measured based on the density profile is smaller than the dynamic surface length scale obtained from local relaxation data, which is a similar observation as reported by Lang and Simmons.[42] The greater value of hint suggests a greater free surface effect on the chain mobility, which is consistent with the observation of MW effect on film glass-transition behaviors. Since the MW effects on polymer relaxation and glass transition in the bulk state can be mainly attributed to the free volume associated with chain length, it is necessary to assess how the local free volume within the film shifts from the bulk for different chain lengths. The DebyeWaller factor (DWF) u2 is a dynamic measurement of the segmental “rattle-space” at the picosecond time scale and can directly provide information on the local mobility and free volume.[43,44] This quantity can also be measured by neutron scattering in experiments.[45,46] The localization model of relaxation reveals that the free volume vf scales with the DWF via the relationship 3/2 α /2 of v f ~ u2 , or more generally, v f ~ u2 .[44,47] In our
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on PMMA films. The dissimilar MW effect on the PαMS film Tg behavior may arise from a higher order of chain alignment as the MW becomes very low as suggested by the authors. Considering these contrasting observations, we believe that the MW-dependent Tg of polymer films could exhibit contrasting confinement behaviors depending on other factors associated with the polymeric system in focus, such as structural properties and cohesive interactions between chains. Future studies investigating the confinement behavior of both free-standing and supported films with varying polymer chemistry will be helpful in understanding the physical origin of diverse confinement phenomena observed for low MW systems. Figure 4. Interfacial thickness hint and normalized Debye–Waller factor of surface regions in 18 nm thick films for different MWs.
simulation, u2 is obtained from the measurement of MSD at t = 10 ps and at 350 K, corresponding to the dislocation time characterizing the crossover from the ballistic to the caged, sub-diffusive regime at low temperatures for the system studied. Here, we assume that the relationship between the local free volume and DWF is the same for bulk and film systems. We measure the local DWF of the surface layer normalized by the bulk value u2 surf / u2 bulk for different chain lengths as shown in Figure 4. Similar to 2 2 trends for hint , the normalized DWF u surf / u bulk is greater for the shortest chain length. Our analysis suggests that the free-surface-induced change in local free volume is greater for low MW films than for high MW. Therefore, the shift of relaxation time and decrease in film Tg compared to the bulk are also greater for low MW. In the recent study by Xue and co-workers,[24] it was proposed that the greater Tg depression of low MW silica-supported films is mainly attributed to the increased interfacial free volume due to the perturbation of interfaces near the substrate. Our simulation results support their argument that the local free volume is associated with MW, although in our system, the change in free volume arises from free surfaces instead of a substrate–film interface. The correlation between the local free volume and Tg-confinement effect shown in our simulations is also consistent with the experimental work by Napolitano et al.,[48,49] who have demonstrated that the shift in Tg is proportional to the degree of chain adsorption, which relates directly to the interfacial free volume. We also note that the Tg depression dependence on MW may exhibit variation for different polymer systems due to molecular chemistry and structural effects. For example, Tsui and co-workers[25] have observed a greater Tg depression for high MW PαMS supported thin films but did not detect significant Tg depression for low MW (1.3 kg mol−1) films, which is qualitatively different from other results
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4. Conclusion In summary, CG-MD simulations of PMMA presented here support the notion that that the depression in film Tg compared to the bulk at nanoscale is greater for very low MW than for high MW, indicating a stronger freesurface effect on lower MW thin films. In addition, local Tg measurements demonstrate that low MW films exhibit a greater Tg reduction in the free-surface layer compared to high MW films. The investigation of the local interfacial structural properties and Debye–Waller factor reveals that the increase in the local free volume at the free surface is greater for low MW, which may further explain the MW dependence of Tg-confinement behaviors. Our findings corroborate recent experimental observations, and highlight the important role of MW and local free volume in characterizing Tg-confinement behaviors arising from the free surface in polymer thin films.
Supporting Information Supporting Information is available from the Wiley Online Library or from the author Acknowledgements: W.X., D.D.H., and S.K. acknowledge support by the University Partnership Initiative between Northwestern University and The Dow Chemical Company and from the Department of Civil & Environmental Engineering and Mechanical Engineering at Northwestern University. The authors acknowledge valuable discussion with Dr. Steven G. Arturo of The Dow Chemical Company. A supercomputing grant from Quest HPC System at Northwestern University is acknowledged. Figure 1 was corrected on August 03, 2015. None of the information represented by the figure was changed. Received: March 31, 2015; Revised: April 23, 2015; Published online: June 1, 2015; DOI: 10.1002/marc.201500194 Keywords: free surfaces; glass transition; molecular weight; polymers; thin films
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Molecular Weight Effects on the Glass Transition and Confinement Behavior of Polymer Thin Films
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[1] H. Ito, Adv. Polym. Sci. 2005, 172, 37. [2] P. M. Ajayan, L. S. Schadler, P. V. Braun, Nanocomposite Science and Technology, Wiley-VCH, Weinheim, Germany 2006. [3] J. L. Keddie, R. A. L. Jones, R. A. Cory, Europhys. Lett. 1994, 27, 59. [4] J. S. Sharp, J. A. Forrest, Phys. Rev. Lett. 2003, 91, 235701. [5] C. J. Ellison, J. M. Torkelson, Nat. Mater. 2003, 2, 695. [6] S. Peter, H. Meyer, J. Baschnagel, R. Seemann, J. Phys. Condens. Matter 2007, 19, 205119 [7] J. L. Keddie, R. A. L. Jones, R. A. Cory, Europhys. Lett. 1994, 27, 59. [8] S. Peter, H. Meyer, J. Baschnagel, J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 2951. [9] J. M. Torres, C. Wang, E. B. Coughlin, J. P. Bishop, R. A. Register, R. A. Riggleman, C. M. Stafford, B. D. Vogt, Macromolecules 2011, 44, 9040. [10] A. Shavit, R. A. Riggleman, Macromolecules 2013, 46, 5044. [11] W. Xia, S. Keten, Langmuir 2013, 29, 12730. [12] W. Xia, S. Keten, J. Mater. Res. 2015, 30, 36. [13] S. Kim, M. K. Mundra, C. B. Roth, J. M. Torkelson, Macromolecules 2010, 43, 5158. [14] J. A. Forrest, K. Dalnoki-Veress, J. R. Dutcher, Phy. Rev. E 1997, 56, 5705. [15] K. Dalnoki-Veress, J. A. Forrest, C. Murray, C. Gigault, J. R. Dutcher, Phy. Rev. E 2001, 63, 031801. [16] C. B. Roth, J. R. Dutcher, J. Electroanal. Chem. 2005, 584, 13. [17] C. B. Roth, A. Pound, S. W. Kamp, C. A. Murray, J. R. Dutcher, Eur. Phys. J. E 2006, 20, 441. [18] P. G. de Gennes, Eur. Phys. J. E 2000, 2, 201. [19] J. E. G. Lipson, S. T. Milner, Macromolecules 2010, 43, 9874. [20] F. Wieberger, D. C. Forman, C. Neuber, A. H. Groschel, M. Bohm, A. H. E. Muller, H. W. Schmidt, C. K. Ober, J. Mater. Chem. 2012, 22, 73. [21] C. J. Ellison, M. K. Mundra, J. M. Torkelson, Macromolecules 2005, 38, 1767. [22] M. Dion, A. B. Larson, B. D. Vogt, J. Polym. Sci., Part B: Polym. Phys. 2010, 48, 2366. [23] T. Lan, J. M. Torkelson, Polymer 2014, 55, 1249. [24] J. Chen, L. Li, D. Zhou, J. Xu, G. Xue, Macromolecules 2014, 47, 3497. [25] K. Geng, F. Chen, O. K. C. Tsui, J. Non-Cryst. Solids 2015, 407, 296.
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[26] A. Rudin, Engineering, Elsevier The Elements of Polymer Science & Engineering, Academic Press, New York 1982. [27] D. S. Fryer, R. D. Peters, E. J. Kim, J. E. Tomaszewski, J. J. de Pablo, P. F. Nealey, C. C. White, W. L. Wu, Macromolecules 2001, 34, 5627. [28] R. D. Priestley, M. K. Mundra, N. J. Barnett, L. J. Broadbelt, J. M. Torkelson, Aust. J. Chem. 2007, 60, 765. [29] W. Xia, S. Mishra, S. Keten, Polymer 2013, 54, 5942. [30] P. Z. Hanakata, J. F. Douglas, F. W. Starr, Nat. Commun. 2014, 5, 4163. [31] D. D. Hsu, W. Xia, S. G. Arturo, S. Keten, J. Chem. Theory Comput. 2014, 10, 2514. [32] M. D. Marvin, R. J. Lang, D. S. Simmons, Soft Matter 2014, 10, 3166. [33] M. Tsige, P. L. Taylor, Phys. Rev. E 2002, 65, 021805. [34] K. Ute, N. Miyatake, K. Hatada, Polymer 1995, 36, 1415. [35] K. O'Driscoll, R. A. Sanayei, Macromolecules 1991, 24, 4479. [36] M. Rubinstein, R. Colby, Polymer Physics, Oxford University Press, Oxford 2003. [37] J. A. Forrest, J. Mattsson, Phys. Rev. E 2000, 61, R53. [38] J. Mattsson, J. A. Forrest, L. Borjesson, Phys. Rev. E 2000, 62, 5187. [39] M. D. Ediger, J. A. Forrest, Macromolecules 2013, 47, 471. [40] K. Paeng, M. D. Ediger, Macromolecules 2011, 44, 7034. [41] D. Hudzinskyy, A. V. Lyulin, A. R. C. Baljon, N. K. Balabaev, M. A. J. Michels, Macromolecules 2011, 44, 2299. [42] R. J. Lang, D. S. Simmons, Macromolecules 2013, 46, 9818. [43] A. Widmer-Cooper, P. Harrowell, Phys. Rev. Lett. 2006, 96, 185701. [44] F. W. Starr, S. Sastry, J. F. Douglas, S. C. Glotzer, Phys. Rev. Lett. 2002, 89, 125501. [45] R. Inoue, T. Kanaya, K. Nishida, I. Tsukushi, K. Shibata, Phys. Rev. Lett. 2005, 95, 056102. [46] C. L. Soles, J. F. Douglas, W. L. Wu, R. M. Dimeo, Phys. Rev. Lett. 2002, 88, 037401 [47] D. S. Simmons, M. T. Cicerone, Q. Zhong, M. Tyagi, J. F. Douglas, Soft Matter 2012, 8, 11455. [48] S. Napolitano, C. Rotella, M. Wübbenhorst, ACS Macro Lett. 2012, 1, 1189. [49] S. Napolitano, S. Capponi, B. Vanroy, Eur. Phys. J. E 2013, 36, 1.
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Communication
Molecular Weight Effects on the Glass Transition and Confinement Behavior of Polymer Thin Films Wenjie Xia, David D. Hsu, Sinan Keten*
Nanoscale polymer thin films exhibit strong confinement effects on Tg arising from free surfaces. However, the coupled influence of molecular weight (MW) and surface effects on Tg is not well understood for low MW film systems below the entanglement length. Utilizing atomistically informed coarse-grained molecular dynamics simulations for poly(methyl methacrylate) (PMMA), it is demonstrated that the decrease in free-standing film Tg with respect to bulk is more significant for low MW compared to high MW systems. Investigation of the local interfacial properties reveals that the increase in the local free volume near the free surface is greater for low MW, explaining the MW dependence of Tg-confinement behaviors. These findings corroborate recent experiments on low MW films, and highlight the relationship between nanoconfinement phenomena and local free volume effects arising from free surfaces.
1. Introduction Predicting the glass-transition behavior of polymer films is essential for numerous applications such as nanoelectronics[1] and nanocomposites.[2] The glass transition temperature (Tg) of polymers is often significantly lower than bulk values at small length scales in thin films where free-surface effects dominate over substrate effects on chain dynamics. Tg depression observed in thin films relative to the bulk is mainly attributed to the free-surfaceinduced enhancement of segmental mobility and shift of chain relaxation.[3–6] Previous experiments and molecular simulations have consistently demonstrated that the freesurface effects on thin film Tg are influenced by factors W. Xia, D. D. Hsu, Prof. S. Keten Department of Civil & Environmental Engineering and Department of Mechanical Engineering Northwestern University Evanston, IL 60208, USA E-mail: [email protected]
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relevant to polymer chain relaxation and dynamics, such as film thickness,[5,7,8] chain rigidity,[9,10] cohesive interactions,[11,12] and others.[13] Among these factors, the role of molecular weight (MW) effects on Tg-confinement behavior has been studied experimentally,[14–17] and has also led to theoretical models such as de Gennes’ sliding motion mechanism[18] and the delayed glassification model.[19] Interest in low MW systems is growing, partially due to their prevalence in applications such as lithography where the size of individual molecules impacts surface roughness.[20] However, previous confinement studies mostly focus on the high MW regime, far above the entanglement length, and systems with MW below the entanglement length remain to be fully explored. Several experimental studies have been performed with disparate observations. Ellison et al.[21] observed that polystyrene (PS) thin films over a broad MW range from 5 to 3000 kg mol−1 have no significant MW effect on the thickness dependence of Tg, suggesting that the factors associated with MW, such as chain-end segregation
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DOI: 10.1002/marc.201500194
Molecular Weight Effects on the Glass Transition and Confinement Behavior of Polymer Thin Films
Macromolecular Rapid Communications www.mrc-journal.de
and entanglement density, play an insignificant role in Tg-confinement. Dion et al.[22] observed that addition of low MW components in poly(methyl methacrylate) (PMMA) thin films can lead to a dramatic decrease in film Tg with decreasing thickness. Lan and Torkelson later confirmed this finding,[23] showing that the Tg depression of silica-supported PMMA and poly(1-ethylcyclopentyl methacrylate) (PECPMA) thin films compared to bulk is greater for low MW than high MW. Xue and co-workers[24] used differential alternating current chip calorimetry to quantify the Tg in silica-supported PS and PMMA films, and found a much more pronounced Tg depression for oligomers and star-shaped polymers, compared to their long linear chain analogues. Conversely, Tsui and co-workers[25] observed that there is no thickness dependent Tg depression for low MW (Mn = 1.3 kg mol−1) poly(α-methyl styrene) (PαMS) films supported by silica, but there is significant depression in Tg for high MW. Understanding the mechanisms of these contradictory experimental observations is challenging due to the experimental limitations in measurement resolution and synthesis such as controlling polydispersity.[26] Moreover, experiments on low MW thin films typically require a substrate support, causing free-surface effects to be obscured.[27–30] To provide mechanistic insight into the confinement and glass-transition behavior of low MW thin films, here we present a study of coarse-grained molecular dynamics (CG-MD) simulations. Rather than using generic CG models, we instead use a two-bead per monomer CG model for PMMA, which has been parameterized from all-atomistic simulations to match local structure and thermomechanical properties.[31] This provides the advantage of reflecting chemical specificity for quantitative experimental comparison while maintaining efficiency of length and time scales. Utilizing this CG model, we carry out free-standing thin film simulations with free surfaces to investigate MW effect on Tg confinement behavior. Employing the layermodel approach, both apparent Tg of free-standing films and local Tg of free-surface layers within the films are analyzed and compared for low and high MW. The results indicate that low MW films exhibit a greater Tg reduction than high MW films, which can be attributed to the reduced interfacial density associated with the perturbation in local free volume and chain packing arising from free surfaces.
2. Simulation Methods The multi-scale approach involves a two-bead per monomer model (Figure 1a) optimized towards structural distributions with additional calibrations to reproduce thermomechanical properties of bulk PMMA such as
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Figure 1. a) Chemical structure of PMMA and mapping scheme of the two-bead CG model. The locations of the mass and force centers for the carbon backbone and side-chain group are labeled by A and B, respectively. b) Snapshot of the CG free-standing thin film.
elastic modulus, density, and Tg.[31] Here, we carry out free-standing thin film simulations for MWs ranging from 2 to 20 kg mol−1, corresponding to chain lengths from 20 to 200 monomers per chain. The thin film systems consist of 14 200 to 46 000 beads, resulting in films with thicknesses varying from ≈10 to 40 nm along the z-axis at room temperature. The initial configurations of films are built using a self-avoiding random walk algorithm with a density of 1.18 g cm−3. The center of the film is aligned with the x–y plane at z = 0 nm. Periodic boundary conditions are applied in both x- and y-directions with dimensions of ≈9 × 9 nm2 and nonperiodic boundary conditions are applied in the z-direction, allowing two free surfaces (Figure 1b). During equilibration, two annealing cycles from 210 to 750 K are carried out for 2 ns, and the system is subsequently equilibrated at 510 K for another 2 ns before cooling. The energy, pressure, and film thickness converge to their respective average values at the end of the equilibration. A time step of 4 fs and the canonical ensemble (NVT) are adopted for all thin film simulations. For each MW and film thickness condition, four separate films with different initial configurations are simulated for the purpose of statistical analysis. Polymer segmental relaxation is evaluated from the self-part of the intermediate scattering function Fs ( q , t ) measured at a wavenumber q = 15.19 nm−1 corresponding to the first peak in the static structure factor. The relaxation time τα is defined as the time at which Fs ( q , t ) decays to 0.2. Note that the exact choice of the decay value will not qualitatively change the results presented herein. The temperature dependent τα can be described by the VogelFulcher-Tammann (VFT) equation. Tg is defined as the temperature at which τα reaches 1 ns, which is consistent with the computational convention employed by Simmons et al.[32] Additionally, we also use the methodology described by Tsige and Taylor[33] to validate our bulk Tg calculations from the measurement of mean-squared displacement (MSD) of CG atoms.
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Detailed description of the simulation and analysis protocols are provided in the Supporting Information.
3. Results and Discussion In order to perform thin film comparisons with the bulk, we first characterize the MW-dependent bulk Tg based on the relaxation measurement (Figure S2, Supporting Information). The MW-dependent bulk Tg can be well captured by the Flory–Fox equation: Tgbulk ( Mn ) = Tg∞ − K / Mn , where Tg∞ and K are fitting constants. The obtained values of Tg∞ and K from the fitting are 400 K and 43 380 K g mol−1, respectively. The experimental values of Tg∞ and K varies from 330 to 400 K and 4 × 104 to 3 × 105 K g mol−1, respectively, depending on the experimental technique and polymer tacticity.[34–36] Our simulation result agrees well with previous experimental values. Next, we focus on the molecular weight-dependent depression of thin film Tg. Figure 2a shows the comparison of τα for bulk and 18 nm-thick films for Mn = 2 and 20 kg mol−1 as a function of temperature, where intersections of the dotted line and VFT curves mark the Tg prediction for each case. We find that the relaxation time τα is lower in the thin film compared to the bulk system indicating that the free surfaces induce higher mobility of polymer chains for both low and high MW. Additionally, it can be observed that the polymer film with low MW exhibits a greater deviation of τα from the bulk than for high MW, suggesting that that the free-surface effect on film Tg is greater for low MW. Figure 2b shows how film Tg depends on film thickness H ranging from ≈10 to 40 nm. Here, we define the difference between the film and bulk Tg as ΔTg = Tgfilm − Tgbulk . We find that the ΔTg slowly vanishes to zero as the film thickness increases. This is because the free-surface layer becomes a smaller portion for thicker films, an observation that is common in experiments as well.[3,23] However, regardless of the thickness of the film, the free-surfaceinduced decrease in Tg is more pronounced for low MW. While there is nearly no difference between the film and bulk Tg for the 40 nm thick film for high MW, the Tg difference is still clearly discernible for low MW. A commonly employed concept in describing the physics of free-standing thin films is a bilayer model that consists of a surface region with enhanced mobility and an interior bulk-like region,[37–39] which is illustrated in Figure 2c. To quantify the coupling between MW and freesurface effects on the glass-transition behavior of films, we investigate the local Tg of the free-surface layer within the film. We estimate the size of the surface layer region by measuring the spatial relaxation time across the film at their bulk Tg (Figure S3, Supporting Information). The spatial relaxation profile indicates that there exists a local
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Figure 2. a) Relaxation time for bulk and 18 nm thick films for low and high MW systems. The solid and dashed curves are the VFT fits to the data. b) Tg depression of the film at different thicknesses. c) Tg depression of the entire film (H = 18 nm) compared to the surface layer for different MWs (left). Dashed curves illustrate trends. Schematic of the bilayer model in describing local Tg (right).
relaxation gradient in the surface region with a thickness of about 3.5 nm, which agrees well with previous experiments on PMMA that measured a length scale of ≈3 nm.[40] The MW effects on ΔTg of the entire film with a thickness of 18 nm as well as at the surface layer only
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are shown in Figure 2c. The local ΔTg at the surface layer increases with MW and exhibits a qualitatively similar trend as that of the entire film. However, the magnitude of local ΔTg is significantly lower than the bulk due to reduced intermolecular constraints at the vicinity of the free surface, resulting in an overall reduction in film Tg. Local structure of polymer chains near the free surface provides further insight into the nature of MW-associated free surface effects on film glass transition and relaxation. Figure 3a shows the density profile as a function of film position (z-coordinate) for low and high MW 18 nm thick film. From the density profile, it can be seen that the local density decreases from the bulk value in the core of the film to zero at the surface. The high MW film exhibits a small local density peak near the surface that is absent in low MW films. This difference in the density profile indicates that local structural properties associated with chain packing are characteristically dissimilar for different MW.
Figure 3. a) Density profile and b) order parameter Sz along the height of 18 nm thick free-standing film for Mn = 2 and 20 kg mol−1.
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We further examine the structural ordering of polymer chains in the film by calculating the orientational order parameter Sz as a function of film position along the height: Sz = (3/2)〈cos2 α〉−1/2, where α is the angle between the backbone bond (AA) vector and z-axis. Figure 3b shows the order parameter results for MW = 2 and 20 kg mol−1. From the plot, a negative value of Sz at the vicinity of the free surface indicates that the bonds generally tend to be parallel to the surface in the surface region, while the bonds have no preferential orientations in the interior region of the film. Sz in the surface region for high MW is more highly negative compared to low MW indicating that the free surface influence on local chain orientation in the high MW system is stronger than the low MW system, leading to greater structural anisotropy in the high MW system. This suggests that the increased local density for high MW systems due to structural ordering and chain packing behaviors near the surface, can effectively reduce the free-surface effect on the Tg compared to low MW. From the density profile, the region near the free surface can be characterized as a liquid-like mobile region with reduced density, often called the interfacial layer. On the basis of the Gibbs dividing surface (GDS) concept, the thickness of the interfacial layer, or interfacial thickness hint, can be calculated by the equation: hint = (hmax − heff )/ 2 , where hmax is the maximum film thickness defined by the distance between the maximum and minimum z-coordinates of the film and heff is the effective film thickness between the two GDS boundaries. Figure 4 shows the comparison of hint for low and high MW systems. The magnitude of hint is about 0.5 nm, which is in a similar range as reported by earlier MD studies of polymer thin films.[11,41] Note that the hint measured based on the density profile is smaller than the dynamic surface length scale obtained from local relaxation data, which is a similar observation as reported by Lang and Simmons.[42] The greater value of hint suggests a greater free surface effect on the chain mobility, which is consistent with the observation of MW effect on film glass-transition behaviors. Since the MW effects on polymer relaxation and glass transition in the bulk state can be mainly attributed to the free volume associated with chain length, it is necessary to assess how the local free volume within the film shifts from the bulk for different chain lengths. The DebyeWaller factor (DWF) u2 is a dynamic measurement of the segmental “rattle-space” at the picosecond time scale and can directly provide information on the local mobility and free volume.[43,44] This quantity can also be measured by neutron scattering in experiments.[45,46] The localization model of relaxation reveals that the free volume vf scales with the DWF via the relationship 3/2 α /2 of v f ~ u2 , or more generally, v f ~ u2 .[44,47] In our
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on PMMA films. The dissimilar MW effect on the PαMS film Tg behavior may arise from a higher order of chain alignment as the MW becomes very low as suggested by the authors. Considering these contrasting observations, we believe that the MW-dependent Tg of polymer films could exhibit contrasting confinement behaviors depending on other factors associated with the polymeric system in focus, such as structural properties and cohesive interactions between chains. Future studies investigating the confinement behavior of both free-standing and supported films with varying polymer chemistry will be helpful in understanding the physical origin of diverse confinement phenomena observed for low MW systems. Figure 4. Interfacial thickness hint and normalized Debye–Waller factor of surface regions in 18 nm thick films for different MWs.
simulation, u2 is obtained from the measurement of MSD at t = 10 ps and at 350 K, corresponding to the dislocation time characterizing the crossover from the ballistic to the caged, sub-diffusive regime at low temperatures for the system studied. Here, we assume that the relationship between the local free volume and DWF is the same for bulk and film systems. We measure the local DWF of the surface layer normalized by the bulk value u2 surf / u2 bulk for different chain lengths as shown in Figure 4. Similar to 2 2 trends for hint , the normalized DWF u surf / u bulk is greater for the shortest chain length. Our analysis suggests that the free-surface-induced change in local free volume is greater for low MW films than for high MW. Therefore, the shift of relaxation time and decrease in film Tg compared to the bulk are also greater for low MW. In the recent study by Xue and co-workers,[24] it was proposed that the greater Tg depression of low MW silica-supported films is mainly attributed to the increased interfacial free volume due to the perturbation of interfaces near the substrate. Our simulation results support their argument that the local free volume is associated with MW, although in our system, the change in free volume arises from free surfaces instead of a substrate–film interface. The correlation between the local free volume and Tg-confinement effect shown in our simulations is also consistent with the experimental work by Napolitano et al.,[48,49] who have demonstrated that the shift in Tg is proportional to the degree of chain adsorption, which relates directly to the interfacial free volume. We also note that the Tg depression dependence on MW may exhibit variation for different polymer systems due to molecular chemistry and structural effects. For example, Tsui and co-workers[25] have observed a greater Tg depression for high MW PαMS supported thin films but did not detect significant Tg depression for low MW (1.3 kg mol−1) films, which is qualitatively different from other results
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4. Conclusion In summary, CG-MD simulations of PMMA presented here support the notion that that the depression in film Tg compared to the bulk at nanoscale is greater for very low MW than for high MW, indicating a stronger freesurface effect on lower MW thin films. In addition, local Tg measurements demonstrate that low MW films exhibit a greater Tg reduction in the free-surface layer compared to high MW films. The investigation of the local interfacial structural properties and Debye–Waller factor reveals that the increase in the local free volume at the free surface is greater for low MW, which may further explain the MW dependence of Tg-confinement behaviors. Our findings corroborate recent experimental observations, and highlight the important role of MW and local free volume in characterizing Tg-confinement behaviors arising from the free surface in polymer thin films.
Supporting Information Supporting Information is available from the Wiley Online Library or from the author Acknowledgements: W.X., D.D.H., and S.K. acknowledge support by the University Partnership Initiative between Northwestern University and The Dow Chemical Company and from the Department of Civil & Environmental Engineering and Mechanical Engineering at Northwestern University. The authors acknowledge valuable discussion with Dr. Steven G. Arturo of The Dow Chemical Company. A supercomputing grant from Quest HPC System at Northwestern University is acknowledged. Figure 1 was corrected on August 03, 2015. None of the information represented by the figure was changed. Received: March 31, 2015; Revised: April 23, 2015; Published online: June 1, 2015; DOI: 10.1002/marc.201500194 Keywords: free surfaces; glass transition; molecular weight; polymers; thin films
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