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Relaxation of surface tracks on polycarbonate thin films induced by MeV heavy-ion impacts
Nuclear Instruments and Methods in Physics Research B 268 (2010) 3080–3083
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Relaxation of surface tracks on polycarbonate thin films induced by MeV heavy-ion impacts R. Leal a,b, C.T. Souza a, M.R. da Silva a, Z. Fakhraai c,*, J.A. Forrest c, R.M. Papaléo a,** a
Faculty of Physics, Catholic University of Rio Grande do Sul, Porto Alegre, Brazil Materials Science Graduate Program, Federal University of Rio Grande do Sul, Porto Alegre, Brazil c Department of Physics and Astronomy, University of Waterloo, Ontario, Canada b
a r t i c l e
i n f o
Article history: Received 13 October 2009 Available online 12 May 2010 Keywords: Ion tracks Cratering Relaxation Polymers Polycarbonate
a b s t r a c t In the present work, the relaxation behavior of nanometer-sized deformations produced by single ion impacts on the surface of monodisperse (Mw = 60,000 u) polycarbonate thin films was investigated at temperatures close to and below the glass transition. The relaxation functions for the length, height and width of the deformations were well described by a stretched exponential law, with characteristic relaxation times s strongly dependent on temperature. For T > 100 °C, the temperature dependence of s obeys a Vogel–Fulcher law, but for lower temperatures it becomes less steep and tends to an Arrhenius-type behavior. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction It has been known since many years that fast heavy-ions penetrating on insulator surfaces can lead to cratering and other nanometer-sized surface modifications [1–5]. The formation and thermalization of surface tracks occurs in tens of picoseconds after the passage of the projectile through the target and the process is fed, primarily, by the energy deposited in the core of the tracks [6]. On polymers, the surface tracks may have typically three distinct regions: a crater, a rim surrounding the crater walls, and at tilted angles, a long tail of protruded material. Recent studies [7] have shown that the rim is most probably formed by molten polymer flowing out from the impact center, whilst the tail is composed of displaced material due to the sudden expansion of the excited core. The size of the tails and craters depend on several factors connected both to the incident ion (angle of incidence, dE/dx, velocity and charge state) and to the target conditions (monomer structure, temperature, molar mass) [2–8]. In addition, there have been a few studies dedicated to investigate the relaxation behavior of the ion impact features [7]. So far only poly(methyl methacrylate) was studied and strong deviations of surface relaxation from bulk behavior was found. Although the ion-induced deformations follow the general relaxation laws of pristine polymers, they showed
* Corresponding author. Current address: Department of Chemistry, University of Wisconsin-Madison, Madison, USA. ** Corresponding author. Address: PUCRS, Av. Ipiranga 6681, 90619-900 Porto Alegre/RS, Brazil. Tel.: +55 51 33203535; fax: +55 51 33203616. E-mail address: [email protected] (R.M. Papaléo). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.05.048
an enhanced mobility, in accordance to what was found for nanoscopic volumes of deformed polymers produced by other means of surface perturbation [9,10]. In this paper, we report on the relaxation behavior of surface tracks induced by individual 18 MeV Au ions impinging on polycarbonate (PC) films at various temperatures, focusing on the long-term temporal evolution of the protruded regions. The results observed for PC are comparable to the ones recently observed for PMMA films [7] and appears to indicate a general trend for the relaxation of single-ion induced deformations on polymers.
2. Experimental The targets were polycarbonate (PC) thin films (around 100 nm thick) spun onto Si substrates from solutions of nearly monodisperse powders in toluene (Mw = 6.0 104 u, Mw/Mn < 1.3, Polymer Standard Services). After spin-coating, the samples were annealed at 130 °C for 24 h. The mean surface roughness of the films (measured with a scanning force microscope in a 500 nm scan) had a typical value of 0.3 nm. The irradiations were performed in vacuum at the Porto Alegre 3MV Tandetron ion implanter with a 18 MeV 197Au7+ beam at low fluences (109 cm2), hitting the samples at h = 84° with respect to the surface normal. A hollow Cu sample holder with a heating stage and cooling system was used for the bombardments and in situ annealing. Cooling of the samples was performed by circulating water at 4 °C, providing a cooling rate of 20 °C/s. Samples were bombarded at 12 different temperatures, between 60 and 106 °C. The samples were kept at
R. Leal et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 3080–3083
3081
the irradiation temperature for a pre-determined period of time, before the relaxation was interrupted by quenching the samples to room temperature. A series of samples was irradiated at each temperature, covering a suitable range of annealing times. The topography of irradiated samples was characterized in air by a Nanoscope IIIa (Digital Instruments) scanning force microscope in the Tapping Mode™ (TM-SFM), with standard Si tips (with nominal radius of curvature 10 nm) and a 1–2 Hz scanning frequency. Typical drive amplitudes were set to give a detector signal around of 3 V. Quantitative analysis of the data was performed only on images acquired with high-quality tips. Whenever possible, a complete set of samples irradiated to obtain the relaxation curve at a given temperature was imaged with the same tip in order to minimize systematic errors due to tip shape. The dimensions of the impact features were extracted from cross-sectional profiles and mean values were calculated from data collected from at least 30 impact features. 3. Results and discussion Fig. 1 shows a series of SFM top-view images of PC surfaces bombarded by 18 MeV Au ions, which give representative snapshots of the relaxation process of the impact features for two different temperatures, 60 and 91 °C. The dimensions of the protrusions (tails) decrease continuously with residence time and eventually they completely vanish. The rate of relaxation is strongly temperature dependent. Whilst for samples at 60 °C, tails are not fully relaxed even after 310 h after the ion impact (Fig. 1(a)–(f)), at 91 °C in less than 1 h the relaxation is fully completed. In contrast, the craters are much more stable than the tails. The general appearance of the craters does not change significantly even after annealing for several hours at the highest temperatures tested (except from a mild increase of the length and width) and full relaxation was never observed. Crater rims were rarely seen on the PC surfaces. In Fig. 2, the average length, height and maximum width of the hillocks are plotted as a function of time and temperature T. Fig. 3 shows the average initial size of the hillocks for the various irradi-
Fig. 2. Average size of surface tracks produced by 18 MeV Au ions on PC surfaces as a function of time for various temperatures: (a) tail length, (b) tail height and (c) tail width.
Fig. 1. TM-SFM images of PC films showing the typical stages of the relaxation behavior of impact features created by 18 MeV Au ions at 60 °C (a)–(e) and at 91 °C (f)–(k). The annealing time t before cooling to room temperature is given in each image. In frame (f), the tail, the rim, and the crater are identified by the letters T, R and C, respectively. The incidence angle is 84° with respect to the surface normal.
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R. Leal et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 3080–3083
Fig. 3. Average initial length of the hillocks as a function of the irradiation temperature.
ation temperatures. Ideally, the initial sizes would be obtained at t = 0 s (i.e., cooling immediately after bombardment). However, the minimum annealing time tmin is not zero, but is determined by the sum of the irradiation time (Dtirr), plus the cooling time (Dtc) (given typically tmin 1–2 s). Thus we use t = 1 s to represent the case were cooling is performed immediately after the bombardment. The initial size of the protrusions is stable up to T 85 °C, but decreases substantially for T > 100 °C. The temperature of full relaxation at tmin, TR is 110 °C. For the lower temperatures, shown in detail in Fig. 2a–c, full relaxation of the tails took from few seconds (T = 106 °C) to several weeks (T = 60 °C). All relaxation curves in Fig. 2 were fitted to Kohlrausch–William–Watts (KWW) functions,
XðtÞ ¼ X 0 expðt=sÞb
ð1Þ
where t is the time, s is the effective relaxation time, X is the particular dimension being considered, and 0 < b < 1. For bulk PC, the reported values of b vary between 0.4 and 0.5 [11]. Best fits were obtained for b 0.46 for T P 98 C and b ¼ 1 for T < 98 C. However, due to limited number of points in time and the large size fluctuations of the individual impact features, it is difficult to assert that the best mathematical fit corresponds to the true best ‘‘physical” b value. The relaxation times of the protrusion length (sl ) as a function of temperature are depicted in Fig. 4. For comparison, the relaxation times of the tail length in PMMA [7] are also shown. The s vary from few seconds to 106 s. Part of the data (the high T portion) was fitted to the Vogel–Fulcher–Tammann (VFT) equation
B sðTÞ ¼ s1 exp T T0
(dashed line in Fig. 4). The best fit was obtained for B ¼ 1330 152 K (similar to values found in the literature for the relaxation kinetics of bulk PC [11]) and T 0 ¼ 332 5 K. The value of s1 was set at 1012 s, as usually assumed, based on typical frequencies of molecular vibrations. The characteristic relaxation times s(T) of the nanodeformations are many orders of magnitude smaller than the typical values found for bulk PC. The fast dynamics of the ion-induced protrusions can be related to different factors. First, the protrusions are regions where the polymer chains are under stress (over the yield stress, since the deformation is plastic). Second, the nanodeformations are formed after a sudden disturbance caused by the ion impact. MD simulations predict the formation time of the protrusions to be of the order of 25ps. As the height of the deformations is around 2 nm in a film with thickness h 100 nm the deformation rate will be ðDl=lDtÞ 108 s1 , a very high value. Thus such regions are in a highly out of equilibrium state and relaxation times on glassy systems are known to depend on the deviation from equilibrium [12]. Finally, the impact features are on the surface of the targets, where the mobility of polymer chains can be significantly larger than the bulk [9,10,12–16]. All the above facts may be contributing to the fast relaxation rates observed for the ion-induced deformations. We note deformations produced by ion bombardment on PC exhibit similar relaxation behavior to those observed in PMMA samples [7]. The rates of relaxation are however slower in PC, as expected due to its more rigid structure and higher glass transition. The temperature at which s = 100s is sometimes used as a practical definition of the glass transition temperature, Tg [12]. This means that the local glass transition temperature at the hillocks (Tglocal) is around 100 °C, roughly 40 °C below the bulk Tg. For T < Tglocal or s(T) > 100 s, the dependence of s on temperature weakens and sðTÞ approaches an Arrhenius-type curve. This means the effective activation energy of the relaxation process becomes independent of the temperature in this regime, reaching a value of approximately 0.08 eV. This value represents the effective energy necessary for the cooperative movement involved in the relaxation of protrusions at T below the local Tg. The appearance of a single activation energy (opposite to a distributions of activating energies in the regime where VFT holds) suggests the cooperative rearranging region [12] involved in the relaxation is of the order of the dimensions of the deformations. 4. Conclusion
ð2Þ
In this work, we have studied the relaxation dynamics of protrusions induced by 18 MeV Au single ions on PC surfaces. It was found that the relaxation times s of the nanometer-sized deformations present strong deviations from typical values found for bulk PC. A local glass transition temperature was obtained for the deformations (Tglocal 100 °C), which is 40 °C below the nominal bulk Tg. For T > Tglocal, the temperature dependence of s obeys a Vogel– Fulcher law, but for lower temperatures it becomes less steep and tends to an Arrhenius-type behavior, as observed previously for PMMA. The activation energy for the hillock relaxation in the Arrhenius region was calculated to be Ea 0.08 eV. Acknowledgements The authors would like to acknowledge the Brazilian agencies CAPES and CNPQ for financial support. References
Fig. 4. Temperature dependence of the relaxation times of the length of the ioninduced deformations in PC and PMMA (from Ref.[7]). The dotted line depict the Vogel–Fulcher equation [Eq. (2)] adjusted to the data above the glass transition region. The local glass transition temperature, defined as s(Tg) = 100 s, is shown.
[1] I.H. Wilson, Surf. Interface Anal. 20 (1993) 637. [2] J. Kopniczky, C.T. Reimann, A. Hallén, B.U.R. Sundqvist, P. Tengvall, R. Erlandsson, Phys. Rev. B 49 (1994) 625.
R. Leal et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 3080–3083 [3] R. Neumann, Nucl. Instr. Meth. Phys. Res. B 151 (1999) 42. [4] E. Akcoltekin, T. Peters, R. Meyer, A. Duvenbeck, M. Klusmann, I. Monnet, H. Lebius, M. Schleberger, Nat. Nanotech. 2 (2007) 290. [5] D. Fink (Ed.), Ion Irradiation of Polymers: Fundamentals and applications, vol. 1, Springer, Berlin, 2004. [6] E. Bringa, R.E. Johnson, R.M. Papaléo, Phys. Rev. B 65 (2002) 094113. [7] R.M. Papaléo, R. Leal, W.H. Carreira, L.G. Barbosa, Phys. Rev. B 74 (2006) 094203. [8] R.M. Papaléo, L.D. de Oliveira, L.S. Farenzena, M.A. de Araújo, R.P. Livi, Phys. Rev. B 62 (2000) 11273. [9] Z. Fakhraai, J.A. Forrest, Science 319 (2008) 600.
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[10] D. Qi, Z. Fakhraai, J.A. Forrest, Phys. Rev. Lett. 101 (2008) 096101. [11] L. Delbreilh, E. Dargent, J. Grenet, J.-M. Saiter, A. Bernès, C. Lacabanne, Eur. Polym. J 43 (2007) 249. [12] R.H. Boyd, G.D. Smith, Polymer Dynamics and Relaxation, Cambridge Press, New York, 2007. [13] T. Kerle, Z. Lin, H. Kim, T.P. Russel, Macromolecules 34 (2001) 3484. [14] A. Karim, S. Kumar (Eds.), Polymer Surfaces, Interfaces and Thin Films, World Scientific, Singapore, 2000. [15] R.D. Priestley, C.J. Ellison, L.J. Broadbelt, J.M. Torkelson, Science 309 (2005) 456. [16] P.A. O’Connel, G. McKenna, Science 307 (2005) 1776.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Relaxation of surface tracks on polycarbonate thin films induced by MeV heavy-ion impacts R. Leal a,b, C.T. Souza a, M.R. da Silva a, Z. Fakhraai c,*, J.A. Forrest c, R.M. Papaléo a,** a
Faculty of Physics, Catholic University of Rio Grande do Sul, Porto Alegre, Brazil Materials Science Graduate Program, Federal University of Rio Grande do Sul, Porto Alegre, Brazil c Department of Physics and Astronomy, University of Waterloo, Ontario, Canada b
a r t i c l e
i n f o
Article history: Received 13 October 2009 Available online 12 May 2010 Keywords: Ion tracks Cratering Relaxation Polymers Polycarbonate
a b s t r a c t In the present work, the relaxation behavior of nanometer-sized deformations produced by single ion impacts on the surface of monodisperse (Mw = 60,000 u) polycarbonate thin films was investigated at temperatures close to and below the glass transition. The relaxation functions for the length, height and width of the deformations were well described by a stretched exponential law, with characteristic relaxation times s strongly dependent on temperature. For T > 100 °C, the temperature dependence of s obeys a Vogel–Fulcher law, but for lower temperatures it becomes less steep and tends to an Arrhenius-type behavior. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction It has been known since many years that fast heavy-ions penetrating on insulator surfaces can lead to cratering and other nanometer-sized surface modifications [1–5]. The formation and thermalization of surface tracks occurs in tens of picoseconds after the passage of the projectile through the target and the process is fed, primarily, by the energy deposited in the core of the tracks [6]. On polymers, the surface tracks may have typically three distinct regions: a crater, a rim surrounding the crater walls, and at tilted angles, a long tail of protruded material. Recent studies [7] have shown that the rim is most probably formed by molten polymer flowing out from the impact center, whilst the tail is composed of displaced material due to the sudden expansion of the excited core. The size of the tails and craters depend on several factors connected both to the incident ion (angle of incidence, dE/dx, velocity and charge state) and to the target conditions (monomer structure, temperature, molar mass) [2–8]. In addition, there have been a few studies dedicated to investigate the relaxation behavior of the ion impact features [7]. So far only poly(methyl methacrylate) was studied and strong deviations of surface relaxation from bulk behavior was found. Although the ion-induced deformations follow the general relaxation laws of pristine polymers, they showed
* Corresponding author. Current address: Department of Chemistry, University of Wisconsin-Madison, Madison, USA. ** Corresponding author. Address: PUCRS, Av. Ipiranga 6681, 90619-900 Porto Alegre/RS, Brazil. Tel.: +55 51 33203535; fax: +55 51 33203616. E-mail address: [email protected] (R.M. Papaléo). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.05.048
an enhanced mobility, in accordance to what was found for nanoscopic volumes of deformed polymers produced by other means of surface perturbation [9,10]. In this paper, we report on the relaxation behavior of surface tracks induced by individual 18 MeV Au ions impinging on polycarbonate (PC) films at various temperatures, focusing on the long-term temporal evolution of the protruded regions. The results observed for PC are comparable to the ones recently observed for PMMA films [7] and appears to indicate a general trend for the relaxation of single-ion induced deformations on polymers.
2. Experimental The targets were polycarbonate (PC) thin films (around 100 nm thick) spun onto Si substrates from solutions of nearly monodisperse powders in toluene (Mw = 6.0 104 u, Mw/Mn < 1.3, Polymer Standard Services). After spin-coating, the samples were annealed at 130 °C for 24 h. The mean surface roughness of the films (measured with a scanning force microscope in a 500 nm scan) had a typical value of 0.3 nm. The irradiations were performed in vacuum at the Porto Alegre 3MV Tandetron ion implanter with a 18 MeV 197Au7+ beam at low fluences (109 cm2), hitting the samples at h = 84° with respect to the surface normal. A hollow Cu sample holder with a heating stage and cooling system was used for the bombardments and in situ annealing. Cooling of the samples was performed by circulating water at 4 °C, providing a cooling rate of 20 °C/s. Samples were bombarded at 12 different temperatures, between 60 and 106 °C. The samples were kept at
R. Leal et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 3080–3083
3081
the irradiation temperature for a pre-determined period of time, before the relaxation was interrupted by quenching the samples to room temperature. A series of samples was irradiated at each temperature, covering a suitable range of annealing times. The topography of irradiated samples was characterized in air by a Nanoscope IIIa (Digital Instruments) scanning force microscope in the Tapping Mode™ (TM-SFM), with standard Si tips (with nominal radius of curvature 10 nm) and a 1–2 Hz scanning frequency. Typical drive amplitudes were set to give a detector signal around of 3 V. Quantitative analysis of the data was performed only on images acquired with high-quality tips. Whenever possible, a complete set of samples irradiated to obtain the relaxation curve at a given temperature was imaged with the same tip in order to minimize systematic errors due to tip shape. The dimensions of the impact features were extracted from cross-sectional profiles and mean values were calculated from data collected from at least 30 impact features. 3. Results and discussion Fig. 1 shows a series of SFM top-view images of PC surfaces bombarded by 18 MeV Au ions, which give representative snapshots of the relaxation process of the impact features for two different temperatures, 60 and 91 °C. The dimensions of the protrusions (tails) decrease continuously with residence time and eventually they completely vanish. The rate of relaxation is strongly temperature dependent. Whilst for samples at 60 °C, tails are not fully relaxed even after 310 h after the ion impact (Fig. 1(a)–(f)), at 91 °C in less than 1 h the relaxation is fully completed. In contrast, the craters are much more stable than the tails. The general appearance of the craters does not change significantly even after annealing for several hours at the highest temperatures tested (except from a mild increase of the length and width) and full relaxation was never observed. Crater rims were rarely seen on the PC surfaces. In Fig. 2, the average length, height and maximum width of the hillocks are plotted as a function of time and temperature T. Fig. 3 shows the average initial size of the hillocks for the various irradi-
Fig. 2. Average size of surface tracks produced by 18 MeV Au ions on PC surfaces as a function of time for various temperatures: (a) tail length, (b) tail height and (c) tail width.
Fig. 1. TM-SFM images of PC films showing the typical stages of the relaxation behavior of impact features created by 18 MeV Au ions at 60 °C (a)–(e) and at 91 °C (f)–(k). The annealing time t before cooling to room temperature is given in each image. In frame (f), the tail, the rim, and the crater are identified by the letters T, R and C, respectively. The incidence angle is 84° with respect to the surface normal.
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R. Leal et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 3080–3083
Fig. 3. Average initial length of the hillocks as a function of the irradiation temperature.
ation temperatures. Ideally, the initial sizes would be obtained at t = 0 s (i.e., cooling immediately after bombardment). However, the minimum annealing time tmin is not zero, but is determined by the sum of the irradiation time (Dtirr), plus the cooling time (Dtc) (given typically tmin 1–2 s). Thus we use t = 1 s to represent the case were cooling is performed immediately after the bombardment. The initial size of the protrusions is stable up to T 85 °C, but decreases substantially for T > 100 °C. The temperature of full relaxation at tmin, TR is 110 °C. For the lower temperatures, shown in detail in Fig. 2a–c, full relaxation of the tails took from few seconds (T = 106 °C) to several weeks (T = 60 °C). All relaxation curves in Fig. 2 were fitted to Kohlrausch–William–Watts (KWW) functions,
XðtÞ ¼ X 0 expðt=sÞb
ð1Þ
where t is the time, s is the effective relaxation time, X is the particular dimension being considered, and 0 < b < 1. For bulk PC, the reported values of b vary between 0.4 and 0.5 [11]. Best fits were obtained for b 0.46 for T P 98 C and b ¼ 1 for T < 98 C. However, due to limited number of points in time and the large size fluctuations of the individual impact features, it is difficult to assert that the best mathematical fit corresponds to the true best ‘‘physical” b value. The relaxation times of the protrusion length (sl ) as a function of temperature are depicted in Fig. 4. For comparison, the relaxation times of the tail length in PMMA [7] are also shown. The s vary from few seconds to 106 s. Part of the data (the high T portion) was fitted to the Vogel–Fulcher–Tammann (VFT) equation
B sðTÞ ¼ s1 exp T T0
(dashed line in Fig. 4). The best fit was obtained for B ¼ 1330 152 K (similar to values found in the literature for the relaxation kinetics of bulk PC [11]) and T 0 ¼ 332 5 K. The value of s1 was set at 1012 s, as usually assumed, based on typical frequencies of molecular vibrations. The characteristic relaxation times s(T) of the nanodeformations are many orders of magnitude smaller than the typical values found for bulk PC. The fast dynamics of the ion-induced protrusions can be related to different factors. First, the protrusions are regions where the polymer chains are under stress (over the yield stress, since the deformation is plastic). Second, the nanodeformations are formed after a sudden disturbance caused by the ion impact. MD simulations predict the formation time of the protrusions to be of the order of 25ps. As the height of the deformations is around 2 nm in a film with thickness h 100 nm the deformation rate will be ðDl=lDtÞ 108 s1 , a very high value. Thus such regions are in a highly out of equilibrium state and relaxation times on glassy systems are known to depend on the deviation from equilibrium [12]. Finally, the impact features are on the surface of the targets, where the mobility of polymer chains can be significantly larger than the bulk [9,10,12–16]. All the above facts may be contributing to the fast relaxation rates observed for the ion-induced deformations. We note deformations produced by ion bombardment on PC exhibit similar relaxation behavior to those observed in PMMA samples [7]. The rates of relaxation are however slower in PC, as expected due to its more rigid structure and higher glass transition. The temperature at which s = 100s is sometimes used as a practical definition of the glass transition temperature, Tg [12]. This means that the local glass transition temperature at the hillocks (Tglocal) is around 100 °C, roughly 40 °C below the bulk Tg. For T < Tglocal or s(T) > 100 s, the dependence of s on temperature weakens and sðTÞ approaches an Arrhenius-type curve. This means the effective activation energy of the relaxation process becomes independent of the temperature in this regime, reaching a value of approximately 0.08 eV. This value represents the effective energy necessary for the cooperative movement involved in the relaxation of protrusions at T below the local Tg. The appearance of a single activation energy (opposite to a distributions of activating energies in the regime where VFT holds) suggests the cooperative rearranging region [12] involved in the relaxation is of the order of the dimensions of the deformations. 4. Conclusion
ð2Þ
In this work, we have studied the relaxation dynamics of protrusions induced by 18 MeV Au single ions on PC surfaces. It was found that the relaxation times s of the nanometer-sized deformations present strong deviations from typical values found for bulk PC. A local glass transition temperature was obtained for the deformations (Tglocal 100 °C), which is 40 °C below the nominal bulk Tg. For T > Tglocal, the temperature dependence of s obeys a Vogel– Fulcher law, but for lower temperatures it becomes less steep and tends to an Arrhenius-type behavior, as observed previously for PMMA. The activation energy for the hillock relaxation in the Arrhenius region was calculated to be Ea 0.08 eV. Acknowledgements The authors would like to acknowledge the Brazilian agencies CAPES and CNPQ for financial support. References
Fig. 4. Temperature dependence of the relaxation times of the length of the ioninduced deformations in PC and PMMA (from Ref.[7]). The dotted line depict the Vogel–Fulcher equation [Eq. (2)] adjusted to the data above the glass transition region. The local glass transition temperature, defined as s(Tg) = 100 s, is shown.
[1] I.H. Wilson, Surf. Interface Anal. 20 (1993) 637. [2] J. Kopniczky, C.T. Reimann, A. Hallén, B.U.R. Sundqvist, P. Tengvall, R. Erlandsson, Phys. Rev. B 49 (1994) 625.
R. Leal et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 3080–3083 [3] R. Neumann, Nucl. Instr. Meth. Phys. Res. B 151 (1999) 42. [4] E. Akcoltekin, T. Peters, R. Meyer, A. Duvenbeck, M. Klusmann, I. Monnet, H. Lebius, M. Schleberger, Nat. Nanotech. 2 (2007) 290. [5] D. Fink (Ed.), Ion Irradiation of Polymers: Fundamentals and applications, vol. 1, Springer, Berlin, 2004. [6] E. Bringa, R.E. Johnson, R.M. Papaléo, Phys. Rev. B 65 (2002) 094113. [7] R.M. Papaléo, R. Leal, W.H. Carreira, L.G. Barbosa, Phys. Rev. B 74 (2006) 094203. [8] R.M. Papaléo, L.D. de Oliveira, L.S. Farenzena, M.A. de Araújo, R.P. Livi, Phys. Rev. B 62 (2000) 11273. [9] Z. Fakhraai, J.A. Forrest, Science 319 (2008) 600.
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[10] D. Qi, Z. Fakhraai, J.A. Forrest, Phys. Rev. Lett. 101 (2008) 096101. [11] L. Delbreilh, E. Dargent, J. Grenet, J.-M. Saiter, A. Bernès, C. Lacabanne, Eur. Polym. J 43 (2007) 249. [12] R.H. Boyd, G.D. Smith, Polymer Dynamics and Relaxation, Cambridge Press, New York, 2007. [13] T. Kerle, Z. Lin, H. Kim, T.P. Russel, Macromolecules 34 (2001) 3484. [14] A. Karim, S. Kumar (Eds.), Polymer Surfaces, Interfaces and Thin Films, World Scientific, Singapore, 2000. [15] R.D. Priestley, C.J. Ellison, L.J. Broadbelt, J.M. Torkelson, Science 309 (2005) 456. [16] P.A. O’Connel, G. McKenna, Science 307 (2005) 1776.