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Langmuir 2008, 24, 1884-1890
Influence of Progressive Cross-Linking on Dewetting of Polystyrene Thin Films Samer Al Akhrass,*,† Roxana-Viorela Ostaci,‡,§ Yves Grohens,§ Eric Drockenmuller,‡ and Gu¨nter Reiter*,† Institut de Chimie des Surfaces et Interfaces, UHA-CNRS, 15 rue J. Starcky, 68057 Mulhouse Cedex, Laboratoire des Mate´ riaux Polyme` res et Biomate´ riaux (LMPB/IMPsUMR CNRS 5223), UniVersite´ Claude Bernard Lyon 1, 15 BouleVard Latarjet, 69622 Villeurbanne Cedex, and Laboratoire des Polyme` res Proprie´ te´ s aux Interfaces & Composites (L2PIC), UniVersite´ Bretagne Sud, rue Sainte Maude´ , 56321 Lorient Cedex, France ReceiVed September 27, 2007. In Final Form: NoVember 12, 2007 We present dewetting experiments on thin polymer films as a function of cross-linking density. Covalent cross-links were obtained in the glassy state on the basis of azide photochemistry of linear random copolymers of styrene and p-(azidomethyl)styrene, i.e., 106 and 2500 kg/mol with 7% and 1% azide functionality among the polymer backbone, respectively. Upon ultraviolet radiation, azides generate highly unstable nitrene radicals which react with the surrounding polymer backbone, yielding covalent cross-links. We determined the probability for film rupture, defined by the number of holes formed per unit area, and the relaxation time (τw) of residual stresses which resulted from the film preparation process. For the lower molar mass polymer studied and for azide conversion rates lower than 60%, only partial cross-linking occurred. The effective molar mass of the polymer increased, and consequently, an increase in τw was observed. The increase in τw was accompanied by a decrease in hole density, indicating that the still present residual stresses in the films were not able anymore to rupture the films at the high probability of un-cross-linked polymers. For high conversion (>60%), cross-linking was significant enough to lead to the formation of a threedimensional rubbery network which, in turn, generated an elastic force that counteracted the driving forces. This elastic force eventually inhibited dewetting and the relaxation of residual stresses. Thus, at high conversions, the relaxation time τw grew exponentially and the number of holes tended toward zero. For the higher molar mass polymer, no changes in the relaxation time τw were observed for low conversion ( 500 (11) Reiter, G.; Hamieh, H.; Damman, P.; Sclavons, S.; Gabriele, S.; Vilmin, T.; Raphae¨l, E. Nat. Mat. 2005, 4, 754. (12) Reiter, G.; de Gennes, P. G. Eur. Phys. J. E 2001, 6, 25. (13) Damman, P.; Gabriele, S.; Coppe´e, S.; Desprez, S.; Villers, D.; Vilmin, T.; Raphae¨l, E.; Hamieh, M.; Al Akhrass, S.; Reiter, G. Phys. ReV. Lett. 2007, 99, 036101. (14) Vilmin, T.; Raphae¨l, E. Eur. Phys. J. E 2006, 21, 161. (15) Vilmin, T.; Raphae¨l, E. Phys. ReV. Lett. 2006, 97, 036105. (16) Yang, M. H.; Hou, S. Y.; Chang, Y. L.; Yang, A. C.-M. Phys. ReV. Lett. 2006, 96, 066105. (17) Gabriele, S.; Damman, P.; Sclavons, S.; Desprez, S.; Coppe´e, S.; Reiter, G.; Hamieh, M.; Al, Akhrass, S.; Vilmin, T.; Raphae¨l, E. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 3022. (18) Hamieh, M.; Al Akhrass, S.; Hamieh, T.; Damman, P.; Gabriele, S.; Vilmin, T.; Raphae¨l, E.; Reiter, G. J. Adhes. 2007, 83, 367. (19) Vix, A. B. E.; Mu¨ller-Buschbaum, P.; Stocker, W.; Stamm, M.; Rabe, J. P. Langmuir 2000, 16, 10456.
10.1021/la702984w CCC: $40.75 © 2008 American Chemical Society Published on Web 01/19/2008
Cross-Linking Influence on Dewetting of PS Films
kg/mol) indicated that these residual stresses could relax at times much shorter than the reptation time (τrep) of polymer chains in the bulk.11,13,17,18 In most cases residual stresses may be undesirable, in particular if they are damaging the film. However, one may also think of examples where they might be advantageous. One possibility is to “freeze-in” this highly metastable form of matter caused by residual stresses. Such may generate materials which have new properties such as a “permanent” negative thermal expansion coefficient. By precisely tuning the cross-linking degree of the polymers in the thin film, we could study their mechanical properties in time and elucidate the role of elasticity in stabilizing thin films. By increasing the degree of cross-linking, we expect to observe a progressive change in dewetting behavior until dewetting eventually will be inhibited. Previous studies have followed various strategies for suppressing dewetting and for stabilizing thin polymer films. Additives have been shown to inhibit dewetting. Buckminster fullerene nanoparticles were introduced into the spin-casting polymer solution,20 polystyrene nanoparticles21 and dendrimers22 were added to a high molar mass, and linear polystyrene (PS) or branched polymers were used.23 Recently, photoactive additives for cross-linking polymer films24 were found to eliminate dewetting of thin polymer films. Also, the use of low-energy (“sticky”) end groups led to a reduction of the liquid-air interfacial tension, which obviously could stop dewetting.25 An oligostyrene liquid was stabilized on Si wafers by grafting PS onto the substrate surface and by mixing long PS chains into the liquid.26 Another film stabilization technique is blending of random functional copolymers into unstable films.27 Aging of polystyrene thin films below the glass transition temperature of the polymer can also improve the stability of such films.11 In this work, stabilization will be achieved by chemically crosslinking the polymers in the glassy state. This process also allows fixing potential nonequilibrated chain conformations. Our crosslinked thin film networks are based on azide photochemistry of tailor-made linear random copolymers of styrene and p(azidomethyl)styrene (Scheme 1). The advantage of this crosslinking process is that the reaction can be induced by ultraviolet (UV) radiation and that it can be performed in the glassy state at ambient temperature, which avoids possible relaxation of the polymer induced by heat (which would be the case for thermal cross-linking). A thermally activated cross-linking approach has been previously developed to efficiently screen the underlying substrate and allow block copolymer self-assembly.28,29 Moreover, under UV radiation azides cleanly generate nitrenes, with nitrogen being the only byproduct, and there is no need to add crosslinking agents (e.g., initiators, monomers, catalysts, ...) which generally remain in the resulting network and might disturb further (20) Barnes, K. A.; Karim, A.; Douglas, J. F.; Nakatani, A. I.; Gruell, H.; Amis, E. J. Macromolecules 2000, 33, 4177. (21) Krishnan, R. S.; Mackay, M. E.; Hawker, C. J.; Van Horn, B. Langmuir 2005, 21, 5770. (22) Mackay, M. E.; Hong, Y.; Jeong, M.; Hong, S.; Russell, T. P.; Hawker, C. J.; Vestberg, R.; Douglas, J. F. Langmuir 2002, 18, 1877. (23) Barnes, K. A.; Douglas, J. F.; Liu, D. W.; Karim, A. AdV. Colloid Interface Sci. 2001, 94, 83. (24) Carroll, G. T.; Sojka, M. E.; Lei, X.; Turro, N. J.; Koberstein, J. T. Langmuir 2006, 22, 7748. (25) Yuan, C.; Ouyang, M.; Koberstein, J. T. Macromolecules 1999, 32, 2329. (26) Yerushalmi-Rozen, R.; Klein, J.; Fetters, L. J. Science 1994, 263, 793. (27) Wunnicke, O.; Mueller-Buschbaum, P.; Wolkenhauer, M.; Lorenz-Haas, C.; Cubitt, R.; Leiner, V.; Stamm, M. Langmuir 2003, 19, 8511. (28) Ryu, D. Y.; Shin, K.; Drockenmuller, E.; Hawker, C. J.; Russell, T. P. Science 2005, 308, 236. (29) Ryu, D. Y.; Wang, J.-Y.; Lavery, K. A.; Drockenmuller, E.; Satija, S. K.; Hawker, C. J.; Russell, T. P. Macromolecules 2007, 40, 4296. (30) Dao, J.; Benoit, D.; Hawker, C. J. J. Polym. Sci., Part A: Polym. Chem. 1998, 36, 2161.
Langmuir, Vol. 24, No. 5, 2008 1885 Scheme 1. Principle of the Cross-Linking Reactiona
a After UV irradiation and formation of nitrene transient radicals, several reaction paths can be followed. The majority products yield to a covalent cross-linking of the polymer through chemical pathways a and b. The polymers used in this study have a low content of azide functionality, and therefore, cross-linking through reaction a is favored.
analysis. Herein, we focus on a detailed analysis of the dewetting behavior of partially cross-linked polystyrene films and effects of the thickness of the films and molar mass of the polymer with the aim to extract information on the factors which are responsible for the stabilization of these films. 2. Experimental Section 2.1. Materials. TIPNO-based (1-phenylethyl)alkoxyamine was synthesized as described previously.29 Styrene (Acros, 99%) was distilled over calcium hydride. p-(Chloromethyl)styrene (Acros, 99%) was passed through a short column of neutral alumina to remove the inhibitor. PDMS with Mw ) 139 kg/mol and PDI (polydispersity index) ) 1.05 was purchased from ABCR Karlsruhe, Germany, and used as received. All other reagents and solvents were purchased from Aldrich and used as received. Silicon wafers (381 µm thick with a SiO2 layer of 3 nm) were purchased from Mat. Technology (Morangis, France). 2.2. Characterization Methods. Monomer conversions were determined by 1H NMR (Bruker 300 MHz) in CDCl3. SEC experiments were performed in tetrahydrofuran at 22 °C and a flow rate of 0.5 mL/min using a system equipped with a Waters 410 differential refractometer and PLGel mixed C columns (internal diameter 7.8 mm, length 30 cm). Mw values and PDIs were calculated using a calibration curve obtained from polystyrene standards. Fourier transform infrared (FT-IR) spectra were taken on a Bruker IFS66 spectrometer using KBr pellets. Film thicknesses were measured with a Sopra Spectroscopic ellipsometer at a fixed angle of incidence of 70°, on at least five different places on the sample. Real time dewetting was observed using an optical microscope (Leitz Metallux 3, Germany), using a hot stage (Linkam TMS 91, Surrey, U.K.). 2.3. General Procedure for the Synthesis of Poly(styrene-r(p-(chloromethyl)styrene)) by Nitroxide-Mediated Radical Polymerization. A solution of TIPNO-based (1-phenylethyl)alkoxyamine (79 mg, 0.21 mmol) in styrene (6.0 g, 58 mmol) and p-(chloromethyl)styrene (0.62 g, 4.1 mmol) was degassed by three freeze-pump-thaw cycles before being sealed under vacuum. After 7 h at 123 °C the polymerization medium was diluted in dichloromethane, precipitated twice in heptanes, and dried under vacuum. Poly(styrene-r-(p-(chloromethyl)styrene)) having 7% p-(chlorom-
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Table 1. Characteristics of Synthesized Polystyrene-Azide Mw Mn PDI ) azide group no. of azide groups sample (kg/mol) (kg/mol) Mw/Mn content (%) per chain A B
106 2500
82 1000
1.26 2.5
7 1
36 63
ethyl)styrene units was recovered as a white powder (4.3 g, Y ) 65%, Mw ) 106 kg/mol, PDI ) 1.20). 2.4. General Procedure for the Synthesis of Poly(styrene-r(p-(chloromethyl)styrene)) by Emulsion Polymerization. Styrene (6.2 g, 60 mmol), p-(chloromethyl)styrene (92 mg, 0.6 mmol), potassium sulfate (11 mg, 0.04 mmol), sodium dodecyl sulfate (150 mg, 0.05 mmol), and 15 mL of distilled water were added to a 50 mL round-bottom flask equipped with a condenser and a septum. The mixture was degassed at room temperature by argon bubbling for 30 min and was then vigorously stirred at 70 °C for 17 h. The polymerization medium was concentrated under reduced pressure and precipitated twice in water and methanol. After drying under vacuum, poly(styrene-r-(p-(chloromethyl)styrene)) having 1% pchloromethyl units was recovered as a white powder (5 g, Y ) 80%, Mw ) 2 500 kg/mol, PDI ) 2.5). 2.5. General Procedure for the Synthesis of Poly(styrene-r(p-(azidomethyl)styrene)). Poly(styrene-r-(p-(chloromethyl)styrene)) (1 g) and NaN3 (2 equiv according to the chloromethyl functionality) were dissolved in dimethylformamide (10 mL), and the mixture was stirred in the dark for 24 h at room temperature. The reaction mixture was then filtered, concentrated under reduced pressure, and precipitated twice in water and methanol. After freezedrying from benzene, poly(styrene-r-(p-(azidomethyl)styrene)) was recovered as a white powder and stored in the dark (Y ) 95%, Mw ) 106 kg/mol, PDI ) 1.26, 7% (azidomethyl)styrene units). The same procedure was applied to the polymer made by emulsion polymerization, yielding a white powder (Y ) 95%, Mw ) 2500 kg/mol, PDI ) 2.5, 1% azidomethyl units). The characteristics of PS-N3 synthesized are given in Table 1. 2.6. Film Preparation. First, the silicon substrates were properly cleaned by a UV-ozone treatment to remove organic contaminants. Then, thin polystyrene-azide films were directly obtained from toluene solutions by spin-coating onto poly(dimethylsiloxane) (PDMS)-coated silicon wafers. A quasi-liquid coating such as PDMS provides a smooth and chemically homogeneous surface. In addition, a PDMS coating provides a significantly lower surface tension, which considerably lowers the attraction of contaminants from air and, most importantly, enhances the capillary forces driving dewetting. We used a PDMS with Mw ) 139 kg/mol. The PDMS monolayers were formed from comparatively thick films (ca. 50 nm) prepared by spin-coating from a heptane solution of PDMS. Solvent evaporation resulted in a thin and uniform film, where the thickness was a function of the concentration of the solution and of the spinning speed. The PDMS chains were strongly adsorbed onto the UV/ ozone cleaned substrate by hydrogen bonds with the silanol groups at the surface of a silicon wafer. The formation of such links was facilitated by annealing the films under vacuum at elevated temperatures (T ) 130 °C) for 5 h. Under these conditions, covalent bonds between the hydroxyl (-OH) groups at the substrate surface and the chain ends may also have formed. Both substrate-PDMS interactions finally led to irreversible anchoring of the PDMS chains onto the substrate. After annealing, the PDMS films were washed in a heptane bath (good solvent for PDMS) for 2 h to eliminate the polymer chains that did not anchor to the substrate. Ellipsometric measurements were performed to determine the thickness (e) of the PDMS layer. Similar to the PDMS films, the PS-N3 films were prepared by spin-coating a rather dilute toluene solution onto silicon substrates covered with a PDMS monolayer. 2.7. Film Cross-Linking. The principle of the cross-linking process is detailed in Scheme 1. It consists in irradiating the PS-N3 thin film under ambient conditions by an ultraviolet (UV) light with a wavelength of 365 nm (VL-115, 7 mW/cm2, distance between sample and UV lamp ∼5 cm). This energy is able to break up the photosensitive azide functionality (-N3) and to create highly reactive nitrene radicals. These transient radicals promote the polymer network
Figure 1. Monitoring of azide conversion as a function of UV exposure time for a polystyrene-azide sample (Mw ) 106 kg/mol, 45 nm thickness). (A) FT-IR spectrum illustrating the decrease of the absorbance peak of azides located at 2094 cm-1 as the UV exposure time increased. The exposure time (min) is indicated in the figure. (B) Change of the absorbance at 2094 cm-1 under UV irradiation: the exponential fit allows us to derive A0 and Aresidual. (C) Evolution of azide conversion during UV irradiation.
formation mainly through chemical pathways a (major) and b (minor) illustrated in Figure 1. The cross-linking density of the resulting polymer network mainly depends on the amount of azide functionality among the polymer backbone and the exposure time to UV irradiation. 2.8. Monitoring of the Cross-Linking Process by Infrared Spectroscopy. The prepared films were then exposed to UV radiation for various irradiation times to promote covalent cross-linking. The photoactivation of an azide initially produces the corresponding singlet nitrene which can undergo intersystem crossing to the triplet
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Figure 2. Influence of the cross-linking degree on the probability of film rupture, expressed by the maximum number of circular holes per unit of area (Nmax per 56.4 × 104 µm2) normalized by Nmax in films without cross-linking. (A) Optical micrographs showing the decrease in the number of holes with increasing exposure time (without UV, 10, 20, and 30 min) in a 45 nm thick PS-N3 partially cross-linked film (Mw ) 106 kg/mol) on a PDMS (11 nm) coated Si wafer at 125 °C after 1 h. Image size: 125 × 125 µm2. (B) Density of holes per unit area (N) taken from (A) as a function of time with increasing UV exposure times (from top to bottom, 0, 10, 20, 30, and 40 min). (C) Systematic study of Nmax for two film thicknesses (20 and 45 nm) dewetting at 125 °C as a function of azide conversion. The solid lines represent guides to the eye. state.31-35 This process becomes favored when the temperature is lowered.31,34 Triplet nitrenes can react eventually with other species present in the environment, yielding products presented in Scheme 1. When the concentration of azide groups is high enough, triplet nitrenes dimerize to form an azo derivative (-NdN-) as the majority product.31,34 In our case, the amount of N3 is comparatively low and the aromatic groups are quite abundant, which increases the probability of reaction between the nitrene radicals and aromatic groups. Therefore, the majority product will be obtained along pathway a in Scheme 1. However, both reactions a and b lead to a covalent cross-linking of the polymer. The disappearance of the azide groups, directly related to the photo-cross-linking process, was determined by FT-IR spectroscopy for films of comparable thickness deposited onto KBr pellets. Figure 1A shows the FT-IR spectra of the PS-N3 films before and after UV exposure for different periods of time (t), presenting the spectral changes due to the photo-cross-linking reaction. The azide characteristic band located at 2094 cm-1 decreased systematically upon UV exposure. The absorbance data (Figure 1B) were fitted to an exponential function, At ) A0 exp(-t/R) + Aresidual, to determine the residual absorbance (Aresidual), which served to determine azide conversion (%) (Figure 1C) given by χ ) (A0 - At)/(A0 Aresidual) × 100. At is the absorbance after exposure time t and A0 the absorbance at t ) 0 (no exposure). R is a constant. 2.9. Measurements of Dewetting of Partially Cross-Linked PS Films. The films prepared as mentioned above were used in the dewetting experiments. Dewetting of partially cross-linked PS films (31) Buchmueller, K. L.; Hill, B. T.; Platz, M. S.; Weeks, K. M. J. Am. Chem. Soc. 2003, 125, 10850. (32) Iddon, B.; Meth-Cohn, C.; Scriven, E. F. V.; Suschitzky, H.; Gallagher, P. T. Angew. Chem., Int. Ed. Engl. 1979, 18, 900. (33) Smith, P. A. S. In Azides and Nitrenes, ReactiVity and Utility; Scriven, E. F. V., Ed.; Academic Press: New York, 1984; p 95. (34) Schuster, G. B.; Platz, M. S. AdV. Photochem. 1992, 17, 69. (35) McClelland, R. A.; Gadosy, T. A.; Ren, D. Can. J. Chem. 1998, 76, 1327.
was induced by heating the sample under nitrogen on a hot stage to a temperature (T) above the glass transition temperature of the bulk PS (here, T ) 125 °C). The temperature was controlled within 0.5 °C. Real time dewetting was observed by optical microscopy.
3. Results and Discussion Figure 2A shows a typical series of micrographs which clearly indicate the decrease of the number of holes with increasing UV exposure time. Figure 2B shows the density of holes (N) per unit area as a function of time for increasing UV exposure times. A significant reduction in the number of holes was observed. Independent of the UV exposure time, all holes were formed within a rather short initial period of 700 s. Consequently, the maximum number of holes could easily be determined after about 1 h of annealing. These values are given in Figure 2C. They imply that the relaxation process of residual stresses is not linked to the hole formation process. It seems to be that the initial strength of the residual stress controls film rupture and the rupture probability decays in the course of stress relaxation. Thus, no holes are formed at later stages. Figure 2C shows the results of a systematic study of the influence of cross-linking on the probability for film rupture. This probability is defined by Nmax, the maximum number of circular holes per unit of area. Results for films of two different thicknesses (20 and 45 nm) and a molar mass of 106 kg/mol are shown as a function of azide conversion, which is proportional to the degree of cross-linking. For an azide conversion of less than 60%, we have a slight decrease of the density of holes. This trend becomes more significant for a conversion higher than 60%. At 90%, holes did not appear in films with a 45 nm thickness. In contrast to that,
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Figure 3. (A) Optical micrographs showing the evolution of the hole diameter for polystyrene-azide films (Mw ) 106 kg/mol, 45 nm thickness) after different UV exposure times. The images were taken after 600 s of dewetting at 125 °C on a PDMS adsorbed monolayer. Images size: 87 × 87 µm2. Hole diameter (B, C) and dewetting velocity (D, E) vs time for two molar masses: Mw ) 106 and 2500 kg/mol; film thicknesses were in the range from 40 to 45 nm. The exposure times (min) are indicated in the figure.
we found that even 100% conversion was not sufficient to prevent hole formation and completely dewetting in the 20 nm film. A greater amount of azide functionality per chain would be necessary to stabilize very thin films, which obviously have a stronger tendency to dewet than thicker ones. Moreover, it is highly probable that the number of the crosslinks between individual chains decreased with decreasing film thickness due to a low number of polymer chains and little overlap between them in the thinnest layers. A decrease in entanglement density in ultrathin films was reported by several authors.24,36-38 For thickness less than the diameter of an unperturbed random coil, chains start to separate. In quasi two dimensions, i.e., in “very thin films”, the chain overlap is reduced, so the probability of cross-link formation between separated chains will be highly reduced. (36) Brown, H. R.; Russell, T. P. Macromolecules 1996, 29, 798. (37) Dalnoki-Veress, K.; Nickel, B. G.; Roth, C.; Dutcher, J. R. Phys. ReV. E 1999, 59, 2153. (38) Bodiguel, H.; Fretigny, C. Eur. Phys. J. E 2006, 19, 185.
Dewetting of polystyrene thin films on a slippery PDMScoated substrate showed that the nucleated holes (dry patches) grew in diameter with time. These holes were surrounded by an asymmetric rim which collected the dewetted liquid. A characteristic time, τw, which is attributed to the relaxation of residual stresses, can be deduced from the temporal evolution of the width of the rim.11,13-15,17,18 Figure 3A shows a typical series of micrographs pointing out that for a fixed time of dewetting the size of the holes decreased with UV exposure time and therefore cross-link density. From each micrograph (exploiting line profiles reflecting the interference contrast), we calculated the values of the dewetted distance (d) and the width of the rim (W). Complete temporal series of images during dewetting were systematically examined. As an example for such a systematic analysis, we present d(t) in Figure 3B,C and W(t) in Figure 4A,B for two molar masses of PS-N3. The velocity [V(ti)] was determined by taking differences, V(ti) ) [d(ti) - d(ti-1)]/(ti - ti-1), and is plotted in Figure 3D,E for
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Figure 4. Width of the rim as a function of time and UV exposure for dewetting at 125 °C of polystyrene-azide films: (A) Mw ) 106 kg/mol, 45 nm thickness, (B) Mw ) 2500 kg/mol, 45 nm thickness. The exposure times (min) are indicated in the figure. (C) Wmax taken from (A) and (B) as a function of azide conversion; the lines represent linear fits to the data. (D) τw taken from (A) and (B) as a function of azide conversion; the lines represent exponential growth fits (τ(χ) ) τ(0) + k exp(χ/R); k and R are constants) to the data.
both molar masses studied (106 and 2500 kg/mol) and film thicknesses of ca. 45 nm. A decrease of the initial dewetting velocity with cross-linking density was observed. In time and independent of the molar mass of the polymer and cross-linking degree, this velocity decreased according to a t-1 power law. According to theory, such behavior could correspond to the viscoelastic regime dominated by nonlinear friction at the PS-PDMS interface. The observed decrease in the initial dewetting velocity can be interpreted by assuming a decrease in the contribution of residual stresses. Theoretically, the contribution of residual stresses to the dewetting dynamics can be considered as an additional driving force, which acts in parallel to the capillary forces. Cross-linking leads to a macromolecular network and generates an elastic force which counteracts these driving forces and, if large enough, may even inhibit dewetting. In addition, cross-linking also slows and eventually stops the relaxation of residual stresses. To point out the relaxation of the residual stresses, parts A and B of Figure 4 show the temporal evolution of the width of the rim. These curves allow determination of a characteristic time, τw (attributed to the relaxation of the residual stress), as a function of cross-linking degree for the two chain lengths of PS-N3 studied. The evolution of W exhibited two regimes separated by τw. For t < τw, W increased approximately logarithmically in time. This regime was followed by a second one (t > τw) characterized by an almost constant (or slightly decreasing) rim width. Such behavior was identical for all films differing in cross-linking degree and molar masses of PS-N3. In contrast, the maximum value of the width (Wmax) of the rim showed a
considerable decrease with increasing cross-linking degree. Figure 4C suggests a linear decrease in Wmax with azide conversion. Such behavior holds for all samples, independently of molar mass and film thickness. This decrease in Wmax correlates with the decrease in the number of holes and finally the absence or low number density of holes for high conversions (Figure 2B). However, thicker films from a higher molar mass polymer stabilized already at a lower conversion than thinner ones of a lower molar mass. To understand how cross-linking affects the relaxation of the residual stress, Figure 4D shows the evolution of τw as a function of azide conversion. Independently of the polymer molar mass or the film thickness, τw increased drastically (most likely exponentially) with conversion (for χ g 50%). From the fits (exponential growth, τ(χ) ) τ(0) + k exp(χ/R); k and R are constants), it is possible to calculate τw(100%) at complete conversion (χ ) 100%). We found τw(100%) ≈ 800 s and τw(100%) ≈ 2200 s for the PS-N3 (Mw ) 106 kg/mol) 20 and 45 nm thicknesses, respectively, and for the PS-N3 (Mw ) 2500 kg/mol) τw(100%) ≈ 25 × 105 s. That means, even for a completely cross-linked film (please note that the percentage of azide groups per chain is 7% in mass for Mw ) 106 kg/mol and 1% in mass for Mw ) 2500 kg/mol), the relaxation of the residual stress cannot be stopped completely. On the other hand, thin polymer films (∼45 nm) can be stabilized, as indicated by Nmax and Wmax tending to zero, even at azide conversions of less than 90%.
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4. Conclusions In summary, our observations concerning the evolution of τw and hole density with the cross-linking degree may be interpreted in the following way. For the lower molar mass polymer (Mw ) 106 kg/mol) and for azide conversion of less than 60%, only partial cross-linking occurred. The effective molar mass of the polymer increased, and consequently, an increase in τw was observed. That means that residual stresses relaxed more slowly due to cross-linking. Such is in agreement with previous results on the influence of the molar mass.13 However, there, the expected increase of the relaxation time according to τrep ∝ M3,4 was only observed for Mw lower than about 300 kg/mol. For higher molar masses, τw was found to be almost constant, independently of molar mass. The increase in τw was accompanied by a decrease in hole density, indicating that the still present residuals were not able anymore to rupture the films at the high probability of uncross-linked polymers. For high azide conversions (χ > 60%), cross-linking was significant enough to lead to the formation of a three-dimensional rubbery network which generated an elastic force that counteracted the driving capillary forces. This elastic force eventually inhibited dewetting and the relaxation of residual stresses. Thus, at high conversions the relaxation time τw grew exponentially and the number of holes tended toward zero.
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For the higher molar mass polymer (Mw ) 2500 kg/mol), no changes in the relaxation time τw were observed for low conversion (χ < 30%). This is consistent with the independence of τw for long-chain polymers observed in ref 13 (τw was constant for Mw > 300 kg/mol). However, for an azide conversion rate higher than ca. 30%, τw increased drastically, extrapolating to an extremely long relaxation time at 100% conversion. Although residual stresses could not relax due to cross-linking of the polymer, i.e., these stresses remained at a high level, the permanent elasticity of the now cross-linked PS film opposed the forces responsible for hole opening. Thus, at best, very small holess too small to be visible by optical microscopyscould be formed, where the forces driving dewetting were fully balanced by elastic forces resulting from the deformation of the rubbery PS film. Our experiments suggest that, to successfully stabilize thin polymer films by cross-linking, it is preferable to use long polymer chains. Acknowledgment. We are grateful for the financial support from the European Community’s “Marie-Curie Actions” under Contract MRTN-CT-2004-504052 [POLYFILM]. LA702984W
