Article pubs.acs.org/Macromolecules
Equilibration of Polymer Films Cast from Solutions with Different Solvent Qualities Ranxing Nancy Li, Andrew Clough, Zhaohui Yang,† and Ophelia K. C. Tsui* Department of Physics, Boston University, Boston, Massachusetts 02215, United States ABSTRACT: We study the effect of film preparation on the equilibration and viscoelastic properties of polymer films. Polystyrene films with a thickness of 14 nm are spun-cast from decalin solutions at different temperatures near the theta temperature to produce films with different chain conformations. We find that the equilibration time of the films increases significantly near the theta temperature. We attribute this to the onset of a rapid collapse in the polymer coil size at the theta condition, along with an increase in the solvent concentration in the films and thereby interchain separation at the time of vitrification. We find that these effects also cause the plateau modulus and equilibrium viscosity of the films to decrease.
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spin-coated polymer films well below the Tg.2,3,8 Recently, Raegen et al.8 measured the aging rate of polystyrene (PS) films spin-coated on poly(dimethylsiloxane) from solutions made of good to near-theta solvents. They found that the aging rate increased abruptly as the theta condition was approached. Since the entanglement reduction should be bigger while the residual stress smaller on approaching the theta condition, this result shows that the effect of entanglement reduction dominates that of the in-plane residual stress. In this experiment, we study whether polymer films prepared from solutions with different solvent qualities equilibrate differently upon annealing above the Tg. On the one hand, reduced entanglement may speed up the polymer dynamics and hence the equilibration process. On the other hand, a more compact conformation the chains may inherit from a poor solution can on the contrary render the chains a longer time to re-entangle to the full equilibrium state. Besides studying how the films equilibrate, we shall also examine whether upon equilibration the films will settle on the same dynamic properties. Recently, Fujii et al.10 found that the polymer chains in the films can bind irreversibly to the supporting substrate. If the binding occurs before equilibration completes, part of the initial, out-of-equilibrium conformation can get locked in and affect the final equilibrium state.
INTRODUCTION The conformation of polymer chains in a solution is a strong function of the solvent quality. In a good solvent, the interaction between the chain segments and solvent molecules is more favorable that that between the chain segments. This causes the chains to swell. In a bad solvent, the converse is true and that causes the chains to collapse. In between is the theta solvent, in which the two kinds of interactions have the same strength so the polymer chains assume the same conformation as in a melt. When a polymer solution is subject to rapid drying, as in spin-coating, the polymer chains in the solution may not have enough time to attain equilibrium before vitrifying. As a result, some memory of the chains’ conformation in the solution can get carried over to the resultant, dried film. Such an effect has been speculated to be the cause for some of the more bizarre properties found of spin-coated polymer films, including negative thermal expansion and visible aging well below the glass transition temperature, Tg.1−9 When a polymer solution is dried, the sample volume decreases; thereby, the interpenetration between neighboring chains increases. Rapid drying can, however, preclude the chains from achieving full interpenetration before vitrification, resulting in the final, dried film having a smaller degree of entanglement than equilibrium. The notion that spin-coated polymer films possess less entanglement than equilibrium has been confirmed in recent experiments studying the viscosity of freshly spin-coated polystyrene films supported by silicon.6,7 By using solvents with different qualities, the degree of entanglement can be further fine-tuned. Specifically, when solvents with poorer quality are used, individual polymer chains would be more compact, and so the interchain entanglement further reduced. In addition, the vertical shrinkage of the films upon drying may force the chains into an oblate conformation, creating a residual in-plane stress in the films. Such a residual stress has been suggested8 to be at least in part responsible for the occurrence of physical aging in © 2012 American Chemical Society
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EXPERIMENTAL SECTION
Polystyrene (PS) with Mw = 212 kg/mol and polydispersity index = 1.08 was purchased from Scientific Polymer Products (Ontario, NY). Silicon (100) wafers covered with a 102 ± 5 nm thick thermal oxide layer and cut into 1 × 1 cm2 slides were used for the substrates. Prior to use, the slides were cleaned in a piranha solution (H2SO4:H2O2 in 7:3 volume ratio) at 140 °C for 20 min followed by thorough rinsing Received: December 1, 2011 Revised: December 28, 2011 Published: January 11, 2012 1085
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Figure 1. (a) Power spectral density of a PS/decalin film prepared at 20 °C upon annealing at 130 °C for different times (from bottom to top): 0, 60, 180, 420, 900, 1860, 7620, 15 300, 30 660, 60 960, 124 560, and 219 240 s. (b) Fitted value of η plotted versus time for the data shown in (a). The open symbols denote the values obtained when the film was in the rubbery state or the PSDs made negligible evolution.13,14 The solid line is a fit of the data to the relation η = 2μ0t valid in the rubbery state prior to the saturation in η as seen in the data.13,14 The dashed line is the best fit of the data in the saturated region to a constant value.
⎡ ⎤ kBTa ⎥ Aq2(t ) = Aq2(0) exp(2ωqt ) + ⎢ 2 ⎣⎢ d G(h)/dh2 + γq2 ⎥⎦
with deionized water and then drying with 99.99% nitrogen. Afterward, the substrates were further cleaned in an oxygen plasma for 25 min. Polystyrene films were spin-coated from solutions of toluene (a good solvent) and decalin (a PS solvent with a theta temperature, Θ, of ca. 16 °C) with concentrations of 0.4−0.7 wt % polymer. The quality of the solvent can be characterized by the coil size of the polymer in the solution, commonly expressed in terms of the expansion factor, α, by
α=
× (1 − exp(2ωqt ))
where Ta is the annealing temperature, ωq is the relaxation rate of the surface capillary mode with wavevector q, and G(h) and γ are respectively the van der Waals (vdW) potential and surface tension of the film. For (viscoelastic) entangled polymer films that exhibit elastic behavior (while in the rubbery state) at short times, but viscous behavior after time, τrep, where the film enters the terminal flow regime, we have shown13,14 that ωq can be expressed by
⟨R2⟩ ⟨R 02⟩
(1)
where R and R0 are the radius of gyration of the polymer in the solution and melt, respectively. Typically, the solvent quality and hence α decrease as the solution temperature, T, is decreased. It has been shown that α and T are related by11 3 Θ 1 ⎡⎢ 14 2 α min ⎤⎥ = −1 (α3 − α5) + 3 3 σ ⎢⎣ 3N α min 3 α ⎥⎦ T
(3)
ωq =
ω liq 1 − ω liq τrep
(4)
In eq 4, ωliq = −(h /3η)[(d G(h)/dh )q + γq ] and η is a parameter identifiable with the effective or average film viscosity upon equilibration. To analyze the PSDs, we first fitted the high-q segment of the data to kBTa/γq215 using γ as the fitting parameter while setting Ta equal to 403 K (130 °C). This allows the value of γ to be determined.15 We find that the values of γ found this way typically lie between 0.029 and 0.032 J/m2, consistent with the literature value of 0.03 J/m2.6,16 Next, we fitted the full PSDs to eq 3 with η being treated as the only fitting parameter and h and d2G(h)/dh2 set equal to respectively the film thickness measured by ellipsometry and a value obtained in a previous calculation.17 It should be emphasized that while the present method measures the viscoelastic properties of the films (see below and refs 13 and 14 for further details), it differs notably from the typical AFM-based techniques for similar purposes.18−20 In particular, the AFM in those techniques acts actively to produce a mechanical perturbation to the film and thereafter monitors the overarching response. But in here, the AFM acts as a passive monitor of the surface topography of the film as the film roughens with time. 3
(2)
where αmin is the amount of swelling in the totally collapsed state and σ = 1 − ΔS/kB, with kB being the Boltzmann constant and ΔS the entropic change associated with segment−segment interactions. For PS in decalin, α varies between 1.0 and 1.2 when the solution temperature is varied from 16 °C (= Θ) to 60 °C; while for PS in toluene at room temperature, α = 1.4. Prior to spin-coating, the solution was placed in a water bath with the temperature controlled at the desired temperature for at least 12 h. To bring the core temperature of the spin-coater to the desired temperature, we adjusted the position of an incandescent lamp from the spin-coater chuck if the desired temperature was above ambience; otherwise, we adjusted the time dry ice was placed in the proximity of the spin-coater before spincoating. All films were prepared with a thickness of 14 nm as determined by ellipsometry. Ex-situ measurements of the surface topographic image of the films were made using tapping-mode atomic force microscopy (AFM) at different times, t, as the films were annealed at 130 °C (cf. Tg = 100 °C). To prepare the AFM data for analysis, each topographic image was multiplied by a Welch function before Fourier transformed. The resultant two-dimensional image was radially averaged to give the power spectral density (PSD). We have previously shown that in the initial stage of annealing when the height fluctuations in the film were small compared to the film thickness the temporal evolution of the PSD (Aq2(t)) could be described by6,12,13
2
2
2
4
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RESULTS AND DISCUSSION Figure 1a shows a typical sequence of PSDs we obtained in experiment (symbols) and the corresponding best fits to eq 3 (solid lines), where good agreement between the two is clearly evident. The values of η used to produce the fitted lines in Figure 1a are shown in Figure 1b. As seen, η increases with t from t = 0 to ∼104 s. It has been shown13,14 that the value of η acquired when a film is in the rubbery state (denoted by the 1086
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Figure 2. (a) Fitted value of η plotted versus time for the PS/decalin film prepared at 60, 25, and 16 °C on annealing at 130 °C. (b) Reciprocal of the equilibration time (1/τ) plotted as a function of the preparation temperature (solid and open symbols). The solid line is a guide to the eye. The dashed line denotes the expansion factor, namely, the ratio of the coil size of PS in decalin to that in a melt, calculated by using the model described in ref 11.
open symbols) is related to the plateau modulus of the film, μ0, by η = 2μ0t. This prediction is validated by the good agreement between the measurement (open symbols) and the best fit to this equation as seen by the solid line in Figure 1b. Figure 2a shows the fitted value of η plotted versus annealing time, t, for PS/decalin films prepared at various temperatures, T, of 60, 25, and 16 °C. It is apparent from the data taken in the rubbery state (open symbols) that μ0 varies systematically with T. Beyond the rubbery state (solid symbols), η is seen to increase with time in all the films, suggesting a progressive increase in the entanglement density as reported before.7,14 After sufficiently long times, η either reaches a saturation steadily or shows a dramatic decrease at one point before coming to a steady state. The latter behavior was only found in the films prepared at 16 °C (=Θ) and was reproducible in another similarly prepared film. We determined the equilibration time, τ, from the intercept between the asymptotic behaviors of the data in the rubbery state and that representing the maximum level reached by η as illustrated by the solid and dashed lines in Figure 2a. The result is plotted in Figure 2b as 1/τ vs T (symbols). We first notice that all values of τ found here are bigger than the reptation time of the bulk polymer (≈1600 s, as determined from η/μ0 of the bulk polymer). This is in keeping with the above observation that the equilibration process probably involves rearrangement of the chain conformation to increase the entanglement density. In addition, the data also show that 1/τ decreases continuously with decreasing temperature and starts to plummet near 16 °C. To gain some insight about what causes the equilibration time, τ, to increase (or 1/τ to decrease) with decreasing T, we plot 2μ0 and ηmax, the maximum level attained by η, as a function of T in parts a and b of Figure 3, respectively. These plots show that with decreasing T0 μ0 decreases but ηmax increases. The former signifies a slowing down in the temporal growth of η with decreasing T; the latter shows that a higher maximum η is attainable by the films prepared at lower T. Either tendency has the effect of increasing τ. The slowing down in the temporal growth of η is likely caused by the increasing difficulty for the chains to interpenetrate as the polymer chains in the as-cast films become more compact as T is lowered toward Θ. Another factor to consider is the solvent concentration, ϕs, at which the film solution vitrifies during
Figure 3. Upper panel: 2μ0 or dη/dt obtained from the data before the onset of saturation or maximum in η plotted versus the preparation temperature. Lower panel: maximum or saturation value of η plotted as a function of preparation temperature. The solid and dashed lines in the upper and lower panel denote the values of 2μ0 and ηmax obtained from the PS/toluene films, respectively.14
spin-coating, which can also affect the amount of interpenetration between neighboring chains in the films. It has been established that ϕs is a function of T, obtainable by substituting T for the vitrification temperature, Tv, in the following modified Fox equation:8
ϕ 1 − ϕs 1 = s + Tv Tm Tg
(5)
where Tm is the melting temperature of the solvent and all temperatures are in kelvin. For decalin, Tm = −30 °C (manufacturer’s data) with which eq 5 predicts that ϕs increases monotonically with decreasing T and is 0.22 and 0.54 at T = 60 and 16 °C, respectively. Taken together, the degree of entanglement decreases with decreasing T not only because the coil size of the polymer in the solution is smaller but also because the solvent content in the film, and thereby interchain separation is bigger at the time of vitrification. The reason for the increase in ηmax with decreasing T (Figure 3b) may not be as readily perceivable, however. Fujii et al.10 observed that PS adsorbed irreversibly on silicon (with or without an oxide cover layer). The presence of strong pinning 1087
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ϕs = 0.22 and 0.25 for the PS/decalin(60 °C) and PS/toluene films, respectively, the ratio of pervaded volume in the two kinds of films upon complete drying is ≈1.36 × (0.75/0.78) = 1.31. This ratio can be related to the ratio of the plateau moduli in the films. Studies had been performed to examine the relation between the plateau modulus and chain conformation in bulk polymer.22,23 More recently, Si et al.24 addressed the issue for polymer under confinement in thin films. According to their result, the effective interchain entanglement density in ultrathin films is
between the polymer and substrate can prevent the polymer chains from attaining the equilibrium conformation. As T is decreased, the coil size and hence the surface area per chain in contact with the substrate get smaller. Correspondingly, the number of pinning sites per chain would also get smaller whereby the chains may be able to re-entangle more and reach a higher ηmax. To determine whether the polymer−substrate pinning may differ between films prepared at different preparation temperatures, T, we measured the thickness of the residual (or adsorbed) films as a function of T. To make the residual films, PS/decalin films were prepared as described in the Experimental Section and then annealed at 130 °C for several days. Afterward, the films were thoroughly rinsed with toluene before being soaked in a fresh toluene bath three times for over 30 min to remove any polymer chains that were not adsorbed to the substrate. The thickness of the residual film that remained was measured with ellipsometry. The result is shown in Figure 4.
νinter = ν(1 − PVp/Vp, i)
(6)
where ν is the unperturbed, total entanglement density, P is a constant, Vp is the average volume pervaded by an unperturbed chain, and Vp,i is the volume pervaded by a chain in solution i. By eq 6, we can write PVp/Vp,i = 1 − νinter,i /ν (i = t and d denotes toluene at room temperature and decalin at 60 °C, respectively.) To proceed further, we need to know the value of P for each system. To get some idea, we adopt the simple assumption that P = 0 (i.e., all the entanglements are interchain) in the bulk but is nonzero and about the same in the PS/toluene and PS/decalin(60 °C) films. With this and the additional assumptions that the rubbery plateau modulus μ0 is ∼νinter,i and the μ0 value of entangled PS in bulk, PS/toluene films, and PS/decalin(60 °C) films is 1 × 105,25 1.2 × 104,14 and 4366 Pa (Figure 3b) as found in experiment, respectively, we estimate that 1 − νinter,i/ν = 0.87 and 0.956 for i = t and d, respectively. These give Vp,t/Vp,d = 0.956/0.87 = 1.1. This is ∼16% smaller than that estimated above by using the expansion factors. Given the crudeness of the estimates, the agreement found here is not bad indeed. This may help show that the variation in the plateau modulus of the films is caused by the variation in the chain conformation that gets frozen in the films upon spin-coating.
Figure 4. Thickness of the residual film as a function of preparation temperature for the PS/decalin films (symbols). The dashed line represents the expansion factor, α.
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CONCLUSION We have shown that the time required for spin-coated polymer films supported by a substrate to reach equilibrium on heating above the Tg is significantly affected by the quality of the solvent the film is cast from. In particular, as the temperature the films are cast at is reduced toward Θ resulting in a worsening solvent quality, the equilibration time increases drastically. We found that this increase near Θ is due to both a decrease in μ0 and an increase in ηmax with decreasing T. The decrease in μ0 is attributed to a reduced entanglement in the cast film due to a more compact chain size and higher solvent volume fraction at vitrification. The increase in ηmax may be associated with the reduced amount of pinning between the polymer chains and substrate allowing the chains to re-entangle more and thereby reach a higher ηmax.
The data clearly show that the pinning strength plummets as T approaches Θ, consistent with the picture surmised above. We notice that while the ηmax of the T = 16 °C film is bigger than the other films, its steady-state viscosity is actually smaller, attributable to the distinctive collapse exhibited by its η vs t plot just before equilibrium (Figure 2a). We do not have a good explanation for this result. We speculate that it may be due to the onset of slip in the film. As noted above, the coil size in this film is smaller than the other films, and so the grafting density of the pinned layer should be bigger initially. As the chains equilibrate and re-entangle, at one point the pinned layer may get overcrowded, and the strain that builds up may be big enough to cause some of the pinned chains to break off from the substrate and slip atop the remaining pinned layer. With the onset of slip, the apparent viscosity can be smaller than that demonstrated by the other films that do not slip (or slip less).21 It is interesting to see from Figure 3a that even at a high preparation temperature of 60 °C, the plateau modulus and hence density of entanglement of the PS/decalin(60 °C) films (i.e., PS films cast from a decalin solution at 60 °C) are lower than those of the PS/toluene films. We examine whether this discrepancy can be accounted for by the different expansion factorsαtol = 1.4 and αdecalin,60 °C = 1.2of the PS chains in the two solutions. Because the radius of gyration of the polymer (∼12 nm) is comparable to the film thickness (= 14 nm), the ratio of the pervaded volume of the chains in the two films just before complete drying is ≈(αtol/αdecalin,60 °C)2 = 1.36. Because
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address
† Center for Soft Condensed Matter Physics & Interdisciplinary Research, Soochow University, Suzhou 215123, P. R. China.
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ACKNOWLEDGMENTS We thank Dongdong Peng for useful discussions. We are grateful to the support of the National Science Foundation through the projects DMR-0908651 and DMR-1004648. 1088
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