Langmuir 2005, 21, 9721-9727
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Self-Assembly of pODMA-b-ptBA-b-pODMA Triblock Copolymers in Bulk and on Surfaces. A Quantitative SAXS/AFM Comparison Wei Wu, Jinyu Huang, Shijun Jia, Tomasz Kowalewski, and Krzysztof Matyjaszewski Center for Macromolecules Engineering, Department of Chemistry, Carnegie Mellon University, 4400 Fifth Avenue, Pittsburgh, Pennsylvania 15213
T. Pakula† Max-Planck Institut fu¨ r Polymerforschung, Postfach 3148, 55128 Mainz, Germany
A. Gitsas and G. Floudas* Department of Physics and Foundation for Research and Technology-Hellas, Biomedical Research Institute (FORTH-BRI), University of Ioannina, P.O. Box 1186, 451 10 Ioannina, Greece Received April 27, 2005. In Final Form: July 15, 2005 The phase state of a series of poly(n-octadecyl methacrylate)-b-poly(tert-butyl acrylate)-b-poly(n-octadecyl methacrylate) (pODMA-b-ptBA-b-pODMA) triblock copolymers, synthesized through atom transfer radical polymerization, has been investigated in bulk and on surfaces using small-angle X-ray scattering and atomic force microscopy, respectively. The mean-field theory was employed to construct the bulk phase diagram. Excellent agreement was found between the bulk and surface morphologies as well as for the domain spacing (domain spacing scaled as d ≈ N0.64), suggesting that the strong polymer-polymer interactions in bulk are also the dominant interactions on surfaces.
I. Introduction Block copolymers self-assemble into well-controlled nanoscale structures ranging from spheres, cylinders, and lamellae to the more complex bicontinuous cubic phase, with a Ia3 h d symmetry group, known as a double gyroid.1,2 The self-assembly of block copolymers in bulk depends on several factors: (1) the product of the Flory-Huggins interaction parameter χ with the total degree of polymerization N, (2) the volume fraction f, (3) the copolymer architecture,3-9 (4) the conformational asymmetry,10,11 and (5) the fluctuation effects.12 According to the mean-field theory (MFT)3,13,14 the phase state was discussed only in terms of the first two parameters (χN and f), but it soon †
Deceased June 7, 2005.
(1) Hadjichristidis, N.; Pispas, S.; Floudas, G. Block Copolymers: Synthetic Strategies, Physical Properties and Applications; WileyInterscience: Hoboken, NJ, 2002. (2) Hamley, I. W. The Physics of Block Copolymers; Oxford University Press: Oxford, 1998. (3) Leibler, L. Macromolecules 1980, 13, 1602. (4) de la Cruz, M. O.; Sanchez, I. C. Macromolecules 1986, 19, 2501. (5) Dobrynin A. V.; Erukhimovich, I. Ya. Macromolecules 1993, 26, 276. (6) Floudas, G.; Hadjichrisitidis, N.; Iatrou, H.; Pakula, T.; Fischer, E. W. Macromolecules 1994, 27, 7735. (7) Floudas, G.; Pispas, S.; Hadjichristidis, N.; Pakula, T.; Erukhimovich, I. Macromolecules 1996, 29, 4142. (8) Hodrokoukes, P.; Floudas, G.; Pispas, S.; Hadjichristidis, N. Macromolecules 2001, 34, 650. (9) Pochan, D. J.; Gido, S. P.; Pispas, S.; Mayes, J. W. Macromolecules 1996, 29, 5099. (10) Vavasour, J. D.; Whitmore, M. D. Macromolecules 1993, 26, 7070. (11) Matsen, M. W.; Bates, F. S. J. Polym. Sci., Part B: Polym. Phys. 1997, 35, 945. (12) Fredrickson, G. H.; Helfand, E. J. Chem. Phys. 1987, 87, 697. (13) Mori, K.; Tanaka, H.; Hashimoto, T. Macromolecules 1987, 20, 381. (14) Mayes A. M.; de la Cruz, M. O. J. Chem. Phys. 1989, 91, 7228.
became apparent that the remaining three factors have a crucial role in the phase behavior. The established techniques that have been employed in obtaining these phase diagrams are small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). In some cases, the different viscoelastic contrast of the various nanostructures assisted in the construction of these phase diagrams. Recently, atomic force microscopy (AFM), with its nanometer spatial resolution and ability to distinguish different materials without staining, emerged as an attractive method for surface structure characterization. Because AFM relies on the mechanical interrogation of the sample surface by the ultrasharp tip, interpretation of AFM images is not always as straightforward as it might initially appear, and it may necessitate taking into account artifacts related to the tip geometry and the mechanical response of the sample, which could, for example, lead to complex contrast-reversal phenomena.15,16 The presence of external surfaces and the confinement effects in ultrathin films may alter the morphology of materials,17-21 or even, as described below, lead to the stabilization of unusual, nonbulk structures. For example, a bounding (15) Knoll, A.; Magergle, R.; Krausch, G. Macromolecules 2001, 34, 4159. (16) Wang, Y.; Song, R.; Li, Y.; Shen, J. Surf. Sci. 2003, 530, 136. (17) Roettele, A.; Thurn-Albrecht, T.; Sommer, J.-U.; Reiter, G. Macromolecules 2003, 36, 1257. (18) Mansky, P.; Russell, T. P.; Hawker, C. J.; Mays, J.; Cook, D. C.; Satija, S. K. Phys. Rev. Lett. 1997, 79, 237. (19) Pickett, G. T.; Balazs, A. C. Macromolecules 1997, 30, 3097. (20) Pickett, G. T.; Balasz, A. C. Macromol. Theory Simul. 1998, 7, 249. (21) Cheng, J. Y.; Ross, C. A.; Thomas, E. L.; Smith, H. I.; Vancso, G. J. Adv. Mater. 2003, 15, 1599.
10.1021/la051130u CCC: $30.25 © 2005 American Chemical Society Published on Web 09/08/2005
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surface with a preference for one of the two blocks can induce order in diblock copolymer melts, as found experimentally.22 The order-to-disorder transition temperature (TODT) in films of polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) was found to increase as the film thickness was reduced.23 More recently, for a lamellarforming triblock copolymer of polystyrene-b-polybutadiene-b-poly(methyl methacrylate) (SBM), the nearsurface morphology was found to deviate from the bulk lamellar morphology:24 isolated microdomains of the backfolding species embedded in a perforated lamellar of the respective other end block were identified by AFM. For cylinder-forming block copolymers, the deviations from the bulk structure include a wetting layer,25 spherical microdomains,26 perforated lamellae,26 and cylinders with necks.27 For a polystyrene-b-polybutadiene-b-polystyrene (SBS) triblock copolymer with a cylindrical microdomain structure in bulk, several different structures were found on the Si substrate, after being annealed from chloroform vapor, as a function of film thickness: from a disordered phase in the thinner part of the film to cylinders with parallel (C|) and perpendicular (C⊥) orientations and perforated layers. The cylindrical orientation was found to change in sequence as C| f C⊥ f C| at steps between terraces (as with the lamellar orientation).28,29 The above systems are some examples of surface reorganization revealing a strong interplay between the strength of the surface field and the deformation of the structure. This interplay can either cause the orientation of the bulk structure or lead to surface reconstruction. In addition, the film thickness modulates the stability regions of the different phases via interference and confinement effects. With respect to the latter, recent studies revealed that the severe confinement of a symmetric diblock copolymer in the nanoscopic cylindrical pores of alumina membranes can break the symmetry, forcing a change away from the bulk morphology.30 Similarly, for a cylinderforming diblock copolymer, a helical morphology is found under certain conditions.31 On the basis of the above, it is evident that one cannot infer the bulk morphology from the surface structure alone. In this study, we make a detailed comparison between the phase behavior of a triblock copolymer system in bulk and on the surface using SAXS and AFM, respectively. The system investigated is the poly(n-octadecyl methacrylate)-b-poly(tert-butyl acrylate)-b-poly(n-octadecyl methacrylate) (pODMA-b-ptBA-b-pODMA) triblock copolymer, which is synthesized through atom transfer radical polymerization (ATRP).32-34 pODMA undergoes (22) Anastasiadis, S. H.; Russell, T. P.; Satija, S. K.; Majkrzak, C. F. Phys. Rev. Lett. 1989, 62, 1853. (23) Menelle, A.; Russell, T. P.; Anastasiadis, S. H.; Satija, S. K.; Majkrzak, C. F. Phys. Rev. Lett. 1992, 68, 67. (24) Rehse, N.; Knoll, A.; Konrad, M.; Magerle, R.; Krausch, G. Phys. Rev. Lett. 2001, 87, 035505. (25) Karim, A.; Singh, N.; Sikka, M.; Bates, F. S.; Dozier, W. D.; Felcher, G. P. J. Chem. Phys. 1994, 100, 1620. (26) Radzilowski, L. H.; Carvalho, B. L.; Thomas, E. L. J. Polym. Sci., Part B: Polym. Phys. 1996, 34, 3081. (27) Konrad, M.; Knoll, A.; Krausch, G.; Magerle, R. Macromolecules 2000, 33, 5518. (28) Knoll, A.; Horvat, A.; Lyakhova, K. S.; Krausch, G.; Sevink, G. J. A.; Zvelindovsky, A. V.; Magerle, R. Phys. Rev. Lett. 2002, 89, 035501. (29) Krausch, G.; Magerle, R. Adv. Mater. 2002, 14, 1579. (30) Shin, K.; Xiang, H.; Moon, S. I.; Kim, T.; McCarthy, T. J.; Russell, T. P. Science 2004, 306, 76. (31) Xiang, H.; Shin, K.; Kim, T.; Moon, S. I.; McCarthy, T. J.; Russell, T. P. Macromolecules 2005, 38, 1055. (32) Matyjaszewski, K.; Xia, J. Chem. Rev. 2001, 101, 2921. (33) Matyjaszewski, K.; Patten, T. E.; Xia, J. J. Amer. Chem. Soc. 1997, 119, 674. (34) Qin, S. H.; Saget, J.; Pyun, J. R.; Jia, S. J.; Kowalewski, T.; Matyjaszewski, K. Macromolecules 2003, 36, 8969.
Wu et al.
side-chain crystallization35 below ∼285 K (with a melting temperature at 300 K), whereas ptBA is an amorphous polymer with a glass transition temperature (Tg) at 320 K (i.e., above the crystallization and melting temperatures of the pODMA). AFM and SAXS studies reported here were made above the pODMA melting temperature using the samples prepared in a way intended to ensure the formation of equilibrated morphologies. Remarkably, both methods were found to be in excellent agreement, suggesting that the surface morphologies did not deviate significantly from the bulk microdomain structures. In particular, domain spacings obtained from SAXS and AFM for the nearly symmetric block copolymers agreed very well with each other, suggesting strongly segregated blocks that were in agreement with their phase state. Moreover, some additional AFM studies, described in Supporting Information, pointed to the relative insensitivity of the salient features of the surface morphologies of studied copolymers to sample preparation conditions, lending further support to their strong segregation behavior. II. Experimental Section Materials and Characterizations. n-Octadecyl methacrylate (ODMA) (Polysciences Inc.; 99%) was purified by being dissolved in hexane and extracted four times with 5% aqueous NaOH. After the organic phase was dried over magnesium sulfate, the solution was passed through neutral alumina, and solvent was removed under reduced pressure. tert-Butyl acrylate (tBA) (Aldrich; 98%) was dried over calcium hydride and then distilled in a vacuum. Cu(I)Br (Acros; 98%) and Cu(I)Cl (Acros; 99%) were purified by being washed with glacial acetic acid, followed by absolute ethanol and acetone, and then dried under vacuum. 4,4′-Di(5-nonyl)-2,2′-bipyridine (dNbpy) was prepared according to the procedures reported in the literature.33 Dimethyl-2, 6-dibromoheptanedioate (DMDBH) (Aldrich; 97%), N,N,N′,N′′, N′′-pentamethyldiethylenetriamine (PMDETA) (Aldrich; 99%), and Cu(II)Cl2 (Aldrich; 99+%) were used as received. All other reagents and solvents were used as received from Aldrich or Acros Chemicals. The monomer conversion of tBA was determined using a Shimadzu GC-14A gas chromatograph equipped with a flame ionization detector (FID) using a J&W Scientific 30-m DB WAX Megabore column. Injector and detector temperatures were kept constant at 250 °C with a heating rate of 20 °C/min. The monomer conversion of nODMA and the copolymer composition were analyzed by 1H NMR in CDCl3 on a Bruker 300 MHz instrument. Copolymer molecular weights were determined using a gel permeation chromatograph (GPC) equipped with a Waters WISP 712 autosampler, Polymer Standards Service guard columns (102, 103, and 105 Å), and a Waters 410 RI detector against linear polystyrene or poly(methyl methacrylate) standards in tetrahydrofuran (THF; 1 mL/min) at 35 °C, and toluene was used as the internal standard. Synthesis of the Difunctional ptBA Macroinitiator. In a 25-mL degassed Schlenk flask, deoxygenated tBA (16 g, 0.12 mol), PMDETA (52 µL, 0.25 mmol), and anisole (4 mL) were added; the reaction mixture was degassed by three freeze-pumpthaw cycles. After the mixture was stirred for 20 min at room temperature, Cu(I)Br (36 mg, 0.25 mmol) was added under N2, and the flask was placed in a thermostated oil bath at 65 °C. After 10 min, DMDBH (21.7 µL; 0.1 mmol) was injected, and an initial kinetic sample was taken. During the polymerization, samples were removed to analyze conversion by gas chromatography (GC) using anisole as the internal standard and molecular weight by GPC. We stopped the reaction cooling the mixture to ambient temperature and opening the flask to the air. The mixture was then diluted with 100 mL of THF, passed through a neutral alumina column, concentrated by rotary evaporation, and precipitated into 800 mL of a MeOH/H2O (80/20 vol ratio) solution. The isolated polymer was reprecipitated (35) Mierzwa, M.; Floudas, G.; Stepanek, P.; Wegner, G. Phys. Rev. B 2000, 62, 14012.
Self-Assembly of pODMA-b-ptBA-b-pODMA Copolymers Table 1. Molecular Characteristics of the pODMA-b-ptBA-b-pODMA Triblock Copolymers Mn Mn Mn (total)a (pODMA)a (ptBA)a wt % sample (g/mol) (g/mol) (g/mol) (pODMA) fpODMAb Mw/Mn S14 S39 S45 S47 S52 S58 S65 S81 S90 S94 a
94900 112600 94900 28100 105200 16000 71000 108800 94900 124200
11400 39400 38900 12100 50500 8600 43300 84900 84500 115500
83500 73200 56000 16000 54700 7400 27700 23950 10400 8700
0.12 0.35 0.41 0.43 0.48 0.54 0.61 0.78 0.89 0.93
0.14 0.39 0.45 0.47 0.52 0.58 0.65 0.81 0.90 0.94
1.18 1.11 1.18 1.18 1.17 1.25 1.24 1.15 1.22 1.35
NMR. b FpODMA ) 0.858 g/cm3; FptBA ) 1 g/cm3.
from THF into MeOH/H2O (80/20 vol ratio) three times to remove the remaining monomer and dried under a vacuum at 40 °C. Synthesis of the pODMA-b-ptBA-b-pODMA Triblock Copolymer. In a 25-mL Schlenk flask, Cu(II)Cl2 (1.22 mg, 0.009 mmol), the ptBA difunctional macroinitiator (1.91 g, 0.045 mmol), and dNbpy (81.5 mg, 0.2 mmol) were added. After the flask was vacuumed and back-filled with nitrogen three times, deoxygenated ODMA (6.5 g, 20 mmol) in 10 mL of toluene were added. After the solution was stirred for 1 h at ambient temperature, Cu(I)Cl (8.9 mg, 0.09 mmol) was added, and the flask was placed in a thermostated oil bath at 90 °C. An initial kinetic sample was taken, and samples were removed to analyze conversion by NMR and molecular weight by GPC during the polymerization. We stopped the reaction by cooling the mixture to ambient temperature and opening the flask to the air. The mixture was then diluted with 30 mL of THF, passed through a neutral alumina column, concentrated by rotary evaporation, and precipitated into 600 mL of hexane. The isolated polymer was reprecipitated from THF into hexane five times to remove the remaining ODMA monomer and dried under a vacuum at 25 °C. The molecular characteristics of the triblock copolymers are shown in Table 1. Differential Scanning Calorimetry (DSC). A Mettler Toledo Star DSC capable of programmed cyclic temperature runs over the range of 113-673 K was used. The samples were first heated at a rate of 10 K/min from ambient temperature to 473 K and then cooled to 250 K with the same rate. In all samples, pODMA underwent side-chain crystallization upon being cooled at a crystallization temperature (Tc) of 285 K. The apparent melting temperature (T′m) is at ∼300 K, that is, below the glass )320 K). The details on transition temperature of ptBA (TptBA g the thermodynamic and dynamic properties of the copolymers (as a function of temperature and pressure) will be the subject of a separate study.41 Rheology. The viscoelastic properties of S14 (fpODMA ) 0.14; fpODMA is the volume fraction of pODMA) and S94 (f ) 0.94) were measured with an advanced rheometric expansion system (ARES), equipped with a force-rebalanced transducer, in the oscillatory mode. A parallel-plate geometry was used with a diameter of 6 mm and a thickness of ∼1 mm. Different types of experiments were performed: (1) dynamic strain sweeps at different temperatures aiming to identify the linear and nonlinear viscoelastic regimes, (2) dynamic temperature ramps at a frequency of 10 rad/s, and (3) dynamic frequency sweeps at temperatures within the range of 293-474 K at carefully selected steps. SAXS. An 18-kW rotating anode X-ray source (Rigaku) was used with a pinhole collimation and a two-dimensional (2D) detector (Bruker) with 1024 × 1024 pixels. A double graphite monochromator for the CuKR radiation (wavelength λ ) (36) Mayes, A. M.; de la Cruz, M. O. J. Chem. Phys. 1991, 95, 4670. (37) Wu, W.; Matyjaszewski, K.; Kowalewski, T. Langmuir, in press, 2005. (38) Helfand, E. Macromolecules 1975, 8, 552. (39) Helfand, E.; Wasserman, Z. R. Macromolecules 1976, 9, 879. (40) Semenov, A. N. Sov. Phys. JETP 1985, 61, 733. (41) Gitsas, A.; Floudas, G.; Pakula, T.; Matyjaszewski, K., submitted for publication, 2005.
Langmuir, Vol. 21, No. 21, 2005 9723 0.154 nm) was used, and the sample-to-detector distance was set at 1.8 m. The recorded 2D scattered intensity distributions were investigated over the azimuthal angle and are presented as a function of the scattering wave vector q (q ) (4π/λ) sin(2θ/2), in which 2θ is the scattering angle). One-hour long measurements were taken within the temperature range of 303-433 K with a stability better than (0.2 K. For the copolymer with the lowest Mn (S58; Mn ) 16000 g/mol), a detailed temperature run was made with a temperature program aiming to extract the structure factor in the disordered phase. Samples used for SAXS were prepared both from chloroform solutions and from melting as 0.5-mm thick films, and the same morphology was found in both cases. Tapping Mode Atomic Force Microscopy (TMAFM). TMAFM experiments were carried out using a Multimode Nanoscope III system (Digital Instruments, Santa Barbara, CA). The measurements were performed under ambient conditions using commercial Si cantilevers with a nominal spring constant and resonance frequency respectively equal to 40 N/m and 300 kHz. The height and phase images were acquired simultaneously at set-point ratio A/Ao ) 0.7, in which A and Ao refer to the “tapping” and “free” cantilever amplitude, respectively. The samples for AFM imaging were prepared by placing an ∼50 µL droplet of a 1 mg/mL copolymer solution in chloroform onto the surface of a precleaned (chloroform washed) silicon wafer coated with a layer of native oxide. The droplets were dried freely in air, and the samples were then vacuum-dried overnight. The thickness of such prepared films was measured from TMAFM images of purposefully made scratches and ranged from 100 to 150 nm. Some additional studies of the effect of different preparation conditions (e.g., spin coating) and annealing are described in Supporting Information.
III. Results and Discussion Bulk Morphology. Before we proceed with the bulk and surface morphologies, we would like to briefly comment on the mechanical properties of the copolymers. The surface morphology, as explored by TMAFM, is sensitive to the inherent differences in the mechanical loss of the two blocks as well as that of the particular phases formed. The mechanical loss, in particular, can best be studied by probing the shear modulus as a function of temperature and frequency. The shear moduli of the triblock copolymers S94 (f ) 0.94) and S14 (f ) 0.14), which have nearly antisymmetric compositions, display some common features as well as some differences (Figure 1). For S14, the degree of side-chain crystallinity is very low, and the high modulus of the glassy ptBA block precludes the identification of the corresponding T′m. In the DSC trace, however, the pODMA side-chain melting temperature can be identified by the small endothermic peak around 303 K.35 Upon an increase in temperature, the loss modulus goes through a maximum and crosses with the storage modulus at 320 K, identifying the ptBA glass temperature. At even higher temperatures, the moduli develop a plateau at G′ ≈ 2 × 105 Pa, suggesting the presence of an entangled transient network. Notice the parallel behavior of the moduli at T > 400 K and that the system does not flow even up to the highest temperature investigated (T ) 423 K), which further suggests the existence of a microphase-separated structure. For S94, rich in the crystallizable block, the features are similar; however, there are two exceptions: (1) the discontinuous decrease of the moduli at the apparent melting temperature (that is in agreement with the position of the endothermic peak in DSC) and (2) the lower plateau modulus (at ∼3 × 103 Pa) reflecting an ordered melt in a “super soft” state. The detailed rheological investigation will be the subject of a separate investigation. For this study it suffices to mention that (1) there exists sufficient mechanical contrast between the glassy ptBA and the pODMA melt, (2) there is no flow up to 400 K, and
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Wu et al. Table 2. Types of Nanostructure and Characteristic Spacings from SAXS and AFM sample
fpODMA
structure
S14 S39 S45 S47 S52 S58
0.14 0.39 0.45 0.47 0.52 0.58
hex lam lam lam lam
S65 S81 S90 S94
0.64 0.81 0.9 0.94
dSAXSa (nm) (T ) 313 K)
dAFM (nm) (T ) 303 K)
36.5 47 45 19.6 46.2 14.3
39.8 47.7 46.6 20.4 46.5 18.1
31.4 35
43.5 41.3 32.1 43.6
323K
lam f dis lam hex cubic cubic
a The spacings for lamellar and hexagonally packed patterns were determined respectively as d ) 2π/q* and d ) (2π/q*)(4/3)1/2, in which q* is the position of the first peak in SAXS and FT magnitude plots.
Figure 1. (Top) Isochronal (ω ) 1 rad/s) temperature runs of the dynamic shear storage (G′; open symbols) and loss (G′′; filled symbols) moduli for two copolymers: S94 (squares) and S14 (circles). The vertical lines indicate the pODMA melting temperature (red) and the ptBA glass temperature (blue). (Bottom) The corresponding DSC traces (rate: 10 K/min) during the second heating run for S94 (red) and S14 (blue).
microdomain morphology. A similar morphology is obtained for the S47 (f ) 0.47) triblock copolymer (peaks with relative positions at 1:2:3). Notice the large shift in q*, which reflects the lower molecular weight of the sample. For S81 (f ) 0.81), peaks with relative positions at 1:41/2: 71/2 are observed, suggesting hexagonally packed cylinders. The domain spacings from SAXS are summarized in Table 2. The SAXS investigation can provide not only the microdomain morphology and the relevant spacings but it also aids in the construction of the complete phase diagram1 by employing the scattering curves from the disordered phase (correlation hole scattering3). In a SAXS experiment, the scattered intensity due to concentration fluctuations, Ic, is related to the static structure factor S(q), through: Ic ) ∆n2VS(q), in which ∆n ) nA - nB and is the difference in the electron density of the two blocks, and V is the volume of the chain. In the context of the MFT,13,14 the structure factor of homogeneous block copolymers arising from composition fluctuations has the general form
N ) F(x,f) - 2χN S(q)
(1)
in which F(x,f) is given by the general expression Figure 2. SAXS curves from four copolymers: S14 (f ) 0.14, T ) 303 K): arrows indicate peaks at positions 31/2:41/2 relative to the main peak; S39 (f ) 0.39, T ) 313 K): arrows indicate peaks at positions 2:3:4:5 relative to the main peak; S47 (f ) 0.47, T ) 313 K): arrows indicate peaks at positions 2:3 relative to the main peak; and S81 (f ) 0.81, T ) 313 K): arrows indicate peaks at positions 41/2:71/2 relative to the main peak.
(3) no order-to-disorder transition exists for the two copolymers investigated. Next we investigate the phase state of the copolymers in bulk using T-dependent SAXS. Figure 2, provides representative scattering curves for some triblock copolymers. The scattering contrast (see below) of the two blocks is rather low; nevertheless, it is still possible to identify the microdomain morphology. The arrows indicate the positions of the higher-order reflections with respect to the primary peak at q*; for S14 (f ) 0.14), some broad peaks with relative (approximate) positions at 1:31/2:41/2 suggest distorted hexagonally packed cylinders (on the basis of nearest neighbors correlations) as the microdomain morphology. For S39 (f ) 0.39), the peaks are at relative positions with ratios 1:2:3:4:5, revealing lamellar
F(x,f) )
gAA + gBB + 2gAB gAAgBB - gAB2
(2)
For an A-B-A triblock copolymer with corresponding block fractions of f1, f2, and f3 these functions take the form
gAA ) gD(f1,x) + gD(f2,x) + gD(f3,x) + gD(1,x) gD(1 - f3,x) - gD(1 - f1,x) gBB ) gD(f2,x) 1 gAB ) [gD(1 - f1,x) + gD(1 - f3,x) - gD(f1,x) 2 gD(f3,x) - 2gD(f2,x)] (3) in which gD is the Debye function:
gD(f,x) )
2 [fx + e-fx - 1] x2
(4)
Self-Assembly of pODMA-b-ptBA-b-pODMA Copolymers
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Figure 3. SAXS curves from the S58 (f ) 0.58) triblock copolymer at different temperatures. Orange circles: T ) 403 K; purple squares: T ) 393 K; gold triangles: T ) 383 K; magenta triangles: T ) 373 K; cyan rhombus: T ) 363 K; blue pentagon: T ) 353 K; green triangle: T ) 343 K; red triangle: T ) 333 K; black circles: T ) 323 K. In the inset, the temperature dependence of the product χN is shown. The solid line is the result of a linear fit to the highest temperature data.
Figure 4. Bulk phase diagram based on the results from the SAXS investigation. The symbols correspond to the different block copolymer compositions measured at different temperatures, resulting in the different χN values shown. The vertical lines give the approximate positions of the phase boundaries. The solid line, which separates the ordered from the disordered regions, is the prediction from the MFT.
and x ) q2Rg2 (Rg is the unperturbed radius of gyration). In the present case (symmetric copolymer, i.e., f1 ) f3), the mean-field phase diagram predicts a first-order transition to body-centered cubic (bcc) spheres for all compositions f * 0.5 and order-to-order transitions from bcc to hexagonal (hex) to lamellar (lam) with increasing χN. However, in contrast to A-B diblock copolymers, the mean-field phase diagram of A-B-A triblock copolymers is highly asymmetric as a result of the higher entropic penalty in deforming the central B blocks to accommodate the two outer blocks into the A domains. We have used the above mean-field structure factor to describe the scattered intensity of the S58 (f ) 0.58, Mn ) 16000 g/mol) in the disordered state. The resulting fits to the disordered I(q) are shown in Figure 3, together with the χN(T) dependence. Notice that the theory satisfactory describes the experimental points, except in the low-q range, in which the theory predicts S(q f 0) ) 0 (incompressible system). The thus extracted interaction parameter displays a strong T dependence as χ ) 0.12 + 38/T (obtained from a linear fit to the highest temperatures that are least prone to fluctuations12,36), resulting in χN ) 18.2 at the transition, which is in agreement with the MFT predictions (f ) 0.58). On the basis of this χ(T), a mean-field phase diagram was constructed and is shown in Figure 4. The phase diagram is dominated by the lamellar phase, with smaller regions of hexagonally packed cylindrical and cubic phases (i.e., the classical phases). We mention here that the introduction of fluctuation corrections,36 using the angle-dependent Hartree approximation, gives rise in asymmetric phase diagrams with only a small region of bcc for symmetric triblock copolymers. For symmetric triblock copolymers with N ) 106, the bcc phase is completely absent, and the corrected phase diagram allows for direct transitions from the disordered to the lam and hex phases. In addition, orderto-order transitions are also predicted for weak/intermediate segregation. For the triblock copolymer investigated herein, no order-to-order transitions were found, which is in agreement with the strong segregation picture. In addition, the double gyroid phase was not observed because of the limited systems existing in weak segregation and within the lam/hex phase boundaries. With the exception of S58 and S47, which are within the weak segregation regime, the high molecular weights and the strong χ(T)
render the remaining copolymers strongly segregated. In this regard, it is of interest to compare the bulk with the surface morphology of both the strongly and the weakly segregated triblock copolymers and to compare the corresponding microdomain spacings. Surface Morphology. The surface morphologies of all of the copolymers were investigated using TMAFM. In this work, we took advantage of the well-known ability of TMAFM to differentiate regions of materials exhibiting different levels of energy dissipation during intermittent tip-sample contacts. This is accomplished by mapping (along with topography) the phase of cantilever oscillation, which is sensitive to energy flow in the tip-sample system. These maps are then displayed in false color scales in which areas of more pronounced phase shift (energy dissipation) appear darker.29,37 Because of this ability, AFM became a particularly popular tool in visualizing the phase structure in phase-separated block copolymers. One of the challenges of AFM in the characterization of block copolymer morphologies is the extent to which the boundary conditions present in thin/ultrathin films “skew” the surface morphology in comparison to that of the bulk. Providing at least a partial answer to this question was one of the goals of this study. Interestingly, despite the above concerns about the sensitivity of morphology to boundary conditions, in all cases the morphologies observed in TMAFM images were in good agreement with the morphologies determined by SAXS. For example, for the triblock copolymer S14, which possesses the lowest volume fraction (fpODMA ) 0.14), the AFM phase images shown in Figure 5a revealed the nearly hexagonal pattern of darker (higher mechanical loss) round features dispersed in a brighter (lower mechanical loss) matrix. On the basis of the results of our previous work,37 these features were identified as phase-separated domains of pODMA surrounded by the ptBA matrix. Their round appearance and hexagonal packing symmetry point to either spherical or cylindrical morphologies (with cylinders normal to the surface). Annealing at 353 K for 1 h helped to identify the exact microdomain morphology (Supporting Information); under these conditions, a fraction of short cylinders appeared parallel to the surface, revealing that the surface morphology is the one suggested by SAXS. Samples with ODMA content of f ) 0.39-0.65 (Figure 5b-g) all showed characteristic striped patterns
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Figure 6. Comparison of the domain spacing from SAXS (filled symbols) and the radially averaged FT magnitude from AFM (open symbols): (a) S14 (f ) 0.14); (b) S39 (f ) 0.39); (c) S47 (f ) 0.47); and (d) S81 (f ) 0.81).
Figure 5. AFM phase images of pODMA-b-ptBA-b-pODMA triblock copolymers. (a) S14 (f ) 0.14); (b) S39 (f ) 0.39); (c) S45 (f ) 0.45); (d) S47 (f ) 0.47); (e) S52 (f ) 0.52); (f) S58 (f ) 0.58); (g) S65 (f ) 0.65); (h) S81 (f ) 0.81); (i) S90 (f ) 0.90); and (j) S94 (f ) 0.94). All of the images are 1 × 1 µm. The film thickness is in the range of 100-150 nm.
of alternating bright and dark areas, which is in excellent agreement with the bulk lamellar structures found in SAXS. These lamellar patterns were highly regular and exhibited little branching, with the exception of S58 (f ) 0.58), for which the stripes were much finer and highly curved. In the copolymers with f > 0.8 (Figure 5h-j), there was a phase inversion, and ptBA became the minority dispersed phase, as manifested in the AFM images showing round bright domains surrounded by a dark
matrix. The AFM morphology for the S81 copolymer (f ) 0.81; Figure 5h) revealed hexagonally packed cylinders (annealing results in some cylinders lying parallel to the surface), which is in agreement with the SAXS morphology. The more asymmetric copolymers S90 (f ) 0.90; Figure 5i) and S94 (f ) 0.94; Figure 5j), exhibited, according to SAXS, a cubic morphology. Apparent hexagonal order in the AFM images of these copolymers could indicate that the spherical domains underwent surface reconstruction into hexagonal packing, which is expected for 2D spherical systems. The AFM surface morphologies exhibited enough periodicity to be analyzed with the aid of a 2D Fourier transform (FT). Subsequently, the 2D FT maps were radially averaged to produce magnitude plots analogous to the scattering patterns. After the spatial frequency scale was recalculated to scattering vector units (2π/d), these curves could be overlaid with the corresponding SAXS data (Figure 6), and the corresponding domain spacings are given in Table 2. As shown in Figure 6 and in Table 2, there is good agreement between the domain spacings. One marked exception here was sample S65, for which the spacing determined by AFM was ∼25% larger than that obtained from SAXS. One possible explanation of this discrepancy could involve the tilting of the lamellae with respect to the sample surface or the frustration effects outlined in the introduction. Theories in the strong segregation limit1,2 (SSL, χN . 10) predict extended block conformations, as opposed to the unperturbed (Gaussian) limit, which has a scaling of the domain spacing as d ≈ Nδ, with δ ≈ 1/2. Chain extension results from the combined effects of the localization of the block junction points at a narrow interface and the requirement for an overall uniform density within the domains. Helfand and Wasserman (HW)38,39 and subsequently Semenov (S),40 treated the chain extension in strongly segregated block copolymers through different approaches and predicted that the domain period in the limit χN f ∞ should scale as
d ≈ Nδχν
(5)
Self-Assembly of pODMA-b-ptBA-b-pODMA Copolymers
Figure 7. Dependence of the SAXS (filled symbols) and AFM (open symbols) domain spacing of the nearly symmetric copolymers on the total molecular weight. The line is the result of the fit to the SAXS data with a slope of 0.64. The error bars are smaller than the symbol size.
in which δ ≈ 9/14 and ν ) 1/7 (HW), and δ ≈ 2/3 and ν)1/6 (S). In the latter approach, the stretched chains were envisioned as the chains in grafted polymer brushes. The high incompatibility of the blocks (χN ≈ 100) makes the comparison of the SAXS (and AFM) domain spacing with the above scaling predictions feasible. The molecular weight dependence of the domain spacing is shown in Figure 7 for the symmetric (S47, S52) and the nearly symmetric (S45, S58) block copolymers in a double logarithmic representation. Notice the good agreement of the surface and bulk spacings, with the exception of S58 in which the AFM value is higher than the SAXS. This difference could originate from (1) the highly curved lamellae in AFM and (2) the lower molecular weight of the block copolymer (weak segregation limit), suggesting the influence of surface effects. Nevertheless, the SAXS domain spacing scales as δ ≈ 0.64, which is in accord with the predictions of the SSL theories (AFM alone results in a somewhat lower value, δ ≈ 0.56). In addition, we have calculated the effective domain size for each of the phases from the AFM images. The discussion of the size of the effective domains can be found in Supporting Information. Having established the microdomain morphology, in a future study41 we will report on the dynamics of the same triblock copolymers as a function of temperature and pressure. More specifically, we will report on the effect of pressure on increasing the crystallization (pODMA) and glass (ptBA) temperatures of the two blocks, along with the consequences of this effect on their thermoplastic behavior. IV. Conclusions ATRP was used to synthesize a series of A-B-A triblock copolymers containing pODMA as the side-chain crystalline segments and ptBA as the amorphous segments. The bulk and surface morphologies were studied using SAXS
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and AFM, respectively, aiding (1) in the comparison of the surface and bulk morphologies and in constructing the relevant phase diagram and (2) in the comparison of the corresponding domain spacings. In the SAXS study, the MFT was employed to obtain the segment-segment interaction parameter and to construct the bulk phase diagram that is composed from the classical structures: cubic, cylindrical, and lamellar. For the majority of the investigated block copolymers, χN ≈ 100, suggesting strong segregation, which is in accord with the absence of any order-to-order transitions and the absence of nonclassical phases. The difference in the mechanical elasticity of the different blocks gave rise to well-resolved microdomain structures in TMAFM images. The surface morphologies of the samples that were prepared by drop casting and visualized with TMAFM were in very good agreement with the SAXS results. Quantitative agreement was found between SAXS and AFM, not only for the phase state, but also with respect to the domain spacing (scaling with a molecular weight as d ≈ N0.64), indicating strong segregation and extended chains. Such good agreement suggests that, for the studied copolymers, substrate and boundary effects did not result in the formation of “nonbulk” morphologies, and the drop casting method produced wellequilibrated samples. The latter assertion was supported by the observation that samples prepared by drop casting showed little change upon annealing. In contrast, samples prepared by spin coating (i.e., under conditions much less favorable for reaching equilibrium) were observed to produced less sharply defined morphologies, which, upon annealing, tended to evolve toward those observed in the case of drop casting. All this suggests that strongly segregating systems, like the ones under study here, are likely to be less prone to be skewed by the boundary conditions and to be more sensitive to kinetic factors mediated by solidification conditions. From a methodological perspective, the results presented here demonstrate the benefits of SAXS (reciprocal space) and AFM (real space) combination in the studies of the phase structure of block copolymers, especially those exhibiting strong segregation behavior. The SAXS-AFM “tandem” appears to be particularly promising in view of recent developments in grazing incidence techniques (GISAXS),42-44 especially those utilizing bright synchrotron sources. Acknowledgment. This work was supported by a GSRT grant (PENED01/529) and the NSF (DMR0090409). Supporting Information Available: Material synthesis and characterization. This material is available free of charge via the Internet at http://pubs.acs.org. LA051130U (42) Lee, B.; Park, I.; Yoon, J.; Park, S.; Kim, J.; Kim, K.-W.; Chang, T.; Ree, M. Macromolecules 2005, 38, 4311. (43) Papadakis, C. M.; Busch, P.; Posselt, D.; Smilgies, D.-M. Adv. Solid State Phys. 2004, 44, 327. (44) Mueller-Buschbaum, P. Anal. Bioanal. Chem. 2003, 376, 3.
