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Harnessing Light to Create Defect-Free, Hierarchically Structured Polymeric Materials Rui D. M. Travasso, Olga Kuksenok, and Anna C. Balazs* Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261 Received September 14, 2005 Computer simulations reveal how photoinduced chemical reactions in polymeric mixtures can be exploited to create long-range order in materials with features that range from the submicron to the nanoscale. The process is initiated by shining a spatially uniform light on a photosensitive AB binary blend, which thereby undergoes both a reversible chemical reaction and a phase separation. When a well-collimated, higher intensity light is rastered over the sample, the system forms defect-free, spatially periodic structures. If a nonreactive homopolymer C is added to the system, this component localizes in regions that are irradiated with a higher intensity light, and one can effectively “write” a pattern of C onto the AB film. Rastering over the ternary blend with the collimated light now leads to hierarchically ordered patterns of A, B, and C. Because our approach involves homopolymers, it significantly expands the range of materials that can be fashioned into a periodic pattern. The findings point to a facile process for manufacturing high-quality polymeric components in an efficient manner.
One of the current grand challenges in the physical sciences is fabricating materials that are spatially periodic on the submicron scale and are defect-free on the millimeter to centimeter scale. This task is even more daunting when the materials encompass multiple components and the required periodicity involves multiple length scales. The development of facile techniques for creating such defect-free materials would enable the efficient production of a vast variety of optoelectronic and magnetic components. Currently, there is a tremendous drive to use polymeric materials in the next generation of devices because polymers are lightweight, flexible, and relatively inexpensive. These materials commonly involve a blend of multiple homopolymers or copolymers because the blending process allows one to fine-tune the properties by tailoring the mix of constituents. Polymer blends, however, phase separate and coarsen into highly disordered structures and not the spatially periodic, defectfree morphologies that are needed for photonic, electronic, or magnetic devices. This poses a significant stumbling block to achieving the goal of manufacturing high quality polymeric devices in a low-cost, efficient manner. Using computational modeling, we show how photosensitive chemical reactions in binary and ternary polymeric mixtures can be harnessed to create hierarchically ordered materials that are defect-free on relatively large length scales. Our system involves a uniform “background” light that initiates a reversible chemical reaction in a binary blend. We then introduce a higher intensity, spatially localized beam that locally increases the rate of reaction. By rastering over the sample with the secondary light, we effectively “comb” out any defects in the material and create highly regular structures. By adding a third component, C, we “write” a well-defined pattern onto the binary system. In particular, C is driven to migrate to the region illuminated by the higher intensity light; in this manner, the free energy of the entire system is minimized. By exploiting this concept, we can create a variety of patterned structures by focusing the light in the desired spatial motif. Rastering light over this ternary system yields a defect-free material that displays periodicity over two distinct lengths scales. The combing process described herein for the binary mixtures is analogous to the zone refinement or directional * Corresponding author. E-mail:
[email protected].
quenching1,2 processes. However, unlike the latter methods, which harness heat to induce a phase transition, the use of light to promote a transformation does not require a physical coupling to the system. This is particularly important in nanostructured thin films in which the lateral dissipation of heat would be detrimental. Here, by sweeping thin films with a well-defined, highly collimated light source, we establish a simple, nonintrusive process wherein long-range order is produced in systems having elements that can be as small as nanoscale. Additionally, our approach for creating ternary hierarchical structures differs critically from directional quenching because we also utilize the light as a “stylus”, with C as the “ink”, to inscribe a chosen pattern. The above process requires an immiscible ternary A/B/C mixture in which the phase separation among all of the components occurs simultaneously with a reversible chemical reaction between A and B, as indicated below: Γ+
A {\ }B Γ -
(1)
An appropriate example of eq 1 is a blend of trans-stilbenelabeled polystyrene (PSS) and poly(vinyl methyl ether) (PVME); upon irradiation with light, the stilbene moieties on the PSS chains undergo a reversible trans-cis isomerization, leading to phase separation within the binary mixture.3,4 The parameters Γ+ and Γ- represent the forward and reverse reaction rate coefficients, respectively. In our ternary system, C is nonreactive; it simply phase separates from A and B. In the case of a homogeneous quench, the structural evolution of a similar ternary mixture was studied previously.5 The incompressible ternary mixture is characterized by two order parameters, φ ) FA - FB and ψ ) FC, in which Fi is the volume fraction of the ith component. With the (1) Furukawa, H. Physica A 1992, 180, 128. (2) Zhang, H.; Zhang, J.; Yang, Y.; Zhou, X. J. Chem. Phys. 1997, 106, 784 and references therein. (3) Nishioka, H.; Kida, K.; Yano, O.; Tran-Cong, Q. Macromolecules 2000, 33, 4301. (4) Tran-Cong, Q.; Kawai, J.; Endoh, K. Chaos 1999, 9, 298. (5) (a) Ohta, T.; Ito, A. Phys. Rev. E 1995, 52, 5250. (b) Tong, C.; Yang, Y. J. Chem. Phys. 2002, 116, 1519.
10.1021/la052511a CCC: $30.25 © 2005 American Chemical Society Published on Web 10/26/2005
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Figure 1. (a) Schematic of system. (b) Late-time morphology with stationary stripe, which represents the secondary light source. (c-e) Morphologies at different times: (c) t ) 2 × 104, (d) t ) 1.7 × 105, and (e) t ) 3.7 × 105. Here, and in all ensuing figures, stripe moves with velocity v ) 0.001, and the size of the simulation box is 206 × 206. Unless specified otherwise, Γ1 ) 0.0003 and Γ2 ) 0.003.
reaction in eq 1, the structural evolution of this mixture is given by
∂φ ) Mφ∇2µφ - (Γ+ + Γ-)φ + (Γ- - Γ+) ∂t
(2)
∂ψ ) Mψ∇2µψ ∂t
(3)
in which the constants Mφ and Mψ are the mobilities of the respective order parameters φ and ψ. The chemical potentials, µφ and µψ, are defined through the free energy functional F(φ,ψ) as
µφ )
δF(φ,ψ) δφ
µψ )
δF(φ,ψ) δψ
(4)
A suitable form of F(φ,ψ) is
F(φ,ψ) )
∫ dr[f(φ,ψ) + κφ(∇φ)2 + κψ(∇ψ)2]
(5)
Figure 2. Dependence of the regularity of the structure, β, on Γ2; each point represents an average over three independent runs. The inset shows the width of the domains (obtained after combing) as a function of Γ1. The slope of the dashed line is -1/4.
in which the local free energy f(φ,ψ) is taken to be6
f(φ,ψ) ) -aφ2 + bφ4 + cψ2 - dψ3 + eψ4 + gφ2ψ2 (6) The two gradient terms in eq 5 are related to the interfacial tensions between the components. The values of the constant coefficients in eq 6 are obtained by constraining f(φ,ψ) to have equal minima at φ ) (1, ψ ) 0 (pure A and B) and at φ ) 0, ψ ) 1 (pure C). This yields a ) 0.02, b ) 0.01, c ) 0.06, d ) 0.16, e ) 0.09, and g ) 0.06.7 We set κφ ) κψ/3 ) 0.015 and Mφ ) 3Mψ ) 0.15; consequently, the interfacial tensions between the different components are equal, and the mobilities of all the phases are the same. (However, as we discuss below, the latter constraints are not necessary conditions for the observed phenomena.) When Γ( ) 0, eqs 2 and 3 together describe phaseseparation in a ternary mixture (e.g., refs 6 and 7 and the references therein). When Γ( * 0 and C is absent, eq 2 describes a phaseseparating binary blend in which the reaction in eq 1 suppresses large wavelength fluctuations and arrests the domain growth at a characteristic wavelength.8,9 Consequently, the system’s morphology resembles the structure formed by microphase-separated diblock copolymers,4,8 forming lamellar-like structures when Γ+ ) Γ- ) Γ and having a hexagonal morphology when Γ+ . Γ- (or Γ+ , Γ-). (6) Good, K.; Kuksenok, O.; Buxton, G.; Ginzburg, V.; Balazs, A. C. J. Chem. Phys. 2004, 121, 6052. (7) Travasso, R.; Buxton, G. A.; Kuksenok, O.; Good, K.; Balazs, A. C. J. Chem. Phys. 2005, 122, 194906. (8) Glotzer, S.; Di Marzio, E.; Muthukumar, M. Phys. Rev. Lett. 1995, 74, 2034. (9) Bahiana, M.; Oono, Y. Phys. Rev. A 1990, 41, 6763.
Herein, we consider reaction rates that vary both dynamically and spatially; hence, Γ((t,r) is a function of both time and space. We first describe how we exploit this feature in a binary blend. In particular, we turn on a spatially uniform, background light, initiating the reaction in eq 1, with Γ+ ) Γ- ≡ Γ1. Then, we introduce a spatially localized secondary light source, which has a higher intensity and is represented by the dark stripe in Figure 1a. The secondary light source locally increases the rate coefficients to Γ+ ) Γ- ≡ Γ2 > Γ1. We numerically solve eq 2 (using a lattice Boltzmann technique6) in two dimensions with the reaction rate coefficients equal to Γ2 within the dark stripe and equal to Γ1 elsewhere. Figure 1b shows the system’s morphology at late times; the width of the lamellar-like domains is smaller within the Γ2 region than it is in the Γ1 areas. Specifically, the domain width λ decreases as Γ-1/4 (see inset in Figure 2), which is consistent with earlier studies (e.g., the results obtained by Oono and Bahiana9). The increase of the reaction rate also causes the absolute value of the order parameter in the bulk to decrease, that is, the domains become more intermixed.5,8,9 We now simulate the motion of the secondary light source over the sample, along the y direction, at a constant speed (see Figure 1c,d). In other words, eq 2 is now solved for both spatially and temporally varying values of the reaction rate coefficients. The rastering speed must be lower than vMAX ≈ 2Γ2w (in which w is the stripe width), given that 1/2Γ2 is the characteristic time for the morphology to reach steady state within the Γ2 region (see eq 2). As this light is moved over the film, we find that the morphology becomes more spatially regular. In effect, the
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Figure 3. (a) Schematic of the system. The two dark stripes that are outlined with solid lines represent stationary regions of Γ2; the dark stripe with dashed boundaries represents the mobile Γ2 region. (b,c) Morphology at different times for a system with two stationary stripes: (b) t ) 8 × 104 and (c) t ) 3 × 105. (d,e) Morphologies at the beginning, (d), and end, (e), of combing. The volume fraction of C is 33%.
light acts as a “comb” that “straightens out” the domains as it passes over the sample (Figure 1e). Because the domains are smaller and more intermixed within the Γ2 region, this region is effectively homogeneous or “neutral” relative to the Γ1 sections. Thus, the motion of the secondary light source creates a moving neutral interface, with the lamellar domains aligning perpendicular to this boundary as the light sweeps across the sample. A way to qualitatively understand this behavior is to recall that lamellar diblock domains orient perpendicular to neutral interfaces.10 In Figure 2, we measure the regularity of these domains, β, as a function of Γ2 and the number of times we repeat the combing process for Γ1 ) 0.0003 and rastering velocity v ) 0.001. We define β ) (〈φ〉y2/〈φ2〉y)x, in which 〈‚‚‚〉i represents the average along the i direction;11 β ) 1 corresponds to the completely ordered phase. After the first passage of the secondary light, we observe defect-free samples for higher values of Γ2 (see Figure 2); the domains are sufficiently narrow, and the components are sufficiently intermixed to guarantee the “neutrality” of the moving boundary with respect to the interfaces in the Γ1 region. No ordering of the stripes is observed for Γ2 values close to Γ1. Between those two regimes, there is a transition region (Γcl < Γ2 < Γcu in Figure 2) for which the ordering is not complete but can be quite significant. We note that the values of Γcl and Γcu depend on the rastering velocity and the width of the Γ2 region; however, a detailed analysis of the transition region will be the subject of a separate study. The ordering is improved by a second passage of the light over the sample (see Figure 2). In our simulations, the imperfections that remain after the first pass are due to the periodic boundary conditions because the alignment of the “combed” lower part of the sample is influenced by the upper “uncombed” part. However, we did not observe any improvement on the third or fourth passes; in effect, the moving, higher intensity light “erases” the underlying morphology, introducing more interfaces and more mixing, so that each following passage is equivalent to the previous one. In other words, in experiments, a single passage over the sample would potentially be sufficient to “comb” the structure. The system’s behavior is even more intriguing for ternary blends, as indicated by Figure 3. Starting with a homogeneous A/B/C mixture, we irradiate the entire sample with a background light (with Γ ≡ Γ1) and focus a spatially localized, higher intensity light on specific areas, which are marked by Γ2. As noted above, there is more intermixing and more A/B interfaces per unit area at Γ2; consequently, the interfacial energy and total free energy of the AB blend per unit area are also higher in (10) Kellog G. J.; Walton, D. G.; Mayes, A. M.; Lambooy, P.; Russell, T. P.; Gallagher, P. D.; Satija, S. K. Phys. Rev. Lett. 1996, 76, 2503. (11) Hashimoto, T. Bull. Chem. Soc. Jpn. 2005, 78, 1.
the Γ2 region than they are in Γ1. To reduce the free energy of the system, C diffuses to the Γ2 region. In other words, in a system that consists of two regions, one with a higher and one with a lower rate of reaction, the C component localizes within the region with the higher reaction rate. We exploit this effect to essentially “write” a pattern of C onto the AB film, as shown in Figure 3b,c. We choose the concentration of C such that it is just sufficient to completely cover the Γ2 regions. This constraint on concentration is the only apparent necessary condition on C (given that it is immiscible with both A and B). Even though all of the mobilities and interfacial tensions γij are identical in the results presented here, we checked the efficiency of “writing” for a variety of ternary blends with different mobilities and interfacial tensions. Differing values of these parameters alter the dynamics of the process; however, the “writing” is robust even for values as high as γCA ) γCB ) 3γAB and as low as γCA ) γCB ) 0.3γAB. Comparable variations in the relative mobilities yielded no effect on the regularity of the patterns. As illustrated in Figure 3d, a final processing step is required to create the defect-free, A/B/C patterns. While the sources of the Γ2 irradiation are kept fixed in the desired configuration, an additional secondary light (of the same intensity, Γ2) is rastered over the sample, much like in the binary example. By “combing” this sample, we obtain a multiscale, hierarchically ordered structure in which vertical stripes of A and B alternate with larger, horizontal stripes of C (Figure 3e). The smallest features of the structure (the width of the AB stripe) are defined by the polymer properties and the light intensity, and the stripe width can be on the order of the interface width (i.e., on the nanoscale). The size of the C domains is limited by the wavelength of the light that is used to create this pattern; thus, the C domains can be much larger than the other features of the system (i.e., on the microscale). Hence, we can easily create a pattern with elements at very different length scales. For a rastering speed on the order of Γ1λ1 (speed at which the A/B material creates regular domains in the Γ1 region), the influence of the moving stripe on the C domains is very small. For each passage, C can only diffuse by a maximum length ≈ λ1 (just as the A and B domains can). By shining light into areas of different shapes, we can control the shape of C domains and create a variety of the hierarchically ordered structures, as seen in Figure 4. In all cases, we start from the homogeneous mixture, and in each case, the C concentration is chosen to cover the corresponding Γ2 regions. First, we consider the high reaction rate areas to be squares of length LC ) 60 so that, at late times, the C component diffuses to those square domains (see Figure 4a); the AB stripes outside the squares are aligned because we “combed” the structure as in Figure 3. The upper and bottom boundaries of the C domains are slightly curved, however, this imperfection will be neg-
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Langmuir, Vol. 21, No. 24, 2005 10915
Figure 4. (a-c) Steady-state morphologies after combing; the volume fraction of C is 16%, 36%, 43%, for panels a, b, and c, respectively. In panels c and d, Γ2 ) 0.004. In panel d, the reaction rates are asymmetric for the Γ1 region, with Γ+ ) 0.0007 and Γ- ) 0.0003, and the C volume fraction is 26%. The “fuzzy” regions in a, c, and d mark the location of the rastering light (which is hidden behind the green domains in b).
ligibly small for larger C squares (i.e., for LC . λ1). In Figure 4b and 4c, the reaction rate is higher outside the central areas.12 In Figure 4c, we use a circular section, instead of a stripe, to align the A/B domains, and consequently, we obtain a spiral pattern. The hexagonal pattern obtained for Γ+ < Γ- can also be “combed” using the same procedure; Figure 4d shows that we can create a hierarchically ordered structure that consists of an AB hexagonal array and C stripes. In summary, by sweeping films with a collimated light source, we establish a facile process for creating defectfree, multicomponent materials that show hierarchical ordering, with periodicity over two distinct length scales, thereby enabling possible new technological applications. (12) The sharpness of the C corners in Figure 4a,b is enhanced by reducing γCA ) γCB. However, in our simulations, we cannot reduce the interfacial width below 3-4 lattice sites, and hence we cannot examine κφ < 0.01. The small A/B “wiggles” near the corners in Figure 4b are due to the fact that the stripes are aligning perpendicular to rounded C domains; these wiggles would be diminished for sharper corners.
Blends of liquid crystalline13 or “comb” copolymers14 and diblocks have also yielded materials that display ordering on two length scales; however, the materials form structures with apparent defects.14 Additionally, the latter systems involve unique, complex polymer architectures.13,14 Because our approach involves homopolymers, it significantly expands the range of materials that can be fashioned into a periodic pattern. The technique also opens up the possibility of writing patterns in three dimensions in a relatively simple manner. Acknowledgment. The authors gratefully acknowledge discussions with Prof. Tom Russell and Prof. Mary Galvin and financial support from NSF and DOE. LA052511A (13) Muthukumar, M.; Ober, C.; Thomas, E. Science 1997, 277, 1225. (14) Ruokolainen, J.; Saariaho, M.; Ikkala, O.; ten Brinke, G.; Thomas, E. L.; Torkkeli, M.; Serimaa, R. Macromolecules 1999, 32, 1152; Science 1998, 280, 560.
