Advances in square arrays through self-assembly and directed self-assembly of block copolymers


  • Christopher G. Hardy,

    1. Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208
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  • Chuanbing Tang

    Corresponding author
    1. Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208
    • Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208
    Search for more papers by this author


This review covers recent advances in developing square arrays in thin films using block copolymers. Theoretical and experimental results from self-assembly of block copolymers in bulk and thin films, directed self-assembly of block copolymers confined in small wells, on substrates with arrays of posts, and on chemically nanopatterned substrates, as well as applications as nanolithography are reviewed. Some future work and hypothesis are discussed. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013


Block copolymers are a class of intriguing soft materials comprised of at least two covalently linked polymer chains.1–3 Thermodynamic immiscibility between these chemically distinct blocks leads to a variety of ordered nanostructures with periodicity at the scale of 10–100 nm. Such length scales enable block copolymers for use in many potential applications including templates for lithography, microelectronic devices, membranes, data storage systems, photonic crystals, and so forth.4–21 The simplest coil–coil diblock copolymers typically self-assemble into body-centered cubic spheres, hexagonally packed cylinders, gyroid structures, and lamellae.2,3,22,23 Microphase-separated structures of block copolymers are dictated by three experimental parameters including the degree of polymerization (N), the volume fraction of the blocks (f), and the Flory-Huggins interaction parameter (χ).24–27 The chemical nature of the blocks determines χ, which essentially describes segment–segment interactions.

Other than AB diblock copolymers, which have been well developed for more than three decades, there are many other strategies for developing novel block copolymer systems.2,3 Linear ABC triblock copolymers have received significant attention because of the existence of the wide range of potential morphologies such as periodic arrays of core/shell spheres and cylinders, tetragonal lattices of cylinders, and novel bi-continuous and tri-continuous ordered mesophases.2,28,29 As opposed to one binary interaction parameter, one volume fraction, and a single block sequence for AB diblock copolymers, the greater diversity in morphology afforded by ABC triblock copolymers is due to their three binary interaction parameters, two independent volume fractions, and three different block sequences.2,28–37 Blends of diblock copolymers such as A-B/B-C and A-B/C-D have also been explored in searching for novel architectures.38–40 However, these systems are somewhat limited due to the occurrence of macrophase separation. In a related approach, supramolecular interactions have been used in A-B/B′-C type block copolymer blends to improve compatibility and limit macrophase separation, as the B/B′ interaction (typically hydrogen bonding) allows the B and B′ block to form a homogenous domain, which in turn allows for microphase separation to occur between the A, B/B′, and C block fractions.41–43 Furthermore, directed self-assembly (DSA) on chemically patterned substrates, in small wells, and on substrates templated with periodic posts have been used to produce desired nanoarchitectures in thin films from diblock and triblock copolymers.44–47

Among various morphologies obtained from the microphase separation of block copolymers, square arrays are of importance for many applications including nanolithography.14,44–46,48–56 One of the main limitations in the manufacture of integrated circuits is the difficulty in scaling the photolithographic techniques currently used during fabrication of complementary metal oxide semiconductor transistors to below 30 nm. One promising technique to achieve this scaling is block copolymer lithography, which affords feature sizes that are dictated by the molecular weight of the block copolymer and are typically 5–30 nm. The development of square arrays in thin films of block copolymers has recently attracted much attention. When compared with hexagonal arrays, square arrays are more compatible with semiconductor integrated circuit design standards based on rectilinear system; however, they are more difficult to achieve due to the unique requirements on block copolymer compositions and chemistry.37,41,43,56–59

The purpose of this review is to summarize work reported over the past 10 years in the development of square arrays from the self-assembly of block copolymers. “Templating Methods” section describes two major templating methods that are used for fabricating square arrays introduced in later sections. “Directed Self-Assembly” section details both theoretical and experimental efforts to coerce diblock copolymers into square arrays by DSA including both topographical and chemical graphoepitaxy. “Supramolecular Comb/Coil” section reviews a recent report that uses a novel comb/coil diblock copolymer system to prepare nonconventional square arrays of cylinders in a cylinder-in-lamellae morphology. In “Triblock Copolymer Approach” section, both theoretical and experimental studies on square arrays of cylinders from triblock copolymers are reviewed. “Supramolecular Block Copolymer Approach” section introduces the first reported square arrays of cylinders in thin films, which used a supramolecular block copolymer blend system. We finish this review by summarizing these efforts as well as offering an outlook into the future development of this field.


Templating methods have been widely used to form a variety of patterns. This section only introduces two templating methods that are used for fabricating square arrays as described in later sections.

Chemical Templating

Nealey and coworkers have explored the use of chemical graphoepitaxy in directing the assembly of block copolymers into desired architectures.60–62 This technique exploits the surface-polymer interactions to guide block copolymers to phase separate in a controlled manner. Chemically different blocks in a block copolymer have different affinities to the substrate that it is in contact with, therefore, one of the blocks will preferentially wet to the surface. It has been well shown that the surface of the substrate can be modified by addition of a brush layer.63 If the brush layer is made up of a homopolymer chemically similar to one of the blocks in a block copolymer, then that block of the copolymer will preferentially wet to the surface. If a random copolymer consisting of repeat units of the block copolymer with desirable compositions is coated to the substrate, the surface affinity can be controlled to be the same for each block, effectively neutralizing the surface. This surface neutralization technique has been used to prepare block copolymers with cylinders oriented perpendicular to the surface as opposed to parallel to the surface.51,54,64,65 An example of the chemical patterning process can be seen in Figure 1.44 Generally, a low molecular weight polystyrene (PS) brush is added onto the surface of a substrate by spin-coating and baking. A poly(methyl methacrylate) (PMMA) photoresist is then spin-coated on top of the PS brush and patterned with either electron beam lithography or extreme ultraviolet interference lithography. Once developed, an oxygen-rich plasma etch generates the nanopattern through the PMMA photoresist and into the PS brush layer. The block copolymer, in this example PS-b-PMMA, is then spin-coated on top of the nanopattern and annealed above the glass transition temperature (Tg) of the block copolymer. The annealing step allows for the block copolymer to microphase separate and self-assemble in recognition with the chemical nanopattern. Previous work has shown that lamella-forming PS-b-PMMA diblock copolymers can be annealed on a nanopatterned surface to produce desirable features including dense lines, bends, arcs, line terminations, and T-junctions.66,67 Additional studies have shown that the average grain size of PS-b-PMMA diblock copolymer that assembles into hexagonally packed cylinders can be increased from less than 1 µm2 on an unmodified substrate to an area over 5 µm × 8 µm on a chemically nanopatterned substrate.68 Resolution enhancements can be produced using this technique by density multiplication, as the density of the features of the block copolymer can exceed the density of the feature of the prepattern by an integer multiple. Defect-free assemblies of hexagonally packed cylinders with up to 4:1 density multiplication have been achieved.45

Figure 1.

Schematic representation of the chemical graphoepitaxy process to create a nanopatterned surface to direct the self-assembly process of a lamella-forming PS-b-PMMA diblock copolymer. (a) Deposition of a self-assembled monolayer of PETS onto a silicon wafer. (b) Photoresist was spin-coated on top of the SAM. (c) Prepatterning of photoresist to create lines and spaces. (d) Photoresist irradiated with soft X-rays in the presence of oxygen to create chemical pattern. (e) Removal of photoresist by solvent washings. (f) Deposition of lamella-forming diblock copolymer PS-b-PMMA. (g) Annealing, resulting in surface-directed block copolymer morphology.44 (From S. O. Kim et al., Nature, 2003, 424, 411–414, © Nature Publishing Group, reproduced by permission.)

Topological Templating

Substrates have been patterned with nanoscale posts in a desirable orientation to influence the packing order and grain size of self-assembled block copolymers. Ross and coworkers have demonstrated that well-defined hexagonal arrays of posts can generate well-ordered hexagonal arrays of spheres.47 Without the presence of the posts, diblock copolymer polystyrene-b-polydimethylsiloxane (PS-b-PDMS) with 16.5% PDMS self-assembled into hexagonally packed spheres with grain sizes of less than 0.4 µm × 0.4 µm. Posts were added in a hexagonal array at various distances relative to L0 and the substrate and post were coated with either homopolymer PS or PDMS. It was observed that when the substrate was coated with the homopolymer of the minor domain (PDMS), better order was obtained than when the post was coated with the major domain (PS), which in this case was attributed to the higher surface diffusivity of PDMS. When the posts were set in distances of <3L0, grain sizes increased to over 4 µm2. Similar results were found for a diblock copolymer PS-b-PDMS with 33.5% PDMS, which organizes into hexagonally packed cylinders of PDMS in a PS matrix in the bulk state.69 When posts were added in a square array and coated with PDMS homopolymer, the PS-b-PDMS organized into cylinders parallel to the substrate and in-line with the posts. Furthermore, cylinders in desired shapes including 90° and 180° turns could be directed by changing the post lattice geometry.70 Recently, posts were placed in square patterns with periods ranging from <L0 to more than 2L0.71 It was observed that diblock copolymer PS-b-PDMS could phase separate into various structures depending upon the spacing of the posts. Cylinders [Fig. 2(a, h)], undulated cylinders [Fig. 2(b)], spheres [Fig. 2(c)], ellipsoids [Fig. 2(d)], periodic superstructures [Fig. 2(e)], perforated lamellae with a perforation at each post [Fig. 2(f)], and perforated lamellae with additional perforations between the posts [Fig. 2(g)] were obtained. As seen in Figure 2, the cylinders that were obtained were parallel to the surface.

Figure 2.

(a–h) SEMs of various morphologies of PDMS microdomains (light gray) within the hydrogen silsesquioxane resist (white): (a) cylinders, (b) undulated cylinders, (c) spheres, (d) ellipsoids, (e) periodic superstructures, (f) perforated lamellae L1, (g) perforated lamellae L2, and (h) double cylinders. (i) Phase diagram of morphologies obtained by varying the distances between post with respect to domain spacing L0. (j) Phase diagram created using 3D SCFT by varying the distances between posts with respect to domain spacing L0. (k) 3D SCFT simulation showing various morphologies obtained in the phase diagram.71 (From K. G. A. Tavakkoli et al., Adv Mater, 2012, 24, 4249–4254, © John Wiley & Sons, Inc., reproduced by permission.)


Directed Self-Assembly

Although there have been no reports on the formation of square arrays of diblock copolymers in bulk, square arrays of cylinders in thin films of diblock copolymers by DSA using topographical graphoepitaxy have been predicted by self-consistent field theory (SCFT). Hur et al. conducted two-dimensional SCFT simulations of a lateral square-well confinement on a diblock copolymer in thin films.72 It is predicted that the edges of confined wells direct the orientation of block copolymer grains when the walls of wells are coated with a homopolymer consistent with one of the blocks, and the bottom and top of wells remains neutral to both blocks. When the size of square wells commensurates with a 3 × 3 square lattice of 9 cylinders and smaller, square arrays can be thermodynamically stable for a simple AB diblock copolymer. However, for square wells compatible with a 4 × 4 square lattice of 16 cylinders, square arrays are merely a kinetically trapped metastable state, as the thermodynamically stable morphology is a twisted hexagonal state. A homopolymer similar to the matrix block must be added to the system to relieve stretching of the matrix block in order to stabilize square lattices. It was found that the size of the square well, the homopolymer used to wet the side wall (either homopolymer A or B), and the relative amount and molecular weight of additive homopolymer could have a substantial impact on the degree of ordering and morphology of the copolymer confined within the square well. Several different morphologies were identified as thermodynamically stable states when these factors were taken into consideration. Hexagonal (HEX) ordering of cylinders, tetragonal (SQR) ordering of cylinders, defective square phase (d-SQR) ordering in which an additional cylinder is positioned in the middle of the well, and three independent macrophase-separated states (MAC I, II, and III) were observed. Multiple phase diagrams were constructed from the results of the SCFT studies, which take into consideration the additive homopolymer molecular weight (α), the amount of additive homopolymer added (VAh), and the side length of the square well (L, relative to the radius of gyration of the diblock copolymer, Rg). Figure 3 is an example of a phase diagram for an AB diblock copolymer/A homopolymer blend (AB/A) confined in a square well with homopolymer A wetting the walls. The phase diagram tracks free energy density at a fixed homopolymer A length fraction of α/ƒ = 3.0, whereas varying the fraction of homopolymer A added (x-axis) and side length of the square well relative to Rg (y-axis). Additionally, the authors noted that they were unable to obtain larger sized square lattices (e.g., 5 × 5 square arrays). Presumably, the confinement effect that induces square lattices on the block copolymer is due to the surface energy of the walls of wells, and this effect is simply overwhelmed in large wells by the bulk energetic preference of the block copolymer to arrange in hexagonal arrays.

Figure 3.

Phase diagram for AB diblock copolymer/A homopolymer blend (AB/A) with homopolymer A-wetting walls and α/ƒ = 3.0. The fraction of added homopolymer A and the side length of the square well relative to Rg are represented on the x and y axis, respectively.72 (From S.-M. Hur et al., Macromolecules, 2009, 42, 5861–5872, © American Chemical Society, reproduced by permission.)

Bao et al. have experimentally used DSA of diblock copolymers to prepare a 2 × 2 square lattice of 4 cylinders in an array of square wells.73 Specifically, a silicon wafer was modified to contain a series of square wells with 126 nm sides and a depth of 50 nm using immersion optical lithography and dry etching. Diblock copolymer polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA, v/v = 70/30) was dissolved in propylene glycol methyl ether acetate, spin-coated onto the modified wafer, and annealed at 180 °C to induce microphase separation. After annealing, the coated wafer was exposed to UV light to crosslink the PS matrix before soaking in acetic acid to selectively degrade and remove the PMMA domain. The resultant nanoporous film was characterized by scanning electron microscopy (SEM), as seen in Figure 4. Clearly, 2 × 2 square arrays of holes were formed within the square wells. Surprisingly, square arrays of cylinders were obtained without modifying the walls of wells. As discussed in “Directed Self-Assembly” section, it was shown that a neutral bottom (typically modified by a brush layer of random copolymer A-r-B) and selective side walls (modified by either A or B homopolymer) were required in order to direct the self-assembly in a square lattice perpendicular to the surface. The authors addressed this issue by suggesting that strong confinement generated from small templates (well length = 2L0) overcomes the affinity difference for PS and PMMA to the bottom of the substrate. This explanation was consistent with the inability to form a 5 × 5 square lattice in a square well by SCFT due to the decreased surface energetic effect that the larger well walls have on the ordering of the block copolymer.

Figure 4.

4-Hole square arrays generated from a PS-b-PMMA diblock copolymer in a square template with a wall width of 126 nm and depth of 50 nm.73

Similarly, Xu et al. have shown that poly(ethylene oxide)-b-polystyrene (PEO-b-PS; wt % PEO = 24%) can form square arrays of cylinders in confined wells.74 When the size of the wells was more than 4 times the natural bulk period (L0 = 29 nm) of the block copolymer, hexagonal cylinders were observed. However, when the size of the well was decreased to ∼3L0 (100 nm), a 3 × 3 square lattice of 9 cylinders per well was often observed [Fig. 5(a)]. However, it should be noticed that the 3 × 3 lattice showed a lot of defects on the square cylinder ordering, as some distorted square packing was evident. When the size of the well was ∼2L0 (60 nm), near perfect square ordering of 4 cylinders was observed [Fig. 5(b)]. A small fraction of defects that occur is likely due to the imperfections in the square wells themselves. These studies demonstrate that at small well sizes (wall widths of 2–3L0), confinement of block copolymers can change the packing symmetry of simple diblock copolymers from hexagonally packed to square-packed cylinders, consistent with Wong's work. Additionally, it was shown that the well walls direct the nucleation and ordering of the grains, as single-grain arrays could be generated for square wells with sizes up to 17L0. Above 17L0, the randomly oriented grains appeared, similar to ordering in the bulk state. This, along with the ability to form square arrays within small wells, experimentally confirmed the theoretical conclusions from the SCFT study, specifically, that the confinement effect by the well walls on the ordering of block copolymers is enough to change the packing structure from the natural bulk phase to a modified phase, in this case from hexagonally packed cylinders to square-packed cylinders.

Figure 5.

Atomic force microscopy (AFM) images of (a) 9-cylinder square lattice in a 100 nm square template and (b) 4-cylinder square lattice in a 60 nm square template for a PEO-b-PS diblock copolymer.74

The chemical nanopatterning technique has been used to direct the assembly of diblock copolymers into morphologies that do not naturally occur in bulk polymers, including square arrays of cylinders. Park et al. reported the use of chemically nanopatterned surfaces consisting of a square array of spots to direct assembly of PS-b-PMMA block copolymer to form a square array of vertical cylinders.57 When the spot diameter and center-to-center distance coincided with the natural domain sizes of the diblock copolymer in the bulk state, square arrays of cylinders were oriented perpendicular to the surface, as seen in Figure 6. However, when the spot diameter or distance between spots were varied to values inconsistent with the natural block copolymer domain sizes, defects referred to “semicylinder” and “loop cylinders” were evident, which refers, respectively, to cylinders that start at the surface of the film but only penetrate partially through the film and cylinders that loop from one vertical cylindrical domain to another. Furthermore, it was found that long-range square array ordering of perpendicular cylinders was found for film thicknesses up to 1.5 times the bulk cylinder diameter. Above such thickness, no square arrays of cylinders were formed due to the limited effect that the chemically modified surface played on block copolymer self-assembly.

Figure 6.

Vertically oriented cylinders of PS-b-PMMA diblock copolymer on (a) a neutral surface and (b) a surface chemically modified to contain an array of dots in a square pattern.57 (From S.-M. Park et al., Macromolecules, 2007, 40, 5084–5094, © American Chemical Society, reproduced by permission.)

Supramolecular Comb/Coil

A recent report shows the formation of tetragonal arrays of cylinders-within-lamellae in bulk from a hierarchical copolymer system composing of a coil and a supramolecular comb block, which, however, is neither a simple diblock copolymer system nor a traditional cylindrical morphology.75 In this report, diblock copolymer polystyrene-b-poly(4-vinylpyridine) (PS-b-P4VP) was modified by complexing the nitrogen atom of the P4VP block with an amphiphilic surfactant, dodecylbenzenesulfonic acid (DBSA), through electrostatic interactions of the strong proton donor (DBSA) to the weak base (4VP). This modified block is referred to as the comb block and denoted P4VP(DBSA). There are two different types of repulsive interactions in this comb-coil copolymer system, which allow for microphase separation to occur at two different length scales. There exists a traditional repulsive interaction between the PS coil and the P4VP(DBSA) comb, which generates predictable microdomains similar to a simple diblock copolymer on the scale of tens of nanometers. However, within the comb block, there is a separate repulsion between the polar backbone of the P4VP and the nonpolar side chains of the DBSA. This allows for a lamellar mesophase to form on the length scale of several nanometers. The overall molecular weight and block fractions of PS-b-P4VP were selected to ensure a traditional hexagonally packed cylindrical morphology. By complete binding of DBSA to P4VP, the morphology could be changed to a nontraditional hexagonally packed cylinder-within-lamellae morphology. In this phase, the PS is the minor cylindrical domain, whereas the matrix is a lamellar mesophase consisting of the P4VP(DBSA) block. By further tuning the binding fraction of DBSA to P4VP to 0.5–0.6, the morphology was changed to a tetragonal array of cylinders-within-lamellae, as illustrated in Figure 7. To account for this change from hexagonally packed to tetragonally packed cylinder-within-lamellae, the authors proposed that when the binding fraction is 0.5–0.6, the unbound P4VP chains pack around the PS cylinder, essentially creating a buffer zone that alleviates the crowding associated with the long DBSA alkyl chain. The authors suggested that outside of the buffer zone, the DBSA chains attain a uniform degree of stretching for regular lamellar stacking around the cylinder which creates planar boundaries for the corona, ultimately allowing for the cylindrical micelles to pack in a tetragonal lattice to minimize the corona deformation. Strictly speaking, square arrays of cylinders have not been confirmed from a simple diblock copolymer in thin films without confinement, though this supramolecular comb/coil block copolymer system was able to produce a square array of complex cylinders-within-lamellae in bulk.

Figure 7.

Schematic illustration of tetragonally arranged cylinder-within-lamellae for diblock copolymer PS-b-P4VP(DBSA) with binding fraction of DBSA = 0.5.75 (From H.-L. Chen et al., Macromolecules, 2007, 40, 3271–3276, © American Chemical Society, reproduced by permission.)


Square arrays produced from ABC triblock copolymers have been well predicted by SCFT simulations. SCFT has been used to predict the formation of square arrays of cylinders in bulk in a symmetric ABC triblock copolymer, in which A and C blocks are of similar volume fractions and form separate minority domains dispersed in matrix B.30,32,76–78 Interconnected square arrays (with a tetragonal lattice) require χABχBC << χAC. The Flory-Huggins interaction parameter between the end blocks (χAC) must be very high in order to overcome the asymmetric stretching of the B block that is observed in hexagonal packing. Without a very large difference between the end blocks, hexagonally packed core/shell cylinders of the A and C blocks in a B matrix would occur due to the preference for uniform stretching of the B block (Fig. 8). Nakazawa and Ohta noted that if χABχBC << χAC was satisfied, hexagonal packing would result in a rectangular sublattice, which would require a high degree of nonuniform stretching of the B block polymer chains.30 This was also proved mathematically by comparing the free energy for both structures. It was found that the free energy for a square lattice system was lower than that of a hexagonal lattice system when the volume fractions of the combined A and C blocks (ƒA, C) were below < 0.36. Furthermore, for ƒA, C < 0.23, the free energy of the cylindrical square lattice becomes lower than the free energy of a lamellar system, indicating that ƒA, C = 0.23 is a critical block ratio in which the phase would have a transition from lamellae to alternating cylinders. Additionally, the angle φ between vectors b and e was varied between π/3 < φ < π/2 (Fig. 9). The minimum of the free energy for ƒA, C < 0.28 always occurred at φ = π/2, further indicating that tetragonally arranged cylinders are the most stable phase according to free energy.

Figure 8.

Core/shell hexagonal, alternating square, and alternating hexagonal packing of symmetric ABC triblock copolymers: (a) Core/shell hexagonal packing: green/blue core/shell cylinders in a symmetric red matrix; (b) alternating square packing: green cylinders symmetrically around blue cylinders in a red matrix; (c) alternating hexagonal packing: green cylinders asymmetrically around blue cylinders in a red matrix.

Figure 9.

Hexagonal (a) and tetragonal (b) structures of A and C cylinders in a B matrix.30 (From H. Nakazawa and T. Ohta, Macromolecules, 1993, 26, 5503–5511, © American Chemical Society, reproduced by permission.)

Mogi et al. experimentally studied the microphase-separated morphologies of a series of polyisoprene-b-polystyrene-b-poly(2-vinylpyridine) (ISP) triblock copolymers.28,29 The volume fraction of the middle-block polymer (PS matrix) was varied while keeping volume fractions of end-block polymers [polyisoprene (PI) and poly(2-vinylpyridine) (P2VP)] equal. The morphologies did not change by annealing, and thus, they are considered to be in equilibrium. They concluded that all morphologies of ABC triblock copolymers having A and C blocks with the same volume fractions possess characteristics of superlattice structures if A/B and B/C interfaces have similar surface energies in the strong segregation limit regime. Hildebrand solubility parameters have been reported for PI, PS, and P2VP:79

  • δPI = 8.2 (cal/cm3)1/2

  • δPS = 9.1 (cal/cm3)1/2

  • δP2VP = 10.0 (cal/cm3)1/2

Based on the following equation to calculate Flory-Huggins interaction parameters:

χ12 = V(δ1δ2)2/RT (where V is the actual volume of a polymer segment), it should have the following relationship: χPI-PSχPS-P2VP << χPI-P2VP. Therefore, upon microphase separation, separation of end blocks should be thermodynamically stable. It was found that a tetragonal lattice with alternating square arrays of cylinders was obtained when the volume fraction of middle block was in the range of 0.68–0.76 (Fig. 10). This was the first-reported experimental block copolymer system exhibiting square arrays through spontaneous self-assembly.

Figure 10.

TEM image of triblock copolymer ISP with volume fractions of isoprene, styrene, and 2-vinylpyridine equal to 0.12, 0.76, and 0.12, respectively.29 (From Y. Mogi et al., Macromolecules, 1994, 27, 6755–6760, © American Chemical Society, reproduced by permission.)

Ross and coworkers have tried to use triblock copolymer polyisoprene-b-polystyrene-b-polyferrocenylsilane (PI-b-PS-b-PFS) to produce square arrays of cylinders in bulk and thin films.58,59 When the triblock copolymer was annealed in the bulk state, square arrays were formed, although no detailed characterization was given. However, the pure triblock copolymer in thin films exhibited a mixture of both hexagonal and square-packed arrays of cylinders. Square arrays in thin film were formed only when the PI-b-PS-b-PFS triblock copolymers were blended with PS homopolymers. A blend of triblock copolymer PI-b-PS-b-PFS and 15 wt % PS homopolymer was used to obtain alternating cylinders in a tetragonal lattice. This blended system was shown to self-assemble into square packed cylinders on an untemplated substrate with relatively low grain sizes (300 nm × 300 nm). However, when the blended copolymer was cast onto a substrate coated with PEO, the average grain size of square packed cylinders increased to 1.75 µm × 1.75 µm, due to a neutralizing effect that the hydrophilic PEO layer has on the three blocks in the triblock copolymer PI-b-PS-b-PFS. To obtain an even higher degree of ordering, Chuang, Son, Ross, and coworkers used DSA, including confinement in rectangular wells as well as rectangular post patterns. Specifically, wells with a height of 32 nm and various widths and lengths were prepared using electron-beam patterning of a negative-tone inorganic hydrogen silsesquioxane resist. The well walls were coated with homopolymer PFS and well bottom was coated with homopolymer PEO. Upon spin-casting the copolymer blend and annealing, single-grain alternating cylinders in a square pattern were formed for well sizes as large as 2 µm × 3 µm and 1.5 µm × 4 µm, as seen in Figure 11.

Figure 11.

(a) Schematic representation of alternating cylinders in a square array for a triblock copolymer blend confined in a well with preferential PFS-coated walls and a neutral PEO-coated bottom. (b) Scanning electron microscopy (SEM) images of alternating square arrays from copolymer blend PS/PI-b-PS-b-PFS in wells of dimensions 1.5 µm × 3 µm (left) and 2 µm × 3 µm (right). (c) SEM images of alternating square arrays from copolymer blend PS/PI-b-PS-b-PFS in wells of dimensions 0.5 µm × 4 µm (bottom), 1 µm × 4 µm (middle), and 1.5 µm × 4 µm (top).58,59 (From J. G. Son et al., Nano Lett, 2011, 11, 2849–2855, © American Chemical Society, reproduced by permission.)

Arrays of posts were also used by Son et al. to obtain long-range order of square arrays of cylinders for the copolymer blend.59 Single posts were placed in a rectangular pattern of size 2L0 × 3L0 and double posts arrays were placed in a 3L0 × 4L0 size pattern. The posts were coated with a PFS homopolymer and the substrate was coated with a PEO homopolymer. After annealing the copolymer blend in a chloroform atmosphere, nearly defect-free square packed arrays of cylinders were obtained for both the single post [Fig. 12(b)] and double post [Fig. 12(c)] arrays over an area of several square micrometers. This was the first demonstration of patterned posts being used to direct the self-assembly process for a triblock copolymer blend.

Figure 12.

SEM images of copolymer blend PS/PI-b-PS-b-PFS after annealing on an: (a) PEO brush layer; (b) 88 nm × 132 nm array of PFS coated single posts on a PEO brush layer; (c) 44 nm spacing PFS double posts on a PEO brush layer.59 (From J. G. Son et al., Nano Lett, 2011, 11, 2849–2855, © American Chemical Society, reproduced by permission.)

The first square arrays of spontaneous self-assembled block copolymers in thin films were reported in 2008.37 Tang et al. observed square packing of core/shell spheres (not cylinders) from PEO-b-PMMA-b-PS ABC triblock copolymers. Because BCC packing was the ordered-state symmetry, the pattern observed (either square or hexagonal) was dependent upon the overall film thickness. Close-packed hexagonal structures were observed when the film thickness correlated to a monolayer (½ layer of spheres) or bilayer (1½ layers of spheres). When the film thickness would accommodate 2½ layers of spheres, both close-packed hexagonal and square packed structures were observed, as seen in Figure 13. Square packing was consistent with a unit cell of a body-centered cubic lattice with the (100) plane of spherical morphology parallel to the surface. Interestingly, a half-sphere layer was formed on the surface of films of all thicknesses, believed to be resulting from the annealing process, as the hydrophilic PEO domain interacts preferably with high water atmosphere during the solvent evaporation stage of the solvent annealing process.

Figure 13.

SEM images of triblock copolymer PEO-b-PMMA-b-PS after annealing and selective removal of the PEO/PMMA domains. A large-scale image is shown in the top image, square packing is shown in the image on the left, and hexagonal packing is shown in the image on the right.37 (From C. Tang et al., Macromolecules, 2008, 41, 4328–4339, © American Chemical Society, reproduced by permission.)


Tang et al.41,43,56 recently introduced a modular and tunable supramolecular block copolymer blend system, namely AB/B′C based on PEO-b-PS and PS-b-PMMA, which contains attractive supramolecular (H-bonding) interactions between B and B′ in addition to the nonspecific interactions present in the block copolymer alloy. By controlling the level of incorporation of H-bonding units in B and B′, the molecular weights and compositions of the block copolymers, as well as the relative amounts of the two block copolymers in the alloy, highly ordered square arrays of cylinders in thin films have been achieved. Specifically, a poly(ethylene oxide)-b-poly(styrene-r-4-hydroxystyrene) [PEO-b-P(S-r-4HS), denoted as A-b-B] and poly(styrene-r-4-vinylpyridine)-b-poly(methyl methacrylate) [P(S-r-4VP)-b-PMMA), denoted as B′-b-C] were prepared so that the B and B′ blocks were the majority fraction in each of the diblock copolymers. These two diblock copolymers were blended together to allow hydrogen bonding to complex the B and B′ blocks, essentially forming a triblock copolymer-like A-b-B/B′-b-C bound at the B/B′ block by supramolecular interactions. Upon solvent annealing in a saturated toluene vapor in a controlled high-humidity atmosphere, square arrays of perpendicular cylinders with grain sizes larger than 5 µm × 5 µm were obtained, as seen in Figure 14.

Figure 14.

TEM image (left) and Fourier transform (left, inset) of a solvent-annealed blend of PEO-b-P(S-r-4HS)/P(S-r-4VP)-b-PMMA). A cartoon (right) of the proposed chain packings for the annealed blended copolymer system.41,43,56 (From C. Tang et al., Science, 2008, 322, 429–432, © AAAS, reproduced by permission.)

The levels of hydrogen donating (P4HS) and hydrogen accepting (P4VP) groups were adjusted, and it was found that near-stoichiometric values of hydrogen-bonding groups are essential for square cylinder formation with long-range order.41,43,56 When the number of hydrogen accepting groups was greater than the number of hydrogen donating groups, both square and hexagonal arrays were observed with small grain sizes. When the number of hydrogen accepting groups was less than the number of hydrogen donating groups, highly ordered hexagonal arrays were observed. Square arrays were only observed when the ratio of hydrogen accepting to hydrogen bonding groups was < 1.5. Furthermore, highly ordered square arrays were obtainable when there was a relatively small number of hydrogen accepting and hydrogen donating groups. However, there was a minimum requirement of hydrogen bonding units, as there was observed a completely disordered state when there was a very low amount of hydrogen bonding groups. These results were correlated into a phase diagram, as seen in Figure 15.

Figure 15.

Morphology of solvent annealed films from supramolecular block copolymer films A-B/B′-C as a function of the number of hydrogen donating and hydrogen accepting groups per chain.41,43,56 (From C. Tang et al., Macromolecules, 2010, 43, 2880–2889, © American Chemical Society, reproduced by permission.)

The thin films of alternating cylinders were further used as lithographic masks to transfer the square arrays to an underlying substrate.41,43,56 To create a nanoporous film, the annealed film was first exposed to ultraviolet light to degrade the PMMA domain and crosslink the PS matrix. The resulting nanoporous film contained holes 22 nm in diameter and 50 nm apart in a square pattern. The nanoporous film was then used as a mask for reactive ion etching using CHF3 to etch the silicon oxide, followed by removal of the organic material by exposure to oxygen plasma. This pattern transfer process, as well as SEM images of the ordered cylindrical pores etched into the silicon wafer, is given in Figure 16.

Figure 16.

Schematic representation of pattern transfer process from supramolecular block copolymer films (top). SEM top view (bottom, left) and cross-sectional view (bottom, right) of cylindrical pores in a square array after reactive ion etching and O2 plasma treatment of UV-degraded supramolecular block copolymer films.41,43,56 (From C. Tang et al., Science, 2008, 322, 429–432, © AAAS, reproduced by permission.)

Soon after, Tang et al. incorporated an acid-cleavable trityl ether junction between the A (PEO) and B (P(S-r-4HS)) blocks in order to allow for the selective removal of the PEO domain after self-assembly.41,43,56 This PEO-trityl-b-P(S-r-4HS) diblock copolymer was blended with diblock copolymer P(S-r-4VP)-b-PMMA to prepare highly ordered alternating cylinders in a square array upon self-assembly [Fig. 17(a)]. Incorporation of the acid-sensitive trityl linker allowed for the PEO domains to be removed by washing the film in an acidic solution, whereas the PMMA domains could be removed by exposure to ultraviolet light, as previously displayed. This provided a strategy to create multiple nanoscale templates from a single supramolecular block copolymer system through sequential degradation reactions. Three separate nanoscale templates were produced from this system including a square array of cylindrical pores from removal of the PMMA domains [Fig. 17(b)], a square array of cylindrical pores from removal of the PEO domains [Fig. 17(d)], and nested square arrays of cylindrical pores from removal of both PMMA and PEO domains [Fig. 17(c, e)]. The reversibility of the removal process was demonstrated by first removing the PMMA domains then the PEO domains, as well as by first removing the PEO domains and then the PMMA domains. This displayed the orthogonality of the degradation processes as well as the ability to create multiple templates from a single block copolymer nanostructure. This work based upon supramolecular block copolymers was the first to achieve square arrays of cylinders in thin films through spontaneous self-assembly rather than DSA with arbitrary confinement.

Figure 17.

(a) AFM image of annealed films from supramolecular block copolymers. (b) SEM image of UV-irradiated films. (c) SEM image of trifluoroacetic acid treated films after UV exposure. (d) SEM image of trifluoroacetic acid treated films. (e) SEM image of UV-irradiated films after trifluoroacetic acid exposure.41,43,56 (From C. Tang et al., ACS Nano, 2010, 4, 285–291, © American Chemical Society, reproduced by permission.)


Over the past 10 years, there have been a lot of efforts to produce square arrays in block copolymer thin films mainly due to their demand as templates for construction of nanodevices. Although diblock copolymers are relatively easy to prepare, theoretical and initial experimental work has shown that square arrays of cylinders are simply not possible without confinement, as discussed in “Diblock Copolymer Approach” section. The overwhelming tendency of diblock copolymers to self-assemble into hexagonally packed cylinders is due to the low free energy of hexagonal packing attributed to the nearly uniform stretching of the matrix polymer chains. As discussed in “Directed Self-Assembly” section of this review, both theoretical and experimental studies have shown that square arrays of cylinders can be produced when diblock copolymers are confined within small wells. However, there is a limit to the size of the wells, as there exists decreased surface energetic effect that larger well walls have on the ordering of the block copolymer, ultimately resulting in hexagonally packed structures due to the overpowering energetic preference for symmetric chain stretching.

As discussed in “Triblock Copolymer Approach” section, triblock copolymers have not been used to prepare perpendicularly aligned square packed cylinders using topological or chemical templating approach, though Ross and coworkers used a triblock copolymer blend to prepare square arrays of alternating cylinders as previously discussed. This is an area requiring further exploration.

As discussed in “Supramolecular Block Copolymer Approach” section, Tang et al. have recently shown that a supramolecular block copolymer blend system, denoted AB/B′C, could be used to prepare square arrays of alternating cylinders in thin films.41,43,56 The incorporation of hydrogen bond acceptors into the B block and hydrogen bond donors into the B′ block allowed for the two separate diblock copolymers to be held together by supramolecular interactions. By finely tuning the amount of hydrogen bonding as well as the ratio of hydrogen donors to hydrogen acceptors, highly ordered square arrays of cylinders were prepared in thin films.

Although predicted by SCFT and observed in the bulk state, square arrays of cylinders from linear triblock copolymers have not yet been achieved in thin films. To overcome this challenge, we believe that the key design is the proper triblock copolymer systems with right chemistries that satisfy χABχBC << χAC. This has been shown as a prerequisite for the formation of square arrays in bulk (Ross group showed square arrays in bulk for triblock copolymer PI-b-PS-b-PFS, but did not give more details). Therefore, we hypothesize that the ISP triblock copolymers pioneered by Mogi et al. has the potential to form square arrays in thin films. As mentioned above, this particular block copolymer meets the requirement on χABχBC << χAC and forms square arrays in bulk with desirable compositions. The challenge is to find an appropriate ordering technique to make cylinders perpendicular to the substrate. Known strategies to prepare highly ordered block copolymer films include the use of external force such as electrical field, magnetic field, shear force, confined surfaces such as graphoepitaxy and chemically patterned substrate, directional solidification, and solvent annealing.36,44,51,52,54,55,80–85

Here, we want to challenge the readers and hypothesize that polyisoprene-b-polystyrene-b-polyethylene oxide (ISO) triblock copolymer could self-assemble into square arrays in thin films if a combination of correct compositions and ordering techniques are provided. Bates and coworkers have prepared an extensive series of ISO triblock copolymers and thoroughly studied their rich array of morphologies in bulk.86–89 Temperature-dependent Flory-Huggins parameters χ(T) have been reported between PEO, PS, and PI:

  • XPEO-PS(T) = 29.8T−1 − 0.0229

  • XPS-PI(T) = 26.4T1 − 0.0287

  • XPEO-PI(T) = 90.0T1 − 0.0579

At temperature T = 298 K, it should have the following relationship: χPEO-PS (0.08) ≈ χPS-PI (0.06) << χPEO-PI (0.24). This system satisfies the interaction parameter relationship χABχBC << χAC, suggesting that the PS domain could separate the PEO and PI domains and the formation of two alternate square arrays of PEO and PI in a tetragonal lattice is possible.

In fact, Morse and coworkers studied phase behavior of completely symmetric systems, with χAB = χBC and equal volume fractions of A and C, fA = fC, using weak segregation theory and numerical SCFT.90,91 The Flory-Huggins interaction parameters were chosen to represent ISO triblock copolymers studied by Bates group experimentally, that is, χABχBC << χAC. They found the appearance of alternating square cylinders of A and C in more strongly segregated symmetric triblock copolymers. Based on the experimental work by Bates along with the SCFT predictions by Morse, it is possible that symmetric ISO triblock copolymers could produce square arrays of cylinders.

Through proper design of chemistry, there should be many other triblock copolymer systems satisfying the “golden” rule χABχBC << χAC. This is a criterion that needs significant attention to overcome the challenges associated with the asymmetric chain stretching required for alternating square arrays. Square arrays of cylinders in thin films can be selectively etched to produce nanoporous films. These nanoporous films can be then used as lithography resists to replicate square packing to underlying substrates through a pattern transfer process. In combination with other techniques and technologies such as DSA, this process could allow for the development of nanoscale integrated circuits with low symmetry that would meet the demand of the International Technology Roadmap for Semiconductors.


This work was supported by the University of South Carolina (start-up funds) and Global Research Collaboration Program of Semiconductor Research Corporation (Task ID 2222.001).

Biographical Information

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Christopher G. Hardy received his B.S. from North Carolina State University in 2009. Since 2009, he has been a graduate student under the supervision of Dr. Chuanbing Tang in Department of Chemistry and Biochemistry at the University of South Carolina. Currently, he is developing metal-containing polymers and their self-assembly in thin films. In addition, he is also working on functional block copolymers as nanodielectric materials for capacitor applications.

Biographical Information

original image

Chuanbing Tang received B.S. from Nanjing University and Ph.D. from Carnegie Mellon University with Profs. Krzysztof Matyjaszewski and Tomasz Kowalewski. He was a postdoctoral scholar at University of California Santa Barbara with Profs. Edward J. Kramer and Craig J. Hawker. Since August 2009, he has been an assistant professor in Department of Chemistry and Biochemistry at the University of South Carolina. His research interests focus on organic polymer synthesis, renewable bio-based polymers from natural resources, metal-containing polymers, block copolymer self-assembly, and polymers for biomedical application.