The influence of confinement and curvature on the morphology of block copolymers



In the bulk, at equilibrium, diblock copolymers microphase separated into nanoscopic morphologies ranging from body-centered cubic arrays of spheres to hexagonally packed cylinders to alternating lamellae, depending on the volume fraction of the components. However, when the block copolymers are forced into cylindrical pores, where the diameter of the pores are only several repeat periods of the copolymer morphology or less, then commensurability of the copolymer period and the pore diameter can impose a frustration on the microdomain morphology. In addition, due to the small pore diameter, a curvature is forced on the microdomain morphology. In combination with interfacial interactions between the blocks of the copolymer and the pore walls, the preferential segregation of one component to the walls, spatial confinement and forced curvature are shown to induce transitions in the fundamental morphology of the copolymers seen in the bulk. Lamellar morphologies transformed into torus-type morphologies, cylinders are forced into helices, and body-centered cubic arrays of spheres are force into helical arrays of spheres due to these restraints. The novel morphologies, not accesssible in the bulk, open a large array of nanoscopic structures that can be used as templates and scaffolds for the fabrication of inorganic nanostructured materials. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3377–3383, 2005


Block copolymers comprised of chemically different polymer chains covalently joined together at one end form a wide variety of morphologies with a characteristic repeat period.1 The simplest block copolymers are linear AB diblock copolymers. In the bulk, at equilibrium, morphologies ranging from body-centered cubic arrays of spheres, hexagonally-packed cylinders, bi-continuous gyroids, and alternating lamellae are observed depending on the volume fractions of the blocks. The nanometer-sized structures and the rich phase behavior have established block copolymers as attractive templates or scaffolds for nanodevice fabrication.2, 3

Diblock copolymers are also ideally suited for the study of structural transitions arising from confinement, because of the rich phase behavior and size scales of structures that can be accessed under relatively simple experimental conditions. The fundamental scientific interest of microphase separation in confined systems lies in a breaking of symmetry in the structure and the consequence of commensurability,4 that is the relationship between the fundamental repeat period of the copolymer to the physical dimensions of the system. If the two are incommensurate, then the morphology of the block copolymer must deviate from its equilibrium morphology to relieve the imposed frustration. Symmetric diblock copolymers confined between two parallel walls have been studied extensively. In the bulk, the copolymer microphase separates into grains of aligned lamellar microdomains with a characteristic equilibrium period L0, where grains are randomly arranged in the sample. In the case of thin films, the preferential segregation of one of the blocks to the interfaces forces an orientation of the microdomains parallel to the interfaces, resulting in a multilayered film structure.5–16 Two types of multilayers are found: in one (the symmetric case), the same block segregates to both interfaces while, in the asymmetric case, different blocks segregate to the two interfaces. Incommensurability between the film thickness and the bulk equilibrium period occurs when the film thickness is not equal to nL0 (symmetric case) or (n + 1/2)L0 (asymmetric case). For thin films on a solid substrate with a free surface, frustration resulting from incommensurability is relieved by the formation of a surface topography consisting of terraces of step height L0, so that a highly oriented layered structure can propagate throughout the entire film. If the energy required to stretch or compress the copolymer chains is greater than the total interfacial energies, then the lamellae will orient normal to the surface. This preserves the natural period of the copolymer at the expense of interfacial energy. If the film is confined between two solid interfaces, the formation of a surface topography, the mechanism to relieve an imposed frustration, is prohibited, so that the copolymer must find an alternative route to respond. If the interfacial interactions are strong, the copolymer chains within the confined multilayers will either stretch or compress. With changes in the thickness of the confined film, the number of layers will change and the total amount of deformation (stretching or compression of the layers) will be distributed throughout the film, so that the extent of deformation of each layer will decrease with increasing thickness. Asymmetric diblock copolymers, on the other hand, have drawn much less attention.17–20 As in the case of symmetric diblock copolymers, the interplay between confinement and preferential interfacial interactions cause deviations from the morphology observed in the bulk.

The confinement imposed by two parallel hard walls discussed above is essentially a one-dimensional confinement. Recently, a two-dimensional confinement method has been used.21–23 In addition to the confinement imposed by the film thickness, placing the copolymer film in photolithographically defined troughs biases the packing of spherical or cylindrical microdomains and can introduce an incommensurability between the natural period and the trough width, causing a perturbation in the lateral packing of the copolymer microdomains. Such an incommensurability has been used by Cheng et al. to introduce defects into the microdomain packing as a means to introduce an external marker for addressing purposes.22 The growth of the microdomains along the trough can be used to induce long-range ordering within the trough, which is key in fabricating sectored surfaces for device applications. Another type of two-dimensional confinement can be imposed by the use of nanoscopic cylindrical pores that can be conveniently prepared in alumina with pore diameters as small as ∼5 nm.24–27 Cylindical confinement is of particular interest, since many situations are met in nature where such confinement influences phase behavior.4 In addition to confinement, cylindrical nanopores force curvature on the copolymer assembly and the resultant morphology must reflect this. So, both commensurability between the pore diameter and natural period and the imposed curvature can strongly influence the morphology of the confined system. Here, the morphology of diblock copolymers, both symmetric and asymmetric, confined in cylindrical nanopores, is discussed. At some ratios of the pore diameter to the natural period of the copolymer, new morphologies are found that cannot be accessed by any other means and have potential use in the fabrication of novel nanostructures.


Anodized aluminum membranes were used in the experiment to provide the cylindrical confinement. The membranes consist of straight, hexagonally-packed cylindrical pores in an alumina matrix where the pores are oriented normal to the surface [Fig. 1(A)].28 Figure 1B shows a schematic diagram of the process used to introduce the copolymer into the cylindrical alumina pores. Films (∼15 μm in thickness) of the copolymers were solvent cast from toluene onto glass slides and dried under vacuum at 80 °C for 24 h. The aluminum oxide membrane was then placed on top of the copolymer film. The assembly was heated to a temperature above the glass-transition temperatures of both blocks. Here, 125 °C was used for diblock copolymers of styrene and butadiene (PS-b-PBD). The copolymer melt was drawn into the pores of the membrane via capillary action. After annealing for one day to one week under vacuum, the copolymer/membrane assembly was quenched to room temperature. The alumina membrane was removed using 5 wt % sodium hydroxide, leaving an array of copolymer nanorods protruding from the copolymer film, very similar in appearance to the bristles of a hair brush. Figure 1C shows scanning electron micrographs (SEM) of the copolymer nanorods. The nanorods have a uniform length and high aspect ratios, ∼15:1. After being freed from the nanoporous template, the nanorods do not stand erect on the supporting copolymer film, but collapse on each other. The dark top surfaces in center of the nanorod ends suggest a meniscus at the end of the nanorod, indicating that the copolymer wets the pore walls.

Figure 1.

(A) Schematic for confining block copolymers in nanoporous alumina membrane. (B) SEM top-view of nanoporous anodized aluminum membranes. (C) SEM micrograph of PS-b-PBD nanorods.


The wetting of the pore-walls surface by the copolymer melt causes a capillary rise of copolymer melt into the nanopores. The maximum height that the copolymer melt can rise within the capillary can, to a first approximation, be calculated by29

equation image(1)

where hmax is the maximum height, γcopolymer/air is the surface tension of the copolymer melt, θ is the contact angle at the copolymer/pore-wall interface, ρ is the density of the copolymer, g is the gravitational constant, and r is the pore radius. The contact angle, estimated from the meniscus seen in the cross-sectional transmission electron microscopy (TEM) image [Fig. 3(B)], is ∼80°.24 The surface tension of polybutadiene is ∼30 mN/m. Using a PS-b-PBD density of 0.95 g/cm3 and pore diameter 200 nm, a maximum height of 11.2 m is predicted from eq 1. This result indicates that the capillary rise and, therefore, the capillary force, are large and that the length and aspect ratio of the copolymer nanorods can be quite large.

Figure 2.

TEM cross-sectional images of bulk lamella-forming PS-b-PBD's confined in cylindrical pores. (A, C, D, F) Views across pore; (B, E, G) Views along pore; (A, B) D/L0 > 3.2; (C) D/L0 = 3.2; (D, E) D/L0 = 2.6; and (F, G) D/L0 > 1.9. Scale bars, 50 nm.

The time required to fill the nanopores with the copolymer can be estimated by30, 31

equation image(2)

where t is the time, η is the viscosity of the copolymer melt, z is the length of the capillary, and R is the hydraulic radius (the cross-sectional area of a stream divided by the wetted perimeter, here, R = 0.5 r). The viscosity of PS-b-PBD is about 106 Pa s. From eq 2, t is ∼26 h for the copolymer melt to fill the cylindrical pores to a height of ∼5 μm. It should be noted that in the above calculation, the microphase separation of the block copolymer melt was not considered and the PS-b-PBD is in the strong segregation limit. This may perturb the microscopic contact angle, since in reality, only the PBD is in contact with the surface.32 The microphase separation should act to retard the flow of the copolymer melt into the nanopores. Taking these points into consideration, the calculated time is in remarkably good agreement with the actual time of 24 h used experimentally.24


To visualize the microphase-separated morphology of the copolymer nanorods, TEM studies were performed. The copolymer nanorods were stained with OsO4, embedded in epoxy resin, and microtomed at room temperature. In the following, we discuss the morphology of bulk lamella-, cylinder-, and sphere-forming copolymers confined in nanopores, separately. Figure 2(A) shows a TEM cross-sectional image, microtomed normal to the nanorod axis, for nanorods of symmetric PS-b-PBD. Under cylindrical confinement, the bulk lamella-forming copolymer assumes a morphology of concentric rings, with a dark ring (PBD) preferentially located at the interface with the pore wall. Microtome sectioning along the nanorod axis [Fig. 2(B)] shows alternating dark and bright (PS) lines parallel to the nanorod axis, with PBD located on the periphery, which is consistent with the other cross sections. If the pore diameter is decreased, a morphology change is observed. For cases where the ratio of pore diameter to the natural period of the copolymer, d/L0, is larger than ∼3.2, the concentric ring morphology with an outermost PDB layer is always observed. However, the phase in the center can either be PS or PBD, depending on the pore diameter, and hence, the number of PS or PBD rings changes, as shown in Figures 2(A,C). The number of rings undergoes a series of discrete increases from n to n + 1 rings where n is an integer and, correspondingly, a deviation of the apparent repeat period from the value of the natural period is seen for each period across the pore. This indicates that confinement causes a perturbation of the fundamental period of the copolymer and, the smaller the pore, the more significant is the perturbation.24 This, of course, must be the case, since the confinement can be distributed over more layers in the thicker nanorods and the amount of the distortion to each period decreases with an increasing number of layers. However, toward the center of the pore where significant curvature is forced on the copolymer, the largest deviation of the period from the bulk is observed. At the pore walls, where PBD preferentially segregates, deviations from the bulk period are also seen.

Figure 3.

TEM cross-sectional images of bulk cylinder-forming PS-b-PBD's confined in cylindrical pores. (A, C, D, F) Views across pore; (B, E, G) Views along pore; (A, B) D/L0 > 4; (C) D/L0 = 4; (D, E) D/L0 = 1.9–2.3; and (F, G) D/L0 = 1.1–1.5. Scale bars, 50 nm.

We performed the same study, but on another copolymer of styrene and methyl methacrylate (PS-b-PMMA), which is in the weak segregation limit, and observed the same changes in the morphology as a function of pore diameter. Similar studies have also been reported by Sun et al. where they examined the diameter-dependence of the morphology of symmetric PS-b-PMMA confined in nanoporous alumina membranes.27 Morphology changes similar to those observed by us were also reported. These results indicate that under this two-dimensional cylindrical confinement, where the diameter of the confining surfaces is large in comparison to the period and one component preferentially segregates to the walls, the symmetric copolymer assumes a concentric multi-cylinder morphology and, like in the case of planar confinement, deviations of the period from the bulk value are seen. He et al.33 and Sevink and coworkers34 recently performed Monte Carlo simulations and self-consistent theoretical calculations, respectively, for the case of lamellar block copolymers confined within cylindrical pores. Assuming a preferential interaction of one block with the pore wall, a so-call “concentric barrel” or “dartboard” morphology was predicted. The results of Sun et al. and our results are consistent with these predictions.

A novel morphology, however, forms in the pores when the pore diameter is made smaller, comparable to the equilibrium period L0 and when d/L0 is not an integer (i.e. incommensurate).25 TEM images of lamellar PS-b-PBD (L0 = 17.6 nm) in 45 nm diameter pores (d/L0 ∼ 2.6) are shown normal to and along the pore axes [Figs. 2(D,E)], respectively. Here, d and L0 are incommensurate. With planar surfaces, a compressed lamellar morphology would be seen. However, in the cylindrical geometry, the high degree of curvature imposed on the planar lamellae morphology produces a change in the structure. Normal to the rod axis, concentric layers are observed with PBD located at the centers and walls of the nanorods. Along the axes of the nanorods, a stacked PS lamellar structure is seen, with a central spine and outer edges of PBD. As seen, this results in a morphological transition from a lamellar to a stacked disc or torus-type structure. This morphology, forced on the block copolymer by curvature and incommensurability, represents a fundamentally new morphology that is not accessible by other means.

As the d/L0 further decreases, another transition in the morphology occurs.25 Shown in Figures 2(F,G) are TEM images of PS-b-PBD (L0 = 23.5 nm) in 45 nm pores (d/L0 ∼ 1.9). Here, only a central core of PS, surrounded by a layer of PBD, is observed. Huh and Jo recently performed cell dynamics simulations on lamellar copolymers under these severe constraints of imposed curvature and found that the loss of one period may be possible when there is a strong preferential segregation of one component to the pore walls (unpublished data). The formation of only one period in the pore of d/L0 ∼ 1.9 requires a significant deformation of the block copolymer chains but, because of the strong immiscibility of PS and PBD and favorable interfacial interactions of PBD with the pore walls, a cylinder-type of morphology persists.

We discuss now the morphology of bulk cylinder-forming copolymers under a similar cylindrical geometry confinement.24, 26 Figure 3(A) shows a cross-sectional TEM image for cylindrical PS-b-PBD nanorods cut normal to the nanorod axis. A rim of PBD is seen around the edges of the sections and within the rim are circularly shaped PBD domains. Cutting the nanorods along the rod axis shows PBD lines parallel to rod axis [Fig. 3(B)]. These results indicate an orientation of PBD cylinders along the pore axes. For cylindrical microdomains confined in pores with different shape and size, the hexagonal packing of the cylindrical domains is maintained. However, the shape and size of the pores place constraints on the packing and both the symmetry and separation distance of the domains can be altered. For nearly circular pores, though, only one grain is found for the cylindrical microdomains. As the pore diameter decreases, fewer cylinders are confined in the pores and for a pore diameter ∼120 nm (d/L0 > 4.1), only seven cylinders are formed within the pore [Fig. 3(C)].24 Such a structure has potential use for multi-level logic application, if the PBD is replaced with a magnetic material.

If the pore diameter decreases to a 56–66 nm (d/L0 = 1.9–2.3), a single cylindrical PBD domain is seen in the center with a PBD rim contacting the pore wall, as shown in Figure 3(D). Views along the pore, Figure 3(E), show clearly an undulation along the interface of PS microdomains with PBD center and rim. This undulation arises from the severe geometric confinement and is a precursor to a change in the morphology. For cases with pore diameters of 33–45 nm (d/L0 = 1.1–1.5), the cross-sectional TEM images in Figure 3(G) show that the microphase-separated morphology of the copolymer is well-developed, with the lower surface-energy PBD domain still located at the pore walls, highlighting the edges of the nanorods. However, the alignment of cylindrical domains along the rod axis, which occurs when d/L0 > 4.1, is no longer observed. Rather, dark lines are seen at a constant angle with respect to the nanorod axis, indicating that PBD forms a helical structure, while maintaining contact with the pore walls. The pitch is measured to be ∼30 nm, quite close to L0. Figure 3(F) shows a TEM image of PS-b-PBD cut normal to the nanorod axis (33–45 nm diameter pores). The morphology seen in the cross section consists of only two domains, PS at center and a PBD ring outside. Two to four protrusions of PBD are seen into a central PS core where the protrusions are evenly distributed around the PS center. This indicates that, depending on d/L0, multiple helices are formed. It is, however, clear that the morphology has changed from simple cylinders oriented along the axis of the nanorods to a morphology that is helical in nature.26

Finally, the morphology of bulk sphere-forming copolymers confined within the cylindrical nanpores was investigated.35 For cases with d/L0 > 3.2, the PBD phase preferentially segregates to the pore wall, with spherical PBD domains aligned along the nanorod axis [Fig. 4(A)]. However, a fluctuation is clearly seen along the interface between outmost PBD layer and PS phase. In the bulk, the morphology consists of PBD spheres in a PS matrix. Within the nanopores, PBD adsorbs to the curved walls of the alumina pores, forcing an opposite curvature on the PS microdomain. When the pore diameter is decreased to d/L0 > 3.2, the reduction in surface energy, due to the wetting of the pore walls with a PBD layer, cannot balance the loss in energy resulting from the deformation of the spherical PBD domains and forces an opposite curvature on the PS microdomain. Hence, un-like the lamellar and cylindrical copolymers under severe cylindrical confinement, an outmost PBD layer is no longer observed for the spherical microdomain case [Fig. 4(B)]. Rather, two lines of PBD spheres are seen making a constant angle with respect to the nanorod axis, possibly indicating the formation of a helical string of PBD spheres. In addition, under geometric confinement, a deformation in the shape of the PBD spherical microdomains is observed.

Figure 4.

TEM cross-sectional images of bulk sphere-forming PS-b-PBD's confined in cylindrical pores. Views along pore. (A) D/L0 > 3.2 and (B) D/L0 = 3.2. Scale bars, 50 nm.

Recently, Wu et al. observed the formation of helical and toroid-like structure in a silica surfactant system, containing a diblock copolymer, confined within similar alumina membranes.36 Upon calcining, exquisite silica structures were obtained that could be thoroughly examined by TEM. These workers presented theoretical arguments that describe the observed structures in these complex, multicomponent systems. The results shown in our study map onto the findings of Wu et al., which speaks to the generality of confinement, induced structural transitions and to the potential of expanding the repertoire of nanoscopic block copolymer scaffolds using confinement.


In summary, self-assembly under cylindrical geometric confinement was discussed for PS-b-PBD diblock copolymers that form lamellar, cylindrical, and spherical microdomain morphologies. Under cylindrical confinement, the microphase separation is well developed. At larger ratios of the pore diameter to the copolymer natural period d/L0, the copolymers retain their bulk morphologies, and the microdomains align along the pore axis due to the preferential wetting of the pore wall with the PBD block. However, confinement effects are found to distort the natural packing of the microdomains and cause an apparent deviation of the repeat period from the bulk values. Under severe confinement, where the pore diameters are comparable to the equilibrium period of the copolymer, morphologies different than those observed in the bulk are seen. Stacked torus-type structures, helical cylinders, and helical strings of spherical structures were seen for lamellar, cylindrical, and spherical copolymers, respectively. These morphologies, forced on the block copolymer by curvature and incommensurability, are not accessible by other means.


We acknowledge the support of the National Science Foundation through the Materials Research Science and Engineering Center (DMR-0213695) and the Nanoscience Interdisciplinary Research Team (DMR-0103024) at University of Massachusetts, Amherst, the U.S. Department of Energy, Office of Basic Energy Sciences (DE-FG02-96ER45612), and the Hyperstructured Organic Materials Research Center supported by the Korea Science Foundation.