Solvent-induced microdomain orientation in polystyrene-b-poly(l-lactide) diblock copolymer thin films for nanopatterning

A series of degradable block copolymers, polystyrene-b-poly(l-lactide) (PS-PLLA), with PLLA hexagonal cylinder (HC) morphology has been synthesized in this study. Well-oriented, perpendicular PLLA cylinders of PS-PLLA thin films were efficiently achieved by spin coating using appropriate solvents regardless of the use of substrates. After hydrolysis of PLLA, well-oriented HC nanochannel arrays over large area in addition to uniform surface with controlled thickness and domain size were obtained; providing a simple and efficient path to prepare nanopatterned templates for applications. The induced orientation of PS-PLLA microdomains was strongly dependent upon the evaporation rate of solvent and its solubility between constituted blocks. The origins for the formed perpendicular HC morphology were systematically studied. The primary concern of controlled morphology for nanopatterning is to develop ordered microphase-separated morphology by considering the time scale for segregation, namely segregation strength during solvent evaporation. The induced orientation is attributed to the permeation discrepancy between phase-separated microdomains. The perpendicular morphology is initiated from the air surface, and formed in order to create an optimized condition (i.e. the fastest path) for solvent evaporation whereas parallel morphology may impede the evaporation of solvent molecules. Following the nucleation of microphase separation, the perpendicular morphology can be kinetically induced by solvent evaporation.     

Perpendicular oriented cylinders via directional coalescence of spheres embedded in block copolymer films induced by solvent annealing

Polystyrene-b-poly(methyl acrylate) (PS-b-PMA) block copolymer with PS volume fraction of 25.2 vol% was synthesized by atom transfer radical polymerization. Non-pretreated silicon wafers were used as the substrates to prepare perpendicular oriented PS cylinders in PMA matrix via solvent annealing which could induce the transformation of spheres to vertically oriented and hexagonally packed cylinders. The spherical microdomains were formed after the evaporation of solvents from the solutions of the block copolymer in selective solvents mixed from methanol, acetone and dichloromethane. The thickness of films could be as thick as 1000 nm, which were much thicker than usual cases and the cylinders came from the directional coalescence of the spheres, thus any pre-treatments of the substrates were not required for perpendicular orientation. The structures were characterized by small angle X-ray scattering (SAXS), transmission electron microscope (TEM), atom force microscopy (AFM) and grazing incidence small angle X-ray scattering (GISAXS).     

Ordering of block copolymer/nanoparticle composite thin films

The ordering behavior of polymer nanocomposites composed of gold nanoparticles confined in the polystyrene (PS) domains of PS based block copolymers was investigated. The results reveal that the self‐assembly of nanoparticles in the PS domains improved the ordering of microdomains. This is attributed to the presence of nanoparticles that reduced the degree of segregation of the system, causing slow phase separation. This facilitates the packing of the cylindrical microdomains, leading to a well‐ordered structure of the composite. When particles were incorporated into the major domains of cylindrically ordered block copolymer, the connectivity of the domains allowed particles to move to the top of the film to gain additional entropy of the system. In contrast, when particles were organized in parallel cylinders in the block copolymer, they were confined in the cylinders which prevented them from diffusing in the depth direction. The aggregation of nanoparticles was amplified when the composite was annealed in air. We believe that the results from this study will enable more understanding of the effects of nanoparticles on the ordering of block copolymer/nanoparticle composite thin films and will provide a tool in the fabrication of composite thin films. Copyright © 2012 Society of Chemical Industry     

The influence of grain size on the alignment of hexagonally ordered cylinders of self-assembled diblock copolymer-based supramolecules

In situ SAXS is used to investigate the shear-induced alignment of a supramolecular system consisting of a polyisoprene-b-poly(2-vinylpyridine) diblock copolymer and octyl gallate (OG), where OG is hydrogen-bonded to the vinylpyridine block of the PI-b-P2VP copolymer. Due to microphase separation, the PI-b-P2VP(OG) system self-assembles forming a domain structure of hexagonally ordered P2VP(OG) cylinders embedded in the PI matrix. The results of the alignment showed that the orientation mobility of the cylinders, lying within the (10) planes parallel to the shear plane, is strongly dependent on the size of the cylindrical domains. Subjected to large amplitude oscillatory shear for 15 min a freshly loaded sample with a small grain size structure exhibited much better alignment compared to that of a pre-aligned/squeezed sample with a considerably larger grain size where the orientation had been first partly destroyed by squeezing.     

A block copolymer nanotemplate for mechanically tunable polarized emission from a conjugated polymer

A polymer blend system consisting of polystyrene grafted onto poly (p-phenylene ethynylene) (PS-g-PPE) and poly (styrene-block-isoprene-block-styrene) triblock copolymer (SIS) yields highly polarized emission due to the unidirectional alignment of the PPE molecules. During the roll casting, the triblock copolymer microphase separates and creates unidirectionally aligned PS cylindrical microdomains in the rubbery PI matrix. PPE, a fluorescent conjugated polymer, was grafted with polystyrene (PS) side chains that enabled sequestration and alignment of these rigid backbone emitter molecules into the PS microdomains of the SIS triblock copolymer. Deforming the thermoplastic elastomer in a direction perpendicular to the orientation direction of the cylinders causes rotation of the PS cylinders and the PPE emitter molecules and affords tunable polarized emission due to re-orientation of the PPE containing PS cylinders as well as film thinning from Poisson effect.     

Microphase separation and crystallization in mixtures of polystyrene-poly(methyl methacrylate) diblock copolymer and poly(vinylidene fluoride)

This study examined the microdomain structures and the crystallization behavior in binary blends consisting of an asymmetric block copolymer and a homopolymer using small-angle X-ray scattering, optical microscopy and differential scanning calorimetry. A polystyrene-block-poly(methyl methacrylate) copolymer (PS-b-PMMA) was mixed with a low molecular weight poly(vinylidene fluoride) (PVDF), where the PS-b-PMMA had a 0.30 wt fraction of the PMMA block. At a PVDF concentration of <13.0 wt%, the PVDF was completely miscible with the PMMA microdomains, and the blends had a cylindrical structure. The addition of PVDF altered the morphology from a PMMA-cylindrical structure to a lamellar structure and finally to a PS-cylindrical structure. When the PVDF concentration was <23.0 wt%, the PVDF was distributed uniformly within the PMMA microdomains. After adding more PVDF, some of the PVDF was locally dissolved in the middle of the PMMA microdomains. The addition of PVDF also affected the ordered microstructure in the blends, leading to a well-defined microdomain structure. However, PVDF crystallization significantly disturbed the pre-existing microdomain structure, resulting in a poorly ordered morphology. In the blends, PVDF had unique crystallization behavior as a result of the space constraints imposed by the microdomains.     

Macroscopically oriented lamellar microdomains created by “cold zone-heating” method involving OOT

The zone-heating method, which involves ordering of materials under moving temperature gradient ∇T, has been widely used as a technique to create macroscopically oriented ordered structures of various kinds of materials. We applied this method to a large molecular weight symmetric polystyrene-block-polyisoprene diblock copolymer (dibcp) at a temperature where the ∇T field exists below its order-disorder transition temperature T_ODT of the dibcp. In this method we first prepared the solvent-cast bulk films of the dibcp having a nonequilibrium morphology of hexagonally packed cylindrical microdomains (hex-cyl) by using a solvent selectively good for polyisoprene blocks. Then the zone-heating method was applied to the order-order transition process from the nonequilibrium hex-cyl to equilibrium lamellae. The “cold zone-heating” method, “cold” in the sense of the ∇T field existing below T_ODT, successfully created macroscopically oriented lamellae with their normals preferentially oriented parallel to the ∇T axis and their edges preferentially standing with respect to the bulk film surfaces. It was also found that the initial orientation of the (100) plane of hex-cyl normal to the ∇T axis prefers to that parallel to the ∇T axis for a better macroscopic alignment of lamellae. A possible model for the cold zone-heating-induced lamellar orientation will be discussed in the text.     

Complex microstructures of ABC triblock copolymer thin films directed by polymer brushes based on self-consistent field theory

The morphology and the phase diagram of ABC triblock copolymer thin film directed by polymer brushes are investigated by the self-consistent field theory in three dimensions. The polymer brushes coated on the substrate can be used as a good soft template to tailor the morphology of the block copolymer thin films compared with those on the hard substrates. The polymer brush is identical with the middle block B. By continuously changing the composition of the block copolymer, the phase diagrams are constructed for three cases with the fixed film thickness and the brush density: identical interaction parameters, frustrated and non-frustrated cases. Some ordered complex morphologies are observed: parallel lamellar phase with hexagonally packed pores at surfaces (LAM₃ ^ll -HFs), perpendicular lamellar phase with cylinders at the interface (LAM^⊥-CI), and perpendicular hexagonally packed cylinders phase with rings at the interface (C₂^⊥-RI). A desired direction (perpendicular or parallel to the coated surfaces) of lamellar phases or cylindrical phases can be obtained by varying the composition and the interactions between different blocks. The phase diagram of ABC triblock copolymer thin film wetted between the polymer brush-coated surfaces is very useful in designing the directed pattern of ABC triblock copolymer thin film.     

The effects of the selectivity of the toluene/ethanol mixture on the micellar and the ordered structures of an asymmetric poly(styrene-b-4-vinylpyridine)

The effects of the solvent selectivity of toluene/ethanol mixtures on the micellar and ordered structures of an asymmetric diblock copolymer of PS(19.6 K)-b-P4VP(5.1 K) in the dilute (1 wt%) and semi-dilute (8 wt%) solutions, as well as in the gel and solid films, were studied using small angle X-ray scattering (SAXS), generalized indirect Fourier transform (GIFT), and transmission electron microscopy (TEM) methods. The solvent selectivity was controlled by ? (weight percentage of ethanol in toluene/ethanol mixture). Individual micelles, space-filled micellar structure (without three-dimensional order), and three-dimensionally ordered gel and solid structures were observed from the 1 and 8 wt% solutions, the gel, and the solid film, respectively. In the 1 wt% solution, the individual micellar structures were strongly dependent on ?; the spherical micelles with P4VP core at ? = 0, the unimer state at 10 ≤ ? ≤ 50, the spherical micelles with PS core at ? = 60, the cylindrical micelles with PS core at ? = 70 and 80, and precipitation at ? = 90 and 100 were observed. The 8 wt% solution was close to overlap concentration with the unimer state in the regions of 20 ≤ ? ≤ 40. In the gel, the ordered structure was observed in the sequence of bcc, hexagonal, gyroid, lamellar, reverse hexagonal and random as ? increased, and could be explained by the change of the relative volume fraction of each block as ? changed, similar to the phase sequence in the phase diagram of the diblock copolymer. The solid films showed the various kinetically frozen ordered microstructures such as randomly packed sphere, hexagonal, gyroid, hexagonally perforated lamella, reversed hexagonal, and randomly packed cylinder, which were controlled by the solvent quality in the gel before solidification. We believe that these results can be applied to photonic crystals, self-assembled nano-patterning, and functional nanoparticles in which the structural control is most important.     

Alignment and orientational proliferation of HEX cylinders in a polystyrene-block-polyisoprene-block-polystyrene copolymer in the presence of clay

We investigated the effect of an anisotropic silicate layer on the alignment and orientational proliferation of hexagonally packed cylinder microdomains of a block copolymer in the presence of a clay by using synchrotron small angle X-ray scattering (SAXS), rheology, and transmission electron microscopy (TEM). The block copolymer employed in this study was polystyrene-block-polyisoprene-block-polystyrene copolymer (SIS). The degree of intercalation of the clay in the presence of SIS was examined by wide angle X-ray diffraction (WAXD).Almost all of the HEX cylinders in neat SIS are aligned toward the flow direction after large amplitude oscillatory shearing is applied to the specimens. However, some tactoids in nanocomposites are not aligned, although most tactoids are also aligned to the flow direction. Due to HEX cylinders near tactoids, which are not aligned to the flow direction, the orientational factor of HEX cylinders in SIS/clay nanocomposites is smaller than that of neat SIS. However, once HEX cylinders in SIS/clay nanocomposites are degenerated after experiencing body-centered cubic microdomains, the decrease in the orientational factor from original aligned HEX is smaller compared with neat SIS.     

Fabrication of Highly Ordered Polymeric Nanodot and Nanowire Arrays Templated by Supramolecular Assembly Block Copolymer Nanoporous Thin Films

Realizing the vast technological potential of patternable block copolymers requires both the precise controlling of the orientation and long-range ordering, which is still a challenging topic so far. Recently, we have demonstrated that ordered nanoporous thin film can be fabricated from a simple supramolecular assembly approach. Here we will extend this approach and provide a general route to fabricate large areas of highly ordered polymeric nanodot and nanowire arrays. We revealed that under a mixture solvent annealing atmosphere, a near-defect-free nanoporous thin film over large areas can be achieved. Under the direction of interpolymer hydrogen bonding and capillary action of nanopores, this ordered porous nanotemplate can be properly filled with phenolic resin precursor, followed by curation and pyrolysis at middle temperature to remove the nanotemplate, a perfect ordered polymer nanodot arrays replication was obtained. The orientation of the supramolecular assembly thin films can be readily re-aligned parallel to the substrate upon exposure to chloroform vapor, so this facile nanotemplate replica method can be further extend to generate large areas of polymeric nanowire arrays. Thus, we achieved a successful sub-30 nm patterns nanotemplates transfer methodology for fabricating polymeric nanopattern arrays with highly ordered structure and tunable morphologies.     

Highly aligned,large pore ordered mesoporous carbon films by solvent vapor annealing with soft shear

Macroscopic alignment of block copolymer (BCP)-templated mesoporous carbon films is challenging, especially for large pores (>10 nm), due to the slow dynamics of the polymer segments that impede re-orientation of the ordered domains. Here, we demonstrate a facile method, solvent vapor annealing with soft shear (SVA–SS), to fabricate unidirectionally aligned, ordered mesoporous carbon films using two different BCP templates, poly(ethylene oxide)-block-poly(n-butyl acrylate) and polystyrene-block-poly(N,N-dimethyl-n-octadecylammonium p-styrenesulfonate), and we illustrate the efficacy of this technique for both cylindrical and spherical morphologies with relatively large accessible pores (≈15 nm). This alignment is preserved through the thermopolymerization of resol and carbonization. The alignment of the mesopores impacts several key properties of these carbon films, especially for the unidirectional cylindrical mesostructures. The highly aligned mesoporous carbon films exhibit a more narrow pore size distribution than the analogous unaligned ordered mesoporous carbon as determined by ellipsometric porosimetry. Moreover, the electrical conductivity becomes anisotropic with nearly 40% difference in conductivity between parallel and perpendicular directions of the cylindrical mesopores. In the parallel orientation, the electrical conductivity is over 20% greater than the analogous unoriented (random) films. These results illustrate the applicability of SVA–SS to obtain unidirectional aligned mesoporous carbon films over large areas without additional physical or chemical templating.     

Unit cell deformation under elongational stress of oriented SIS three-block copolymers

A 50, 000 molecular weight SIS three-block copolymer, containing 30 percent by weight of polystyrene and, presenting the cylindrical morphology, has been oriented by a novel shearing process at high temperature. The orientation has been studied by low-angle X-ray diffraction; the intensity of the (100) reflexion of the hexagonal array has been measured as a function of the angular position of the sample with respect to the direct beam. The samples have been found to be very similar to single crystals; not only the axes of the cylinders lie parallel to the shearing direction, but also the (100) lattice-planes keep the same orientation in space throughout the whole volume of the specimen. Special probes for the mechanical tests have then been cut in the oriented material, parallel and perpendicular to the axis of the cylinders. The deformation under elongational stress of the external shape of the probes has been studied with a traveling microscope; when the cylinders are oriented perpendicular to the stress, the sample deforms elastically, the, size of the probe corresponding to the length of the cylinders remaining constant up to 200 percent deformation. Low-angle X-ray diffraction has been used to study the structural deformation under the same elongational stress; with the stress perpendicular to the cylinders, the unit cell seems to deform in an.affine way with respect to the macroscopic aspect; with the stress parallel to the cylinders, the structure is destroyed rapidly.     

Selective distribution of interacting magnetic nanoparticles into block copolymer domains based on the facile inversion of micelles

We demonstrate a simple methodology to incorporate interacting magnetic nanoparticles (mNPs) into cylinder forming block copolymer templates. Poly(styrene-block-isoprene) (PS-b-PI) with PI cylinders and poly(styrene-block-4vinylpyridine) (PS-b-P4VP) with PS cylinders were used as the block copolymer templates and γ-Fe₂O₃ NPs coated with oleic acids were pre-synthesized for the interacting mNPs. Regardless of the template block copolymers, the selective location of mNPs and the size of mNP aggregates are clearly altered by changing casting solvents. When good solvents for both blocks were used as casting solvents, mNPs are readily aggregated during the solvent evaporation. In contrast, under selective casting solvents for the minor blocks, the mNPs were selectively trapped into the cylinder domains through the facile inversion of micelles during solvent evaporation. The interplay between mNPs and block copolymers was also tested with different molecular weights of block copolymers.     

Tuned phase behavior of weakly interacting polystyrene-block-poly(n-pentyl methacrylate) by selective solvent

We investigated, via small angle X-ray scattering, depolarized light scattering, rheometry, and transmission electron microscopy, the phase behavior of the mixture of a symmetric polystyrene-block-poly(n-pentyl methacrylate) copolymer (PS-b-PnPMA) showing the closed-loop phase behavior and excellent baroplasticity, and dodecanol, a PnPMA-selective solvent. We found that the addition of a selective solvent is simple, but very effective to obtain various microdomains including hexagonally packed cylinders and gyroids. Also, with increasing temperature, the mixtures showed multiple ordered-to-ordered transitions (OOTs) in addition to upper ordered-to-disordered transition (UODT). The first observation of gyroid microdomains in PS-b-PnPMA is very important, although they have been widely reported in many block copolymers, for instance, PS-block-polyisoprene copolymer (PS-b-PI) and PS-block-poly(d,l-lactide) copolymer (PS-b-PLA). Since the gyroid microdomains of PS-b-PnPMA show excellent baroplasticity, external pressure instead of temperature could easily change the microdomains.     

Near-surface morphology effect on tack behavior of poly(styrene-b-butadiene-b-styrene) triblock copolymer/rosin films

The correlation between near-surface morphology and tack behavior of poly(styrene-b-butadiene-b-styrene) triblock copolymer (SBS)/rosin ester films was investigated using probe tack tests, transmission electron microscopy and small-angle X-ray scattering. The SBS/rosin films with rosin composition between 10 and 20 wt% rosin, prepared by slow evaporation of toluene during solvent casting, exhibited uniform near-surface morphology of lamellae oriented parallel to the surface. However, due to the limited solubility of rosin in the PS domains, the rosin started to phase-separate from the PS domains at 15 wt%, and formed fully separated micron-sized domains above 20 wt% rosin. The probe tack force of the SBS/rosin films increased steadily when the near-surface domain orientation changed from perpendicular cylinder to parallel lamellae on addition of rosin. Specifically, for a given lamellar morphology and surface orientation, macrophase separation of rosin plays a critical role in determining the tack properties of SBS/rosin films.     

Periodic nanocomposites: A simple path for the preferential self-assembly of nanoparticles in block-copolymers

The use of diblock copolymers as chemical templates for the self-assembly of patterned and periodic materials has been the focus of extensive research in recent years. In this current work we show how a “one-pot” solution synthesis, which is based solely on the differences in the chemical reactivity of the two blocks towards metallic moiety, can be extended to create 1-, 2- and 3-dimensional ordered arrays of nanoparticles, conforming to the microstructure of the diblock copolymer. Chromium oxide nanoparticles (Cr₂O₃) synthesized in a poly(styrene-b-methyl methacrylate) diblock copolymer solution form, after solvent evaporation and annealing, thin films consisting of a periodic composite material. We show that the preferential incorporation of the Cr₂O₃ nanoparticles into the diblock copolymer through the direct polymer block - metal interactions does not hinder the self-assembly mechanism or the thermodynamically-driven microstructure formation of the diblock copolymer. Results show that the preferential segregation that occurred as early as the mixing stage of the reaction components was maintained throughout the annealing stage and the formation of the bulk ordered composite material.     

Mechanisms of ordering in block copolymer sub-monolayer films upon selective solvent annealing

The solvent annealing induced two-dimensional ordering in poly(styrene–ethylene/butylenes–styrene) (SEBS) triblock copolymer sub-monolayer films with a thickness of 16 nm equaling half of the bulk domain thickness l₀ was investigated by time-resolved ex-situ atomic force microscopy (AFM). Cyclohexane, a selective solvent for majority poly(ethylene/butylenes) block was used. The detailed pathway information on the ordering of highly regular hexagonal spheres was obtained by repeatedly taking images of the same marked area on the sample surface after ex-situ annealing treatments. Two different ordering mechanisms were observed under two different solvent annealing conditions: 1) under a well-sealed environment with a slow cyclohexane evaporation rate, poorly-ordered short cylinders first break into spheres, then the evolution of spherical phase takes place to gradually improve the orderliness of spheres, and finally well-ordered hexagonal spheres are formed; 2) under a poorly-sealed environment with a fast cyclohexane evaporation rate, “holes” and “islands” are instantaneously formed on the sample surface first, and then the surface gradually get even annihilating hole and island areas. Within the hole areas, the transition from short cylinders to hexagonal spheres takes place via a not well-defined microphase separation structure, while in the island areas, the transitions between cylinders and spheres take place to improve the orderliness of cylinders, and finally the enough-ordered cylinders transform into hex-spheres.     

Temperature-composition phase diagrams of binary blends of block copolymer and homopolymer

The temperature-composition phase diagrams for six pairs of diblock copolymer and homopolymer are presented, putting emphasis on the effects of block copolymer composition and the molecular weight of added homopolymers. For the study, two polystyrene-block-polyisoprene (SI diblock) copolymers having lamellar or spherical microdomains, a polystyrene-block-polybutadiene (SB diblock) copolymer having lamellar microdomains, and a series of polystyrene (PS), polyisoprene (PI), and polybutadiene (PB) were used to prepare SI/PS, SI/PI, SB/PS, and SB/PB binary blends, via solvent casting, over a wide range of compositions. The shape of temperature-composition phase diagram of block copolymer/homopolymer blend is greatly affected by a small change in the ratio of the molecular weight of added homopolymer to the molecular weight of corresponding block (M_H,A/M_C,A or M_H,B/M_C,B) when the block copolymer is highly asymmetric in composition but only moderately even for a large change in M_H,A/M_C,A ratio when the block copolymer is symmetric or nearly symmetric in composition. The boundary between the mesophase (M₁) of block copolymer and the homogeneous phase (H) of block copolymer/homopolymer blend was determined using oscillatory shear rheometry, and the boundary between the homogeneous phase (H) and two-phase liquid mixture (L₁+L₂) with L₁ being disordered block copolymer and L₂ being macrophase-separated homopolymer was determined using cloud point measurement. It is found that the addition of PI to a lamella-forming SI diblock copolymer or the addition of PB to a lamella-forming SB diblock copolymer gives rise to disordered micelles (DM) having no long-range order, while the addition of PS to a lamella-forming SB diblock copolymer retains lamellar microdomain structure until microdomains disappear completely. Thus, the phase diagram of SI/PI or SB/PB blends looks more complicated than that of SI/PS or SB/PS blends.     

Effects of sample preparation and flow geometry on the rheological behaviour and morphology of microphase-separated block copolymers: comparison of cone-and-plate and capillary data

The steady shear viscosities of two microphase-separated triblock copolymers, a polystyrene-block-polybutadiene-block-polystyrene copolymer (Kraton 1102) and a polystyrene-block-polyisoprene-block-polystyrene copolymer (Kraton 1107), were measured at various temperatures, using a cone-and-plate rheometer at low shear rates (ca. 0.01–10s⁻¹) and a capillary rheometer at high shear rates (ca. 5–5000 s⁻¹). In order to investigate the effect of sample preparation on the viscosity, specimens of Kraton 1102 were prepared using two different methods: (a) solvent film casting and (b) compression moulding. Samples of Kraton 1107 were prepared only by compression moulding. In the present study we found that (a) for compression-moulded specimens the shear viscosities obtained using a cone-and-plate rheometer did not overlap those obtained using a capillary rheometer, while for solvent-cast specimens there was a reasonably good agreement between the two, and (b) the viscosities of solvent-cast specimens were much lower than those of compression-moulded specimens. This observation was explained with the aid of transmission electron micrographs, which were taken of ultrathin sections cut parallel and perpendicular to the direction of shear. We found from transmission electron micrographs that the application of steady shear flow affected greatly the morphology of Kraton 1102 having cylindrical microdomains of polystyrene phase, whereas it affected little the morphology of Kraton 1107 having spherical microdomains of polystyrene phase. Also measured were the complex shear viscosities of the two block copolymers at various temperatures. We have shown that neither time-temperature superposition nor the Cox-Merz rule is applicable to microphase-separated block copolymers.