Frank-Kasper σ and A-15 Phases Formed in Symmetry and Asymmetry Block Copolymer Blend System

Abstract

Frank Kasper (FK) σ and A15 phases were found in the blend system of asymmetric and symmetric polystyrene-b-poly(methyl acrylate) block copolymers. Bates and co-workers first discovered these complex particle packings in the blend system where the diblock copolymers with a constant chain length of one component which consists of corona chains and variable chain lengths being micelle core. It is significantly important to have discover the formation of these complex phases in different block copolymer systems and also from a different research group, which strongly supports the prediction that the FK and A15 packing. Such complex phases had been found in limited conditions with a low molecular weight BCP with high χ (strongly segregated system) and conformationally asymmetric BCP system (flexibility asymmetry between constituent blocks). Discovery of the FK and A15 phases in a high molecular weight diblock copolymer without high χ or conformational asymmetry indicates a universal phenomenon of the formation of the complex particle packing in a substantially wide range of polymers.

1. Introduction

When the composition of a block copolymer (BCP) composed of two different kinds of polymer is large asymmetry (volume fraction of one component is less than about 20%), spherical microdomains are generally formed in the phase-separated state and the microdomains are normally arranged in a body-centered cubic (BCC) lattice.^1,2) In a rare case, a face-centered cubic (FCC) lattice phase has been discovered experimentally which was predicted theoretically.³⁾ In a block copolymer blend system, microphase separated structure diverse are predicted and confirmed experimentally.^4–20) Scarce morphologies of microphase separated structure in the blend system had been discovered. For example, ordered-bicontinuous-double-diamond (OBDD) network structure,^16–18) Frank-Kasper (FK) σ phase,^19,20) A15,²¹⁾ and dodecagonal quasicrystal (DDQC; not equilibrium)^20,21) has been reported in the recent decade. Matsushita et al.²²⁾ first reported that quasicrystal (Archimedean tiling pattern) in the BCP system was observed in the microphase separation of a triblock copolymer with three arms whose microphase separated structure was a cylinder. A plane cut vertical to the cylinder long axis indicated three domains composed of each constituent polymer and shapes of the domains were polygonal, trigonal and tetragonal, which self-assembled to eventually form the specific tiling pattern. The QC, the related QC approximant, other specific morphologies observed in spherical microdomains of the BCP blend system as well as a single BCP system have been already predicted and confirmed experimentally. Only a few studies related to the QC, FK σ-phase, and Laves phases were reported in BCP system so far. Besides, the reported complex phases may appear in only specific BCP, i.e., may require specific chemical structure. These complex sphere packings have only been found in low molecular weight BCP less than 10,000. Recently, a very common block copolymer blend system, polystyrene-b-polybutadiene (PS-b-PB) with relatively high molecular weight (over 30,000), provided FK phases.²¹⁾ The FK σ-phase and A15 phase were observed in the blend of compositionally symmetric BCP (PS 51 vol%) and asymmetric BCP (PS 82 vol%) gave within a range of symmetric BCP blend ratio from 0.26 to 0.41 mass%, which have been predicted by self-consistent field theory (SCFT).²³⁾ In this paper, we will show such complex morphologies observed in a similar system using completely different BCP (polystyrene-b-poly(methyl acrylate): PS-b-PMA) which can be easily synthesized and has a relatively high thermal resistance. The discovery of the complex phases in different kinds of BCP indicates the formation of the FK phase in addition to an associated QC would be a universal phenomenon.

2. Experimental Procedure

2.1 Material

Styrene (ST, Extra Pure Reagent, Nacalai Tesque Co., Ltd.), methyl acrylate (MA, Extra Pure Reagent, Nacalai Tesque), and toluene (Extra Pure Reagent, Nacalai Tesque) were distilled under reduced pressure. N,N,N′,N′,N′′-Pentamethyldiethylenetriamine (PMDETA, 99%, Aldrich).

2.2 Sample preparation

PS-b-PMA was synthesized using atom transfer radical polymerization (ATRP).²⁴⁾ As a first component, PS was polymerized at 383 K using the CuBr/PMDETA complex and 1-PEBr as an initiator. After the polymerization, the PS was purified by the precipitation from a toluene solution into excess methanol. The PS was dried in a vacuum at 323 K for 24 h. The synthesized PS was chain-extended with PMA via the ATRP at 368 K using the CuBr and PMDETA. After the extension reaction, the reaction mixture was purified by the precipitation from a toluene solution into excess methanol. After sufficient drying, the resultant polymer was washed with cyclohexane at 308 K in order to remove unreacted PS prepolymer. The characteristics of the synthesized PS-b-PMA were listed in Table 1. The M_n and M_w are number and weight average molecular weight, respectively. The polydispersity index of molecular weight is represented with M_w/M_n. SMA_A and SMA_S are compositionally asymmetric and symmetric block copolymer, respectively. Chemical structure of the used block copolymer and compositional image of the polymer chains are shown in Fig. 1. The PS-b-PMA block copolymers and their blend samples were dissolved in toluene at 10 mass%. The range of the blend ratio ϕ_S (mass%) of symmetric SMA_S to total BCP were 20–42 mass%. Each solution was dried at 298 K for a week. Two non-blended samples (PS-b-PMA) were annealed at 413 K for 48 h. The blend samples were annealed at 453 K for 4 days under vacuum. After annealing, the sample was cooled rapidly to room temperature (below the glass transition) to retain the morphology at the annealing temperature.

Table 1 Characteristics of synthesized block copolymer.

Fig. 1

Chemical structure of the used block copolymer and compositional image of the polymer chains.

2.3 Measurements

Small-angle X-ray scattering (SAXS) measurements were performed at beamline BL8S3 in the Aichi synchrotron radiation center (Aichi, JAPAN) and at beamline BL10C in the Photon Factory (PF) KEK (Tsukuba, Japan). Camera lengths were 4 m (Aichi) and 3 m (PF), and the wavelength of X-ray was 0.092 nm. Pilatus 100K and 2M (Dictris) were used as detectors for SAXS. The acquisition time was 120 sec for each. The two-dimensional SAXS pattern was sector-averaged to obtain a 1D SAXS profile. The experimental SAXS data were corrected for the background and sample absorption.

3. Results and Discussions

Figure 2 shows the SAXS profiles of SMA_A and SMA_S after annealing at 413 K for 48 h. The measurement temperature at 298 K. SAXS profile from SMA_A gave a broad and a single peak which means the sample did not undergo microphase separation, i.e., the sample was probably in a disordered state or formed spherical microdomains with a random distribution. The segregation power χN at annealing temperature (413 K) was estimated to be 18.1, where χ is the Flory-Huggins interaction parameter between the constituent polymer segment and N is the total segment number associated with the molecular weight. For PS-b-PMA, χ = 0.0466 + 15.3/T was reported previously.²⁵⁾ The normalized segment number of total BCP, N, is defined as   

\begin{equation*} N = \frac{\nu_{\textit{PS}}N_{\textit{PS}} + \nu_{\textit{PMA}}N_{\textit{PMA}}}{\sqrt{\nu_{\textit{PS}}\nu_{\textit{PMA}}}} \end{equation*}

where N_PS and N_PMA denote the degree of polymerization for PS and PMA, respectively, and ν_PS and ν_PMA are molar volume of the repeating units of PS and PMA chain, respectively. Here, ν_PS and ν_PMA are 99.1 and 72.9 cm³/mol, respectively, which was calculated using the mass density of PS (1.05 g/cm³) and PMA (1.18 g/cm³).²⁶⁾ According to the random phase approximation theory of block copolymer proposed by Leibler,²⁷⁾ the phase boundary, χN_ODT, of order-to-disorder transition at a volume fraction of 19.1 vol% is 26.3. Besides, the theoretical phase diagram reported by Matsen showed the order-disorder transition occurs at χN_ODT of 23–24.²⁸⁾ In our case, the value of χN at 413 K was much lower than the χN_ODT, which means the SMA_A was in a disordered state.

Fig. 2

SAXS profiles of SMA_S and SMA_A observed at room temperature. The samples were annealed at 413 K for 48 h. Each profile is vertically shifted to avoid overlapping.

On the other hand, the SAXS profile of SMA_S indicates some sharp diffraction peaks and the relative peak position appeared in integer multiple (q^*, 2q^*, and 3q^*; q^* denotes the primary peak.), which means that the microphase separated structure of SMA_A is lamellar. For SMA_S, the value of χN at 413 K was calculated to be 29.5 which is much higher than the χN_ODT (∼10.5) at a volume fraction of 0.509.

As shown in Fig. 3, the blend samples indicated developed long-range order after annealing at 353 k for 4 days with a blend ratio ϕ_S of 28 and 38 mass%. Each displayed more than 10 reflections with P4₂mnm and $Pm\bar{3}n$ symmetry. Peak positions were calculated for σ with lattice parameters a = 100.8 nm and c = 53.21 nm, and calculated for A15 phase with lattice parameter a = 56.48 nm. The calculated positions are indicated with thin broken sticks in Fig. 3. The observed reflection peaks also are displayed in the figure with thin black bars. The previous wrok²¹⁾ by Bates et al. examined the phase diagram for binary blends of the block copolymer, PS-b-polybutadiene (SB). In their work, the asymmetric diblock, SB_A, with total M_n = 25000 and f_PB = 18 vol% and the symmetric deblock, SB_S, with total M_n = 38000 and f_PB = 49 vol% were used, which are very slightly different from our case. The SAXS profiles observed in this work were identical to those reported by Bates. As compared to the previous report, the observed phases in our study can be assigned to the σ and A15. The σ phase with P4₂mnm symmetry and c/a of 0.532 was identical with the previous study. The 2D scattering pattern from the σ phase was spotty as shown in Fig. 3, which is indicative of large grain size with a high degree of long-range translational order. The reported phase diagram in the blend of SB_A and SB_S is shown in Fig. 4. At 353 K, they observed the sequence of phases disorder (DIS) → σ → A15 → hexagonally packed cylinder (HEX_C) with an increase in ϕ_S. From their report, at ϕ_S = 0.31, poorly resolved scattering profile was observed, which was assigned to the sate of σ/dodecagonal quasicrystal (DDQC) coexistence. In our study, at ϕ_S = 0.33, the broad scattering profile was obtained as shown in Fig. 4. It is hard to determine the morphology from only the SAXS profile. Normally, a DDQC is speculated to be a metastable precursor to its periodic approximant σ phase.^20,29) Even after a long time annealing for 4 days, the sample did not reach equilibrium.

Fig. 3

SAXS profiles of the SMA_S/SMA_A blend samples with ϕ_S of 0.28, 0.33, and 0.38 observed at room temperature. All samples were annealed at 353 K for 4 d. Each profile is vertically shifted to avoid overlapping. The thin sticks denote scattering reflections corresponding σ (ϕ_S = 0.28) and A15 (ϕ_S = 0.38) packings. The bold sticks indicate the hexagonally packed cylinder lattice.

Fig. 4

Experimental phase diagram for blends of SB_A and SB_S and SMA_A and SMA_S. The base phase diagram was obtained from the Ref. 28) with partial modification. DIS, LLP, QC, HEX_C, and LAM means disorder, liquid-like packing, a DDQC, hexagonally packed cylinders, and lamellar phases, respectively. Top axis ⟨f_PS⟩ denotes the total volume fraction of polystyrene in the blend system, in the present study, the most upper axis is referred. The nanostructures obtained in our experiment are plotted with larger (circle) symbols enclosed with a red dotted line. Open white circles indicate a disordered state. The circles filled with green, blue, purple, and grey color are the σ phase, A15, HEX_C phases, and LAM phases respectively. The circle symbols filled with black is not assigned so far.

Figure 4 shows the previously reported phase diagram²⁸⁾ by Bates and also the phases observed in our study are plotted in the diagram. We newly found the σ and A15 phase in the BCP blend system. Not only both complex structures but also other phases appeared at almost the same window of the phase diagram as shown in Fig. 4. It is quite important to observe the similar phase behavior with different block copolymer system SMA and SB, which indicates the universality of the formation of complex packings of spherical microdomains (particles).

4. Conclusion

We have reported that σ and A15 phases were found in the blend system of asymmetric and symmetric SMA block copolymers. The associated QC was not observed in our case so far. The diblock copolymers with a constant chain length of one component which consists of corona chains and variable chain lengths being micelle core gave access to the FK σ and A15 phases, which was first discovered by Bates and co-workers. Although the discovery of the complex packing σ and A15 phases in our system is the second report, it is significantly important to find the formation of these complex phases in different block copolymer systems, which supports the prediction that the FK and A15 packing in a high molecular weight diblock copolymer without high χ and conformational asymmetry (flexibility asymmetry between constituent blocks) indicate a potential for facilitating discovery to complex particle packing in a substantially wide range of polymers pointed out by Bates et al. Our block copolymer polystyrene-b-poly(methyl acrylate) does not have double-bonds in the chemical structure which normally can react with other chemicals, especially oxygen, and be degradable easily. That is, the polystyrene-b-poly(methyl acrylate) has a high thermal resistance to endure a long time and high-temperature annealing as compared to the polybutadiene based block copolymer. Thus, we would like to investigate the kinetic behavior of the structure formation in the next work.

Acknowledgments

This work was financially supported by JSPS KAKENHI 20H05269 Grant-in-Aid for Scientific Research on Innovative Areas. SAXS measurements were performed at the beamline BL8S3 in Aichi Synchrotron Radiation Center (Experimental numbers 202002032 and 20200324) and at the beamline BL10C in Photon Factory (Proposal 2018G099 KEK Tsukuba).

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