Interplay between the Phase Transitions at Different Length Scales in

Nov 22, 2013 - Asymmetric supramolecular double-comb diblock copolymers: From plasticization, to confined crystallization, to breakout. Anton H. Hofma...
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Interplay between the Phase Transitions at Different Length Scales in the Supramolecular Comb−Coil Block Copolymers Bearing (AB)n Multiblock Architecture Wei-Tzu Kuo,† Hsin-Lung Chen,*,† Raita Goseki,‡ Akira Hirao,‡,§ and Wen-Chang Chen§ †

Department of Chemical Engineering and Frontier Research Center on Fundamental and Applied Sciences of Matters, National Tsing Hua University, Hsin-Chu 30013, Taiwan ‡ Department of Organic and Polymeric Materials, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo, 152-8552, Japan § Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan S Supporting Information *

ABSTRACT: We introduced the concept of comb−coil supramolecule into linear (AB)n-type multiblock copolymer and investigated the self-assembly behavior of the copolymers as a function of the unit number n. Linear (polystyrene-blockpoly(2-vinylpyridine))n (denoted as (PS-b-P2VP)n, where n = 1, 2, 3) was complexed with a surfactant, dodecylbenzenesulfonic acid (DBSA), to yield the comb−coil multiblock copolymers, in which DBSA bound stoichiometrically with P2VP block via physical bonds. All three comb−coil block copolymers, including diblock (n = 1), tetrablock (n = 2), and hexablock (n = 3), self-organized to form cylinder-withinlamellae morphology at the lower temperature, where the cylindrical microdomains formed by the PS block embedded in the matrix composed of the lamellar mesophase organized by the P2VP(DBSA) comb block. The disordering of the smaller-scale lamellar mesophase formed by the comb block occurred upon heating; at the same time, the larger-scale cylindrical domains transformed to body-centered cubic-packed spheres in the diblock complex and to another hexagonally packed cylinder structure with smaller domain spacing in tetrablock and hexablock complexes, indicating that the order−disorder transition (ODT) of the smaller-scale structure drove an order−order transition (OOT) of the larger-scale structure irrespective of n. The transition temperatures were found to increase with increasing n due to the introduction of more interfacial area in the microphaseseparated state of the multiblock with larger unit number.

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INTRODUCTION Block copolymers are able to self-assemble to form a variety of long-range ordered nanostructures driven by the repulsion between the chemically bonded blocks.1,2 The type of morphology formed depends on the interplay between the interfacial free energy and the conformational entropy of the stretched block chains under the constraint of melt incompressibility.3,4 Polymers with comb-shaped architecture may also undergo microphase separation due to the repulsion between the backbone and the side chains.5 The so-called “supramolecular comb polymer” is constructed by the complexation of a linear polymer with a surfactant whose headgroup may bind to the polymer backbone by the physical bonds, such as hydrogen bonds,6−9 ionic bonds,10,11 and metalmediated coordination bonds.12−14 In the case where the surfactant selectively binds with one of the blocks in the coil−coil diblock copolymer, a “supramolecular comb−coil diblock copolymer” is formed.15 This type of copolymer may exhibit the hierarchical structures with two distinct length scales. The larger-length-scale copolymer domain typically with tens of nanometers in dimension is © 2013 American Chemical Society

generated by the microphase separation between the coil and comb blocks, while the smaller-length-scale lamellar mesophase with several nanometers in characteristic length is formed by the microphase separation between the backbone and the side chains of the comb block. The two structure units in the supramolecular comb−coil block copolymers may exhibit their respective phase transitions, such as order−order transition (OOT) or order−disorder transition (ODT).16,17 The interplay between these phase transitions may serve as an interesting switch for the property or functionality of the materials. Supramolecular comb−coil block copolymers were first introduced by Ikkala et al.15,17−23 One of the mostly studied systems is formed by the hydrogen-bonding complexation of the poly(4-vinylpyridine) (P4VP) block of PS-b-P4VP with pentadecylphenol (PDP) (denoted as PS-b-P4VP(PDP)).17−19 This comb−coil diblock system was found to exhibit a variety of hierarchical structures depending on the compositions of the Received: July 29, 2013 Revised: October 10, 2013 Published: November 22, 2013 9333

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(n = 2), and hexablock (n = 3) are studied here. These multiblock copolymers have been recently synthesized by the iterative linking reaction of living α-chain-end-(3-tert-dimethylsilyloxypropyl)-functionalized PS-b-P2VP with either α-chainend-(α-phenyl acrylate)-functionalized PS-b-P2VP or α-chainend-(α-phenyl acrylate)-functionalized PS-b-P2VP-PS-bP2VP.33 The phase behavior of the conventional multiblock copolymers bearing linear coil blocks has been examined and compared with that of the corresponding diblocks both theoretically and experimentally.34 Matsen and Schick demonstrated that the phase diagram of the linear (AB)n multiblock copolymers is similar to that of AB diblock,35−37 but with a shift of the boundaries of the microphases in the former relative to the latter, since a multiblock copolymer molecule is just a string of diblock molecules connected with each other.38 Wu et al.39 calculated the (χN)ODT of the linear multiblock copolymers. Using the random phase approximation (RPA), the specific value of (χN0)ODT, where N0 denotes the degree of polymerization of the diblock subunits, approaches a constant as the number of blocks increases. Furthermore, as the block number increases, the TODT of the copolymers initially increases and then approaches an asymptotic value. In this study, we will show that despite the more complicated architecture, the hierarchical structures with two distinct length scales were still formed in the multiblock comb−coil copolymers. An interesting aspect focused here is the interplay between the phase transitions associated with the hierarchical structures. It will be shown that an OOT of the larger-scale copolymer domain structure occurred concurrently with the disordering of the smaller-scale lamellar mesophase organized by the comb block, and the transition temperature increased with increasing unit number (n). The observed phase behavior will be discussed by considering the influence of multiblock architecture on the entropy and enthalpy of transition.

constituting blocks. Upon heating, the smaller-scale lamellar mesophase underwent an ODT, and the PDP molecules gradually dissociated from P4VP. With further heating, PDP became also soluble in PS microdomains, which caused an increase of the effective volume fraction of PS-containing domains, and then drove an OOT of the large-scale copolymer domain structure. In this case, the phase transition of the smaller-scale structure formed by the comb block influenced the larger-scale structure. “Transition-driving-transition” may be an appropriate term to describe such a phenomenon.24 The concept of supramolecular comb−coil block copolymer has recently been utilized to develop functional materials.25−30 Xu et al. have demonstrated the use of PS-b-P4VP(PDP) comb−coil diblocks to direct the assembly of CdSe and PbS nanoparticles selectively incorporated in the P4VP(PDP) microdomains.26 The selective complexation of an oligothiophene bearing phenol end group with the P4VP block in PS-bP4VP was shown to form the thermoresponsive materials that converted heat into mechanical energy. Moreover, the incorporation of such an oligomer effectively increased the domain spacing of the block copolymers and may thus offer an effective strategy to tailor their optical properties.27 Osuji et al. have used hydrogen bonding to sequester imidazole-terminated mesogens into the poly(methyl methacrylic acid) (PMAA) domains of a PS-b-PMAA. The resulting supramolecular comb−coil diblock was found to possess a photonic bandgap in the green with the gap tunable by the composition of the system.28 In addition to generating the nanostructured materials with designated functionalities, Osuji et al. have also demonstrated that selective complexation of rigid small molecules bearing anisotropic diamagnetic susceptibility with one of the block may lead to the large-scale alignment of the microdomains of the block copolymers by the application of magnetic fields.29,30 In our previous studies,31,32 we have investigated the hierarchical structures and phase transitions of the supramolecular comb−coil block copolymers bearing nonlinear architecture, where the poly(2-vinylpyridine) (P2VP) block in PS−P2VP block-arm star and heteroarm copolymers were selectively complexed with dodecylbenzenesulfonic acid (DBSA). It was found that the order−disorder transition temperature (TODT) of the smaller-scale lamellar mesophase in block-arm (PS-b-P2VP)5(PS)5 star copolymer was lower than that of the corresponding linear PS-b-P2VP(DBSA) complex.31 This phenomenon was attributed to the chain-crowding effect at the star junction point and the peculiar block-arm star architecture studied, where the length of free PS arms was much longer than that of the PS chains in the diblock arms. In the case of the heteroarm (PS)5(P2VP)5(DBSA) complex, the TODT of the smaller-scale lamellar mesophase was significantly higher than that of linear PS-b-P2VP(DBSA).32 This was ascribed to the lower transition entropy of the heteroarm complex due to the junction constraint. The interdomain distances in both nonlinear copolymers were observed to be smaller than that in the linear complex due to the lower aggregation number of PS star arms in the microdomains.31,32 This work extends our previous attempt in resolving the molecular architecture effect on the self-assembly behavior of comb−coil blocks by investigating the linear copolymers bearing (AB)n multiblock architecture. The copolymers were formed by stoichiometric complexation of P2VP blocks in (polystyrene-block-poly(2-vinylpyridine))n (PS-b-P2VP)n multiblock copolymers with DBSA, where diblock (n = 1), tetrabock

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EXPERIMENTAL SECTION

Synthesis of (PS-b-P2VP)n Multiblock Copolymers. The detailed procedure for synthesizing tetrablock and hexablock (PS-bP2VP)n has been described in the Supporting Information. Briefly, the multiblock copolymers were synthesized starting from α-chain-end-(αphenyl acrylate (PA))-functionalized PS-b-P2VP by repeating the same iterative synthetic sequence. Details of the preparation of αchain-end-SiOP-functionalized living PS-block-P2VP and the chain-end modification reactions to PA function via the SiOP terminus are also described in the Supporting Information. The resulting α-chain-endSiOP-functionalized multiblock copolymers were characterized by size exclusion chromatography (SEC), light scattering, and 1H magnetic nuclear resonance (NMR) spectroscopy in order to determine the absolute molecular weights, molecular weight distributions, composition ratios, and degree of SiOP-functionalities. Table 1 lists the molecular characteristics of the copolymers studied. Complex Preparation. The block copolymers and DBSA were first dissolved separately in dimethylformamide (DMF) to form 3 wt % clear solutions. The complexes were then prepared by mixing appropriate quantities of these two solutions prescribed by the binding fraction of DBSA to P2VP. After complete mixing, the samples were stored at ca. 60 °C to evaporate most of the solvent, followed by drying in vacuum at 80 °C for 48 h to remove the residual solvent. The overall binding fraction of DBSA to P2VP block is denoted by x, which expresses the average number of DBSA molecules bound with a P2VP monomer unit. The comb−coil copolymers with x = 1.0 (i.e., the stoichiometric compexation between P2VP and DBSA) were prepared in this study. Small-Angle X-ray Scattering (SAXS) Measurements. Temperature-dependent SAXS measurements were performed at Beamline 23A1 of the National Synchrotron Radiation Research Center 9334

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Table 1. Molecular Characteristics of (PS-b-P2VP)n Multiblock Copolymers sample

Mn overalla

Mn PS blockb

Mn P2VP blockc

Mw/Mn

PS-b-P2VP (PS-b-P2VP)2 (PS-b-P2VP)3

19 300 38 300 57 800

10 200 10 300 10 200

9100 8850 9070

1.03 1.04 1.03

f PS,x=0d f PS,x=1.0e 0.55 0.56 0.55

0.20 0.19 0.19

a

Number-average molecular weight of the whole copolymer. Number-average molecular weight per PS block. cNumber-average molecular weight per P2VP block. dOverall volume fraction of PS in the copolymers before complexation with DBSA. eOverall volume fraction of PS in the copolymers after complexation with DBSA. b

(NSRRC), Hsin-Chu, Taiwan. The energy of the X-ray source and the sample-to-detector distance were 10 keV and 1915 mm, respectively. A two-dimensional MarCCD detector with a resolution of 512 × 512 pixels was employed to record the SAXS signals. The sample was equilibrated at each temperature for 5 min before data collection. The SAXS profiles were corrected for the empty cell beam scattering, the sample transmission, and the detector sensitivity. The domain spacing (D) was calculated by D = 2π/qm with qm being the position of the primary scattering peak. Transmission Electron Microscopy (TEM) Observation. The real-space morphology of the hexablock complex was observed by a JEOL JEM-2000EX II transmission electron microscope (TEM) operated at 100 kV. The specimens were microtomed at −60 °C using a Reichert Ultracut E low-temperature sectioning system. The ultrathin sections were gathered onto copper grids coated with carbon-supporting films and subsequently stained for 12 h by iodine vapor. Since iodine is a preferential staining agent for P2VP(DBSA), the P2VP(DBSA) phase appears dark in the TEM micrographs.

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Figure 1. (a)Temperature-dependent SAXS profiles of PS-b-P2VP(DBSA) diblock comb−coil copolymer collected in situ from 30 to 170 °C in a heating cycle. The relative positions of the observable lattice peaks are marked by the arrows. (b) The enlarged SAXS profiles in the low-q region showing the formation of HEX and BCC phase at 120 and 150 °C, respectively. (c) Im(S)−1 (●) and D (○) versus T−1 plot of PS-b-P2VP(DBSA) diblock copolymer for the determination of the TODT of the smaller-scale structure and the TOOT of the larger-scale structure. Im(S)−1 corresponds to the intensity of the primary scattering peak associated with the smaller-scale structure, and D is the domain spacing of the larger-scale structure. The shade region marks the phase transition.

RESULTS AND DISCUSSION 1. Hierarchical Structure and Phase Transition of the Comb−Coil Diblock Copolymer (n = 1). The phase behavior of the linear (PS-b-P2VP)n(DBSA) multiblock comb−coil copolymers was investigated by SAXS measurement. Figure 1a displays the temperature-dependent SAXS profiles of the diblock complex PS-b-P2VP(DBSA). The SAXS profile at room temperature showed a weak primary peak at 0.23 nm−1 and another peak of stronger intensity at 2.06 nm−1. The low-q peak, corresponding to domain spacing of 27.61 nm, was associated with the larger-scale structure formed by the microphase separation between PS and P2VP(DBSA) blocks. The high-q peak was attributed to the lamellar mesophase organized by P2VP(DBSA) comb block with the interlamellar distance of 3.05 nm. The low-q peaks became more intense with increasing temperature, and at 120 °C the scattering profile showed a series of lattice peaks with the position ratio of 1:31/2:41/2:71/2 in the low-q region, signaling the formation of the hexagonally packed cylinder structure (HEX phase). On further heating to 130 °C, a remarkable change in the scattering profile clearly occurred. In this case, the high-q peak dropped in intensity and broadened significantly, signaling the occurrence of an ODT of the smaller-scale lamellar mesophase. The broad peak associated with the disordered state of P2VP(DBSA) block corresponds to the correlation hole scattering arising from the characteristic concentration fluctuations in the disordered phase. The fact that the correlation hole peak was present implied that a significant fraction of DBSA remained attached with the P2VP block in the disordered state. At the same time, the low-q peak was found to shift to higher q and the higher-order peaks associated with the hexagonal

lattice vanished. With further increasing temperature to 150 °C, a series of lattice peaks with the position ratio of 1:21/2:31/2 emerged (as shown in the enlarged plot in Figure 1b), indicating that the PS cylindrical domains transformed into spheres packed in body-centered cubic (BCC) lattice. The change of scattering pattern hence revealed the occurrence of an OOT of the larger-scale copolymer domain. Figure 1b compares the SAXS profiles at 120 and 150 °C, which showed clearly that the domain spacing decreased drastically from 25.77 nm in HEX phase to 20.45 nm in BCC phase across the OOT. In Figure 1c, the inverse intensity (Im(S)−1) of the high-q peak associated with the smaller-scale lamellar mesophase and the domain spacing (D) pertaining to the larger-scale structure are plotted as a function of the inverse absolute temperature (T−1) for PS-b-P2VP(DBSA). The plot showed the abrupt changes of Im(S)−1 and D at ca. 120 °C, which strongly resembled the first-order phase transition. The result also showed that the ODT of smaller-scale lamellar structure and the OOT of the larger-scale copolymer domain occurred concurrently at ca. 120 °C. 9335

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It is interesting that PS block self-assembled to form cylindrical microdomain when the comb block formed the mesophase, although its volume fraction was as low as 0.20. According to the classical phase diagram of coil−coil diblock copolymer, this composition should fall in the region of spherical morphology in the strong segregation regime. The deviation may be attributed to the fact that in the temperature range where the smaller-scale lamellar structure still persisted the formation of cylindrical domain by PS block would favor the lamellae surrounding the cylinder to stack over a longer distance (comparing to the case of spherical domain) along the length axis. Therefore, the tendency of the smaller-scale lamellae to stack regularly over a long distance stabilized the cylindrical microdomain over the spherical one. When the comb block became disordered above its TODT, DBSA may act simply like a selective solvent to P2VP. In this case, the system behaved more or less like the conventional mixture of a diblock with a selective solvent, such that the PS block formed spherical microdomain as prescribed by its volume fraction. 2. Hierarchical Structure and Phase Transition of the Multiblock Comb−Coil Copolymer. A. Tetrablock System (n = 2). Figure 2a displays the temperature-dependent SAXS profiles of (PS-b-P2VP)2(DBSA). At 120 °C, the scattering curve showed two clear peaks with the position ratio of 1:31/2 in the low-q region, signaling the presence of hexagonally packed PS cylinders with the domain spacing of 24.39 nm. The peak marked by “i = 1” was attributed to the first-order form factor peak of the cylinder. The radius of the cylinder deduced from its position via R = 4.98/qmi=1 was 6.73 nm. The sharp high-q peak at 2.25 nm−1 was due to the mesophase formed by the P2VP(DBSA) comb block. Therefore, similar to the diblock system, the tetrablock comb−coil copolymer also formed the cylinder-within-lamellae morphology at the lower temperature. Upon heating to 140 °C, the high-q peak contributed by the comb block broadened significantly, and an additional peak (marked by “1′”) emerged at 0.31 nm−1. This peak grew in the expense of the original low-q peak, and at 160 °C, where the smaller-scale lamellar mesophase almost vanished, the original low-q peak almost completely converted to the new peak. The enlarged SAXS profile at 170 °C shown in Figure 2b revealed that the tetrablock still exhibited the hexagonally packed cylinder structure when the comb block was in the disordered state. Consequently, the ODT of the smaller-scale mesophase induced a transformation from the original HEX phase to another HEX structure with smaller domain spacing. This was different from the diblock counterpart where the ODT of the mesophase transformed the cylindrical domain into sphere. The tendency was however the same; that is, the disordering of the mesophase of the comb block tended to increase the curvature of the copolymer domain. The plot of Im(S)−1 and D versus T−1 for (PS-bP2VP)2(DBSA) is displayed in Figure 2c. Abrupt changes of Im(S)−1 and D were both located at ca. 140 °C, confirming that the OOT of the larger-scale structure occurred almost simultaneously with the ODT of smaller-scale structure. The observed transition temperature of the tetrablock comb−coil copolymer was obviously higher than that of diblock analogue (≃120 °C), implying that the increase of the unit number (n) tended to raise the transition temperatures. B. Hexablock System (n = 3). Figure 3a presents the temperature-dependent SAXS profiles of the hexablock copolymer, i.e., (PS-b-P2VP)3(DBSA). Again the scattering profiles at the lower temperatures (e.g., 140 °C) exhibited two

Figure 2. (a) Temperature-dependent SAXS profiles of (PS-bP2VP)2(DBSA) tetrablock comb−coil copolymer collected in situ from 30 to 180 °C in a heating cycle. The relative positions of the observable lattice peaks are marked by the arrows. (b) Enlarged SAXS profiles in the low-q region showing the formation of the HEX phase with larger and smaller domain spacing at 120 and 170 °C, respectively. (c) Im(S)−1 (●) and D (○) versus T−1 plot of (PS-bP2VP)2(DBSA) tetrablock copolymer for the determination of the TODT of the smaller-scale structure and the TOOT of the larger-scale structure. Im(S)−1 corresponds to the intensity of the primary scattering peak associated with the smaller-scale structure, and D is the domain spacing of the larger-scale structure. The shade region marks the phase transition.

peaks with the position ratio of 1:31/2 in the low-q region, showing the formation HEX morphology at the larger length scale. The sharp high-q peak at 2.11 nm−1 signified the presence of the lamellar mesophase at the smaller length scale. On heating to 160 °C, a new peak (marked by “1′”) appeared beside the original peak, and the high-q mesophase peak broadened significantly. As the temperature reached to 170 °C, the low-q primary peak was completely replaced by the new one. Because of the lack of the higher-order diffractions, it was difficult to identify the morphology of the copolymer domain formed. Accordingly, TEM was used to observe the morphology in real space. Figure 4 shows the TEM micrographs of the as-cast hexablock comb−coil copolymer and the sample quenched from 190 °C. Cylindrical structure was clearly observed for both samples, as manifested by the presence of the both top and side-view images of the cylinders. Consequently, similar to the tetrablock system, the hexablock copolymer also exhibited an OOT from a HEX phase to another HEX phase with smaller domain spacing, and this 9336

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transition process took place concurrently with the ODT of lamellar mesophase of the comb block. Figure 3c displays the plot of Im(S)−1 and D versus T−1 for (PS-b-P2VP)3(DBSA), which identified the transition temperature at ca. 160 °C. The transition temperature of the hexablock copolymer was even higher than that of the tetrablock, which demonstrated that multiblock with larger unit number exhibits a higher transition temperature. It is interesting to note that both the OOTs of the copolymer domains in tetrablock and hexablock transformed from a cylindrical structure to another cylindrical structure with smaller domain spacing (rather than to spherical structure), although the overall volume fractions of PS were lower than that of the diblock. The reason that cylinder is favored over sphere in the multiblocks may be attributed largely to the higher interfacial energy under a given microphase-separated morphology. Let us use lamellar domain as the example to demonstrate such an effect. Under a given length of A and B block, the microphase separation of two diblock molecules generates the interfacial area of 2Σ, with Σ being the crosssectional area of a junction point (cf. Supporting Information Figure S5). In the case of tetrablock, each molecule is composed of two A blocks and two B blocks. Because of the introduction of an additional junction point, the microphase separation between A and B block creates an additional junction area, such that the interfacial area becomes 3Σ irrespective of whether the middle blocks adopt bridge (Figure S6a) or loop (Figure S6b) conformation. In general, the microphase separation in a (A−B)n molecule generates the interfacial area of (2n − 1)Σ; consequently, a microphaseseparated multiblock copolymer is expected to show higher interfacial energy than the corresponding diblock. Multiblock copolymer may then self-assemble to form the microdomain structure with smaller surface-to-volume ratio to reduce the interfacial energy contribution. Such an effect results in a shift of the boundary between cylindrical and spherical structure to higher majority block composition (compared to that of the diblock). Figure S3 combines the Im(S)−1 vs T−1 and D vs T−1 plots of the three copolymers. It revealed clearly that TODT of the smaller-scale structure and TOOT of the larger-scale structure increased with increasing unit number. The two types of transition temperature took place concurrently, where the disordering of the mesophase of the comb block drove the transition of the PS domain structure. When the comb block formed the mesophase, the polar−nonpolar repulsion between the P2VP backbone and the DBSA side chain caused P2VP blocks to stretch significantly normal to the interface of the copolymer domain (cf. Figure 5). Under the constraint of melt incompressibility, such a chain stretching also led to great stretching of the PS block. When the mesophase was disrupted, both P2VP and PS blocks were allowed to relax, and DBSA now acted like a simple selective solvent in the P2VP domain. The increase of the cross-sectional area of the junction point made the PS domain adopt a larger curvature. In the diblock copolymer, such an effect even led to a transformation of microdomain morphology from cylinder to sphere. Now it is important to explain why the TODT and TOOT of the lamellar mesophase and the copolymer domain, respectively, in the multiblocks were higher than those in the diblock. Since the binding mode of DBSA to P2VP in all the three complexes were the same, the difference in transition temperature must arise from the architecture effect. In a previous study, we have

Figure 3. (a)Temperature-dependent SAXS profiles of (PS-bP2VP)3(DBSA) hexablock comb−coil copolymer collected in situ from 30 to 190 °C in a heating cycle. The relative positions of the observable lattice peaks are marked by the arrows. (b) Enlarged SAXS profiles in the low-q region showing the formation of the HEX phase at 140 °C. (c) Im(S)−1 (●) and D (○) versus T−1 plot of (PS-bP2VP)3(DBSA) hexablock copolymer for the determination of the TODT of the smaller-scale structure and the TOOT of the larger-scale structure. Im(S)−1 corresponds to the intensity of the primary scattering peak associated with the smaller-scale structure and D is the domain spacing of the larger-scale structure. The shade region marks the phase transition.

Figure 4. TEM micrographs of (PS-b-P2VP)3(DBSA) (a) as-cast sample and (b) the sample quenched from 190 °C. The presence of both top-view and side-view images of cylinders demonstrates that both samples exhibit HEX structure. P2VP(DBSA) phase appears dark in the TEM micrographs due to I2 staining. 9337

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Figure 5. Schematic illustration of the relaxation of the comb blocks and coil blocks upon disordering of the smaller-scale lamellar structure formed by the comb blocks. The copolymer self-assembles to form the hierarchical structures with two distinct length scales at lower temperatures (state I). In order to allow the surfactant molecules to pack into a long-range ordered lamellar structure, the backbones attached with the surfactant molecules have to stretch significantly. When this copolymer is heated to sufficiently high temperature, the smaller-scale lamellar structure formed by the comb block is disrupted (state II). In this case, the surfactant molecules act like a selective solvent for one of the blocks, and the interfacial areas of the copolymer domains enlarge due to the relaxation of the block chains.

Figure 6. Schematic illustration of the pathways for calculating the (n) enthalpy and entropy of transition, ΔH(n) t and ΔSt , associated with the OOT of the copolymer domain.

ΔS b ≃ −(n − 1)kB ln Σf

elaborated on the morphological transitions occurred in the hierarchically organized supramolecular comb−coil block copolymers.32 As illustrated in Figure 5, the copolymer selfassembles to form the hierarchical structures with two distinct length scales at lower temperatures (state I). In order to allow the surfactant molecules to pack into a long-range lamellar structure, the backbones attached with the surfactant molecules have to stretch significantly. When this copolymer is heated to sufficiently high temperature, the smaller-scale lamellar structure formed by the comb block is disrupted (state II). In this case, the surfactant molecules act like a selective solvent for one of the blocks. Moreover, the interfacial areas of the copolymer domains enlarge due to the relaxation of the block chains. Considering the phase transition as the first-order transition, (n) (n) the transition temperature is given by T(n) tr = ΔHt /ΔSt , (n) (n) where ΔHt and ΔSt are the enthalpy and entropy of transition, respectively. To derive the transition entropy, let us consider the OOT between the copolymer domains associated with ordered and disordered smaller-scale structure, as illustrated in Figure 6. According to Figure 6, ΔS(n) t is given by ΔSt(n) = ΔSa + ΔSt(1) + ΔS b

where Σf is the area after the disordering of the mesophase. Substituting eqs 2 and 3 into eq 1, we have ΔSt(n) = ΔSt(1) − (n − 1)kB ln

Σf Σi

(4)

For an (AB) section in the multiblock, the entropy of transition is given by ΔSt̃

(n)

= ΔSt̃

(1)

−

Σf ⎛ n − 1⎞ ⎜ ⎟k ln ⎝ n ⎠ B Σi

(5)

Similarly, the enthalpy of transition is given by ΔHt(n) = ΔHa + ΔHt(1) + ΔHb

(6)

Considering that the difference in the number of junction points between n (AB) diblock molecules and one (AB)n multiblock molecule would give rise to a difference in the interfacial energy, ΔHa and ΔHb are given by ΔHa = [n − (2n − 1)]Σ iγ = − (n − 1)Σ iγ

(7)

ΔHb = (n − 1)Σf γ

(8)

(1)

where ΔS(1) is the transition entropy of the diblock. We t roughly assume that the conformational entropies of the block chains in their respective microdomains are approximately independent of n. We further assume that both a chain end and a block junction point are allowed to move over the area of Σ, i.e., the cross-sectional area of a junction point. Then their entropy is proportional to kBlnΣ. For n (AB) diblock molecules, the total entropy contributed by the chain ends and junction points is hence 3nkBlnΣ, while for one (AB)n molecule the corresponding entropy is (2n+1)kBlnΣ. Consequently, ΔSa is given by ΔSa ≃ (n − 1)kB ln Σi

(3)

where γ is the surface energy per unit area. The transition enthalpy per (AB) diblock section is hence ΔH̃ t(n) = ΔH̃ t (1) +

⎛ n − 1⎞ ⎜ ⎟ (Σ − Σ )γ i ⎝ n ⎠ f

(9)

From eqs 5 and 9, the transition temperature of the multiblock is expressed as Ttr(n)

(2)

where Σi is the area before the disordering of the smaller-scale mesophase. We assumed that Σi is independent of n. Similarly

=

ΔH̃ t(n) ΔSt̃

(n)

≃

( n −n 1 )(Σf − Σi)γ (1) Σ n−1 ΔSt̃ − ( n )kB ln Σ

ΔH̃ t (1) +

f

i

(10)

(1) ̃(1) Since ΔH̃ (1) t = Ttr ΔSt , we have

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=

Article (1)

( n −n 1 )(Σf − Σi)γ (1) Σ n−1 ΔSt̃ − ( n )kB ln Σ

ΔTtr(1)ΔSt̃

f

(11)

i

Because the denominator ΔS̃(1) t , we conclude Ttr(n) > Ttr(1) +

E-007-036. We thank the National Synchrotron Radiation Center for supporting us to carry out the SAXS experiments at beamline BL23A1. We also thank Yu-Chiao Lin and Kei-Yu Kao for assistance in TEM experiment.

+

̃ ΔS(1) t

■

− [(n − 1)/n]kB ln(Σf/Σi)
Ttr(1) ⎝ n ⎠ ΔS ̃ (1) t

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for n > 1

As a result, the transition temperature of the multiblock is higher than that of the diblock, which is consistent with the experimental observation. It is noted that the argument presented above considered only the entropic and enthalpic contributions arising from the difference in interfacial area (or number of junction points) between diblock and multiblock, while the difference in the free energy stemming from the conformation of the chains confined in the microdomain was neglected. The analysis is however able to qualitatively explain the higher phase transition temperature exhibited by the multiblock as compared to that of the diblock counterpart.

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CONCLUSIONS We have investigated the architecture effect on the phase behavior of the comb−coil block copolymers formed by the selective stoichiometric complexation of DBSA with the P2VP block in (PS-b-P2VP)n multiblock copolymers. The hierarchical structures with two distinct levels were observed in all copolymers studied irrespective of the unit number. Upon heating, the OOT of the larger-scale copolymer domains occurred concurrently with the ODT of the smaller-scale lamellar mesophase, a process which may be called “transitiondriving-transition”. In the diblock system, the morphology of the larger-scale domain transformed from HEX to BCC phase across the OOT. In tetra- and hexablocks, the original HEX structure was found to transform into another HEX phase with smaller domain spacing. The phase transition temperature increased with increasing unit number of the multiblock. This phenomenon was attributed to the introduction of additional interfacial area in the microphase-separated state of the multiblocks with n > 2.

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ASSOCIATED CONTENT

S Supporting Information *

Synthesis and characterization of the (PS-b-P2VP)n multiblock copolymers; schematic illustration of the microphase separation of two diblock molecules; schematic illustration of the microphase separation of a multiblock molecule; Im(S)−1 vs T−1 and D vs T−1 plots of the diblock, tetrablock, and hexablock complexes to demonstrate that the transition temperatures increase with increasing n. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (H.-L.C.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the financial support from the National Science Council Taiwan under Grant NSC 100-22219339

dx.doi.org/10.1021/ma401587m | Macromolecules 2013, 46, 9333−9340

Macromolecules

Article

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