Mesophase Separation and Rheology of Olefin Multiblock

Article pubs.acs.org/Macromolecules

Mesophase Separation and Rheology of Olefin Multiblock Copolymers Peng He, Wei Shen, Wei Yu,* and Chixing Zhou Advanced Rheology Institute, Department of Polymer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China S Supporting Information *

ABSTRACT: Chain shuttling polymerization enables an efficient production of ethylene−octene block copolymers (OBCs) that combine different mechanical properties in a polymer chain. However, this method results in molecular weight polydispersity and multiblock chain structure. The melt-phase behavior and mesophase transition of the polydisperse OBCs with low octene content but different molecular weight and block composition were investigated by rheology, differential scanning calorimetry (DSC), atomic force microscopic (AFM), polarized optical microscopy (POM), and small-angle X-ray scattering (SAXS). Three rheological methods, namely the deviation of the scaling dependence of zero shear viscosity on molecular weight, the terminal behavior and the failure of time−temperature superposition (TTS), and two-dimensional rheological correlation spectrum, are used to reveal the mesophase separation with increasing sensitivity. The occurrence of mesophase separation transitions (MST) was observed in such low octene content and low molecular weight OBC systems, with much lower degree of segregation than the theoretical predictions in diblock copolymers. The extent of mesophase separation is further justified by its effect on subsequent crystallization behaviors.

1. INTRODUCTION Block copolymers are macromolecules comprising two or more chemically distinct monomer blocks connected in a variety of ways in the polymer chains. In the past few decades, these materials have been the focus of considerable research both theoretically and experimentally, stemming from the significant technological applications that are crucially depend on their fascinating self-assembly at the nanoscale.1,2 These works on block copolymers have been generally concerned with “model” block copolymers that contain nearly monodisperse blocks typically prepared by living anionic polymerization. It is demonstrated that most block copolymer melts undergo the microphase separation transitions, resulting in the formation of ordered nanostructures. The phase behavior of AB diblock has been well established, and four typical equilibrium nanostructures have been observed experimentally and supported by theoretical studies.3 The microphase transitions and microdomain morphology can be tuned by the volume fraction of the diblock copolymer ( fA) and the extent of segregation between the A and B blocks, which is the product of the overall degree © 2014 American Chemical Society

of polymerization (N) and Flory−Huggins interaction parameter (χ) between two segments.4 However, in practice, the living polymerization for producing near monodisperse blocks is generally expensive and time-consuming in largevolume production of block copolymers. To overcome these shortcomings, alternative synthetic strategies have been developed, but they usually lead to a certain degree of polydispersity. Thus, an important question emerges as how polydispersity influences the phase behaviors of block copolymers. Some theoretical studies5−10 have been devoted to the effects of polydispersity on phase behaviors of di-, tri-, and multiblock copolymers, but this area remains largely unexplored in experiments. Recent development in olefin polymerization enabled the production of a novel class of olefin block copolymers (OBCs) with ethylene−octene block length polydispersity.11 These Received: November 11, 2013 Revised: December 30, 2013 Published: January 6, 2014 807

dx.doi.org/10.1021/ma402330a | Macromolecules 2014, 47, 807−820

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Table 1. Molecular Parameters of Ethylene−Octene Multiblock Copolymers

a

sample code

Mw (kg/mol)

PDI

f harda (wt %)

f hardb (wt %)

total C8 (mol %)

C8 in hard segment (mol %)

C8 in soft segment (mol %)

ΔC8 (mol %)

SLhard

SLsoft

χNc

L01 L02 M01 M02 M03 H01

79.8 126.5 61.7 82.6 156.6 77.6

1.97 2.06 1.83 2.15 1.97 1.92

13.5 12.3 24.6 22.0 27.0 39.2

11.0 11.0 25.0 25.0 25.0 35.0

13.7 14.0 11.7 12.0 11.5 9.6

1.9 1.4 1.9 1.8 1.9 2.1

18.6 17.8 17.0 16.8 17.2 17.1

16.7 16.4 15.2 15.0 15.2 15.0

36.6 32.4 38.7 37.4 39.9 46.9

102.0 155.7 82.5 92.1 74.9 50.9

3.0 4.2 2.2 2.5 5.2 2.6

Hard block content from 13C NMR analysis. bHard block content supplied by DOW. cχN calculated according to refs 32 and 33.

segments is equal to 2, the critical value of χN to achieve ordered state is 4,5 which is lower than the value of 10.5 in monodisperse diblock systems.31 This suggests that this value of χN would be much lower in polydisperse multiblock systems, resulting in a substantial decrease in molecular weight for microphase transition. In multiblock OBCs with a most probable distribution (PDI = 2) in block length, χ is determined by the difference in the molar octene content between soft and hard blocks, defined as ΔC8.14,32,33 Most previous studies on OBCs’ phase behavior have focused on the polymer with high ΔC8 (17.5−33.6 mol %) and high weightaverage molecular weight Mw (122−249 kg/mol).15,17,18,30 Considering the commercially available OBCs, the phase behavior of such material with low ΔC8 and low Mw is of practical importance. However, in the reported low ΔC8 systems, OBC melts have been supposed to be homogeneous from the spherulitic morphology observed by optical microscopy.13,34 In the present work, several OBCs with low ΔC8 and low Mw were selectively chosen to investigate their melt structure. We will demonstrate that mesophase separation can also be observed for such OBCs with low ΔC8 ≈ 15.1 mol % and the Mw as low as 61.7 kg/mol. In contrast to the previously reported OBCs systems with high ΔC8 and high Mw whose TMST are close to their thermal degradation temperature,17,35 we find that the mesophase transition temperature of OBCs with low ΔC8 and low Mw lie in the processing window of these materials, which implies the importance of phase transition to the morphology and mechanical properties in solid state. For this purpose, we will suggest and discuss several different rheological techniques with different sensitivity to mesophase separation.

OBCs, synthesized by chain shuttling polymerization, are statistically coupled linear multiblock copolymers of alternating soft segments (high octene content) and hard segments (low octene content). The soft segment is amorphous blocks having a low glass temperature similar to ultralow-density polyethylene, while the hard segment is semicrystalline blocks having a high melting point close to that of high-density polyethylene. This new olefin-based block architecture imparts excellent elastomeric properties at higher temperatures than conventional random copolymer of same densities12,13 and can produce periodical mesophases with interesting optical properties.14 Because of the polydisperse multiblock architecture, the phase behaviors of OBCs could be quite different from the traditional monodisperse systems. Li et al. found that the polydispersity can increase the microdomain size, and the lamellar domain spacing (102−158 nm) in polydisperse diblock or multiblock OBCs is 3−5 times larger than that in equivalent monodisperse systems.15,16 As the much larger domain size, the mesophase separation is more preferred in polydisperse OBCs to the microphase separation commonly used in monodisperse systems. For the crystallizable OBCs, Jin et al. noted the competition between the sphere-forming mesophase separation in melts and the crystallization of OBCs.17 However, the above work on the melt structure of OBCs has been investigated indirectly by characterizing the solid state structure, if the mesophase separation in OBC melts has a strong confinement on subsequent crystallization and the final solid state morphology could be a relative reflection of the melt structure. To further understand the mesophase separation transition (MST) in OBC melts, the real-time experimental studies such as synchrotron small-angle X-ray scattering (SAXS) and rheology are necessary. But the direct inspection on the OBCs melt structure by SAXS is unattainable as the near-zero electron density contrast between the two ethylene−octene blocks.16,18 On the other hand, the viscoelastic response of polymers can sensitively reflect the subtle structure change during phase transition such as microphase separation in diand triblock copolymer,19−24 liquid−liquid phase separation in polymer blend,25,26 crystallization,27,28 and gelation.29 Until recently, the only high-temperature melt structure study of OBCs was carried out by Park et al.30 using rheology as a main tool. They found the failure of time−temperature superposition (TTS) for all OBCs; the OBCs underwent mesophase separation upon raising the temperature, but the transition did not occur abruptly in rheological properties as that observed in monodisperse diblock and triblock copolymers. Theoretical work has shown that minimum χN for the order−disorder transition (ODT) in diblock copolymers decreases as polydispersity in one or both segments is increased.7 When the PDI (polydispersity index) in both

2. EXPERIMENTAL SECTION 2.1. Materials. The OBCs polymerized by the chain-shuttling technology11 were provided as pellets by The Dow Chemical Company. Six low octene content OBCs with different block structure were selected in this work. The detailed information on molecular structure is given in Table 1. In the polymerization process, the octene content in the hard and soft segments in these six OBCs are all controlled to be around 1.0 and 18.0 mol %, respectively, by utilizing the same catalyst pair with dramatically different octene selectivities. The linear multiblock structures for OBCs are formed as a result of a chain shuttling agent (CSA), which allows the growing chains to transfer between the active centers of the two catalysts. The main differences between the six OBCs are the total hard block content adjusted by the relative amounts of the two catalysts and the total molecular weight controlled by the concentrations of CSA and the hydrogen to induce growth termination between the two catalysts. These six OBCs are identified by the codes Hx/Mx/Lx, where H/ M/L reflects the relatively high/medium/low content of hard block, and the subscripts x are numbers that increase with the total molecular weight. The octene content and block structure of OBCs were further confirmed and analyzed by 13C NMR, measured at 125 °C in the 808


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Figure 1. Sequence distribution of ethylene and octene unit for M01 and classification of hard/soft block. The height of a bar denotes the length (number of monomer) of a continuous ethylene or octene unit. lc stands for the critical chain length to form the hard block. The regions that denote the soft blocks and hard blocks are marked. polymer solutions of up to 15 wt % using the deuterated odichlorobenzene as solvents. The total molecular weight (Mw) and polydispersity index (PDI = Mw/Mn) were measured by hightemperature gel permeation chromatography (GPC) using 1,2,4trichlorobenzene (TCB) as solvents at 145 °C. The column was calibrated with monodisperse polystyrene (PS) standards. 2.2. Measurements. Differential scanning calorimetry (DSC) measurements were carried out on a TA Instruments Q2000 for thermal analysis using sealed aluminum pans and specimens with the weight 5−8 mg cut from pellets. The DSC was calibrated using indium and tin. All experiments were performed in nitrogen atmosphere with a flow rate of 50 mL/min. For OBCs, the heating and cooling thermograms were conducted between −60 and 200 °C at 10 °C/min. The first cooling scans and the second reheating scans were taken for determining the crystallization and melting transition temperatures. The crystallinity was calculated by comparison to the theoretical heat of melting (ΔHm =292 J/g) of polyethylene with 100% crystallinity. Polarized optical microscopy (POM) observations were conducted on a Leica microscope (DM2500P), equipped with a Linkam hotstage (CSS450). Thin films of about 100 μm for POM were prepared by pressing samples between two glass slides at 200 °C for 10 min and then cooling down to room temperature at 10 °C/min. In-situ synchrotron SAXS measurements were carried out at the Shanghai Synchrotron Radiation Facility (SSRF) beamline BL16B1. The wavelength (λ) of the synchrotron radiation was 0.124 nm. The X-ray scattering images were collected on a MAR-USA CCD detector having a resolution of 2048 × 2048 pixels (pixel size: 79 × 79 μm2). The distance between sample and detector was around 5190 mm, with a q range from 0.04 to 0.8312 nm−1. Here, q = 4π sin(θ/2)/λ, where θ is the scattering angle. The data acquisition time was 300 s for each scattering image. Air and other background scattering were subtracted in all X-ray images. The resulting 2D images were azimuthally averaged to obtain the scattering intensity I(q) versus q. The long period was calculated from the equation L = 2π/qmax, where qmax is the peak value determined in the Lorentz-corrected SAXS (q2I(q) versus q) plot. All rheological properties were obtained from small-amplitude oscillatory shear (SAOS) measurements using a stress-controlled AR G2 rheometer (TA Instruments) with 25 mm parallel plate geometry and a gap of 0.9 mm. The disk samples were made by compressing molding into films of 1 mm at 200 °C under a pressure of 10 MPa. All experiments were performed in the linear viscoelastic region determined by the strain sweeps. The dynamic frequency sweep tests were conducted between 0.01 and 100 rad/s with a strain amplitude of 5% at different temperatures. Samples were allowed to

equilibrate at each temperature for at least 20 min before collecting data. Temperature ramp tests were performed to determine the mesophase separation temperatures. At sufficiently low frequencies the width of the MST is frequency independent.20,36 The chosen angular frequency of 0.1 rad/s is within this range. The samples were hold at the specific high temperatures to remove the thermal history and then cooled down to 125 °C at a rate of 0.5 °C/min. During temperature ramp, the samples were kept at each temperature point for 1 min to achieve equilibrium states.

3. RESULTS AND DISCUSSION 3.1. Molecular Structure and Thermal Properties. 13C NMR has been the most successful analytical tool to characterize the structure and composition of ethylene−αolefin copolymers.37 In this work, 13C NMR spectroscopy was applied to confirm and analyze the chain structures of the multiblock OBCs. Randall38 had suggested a triad analysis method to determine the content of octene in polyethylene. The total octene content of the six OBCs is calculated according to this method, and the results are listed in Table 1. As shown in Table 1, no major difference in the octene content can be observed among the six OBCs. A typical 13C NMR spectrum of OBC M01, the structure assignments for the peaks in the spectrum, and the details to calculate the total octene content and the average sequence lengths of ethylene and octene in OBCs can be found in the Supporting Information (Figure S1 and Table S1). The average octene length of the six OBCs is around 1.1−1.2, and the average ethylene length ranges from 6.5 to 10.4 (detailed data in Table S1). However, neither the total octene content nor the average sequence length of monomers can be correlated with the content of hard segments, which implies the distribution of octene is rather different in different OBCs. In practice, since there are more peaks in 13C NMR spectrum than the number of triads, it is expected that the concentrations of triads will depend on the different combinations of peaks, which implies that the triad analysis is overdetermined. More accurate analysis has been suggested recently,37,39 which assigned as much as 17 peaks at different chemical shifts to the contributions from 32 pentads. However, since the number of pentads becomes much larger 809


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Table 2. Physical Properties of Ethylene−Octene Multiblock Copolymers sample code

Tm,onset (°C)

Tm,peak (°C)

Tm,coma (°C)

Tc,onset (°C)

Tc,peak (°C)

Tc,comb (°C)

TMSTc (°C)

ΔHm (J/g)

Xc,ΔHd (wt %)

Le (nm)

L01 L02 M01 M02 M03 H01

110.0 106.0 107.6 110.0 107.2 113.9

122.8 120.7 122.9 122.8 119.7 123.7

126.3 125.9 126.8 128.6 124.6 129.2

102.0 97.1 106.2 103.1 100.0 107.2

94.6 89.9 101.0 95.9 96.3 102.3

88.6 83.5 94.3 88.7 89.6 95.2

163.5

21.4 20.3 40.7 43.1 41.5 65.9

7.4 7.0 14.0 14.8 14.3 22.7

43.7 31.3 43.7 38.0 28.5 38.3

153.8 160.4 154.0

a

The completion temperatures of the melting processes. bThe completion temperatures of the crystallization processes. cMesophase separation temperature determined from rheology. dCrystallinity from heat of melting. eLong period calculated from the SAXS.

than the number of peaks that can be well resolved in 13C NMR, the problem becomes underdetermined. In this work, we adopted a first-order Markovian statistical model, with two parameters POO (probability of octene insertion after octene) and PEO (probability of octene insertion after ethylene) to describe the polymerization of OBCs. These two parameters can be determined from minimizing the difference between the normalized experimental peak areas in 13 C NMR and simulated peak areas of a chain generated using first-order Markovian model. An example for the comparison between the experimental and simulated data for normalized peak areas is shown in Figure S1b for M01. Generally, the firstorder Markovian model works well for OBCs that are studied in this work, and the probabilities POO and PEO are also listed in Table S1. Therefore, it is possible to generate a chain of ethylene−octene copolymers with the sequence distribution determined by the probabilities POO and PEO. An example is shown in Figure 1 for a model sequence distribution in M01, where the height of a bar denotes the length (number of monomer) of a continuous ethylene or octene unit. It is seen that the length of octene monomer is one in most of the units, which is close to the average sequence length of octene from Randall analysis. In contrast, the length of ethylene unit varies greatly from one monomer to tens of monomers. Statistics on the length distribution of ethylene can also give the average sequence length of ethylene. However, as denoted from the Randall’s analysis, the average sequence length of ethylene cannot be used to determine the content of hard segment and is not related to the phase behavior of OBC. To determine the hard block and soft block from the sequence distribution of monomers, a criterion needs to be defined first to differentiate two kinds of segments. Considering the low octene content in hard blocks making it easy to crystallize, the minimum chain length (lc, 40 C atoms or 20 ethylene monomers) to form 5 nm lamellar stem34 is regarded as the suitable critical parameter to define the hard block. The protocol to define the hard block is as follows: (1) Any ethylene sequence with continuous number of ethylene monomer larger than the critical length is a hard block. (2) Two neighboring ethylene sequences separated by a octene sequence with one or two octene monomers can form a hard block if the total length of two ethylene sequences is larger than the critical length and two ethylene sequences are long enough (>10 ethylene monomers). (3) If an ethylene sequence is long enough (>10 ethylene monomers) and is separated from a hard block only by one octene sequence with one or two octene monomers, such ethylene sequence should be included in the hard block. A classification of a part of OBC chain generated using first-order Markovian model is shown in Figure 1. Then the chain structure can be described by alternating hard blocks and soft blocks. Statistics can be made on the average octene

content in hard block and soft block and average length of hard block and soft block, from which the difference between the octene content in hard and soft block (ΔC8) and ratio between the average length of hard block and soft block (SLhard/SLsoft) can be obtained. All these information on different OBCs are also shown in Table 1. It is seen that ΔC8 is quite close in all OBCs studied here. Since the interaction between the hard block and soft block depends largely on the difference of octene content in two blocks, similar ΔC8 in these samples implies that the possible difference in phase behavior would result from the difference in the molecular weight and its distribution, instead of the interaction parameter between soft block and hard block. The melting and crystallization properties of OBCs are summarized in Table 2. Because of the different molecular weight and hard block content, there are obvious differences between these transition temperatures. The melting and crystallization temperature range for OBCs are within 106.0− 129.2 and 83.5−106.2 °C, respectively. The following investigation on mesophase separation in OBC melts will be above the melting range. It is seen that OBCs with similar hard block content have close crystallinity. If all the crystallization is ascribed to the hard block, the crystallinity in hard block can be estimated as 54−67 wt %, which is lower than the value (>90 wt %) of high-density polyethylene. This implies the hindrance of crystallization due to the incorporation of octene unit in hard segment, which is similar to that of linear low density polyethylene. It is also seen that although the melting point varies in OBC samples with similar crystallinity, the difference in the onset of crystallization temperature is more obvious. 3.2. Rheological Properties and Mesophase Separation. Rheology provides very useful methods to detect the microphase separation in diblock copolymers.19−21 The basic principle is to find the deviation from the reference scaling laws, which have been well established for homopolymer. The frequently used scaling laws include the dependence of characteristic rheological parameters (such as zero shear viscosity) on molecular weight and the terminal behavior of dynamic moduli. Therefore, the problem to detect the phase separation in copolymer via rheology turns into checking the applicability and sensitivity of the available scaling laws. 3.2.1. Shear Viscosity. For linear flexible polymer, both experimental and theoretical works have shown the power law dependence of zero shear-rate viscosity (η0) on the weightaveraged molecular weight (Mw) with the power law exponent about 3.4−3.6.40 Deviation from such power law scaling has been successfully applied to analyze very low amount of longchain branching.41,42 It is expected that this method could be used for verifying the homogeneity of the linear multiblock OBCs; i.e., in homogeneous states, all differences in viscosity should be due to different overall molecular weight. To determine the zero shear viscosity, frequency sweeps were 810


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than in viscosity, so the viscosity scaling law can only be used to evaluate the strong mesophase separation. 3.2.2. Failure of Time−Temperature Superposition. In principle, the rheological response of a material has contributions from different components or phases in multiple components or multiphase system. Then, the success of TTS implies either the temperature dependences of these stress contributions are similar or the contribution from an abnormal temperature dependence is weak. More importantly, rheological measurements usually correspond to longer relaxation (or larger heterogeneity) as compared to other methods like dielectric measurement.44 Therefore, although the success of TTS cannot guarantee the homogeneity of materials, its failure can indicate the appearance of inhomogeneity. Such inhomogeneity can or cannot develop into phase separation, which is strongly related to the interaction between polymer chains (or segments) and the (dynamic) asymmetry between polymer chains (or segments). As for OBCs, soft block and hard block are two types of segments that contribute to its rheological functions. The temperature dependences of these contributions are hardly differentiable since two kinds of blocks are connected by chemical bonds in a polymer chain. Therefore, the failure of TTS in OBCs can be attributed to the appearance of additional contribution, possibly from the mesophase-separated domains. Actually, most of previous studies concern diblock or triblock copolymers, whose linear viscoelastic properties are well correlated with its ordered morphology.45 Some recent work30 also tried to use the same correlation to infer the morphology in multiblock copolymers, although the morphology and chain conformation in diblock/ triblock copolymer and multiblock copolymer could be very different. However, the underlying assumption to determine the transition temperature in diblock/triblock copolymer and multiblock copolymer using the TTS principle are similar; i.e., the concentration fluctuation appeared during phase transition brings additional contribution to the dynamic moduli, and the temperature dependence of such contribution differs from that of pure polymer. The only problem is whether such frequency dependency is sensitive enough to the variation of state. In fact, for spherical nanostructures the drop in G′ or failure of superposition at the MST can be rather subtle.22 Considering spherical morphology is the most probable one for OBC with low octene content and low fraction of hard segment, that is why phase transition is hard to observe and less studied especially in commercially available samples. Then the problem becomes how to enhance the sensitivity to judge the failure of TTS. The dynamic moduli of OBCs with similar hard block content (M01, M02, and M03) under different temperatures are shown in Figure 3. Dynamic moduli for other samples can be found in the Supporting Information (Figure S3). All the data have been shifted to the reference temperature Tref = 135 °C. The vertical shift factor varies little over the temperature range and can be neglected, and the horizontal shift factor aT is determined by supposing the elastic modulus and loss modulus at higher frequencies to obtain the master curve. The TTS principle works successfully for both G′ and G″ in the experimental temperature range for M01, which has the lowest molecular weight among three OBC samples. The terminal slope of 2 for storage modulus and 1 for loss modulus in the log−log plot is seen clearly, which implies that M01 resembles the typical viscoelastic fluid in spite of its multiblock structure and the polydispersity in molecular weight.40 Both the

performed for different OBCs under different temperatures. The zero shear viscosity was determined by fitting the frequency-dependent complex viscosity using the Carreau− Yasuda model43 (Figure S2). A plateau region is reached at low frequency for all OBCs except M03 and L02, which is ascribed to the slow relaxation process and the terminal behavior has not been reached during frequency sweep down to 0.01 rad/s. The complex viscosity at 0.01 rad/s were taken for M03 and L02 as an approximation of the zero shear viscosity, while the true η0 of these two samples should be higher. The fitted η0 from the Carreau−Yasuda model for the four low-Mw OBCs (M01, M02, L01, H01) and the η0 (0.01 rad/s) for the high-Mw OBCs (L02, M03) are plotted against Mw in Figure 2. The relationship between η0 and molecular weight for

Figure 2. Zero shear viscosity vs molecular weight for OBCs at various temperatures. The hollow symbols denote the zero shear viscosity of OBCs, while the solid stars are the contribution from fast mode by fitting using the Cole−Cole function. The straight lines denote the apparent linear fit in log−log scale for OBCs except L02 and M03. Inset: dependence of power law exponent n in η0 ∝ Mwn on temperature, where scatter symbols are obtained from fitting using the zero shear viscosity of M01, H01, M02, and L01. The solid line is drawn to guide eyes. The dashed lines denotes the fitting result using the fast mode contribution.

the four low-Mw OBCs can be well described by a power law, η0 ∝ Mwn, where n decreases slightly from 3.51 to a constant around 3.34 as temperature increases from 135 to 195 °C (inset of Figure 2). Such ranges of power law exponent agree quite well with the classical scaling for linear polymers, which implies the homogeneous state of four OBCs. The weak temperature dependence of the power law exponent and a constant value at high temperature for four low-Mw OBCs also implies the homogeneous state at high temperature, although the η0−Mw relation is not sensitive enough to be unambiguously used for the detection of weak mesophase separation of the low-Mw OBCs. Moreover, η0 of linear ethylene/octene multiblock copolymers is independent of the hard block fraction and the total octene content at a fixed weight-average molecular weight. It can also be seen that the deviation of L02 from such scaling law is weak, but it becomes much evident for M03 over a wide temperature range. Considering the linear topology of molecules of these OBCs, the deviation in the scaling law of zero shear viscosity implies strong mesophase separation even at high temperatures for M03 and L02. As will be shown later, mesophase separation brings more changes in elastic properties 811


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time scale of frequency sweep. The low molecular weight of M01 may account for this since it is well documented that the molecular weight needs to exceed a threshold molecular weight to induce microphase separation in a block copolymer.31,46 For L01, the low fraction of hard segment requires much higher molecular weight to cause evident phase separation according to the classical phase diagram of diblock copolymer. As molecular weight increases, failure of TTS at low frequency is obvious in G′. For M02, the typical terminal behavior is still seen at high temperatures, while slight deviation of G′ at low frequency starts to appear when the temperature is lower than 165 °C. However, for M03 with the largest molecular weight among three OBCs, the deviation from slope 2 in terminal regime of storage modulus is obvious at high temperatures, although there is no distinct failure of TTS at the same temperature range. Evident failure of TTS is seen below 175 °C for M03 from G′. Failure of TTS as the molecular weight increases is also found in L02 sample (see Figure S3). In addition, the failure of TTS can also be seen if the fraction of hard segment increases while molecular weight is kept unchanged, which is the case of H01 as compared with L01 (see Figure S3). Generally, the deviations in G′ are small but distinguishable in M02 and M03 samples (and also L02 and H01 samples), although the exact transition temperature is hard

Figure 3. Shifted storage and loss moduli from SAOS for OBCs M01 (a), M02 (b), and M03 (c). Only the horizontal shift factor is determined by supposing the elastic modulus and loss modulus at higher frequencies, and the reference temperature is 135 °C.

appearance of typical terminal behavior and the success of TTS imply that mesophase transition is unlikely to happen or extremely weak in M01 (and also L01, see Figure S3) in the

Figure 4. Shifted Cole−Cole plots for OBCs (a) L01 and L02, (b) M01, M02 and M03, and (c) H01. The horizontal shift factor aT is used to shift both η′ and η″ to obtain a Cole−Cole master curve for each OBC at the reference temperature of 135 °C. η0homo is the zero shear viscosity of the corresponding polymer at the homogeneous state, which is calculated using the η0−Mw correlation at 135 °C (Figure 2). The shifted Cole−Cole plots for L01, M01, and H01 under homogeneous state are compared in (d). 812


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The shifted Cole−Cole plots at different temperatures for six OBCs are shown in Figure 4. First, the horizontal shift factor aT is used to shift both η′ and η″ for each OBC sample. Above a certain temperature, i.e., in the homogeneous region for OBCs, a master curve is obtained after shifting, while below this temperature, that is, in heterogeneous regime, the deviation from master curve will appear at large η′ (low frequency). Then, the shifted Cole−Cole plots of the six OBCs are further normalized by the zero shear viscosity (η0homo) at the homogeneous state of polymer with the same molecular weight, which is calculated from the η0−Mw relation at 135 °C (Figure 2). For clarity, the shifted Cole−Cole plots are divided into three groups in Figure 4 according to their hard block content. Different forms of Cole−Cole plots, indicating different temperature-dependent mesophase structure or the varying extent of mesophase separation, can be seen in Figure 4. For L01 and M01, the shifted Cole−Cole plots at various temperatures overlapped well except a very slight deviation from the master curve in L01 at 135 °C, indicating weaker mesophase separation (L01) or a homogeneous state (M01). For M02 and H01, the shifted Cole−Cole plots at high temperatures superimpose perfectly and form a semicircular arc, but a certain degree of deviation from the master curve is clearly seen at low temperatures. The transition happens at 145−155 °C for H01 and 155−165 °C for M02. For L02 and M03, significant deviation from the semicircle starting from the maximum of η″/(aTη0homo) can be seen as the temperature decreases. In contrast to the dynamic moduli in Figure 3, the shifted Cole−Cole plots always fail to superimpose for L02 and M03 within all the experimental temperature range, indicating that the homogeneity of L02 and M03 at higher temperatures cannot be reached in the experimental temperature range. It is interesting to see that the Cole−Cole plots of M01 and M02 superimpose at high temperature (the homogeneous state, Figure 4b) after the correction using horizontal shifting factor and η0homo, which removes the influence of temperature and molecular weight. It suggests that the relaxation in homogeneous state is similar for OBCs with similar hard block content. Then, we suppose that such superimposed Cole−Cole plot also represents the homogeneous state of M03 (also L02 in Figure 4a), which means that the phase transition temperature of M03 (and L02) would be much higher than the tested temperature here. Moreover, it is also seen that the shifted Cole−Cole plot in homogeneous state is almost identical when the hard block content is slow (L01 and M01 in Figure 4d), but deviation appears in OBC with high hard block content (H01). That means the hard block content does not affect the relaxation behavior of OBC in homogeneous state unless it is large enough. Both Havriliak−Negami (H−N) function53 and Cole−Cole (C−C) function54 have been suggested to describe the linear viscoelastic mechanical properties of molten polymers. Compared with the C−C function, the H−N function with four parameters have more flexibility in reproducing the asymmetric relaxation spectra. However, the increase of parameter numbers sometimes may cause the nonuniqueness in fitting the parameters. Thus, we adopt the sum of C−C function to fit the data.

to determine. The fact that TTS fails via either increasing the hard block fraction from L01 to H01 or increasing the molecular weight from M01 to M03 is reminiscent of the similar effects in microphase separation of diblock or triblock copolymer, which implies that the failures of TTS in OBCs can be related to the phase transitions. In most diblock copolymers, microphase separation is also order−disorder transition; i.e., long-range order is essential to exhibit terminal behavior with G′∝ ωn (n = 0 for cubic, 1/3 for cylinder, and 1/2 for lamellae).19,45 It is observed that the mesophase-separated OBCs do not exhibit the characteristic values of the ordered phases, with the similar terminal behavior of n = 1−1.5 at the lower temperature of 135 °C. This may indicate that the lack of long-range order in OBC melt. In a kinetic investigation of sphere-forming diblock and triblock copolymers by Adams et al.,21 they found that disorder−order transition may go through some intermediate states which are lack of long-range order but have evident concentration fluctuation. Apparently, such a state is metastable in diblock and triblock copolymer and transition to an ordered state happens quickly, while such a state in OBCs is rather stable possibly due to the broader sequence distribution of hard segments and wide distribution in molecular weight. Moreover, a theoretical prediction made by Matsen is that there are regions of coexisting phases as polydispersity increase to a critical value in diblock copolymer.10 Experimental works by Noro and Matsushita et al.47,48 have found macrophase separation in blends of near monodisperse diblock copolymers that differ in molecular weight and/or composition, but the overall molecular weight distribution are not continuous or unimodal. So far, no systematic work has been reported to demonstrate definitely the occurrence of macrophase separation in diblock copolymer with a unimodal molecular weight distribution. Here, the OBC has a unimodal and continuous molecular weight distribution,11 and the likelihood of macrophase separation is excluded since the change in the storage modulus of OBCs at low frequency over 12 h at 135 °C is negligible. Therefore, the phase transition in OBCs is ascribed to the mesophase transition. Although the shifting in dynamic moduli is useful to judge the failure of TTS, the deviation from master curve is rather weak especially in weak mesophase-separated samples. Other methods using loss tangent,49 Han plot,22 and vGP plot50 had also been suggested to check the validity of TTS. Here we adopted the shifted Cole−Cole plot, which had been proved to be sensitive to the liquid−liquid phase separation of polymer blends.25,26 The shifted Cole−Cole plot (plotting η″/aT vs η′/ aT, where η″ = G′/ω and η′ = G″/ω) utilizes dynamic viscosities instead of dynamic moduli. The advantages of the plots are that the frequency dependence has been eliminated, and the aforementioned weak variation in G′ at low frequency can be amplified through dividing it by the frequency. Plotting the shifted dynamic viscosities (η″/aT vs η′/aT) instead of the original dynamic viscosities (η″ vs η′) eliminates the effect of temperature. Then, the shifted Cole−Cole plots under different temperatures will collapse into a single curve if the TTS principle works. For polymer melts with unimodal distribution of molecular weight, the Cole−Cole plot is a half circle, but it displays two circular arcs in some systems like pure polymer with bimodal distribution of molecular weight,51 long chain branching polymer,52 phase-separated polymer blends,26 etc., which were interpreted by the simultaneous occurrence of two processes with largely different relaxation times.

η* =

∑ j = fast,slow

813

η0, j 1 + (iωτj)αj

(1)


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Figure 5. Shifted Cole−Cole plots for OBCs. (a) M02 at 135 and 195 °C. Solid lines denote the fitting curve of one-mode C−C function (195 °C) and two-mode C−C function (135 °C). (b) M03 at 135 and 215 °C. Solid lines denote the fitting curve of two-mode C−C function (135 and 215 °C). An example of the fitting result using two-mode C−C function for M03 at 135 °C is shown in (d) with the dash-dotted lines and dashed lines representing the slow mode and fast mode contributions to η′ and η″, respectively.

Here, η0,j, τj, and αj are characteristic viscosity, relaxation time, and symmetric broadening parameter for j mode. For OBCs in homogeneous state, only the fast mode is used, which represents the relaxation of linear flexible chain. The single mode C−C function has been used successfully to fit all the homogeneous state data. The slow mode is added in the heterogeneous state of OBC, which represents the relaxation behavior of concentration fluctuation or phase-separated domains. Typical fitting results in Cole−Cole plot are shown in Figures 5a and 5b for M02 and M03, respectively. Two mode C−C model can fit the data quite well. The contributions of fast mode and slow mode to η′ and η″ can be seen more clearly in Figure 5c for M03 at 135 °C, where two relaxation modes are well resolved due to the big difference in the relaxation time. The fitted characteristic viscosity and relaxation time from the C−C function are shown in Figures 6a and 6b, respectively. For OBCs in homogeneous state, where no failure of TTS is observed in both dynamic moduli and shifted Cole−Cole plot,

η0,fast/aT are found to be independent of temperature. This is seen for M01 in the whole temperature range and for M02 at high temperature, which indicates a simple thermorheological behavior of M01 and M02 under such a temperature range. For M02, when the temperature goes below about 160 °C, the slow mode relaxation can be identified, whose relaxation time is around 10 times that in the fast process (Figure 6b). As the temperature decreases, η0,fast/aT decreases and η0,slow/aT increases, while both τfast/aT and τslow/aT decrease. The former can be regarded as that more OBC molecules in homogeneous state are transformed into heterogeneous state, and such transition continues as temperature decreases. However, the latter means the weaker dependence of relaxation times (τfast and τslow) in the phase-separated state than in the homogeneous state. In contrast, the fast mode viscosity η0,fast/aT and relaxation time τfast/aT of M03 keep constant in the whole temperature range, while the slow mode viscosity η0,slow/aT and relaxation time τslow/aT increase as temperature decreases, which implies a stronger temperature dependence of the slow mode parameters. This implies that the phase transition in M03 as temperature decreases is not the transform from homogeneous part to heterogeneous part. Instead, it looks more like the evolution of heterogeneous domain itself. Actually, if the fast mode viscosity η0,fast is plotted versus molecular weight (solid stars in Figure 2), the power law exponent is obtained around 3.2, which is shown as the dashed line in the inset of Figure 2. Such a value is smaller than the constant n reached at high temperature. The main reason is the relatively small η0,fast of L02 and M03. The interplay of fast mode and slow mode relaxation may account for such complexity in the phase transition of M03. Although the reason to cause the difference in mesophase transition of OBCs is still unclear, it is supposed to be strongly correlated with the intrachain and interchain block size distribution and polydispersity in molecular weight. 3.2.3. Temperature Ramp and 2D Mechanical Correlation Spectrum. TMST is regarded as being a very important processing variable for block copolymer. From the TTS principle and Cole−Cole plots, only the temperature range of transition can be determined, while a specific TMST for OBCs could not be quantified. Another rheological method to

Figure 6. Dependence of characteristic viscosity (a) and relaxation time (b) on temperature for OBCs with similar hard block content: M01 (blue), M02 (red), and M03 (black). Solid symbols denote the fast mode, and open symbols denote the slow mode. The dashed lines are drawn to guide the eyes. 814


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determine the TMST of a block copolymer is to perform isochronal dynamic temperature ramp experiments, which has been used successfully in symmetric monodisperse diblock copolymers with lamellar morphology to locate the order− disorder transition (ODT). Usually, a sharp drop or discontinuity in the elastic modulus G′ can indicate the change from an ordered phase to a disordered phase.20 However, the sharp drop in G′ at the MST could be lost for polydisperse diblock systems with lamellar morphology.55 Instead, a gradual transition is also observed in polydisperse multiblock systems.30 Examples of temperature-dependent storage modulus for M02 and H01 are shown in Figure 7, where the transition range

mechanical correlation spectra (2D-MCS), which is an adaptation of generalized 2D correlation spectroscopy.57 In a dynamic oscillatory shear experiment, supposing the input is the sinusoidal strain signal, the output stress signal is σ(v,t), where t is time ranging from tmin to tmax and v could be temperature, frequency, or strain amplitude. In a dynamic temperature ramp test, the frequency and strain amplitude are fixed; v denotes temperature. The two-dimensional correlation spectrum can be defined through a cross-correlation function54 X(v1 , v2) = ⟨σ(v1 , t ), σ(v2 , t )⟩ =

∫0

∞

1 × π (tmax − tmin)

σ (̃ v1 , ω)σ * ̃ (v2 , ω) dω

(2)

The symbol ⟨ ⟩ denotes for a cross-correlation function. The term σ̃(v,ω) is the forward Fourier transform of the stress signal σ(v,t) measured at a given spectral variable v with respect to time t. ∞

σ (̃ v , ω) =

∫−∞ σ(̃ v , t )e−iωt dt

(3)

The term σ̃(v,ω) is the complex conjugate of the corresponding forward Fourier transform. The intensity of X(ν1,ν2) represents the quantitative measure of a comparative similarity or dissimilarity of stress wave σ(ν,t) measured at two different spectral variables, ν1 and ν2, during a fixed interval (one period). The two-dimensional correlation spectrum can be decomposed into synchronous intensity Φ(v1,v2) and asynchronous intensity Ψ(v1,v2) as X(v1 , v2) = Φ(v1 , v2) + i Ψ(v1 , v2)

Figure 7. Storage modulus G′ of OBCs as a function of temperature. The angular frequency is 0.1 rad/s, and the ramp rate is 0.5 °C/min. The solid lines are drawn to guide the eyes. The transition temperature range determined from Cole−Cole plots and the deviation temperatures representing the start deviation of G′ from the low temperature trend are denoted by arrows.

(4)

which represents the similarity and dissimilarity between two separate stresses measured at different spectral variables, respectively. The general method to calculate the 2D spectrum has been suggested by Noda.57 For oscillatory data, if the stress can be expressed as a Fourier series59−61 ∞

from shifted Cole−Cole plots are denoted by arrows. Slight gradual change in the slope is seen, where the deviation points are also marked by arrows. Obviously, such deviation temperatures are higher than the ranges obtained from shifted Cole−Cole plots. This delayed effect can be related to the less sensitivity of storage modulus in detecting phase transitions for polydisperse systems, which represents only one aspect of the viscoelastic responses to the strain input. Such behavior resembles the liquid−liquid phase separation in blends with weak dynamic asymmetry,56 and it is really difficult to define the transition temperature from the temperature dependence of storage modulus. The absence of a sharp transition from homogeneous state to composition fluctuations and further MST could be attributed to the weak dynamic asymmetry between soft block and hard block. Actually, all previous methods to determine the phase transition utilizing either storage modulus or phase angle, which represent only one aspect of the viscoelastic responses to the strain input. In oscillatory shear, the waveform of the signal contains all the information on viscoelastic responses, including amplitude, phase lag, and even deviation from sinusoidal shape. Direct comparisons on waveforms under different temperatures are believed to contain the complete information on the difference in structures. One of the simplest method is the cross-correlation, which has been widely used in two-dimensional spectrum.57,58 Here, we suggest to use the 2D

σ (v , t ) =

∑ Ak (v) sin[kωt + βk(v)] k=1

(5)

with Ak and βk the amplitude and phase angle at the kth harmonic, respectively. For linear viscoelastic response, only the first harmonic exists. Although the temperature ramp is often performed under small amplitude, it is important to include the nonlinear contribution (high harmonics) in consideration of possible coupling between phase transition and flow near MST. 2D spectra can be calculated for oscillatory stresses as ∞

Φ(v1 , v2) =

∑ k=1 ∞

Ψ(v1 , v2) =

∑ k=1

1 Ak (v1)Ak (v2) cos[βk (v1) − βk (v2)] 2

(6)

1 Ak (v1)Ak (v2) sin[βk (v1) − βk (v2)] 2

(7)

It is seen that both the amplitude and the difference in the phase angle influence the spectrum Φ(v1,v2) and Ψ(v1,v2). Moreover, if there is certain nonlinearity in the stress signal, the contributions from high harmonics are cumulative and there is no cooperative contribution from different harmonics. In practice, the 2D correlation spectra can be obtained as follows. First, the waveforms of stress signal (under strain controlled condition) are recorded during parameter sweep (or ramp). Second, Fourier transform is applied on each waveform with 815


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Figure 8. Synchronous (a) and asynchronous (b) 2D correlation spectra of temperature ramp for OBCs H01 from 125 to 195 °C.

Figure 9. (a) The normalized asynchronous 2D correlation intensity Ψ̃n(T,T0) as a function of temperature for OBCs. (b) Ψ̃n(T,T0)/aT(1 − aT) versus temperature for H01. TMST is determined as the deviation from the constant value as temperature decreases. Dependence of Ψ̃n(T,T0)/aT(1 − aT) on temperature of all OBC samples is shown in the inset.

different parameter v. The intensities Ak and phase angle βk can be obtained at different parameter v. Finally, the 2D spectra can be calculated using eqs 6 and 7. Note that the Fourier analysis on the waveform is important especially in the process of phase transition, which can include any coupling effect between oscillatory shear and the concentration fluctuation. Figure 8 shows the typical synchronous and asynchronous 2D correlation spectrum for H01. A gradual decrease in the synchronous spectrum is seen as temperature increases, which implies that similarity between the stress waveforms at different temperatures decreases. There is no obvious transition can be observed. In contrast, asynchronous spectrum exhibits nonmonotonic change, where a bump is clearly seen. When we plot the asynchronous 2D correlation intensity Ψ (T, 125 °C) versus the temperature, T, it is interesting to observe the transition peaks for all OBCs in Figure 9a. Since the correlation intensity is proportional to the stress amplitude, which is related to the molecular weight of material, the asynchronous correlation intensity Ψ̃n(T,T0) in Figure 9a has been normalized by its maximum. It is seen in Figure 9a that Ψ̃n(T,T0) increases as T increases at low temperature. This is ascribed to the temperature effect on the viscoelastic properties. In the simplest case where only linear viscoelasticity is considered, the asynchronous 2D correlation intensity can be calculated from eq 7 as

Ψ(T , T0 ; ω) =

1 [G″(T , ω)G′(T0 , ω) − G′(T , ω)G″(T0 , ω)] 2

(8)

Suppose the angular frequency is low enough and lies in the terminal regime, dynamic moduli satisfy G′ = η0λwω2 and G′ = η0ω with η0 and λw representing the zero-shear viscosity and terminal relaxation time, respectively. Then, eq 8 can be reformulated as Ψ(T , T0 ; ω) =

1 3 2 ω η0 (T0)λw(T0)aT (1 − aT ) 2

(9)

where aT = η0(T)/η0(T0) = λw(T)/λw(T0) is the horizontal shifting factor and T0 is the reference temperature. The shifting factor is positive and smaller than 1 if T > T0, which implies the asynchronous correlation intensity Ψ(T,T0;ω) is positive. It can be seen from eq 9 that Ψ(T,T0;ω) is a parabolic function of aT, and has a maximum when aT = 0.5, which means temperature effect alone can cause a peak in asynchronous correlation intensity. This implies that we cannot correlate the peak temperature directly to any transition in materials if transition peaks appear near aT = 0.5. In fact, it is found that all OBCs used in this study exhibit similar temperature dependence of horizontal shifting factor aT, which is 0.5 around 150 °C when the reference temperature is 125 °C. To eliminate the effect of temperature, we plot ψ(T,T0;ω) = Ψ̃n(T,T0)/aT(1 − aT) in 816


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including the fluctuation corrections. By utilizing the above results of (χN)ODT in symmetric diblocks and (χN)ODT = 7.568 in monodisperse symmetric multiblocks, Li et al.15 made an approximation to determine the value of (χN) ODT in polydisperse symmetric multiblock OBCs to be 3. However, it is difficult for current mean-field theories to predict microphase separation temperatures for block copolymers with sphere-forming morphology, when their values of N are on the order of 103 usually encountered in practice.69 The OBCs in this study are highly asymmetric multiblock copolymers with low value of N and polydispersity in block lengths. It is very necessary to develop a theory that can predict the phase behaviors for such systems. Here, we are trying a preliminary work in constructing a phase diagram from experiments, which is expected to give some insights to further work on mean-field theory. In order to construct this phase diagram, we calculate χN of multiblock OBCs, where χ is determined by the correlation with octene content from the experimental results of Reichart.33 The values of χN calculated are listed in Table 1. Two reference phase diagrams are also shown in Figure 10 according to Burger et al.5 for N = 1 × 106 . As the PDI increase

Figure 9b. It is expected that the asynchronous correlation intensity ψ(T,T0;ω) should be independent of temperature T when the material is in homogeneous state. It is seen that four OBC samples, namely L01, M01, M02, and H01, exhibit constant ψ(T,T0;ω) at high temperature, denoting a homogeneous state. As temperature decreases, the deviation from constant value appears which represents the start of mesophase separation. The deviation from the constant value at high temperature can be specified as the mesophase separation temperature. In contrast, the other two samples, L02 and M03, show monotonically increase of ψ(T,T0;ω) with temperature. This is related to the heterogeneous state of these samples in the full temperature range as well as the nonterminal frequency (0.1 rad/s) adopted in temperature ramp. However, since the peak in Ψ(T,T0;ω) induced by temperature variation appears near 150 °C for all OBCs (aT = 0.5), which is far from that observed for L02 and M03 in Figure 9a, the peaks near 190 °C for L02 and M03 are supposed to be correlated with certain phase transition. The transition temperatures of OBCs are listed in Table 2. It should be noticed that two different methods are used to determine the transition temperature depending on whether the temperature effect will influence the peaks in Ψ̃n(T,T0;ω)− T curve. The transition temperatures can be determined from the deviation from the constant high temperature value as 154.0 and 159.7 °C for H01 and M02, respectively, which are in consistent with the failure range of TTS. It is found that L02 and M03 show transition peaks as 187.0 and 192.4 °C, within the weaker transition range as seen in the failure of TTS in storage modulus. Transition peaks to homogeneous state might exist as temperature increases, but it is difficult to determine them since it could be much higher than the initial degradation temperatures of OBCs. In addition, it is also seen that even L01 and M01 exhibit transition peaks in the asynchronous spectrum, which implies both copolymers can undergo mesophase separation as temperature decreases. For L01, the trace of MST is also found in the shifted Cole−Cole curve, while frequency sweep tests under different temperatures show success of TTS. For M01, tests of TTS using G′ and shifted Cole−Cole plot show no sign of phase transition. It is possible that the mechanical contrast before and after mesophase separation of M01 is so weak that the neither moduli nor phase angle alone is sensitive enough to show the transition. Other evidence of mesophase separation in M01 will be shown below. 3.3. Phase Diagram. Up to the present, the theoretical work on binary multiblock copolymers was mainly focused on two important classes: regular and correlated random copolymers (the simplest one is that the units distribution in the polymer chains can be described by the Markovian firstorder statistics).62,63 By using the mean-field theory methods, the phase diagrams have been constructed for melts of correlated random multiblock copolymers.64,65 In the past decades, considerable theoretical and experimental studies have been devoted to the effect of polydispersity on AB diblock copolymers, but publications on polydisperse multiblock copolymers are still relatively scarce.6,66 In early studies, Leibler et al.31 have predicted that the critical value of χN are required to be greater than 10.5 to display an order−disorder transition (ODT) in monodisperse diblock copolymers with equal volume fraction. Theoretical work by Burger et al.5 has shown that this minimum χN would decrease to 4 as the polydispersity increase from 1.0 to 2.0 in both blocks, based on the framework of Fredrickson and Helfand67

Figure 10. An illustration of (χN)MST versus volume fraction of hard block (f hard block) phase diagram for OBC multiblock copolymers with PDI = 2.0. Points are plotted against χN at a reference temperature of 167 °C. Two phase diagrams for diblock copolymer melts with N = 1 × 106 were selected as references.5,31 The black line represents the phase diagram at PDI = 1.0, and the red lines represents the phase diagram at PDI = 2.0.

in diblock copolymers, the values of (χN)MST decrease dramatically, and the regions for microphase-separated melts in phase diagram increase. In our experiments, L02 and M03 samples are heterogeneous while other samples are homogeneous at 167 °C according to the above rheological results. Therefore, the phase boundary should lie between L02, M03, and other OBCs, as shown by the dashed line in Figure 10. The critical χN for mesophase separation of OBCs with equal volume in hard and soft blocks can be approaching to 3.0, in accordance with Li’s estimation.15 Obviously, increasing the polydispersity in diblock can greatly decrease the critical χN from 10.5 to about 4, and increase in the block number from diblock to multiblock can further decrease the critical χN to 817


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Figure 11. Polarized optical micrographs of OBCs (a) M01, (b) M02, and (b) M03. The scale bar is 50 μm.

starts from the hard block-rich domains in the microphaseseparated sample, and the shortage of hard segments in soft block-rich domains makes it difficult for the growth of spherulites, which exhibit irregular distribution of spherulites as seen in M03. In contrast, nucleation of crystal can happen in homogeneous bulk, and spherulites grow without the constraints of phase-separated domains, which makes the spherulites easily grow and becomes space-filling, as seen in M01. Furthermore, it is interesting to observe that the long period decreases as the molecular weight increases in OBC samples with similar hard block content (Table 2). This is inconsistent with linear polymers where long periods increase with the molecular weight.75 Since the melting point is not so different between M01 and M02, the obvious difference in long period could rely on the difference in the thickness of amorphous phase, which is expected to be larger in homogeneous M01 due to the large possibility to retain soft block between crystal lamellae. The different long period in OBC samples with similar hard block content manifests the different extent of microphase separation in these samples. The OBCs may exhibit the time-dependent mesophase separation evolution since the phase-separated morphology is probably not in thermodynamic equilibrium. Moreover, it has been shown by the 2D mechanical correlation spectrum that M01 can exhibit trace of mesophase separation. However, the cyclic frequency sweeps on M01 and M03 at 135 °C for 12 h cannot show the development of mesophase separation. Then, DSC scans were performed to see if phase transition would affect the subsequent crystallization. Two scans of the nonisothermal crystallization for different OBCs were carried out: the first scan starts from 200 to 0 °C at a cooling rate of 10 °C/min, while the second scan starts from 200 to 135 °C at a cooling rate of 10 °C/min and then anneals at 135 °C for 12 h before cooling to 0 °C at the same cooling rate. The crystallization behaviors for M01 and M03 with and without annealing are illustrated in Figure 12. After a long time annealing, the crystallization onset temperature becomes higher and the exothermic peak shifts to lower temperature in M01, while a much weaker shift of exothermic peak can be found in M03. These may be related to the mesophase separation kinetics of the two OBCs with different mesophase structures. In the previous sections, the mesophase separation of M01 cannot be judged from the TTS results but is detectable from the 2D correlation rheological spectrum. Here, from the DSC results, the initial acceleration of crystallization of M01 is ascribed to easier nucleation in mesophase-separated hard segments-rich domains, while the latter slowdown of the crystallization (shift of Tc to lower temperature) can be regarded as the hindrance of spherulites growth by the phaseseparated domains. For M03, only a very weak shift of the exothermic peak is seen, while the initial crystallization speed is not affected by annealing. This is ascribed to the extremely slow

about 3. Moreover, as compared to the decrease of (χN)crit in polydisperse multiblock copolymer, the decrease of χN(MST) at low f hard block is more significant. Actually, one can find the dependence of χN(MST) on low f hard block becomes weaker as PDI increases in diblock copolymer, and such dependence becomes much weaker in polydisperse multiblock copolymer. It means that mesophase separation may happen readily in polydisperse multiblock copolymer at low fraction of one type of segments by either a slight increase in molecular weight or the decrease in temperature as compared to diblock copolymer. It should be stressed about the difference between the phase transition in OBCs and that in diblock copolymer. The main difference is that the disorder−order transition in diblock copolymer is hardly observed in OBCs, whose transition is denoted as the mesophase separation. Actually, it is difficult to confirm the capability of multiblock random copolymer for ordering, probably due to the extremely long time to reach the ordered state. Such a phenomenon has been proved by a simulation study on Markovian AB multiblock copolymer melts,70 where microemulsion-like microstructures without long-range order are formed by fluctuations whose amplitude increases in proportion to the squared number of blocks in a chain and in inverse proportion to the average block length. It was assumed that the microemulsions were not at equilibrium and that, in longer numerical experiments, the melt would be further ordered. In our experiments, the phase-separated morphology of OBCs in this study is spherical even for H01 with the hard block content nearly 40% (Figure S4 in Supporting Information). Random distributed spheres are observed in sample with a long time annealing in heterogeneous state. Ordering has not been observed in our experiments and also in the literature for polydisperse multiblock copolymer.71,72 3.4. Mesophase Separation and Crystallization. In semicrystalline OBCs, mesophase separation and crystallization always coexist and complete with each other, and the solid state could be a relative reflection of the melt structure.17 Polarized optical micrographs in Figure 11 show the difference in crystalline morphology of the OBC with similar hard block content (and also similar crystallinity): M01, M02, and M03. Space-filling spherulites are observed in all three samples, and M01 exhibits the largest spherulites size of them. With the molecular weight increase, the average spherulites diameter decrease from around 38 μm (M01) to around 12 μm (M03). Such decrease in the spherulite size could be partially attributed to the slower crystallization speed in M03 due to its larger molecular weight.73,74 However, the distribution of spherulite size become broader from M01 to M03, and M03 shows the most irregularly developed spherulites. This could be seen as an evidence to demonstrate that the stronger microphase separation in M03 melts has some influence on subsequent formation of crystal lamella structure. In fact, the crystallization 818


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crystallization kinetics, which proves the power of the 2D rheological correlation spectrum to detect weak phase transition.

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ASSOCIATED CONTENT

S Supporting Information *

Typical 13C NMR spectrum for OBC M01 and the detailed molecular parameters of OBCs calculated from the first-order Markovian model, the master curves of the dynamic viscosity function for OBCs, and the method to determine the zero shear viscosity for OBCs; the mesophase separation characterization by atomic force microscopy (AFM) and the discussion of the structure for OBC H01. This material is available free of charge via the Internet at http://pubs.acs.org.

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Figure 12. Nonisothermal crystallization of OBCs: (a) M01 and (b) M03. Solid lines denote the heat flow of direct cooling from 200 to 0 °C at a cooling rate of 10 °C/min, and the dashed lines denote the heat flow of cooling from 135 to 0 °C at a cooling rate of 10 °C/min after annealing at 135 °C for 12 h.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (W.Y.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the support from the National Natural Science Foundation of China (No. 50930002) and the National Basic Research Program of China (973 Program) 2011CB606005. W. Yu is supported by the Program for New Century Excellent Talents in University and the SMC project of Shanghai Jiao Tong University. The authors also thank beamline BL16B1 of Shanghai Synchrotron Radiation Facility for providing the beam time under Project No. 12SRBL16B11672.

evolution the phase-separated structure in M03 during annealing. The crystallization behaviors that altered by annealing indicate the difference in the mesophase separation of different OBC samples, which justifies the results from rheology. The interplay between mesophase separation and crystallization will be studied in detail in future work.

4. CONCLUSIONS In this work, the high-temperature melt structures of a series polydisperse multiblock OBCs with low ΔC8 were studied by rheological measurements. The mesophase separation can be evaluated by different rheological measurements with different sensitivities. The scaling law of zero shear viscosity−molecular weight still works well in the homogeneous state of OBC, and the deviation is obvious only in strongly phase-separated samples (L02 and M03 with the highest molecular weight). The terminal behavior of storage modulus and its dependence on temperature are adopted to check the failure of TTS. Although the deviation is not significant, the mesophase separation is believed to happen in two OBCs with intermediate molecular weight. The range of transition temperatures is further determined by the shifted Cole−Cole plot, which supplies further details about the transition from homogeneous state to heterogeneous state using the two-mode Cole−Cole function. Furthermore, the transition temperature is determined by the 2D mechanical correlation spectrum. Similar transitions can also be observed in low-molecular-weight OBCs (L01 and M01), which exhibit almost no failure of TTS in both dynamic modulus and shifted Cole−Cole. A phase diagram was then constructed based on the phase behavior of different OBCs. It implies that the critical N for phase transition in block copolymer can be as low as about 3.0 due to the polydispersity in molecular weight and multiblock chain structure. The mesophase separation behavior is further justified by AFM and its effect on crystallization is illustrated by optical microscopy and thermal analysis. The dependence of spherulites morphology and the long period on the molecular weight imply the different extent of mesophase separation in OBCs. Interestingly, annealing below the mesophase separation temperature for M01 has a discernible effect on the subsequent

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Mesophase Separation and Rheology of Olefin Multiblock

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