Smectic–Smectic Phase Segregation Occurring in Binary Mixtures of

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Smectic−Smectic Phase Segregation Occurring in Binary Mixtures of Long and Short Rigid-Rod Helical Polysilanes Itsuki Kato, Katsuhiko Sunahara, and Kento Okoshi* Department of Applied Chemistry and Bioscience, Chitose Institute of Science and Technology, 758-65 Bibi, Chitose, Hokkaido 066-8655, Japan

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S Supporting Information *

ABSTRACT: Small-angle X-ray scattering and atomic force microscopy were used to observe smectic−smectic phase segregation in binary mixtures of rigid-rod-like helical poly[ndecyl-(S)-2-methylbutylsilane] (PDMS) polymers with molecular-weight ratios of 4.82 and narrow molecular-weight distributions. Phase segregation is attributed to entropic effects as the homopolymers in the binary mixture differ only in molecular weight. Entropy-driven segregation in smectic phases was theoretically predicted in mixtures of rodlike particles with different lengths under high pressure. Binary mixtures of long and short PDMS with broader molecular-weight distributions, which do not form smectic phases, showed no such segregation, verifying that the driving force for segregation is the entropy gained through smectic-phase formation. The binary mixture of a long PDMS with a narrow molecular-weight distribution and a short PDMS with a broad molecular-weight distribution showed segregation of each component, indicating that the entropy gain of short-polymer-only smectic phase formation surpasses the loss of mixing entropy.

1. INTRODUCTION

However, these theoretical studies were performed without regarding positionally ordered phases such as the smectic phase. The first theoretical study on smectic phases formed by binary mixtures of rodlike particles of the same breadth but with different lengths was conducted by Koda and Kimura.13 Various smectic structures were predicted to appear with increasing length ratio to accommodate two smectic phases of incommensurate layer spacing.13,14 A strong tendency toward smectic−smectic (S−S) demixing at high pressure was later observed in binary systems with different lengths. The pressure−composition phase diagram also revealed that the required pressure for S−S demixing decreases with increasing length ratio.15−17 Likewise, S−S demixing was observed in binary systems with the same lengths but different breadths under sufficiently high pressure.18 In contrast, there are few experimental approaches that demonstrate these theoretical predictions. Itou and Teramoto experimentally observed isotropic−cholesteric−cholesteric triphasic equilibria in aqueous solutions of binary mixtures of rodlike polysaccharides (schizophyllan) with different molecular weights19,20 in a qualitative reproduction of Abe and Flory’s prediction.4 Colloidal dispersions of the rodlike mineral boehmite with bidispersed lengths were reported to show I− N−N equilibria.21 In addition, binary aqueous systems of rodlike fd viruses having bidispersed thicknesses through

Theoretical and computational studies performed on liquidcrystal (LC) phases formed by rodlike particles have successfully reproduced the most common LC phase behavior of columnar−smectic−nematic phases.1−3 These results are intuitively understood in light of the close packing of rigid bodies. Most studies have considered only hard-core repulsions between particles, but not attractions. This approach has been extended to binary mixtures of rodlike particles with different lengths and breadths, whose structural behavior was shown to be rich despite consisting of simple rodlike particles interacting through excluded-volume interactions. Previously, Abe and Flory predicted triphasic equilibria (two anisotropic phases and an isotropic phase) in athermal ternary systems of two rodlike particles with significantly different length-to-breadth ratios and a solvent, which showed pronounced fractionation between the two rodlike components.4 This first attempt was followed by a number of detailed studies on binary mixtures of thick and thin, or long and short, rodlike particle systems. The partitioning of binary mixtures of rodlike particles with sufficiently unequal lengths into coexisting isotropic−nematic (I−N), nematic−nematic (N−N), and isotropic−nematic− nematic (I−N−N) phases was reported to take place because of a competition between orientational entropy and the entropy of mixing.5−8 Similar I−N, N−N, and I−N−N demixings were found with sufficiently different breadths, which were attributed to the depletion effect; the pressure− composition phase diagram was subsequently elucidated.9−12 © XXXX American Chemical Society

Received: November 17, 2018 Revised: January 14, 2019

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DOI: 10.1021/acs.macromol.8b02462 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Schematic illustration of S−S demixing in a binary mixture of PDMS with a narrow molecular-weight distribution and a large molecularweight ratio. and methanol as precipitants to obtain samples with different molecular weights and narrow molecular-weight distributions, as determined by SEC calibrated with polystyrene standards (Showa Denko). Binary mixtures for AFM were prepared by solution mixing in chloroform at designated mixing ratios followed by solution casting onto glass substrates and the gradual evaporation of the solvent under saturated chloroform vapor. Samples for SAXS experiments were prepared by casting the chloroform solution onto a polytetrafluoroethylene substrate in the same manner and placing them in glass capillary tubes for X-ray analysis. Instruments. SEC was performed using a LabSolutions GPC system (Shimadzu, Kyoto, Japan) fitted with two GPC K-805L columns (Showa Denko, Tokyo) with chloroform as the eluent at 40 °C at a flow rate of 1 mL/min. SAXS experiments were carried out at the Institute of Materials Structure Science, Tsukuba, Japan (Photon Factory) with the approval of the Photon Factory Program Advisory Committee (No. 2017G606), using a synchrotron-radiation X-ray beam with a wavelength of 0.15 nm, and small-angle X-ray equipment installed at beamline BL6A. Diffraction data were collected by a PILATUS3 1 M detector (Dectris, Daettwil, Switzerland) with a camera length of 2576 mm and 120 s X-ray exposure time at ambient temperature, as functions of q (scattering vector) after normalizing against the primary X-ray beam intensity, background-scattering subtractions, and Lorentz corrections. AFM was performed using a JSPM-5200 atomic force microscope (JEOL, Ltd., Tokyo) in ACAFM mode at room temperature under ambient conditions. Polarized optical microscopy was performed with an Olympus BX53-P polarized optical microscope (Olympus, Tokyo).

covalent modifications of their surfaces with polyethylene glycol exhibited N−N phase separation.22 However, since these systems have almost no structural-design flexibility, further systematic experimental verification of theoretical predictions has hardly progressed. An extremely rigid synthetic polymer whose length can be freely controlled is a desirable experimental system for verifying the numerous preceding theoretical predictions. We found that poly[n-decyl-(S)-2-methylbutylsilane] (PDMS), a helical polysilane, is an ideal experimental system for verifying these theoretical predictions because of its nonpolar nature and extremely stiff backbone, a result of its bulky side chains.23,24 We recently demonstrated that a variety of smectic structures predicted in binary mixtures of rodlike particles with different lengths13,14 were reproduced in binary systems of PDMS with narrow molecular-weight distributions and different molecular weights.25,26 In this study, we prepared binary mixtures of PDMS with molecular-weight ratios of 4.82 and demonstrated the theoretically predicted S−S demixing at high length ratios or high pressures, as illustrated in Figure 1.

2. EXPERIMENTAL SECTION Materials. For synthesis of the dichlorosilane monomer, decyltrichlorosilane and 1-chloro-2-methylbutane were purchased from Tokyo Chemical Industry Co., Ltd. (Tokyo), and magnesium and anhydrous tetrahydrofuran were purchased from the Fujifilm Wako Pure Chemical Corp. (Osaka, Japan). Toluene (Kanto Chemical Co., Inc., Tokyo) and sodium (Sigma-Aldrich Co. LLC, St. Louis, USA) were purchased and used for the Wurtz-type condensation of the dichlorosilane monomer. 2-Propanol, ethanol, and methanol were purchased from the Fujifilm Wako Pure Chemical Corp. (Osaka, Japan) and used for solvent fractionation. Extra-puregrade chloroform (Kanto Chemical Co., Inc.) was purchased and used as the eluent for size exclusion chromatography (SEC) and a solvent for cast-film preparation for atomic force microscopy (AFM) and small-angle X-ray scattering (SAXS) experiments. Sample Preparation. The (S)-2-methylbutyl- and n-decylbearing dichlorosilane monomer was synthesized by the Grignard reaction between decyltrichlorosilane and (S)-2-methylbutylmagnesium chloride. PDMS was synthesized by the Wurtz-type condensation of the dichlorosilane monomer in toluene at 120 °C according to the previously reported method.27 The obtained polymer was fractionated by fractional precipitation using 2-propanol, ethanol,

3. RESULTS AND DISCUSSION Figure 2 shows SEC traces, SAXS profiles, and AFM images of the binary mixtures of PDMS with molecular-weight ratios of 4.82 and various mixing ratios of the long polymer (Mw = 6.60 × 104, Mw/Mn = 1.22) to the short polymer (Mw = 1.37 × 104, Mw/Mn = 1.16). The molecular-weight distributions of these component polymers are sufficiently narrow to form smectic phases, and one can clearly observe the smectic layers in the AFM images of each polymer, with layer spacings of 39.04 and 12.56 nm for the long and short polymers, respectively (Figure 2C). The corresponding smectic-layer reflections are observed in the SAXS profiles, which show comparable layer spacings (39.40 and 13.47 nm for the long and short polymers, respectively) to those observed by AFM. These reflections remained even in binary mixtures and shifted slightly in the B

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Figure 2. (A) SEC traces, (B) SAXS profiles, and (C) AFM images of binary mixtures of a long PDMS (Mw = 6.60 × 104, Mw/Mn = 1.22) and a short PDMS (Mw = 1.37 × 104, Mw/Mn = 1.16) with narrow molecular-weight distributions.

Figure 3. (A) SEC traces, (B) SAXS profiles, and (C) AFM images of binary mixtures of a long PDMS with a broad molecular-weight distribution (Mw = 7.42 × 104, Mw/Mn = 3.05) and a short PDMS with a narrow molecular-weight distribution (Mw = 1.16 × 104, Mw/ Mn = 1.11).

small-angle direction as the mixing ratios of other polymers increased. This can reasonably be explained by the AFM images, as smectic layers of long and short polymers are segregated from each other and become dilated in the binary mixture (Figure 2C). The dilation of the smectic layers is attributed to the segregation of the polymer in the interstitial region of the smectic layers of the other polymer, as can be seen in Figure 4. The prediction of entropically driven S−S demixing in binary systems of rodlike particles with greatly different lengths was experimentally demonstrated for the first time. However, it is still unclear what contribution smectic-phase formation makes to demixing, which has never been considered in theoretical studies. Figure 3 shows the SEC traces, SAXS profiles, and AFM images of binary PDMS mixtures of various mixing ratios of a long polymer (Mw = 7.42 × 104, Mw/Mn = 3.05) with a broad molecular-weight distribution and a short polymer (Mw = 1.16 × 104, Mw/Mn = 1.11) with a narrow

molecular-weight distribution. The long polymer does not form a smectic phase, as it exhibited no smectic-layer reflections in the SAXS profiles (Figure 3B), and no smectic layers were observed by AFM (Figure 3C), although birefringence was retained as evidenced by polarized optical microscopy. However, the short polymer showed a smecticlayer reflection with a spacing of 13.22 nm, which was retained in binary mixtures containing up to 60% of the long polymer, with slight shifts in the small-angle direction observed. This can also be explained by the AFM image of the binary mixture, which shows segregated domains without smectic layers and with smectic layers with spacings (13.74 nm) comparable to those of the short polymer. These results indicate that demixing occurs even without a smectic phase in the longer polymer because the entropy gained by the formation of the C

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short polymer between the smectic layers of long polymers, as shown in Figure 4. The insertion of spherical particles between smectic layers of rodlike particles in the mixture has been theoretically predicted28,29 and experimentally demonstrated.30−32 A smectic layer of short particles inserted between the smectic layers of long particles was also theoretically predicted in a binary mixture of long and short rodlike particles,13 which was also reproduced in a binary mixture of long and short polysilanes with a molecular-weight ratio of approximately 3.26 Although it is not known why the short polymer with the broad molecular-weight distribution inserts between the smectic layers of the long polymer, it is possible that smaller molecular-weight fractions, which behave as spherical particles, are selectively inserted between the layers. Nonetheless, there is no doubt that the driving force is entropy gain through packing because these are identical homopolymers that differ only in molecular weight. Furthermore, smectic-phase formation is shown to play an important role because there was no sign of demixing in the binary mixtures of a long PDMS (Mw = 7.42 × 104, Mw/Mn = 3.05) with a broad molecular-weight distribution and a short PDMS (Mw = 1.22 × 104, Mw/Mn = 1.41) with a broad molecular-weight distribution, as far as can be observed by AFM (see Supporting Information).

short polymer-only smectic phase surpasses the loss of mixing entropy. The reverse combinations of binary PDMS mixtures of a long polymer (Mw = 6.60 × 104, Mw/Mn = 1.22) with a narrow molecular-weight distribution and a short polymer (Mw = 1.22 × 104, Mw/Mn = 1.41) with a broad molecular-weight distribution were also investigated. Figure 4 shows the SEC

4. CONCLUSION In summary, we have demonstrated that S−S phase separation takes place in binary mixtures of long and short rigid-rod-like PDMS with molecular-weight ratios of 4.82 and narrow molecular-weight distributions. Demixing has been theoretically predicted in binary mixtures of rodlike particles with sufficiently different lengths under high pressure, although it will be difficult to experimentally reproduce the theoretically predicted pressure−composition phase diagram with the thermotropic PDMS system. However, it should be noted that binary mixtures of PDMS with different molecular weights have shown structural behavior qualitatively consistent with theoretical predictions that depend on the molecular-weight ratio: (i) those with molecular-weight ratios of approximately 3 form alternately laminated smectic layers of long and short polymers;25 (ii) those with molecular-weight ratios of 2 form smectic layers of long polymers with two smectic layers of short polymers nested within;26 and (iii) those with molecularweight ratios below 1.7 form smectic layers containing mixtures of long and short polymers.26 It is surprising that the theoretical predictions for the system that consider only hard-core repulsions, which tend to deviate from experimental trends at high densities because of short-range attractive interaction like van der Waals interactions, have been reproduced in high-density thermotropic liquid-crystal systems. Although it has been shown that the attractive intermolecular interactions stabilize the smectic phase, it has also been shown that it is not possible to form a smectic phase by the attractive intermolecular interaction alone.33 These points suggest that entropy gain can be considered as the major driving force of the structural formation. We also found that both long and short polymers with broad molecular-weight distributions that do not form smectic phases in their pure forms exhibit no demixing, although demixing does occur with the long polymer with a broad molecularweight distribution that does not form a smectic phase, and the short polymer with a narrow-molecular-weight distribution

Figure 4. (A) SEC traces, (B) SAXS profiles, and (C) AFM images of binary mixtures of a long PDMS with narrow molecular-weight distributions (Mw = 6.60 × 104, Mw/Mn = 1.22) and a short PDMS with a broad molecular-weight distribution (Mw = 1.22 × 104, Mw/Mn = 1.41).

traces, SAXS profiles, and AFM images of binary mixtures with various mixing ratios. The short polymer shows no smecticlayer reflections in the SAXS profiles (Figure 4B) and no smectic layers are observed in the AFM images (Figure 4C). However, weak birefringence is retained as evidenced by polarized optical microscopy. In contrast, the long polymer exhibits distinct smectic-layer reflections, which greatly shifts in the small-angle direction, indicating layer dilation as the proportion of short polymer increased. AFM revealed that the increase in layer spacing is the result of the insertion of the D

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Spheres. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1997, 56, 5594−5602. (11) van Roij, R.; Mulder, B.; Dijkstra, M. Phase Behavior of Binary Mixtures of Thick and Thin Hard Rods. Phys. A 1998, 261, 374−390. (12) Varga, S.; Purdy, K.; Galindo, A.; Fraden, S.; Jackson, G. Nematic-Nematic Phase Separation in Binary Mixtures of Thick and Thin Hard Rods: Results from Onsager-Like Theories. Phys. Rev. E 2005, 72, 051704. (13) Koda, T.; Kimura, H. Phase Diagram of the Nematic-Smectic A Transition of the Binary Mixture of Parallel Hard Cylinders of Different Lengths. J. Phys. Soc. Jpn. 1994, 63, 984−994. (14) Varga, S.; Velasco, E. Modeling and Understanding SmecticPhase Formation in Binary Mixtures of Rodlike Polysilanes: Comparison of Onsager Theory and Experiment. Macromolecules 2010, 43, 3956−3963. (15) Cinacchi, G.; Velasco, E.; Mederos, L. Entropic Segregation in Smectic Phases of Hard-Body Mixtures. J. Phys.: Condens. Matter 2004, 16, S2003−S2014. (16) Cinacchi, G.; Velasco, E.; Mederos, L. Liquid − Crystal Phase Diagrams of Binary Mixtures of Hard Spherocylinders. J. Chem. Phys. 2004, 121, 3854−3863. (17) Cinacchi, G.; Martínez-Ratón, Y.; Mederos, L.; Velasco, E. Binary Mixtures of Hard Rods: A Short Account. Mol. Cryst. Liq. Cryst. 2007, 465, 121−132. (18) Varga, S.; Gábor, A.; Velasco, E.; Mederos, L.; Vesely, F. J. Demixed and Ordered Phases in Hard-Rod Mixtures. Mol. Phys. 2008, 106, 1939−1947. (19) Itou, T.; Teramoto, A. Triphase Equilibrium in Aqueous Solutions of the Rodlike Polysaccharide Schizophyllan. Macromolecules 1984, 17, 1419−1420. (20) Itou, T.; Teramoto, A. Multi-Phase Equilibrium in Aqueous Solutions of the Triple-Helical Polysaccharide, Schizophyllan. Polym. J. 1984, 16, 779−790. (21) Buining, P. A.; Lekkerkerker, H. N. W. IsotropicNematic Phase Separation of a Dispersion of Organophilic Boehmite Rods. J. Phys. Chem. 1993, 97, 11510−11516. (22) Purdy, K. R.; Varga, S.; Galindo, A.; Jackson, G.; Fraden, S. Nematic Phase Transition in Mixtures of Thin and Thick Colloidal Rods. Phys. Rev. Lett. 2005, 94, 057801. (23) Okoshi, K.; Kamee, H.; Suzaki, G.; Tokita, M.; Fujiki, M.; Watanabe, J. Well-Defined Sequence Including Cholesteric, Smectic A, and Columnar Phases Observed in a Thermotropic LC System of Simple Rigid-Rod Helical Polysilane. Macromolecules 2002, 35, 4556− 4559. (24) Okoshi, K.; Saxena, A.; Naito, M.; Suzaki, G.; Tokita, M.; Watanabe, J.; Fujiki, M. First Observation of a Smectic A−Cholesteric Phase Transition in a Thermotropic Liquid Crystal Consisting of a Rigid-Rod Helical Polysilane. Liq. Cryst. 2004, 31, 279−283. (25) Okoshi, K.; Suzuki, A.; Tokita, M.; Fujiki, M.; Watanabe, J. Entropy-Driven Formation of SmecticA1, A2, and A3 Phases in Binary Mixtures of Rigid-Rod Helical Polysilanes with Different Molecular Weights. Macromolecules 2009, 42, 3443−3447. (26) Okoshi, K.; Watanabe, J. Alternating Thick and Thin Layers Observed in the Smectic Phases of Binary Mixtures of Rigid-Rod Helical Polysilanes with Different Molecular lengths. Macromolecules 2010, 43, 5177−5179. (27) Fujiki, M. A Correlation between Global Conformation of Polysilane and UV Absorption Characteristics. J. Am. Chem. Soc. 1996, 118, 7424−7425. (28) Koda, T.; Numajiri, M.; Ikeda, S. Smectic-A Phase of a Bidisperse System of Parallel Hard Rods and Hard Spheres. J. Phys. Soc. Jpn. 1996, 65, 3551−3556. (29) Dogic, Z.; Frenkel, D.; Fraden, S. Enhanced Stability of Layered Phases in Parallel Hard Spherocylinders due to Addition of Hard Spheres. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2000, 62, 3925−3933. (30) Adams, M.; Dogic, Z.; Keller, S. L.; Fraden, S. Entropically Driven Microphase Transitions in Mixtures of Colloidal Rods and Spheres. Nature 1998, 393, 349−352.

that does form a smectic phase. This indicates that the driving force for this phase separation is also the increase in packing entropy gained by smectic-phase formation. In other words, it is possible to construct various structures with mixtures of rigid-rod-like polymers by precisely designing their molecularweight distributions. Studies along this line are in progress.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b02462. SEC traces and AFM images of the binary mixtures of long and short PDMS with broad molecular-weight distributions (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Kento Okoshi: 0000-0002-4837-8657 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by JSPS KAKENHI Grant Numbers JP16K04867 and JP17K06033, the Nanotechnology Platform Program (Synthesis of Molecules and Materials) of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan, and the Cooperative Research Program of Network Joint Research Center for Materials and Devices (NJRC).

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REFERENCES

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DOI: 10.1021/acs.macromol.8b02462 Macromolecules XXXX, XXX, XXX−XXX