Small angle x-ray analyses show that the shear-induced hexagonal perforated layer phase in a poly(ethylene oxide)-b-polystyrene diblock copolymer consists of trigonal (R3(overbar)m) twins and a hexagonal (P6(3)/mmc) structure, with trigonal twins being majority components. Transmission electron microscopy reveals that the hexagonal structure is generated through sequential intrinsic stacking faults on the second layer from a previous edge dislocation line, while the trigonal twins are formed by successive intrinsic stacking faults on neighboring layers due to the plastic deformation under mechanical shear

Cheng, Stephen Z. D.

Ge, Qing

Hsiao, Benjamin S.

Huang, Ping

Liu, Lizhi

Lotz, Bernard

Quirk, Roderic P.

Thomas, Edwin L.

Wittmann, Jean-Claude

Yeh, Fengji

Zhu, Lei

English

The University of Akron

The University of AkronIdeaExchange@UAkronCollege of Polymer Science and Polymer Engineering6-25-2001Dislocation-Controlled Perforated Layer Phase in aPeo-B-Ps Diblock CopolymerLei ZhuUniversity of Akron Main CampusPing HuangUniversity of Akron Main CampusStephen Z. D. ChengUniversity of Akron Main Campus, scheng@uakron.eduQing GeUniversity of Akron Main CampusRoderic P. QuirkUniversity of Akron Main CampusSee next page for additional authorsPlease take a moment to share how this work helps you through this survey. Your feedback will beimportant as we plan further development of our repository.Follow this and additional works at: http://ideaexchange.uakron.edu/polymer_ideasPart of the Polymer Science CommonsThis Article is brought to you for free and open access by IdeaExchange@UAkron, the institutional repository ofThe University of Akron in Akron, Ohio, USA. It has been accepted for inclusion in College of Polymer Science andPolymer Engineering by an authorized administrator of IdeaExchange@UAkron. For more information, pleasecontact mjon@uakron.edu, uapress@uakron.edu.Recommended CitationZhu, Lei; Huang, Ping; Cheng, Stephen Z. D.; Ge, Qing; Quirk, Roderic P.; Thomas, Edwin L.; Lotz, Bernard;Wittmann, Jean-Claude; Hsiao, Benjamin S.; Yeh, Fengji; and Liu, Lizhi, "Dislocation-Controlled Perforated LayerPhase in a Peo-B-Ps Diblock Copolymer" (2001). College of Polymer Science and Polymer Engineering. 14.http://ideaexchange.uakron.edu/polymer_ideas/14AuthorsLei Zhu, Ping Huang, Stephen Z. D. Cheng, Qing Ge, Roderic P. Quirk, Edwin L. Thomas, Bernard Lotz,Jean-Claude Wittmann, Benjamin S. Hsiao, Fengji Yeh, and Lizhi LiuThis article is available at IdeaExchange@UAkron: http://ideaexchange.uakron.edu/polymer_ideas/14VOLUME 86, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 25 JUNE 2001Dislocation-Controlled Perforated Layer Phase in a PEO-b-PS Diblock CopolymerLei Zhu,1 Ping Huang,1 Stephen Z. D. Cheng,1,* Qing Ge,1 Roderic P. Quirk,1 Edwin L. Thomas,2 Bernard Lotz,3Jean-Claude Wittmann,3 Benjamin S. Hsiao,4 Fengji Yeh,4 and Lizhi Liu41Maurice Morton Institute and Department of Polymer Science, The University of Akron, Akron, Ohio 44325-39092Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 021393Institute Charles Sadron, 6 Rue Boussingault, Strasbourg 67083, France4Department of Chemistry, The State University of New York at Stony Brook, Stony Brook, New York 11794-3400(Received 8 March 2001)Small angle x-ray analyses show that the shear-induced hexagonal perforated layer phase in apoly(ethylene oxide)-b-polystyrene diblock copolymer consists of trigonal (R3m) twins and a hexagonal(P63mmc) structure, with trigonal twins being majority components. Transmission electron microscopyreveals that the hexagonal structure is generated through sequential intrinsic stacking faults on thesecond layer from a previous edge dislocation line, while the trigonal twins are formed by successiveintrinsic stacking faults on neighboring layers due to the plastic deformation under mechanical shear.DOI: 10.1103/PhysRevLett.86.6030 PACS numbers: 82.35.Jk, 61.72.Ff, 82.35.Lr, 83.80.UvDiblock copolymers are of tremendous scientific interestdue to their ability to self-assemble into various orderedmorphologies on a nanometer length scale [1]. Be-sides three conventional phase morphologies for diblockcopolymers, i.e., lamellae, hexagonal cylinders, and body-centered cubic spheres, additional complex morphologieshave also been observed such as double gyroid [2,3] andhexagonal perforated layers (HPL) [4–11]. The stackingsequences of the hexagonal perforations in the HPL phasehave been modeled as ABCABC (trigonal R3m) and/orABAB arrangements (hexagonal P63mmc). Theoreticalcalculations [12–14] were also carried out using a broadbase of symmetries (e.g., fcc, hcp, R3m, P63mmc, andbcc, etc.) to predict the stability of the shear-inducedHPL phase. Experimental findings suggested that theHPL phase was induced by mechanical shear, and itwas a nonequilibrium, long-lived metastable phase orintermediate state [10,11,15].In order to determine the phase structure of theshear-induced HPL phase and further investigate theorigin of this unique phase, we study a poly(ethyleneoxide)-b-polystyrene (PEO-b-PS) diblock copolymer withMPEOn  11 kgmol and MPSn  17 kgmol. A detailedmethod of the sequential anionic block copolymerizationfor this sample can be obtained from Ref. [16]. ThePEO-block volume fraction is 0.39. The sample wascast from toluene and annealed at 100 ±C for 12 h. Theorder-disorder transition temperature was identified bysmall-angle x-ray scattering (SAXS) at 230 ±C. ThexN at 50 ±C is estimated to be 24.7 [16], suggestingthat the sample is in the weak segregation regime. Themicrophase-separated sample was then subjected to alarge-amplitude planar shear at 120 ±C under a dry argonatmosphere, using a laboratory-built shear apparatus. Theshear frequency was 0.5 Hz, and the amplitude was 150%.The shear direction is defined as the x direction, and theshear gradient is along the z direction. After shear, thesample was quenched to room temperature. A small pieceof the sample (1.0 3 1.0 3 0.2 mm3) was used forSAXS study.Two-dimensional (2D) SAXS experiments were per-formed at the synchrotron x-ray beam line X27C of the Na-tional Synchrotron Light Source in Brookhaven NationalLaboratory using imaging plates as detectors. The x-raywavelength was l  0.1307 nm, and the scattering vec-tor (q  4p sinul, where 2u is the scattering angle) wascalibrated with silver behenate. Transmission electron mi-croscopy (TEM) experiments were carried out on a JEOL1200 EX II at 120 kV. Thin sections for TEM were ob-tained using a Reichert Ultracut S (Leica) microtome at240 ±C. Samples were subsequently stained using RuO4vapor at room temperature for 20 min [17].The 2D SAXS patterns along the x, y, and z directionsare shown in Figs. 1a–1c, respectively. The sharp SAXSreflections are caused by the PEO crystallization [16]. Be-sides the primitive unit cell, the R3m structure can also bepresented using a nonprimitive hexagonal cell. Therefore,we use hexagonal indices (hkil) to index both the trigo-nal and hexagonal reciprocal lattices. Careful inspectionof the x-ray patterns reveals that the patterns comprisedtwo superposed structures: trigonal ABCABC (R3m) andhexagonal ABAB (P63mmc) stackings. The calculatedSAXS patterns are shown in Figs. 2a–2c. In order tofit the experimental observation in Fig. 1a with the cal-culated SAXS pattern along the 1210 (the x) directionin Fig. 2a, we need to superpose equally twinned trigo-nal reciprocal lattices with a hexagonal reciprocal lattice.Note that the trigonal twins have sequences of ABCABCand ACBACB, respectively. It is recognized in the mixedpattern of Fig. 2a that in every third layer the reciprocallattices of the two trigonal components overlap to forma partial merohedral twinning and the twin element isthe 0003 plane. In Fig. 2b, the trigonal twins give anidentical diffraction pattern along the 1010 (the y) di-rection, and this pattern is superposed with the hexagonaldiffraction pattern to construct a mixed pattern as shown in6030 0031-90070186(26)6030(4)$15.00 © 2001 The American Physical SocietyVOLUME 86, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 25 JUNE 2001FIG. 1. High-resolution synchrotron SAXS patterns along the x (a), y (b), and z (c) directions.Fig. 2b. This mixed pattern provides good correspondencewith the experimental observation along the y direction ofFig. 1b. The 000l SAXS pattern along the z directionprovides direct evidence for the existence of the hexagonalstructure. The trigonal twins again show identical diffrac-tions in the z direction. However, the first order reflectionsof the trigonal reciprocal lattice are extinct for R3m [18].Therefore, the sixfold first order reflections must solelyFIG. 2. X-ray crystallographic analyses for the SAXS patterns along the 1210 (a), 1010 (b), and 000l (c) directions. Notethat both trigonal and hexagonal structures use hexagonal lattice indices.6031VOLUME 86, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 25 JUNE 2001result from a hexagonal lattice, which has the same a anda values but a different c dimension. Thus, the mixedpattern along the z direction in Fig. 2c also fits our experi-mental observation in Fig. 1c.From the above x-ray crystallographic analyses theprimitive unit-cell parameters for the trigonal lattice are de-termined to be at  bt  ct  24.3 nm and at  bt gt  66.3±, and the hexagonal lattice has unit-cell parame-ters of ah  26.6 nm, ch  37.8 nm, and ah  120±. Ifthe nonprimitive hexagonal cell is used to describe thetrigonal cell, the new unit cell possesses identical a and avalues as the hexagonal cell, but the c axis becomes cth 3ch2  56.7 nm. Therefore, one layer thickness in theHPL phase is d  ch2  cth3  18.9 nm. Moreover,judging from the intensity difference between the 1010reflections in the hexagonal lattice and the 1011 reflectionsin the trigonal lattice in Fig. 1a (note that both are firstorder reflections), one can qualitatively estimate that thepopulation of the hexagonal phase is less than that ofthe trigonal twins, although the structure factors for bothstructures are unavailable.It is interesting that both the trigonal and hexagonalstructures in the HPL phase have identical in-plane bondand orientational orders. These two phases must be inter-related and we speculate that they are induced by plasticdeformation during mechanical shear (similar to mechani-cal slip in metals [19]). In order to visualize the plasticdeformation in real space, a TEM study was carried out tounderstand the interrelationship between these two struc-tures. It should be noted that the trigonal and hexagonalstructures in the HPL phase can be easily differentiatedthrough a 2D TEM projection image along the 1210 (thex) direction.Bright-field TEM micrographs of RuO4 stained thin sec-tions have been taken, and Fig. 3a is one example. Thealternating perforated layers (0003 planes) are orientedin the horizontal direction. Since the PEO phase is moreeasily stained than the PS phase [16], the PEO phase pro-jections are darker than those of the PS phases in Fig. 3a.To clarify our analysis, a reproduction of the 2D TEM pat-tern is shown in Fig. 3b. At the top left part of Fig. 3ba trigonal ABCABC stacking can be identified, while thehexagonal ABAB stacking is observed in the bottom left.Different edge dislocations can be recognized in this mi-crograph. The first type is the Frank partial dislocation(see  or  label in Fig. 3b). A Frank dislocation loopcan be formed by the absence of a layer (“vacancy loop”)with the subsequent collapsing of the surrounding layers.Therefore, the Burgers vector of the Frank partial dislo-cations is bF  c30003. For the “vacancy loop,” byremoving a layer, e.g., a B layer at 1 in Fig. 3b, thestacking sequence changes from the original ABCABCA toABCA#CA sequence (area I in Fig. 3b), where the verticalarrow indicates the position of an intrinsic stacking fault.Note that this fault creates a four-layer hexagonal CACAsequence. By inserting a C layer at  in Fig. 3b (“in-terstitial loop”), the normal ABCABC sequence becomesan ABCA#C#BC sequence (area II in Fig. 3b), which repre-sents an extrinsic stacking fault.A second type of edge dislocation evident in the imageis the unit (perfect) dislocation (see  or  label inFig. 3b). These defects correspond to 0003 1210 slip. Ithas a Burgers vector, bU  a1210, and is always dissoci-ated into two Shockley partial dislocations. Each Shockleypartial dislocation has a Burgers vector, bS  a31010.In principal, the relative energies involved in the Shock-ley partial dislocation (ES), Frank partial dislocation (EF),and unit dislocation (EU) have a relationship of ES :EF :EU  1:2:3. Therefore, Shockley partial dislocations arethe most frequent defects under plastic deformation. Ingeneral, a single a31010 shear produces an intrinsicstacking fault, while a second shear on the adjacent planecauses an extrinsic stacking fault. Both these stacking de-faults are geometrically equivalent to those formed by theFrank partial dislocation. If Shockley partial dislocationsFIG. 3. (a) Bright-field TEM image of a RuO4 stained thin slice PEO-b-PS sample sectioned perpendicular to the x direction. (b) Aschematic reproduction of the TEM 2D lattice. The dark, gray, and white symbols represent the PEO domains in the A, B, and Clayers, respectively. The stacking sequence is labeled based on the lattice analysis.6032VOLUME 86, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 25 JUNE 2001occur successively on the second layer from a previousdislocation line, a relatively large hexagonal domain canbe formed. There are two intrinsic stacking faults in thebottom left part of Fig. 3b where two Shockley disloca-tion lines, a and b, are evident. The b is formed by anext Shockley partial dislocation on the second layer fromthe a.If the a31010 shear is carried out plane by planeabove an A layer (i.e., a series of intrinsic stacking faultson neighboring planes), a coherent twin is produced (e.g.,ABCA#C#B#A#C#B). This explains our analysis of the SAXSpattern along the x direction (Figs. 1a and 2a). It is specu-lated that the 0003 twinning in the HPL phase may bepolysynthetic (lamellar) twins with relative large grainsizes, similar to those in minerals and metals [20]. Notethat deformation twinning is energetically more favorable,since the stacking-fault energies for twin (gtwin), intrinsic(gint), and extrinsic (gext) stacking faults usually possess arelationship of 2gtwin 	 gint , gext , 2gint. Therefore,the trigonal twin structures should be a major componentunder plastic deformation, as observed in our SAXSresults.In summary, the plastic deformation-induced HPL phaseis identified as a mixture of majority trigonal (R3m) twinsand minority hexagonal (P63mmc) structure. The hex-agonal structure is generated by either Shockley or Frankpartial dislocations through sequential intrinsic stackingfaults on the second layer from a previous dislocation line,and the trigonal twin structures are formed by successiveintrinsic stacking faults on neighboring layers due to plas-tic deformation. We thus conclude that the HPL phaseis controlled by dislocations under mechanical shear, andnone of the trigonal twins or hexagonal structure is inequilibrium.This work was supported by the NSF (DMR-9617030).The synchrotron SAXS experiment was carried out atNSLS in BNL supported by DOE.*To whom correspondence should be addressed.Email address: cheng@polymer.uakron.edu[1] F. S. Bates and G. H. Fredrickson, Annu. Rev. Phys. Chem.41, 525 (1990).[2] D. A. Hajduk, P. E. Harper, S. M. Gruner, C. C. Kim,E. L. Thomas, and L. J. Fetters, Macromolecules 27, 4063(1994).[3] M. F. Schulz, F. S. Bates, K. Almdal, and K. Mortensen,Phys. Rev. Lett. 73, 86 (1994).[4] E. L. Thomas, D. M. Anderson, C. S. Henkee, and D. Hoff-man, Nature (London) 334, 598 (1988).[5] R. J. Spontak, S. D. Smith, and A. Ashraf, Macromolecules26, 956 (1993).[6] M. M. Disko, K. S. Liang, S. K. Behal, R. J. Roe, and K. J.Jeon, Macromolecules 26, 2983 (1993).[7] K. Almdal, K. A. Koppi, F. S. Bates, and K. Mortensen,Macromolecules 25, 1743 (1992).[8] I. W. Hamley, K. A. Koppi, J. H. Rosedale, F. S. Bates,K. Almdal, and K. Mortensen, Macromolecules 26, 5959(1993).[9] S. Förster, A. K. Khandpur, J. Zhao, F. S. Bates, I. W.Hamley, A. Ryan, and W. Bras, Macromolecules 27, 6922(1994).[10] M. E. Vigild, K. Almdal, K. Mortensen, I. W. Hamley,J. P. A. Fairclough, and A. J. Ryan, Macromolecules 31,5702 (1998).[11] J. H. Ahn and W. C. Zin, Macromolecules 33, 641 (2000).[12] M. Laradji, A. C. Shi, R. C. Desai, and J. Noolandi, Phys.Rev. Lett. 78, 2577 (1997).[13] S. Qi and Z. G. Wang, Macromolecules 30, 4491 (1997).[14] P. D. Olmsted and S. T. Milner, Macromolecules 31, 4011(1998).[15] D. A. Hajduk, H. Takenouchi, M. A. Hillmyer, F. S. Bates,M. E. Vigild, and K. Almdal, Macromolecules 30, 3788(1997).[16] L. Zhu, S. Z. D. Cheng, B. H. Calhoun, Q. Ge, R. P. Quirk,E. L. Thomas, B. S. Hsiao, F. Yeh, and B. Lotz, Polymer42, 5847 (2001).[17] J. S. Trent, J. I. Scheinbeim, and P. R. Couchman, Macro-molecules 16, 589 (1983).[18] International Tables for Crystallography, edited byT. Hahn (Kluwer Academic Publishers, Dordrecht, 1996).[19] W. Hume-Rothery, R. E. Smallman, and C. W. Haworth,The Structure of Metals and Alloys (The Institute of Metals,London, 1988).[20] Deformation Twinning, edited by R. E. Reed-Hill, J. P.Hirth, and H. C. Rogers (Gordon and Breach, New York,1964).6033

Dislocation-Controlled Perforated Layer Phase in a Peo-B-Ps Diblock Copolymer

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Dislocation-Controlled Perforated Layer Phase in a Peo-B-Ps Diblock Copolymer

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