Unyong Jeong et al- Kinetics and Mechanism of Morphological Transition from Lamella to Cylinder Microdomain in Polystyrene-block-poly(ethylene-co-but-1-ene)- block-polystyrene Triblock

8/3/2019 Unyong Jeong et al- Kinetics and Mechanism of Morphological Transition from Lamella to Cylinder Microdomain in P

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Kinetics and Mechanism of Morphological Transition from Lamella to

Cylinder Microdoma in in Polystyrene-block-poly(ethylene-co-but-1-ene)-

block-polystyren e Triblock Copolymer

U n y o n g J e o n g , H e e H y u n L e e , H . Ya n g , a n d J i n K o n K i m *

Department of Chemical Engineering and Polymer Research Institute, Electronic and Computer Engineering Divisions, Pohang University of Science and Technology, Pohang,

Kyungbuk 790-784, Korea

S h i g e r u O k a m o t o

Department of Material Science & Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Jap an

S a k a e A i d a a n d S h i n i c h i S a k u r a i *

Department of Polymer Science & Engineering, Kyoto Institute of Technology, Sakyo-ku,Kyoto 606-8585, Japan

Received August 22, 2002

ABSTRACT: The kinetics and mechanism of morphological transition from nonequilibrium lamella tocylinder m icrodomain in a p olystyrene-block-poly(ethylene-co-but-1-ene)-block-polystyrene (SEBS) triblock

copolymer were studied by using time-resolved synchrotron small-angle X-ray scattering (SAXS),tra nsmission electr on microscopy (TEM), and rheology. The sam ple cast from toluene solution formed anonequilibrium morphology of the altern ating lamellae (LAM) of polystyrene (PS) an d poly(ethylene-co-but-1-ene) (PEB) blocks because toluene is a good solvent for PS chains but a poor solvent for PEB chains.LAM of PS and PEB blocks was transformed into the hexagonally close packing (HEX) of PS cylindersin PEB matrix when the as-cast sample was annealed above 140 C, which is above the glass transitiontemperature of the PS block. From the time-resolved SAXS and TEM, the coexistence of the LAM andHEX microdomains was clearly confirmed during the entire process of the order-to-order transition (OOT)from LAM to HEX, and the lamellar fraction in the coexisting phase decreased with increase of theann ealing time. It was also found t hat the st orage modulus dur ing the tra nsition linear ly decreased withthe lam ellar fraction. The t emporal change in t he LAM fra ction in the coexisting phase wa s fitted by theAvrami-type exponential decay function. The mechanism of the OOT was discussed on the basis of theevaluated Avrami exponent (n ). We found that the value ofn wa s 1 at higher annealing temperatures(above 160 C), wherea s it wa s 0.5 at lower ann ealing temperatu res. Thus, it is concluded that at h ighertemperatur es the nucleation and growth of the HEX microdomains from LAM pha se result from bothinterlayer correlat ion of the m odulation and in-layer modulation of LAM layers (2-dimensional growth).

On th e other ha nd, at lower temper atu res, one-dimensional growth from the in-layer modulation inducedthe nucleation and growth of HEX microdomains.

I . I n t r o d u c t i o n

Block copolymer s form r egular ly ordered microdoma ins t r uct ur es at t he t her m odynam i c equil ibr ium s t at ebecau se of the repulsive energetic inter action betweenconstituent block chains.1-4 It is well-known that thosemicrodomain structures are spheres arranged in a body-centered-cubic lattice, cylinders in a hexagonal lattice,double gyroid, or altern ating lamellae depending u ponthe composition, molecular weight, and temperature.2-4

The contr ol of morphologies of a block copolymer is

important , s ince mechanical properties of the blockcopolymer strongly depend on their morphologies.5

Many experimental and theoretical studies have beenperformed on phase behavior of block copolymers.6-35

Phase transitions between ordered microdomain struc-tur es, so-called order-to-order tra nsition (OOT), ha veattra cted much attention both theoretically6-11 a n dexperimentally.12-35 It is kn own t ha t t he design of blockcopolymer s wit h OOT n eeds a judicious choice of block

composition and total molecular weight of block copoly-mer.17 -35 C on t r a r y t o e xp er im e nt s on t h e O OT inequilibrium morphologies, nonequilibrium morphologiescan provide an alternative method to study the OOT.This is because a nonequilibrium morphology can beeasily formed when block copolymers are cast fromsolution with a selective solvent.14,29

One of us studied the kinetics of OOT from nonequi-librium polybutadiene (PB) cylinders to equilibriumlamellae in polystyrene-block-polybutadiene-block-poly-

styrene (SBS) triblock copolymers.14

It is of interest tostudy whether the kinetics of OOT from nonequilib-rium lamellae to equilibrium cylinders is described bythe sa me mechanism of the a bove. In th e present paper,we r eport on the kinetics of OOT from nonequilib-rium lamellae to equilibrium PS cylinders in a polysty-r ene-block-poly(ethylene-co-but-1-ene)-block-polysty-rene (SEBS) triblock copolymer. The apparent activationenergies and the Avrami exponents for the OOT wereevaluated in order to discuss th e mechanism of the OOT.Furth ermore, th e rheological change during t he OOTwas monitored and compared with SAXS results.

* T o w h om cor r e s pon d e n ce s h ou ld b e a d d r es s e d. E - m a il :[email protected] an d shin @ipc.kit.ac.jp.

1685Macromolecules 2003, 36 , 1685-1693

10.1021/ma021376v CCC: $25.00 2003 American Ch emical SocietyPublished on Web 02/13/2003


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I I . E x p e r i m e n t a l S e c t i o n

T h e s a m p le u s ed i n t h is s t u dy w a s a n S E BS t r ib lock copolymer [Kraton G1652; Shell Development Co.]. The n umber -average molecular weight, Mn, the heterogeneity index formolecular weight distribution, Mw/Mn, and the volume fractionof polystyrene (PS), PS , were determined t o be 5.4 10 4, 1.10,and 0.227, which are measured by membrane osmometry, gelpermeation chromatography, and 1H nuclear magnetic reso-nance spectroscopy (NMR), respectively. The average numberof ethyl side group on the poly(ethylene-co-but-1-ene) (PEB)

block chain was determined by13

C NMR to be 71 per 1000carbon atoms in the PEB block chain. From this value themicrostructure in the original PB before hydrogenation isestimated to be 25 and 75 mol % for 1,2- and 1,4-linkages,respectively. The film samples subjected to the SAXS mea-surement s were prepar ed by solution-casting at room t emper-at ur e using t oluen e, which is a selective solvent for PS block.36

The SAXS measu rement s with synchrotron radiations wereconducted at the 4C1 beam line in the Pohang Light Source(PLS), Korea. The primary beam was monochromatized withdouble Si(111) crystals at the wavelength of 0.1598 nm, andthen it was focused on a detector plane by a bent cylindricalmirror. A one-dimensional position-sensitive detector (Diode-Array PSD; Princeton Instruments Inc.; model ST-120) withthe dista nce of each d iode of 25 m wa s used. Typical exposur etime for G1652 samples with 1.2 mm thickness was 30 s. The

sample was settled in such a way that the film normal wasparallel to the incident beam trajectory (through view). Themeasured scattering intensities were corrected for air scat-tering, for absorption due to the sample, and further for thetherm al diffuse scattering (TDS) arising from density fluctua -tions. Here, the scattering intensity of TDS was conventionallyassumed to be that measured at the highest q region coveredin th is study (1.2 nm-1 < q < 1.5 nm -1), where the scatteringintensities reached an almost constant level, irrespective ofthe scattering angle.14-16 T h e mag n i t u d e o f t h e s cat t eri n gvector (q) is given by

where is the wa velength of the X-ray a nd is the scatteringangle.

For t he stu dy of the kinet ics of the morph ological tr an sition,time-resolved SAXS measurements were performed upontemper atu re-jump (T-jump). A copper sample cell conta iningthe sample preheated at 110 C for 5 h was put into anothercell holder maintained at specific temperatures (140, 150, 157,1 62 , an d 1 68 C), w h ich w ere ab ov e t h e g las s t ran s i t iont emp erat u re of P S b lock s (Tg,PS) o f 8 9 C m e a s u r e d b y adifferential scanning calorimeter (DSC 7 series, Perkin-Elmer)at a h eating ra te of 10 C/min. The temper atu re was st abilizedat a preset temperature within 1 min after the T-jump.

The temporal storage modulus, G, w as meas u red b y anAdvanced Rheometrics Expanded System (ARES) a fter thespecimen was jumped from 110 C to a preset temperat ure.The strain am plitude (0) and th e frequency () are 0.005 and0.1 rad/s, resp ectively, which lie in a linea r viscoelast ic region.

The micodomain structures of the samples were examined

by transmission electron microscopy (JEOL 1200EX) operatedat 120 kV. Cryogenic ultrasectioning was performed with anRMC (MT-700) microtomer a t -100 C. Then, specimens werestained with RuO4 for 30 min, which selectively stained thePS microdomains.

I II . R e s u l t s a n d D i s c u s s i o n

Figure 1 shows SAXS profiles [intensity (I(q)) vs q]for the sam ples with various th erma l histories: (a) as-cast, (b) annealed at 110 C for 300 min, (c) annealedat 120 C for 120 min after annealing at 110 C for 300min, (d) annealed at 140 C for 60 min after annealingat 110 C for 300 min, and (e) annealed at 168 C for120 min after annealing at 110 C for 300 min. Diffrac-tion peak s of the a s-cast sample are seen a t th e relative

q-positions of 1:2:3, reflecting well-ordered lamellarmicrodomains (LAM). Such nonequilibrium morphologyin the casting solution is kinetically locked when thePS domains vitr ify as the polymer concentration in-creases. Nam ely, t he nonequilibrium morphology doesnot have a chance to tr ansform into more sta ble HE Xmicrodomains during the subsequent casting processwhere the remaining solvent was thoroughly evacuated.For a sample annealed at 110 C, SAXS peaks weresharpened, but the first-order peak moved to slightlyhigher q (4% increase), indicating that LAM ordering

was improved at 110 C, and the tra nsition t o HEX didn ot occu r a t a ll a t t h is t e m pe r at u r e. T h e s ligh t lyincreased q* (or slightly decrease in d spacing) withannealing at 110 C was due to the fact that the residualstress stored during the vitrification of PS block wasrelaxed at h igher tempera tur es. In other words, vitrifiedPS chains can slowly relax at 110 C, allowing betterLAM perfection, but this temperature was still insuf-fi ci ent t o a chi eve t he t r ans it i on t o H E X due t o t h evicinity ofTg,PS.

On the other hand, for a sample annealed at 168 C,three peaks appeared at q positions of 1:3:7, typicalof the scattering from hexagonally pa cked cylinders(HEX). This SAXS profile indicates thermally inducedmorphological transition from nonequilibrium LAM toequilibrium HEX upon annealing at 168 C (far aboveTg,PS). I t is quite natu ral th at G1652 with PS ) 0.227has HEX microdomains at equilibrium condition. TheSAXS profiles (c) an d (d) showed th e double first -orderpeaks arising from LAM an d H EX microdomains, su g-gesting that LAM and HEX phases coexist at these t woann ealing conditions.

To investigate in detail th e double first-order peaks,w e per for m ed t he T -jum p fr om 110 C t o a pr esettemperature. Figure 2 shows typical examples of thechange in t he SAXS profiles with the annealing t imeat t w o t em per at ur es (140 and 168 C ). For bot h T - jumps, a gradual disappearance of higher-order LAMpeaks at the expense of the evolution of HEX peaks was

q ) (4/) sin( /2) (1)

F i g u r e 1 . SAXS pr ofiles of th rough view of the film for SE BSat var ious th erma l histories: (a) as-cast; (b) ann ealed at 110C for 300 min; (c) ann ealed at 120 C for 120 min afterannealing at 110 C for 300 min; (d) annealed at 140 C for 60

min after annealing at 110 C for 300 min; and (e) annealedat 168 C for 120 min after annealing at 110 C for 300 min.To avoid overlap, the SAXS profiles were shifted vertically.

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observed. This tendency was observed in all otherT-jumps, although LAM peaks disappeared earlier withincreasing T-jump tempera tur e. For t he T-jump to 168C, the LAM peaks completely disappeared at tg 12 0min, whereas t he LAM peaks were still dominan t evenat 160 min for the T-jump to 140 C.

TEM images after T-jumps to 140 and 168 C followedby annealing for 20 min are shown in Figure 3. I t isseen in Figure 3a that HEX microdomains a re clearly

generated from LAM layers, although the area of HEXis small. The bounda ry between LAM and HE X phaseswas distinct. For the specimen annealed at 168 C for20 min, the HEX phase becomes dominant over theLAM phase, as shown in Figure 3b. Interestingly, themodulation and perforation of LAM, marked by th earrows in Figure 3b, are visible, even though the areacorresponding to these regions was very small. However,this kind of the LAM modulation (ML) or perforation(PL) is barely seen in Figure 3a . This suggests th at thetransit ion mechanism of OOT from LAM to HEX atlower t empera tu re (or sha llow T-jum p) is differen t fromtha t at higher temp erat ure (deep T-jump). This behaviorwill be complemented with different values of t heAvrami exponent at two temperatur e regimes, whichwill be discussed later.

Very recently, Wang and Lodge30 s how ed t hat t heOOT from HEX to gyroid for a solution consisting ofpolystyrene-block-polyisoprene and dibutyl phtha lateproceeds directly by a nucleation and growth for shallowquench, but a m et as t abl e i nt er m ediat e s t r uct ur e of hexagonally perforated layer (HPL) was observed fordeep quenches. Thus, TEM images given in Figure 3might be consistent with the results given in ref 30,although the OOT in this study was the transit ion of kinetically frozen LAM to equilibrium HEX phase.However, we did not observe a clear evidence of ML orPL du ring th e OOT from SAXS or rh eology results. Th isindicates that even though this kind of intermediate

state might exist du ring the OOT at higher a nnealingtemperatures (deep T-jumps), it would be a short-livedintermediate, or th e a mount of this intermediate wassmall.

Of course, it cannot be completely excluded that SAXSprofiles of ML (or PL) are not much different from LAMwith random grains, and the difference in rheologicalproperties between ML (or PL) and LAM is not large.The best wa y to test the existence of ML (or HPL) is to

use shear-aligned LAM.28 In ref 28, two intermediatestru ctures (ML and HPL) were clearly observed betweenLAM and HEX. According to Wang and Lodge,30 t h etran sit ion mechanism between HEX a nd Gyroid foraligned sample is s imilar to u naligned sample. Thus,we tried to perform macroscopically shear alignmentusing a large-amplitude oscillatory shear ing (LAOS)with ) 0.08 ra d/s and 0 ) 50% for specimen with1.2 mm thickness an d 50 mm diameter. However, wefoun d via 2-D SAXS experimen t t ha t LAM did not a ligneven under LAOS at 110 C for 4 h. This is attributedto the fact t hat the t emperature was close to the Tg ofPS block. I n t he m eant im e, w hen a s peci m en w asaligned under LAOS at 140 C for 1 h, we found, via2-D SAXS, that both HEX cylinders and LAM layerswere well-aligned t oward t he flow direction (x-direction).However, we barely saw any scattering peaks or TEMimages corresponding to HPL (or ML or PL) for thisaligned sa mple. Na mely, both 6-fold diffra ction spots inqx-qz (shear plane) and four additional weak spots inqx-qy plane, corresponding to the chara cteristics of HPL,28 were not observed.

Hajduk et al.29 showed that, during OOT from kineti-cally frozen state of LAM to equilibrium HEX, thereexists a n int ermediate st ate of ML, and t his ML wouldbe a long-lived or pseudo-equilibrium state. Interest-ingly, they employed P S-PEB diblock copolymer castfrom tetrahydrofuran (THF), which is a selective solventto PS block. They also showed th at this ML was detected

F i g u r e 2 . Chan ges in th e SAXS profiles with t he a nnea ling time at two different T-jumps from 110 C: (a) 140 C; (b) 168 C.

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after the sample was cooled from equilibrium HEXs t at e. T hese r esul t s i m ply t hat t he s t abil it y of t heintermediate state depends on volume fraction of PSblock. The volume fractions of the minor block studiedin refs 28, 29, and 30 are 0.35, 0.29, and 0.30, respec-t i vely, w hi ch ar e l ar ger t han t hat (0.23) of SE B Sinvestigated here. This indicates tha t t he sta bility of MLfor a block copolymer with higher amount of the minorbl ock m i ght be bet t er t han t hat w i t h l ow er am ount .

Furthermore, we did not observe any evidence of MLor PL in SAXS a nd TE M, when t he specimen wa s cooledfrom equilibrium HEX. Therefore, we conclude th atL AM and H E X phas es coexi st ed dur ing t he ent ir e

process of this OOT, and that even though an interme-diate ML or PL m ight be formed a t h igher T-jumps, theamount would be very small or it would be short-lived.

To estimate the conversion (or the amount) of HEXphase from LAM, SAXS profiles in Figure 2b wereexpanded in Figure 4a, where I(q) in the range 0.15 eq e 0.30 nm -1 for the double f irst-order peaks arehighlighted. These peaks are easily decomposed byusing a mat hema tical expression comprising Gau ssianpeak function

where A i, i, qi, a n d B a r e t h e p e a k a r e a , s t a n d a r ddeviation, and q position for the ith peak (i ) 1 for LAMa nd i ) 2 for HEX), and background, respectively. Anexample of the peak decomposition is shown in Figure4b for the annealing t ime of 10 min at 168 C. Fromthe evaluated peak area of LAM a nd HEX first-orderpeak, the fraction of LAM phase in coexisting phases(L) is estimated by L ) A LAM/(A LAM + A HE X), becauseof isotropically or randomly oriented polygrain struc-tur es for both microphases.

Figure 5 gives temporal chan ges in L vs the anneal-ing time at several T-jump temperat ures. It is seen th atat temperatures lower than 160 C the morphological

F i g u r e 3 . TEM im ages a fter t wo T-jumps ((a) 140 C; (b) 168C) followed by annealing for 20 min. Before T-jumps, speci-mens were an nealed at 110 C for 5 h.

F i g u re 4 . (a) Temporal chan ges in SAXS profiles for theT-jump to 168 C, where the scattering intensity I(q) is plott edagainst q i n t h e ran g e 0 . 1 5 e q e 0.30 nm -1 covering thedouble first-order peaks. (b) An example of the computationalpeak decomposition for t ) 1 0 m i n b y u s in g e q 2 . T h edecomposed peaks are shown as dotted curves.

I(q) ) i {

A i

2i

ex p[-(q - qi)

2

2i2 ]} + B (2)



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transition from LAM to HEX was not completed evenat prolonged annealing times above 200 min, indicatingthat the mixture of LAM and HEX phases still exists.But, as the T-jump was elevated (above 162 C), thetransition was more accelerated and the HEX formationseems to be completed within 120 min. The decay ofL

with the a nnealing t ime, t, was a nalyzed by using theAvrami-type decay function

where L is the a mount of LAM phase at t ) , is a

decay t ime, and n is the Avrami exponent. The curve

fittings with a djusting , n , and L shown by solid lines

in Figure 5 give good agreements with experimentaldata. The complete transition to the HEX cylinders wasattained at tg 120 min for 162 an d 168 C. Since, thefitting with eq 3 became far from the experimental dataat t ) 120 min, we neglected SAXS data at 120 min forboth 162 and 168 C in the fitting shown in Figure 5.

T he i ns et i n F i gur e 5 s how s t he plot of L v s t h eann ealing temperat ure, where t he values below 157 Car e evaluat ed by the fitting, while th ose for 162 and 168

C are set a s L ) 0, which are directly obtained from

the SAXS mea suremen ts. The beha vior ofL exhibits a

discontinuity a round 160 C.Figure 6 gives temp oral changes ofG for two T-jum ps

(157 and 168 C). We also carried out other T-jumps,although the results are not shown here due to the spacelimit. The temper atu re profiles for this experiment ares how n i n t he upper panel of Figur e 6. A t poi nt A,temperature was jumped up from 90 to 110 C, at B to168 C (or 157 C), and then finally at C from 168 C(or at C from 157 C) to 110 C. The du rat ion time a t

1 57 C w a s l on ge r t h a n t h a t a t 1 68 C , s in ce t h etransition of HEX was slower for lower temperatures,

as shown in Figure 5.It is seen tha t du ring the first heat ing from 90 to 110

C G increased very rapidly, and then i t approachedsteady value a fter ca. 60 min. A sharp increase in G isat t r i but ed t o t he i ncr eas ed per fect i on of t he L AMor der ing, as dis cus s ed i n Fi gur e 1. B ecaus e of t heT-jump at point B, G decreased stepwise and thenstarted to increase and approached their asymptoticvalues. G at 168 C starts from a slightly smaller valuet han t hat at 157 C s i nce hi gher t em per at ur e gi vessmaller G. But, the increasing rate was faster for thefor m er , s ugges t ing t hat t he t r ans it i on of H E X w asachieved earlier.

Finally, when we quenched from higher temperatures

to 110 C at point C (or C ), G at point D (or D) waslarger than G at point B. Also, G at point D was highert han t hat at poi nt D. The microdomain structures a tpoint D after quenching are essentially the same asthose at higher temperatures (or point C) because of theimmobilization of PS blocks. Therefore, the differencein G bet w een poi nt D and poi nt B depends on t hefraction of LAM phase and macroscopic grain conditionssuch as size, shape, and number. The reason why G ofHEX microdomains becomes higher than that of LAMis not clear. To the best of our knowledge, there has beenno report on the viscoelastic behavior during the directtr an sition from LAM to HEX. However, it is consider edtha t, within t he linear viscoelastic region, th e modulusdepends ma inly upon t he inter faces normal t o the flowdirection 23 an d microstructure connectivity.17,32 Th etran sit ion from LAM to HEX gives m ore interfaces;thu s, an increase in newly-generated int erfaces normalt o t he fl ow dir ect i on r esul t s i n l ar ger G. Similarbehavior has been observed for OOTs from HEX to BCCand from LAM to H PL str ucture.17 -23,28-34

To examine the dependence of G on the amount of LAM phase du ring the OOT, the changes ofG/G0 withtime dur ing the pr ocess B f C are m agnified in Figure7a. Here, G0 is the minimum value of G during thisprocess, which decreases with increasing tempera tur e.It is seen that with increasing T-jump the value ofG/G0 increases, and the steady value would be achievedat earlier times. Since we assume that G of HEX sta te

Figure 5. (a) Temporal changes in the amount of LAM phase,L. The solid curves are the fitting by the Avrami-type decay

function as given by eq 3. (b) Plot ofL (the amount of LAM

phase at t ) ) vs the a nnealing temperat ure. The values wereevaluated by the fitting below 157 C, while they were set as

L ) 0, which a re directly determ ined by the SAXS r esults for

162 and 168 C.

L(t) ) (1 - L) exp{(-t/)n} + L

(3)

F i g u r e 6 . Temporal changes in G measured at a frequency0.1 rad/s and a strain of 0.005. Temperature profiles are shownin the upper panel: 157 C (O); 168 C (b).



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is larger th an that of LAM state, the value of G/G0 isdirectly related to th e am ount of HEX phase. Since theamount of HEX (or LAM) phase was a lready estimat edfrom S AXS experim ent s (see Figur e 5), we plot G vs Lat two temperatures, as given in Figure 7b. It is seenthat a linear relationship between these two parametersis valid: GTOTAL ) LGLAM + (1 - L)GHE X. Previously,Floudas et al.25 simply assumed th is relationship with-out showing experimental data. From the results of Figure 7, we conclude that G linearly increases withincreasing amount of HEX phase, and the conversionto HEX phase from LAM phase increases an d the st eadyvalue is achieved faster with increasing T-jump tem-perature.

The tempera tur e dependence of the Avrami exponentn can give a primitive idea on the t ra nsition mechan ism.Figure 8 displays the Avrami exponent n from SAXSexperime nt s (open circle) and rh eology (solid circle). Theexponents from the two approaches are in good agree-ment except those of 157 C T-jump. Quite interestingly,

n of 140 and 150 C T-jump is ca. 0.43, whereas n of162 and 168 C T-jump is ca. 0.8. According to theAvra mi-type crystallizat ion th eory,38,39 the exponent (n )is correlated with the dimensionality of the crystal

growth, for instan ce, 0.5 for one-dimensiona l growth(rodlike crysta llite) an d 1.0 for two-dimensiona l growth(disklike crystallite) when the crystallization is con-trolled by diffusion of molecules. The discontinuity ofthe exponents at 160 C, as shown in Figure 8, suggestsdifferent dimensiona lity of growth of HEX cylindersbelow and above ca. 160 C, although OOT is not thesame phenomenon as the crystall ization where mol-ecules migrate from disordered state to ordered state(crystals).

Peak pos it i ons and ful l w i dt h at hal f-m axim um(fwhm) are valuable information on the temperaturedependence of th e tran sit ion mechanism. Temporalchanges in the double f irst-order peak posit ions ares how n i n Fi gur e 9a. B elow 157 C , t he L AM peakposit ion remains almost constant, while i t graduallyincreases with t ime above 162 C. For the temporalchange in the HEX peak posit ion, th ere seems to be ageneral tendency that peak position remains constantat the early stage, then gradually increases with time,and finally reaches consta nt. If we define th e th resholdtime (tX) as an ann ealing time after which th e HEX peakposition increases, tX was found to decrease with in-creasing the a nnealing temperature. I t was seen fromFigures 5 and 9a tha t th e value of L a t tX was almostthe same (0.73) irrespective of the a nnea ling t emper-atu res. It is ment ioned, however, tha t t he critical valueof L (L,crit 0.73) was experimentally determinedwithout any theoretical a rgument.

F i g u r e 7 . (a) Temporal changes in G/G0 at a frequency of0.1 rad/s during T-jumping from 110 C to several tempera-t u res : 1 40 (4), 150 (0), 157 (O), 162 (]), and 168 C (b). (b)Plot ofG vs L for t wo T-jumps: 157 (O) and 168 C (b). TheL was evaluated independently from the SAXS results:

F i g u r e 8 . Avrami exponent (n ) with the annealing temper-ature, which is evaluated from SAXS (O) and rheology (b).

F i g u r e 9 . (a) Tempora l changes in t he SAXS peak positionsof L AM a n d H E X p h a s es d u r in g t h e O OT . ( b) P l ot s of normalized cylinder peak positions (qHE X) vs normalized an -nealing time (t). Here, qHE X is defined by qHE X divided by t he

lamellar peak position (qLAM0 ) a t t ) 0 a n d t ) t/tX. tX is

defined as an ann ealing time at which L reaches L,crit ()0.73).



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Figure 9b shows plots of normalized cylinder peakpositions (qHE X) vs norma lized ann ealing time (t). Here,qHE X is defined by qHE X divided by the lamellar peak

position (qLAM0 ) a t t ) 0, and t ) t/tX, in which tX is an

annealing time at which L reaches L,crit. It is seen inFigure 9b that the qHE X does n ot change with time forte 1, implying tha t t he genera tion of the HE X cylindersfrom LAM phase is frustra ted by th e ma jority pha se ofthe remaining LAM phase as long as L is larger tha nL,crit. O n t h e ot her hand, as s how n i n Fi gur e 9a, t heLAM first -order peak above 162 C shifts towar d h igher

q with t ime after 10 min at which L reaches 0.4-0.5(see Figure 5). Note that the LAM first-order peak below157 C does not sta rt to shift even a t t he sa me value ofL (0.4-0.5). This fact indicates that the shift of theLAM first-order peak cannot be accounted for in termsof the change in L, as opposed to th e shift of the HEXfirst-order peak. It ma y be therefore suggested tha t th emorphological chan ge to HE X phase occurring inside t heLAM phase at the T-jump below 157 C is different fromt h a t for t h e T -ju m p a b ove 1 62 C . T h is r e su lt isconsistent with the growth mechanism (dimensionality)based on the Avrami exponent n .

The change in fwhm of the double first-order peaksw it h t he anneal ing t i m e at s ever al t em per at ur es i sshown in Figure 10. There seems to be a correlationbetween the behaviors of fwhm and the peak position.N ot e t h a t t h e p ea k w id t h r e la t e s t o t h e d egr e e o f regularity of ordered microdomains. Overall, the peakwidth for the HEX cylinders monotonically decreasesw it h t i m e, i ndi cat i ng i m pr ovem ent of t he packingregularity. The only exception is the case of the 140 Cann ealing, where the fwhm stayed consta nt in the ea rlysta ge below about 20 m in, which closely coincides withthe behavior of th e peak position. As for t he LAM pha se,the fwhm stays almost consta nt below 157 C, while its uddenly i ncr eas es at ca. 10 m i n for t he anneal ingtemperatures above 162 C. Namely, the remaininglamellar phase is una ffected by the ongoing tra nsitionfor th e form er case, while it is significant ly affected for

the latter case. These facts again suggest the differencein the t ran sition mechan ism between lower an d highertemperatures.

Wang et al.10,11 theoretically showed that the transi-tion from weakly segregated LAM to HEX by T-jumpundergoes stepwise processes with modulation andperforation of LAM. For shallow T-jumps where thetransition occurs slowly, the initial stage of the HEXevolut ion is a simple decay of LAM order ing an d in-layer

density modulation begins to emerge. H owever, theinterlayer correlation of the modulations would n ot behigh, suggesting that in-layer modulation plays a majorr ol e. O n t he cont r ar y, f or deep T -jum ps w her e t hetra nsition occurs fast, th e inter layer correlation of themodulation as well as the in-layer modulation can beeffective. This suggests that the remaining LAM isstrongly affected by the other in-layer fluctuat ions,possibly resulting in considera ble interlayer correlat ion.These two transition mechanisms result in differencein the dimensionality of the growth of HEX micro-domains, as inferred from the Avrami exponent s. Two-dimensional fluctuation, corresponding to the fast tran-sition, may cause perforated structure as a n intermediatestate with a periodicity of twice the lamellar spacing

during LAM to HEX tran sition, alth ough the detectionof this intermediate state depends on its lifetime. Ont h e ot h e r h a n d , i n a t r a n s it ion g ove r n ed b y o n e-dimensional fluctuation corresponding to slow transi-t ion, the formation of the intermediate state such asperforated structure is as little as possible. The TEMresults in Figure 3 a re consistent with different t ran si-tion mechanisms.

On the basis of the above-mentioned arguments, thepossibility to observe an intermediate state (or meta-stable state) becomes higher as the dimensionality ofthe fluctuat ion (or tra nsition r ate) increases. Then, weconsider tha t 3-dimensional fluctuat ion (or spinodaldecomposition) might be expected for a very r apid

transition, namely a very high annealing temperature,al t hough t he det ect i on of a n i nt er m ediat e s t at e byexperiments is not easy due to very short lifetime. Onthe other hand, if an as-cast sample has poor ordering(or regularity) of LAM, the transition to equilibriumHEX stat e becomes very ra pid. This kind of very ra pidtransit ion might be achieved if the mismatch of thelattice spacing between LAM in an as-cast sample a ndequi li br i um H E X i s s m all . I n t hes e t w o cases, t hetra nsition from nonequilibrium LAM t o equilibriumHEX ta kes pla ce via spinodal-like fluctua tion, giving anintermediate state (or metastable state).9 The validityof th is scenario is currently under investigation. I tshould be mentioned that the existence of an intermedi-ate state is also dependent upon volume fraction of

minor block (PS ). As the difference between PS a n d avol um e fr act i on at w hich PL (or M L) s t r uct ur e i sexpected is smaller, the possibility of the appearanceof PL (or ML) becomes higher during the transition fromnonequilibrium LAM to equilibrium HEX. The volumefraction ofPS in SEBS studied here was 0.23, whichw as s m all er t h an t hat (PS ) 0.3 -0.35) in refs 28-30where an intermediate state was confirmed.

Finally, we evaluated the apparent activation ener-gies for the morphological transit ions based on thetemperat ure dependence of the decay time, , which areobtained from SAXS and rheology. Figure 11 gives theArrhenius plot of the decay rate, -1, vs the inverse oft he abs ol ut e t em per at ur e. T he appar ent act i vat i on

F i g u re 1 0. T emp oral ch an g es i n t h e fu l l w i dt h at h al f-

maximum (fwhm) of double first-order peaks with the ann eal-ing time as a function of the a nnealing temperature.



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energy obtained from SAXS (open circle) is 42 kcal/mol,which is close to that (36 kcal/mol) from rheology (solidcircle). Interestingly, this value is quite close to that ofthe transit ion from n onequilibrium PB cylinders toequilibrium P S-PB lamellae in SBS triblock copolymers(ca. 40 kcal/mol) stu died pr eviously.14 Furt hermore, thisvalue is close to that (38 kcal/mol) of PS homopolymeri n t he r el evant t em per at ur e r anges but m uch l ar ger

tha n tha t (4.8 kcal/mol) of neat polybutadiene or PEB.Since the rate of the OOT, however, is determined

by th e degree of regularity and orientation of micro-domains,30 i t is reasonable to compare the activationenergy for other OOTs. Floudas et al.25 have reportedsimilar va lues of th e activat ion en ergy (ca. 47 kcal/mol)for epitaxial OOT from cylinder to gyroid in polyiso-prene-block-poly(ethylene oxide) copolymers based onth e SAXS resu lts. They a lso found ca. 60 kcal/mol fromr heol ogical m eas ur em ent w it h a s m all s t r ain (0 )0.005). Note that these values are much higher thanthat of polyisoprene and poly(ethylene oxide) localsegmental relaxation (typically 5-10 kcal/mol at T -Tg ) 220 K). They argued t hat the OOT was contr olled

by a collective motion associated with the bicontinuouscubic phase (gyroid). This argument is also applied tot he O OT s t udied i n t hi s s t udy. For i nst ance, event hough t he act i vat i on ener gy for O OT i n t he SBSstudied previously (from HE X to LAM) and t hat in th epresent SEBS case (from LAM to HEX) was similar, thetransition for the SEBS was much slower. For instance,the SBS exhibited complete transformation from HEXt o L AM a ft e r 1 70 m in a n n e a lin g e ve n a t 1 27 C ,wherea s for SE BS a slight t ra nsition to HEX from LAMis expected at 127 C even a t very pr olonged a nn ealingtime (maybe over 180 min). This a lso shows that thecollective motion of the interface plays a main role inthe transition; that is, OOT in this study is controlledby the segregation power and the degree of perfection

(or regularity) of microdomain structure rather than themotions of PS block chains themselves.

IV . C oncl usi ons

In this study, we have shown, via time-resolved SAXS,TEM, and rheology, that a nonequilibrium LAM micro-domains formed du ring toluene casting was tr an sformedinto HEX microdomains at higher temperatures. Duringthis t ransit ion, the coexistence of the LAM and HEXmicrodomains was clearly observed during the entireprocess of OOT from LAM to HEX, and the lamellarfraction in t he coexisting pha se decreased with ann eal-ing time. Even though a small portion of the intermedi-at e str uctu re of PL (or ML) was observed only at higher

annealing temperatures, which was confirmed by TEM,we did not f ind a clear evidence of this intermediatestru cture by SAXS and rheology.

We h ave al so s how n t hat t he G of the HEX phasew as l ar ger t han t hat of t he L A M phas e and t hat Gincreased l inearly with the amount of HEX phase incoexisting phases. The Avrami exponent (n ) at higherann ealing temperatu res (above 160 C) was lar ger tha nthat at lower annealing temperatures. Thus, at lowertempera tur es, one-dimensional growth from th e in-layermodulation indu ced th e nu cleation an d growth of HEXmicrodomains, but at higher temperatures the nucle-ation and growth resulted from both interlayer correla-tion of the modulation and in-layer modulation of LAMlayers (2-dimensional growth).

A c k n o w l e d g m e n t . This work was supported by theKorean -J apan joint Research program (986-0300-004-2) s uppor t ed by K OSE F and J SPS and by Appli edRheology Center governed by KOSEF. SynchrotronSAXS at th e PLS (4C1 beam lines) was su pported by th eMinistry of Science and Technology (MOST) and PohangIron a nd Steel Co. (POSCO). The finan cial su pport byGrant-in-Aid from Japan Ministry of Education, Science,

Culture, and Sports with 08751048 granted to S.S. isalso gratefully acknowledged.

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