Chu, Macro Molecules (1995) Synch Rot Ron SAXS of Slow Spinodal Decomposition in a Block Copolymer

8/8/2019 Chu, Macro Molecules (1995) Synch Rot Ron SAXS of Slow Spinodal Decomposition in a Block Copolymer

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2700 Macromolecules 1995,28, 2700-2704

Sync hrotron Small-Angle X-ray Scat ter ing of Slow SpinodalDecomposition in a Block CopolymerMikihito Takenaka, Kung Linliu, Qicong Ying, and Benjamin Chu*Department of Chemistry, State University of New York at Stony Brook, Stony Brook,Long Island, New York 11794-3400Dennis PeifferCorporate Research Laboratories, Exxon Research and Engineering Company,Clinton Township, Annandale, New Jersey 08801-0998Received October 7, 994; Revised Manuscript Received Ja nu ar y 31, 1995@

ABSTRACT: A block copolymer poly(styrene-b-tert-butylstyrene)n the frozen disordered sta te h as beenprepared by fast solution casting. The time changes in the sca ttered intensity induced by a temperaturejump from the frozen disordered state at room temperature to above the glass transition temperatu rewere measured by using time-resolved synchrotron small-angle X-ray scattering. It was found th at thetime changes in the scat tered intensi ty could be approximated by the Cahn linearized theory. Thewavenumber q-dependence of the Onsager coefficient, Nq ) , derived from the growth rate, R(q), wasdiscussed.

I. IntroductionPhase transitions of block copolymers have been animportant and interesting topic in nonequilibrium sta-tistical physics in recent years. Block copolymersexhibit microphase separation transition and formperiodical microdomains. However, most of the studieshave been concerned with the phase diagram and theequilibrium structure. Both experimenta1112 andworks explored mainly the various highlyordered structures of block copolymer melts. Hash-imoto6 proposed the Cahn-Hilliard-Cook (CHC) typeequationsgJOor the dynamics of block copolymers in theearly stage of phase separation by using the time-dependent Ginzburg-Landau (TDGL) heory. He pos-

tulated t ha t the dynamics of the ordering process couldoccur via the spinodal decomposition in polymer blends.Kawasaki and Sekimot0~7~btained a new stochasticequation t o describe the dynamics of block copolymersand predicted that the Onsager coefficient A had awavenumber q-dependence. For the dynamics of spin-odal decomposition in polymer blends, the q-dependenceof A(q)was investigated by small-angle neutron scat-tering.11,12 Many paper~~-~Oeported the experimentalresults for the ordering process of block copolymers.However, only two papers, by Connel and Richards15and by Stuhn et a1.,20 ompared the experimental resultswith the CHC theory. However, they did not find theq-dependence of A(q). The other papers reported thatthe ordering dynamics of block copolymer progresses vianucleation and growth because the systems werequenched near the order-disorder transition (ODT)point where the fluctuation effects played a very im-portant role.

In this paper we investigated the ordering dynamicsin the block copolymerpoly(styrene-b-tert-butylstyrene)quenched deeply by means of small-angle X-ray scat-tering (SAXS). The experimental results are comparedwith the CHC equation, and then the q-dependenceofA(q) s obtained.

* Author to whom correspondence should be addressed.@ Abstract published in Advance ACS Abstracts, March 1,1995.

0024-929719512228-2700$09.0010

Table 1. Characterizationof the Sample Used in thisStudy

Mn(10T5) MdM, PSwt% R,,,,dnma z,b1.63 1.13 50 11.0 158

PS PtBSmolar volume of monomeso(cm3/mol) 10 7 167segment length30 (nm) 0.67 0.76polymerization index between 128 188

aR, = (Rg,ps2+R,RBS~)~.e= (NQS+ N,,RBs)/~.

-

entanglements30-11. Experimental Method11-1. Specimens. The diblock copolymer was selectedpartially because of its high glass transition temperature Tg

[Tg of polystyrene (PSI is 100 C and T,of poly(tert-butyl-styrene) (PtBS) is 149 C]. Thus, we had the followingadvantages for our experimental study: (i) The disorderedsta te obtained through a fa st solution casting of the thin filmremained disordered even at room tempe rature which shouldbe the tempera ture of the ordered region. The frozen-instructure (disordered state in our case) due to the high Tgmeans t ha t we could measure t he dynamics of high molecularweight block copolymers in the bulk. (ii) The dynamics of theordering process became extremely slow if we quenched t o atemperature near Tg. y using these two advantages we couldmeasure the slow dynamics of the ordering process in blockcopolymers. The characteristics of the sample we used ar elisted in Table 1.A benzene solution of the diblock copolymer was quickly

dried on a watch glass at 60 C. Then the diblock copolymerfilm in the disorder state (which can be demonstrated indi-rectly at this time; further experiments are under way) wasdried in a vacuum oven at 100 C (below the glass trans itiontemperature), cut into 5 mm squares, stacked, and molded at105 C . The thicknesses of the molded samples were on theorder of 0.15 mm.11-2. Experimental Technique. SAXS xperiments wereconducted at the SUNYX3A2 beamline, National SynchrotronLight Source, Brookhaven National Laboratory. We used amodified Kratky collimatorz1and a one-dimensional position-sensitive detector. The X-ray wavelength A was 0.154 nm. Thesample was subjected to a temperature jump from 23 to 228C. All scattered intensity profiles were corrected for back-ground and smearing effects.z2

0 995 American Chemical Society


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Macromolecules, Vol.28,No. 8,1995Time-change in the scattered intensity

SAXS of Slow Spinodal Decomposition 2701'iy= 10

n" 0.1 0.2 0.3 0.4 0.5q/nm-'

Figure 1. Time change in scattered intensity as a functionof q after a temperature ump from 23 to 228 "C . Measure-ment time per curve was 60 s. Sample thickness was 0.15mm. It should be noted that we have most likely prepared adisordered diblock copolymerby the quick solvent evaporationprocedure at 60 "C . The scattered intensity from the initial"disordered" state (hollow circles) agreed with the estimates(eq 7) of the scattered intensity based on RPA with x = 0.0075and parameters listed in Table 1.111. Experimental Results

Figure 1 shows the time change in the scatteredintensity plotted as a function of the magnitude ofscattering vector q[=(4n/A) in(f3/2), with 8 being thescattering angle]. The scattered intensity a t the ob-served q-region increased with time; but the peakposition did not change with time. It is expected th atthe peak should shifk to smaller q values a t later timesbecause of nonlinear effects.IV. Analyses and Discussion

IV-1. Test of the Cahn Linearized Theory. Fig-ure 2 shows the time change in the scattered intensityI ( q , t )as a function of time t at various fixed q values.The semilogarithmic plot indicates that the scatteredintensity a t various q values increases exponentially upt o 4.9 x lo3 s. Such an exponential growth wasobserved in the phase separation dynamics of poly-(styrene-b-isoprene) in the presence of C ~ H I Z / C ~ D ~ ~ . ~ ~However, the time region for the exponential growthwas only 40 s for the poly(styrene-b-isoprene) n thepresence of C6HldC6D12.According to Hashimoto6 and Kawasaki and Sekim-o ~ o , ~ , ~he dynamics of spinodal decomposition (SD) ina block copolymer A-B is described by the followingTDGL theory:

where q(q,t),Mq), and &,t) are th e order parameterof A, the Onsager coefficient, and the chemical potential,respectively. In this study, A and B correspond to PSand PtBS, respectively. The random forcef(q,t) obeysthe following fluctuation-dissipation relation:

with the subscript T denoting a thermal average. Ifq(q,t) is small, p(q,t) can be calculated by the relation

2.0J-Y

I2 . 8 7 - q=O. 156 nm-'2.41 I

4

q=0.301 nm'l0.8

0 lo00 2000 3000 4Ooo 5000time (sec.)

Figure 2. Semilogarithmic plot of scattered intensity as afunction of time at various fixed q values.&,t) = W(a,tYST(q> (3 )

where ST ( q )s the virtual structure factor. From eqs 1t o 3 we obtain the CHC equation for the structure factorS(q t1:S(q,t)= 1q(q$)12)T ST(4)+[ s ( ~ , o )sT(q)1xp[2~(q)t1 4)where R( q ) s the growth rate at q defined by

If the quench depth is deep, the effects of thermal noisebecome negligible and the time evolution of S(q,t)canbe expressed by the Cahn t h e ~ r y : ~

The Cahn linearized theory also predicted tha t the peakposition does not change with time. The experimentalresults agree with these features and indicate that thetime change in the scattered intensity corresponds tothe increase in the concentration fluctuations from thehomogeneous state. Leiblefi calculated ST ( q ) n thecontext of the Laudau-type mean-field theory by usingthe random-phase approximation (RPA). The effects ofpolydispersity and composition distribution were thentaken into account in ST(q).23-25he results suggestthat ST(q) an be expressed by(7)


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2702 Takenaka et al. Macromolecules, Vol.28, No . 8, 1995with x being the Flory-Huggins interaction parameterper segment. According t o ref 2 5 , S(q) and W ( q )aregiven by

(8 )(q )= s,(q) + 2sm(q)+ B B ( q )and

S&), S d q ) , and SAA(Q)re expressed by

and

and

(14)where

XK,n = N K , n a 2 q 2 l 6 (15)and

'K = NK,dNK,n (16)Here NK , n , N K , ~ ,nd UK are respectively the number-average degree of polymerization (DP), the weight-average DP, and the statistical segment length of K ( K= A o r B). r , and fA,n are respectively the effectivenumber-average DP of the block copolymer and thenumber-average fraction of A and are defined by

rn= uA / vo )NA , , + uB/uO)NB, , (17)and

fA,n = uANA,n/(uANA,~ + U f l B , n ) (18)where UK denotes the molar volume ofK, nd uo denotesthe molar volume of the reference cell of the systemgiven by

U O = uAuB ) ~" (19)Around the peak position q * , ST(q) ould be approxi-mated by the Orstein-Zernike-Debye (OZD) formz6

where the correlation length 5 is defined by(20)

(21)

o.ob0 1 2 3(q-q*? (10211rn~*)

Figure 3. R(q ) / q2 s a function of (q - q*)2 for q > q*with x s being the value at the spinodal point of theorder-disorder transition of a block copolymeror S(q*) /W(q* ) .At q > q* , ST(q)an be approximated well by eq20. It is noted t ha t the slope [(slope)oz~I nd theintercept [(intercept)oml in an OZD plot or l/ST(q)s(q - q*Y are described byand

respectively, and that (slope)ozD is independent oftemperature. By using eqs 8-19 with the characteristicproperties of the block copolymer listed in Table 1,wecalculated xs = 0.007 4 9 , (slope)ozD= 0.385, and qeal*=0.162nm-', which is in reasonable agreement with qeY*= 0.17 nm-l. By substituting eq 20 into eq 5, we obtain

IfA(q) s independent of q , a plot ofR(q)/q2 s (q - q*I2,also known as the "Cahn plot", should show a linearcurve. Figure 3 shows the R(q)/q2 s (q - q*P plot forq > q*. The curve clearly implies that A(q) is notindependent of q.Kawasaki and Sekimoto8proposed the followingA(q)expression.2A h ) = ~ [ ~ R B SP S + ~ P SRBS + +PS+RSSVPSVP~BS]

( 25 )where @K and Ao are the volume fraction of the Kthcomponent and the Onsager coeficient at q = 0,respectively. V K is defined by

where Rgs s the radius of gyration of the Kth compo-nent given by

with NK and UK being the polymerization index and thestatistical segment length of the Kth component, re-


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Macromolecules, Vol.28, No. 8,1995 SAXS of Slow Spinodal Decomposition 2703

2 30 1 2 3(q-q*)' (IO*m.' )

Figure 4. R ( q )as a function of (q - *) 2 fo r q > q* . The solidline indicates the fitting result with R ( q )= 7.09 x 10-5-5.97spectively. Equation 25 denotes the "fast theory",whereby a constant chemical potential for the totalmonomer density has been assumed.8 For qRg,ps>> 1and QRg,Ptss>> 1

A(q)- q-' (28)

x 10-4 4 - q*y.

Equation 24 then becomes(29)

In eq 29, R( q ) is proportional to (q - q*)z for q > q*where K is a constant. In Figure 4,R( q ) s plottted asa function of (q - q*)2 or q > q* . The relationshipbetween R( q )and (q - q* ) z becomes linear so that A(q)is found to be proportional to qw2 n the high q-region.There is a deviation from the linear relationship around(q - . q , * ) 2 = 0 because q cannot be satisfied with theconditions qRg,ps>> 1 and qRg,PtBS >> 1.IV-2. Estimationsof the rParameter and Nq ) .The slope [(slope)~(,)lnd the intercept [(intercept)~(,,lin Figure 4 are given by

(30)and

(intercept),(,, = K/ST(q*) 2K (x - x,) (31)respectively. From eqs 23 and 31,

(32)we then obtained K = -646 s-l so that x at 228 "C canbe estimated by using eq 31 with the estimated K. Theestimated value of x is 0.0304, and the thermodynamicforce E defined by

(33)is 3.06 which is more than unity. The value of Eindicates that the phase separation condition of thesystem a t 228 "C corresponds t o a deep quench and tha tthe thermal noise effects can be neglected a t 228 "C.

E = (x - xJx,

q (nm.')Figure 5. Onsager coefficient A(q)as a function of q . Thesolid line and the dotted line correspond to the Kawasaki andSekimoto theory (eq 25 ) and the Pincus theory (eq 361,respectively. The broken line has a slope of -2. Data pointsat q -= 0.14 nm-l should be ignored.This result is consistent with the exponential growthof the scattered intensity. Further experiments at othertemperatures could determine the temperature depend-ence of 2. Then the order-disorder transition (ODT)temperature could be estimated.The theory of Fredrickson and Binderz7 and theexperimental results by Bates et a1.16 suggested that thephase separation of block copolymers near the ODTtemperature progresses via nucleation and growthbecause of the fluctuation effects. However, accordingto Muthukumar,z8composition fluctuation effects domi-nante over a narrow range of xN , (xNtxN < (xNt1,where xN is the product ofx and polymerization indexN of block copolymers and ( xN ) t is the value of xN atODT. (xNt s given byz7

(34)and the value of (xNt s 14.32 for PS-PtBS. Since thevalue of xN at 228 "C s 37.51 and is much higher than(xNt+ 1. It is, hence, expected that the fluctuationeffects become small and that the phase separationoccurs via spinodal decomposition in the strong segrega-tion limit.By using the estimated x, eqs 8-19, ST(q) an becomputed so that we can determine the q-dependenceof N q ) . From eq 5 , N q ) s given by

(xNt= 10.495+ 41.0N-1'3

A(q)= - R ( q ) ST ( q ) / q z (35)Figure 5 shows the q-dependence ofA(q)as calculatedby eq 35. The solid line is the theoretical results basedon the Kawasaki and Sekimoto theory.8 We fitted theregion with a q-z-dependence by using eq 25 and thevalues of Rgpsand Rg,PtBS estimated from the polymer-ization indices and the statistical segment length of bothcomponents. We treated A0 as a floating parameter. Inthe high q-region,A(q) s proportional to q-2 as repre-sented by the broken line. Theq-2 dependence at highq values agree with the Kawasaki and Sekimoto result.However, the experimental result bends down at q =0.2 nm-l (point B in Figure 5) which is smaller thanthat of the theoretical result (pointA, q = 0.28 nm-I inFigure 5). Furthermore, the experimental data bendupward at q x 0.14 nm-l (point C in Figure 5) which isnot expected in the theoretical prediction. The reason


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2704 Takenaka et al. Macromolecules, Vol.28, No. 8, 1995for the upward bend could be an experimental artifactdue t o strong stray X-rays. Further experiments areneeded t o ascertain the upward bend at smaller qvalues.In the Pincus theory,29

is compared with A(q) or polymer blends,11J2where R ,is the radius of gyration of the block copolymer. Wefitted the data with eq 36 by tregting R, and A0 asfloating parameters and obtginedR, = 9.0 nm and A0= 0.13 nm2/s. The value of R, was about 0.82 times aslarge as that (Rg,block) estimated from the molecularweight measurement (see Table 1).V. Summary

In summary, we have investigated the extremely slowphase separation process via spinodal decomposition inpoly(styrene-b-tert-butylstyrene).The exponential growthof the scattered intensity with time is found to continueup to 4.9x lo 3 s, and th e early stage of the ordering inthe block copolymer can be approximated by the Cahnlinearized theory. The value of R( q ) and that of the xparameter at the phase separation temperature, to -gether with the q-dependence of Nq ) ,are obtained byan analysis of the Cahn linearized theory. At qRg,ps>>1and qRg,ptBs>> 1,we found that q-2-dependence inNq )as predicted by Kawasaki and Sekimoto. The experi-mental results over the entire q-range, however, wereinconsistent with the theoretical predictions as shownin Figure 5.Acknowledgment. Support of this work by thePolymers Program (DMR 9301294) of the NationalScience Foundation is gratefully acknowledged. Wethank Professor Muthukumar for helpful discussions.

References and Notes(1) Hashimoto, T. In Thermoplastic Elastomers; Legge, N . R.,Holden, G ., Schroeder, H.E., Eds.; Hanser: Vienna, Austria,1987; Chapter 12, Section 3, p 349.(2) Bates, F. S.;Fredrickson,G. H.Annu.Rev. Phys. Chem. 1990,41, 25.(3) Helfand, E. Macromolecules 1975, , 552.(4) Leibler, L. Macromolecules 1981, 3, 602.(5) Kawasaki, K.; Ohta, T.; Kohrogui, M. Macromolecules 1988,(6) Hashimoto, T. Macromolecules 1987,20,56.(7) Kawasaki, K.; Sekimoto, K. Physica A 1988,148, 61.(8) Kawasaki, K.; Sekimoto, K. Macromolecules 1989,22,063.(9) Cahn, J. W. Acta M etall. 1961, , 95.(10)Cook, H. E. Acta Metall . 1970, 8, 97.(11) Schwahn,D.; Janssen, S.;Springer, T. J . Chem. Phys . 1992,

(12) Jinnai , H.; Hasegawa, H.; Hashimoto,T.; Han, C. C. J . Chem.(13) Hashimoto. T.: Kowsaka. K.: Shibavama. M.: Kawai, H.

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97, 775.Phys. 1993, 9, 154.

" 1Macromolecules 1986, 9,'54.(14) Harkless. C. R.; Singh, M. A.; Nader. S. E.; Stephenson,G.B.; Jordan-Sweet, J-L. P h y s. R e L L e t t . 1990, 2, 2285.(15) Connel, J. G. ; Richards, R. W. Polymer 1991, 2, 033.(16) Bates, F. S.;Rosedale, J. ;Frederickson, G . H. J . Chem. Phys .(17) Schuler, M.; Stiihn,B. Macromolecules 1993,26,12.(18)Anastasiadis, S.H.; Fytas, G. ;Vogt, S.;Fischer, E. W. Phys.(19) Russel, T. P.; Chin, I. Colloid.Polym. Sei . 1994,272,373.(20) Stiihn, B.; Vilesov, A.; Zachmann, H. G .Macromolecules 1994,(21) Chu, B.; Wu, D.; Wu, C. Rev. Sei . Znstrum. 1987, 8, 158.(22) Lake, J. A.Acta Crystallogr. 1967,23,91.(23) Leibler, L.; Benoit, H. Polymer 1981,22, 95.(24) Burger, C.; Ruland, W.; Semenov,A. . Macromolecules 1990,(25) Sakurai, S.; Mori, K.; Okawara, A.; Kimishima, K.; Hash-(26) de la Cruz,M. 0 .;Sanchez, I. C. Macromolecules 1986, 9,(27) Fredrickson,G. .; Binder, K. J . Chem. Phys. 1989,91,7265.(28) Muthukumar, M. Macromolecules 1993,26,259.(29) Pincus, P. J . Chem. Phys . 1981, 5, 996.(30) Fetters, L. J.; Lohse, D. J.; Richter, D.; Witten, T. A,; Zirkel,

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Chu, Macro Molecules (1995) Synch Rot Ron SAXS of Slow Spinodal Decomposition in a Block Copolymer