Micellization of Polystyrene-b-poly(ethylene/butylene)-b-polystyrene Triblock and

Polystyrene-b-poly(ethylene/propylene) DiblockCopolymers in n-Octane

Jose R. Quintana, Marıa D. Janez, and Issa Katime*

Grupo de Nuevos Materiales, Departamento de Quımica Fısica, Facultad de Ciencias, Campusde Leioa, Universidad del Paıs Vasco, Apartado 644, 48080 Bilbao, Spain

Received September 30, 1996. In Final Form: February 20, 1997X

Static anddynamic light scatteringandviscometry experimentswereperformed to study themicellizationthermodynamics, micelle structural parameters, and micelle size distribution of a polystyrene-b-poly-(ethylene/propylene) diblock copolymer, SEP2, and a polystyrene-b-poly(ethylene/butylene)-b-polystyrenetriblock copolymer, SEBS2, in n-octane solutions. n-Octane is a selective solvent for the olefin blocks.Both copolymers have similar chemical composition andmolarmass, but whereas SEP2will form classicalmicelles, SEBS2 will have to formmicelles with a corona constituted by loops of the middle poly(ethylene/butylene) block in order to bring the two end polystyrene blocks into the core and it is also conceivablethat some of these end blocks become extended into solution. The influence of the different micellearchitecture in themicellizationprocesswasanalyzed. Standard thermodynamic functions ofmicellizationwere determined from light scattering measurements. All the functions obtained for SEBS2 are muchsmaller than those for SEP2. SEBS2 micelles have also lower association number and size than those forSEP2. Interestingly, an aggregation process of micelles was detected for SEBS2 solutions at relativelylowconcentrationwhereas in theSEP2solutionsonlymicelleswithanarrowsizedistributionwereobserved.The different behaviors observed for both copolymers confirm the possible structure suggested above fora triblock copolymer dissolved in a selective solvent of the middle block.

Introduction

A large number of investigations have been carried outon the association of AB and ABA block copolymers inselective solvents of the A blocks. A solvent is consideredaselective solvent if it is a thermodynamicallygoodsolventfor one type of block but nonsolvent for the other type ofblock. It is now well established1-3 that for these aggre-gation systems, uniform spherical micelles are formed indilute solutions. The relatively compact core of micellethus formed consists predominantly of insoluble B blocksand is surrounded by a swollen protective corona ofsolvatedA blocks extending into solution. In general, thesize distribution of these micelles is very narrow and themicellization process obeys the closed association mech-anism.However, relatively little understanding has been

achieved about the solution properties of triblock copoly-mers in solvents that preferentially dissolve the middleblock. Few have been the articles published about thesesystems,4-20 and besides, they become contradictory in

their conclusions. Whereas someauthors5,6,8 fail to detectany multimolecular association, others find well-definedmicelles4,9,11-16 or aggregates with a loose structure.18,19In addition, some authors7,10,19,20 suggest that branchesor network-like structures due to the interchain associa-tion might exist in the semidilute region.Theoretical aspects of possible micelle formation for

these systems were considered by ten Brinke and Hadzi-ioannon.21 They analyzed the formation of micelles withlooped coronal blocks and concluded that the entropy lossassociated with the looping of the middle block wouldpreclude the possibility of micelle formation. However,Balsara et al.11 considered later that the micellizationprocess was possible under some conditions, in spite ofthe additional entropic penalty arising from the loopedcoronal blocks. Simulations have recently documentedthe micellization of these types of copolymers, as well asthe formation of physical networks.22-25

The aim of the present work is to improve our under-standing of these systems, focusing on the colloidalproperties of a polystyrene-b-poly(ethylene/butylene)-b-

* TowhomcorrespondencemaybeaddressedatAvda.Basagoiti,8-1˚C, 48990 Algorta, Getxo, Vizcaya, Spain.

X Abstract published in Advance ACS Abstracts, April 15, 1997.(1) Brown, R. A.; Masters, A. J.; Price, C.; Yuan, X. F. Comprehesive

Polymer Science; Booth, C., Price, C., Eds.; Pergamon Press: Oxford,1989; Vol. 2, Chapter 6.

(2) Quintana, J. R.; Villacampa, M.; Katime, I.Rev. Iberoam. Polim.1992, 1, 5.

(3) Tuzar, Z.; Kratochvil, P. Surface and Colloid Science; Matijevic,E., Ed.; Plenum Press: New York, 1993; Vol. 15(1).

(4) Krause, S. J. Phys. Chem. 1964, 68, 1948.(5) Tanaka, T.; Kotaka, T.; Inagaki, H. Polym. J. 1972, 3, 327.(6) Tanaka, T.; Kotaka, T.; Inagaki, H. Polym. J. 1972, 3, 338.(7) Kotaka, T.;Tanaka, T.; Hattori, M.; Inagaki, H.Macromolecules

1978, 11, 138.(8) Tang, W. T.; Hadziioannou, G.; Cotts, P. M.; Smith, B. A.; Frank,

C. W. Polym Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1986, 27 (2),107.

(9) Plestil, J.; Hlavata, D.; Hronz, J.; Tuzar, Z. Polymer 1990, 31,2112.

(10) Tuzar, Z.; Konak, C.; Stepanek, P.; Plestil, J.; Kratochvil, P.;Prochazka, K. Polymer 1990, 31, 2118.

(11) Balsara, N. P.; Tirrell, M.; Lodge, T. P. Macromolecules 1991,24, 1975.

(12) Zhou, Z.; Chu, B. Macromolecules 1994, 27, 2025.(13) Zhou, Z.; Chu, B.; Peiffer, D. G. Langmuir 1995, 11, 1956.(14) Chu, B.; Wu, G.; Schneider, K. J. Polym. Sci., Part B: Polym.

Phys. 1994, 32, 2605.(15) Chu, B.; Wu, G. Macromol. Symp. 1994, 87, 55.(16) Chu, B.; Wu, G. Macromol. Symp. 1995, 90, 251.(17) Wu, G.; Zhou, Z.; Chu, B. Macromolecules 1993, 26, 2117.(18) Raspaud,E.; Lairez,D.;Adam,M.;Carton, J.-P.Macromolecules

1994, 27, 2956.(19) Lairez, D.; Adam, M.; Raspaud, E.; Carton, J.-P.; Bouchaud,

J.-P. Macromol. Symp. 1995, 90, 203.(20) Quintana, J. R.; Dıaz, E.; Katime, I.Macromol. Chem. Phys., in

press.(21) TenBrinke,G.;Hadziioannou,G.Macromolecules1987,20, 486.(22) Rodrigues, K.; Mattice, W. L. Polym. Bull. 1991, 25, 239.(23) Rodrigues, K.; Mattice, W. L. Langmuir 1992, 8, 546.(24) Wang, Y.; Mattice, W. L.; Napper, D. H.Macromolecules 1992,

25, 4073.(25) Nguyen-Misra, M.; Mattice, W. L. Macromolecules 1995, 28,

1444.

2640 Langmuir 1997, 13, 2640-2646

S0743-7463(96)00952-3 CCC: $14.00 © 1997 American Chemical Society

polystyrene copolymer, SEBS, dissolved in n-octane. Wecompared the associationprocess of this copolymer to thatof a polystyrene-b-poly(ethylene/propylene) diblock co-polymer with a similar molar mass, polystyrene percent-age, and chemical nature. The main difference betweenboth copolymers is their structure, three and two blocks.By using static and dynamic light scattering and vis-cometry techniques, we studied the micellization ther-modynamics and the aggregate characteristics of bothcopolymers in n-octane, analyzing their differences.

Experimental SectionMaterialsandSolutionPreparation. Polystyrene-b-poly-

(ethylene/butylene)-b-polystyrenecopolymersample,SEBS2,andpolystyrene-b-poly(ethylene/propylene) copolymersample,SEP2,are commercial products kindly provided by Shell Espana, S.A.The samples have been previously characterized in detail.26,27They are homogeneous in chemical composition and their massaverage molar mass, mass average to number average molarmass ratio, and styrene content are shown in Table 1. n-Octane(analytical purity grade) was used without further purification.The solvent used for light scatteringmeasurements was filteredfour times using a 0.02 µmaluminum oxidemembrane filter. Allthe solutions were prepared by dissolving the copolymer inn-octane at temperatures close to 70 °C and in sealed flasks. Inorder to clarify copolymer solutions for static and dynamic lightscattering measurements, they were filtered at 60 °C directlyinto the scattering cells using 0.2 µm PTFE Acrodisc CR filters.The cells were then sealed. For the viscosity measurements,solutions were filtered with number 3 glass filters. Solutionconcentrations used to determine critical micelle temperatures,CMT,were recalculated at the CMTs. As all the used copolymersolutionswere diluted, solutionswere assumed to have the samethermal expansion coefficient as that of pure solvent.Viscometry. The viscosity measurements were made in a

LaudaautomaticUbbelohdeviscometerModelViscoboy2,whichwas placed in a thermostatically controlled bathwith a precisionof (0.01 °C. The viscometer was calibrated using severalstandard solvents. Kinetic energy corrections were carried out.The data were evaluated either according to Huggins andKraemer equations28 or according to Heller equations.28StaticLightScattering. In order todeterminemicellization

thermodynamics and micellar structural parameters, lightscattering techniques were employed. Static light scatteringmeasurements (SLS) were performed on amodified FICA 42000light scattering photogoniodiffusometer. Both light source andoptical block of the incident beam were replaced by a Spectra-PhysicsHe-Ne laser,Model 105,whichemitsverticallypolarizedlight at 632.8 nm with a power of 5 mW. The instrument wascalibrated with pure benzene taking the Rayleigh ratio at 25 °Cas 12.55 × 10-6 cm-1.Block copolymersundergo closedassociation indilute solution

to formmicelles that have an appreciable association number.29For these systems the standard Gibbs energy of micellization,∆G°, can be determined by using the relation

where CMC is the critical micelle concentration, which isexperimentally determined. The critical micelle concentrationis definedas the concentrationatwhich the experimentalmethodin use can just detect the presence of micelles in the solutionwhen the concentration is increased at a constant temperature.Although the assumption of the independence of the associationnumber on temperature is virtuallynever fulfilled, its acceptancedoes not seem to affect the calculated values of the standard

enthalpy of micellization, ∆H°, substantially. Therefore ∆H°can be determined by measuring the temperature dependenceof the critical micelle concentration, since36

Investigations on the thermodynamics ofmicellization of blockcopolymers in organic solvents have shown that it is far betterexperimentally to carry out measurements in which the con-centration is kept constant and the scattered light intensity ismonitoredoverarangeof temperatures inorder to find thecriticalmicelle temperature, CMT, than keeping the temperatureconstant and varying the concentration so as to find the criticalmicelle concentration.31,32 The critical micelle temperature of asolution at a given concentration is the temperature at whichthe formation of micelles can just be detected experimentally inthe solution. Therefore, it has been shown33 that, within theexperimental error

Thus, eq 2 becomes

To establish critical micelle temperatures, measurements oflight scattered intensity were made at a series of temperatureswithin the range of 15-90 °C at a scattering angle of 45°.Todetermine themassaveragemolarmass,Mw, and the radius

of gyration,RG, light scattering measurements were made at 11angles between 30 and 150° for the solvent and each copolymersolutionat 25 °C. The light scatteredbyadilutepolymer solutionmay be expressed as34

whereK is anoptical constant, c thepolymer concentration,∆R(θ)the difference between the Rayleigh ratio of the solution andthat of the pure solvent,Mw the mass average molar mass, q )(4πn/λ0) sin(θ/2) the length of the scattering vector, RG thez-average radius of gyration, n the solution refractive index, λ0the wavelength in vacuum, A2 the second virial coefficient, andθ the scattering angle.The extrapolation of Kc/∆R(θ) at θ ) 0 by means of a mean-

square linear fit allows knowledge of the apparent radius ofgyration,Rapp, from the slope and the apparentmass,Mapp, fromthe ordinate.Refractive Index Increment. To estimateMw andRG, it is

necessary to know the refractive index increment, dn/dc, and thesolvent refractive index, n. The refractive index increment ofthe copolymer solutions were measured using a Brice-Phoenixdifferential refractometer equipped with a He-Ne laser as lightsource (Spectra Physics, Model 156, 632.8 nm and power of 1mW). The differential refractometer was calibrated with solu-(26) Villacampa, M.; Quintana, J. R.; Salazar, R.; Katime, I.

Macromolecules 1995, 28, 1025.(27) Quintana, J. R.; Villacampa, M.; Katime, I. Makromol. Chem.

1993, 194, 983.(28) Lovell, P. A. Comprehensive Polymer Science; Booth, C., Price,

C., Eds.; Pergamon Press: Oxford, 1989; Vol. 1, Chapter 9.(29) Elias, H.-G. Light Scattering from Polymer Solutions; Huglin,

M. B., Ed.; Academic Press: London, 1972; Chapter 9.(30) Stainsby, G.; Alexander, A. E. Trans. Faraday Soc. 1950, 46,

587.

(31) Price, C. Pure Appl.Chem. 1983, 55, 1563.(32) Price, C.; Stubbersfield, R. B.; El-Kafrawy, S.; Kendall, K.D.Br.

Polym. J. 1989, 21, 391.(33) Price, C.; Booth, C.; Canham, P. A.; Naylor, T. V.; Stubbersfield,

R. B. Br. Polym. J. 1984, 16, 391.(34) Katime, I.; Quintana, J. R. Comprehensive Polymer Science;

Booth,C.,Price,C.,Eds.; PergamonPress: Oxford, 1989;Vol. 1,Chapter5.

∆G° ≈ RT ln(CMC) (1)

Table 1. Characteristics of the Block Copolymers: MassAverage Molar Mass of the Copolymer, Mw, of the

Polystyrene Blocks, Mw,PS, and of the Polyolefin Block,Mw,olefin, Polystyrene Weight Percentage, and

Polydispersity Index, I

sampleMw

(g‚mol-1) Iwt %PS

Mw,PS(g‚mol-1)

Mw,olefin(g‚mol-1)

SEBS2 87 200 1.11 32 2 × 14000 59 400SEP2 105 000 1.06 35 37000 68 000

∆H° ≈ R d ln CMCdT-1

(2)

d ln CMCdT-1

) d ln cd(CMT)-1

(3)

∆H° ≈ R d ln cd(CMT)-1

(4)

Kc∆R(θ)

) Mw-1(1 + q2RG

2) + 2A2c (5)

Micellization of Copolymers Langmuir, Vol. 13, No. 10, 1997 2641

tions of highly purified NaCl. The refractive indexes weremeasured in anAbbe refractometer. The dn/dc values of SEBS2andSEP2copolymers inn-octaneat25 °Cwere0.1289and0.1298,respectively.Dynamic Light Scattering. We used a light scattering

spectrometer Amtec in an angle range of 30-150°. Intensitycorrelation function measurements were carried out in the self-beating mode by using a Brookhaven BI-9000AT 522-channeldigital correlator. A Spectra-Physics Model 127 He-Ne laseroperating at 632.8 nmwas employed as the light source. Inmostcasesweacceptedonly thosephotoelectron count time correlationfunctions where the measured baseline, i.e., the average valueof the correlation function at very long delay times, agreed withthe computed baseline to within ∼0.1%.Themeasuredphotoelectroncurrent-timecorrelation function

in the self-beating mode has the form

where g(1)(τ) is the normalized electric field correlation function,τ the delay time, A is the background, and b a spatial coherencefactor, usually taken as an adjustable parameter in the fittingprocedure.For a polydisperse solution

where G(Γ) is the normalized characteristic line-width distribu-tion. The mean characteristic line width, Γh, and the secondmoment, µ2, are defined by

The cumulants35 andnon-negative constrained least-squares36methods were used for the data analysis of the dynamic lightscattering results.Once Γ has been obtained by any of the two methods, the

translational diffusion coefficient, D, and the hydrodynamicradius, Rh (the z-average value with the cumulants method oreach fraction value for the NNLS), can be determined from theequation

and the Stokes-Einstein relation

where D0 is the translational diffusion coefficient extrapolatedto nil concentration, q the scattering vector, kB Boltzmann’sconstant, T the absolute temperature, and η0 the viscosity of thesolvent.

Results and DiscussionThermodynamics Functions of Micellization. In

general, the thermodynamics functions of micellizationare determined from the variation of the critical micelleconcentration with temperature, CMC ) f(T), or thevariation of the concentration with the critical micelletemperature, c) f(CMT). Inotherwords, themicellizationprocess of a block copolymer in an organic solvent can beinitiatedeitherbyan increase in concentrationat constanttemperature (in this case we get the critical micelleconcentration) or a decrease in temperature at constantconcentration (the criticalmicelle temperature is achieved

in this case). For convenience we have determined thecritical micelle temperature at several different concen-trations by following the temperature dependence of theintegrated scattered light intensity of a copolymer solutionat a given concentration. It is known that light scatteringpossesses a considerably high sensitivity for monitoringa variation in the aggregate size. Figure 1 shows twotypical plots of the light intensity scattered to an angleof 45° against temperature for two SEP2 and SEBS2solutions with c ) 2.15 × 10-4 g‚cm-3 and c ) 5.1 × 10-4

g‚cm-3, respectively. The critical micelle temperaturesare shownbyanarrow. Above theCMTthe light intensityis very lowandonlyunimersarepracticallypresent.Whenthe temperature is lowered from a high value, a sharpincrease of the light intensity is detected at the CMT asa consequence of the fact that the micelle formationbecomes increasingly important. When the micellesbecomepredominant, the light intensity tends to stabilizeas the SEP2 curve shows. Similar curves I ) f(T) werefound when increasing and decreasing the temperaturefor all systems studied. On comparison of both intensity-temperature curves, it is clear that theSEP2micellizationis much more favored than the SEBS2 one. For similarconcentration the copolymer SEP2 shows a much highercriticalmicelle temperature. Like other block copolymersin organic solvent, for the micelle systems studied theCMT shifts to a higher value when increasing theconcentration and the CMC shifts to a lower value whendecreasing the temperature. In other words, the micelleformation is an exothermic process as expected.Criticalmicelle temperatureswere determined for both

copolymers inn-octane covering a range of concentrationsbetween 5× 10-6 and 2× 10-4 g‚cm-3 for SEP2 solutionsand 5 × 10-4 and 1.6 × 10-3 g‚cm-3 for SEBS2 solutions.All the plots were similar to the ones shown in Figure 1.Equation 4 can be integrated to yield

provided that the standard enthalpy of micellization isapproximately a constant in the temperature intervalinvolved.Plots of ln c as a function of (CMT)-1 for solutions of

SEP2 and SEBS2 in n-octane obtained on the basis of eq12 are shown in Figure 2. Both plots were linear withinthe experimental error over the temperature rangesstudied, 60-85 °C for SEP2and35-60 °C for SEBS2.The

(35) Koppel, D. E. J. Chem. Phys. 1972, 57, 4814.(36) Grabowski, E. F.; Morrison, J. D. Measurements of Suspended

Particles by Quasielastic light Scattering; Dahneke, B. E., Ed.; Wiley:New York, 1983; p 199.

G2(τ) ) A(1 + b|g(1)(τ)|2) (6)

g(1)(τ) )∫0∞G(Γ) exp(-Γτ) dΓ (7)

Γh )∫G(Γ) Γ dΓ (8)

µ2 )∫G(Γ)(Γ - Γh)2 dΓ (9)

Γ ) Dq2 (10)

D0 )kBT

6πη0Rh(11)

Figure 1. Temperature dependence of the scattered lightintensity at a scattering angle of 45° for two SEP2 (O) andSEBS2 (0) solutions in n-octane. c(SEP2)) 2.15× 10-4 g‚cm-3

and c(SEBS2) ) 5.10 × 10-4 g‚cm-3. CMT (SEP2) ) 84 °C andCMT (SEBS2) ) 35 °C.

ln c ≈ ∆H°R CMT

+ constant (12)

2642 Langmuir, Vol. 13, No. 10, 1997 Quintana et al.

slopes in Figure 2 yield ∆H° ) -158 kJ‚mol-1 for SEP2and∆H°) -41.9 kJ‚mol-1 for SEBS2. At 60 °C,∆G° andT∆S were estimated to be -46.7 and -110 kJ‚mol-1 forSEP2 and -29.9 and -11.9 kJ‚mol-1 for SEBS2, respec-tively.The standard Gibbs energy of micellization shows

negative values for both systems studied, as expected.The standardentropyofmicellization is alsonegativeand,therefore, unfavorable to the micellization process. Thenegative values of ∆S° result from the loss in the com-binatorial entropy due to the fact that the copolymerchains are more ordered in the micellar state than in theunassociated state. The standard enthalpy of micelliza-tion also shows negative values and therefore is solelyresponsible of the micelle formation. These negativevaluesarise fromtheexothermicenergy interchangewhichaccompanies the replacement of polystyrene segment/n-octane interactions by polystyrene segment/polystyrenesegment and n-octane/n-octane interactions in the forma-tion of the micelle cores.Through a comparison of these thermodynamic quanti-

ties betweenSEP2andSEBS2, important differences canbe observed. For SEBS2 in n-octane, the standardenthalpy of micellization shows a much lower value thanSEP2 due probably to the fact that the looping geometrythat the middle poly(ethylene/butylene) block needs toform themicellemakes some polystyrene blocks come outof the core and extend into the solution. Therefore thenumber of polystyrene/n-octane interactions replaced bypolystyrene/polystyrene and n-octane/n-octane interac-tions will be smaller. The existence of these polystyreneblocksoutof themicelle togetherwith the loopinggeometryof the middle block will lead to less order in the micelleand therefore less negative standard entropy of micelli-zation. For SEBS2 in n-octane, the loss of exothermicenergy interchangewhichaccompanies the core formationreduces largely the driving force for micellization. As aresult, the standardGibbs energyofmicellizationbecomesless negative as compared with SEP2. In other words,SEBS2has lower criticalmicelle temperatures andhighercritical micelle concentrations. At 60 °C, SEBS2 showsa CMC of 1.7 × 10-3 g‚cm-3 whereas SEP2 has a CMC of4.7 × 10-6 g‚cm-3. A behavior very similar was found byZhou et al. for a poly(oxypropylene)-b-poly(oxyethylene)-b-poly(oxypropylene) in aqueous solutions12 and a poly-(tert-butylstyrene)-b-polystyrene-b-poly(tert-butylsty-rene) in N,N- dimethylacetamide.13

Static Light Scattering. Static light scatteringmeasurements were mainly performed on solutions of

SEP2 and SEBS2 copolymers, whose concentrationsranged between 3× 10-4 and 9× 10-3 g‚cm-3 in n-octaneat 25 °C. Plots of the reciprocal apparent mass,Mapp, asa function of concentration for both copolymers are shownin Figure 3. For SEP2, the concentration dependence ofthe apparentmolarmass is linear at lower concentrationsas expected for concentrations verymuch higher than thecritical micelle concentration. From the relationshipconcentration-CMT we found a CMC of 5.9 × 10-9

g‚cm-3 at 25 °C. The mass average molar mass obtainedfrom the double extrapolation to nil angle and concentra-tion can be considered as the molar mass of the micelles,since the copolymer samples are chemically homogeneousand, under these experimental conditions, micelle forma-tion is overwhelmingly favored. From the ordinate wefound a micelle molar mass of 9.2 × 106 g‚mol-1. Theslight curvature found at higher concentrations can beconsidered as the typical behavior found for polymersolutions moderately concentrated.37The curvature that the SEBS2 apparent molar mass

presents at the lower concentrations is a consequence ofthe relatively high criticalmicelle concentration that thismicellar system has at 25 °C (2.9 × 10-4 g‚cm-3). For acopolymer micelle system the apparent molar massMapp) ∆R0/Kc, canbe expressedasaweighted sumof themolarmass of the unassociated copolymer chain, Mw

u, andmicelle, Mw

m

where wu and wm are the mass fractions of unimers andmicelles, respectively. By considering that the unimerconcentration in every concentration was the same andequal to the critical micelle concentration, we havedeterminedMw

m for each copolymer concentration usingeq 13 and found values (1.04 × 106 g‚mol-1) virtuallyindependentof copolymerconcentration. This foundvalueis close to that found by Tuzar et al.10 for a similar SEBSsample in n-heptane (2.26 × 106 g‚mol-1).

(37) Hyde, A. J.Light Scattering fromPolymerSolutions; Huglin,M.B., Ed.; Academic Press: London, 1972; Chapter 8.

Figure2. Plot of the logarithmof the copolymer concentrationasa function of the reciprocal of the criticalmicelle temperaturefor the copolymers SEP2 (O) and SEBS2 (0) in n-octane.

Figure 3. Concentration dependence of Kc/∆R0 ) 1/Mapp forthe copolymers SEP2 and SEBS2 in n-octane at 25 °C.

Mapp ) Mwuwu + Mw

mwm (13)

Micellization of Copolymers Langmuir, Vol. 13, No. 10, 1997 2643

The high association number that SEP2 micelles showinn-octane (88) contrastswith the lowvalue of theSEBS2micelles (12). The copolymer SEBS2 in 4-methyl-2-pen-tanone solutions26 also shows a high association number(115). This solvent is selective of the polystyrene blocks.Therefore the low association number of the copolymerSEBS2 in n-octane can be attributed to the difficulty thatthe copolymer chains find to form a micelle with a coreconstituted by the end blocks. The micelle will probablyhave loops formed by the middle block, and some of thepolystyrene end blocks will be out of the micelle coretoo. The less order that the micelle will have does notallow that a large number of chains become part of themicelle.The scattering angle dependences ofKc/∆R for various

solutions of SEP2 and SEBS2 in n-octane with differentcopolymer concentrations are plotted in Figure 4. Kc/∆Rvaries linearly with observation angle for all concentra-tions. Whereas the SEBS2 solutions show a normalbehavior, for the SEP2 solutions the slope of each linedecreaseas the concentration increases, reachingnegativevalues at higher concentrations than 2 × 10-3 g‚cm-3.This behavior has been already reported for SEP copoly-mers inn-decane,38,39 different alkanes,40 andn-dodecane/1,4 dioxane mixtures.41 According to these authors, thisbehavior canbe explained in termsof aweak intermicellarinteraction causingamacroscopic ordering in thesolutionsandaffecting thescatteringpattern through interferences.The apparent radius of gyration obtained from the

angular dependence of Kc/∆R is plotted as a function ofconcentration for both copolymers in Figure 5. Whereasfor SEBS2 the Rapp remains constant with a value of 28nm, forSEP2 it decreases stronglywith the concentration.

The radius of gyration was determined by extrapolatingRapp to nil concentration. The value found was 40 nm. Itshould be pointed out that the RG values thus obtainedare only apparent, lower than the true one because thepolystyrene blocks which form the micelle core have alarger refractive index inn-octane thanthealiphaticblockswhich form the micelle shell.ThevalueRG)28nmobtained for themicelles ofSEBS2

in n-octane is very close to that found by Tuzar et al.10 fora similar SEBS copolymer in n-heptane (24 nm). Fromthe ratioMw/NARG

3 some information on the compactnessof the micelle can be obtained. Thus, for SEP2 we founda value of 0.239 g‚cm-3 whereas for SEBS2 it was 0.079g‚cm-3. Considering that themicelles of both copolymershave similar shape, one can conclude that the copolymerSEP2 forms much more compact micelles than thecopolymer SEBS2. This different compactness would becaused by the different order degree that both types ofmicelles would have as it has been above mentioned.Viscosity. The concentration dependence of the vis-

cosity of copolymersSEP2andSEBS2 inn-octane is showninFigure6. A sharp increase is observed in the semidiluteregion, but no remarkable difference is observed between

(38) Price, C.; Hudd, A. L.; Wright, B. Polymer 1982, 23, 170.(39) Mandema, W.; Zeldenrust, H.; Emeis, C. A. Makromol. Chem.

1979, 180, 1521.(40) Quintana, J. R.; Villacampa,M.;Munoz,M.; Andrio, A.;Katime,

I. Macromolecules 1992, 25, 3125.(41) Quintana,J.R.;Villacampa,M.;Katime, I.Macromolecules1993,

26, 606.

Figure 4. Plots of Kc/∆Rθ versus sin2(θ/2). (a) For severalsolution concentrations of copolymer SEP2 in n-octane at 25°C: 1.07× 10-3 g‚cm-3 (O); 4.09× 10-3 g‚cm-3 (0); 7.75× 10-3

g‚cm-3 (4). (b) For several solution concentrations of copolymerSEBS2 inn-octane at 25 °C: 1.34× 10-3 g‚cm-3 (O); 5.15× 10-3

g‚cm-3 (0); 7.35 × 10-3 g‚cm-3 (4).

Figure 5. Concentration dependence of the apparent radiusof gyration, Rapp, for the copolymers SEP2 (O) and SEBS2 (0)in n-octane at 25 °C.

Figure 6. Concentration dependence of the viscosity, η, forboth copolymers SEP2 (O) and SEBS2 (0) in n-octane at 25 °C.

2644 Langmuir, Vol. 13, No. 10, 1997 Quintana et al.

the viscosity curves of both types of copolymers. At lowconcentration SEP2 shows slightly higher values as aconsequence of forming higher micelles, but as theconcentration increases, SEBS2 has higher values witha sharper increment. This behavior can be explained bythe existence ofmicelle aggregates due to the polystyreneblocks that can come out of the micelle, go into anothermicelle, or interact with another polystyrene block suchas Tuzar et al.10 have suggested.Viscosity extrapolations to zero concentrationaccording

toHugginsandKraemerequations lead todifferentvaluesof the intrinsic viscosity, [η]. The Heller equations wereused as an alternative extrapolation. These equationsare recommended when the Huggins coefficient is higherthan 0.5.42 The concentration dependences of c/ηsp andc/ln ηr for the copolymers SEP2 and SEBS2 in n-octaneat 25 °C are plotted in Figure 7. For both copolymers,both equations extrapolate to a single value of intrinsicviscosity.The linear relationships of viscosity data and concen-

tration found for both copolymers suggest that thehydrodynamic dimensions of the micelles are relativelyconstantwith the concentration. The linear relationshipsallowed us to determined theHuggins coefficients, k1 (0.7for SEP2 and 0.9 for SEBS2). These values are higherthan those corresponding to homoplymers (<0.5) and toSEP and SEBS micelles in ketones.26,43 However theyare similar to others found for SEP copolymers inn-alkanes.39,40The intrinsic viscosity values thus obtained at 25 °C

were 90.9 and 68.0 cm3‚g-1 for SEP2 and SEBS2,respectively. Assuming a sphere model, the viscometrichydrodynamic radius, Rη, can be determined from theintrinsic viscosity and molar mass data using the expres-sion

It must be pointed out that Rη is the radius of sphereswhich are equivalent to the copolymer micelles withrespect to their flow behavior. The Rη values found at 25°C were 52 and 22 nm for SEP2 and SEBS2, respectively.DynamicLightScattering. Dynamic light scattering

measurements were made in order to get information of

the size distribution and to confirm the previous results.Datawere analyzed by cumulants andnon-negative leastsquares (NNLS) methods. According to the Cumulantsmethod, the SEP2 micelles in n-octane show very lowvariance values (µ2Γ2 e 0.05), which suggest a low sizepolydispersity. This behavior has been confirmed by theNNLSmethodswhichprovidedanarrowsize distributionfunction.The values of the translational diffusion coefficient

obtained by using the cumulants analysis for SEP2 inn-octane are shown in Figure 8 as a function of thecopolymer concentration. In the dilute solution regiontheconcentrationdependenceof the translationaldiffusioncoefficient can be expressed by a first-order expression

D0 and kD being the translational diffusion coefficient atinfinite dilutionand thediffusion secondvirial coefficient,respectively. From the slope and intercept in Figure 8the values kD ) 49.5 cm3‚g-1 andD0 ) 9.98× 10-8 cm2‚s-1

were found. By use of the Stokes-Einstein relation (eq15) themicelle hydrodynamic radius for SEP2 inn-octanewas estimated, Rh ) 43 nm.By application of the cumulants method to dynamic

light scattering data from SEBS2 solutions, high valuesof the variance and a large concentration dependence ofthe translational diffusion coefficientwere obtained. Thisanomalousbehavior seemed to suggest thatmicelle aggre-gation could take place as Tuzar et al.10 have suggestedfor a SEBS copolymer in n-heptane. To confirm thispossibility, NNLS analysis was carried out for severalSEBS2 solutions at different copolymer concentrationsand at 25 °C. The NNLS method was used to analyzedthe intensity autocorrelation functions measured at ascattering angle of 45° where qRh < 1 with q being thelength of the scattering vector. Some of the size distribu-tions found are shown in Figure 9. These hydrodynamicradius distributions clearly demonstrate the presence ofparticles larger than micelles at higher copolymer con-centrations. Note that the distribution function is ex-pressed in arbitrary units but normalized to the highestvalue at every concentration. As shown in this figure, forconcentrations lower than 1 × 10-3 g‚cm-3 the intensitycontribution function reveals only a narrow peak at Rh )28 nm,which corresponds to that ofmicelles. The criticalmicelle concentration at 25 °C is so low (CMC) 2.9× 10-4

g‚cm-3) that the copolymer free chains are not detected.At higher copolymer concentrations a second broad peakappeared to higher hydrodynamic radii, which can be

(42) Mandema, M.; Zeldenrust, H.; Emeis, C. A. Makromol. Chem.1979, 180, 1521.

(43) Quintana, J. R.; Villacampa, M.; Katime, I. Polymer 1993, 34,2380.

Figure 7. Concentration dependencies of c/ηsp and c/ln ηr forthe copolymersSEP2 (]and4) andSEBS2 (Oand0) inn-octaneat 25 °C.

Rη3 )

3M[η]10πNA

(14)

Figure 8. Plot of the translational diffusion coefficient, D,versus concentration for SEP2 in n-octane in the dilute regionat 25 °C.

D ) D0(1 + kDc) (15)

Micellization of Copolymers Langmuir, Vol. 13, No. 10, 1997 2645

attributed tomicelle aggregates. Themicellenarrowpeakremained at a similar peak position in each case. Theaggregate peak becomes more important with the co-

polymer concentration. It becomes broader and shifts tolargerhydrodynamic radius. This behavior suggests thatthemicelles associate according to an openmodel insteadof the closed model that the copolymer chains follow toform the proper micelles.Information of themicellar shape can be obtained from

the relationship radius of gyration versus hydrodynamicradius. Whereas for the copolymer SEP2 theRG/Rh ratiohas a value of 0.92, the copolymer SEBS2 shows a valueof 1.00. The theoretical ratio RG/Rh is 0.77 for a hardsphere34 and 1.30 for a linear coil.44 Even considering theapparent character of the radii of gyration estimated, theRG/Rh values indicate that the micelles of both copolymerhave a more loose or open structure than that corre-sponding to hard sphere and this difference is slightlylarger for the SEBS2 micelles. A different behavior hasbeen reported for SEBS copolymers in 4-methyl-2-pen-tanone26 where a value of 0.67 was found.

Acknowledgment. M.D.J. thanks theDepartamentode Educacion, Universidades e Investigacion of GobiernoVasco forhergrant. Wealso thank theCYTED(ProgramaIberoamericanodeCienciayTecnologıaparaelDesarrollo)for their financial support.

LA960952B

(44) Kuk,Ch.M.;Rudin,A.Makromol.Chem.,Rapid.Commun.1981,2, 665.

Figure9. Intensitydistribution functionversushydrodynamicradius Rh for the copolymer SEBS2 in n-octane at differentconcentrations and at 25 °C. The distribution function isexpressed inarbitraryunits butnormalized to thehighest valueat each concentration. The peak area is proportional to thescattered intensity contribution.

2646 Langmuir, Vol. 13, No. 10, 1997 Quintana et al.