Block copolymer micelles near critical conditions

Block Copolymer Micelles near Critical Conditions* ZDENI~K TUZAR, PETR gTt~PdtNEK, (~ESTMiR KONAK, AND PAVEL KRATOCHVIL Institute of Macromolecular Chemistry, Czechoslovak Academy of Sciences, 162 06 Prague 6, Czechoslovakia Received July 28, 1984; accepted November 1, 1984 A three-block copolymer poly(styrene-block-hydrogenated butadiene-block-styrene) forms in 1,4dioxane and 1,4-dioxane/30 vol% n-heptane mixture spherical micelles with aliphatic cores and polystyrene shells. Properties o f these micelles near critical conditions, i.e., above the critical micelle concentration x(CMC) and below the critical micelle temperature (CMT) have been studied by light scattering. Integral light scattering is proportional to the weighted contributions of the molar masses of two species present in the solutions under study. Quasielastic light scattering, on the other hand, can provide in principle, the values of diffusion coefficient pertaining predominantly to micelles. Experimental data, namely concentration dependences of the diffusion coefficient and of the apparent mass-average molar mass, strongly deviate from the expected pattern predicted by the model of closed association. The deviation consists in an increase of both molar mass and hydrodynamic radius of micelles in a particular concentration region above CMC. © 1985AcademicPress,Inc.

INTRODUCTION

Block copolymers in dilute solutions in selective solvents (i.e., thermodynamically good solvents for one block, which are poor solvents for the other block) associate and form micelles (1) resembling thus the behavior of soaps and surfactants. While the cause of micelle formation of low-molar-mass amphiphils consists only in a different solvation of the hydrophilic and lipophilic parts of their molecules, the micelle formation of block copolymers is also influenced by the incompatibility of their blocks. Micellization of block copolymers (similar to soaps and surfactants) obeys the model of closed association (1, 2). This model is characterized by an equilibrium between unimer (molecularly dissolved copolymer) and spherical micelles (having a core formed of the insoluble blocks and a shell containing the soluble blocks) with a narrow molar mass and size distribution. The closed association model also as* This paper is dedicated to Dr. Milton Kerker on the occasion of his 65th birthday.

sumes the existence of a critical micelle concentration (CMC), below which only unimer and above which also micelles can be detected by a given method. Due to a different sensitivity to unimer and micelles, CMC values found by osmometry are higher than those from light scattering as was demonstrated on micellar solutions of a two-block copolymer poly(styrene-block-hydrogenated polyisoprene) in n-decane at different temperatures (3). In comparison with low-molar-mass soaps and surfactants, where CMC data are ample (e.g., (4)), CMC data for block copolymers are scarce (e.g., (3, 5)). Also, very little attention has been paid to the properties of block copolymers near CMC and critical micelle temperature (CMT). The aim of the present study has been to detect and characterize micelles of a threeblock copolymer poly(styrene-block-hydrogenated butadiene-block-styrene) in 1,4dioxane (6) slightly above the CMC and in the mixture 1,4-dioxane/30 vol% n-heptane slightly below the CMT by means of light scattering.

372 0021-9797/85 $3.00 Copyright© 1985by AcademicPress,Inc. All rightsof reproductionin any form reserved.

Journalof Colloidand InterfaceScience,Vol. 105, No. 2, June 1985

373

BLOCK COPOLYMER MICELLES MATERIALS AND METHODS

Copolymer. The raw three-block copolymer poly(styrene-block-hydrogenated butadieneblock-styrene) (Kraton G-1650, Shell product), containing about l - 2 mass% of homopolystyrene, was fractionated in a solventprecipitant system cyclohexane--n-propanol. A middle fraction (ca. 20% of the total mass of the raw sample) had a sharp molar mass distribution and was free of homopolystyrene as checked by GPC. The mass-average molar mass, Mw (72 × 103 g tool-l), and chemical composition (28.5 mass% polystyrene) of this fraction did not differ from the respective values of the original raw sample (6) within the limits of experimental error. Solutions for light-scattering measurements were filtered through a glass bacterial filter (G5, Jena) into cylindrical cells, which were then sealed. Solvents. All sovents used, 1,4-dioxane, nheptane, cyclohexane, and n-propanol (reagent grade; Lachema, Czechoslovakia) were distilled on a laboratory column. Integral light scattering. Integral light-scattering (ILS) measurements were performed with a Sofica instrument, equipped with a H e - N e laser (vertically polarized, X = 633 nm) and a digital voltmeter, in the angular range 30-150 ° . The processed data were represented as Kc/Ro = 1/Mw + 2A2c,

[1]

where K is the optical constant which includes the square of the refractive index increment, Ro is the Rayleigh ratio, proportional to the intensity of light scattered from copolymer molecules and micelles, extrapolated to zero angle of measurement, A2 is the second virial coefficient, and c is the copolymer concentration. Refractive index increments, dn/dc, of the copolymer solutions were measured with a Brice-Phoenix differential refractometer (X = 633 nm). In 1,4-dioxane at 25°C, dn/dc = 0.090 cm 3 g-1 in 1,4-dioxane/30 vol% nheptane (dn/dc)~ = 0.102 and 0.106 cm 3 g-1

at 25 and 50°C, respectively. Values for inbetween temperatures were interpolated. (dn/ dc), is the increment measured after equilibrium dialysis of copolymer solutions against the mixed solvent, as described in (7). In a system where both unimer and micelles are present, Mw is an average value M(av) w =

M~)w(U) + ~.-w )l//(rn)vl2(m) ,

[2]

where w is the mass fraction and (u) and (m) pertain to unimer and micelles, respectively. At a finite concentration, disregarding interparticle interactions (i.e., assuming A2 = 0), Kc/Ro represents the reciprocal value of M(wav) (2). Assuming a closed association model, ILS data should follow the pattern (2) sketched in Fig. 1. In the lowest concentration range up to CMC only unimer is practically present. Kc/Ro value extrapolated to c = 0 leads to 1/M~ ). In the middle region, the equilibrium unimer ~ micelles shifts toward micelles with increasing concentration and Kc/Ro represent values of 1/a/t(av) Linear concentration dependence of Kc/Ro, observed at higher concentrations, corresponds to systems containing practically only micelles, and the extrapolation to c = 0 leads to 1/M~wm). The closed association also implicates that the molar mass of micelles at lower concentrations is constant and equal to that in the high-concentration region. Quasielastic light scattering. Quasielastic light-scattering (QELS) measurements were

(u- rn) I (u-m)

c{

(u--m)

---M~ 1/ II ivl~ 3

CMC

c

FIG. 1. Schematic plot of the reciprocal average molar mass I/M~ v) for a block copolyrner micellizing via closed association (2). Journal of Colloid and Interface Science,

Vol. 105,No. 2, June 1985

TUZAR ET AL.

374

performed with a laboratory-built homodyne spectrometer containing a thermostated sample holder. The temperature of the sample was controlled with an accuracy of +_0.05°C. The incident light was the 514.5-nm line of a Carl Zeiss, Jena, argon laser ILA 120-1. Light scattered at 45 or 90 ° was detected by a photomultiplier RCA C31034 and a photon-counting system Spex PC-1. The photopulse signal was analyzed by a 96-channel digital correlator. Autocorrelation functions G(r) obtained from the measurements on solutions where the contribution of either micelles or unimer could be neglected were treated by a single exponential fit of the form

G(t) = A e x p ( - 2 r r ) + B,

[31

where r is the time delay and A, B are constants. Collective diffusion coefficient, De, was evaluated from P = Dcq 2, q being the scattering vector. For solutions where contributions of both micelles and unimer to scattered light were comparable, the experimental data were fitted by the four-parameter twoexponential fit of the form G(r) = Alexp(-2F(U)r) + Azexp(-2I'{aPP)r) + B,

the studied concentration region 10-2-10 -3 g c m - a - - o f any anomaly, when measured by such methods as ILS, QELS, SAXS, osmometry, and viscometry (6). 1,4-Dioxane could not be used for the investigation of micelles of our copolymer near CMT. Preliminary measurements showed that micelles completely dissociated to unimer only a few degrees below the boiling point of the solvent. Solvent mixtures 1,4-dioxane/n-heptane (n-heptane being a selective solvent for hydrogenated polybutadiene) with more than 30 vol% n-heptane dissolve the copolymer molecularly at c I0 -2 g c m -3 at room temperature. The concentration dependences of Kc]Ro for the copolymer solutions in a mixture 1,4-dioxane/30 vol% n-heptane at different temperatures (Fig. 2) follow the pattern sketched in Fig. 1. At lower temperatures the equilibrium unimer ~ micelles is shifted predominantly toward micelles and M~wm) can be determined. At higher temperatures, the experimental dependences correspond to the middle concentration region as depicted in Fig. 1. The higher the temperature, the more is the unimer ~ micelles equilibrium shifted toward unimer for a given copolymer concentration.

[4]

where ptu) pertains to unimer and is considered as a known parameter, r ~avp)containing contributions from both unimer and micelles will be discussed later. RESULTS AND DISCUSSION

o

o

~30

Choice of Micellar System 2C

Our recent study (6) showed that micelles of raw Kxaton G- 1650 sample in 1,4-dioxane with aliphatic core and polystyrene shell did not start to dissociate even at concentrations as low as 10 -3 g cm -3. Thus, CMC in this system appears to be very low and both ILS and QELS data should not be affected by unimer down to extremely low micellar concentrations. Another reason for choosing this system was the absence--at least, in Journal of Colloid and Interface Science, Vol. 105, No. 2, June t985

~ 0

35oc 25oc

l

i

~

2

4

6

i

i

8 10 c x l O ~ (gcr~ 3 )

FIG. 2. Concentration dependence of K c / R o for the fraction of Kraton G-1650 in 1,4-dioxane]30 vol% nheptane.

375

BLOCK COPOLYMER MICELLES

At 55°C (not shown in Fig. 2) only unimer is present in the solution. Based on these orientation ILS measurements, a convenient system for a study of micelles below CMT has been chosen, i.e., the copolymer solution (C = 5 × 1 0 - 3 g c m -3) in 1,4-dioxane/30 vol% n-heptane.

~10"0

"= ~E9.! ~ s ~g 0

2.5

i

8.oFi 7.5

0

05

~

'

0 0.01

0.05

1.0

0.1

2.0 c "~103 (g cm -3)

3.0

FIG. 4. Concentration dependence of De for the fraction of Kraton G-1650 in 1,4-dioxane at 25°C.

decreasing concentration indicates an increase in molar mass and hydrodynamic radius of micelles. An upward curvature below c ~ 1 × 10 -5 g c m -3 (inserted detail in Fig. 3) seems to resemble the middle part of the curve in Fig. I. A parallel increase of Do values indicates a drop in RH of micelles. Unfortunately, we were unable to proceed with light-scattering measurements below c 1 X 10 -6 g c m -3, since the intensity of excess scattering from the copolymer dropped to only several percents of the intensity of light scattered by the solvent. No anomaly of the above type has been detected in the solvent mixture, 1,4-dioxane/ 30 vol% n-heptane at 35°C (Fig. 5) where the concentration dependence of Do was linear down to c = 1 × 10 -4 g cm -3. This

r t~

/1/f'4{wm)

8.6

85

Micelles near CMC ILS and QELS data in Figs. 3 and 4 illustrate an attempt to follow the properties of micelles in 1,4-dioxane to extremely low copolymer concentrations. Since no angular dependence of the intensity of scattered light has been observed, ILS measurements could not provide any information on the radii of gyration. All Do values were obtained from the autocorrelation functions by a perfect single-exponential fit. Thus Do and hydrodynamic radius, RH (~D21), values in the whole concentration region in Fig. 4 can be treated as pertaining to practically monodisperse micelles. ILS and QELS data in Figs. 3 and 4 for c > 1 X 10 -3 g c m -3, including extrapolated values, M(wm) and O~m), are almost identical with those found earlier for a raw Kraton G1650 sample (6). On the other hand, the concentration dependence of Kc/Ro for c < 1 X 10 -3 g cm -3 in Fig. 3 differs markedly from the pattern predicted in Fig. 1. The drop of both Kc/Ro and Do values with

0

19

..........

i

~

2.5

c~

,

17

16

1.5

1.0 --~

1.0

o 0

0.5 0.0

J 0.5

0.01 ~ 1.0

0.05

14

0.1

O 2.0

5

10

i 15

r 20

c.10 3 (gcrr?)

3.0 c=103 (g cr.63 )

FIG. 3. Concentration dependence of Kc/Ro for the fraction of Kraton G-1650 in 1,4-dioxane at 25°C.

FIG. 5. Concentration dependence of Dc for the fraction of Kraton G-1650 in 1,4-dioxane/30 vol% n-heptane at

35°C. Journal of Colloid and Interface Science, Vol. 105, No, 2, June 1985

376

TUZAR ET AL.

minimum copolymer concentration for which Dc of micelles could be measured with a tolerable accuracy was higher than that for 1,4-dioxane. In 1,4-dioxane/30 vol% n-heptane, the concentration of micelles is lower than that in 1,4-dioxane at a given copolymer concentration due to the partial dissociation of micelles (see the upward curvature of the corresponding curve in Fig. 2). The unexpected behavior of our micelles in 1,4-dioxane for c < 1 X 10 -3 g cm -3 remotely resembles the so-called "anomalous micellization" phenomenon observed in some micellar systems (e.g., (8, 9)). This effect manifests itself in the appearance of unstable particles, larger by order of magnitude than the c o m m o n micelles, at the onset of micellization. The "anomalous micellization" is believed to be caused by the presence of homopolymer impurities in a block copolymer sample (10). In the present case, however, the larger particles are stable, practically monodisperse micelles with somewhat inc r e a s e d RH values and molar mass up to twice higher than M(wm) at higher concentrations. Since no homopolymer impurities could be detected in the copolymer fraction employed, we feel unable to offer any plau-

I

Micelles near C M T

Three temperature regions can be seen in Fig. 6. Dc values in the two outer regions, one corresponding to unimer and the other one to micelles, were evaluated from QELS data by a perfect single-exponential fit. In the central region, the equilibrium unimer micelles shifts toward unimer and micellar molar mass decreases (Fig. 2) with increasing temperature. Thus the micellar system in this region may be considered as a mixture of two monodisperse species, unimer and micelles. The electric field correlation function in this case can be expressed as a sum of two exponentials (cf. (11)) gl(r) = a(ulexp(-£(u)T) + a(m)exp(--r(m)r),

I

(u-m)

(

~

A "FU)

~

%5

(u)

--

x

I

c3

I

t

,,

him)

i

C

[

I

25

i

35

J'~

i

~(avl

,

, C

I

t

t

I

4.5

CMT

55

65 T (°C)

FIG. 6. Temperature dependence of Dc for the fraction of Kraton G-1650 (c = 5 X 10 3 g cm-3) in 1,4-dioxane/30 vol% n-heptane. D(~u), D(¢m) (O) and £¢av)(O) determined by the single-exponential fit (Eq. [3]), D(¢app) (D) from the four-parameter two-exponential fit (Eq. [4]), the fifth parameter (I'(u)) being derived from the extrapolated data (×). Journal of Colloid and Interface Science, V o l .

105, N o . 2, J u n e

1985

[5]

where (u) and (m) pertain to unimer and micelles, respectively, and the a values are normalized amplitudes. For the homodyne correlation function G(T), the following equation holds (11)

I

(m)

7

sible explanation of this anomalous behavior for the time being.

BLOCK COPOLYMER MICELLES G(r) = A(a(U))2exp(-2F(U)r) + A(a(m))2exp(-2F(m)r) + 2Aa(U)a(~)exp[-(r (u) + P(m))r] + B, [6]

where A and B are constants. In order to obtain m o r e detailed information about micelles in the central region than that given by the forced single-exponential fit (Eq. [3], D(g v) in Fig. 6), we have fitted the experimental function G(r) to a fourparameter two-exponential function (Eq. [4]), using £(") values calculated from the extrapolated data ( m a r k e d by crosses in Fig. 6). In this way, we could obtain the amplitudes from Eq. [4], A1 ~ A(a(U)) 2 and A2 ~ A[(a(m)) 2 + 2a(U)a(m)], and also the values o f O (app) from F (app) by a forced single-exponential fit o f the micellar and mixed contributions (seco n d and third terms in Eq. [6]). T h e values o f D(capp) and [ A I / ( A 1 + A2)] 1/2 --- a(U)/(a (ul + a (m)) (i.e., the contribution of u n i m e r to the total integral intensity of scattered light f r o m the copolymer) are shown in Figs. 6

1.00

~ 0.75

~o.5o 0,25

0.00 30

3'5

4'0

& T (°C)

50

FIG. 7. Temperature dependence of the unimer contribution to the total integral intensity of light scattered from the Kraton G-1650 fraction (c = 5 × 10 -3 g cm-3). A1 and A2 are the amplitudes in Eq. [4].

377

and 7, respectively. Near a t e m p e r a t u r e of 34°C, where (a(m)) 2 > 2a(U)a (m), the D (app) value is close to D(cm). At temperatures higher t h a n ca. 34°C the results are influenced by the mixed (third) t e r m in Eq. [6], and D(capp/ > D~m) in the analyzed t e m p e r a t u r e region (up to 46.2°C). This m e a n s that the temperature changes o f D(¢m) in the central region should be less p r o n o u n c e d than those of O(eapp) in Fig. 6. T h e analysis of the experimental function G(r) by direct fitting to Eq. [6] is subject to further investigation. Above 46.2°C in the vicinity of C M T , the contribution of micelles to the total intensity o f scattered light is so small that D (app) (and thus D (m) either) c a n n o t be evaluated. ACKNOWLEDGMENT The authors wish to thank Dr. P. W. Glockner, Shell Development Company, Houston, Texas for the Kraton sample. REFERENCES 1. Tuzar, Z., and Kratochvil, P., Adv. Colloid Interface Sci. 6, 201 (1976). 2. Elias, H.-G., in "Light Scattering from Polymer Solutions" (M. B. Huglin, Ed.), Chap. 9. Academic Press, New York/London, 1972. 3. Price, C., Pure. Appl. Chem. 55, 1563 (1983). 4. Becher, P., in "Nonionic Surfactants" (M. J. Schick, Ed.), Surfactant Science Series, Vol. 1, Chap. 15. Dekker, New York, 1966. 5. Sikora, A., and Tuzar, Z., Makromol. Chem. 184, 2049 (1983). 6. Tuzar, Z., Ple~til, J., Kofifik, (~., Hlavatfi, D., and Sikora, A., Makromol. Chem. 184, 2111 (1983). 7. Tuzar, Z., and Kratochvfl, P., Collect. Czech. Chem. Commun. 32, 3358 (1967). 8. LaUy, T. P., and Price, C., Polymer 15, 325 (1974). 9. Tuzar, Z., Sikora, A., Petrus, V., and Kratochvil, P., Makromol. Chem. 178, 2743 (1977). 10. Tuzar, Z., Bahadur, P., and Kratochvil, P., MakromoL Chem. 182, 1751 (1981). 11. Berne, B. J., and Pecora, R., "Dynamic Light Scattering," p. 41. Wiley, New York, 1976.

Journal of Colloid and Interface Science, Vol. 105, No. 2, June 1985