SONJAKRAUSE
1948
K = 0 by linear extrapolation. The variation in the slope (d log K)/(d(l/T)) in the neighborhood of the consolute temperature makes this feature of the curve understandable. As this temperature is approached, rapid closure of the miscibility gap occurs and the value of (d log K)/(d(l/T)) rapidly becomes large in absolute magnitude. The activity coefficients of cerium and plutonium in liquid zinc have been measured as a function of temperature.lg It is possible therefore to estimate the activity coefficients of both cerium and plutonium in
liquid lead through the use of eq. 2. The results of such calculations are given in Table 11. There are no published data with which to compare these estimates. Acknowledgments. Special thanks are due to J. Vincenzi, who assisted in performing the experiments, and to R. J. Meyer and G. Kesser for their solutions of a number of analytical problems. This research was carried out under the auspices of the Atomic Energy Commission. (19) Unpublished data from this laboratory.
Dilute Solution Properties of a Styrene-Methyl Methacrylate Block Copolymer
by Sonja Krause Research Division, Rohm & Haas Company, Spring House, Pennsylvania
(Receiaed February 17, 1964)
Intrinsic viscosities, radii of gyration, and second virial coefficients of a sample of styrenemethyl methacrylate block copolymer and some of its fractions were obtained in butanone, toluene, acetone, and triethylbensene solution. Some of these data were compared with similar literature data on fractions of a random copolymer of styrene and methyl niethacrylate, and on fractions of polystyrene and of polymethyl methacrylate. In solvents which can dissolve only one of the corresponding homopolymers (acetone and triethyl benzene) , the dilute solution properties of the block copolymer indicate micelle formation. I n buttanone and toluene solution, the intrinsic viscosities, radii of gyration, and second virial coefficients of the block copolymer fractions were appreciably lower than would be expected from averaging the properties of the homopolymers. This behavior is opposite to that of random copolymer fractions, whose intrinsic viscosities, radii of gyration, and second virial coefficients are higher than the average properties of the hornopo1ymers.l The butanone data also indicate that the conformation of the block copolymer molecules in solution is different from that of homopolymer or random copolymer molecules. The data at hand are not sufficient to indicate the exact conformation of these block copolymer molecules.
Introduction Very few studies of the dilute solution properties of copolymers, especially of copolynier fractions, appear in the literature. Among these few are some light scattering and viscosity studies of fractions of the azeotropic copolymer of styrene and methyl methacrylate by The Journal of Physical Chemistry
Stockniayer and co-workers' and some osmotic presSure n~asurements on a few fractions of a block c o ~ o l ~ m eofr styrene and methyl methacrylate by
w.
(1) H. Stockmayer, L, D. Moore, Jr., M. Fixman,and B. N , Epstein, J . Polymer S C ~ .16, , 517 (1955).
DILUTESOLUTION PROPERTIES OF A BLOCK COPOLYMER
Burnett, Meares, and Paton.2 Although a comparison of the properties of the more or less random copolymer (free radically initiated copolymers will be considered random for the purposes of this paper) with those of the block copolynier would have been of great interest, the data obtained using light scattering and viscosity measurements could not be compared directly to those obtained using osniotic pressure measurements. I n the present work, sorne light scattering and viscosity data have been obtained on fractions of a block copolymer of styrene and methyl methacrylate. These data have been compared directly with those of Stock-‘ mayer, et al., and with data available for the honiopolymers. I n addition, the present work shows that block copolymer molecules can form soIuble aggregates, i.e., micelles, in those solvents which normally dissolve only one of the corresponding homopolymers. Using the block copolymer of styrene with methyl methacrylate, micelles were obtained in acetone, a nonsolvent for polystyrene, and in triethylbenzene, a nonsolvent for polymethyl methacrylate. The possibility that block copolymers might form intermolecular micelles in dilute solution in solvents which normally dissolve only one of the corresponding homopolymers has been mentioned by a number of workers, Merrett,3 for example, in the last few years. However, the dilute solution properties of such micelles had not been studied up to this time.
Experimental Materials. The preparation and fractionation of the block copolymer of styrene and methyl methacrylate studied in this work have been described in a previous paper.4 The block copolymer was prepared by anionic polymerization using sodium naphthalene as initiator5; this should be a three-block sample whose sequence is methyl methacrylate-styrene-methyl methacrylate. Reagent grade acetone, butanone, and toluene were used for intrinsic viscosity measurements. For light scattering, reagent grade acetone, butanone, and triethylbenxene were distilled at atmospheric pressure through a packed column. Refractive indices of the solvents just before use were: acetone, n Z 6=~1.35604; butanone, n% = 1.37610-1.37614; and triethylbenzene, n Z 6 D = 1.49296. Reagent grade dichloromethane was used to make up some of the polymer solutions. A p p a ~ a t u sand Methods. Intrinsic viscosities were obtained a t the temperatures noted using CannonUbbelohde semimicroviscometers with solvent flow times above 100 sec. so that no kinetic energy correc-
1949
tions were necessary. No shear corrections were necessary because of the low values of the intrinsic viscosities obtained. All intrinsic viscosities were evaluated from data obtained a t a minimum of three concentrations.6 The refractive index increments of the polymer solutions were measured a t 436 and 546 mp using either a Brice-Phoenix differential refractometer or a Zeiss Rayleigh interferometer. Light scattering data were obtained a t 436 and 546 mp using a Brice-Phoenix light scattering photometer a t scattering angles from 30 to 135’ using at least five different polymer concentrations for each run. The standardization of the instrument for each solvent and the method of extrapolation used to obtain apparent molecular weights have been discussed in a previous paper.4 The extrapolation method used to obtain radii of gyration7 and second virial coefficients8 in this laboratory have also been described previously. I n the calculation of the second virial coefficient from light scattering data, it has been found convenient to assume that the third virial coefficient, r3,is equal to rZ2/3.The reasons for this assumption were discussed by Cohn-Ginsberg, et aLs
Results Table I shows the light scattering and viscosity data of the block copolymer fractions in butanone solution. The apparent molecular weights shown in Table I are averages of the values obtained a t 436 mp and a t 546 mp, It was shown in a previous paper that the apparent molecular weights of these fractions in butanone are probably very close to their weightaverage molecular s ~ e i g h t s . ~The column headed 4 refers to the universal constant in the Flory-Fox equationg $I = [ 7 ] M /[6(2)J3”
(1)
Molecular weights obtained for copolyniers by light scattering measurements must be labeled “apparent” if there is the slightest chance that all the molecules (2) G. M. Burnett, P. Meares, and C. Paton, Trans. Faraday
Soc.,
58, 737 (1962).
(3) E. M. Merrett, J . Polymer Sei.,24, 467 (1957). (4) S.Krause, J. Phys. Chem., 6 5 , 1618 (1961). ( 5 ) R. K. Graham, D. L. Dunkelberger, and E. S.Cohn, J. Polymer Sci., 42, 501 (1960). (6) T. G Fox, J. B. Kinsinger, H. F. Mason, and E . &I. Schuele, Polymer, 3 , 71 (1962). (7) S.Krause and E. Cohn-Ginsberg, ibid., 3, 565 (1962). (8) E. Cohn-Ginsberg, T. G Fox, and H. F. Mason, ibid., 3 , 97
(1962). (9) T. G Fox and P. J. Flory, J . Am. Chem. Soc.. 73, 1909, 1915 (1951).
Volume 68, .Vumber 7
J u l y , 1964
SONJAKRAUSE
1950
Benoitlo have derived eq. 3 in a somewhat different form. Data for some of the block copolymer fractions in toluene solution are shown in Table 11. The column
Table I : Block Copolymer Fractions in Butanone (8%,PL/%,
Frao. no.
1 2 3 4
5 6 7 8 9 10 11 12 13 14 15 16
Vol. % styrene
7 19 25 33 40 44 60 74 75 77 83 76 77 73 80 72
Map,, X
8.2 3.83 2.17 1.46 1.58 1.27 1.15 1.07 0.81 0.704 0.572 0.529 0.425 0.392 0.318 0.278
[nl’oO,
H.,
dl./g.
436 mp
1.79 1.33 1.19 1.22 1.17 1.06 1.05 1.025 0.94 0.85 0.703 0.675 0.563 0.47 0.456 0,395
1910 710 500 410 370 340 350 330 290 280 250 255 230 220 200 240
--I’z, dl./g.-438 mp 5 4 6 m p
0.86 0.95 1.27 1.38 0.70 0.94 0.93 0.83 0.73 0.62 0.76 0.71 0.54 0.41 0.39 0.50
0 0.67 0.89 1.14 0.78 0.88 0.96 0.85 1.18 0.64 0.53 0.57 0.42 0.35 0.26 0.50
@
X 10-21
0.14 0.99 1.39 1.78 2.46 2.36 1,.90 2.07 2.13 1.91 1.78 1.43 1.37 1.17 1.23 0.54
in the sample do not have the same composition. The relatioiiship between the apparent and weight-average molecular weight is1t4
+
(dn/dC)02MBpp = (dn/dc)o’AZV. 2b(dn/dc)o(MAz)
+ b’{M(Az) ’)
(2)
where b = (dn/dc)a - (dn/dc)B and (dn/dc)o is the measured refractive index increment of the solution in the solvent, (dn/dc)a and (dn/dc)B are the refractive index increments of the two corresponding honiopolymers, and (MAz) and (M(Az)’) are parameters connected with the composition distribution of the sample which are defined ( M A X ) = ZM,(Az)i w1 and (M(Az)’) = ZMi(AX)i2Wi
where ill, and w,are the molecular weight and weight fraction of each type of molecule present in the sample and Axl is the difference between the composition of that molecule and the average composition of the sample, Azi = xi - zo. The compositions, zi and 50, must be volume fractions, given in terms of either of the monomers which make up the copolymer. The values of the radii of gyration are labeled “apparent” because they are affected by the composition distribution of the fractions in the same way as the weightaverage niolecular weights, i.e. (dn/dc)ozMapp(?),Dp= (dn/dc)o’(M(S)}
+
+ b’(M(Az)’(sZ))
2b(dn/d~)o(M(Az)(3))
(3)
where the quantities in triangular brackets are defined in the same manner as those in eq. 2. Leng and The Journal of Physical Chemistry
Table I1 : Block Copolymer Fractions in Toluene
3 7 12 16
1.40 1.67 1.05 0.578
500 400 230 230
2.4 1.6 1.00 0.92
0.2 1.6 1.08 0.76
1.63 2.04 3.16 0.87
3.7 1.08 0.92 1.03
labeled M / M b u t gives the ratio of the apparent molecular weight in toluene to that found in butanone, Le., the ratio of the apparent molecular weight in toluene to the weight-average molecular weight. This ratio is appreciably different from one only in the case of fraction 3. This indicates that only in the case of fraction 3 was the MaPpin toluene appreciably affected by the composition differences among the molecules comprising the sample. In the case of fraction 3, then, the values of (G)’/’ and rz, and the derived value, 4, are probably also dependent on these composition differences. Table I11 shows the light scattering data obtained on the unfractionated block copolymer and on one of its fractions in acetone and in triethylbenzene solution. Some of the solutions were made up in the solvent specified, but others were first made up in dichloromethane. The solvent of interest, acetone, for example, was then added, some of the mixed solvent was evaporated, more acetone was added, and so on, until the refractive index of the solution had stabilized near the refractive index of acetone. These solutions are referred to as “transferred.” The abbreviation ‘TJFP” refers to the unfractionated polymer. For the unfractionated block copolymer, values of gw= 1.22 X IO6, (MAx)/il;Z, = -0.16, and ( M ( A X ) ~ ) / #= ~ 0.15 were obtained from light scattering data in six different solvents, as shown in a previous paper.4 Table IV shows some intrinsic viscosity data found for the unfractionated block copolymer in acetone solution. The plots of qyp/c us. c and of In qrei/c V S . c had a strong upward curvature and were thus difficult to extrapolate to infinite dilution. For this reason, two separate sets of runs were made. For series 2, (10) M. Leng and H. Benoit, J . chim. phys., 58,480 (1961).
DILUTESOLETIOX PROPERTIES OF A BLOCK COPOLYMER.
1951
Table I11 : The Rlock Copolymer in Acetone and Triethylbenzene Sample
Eiolvent
Transferred
UFP UFP UFP UFP F7 F7 UFP
Acetone Acetone Acetone Acetone Acetone Acetone Triethylbenzene
No
r--Mapp 436 mp
18.4 15.0 53.6 16.1 26.8 10.3 4.76
NO
Yes Yes
No Yes Yes
Table IV : The Unfractionated Polymer in Acetone: Intrinsic Viscosities Series
200
30'
350
40'
1 2
0.43 0.45
0.43 0.43
0.41 0.43
0.41 0.43
the solutions were albowed to stand at 40" for a t least an hour before runs were made a t any temperature.
Discussion Acetone and Triethylbenzene Data. It is shown in Table I11 that the apparent molecular weights of the unfractionated block copolymer and one of its fractions were extraordinarily high, up to 400 times the weightaverage molecular weight, in acetone solution. Since the unfractionated polymer was previously extensively studied by light scattering technique^,^ all the quaiitities necessary to calculate the expected apparent molecular weight in acetone solution from eq. 2 are known. This value is 1.08 X lo6 a t 436 mp and 1.09 X lo6 a t 546 mk. Both values are below the weight-average molecular weight of the sample, 1.22 x lo6. I n triethylbenzene, the expected apparent molecular weights are 0.99 >: lo6 at 436 nip and 1.08 X lo6 at 546 mp. The enormous apparent molecular weights of this sample in acetone solution could be Eiurniised from the high visible turbidity of the acetone solutions, even a t concentrations of O.lyG.The solutions of the block copolymer in triethylbenzene exhibited no such turbidity, partly because the refractive index of the solvent is closer t o that of the polymer and partly because the micelles are not as large. There was no reproducible difference between molecular weights obtained from sample that was dissolved in acetone directly and data obtained from sample that was transferred into acetone solution from dichloromethane. This is an indication that micelles, i.e., stable aggregates, are the equilibrium conformation
X lo-'--546 m p
18.8 13.7 47.0 17.8 28.0 9.7 4.05
I.,
436 mp
436 mp
Pi,dl./g.-------646 mp
850 790 1100 720 830 560 1240
-22.8 --636 0 0 0 0 0
-30.6 - 72 0 0 0 0 0
(81)1'2,
_ _ I -
M/JfW
145 115 400 135 240 85 35
of these block copolymer molecules in acetone solution. The large negative values of the second virial coefficients of the solutions of unfractionated polymer that was directly dissolved in acetone indicate a tendency toward further aggregation in these solutions. The zero second virial coefficients of the other solutions indicate that there was no net attraction or repulsion between those micelles. It is possible to get an idea of the number of block copolymer molecules in each micelle. If the sample were monodisperse, the value of &f/ATw quoted in the last column of Table I11 would give the number of molecules per micelle directly. The monodispersity would have to be both in molecular weight and in composition. This assumption is much better for the fraction than it is for the unfractionated polymer. However, values of are about the same for the fraction and for the unfractionated polymer. Therefore, it is probably safe to say that there are of the order of 100 molecules per micelle in acetone. With rather less evidence, one can say that there are soniewhat less than half that number of molecules per micelle in triethylbenzene, a nonsolvent for polymethyl methacrylate, than there are in acetone, a nonsolvent for polystyrene. This is probably because triethylbenzene is just barely a noiisolvent for polymethyl methacrylate (0-xylene is a &solvent near room temperature) while acetone is a good precipitant for polystyrene There is a bit of further evidence for this. The measured root mean square radius of gyration of the unfractionated polymer in triethylbenzene is greater than any of the ones measured in acetone, even though the apparent inolecular weight of the micelles in triethylbenzene is much smaller than that measured in acetone solution. This iniplies that the micelles are taking up more space in triethylbenzene, probably because the insoluble portion of the micelle contains some solvent and is spread out more than it is in acetone. 'The relatively low values of the radii of gyration measured for both the unfractionated block copolyiner
M/aw
Volume 68, Number 7
J u l g l ,1964
SOIYJA KRAUSE
1952
and its fraction in acetone also irnply that part of the micelle probably contains very little solvent and that this part of the micelle is probably located close to the center of the micelle. A root mean square radius of gyration of 850 8.,for example, would usually correspond to a polymer molecule whose molecular weight was between lo6 and 6 X lo6, assunling that this were an ordinary polymer molecule. The niicelles, however, have molecular weights of the order of lo8. Table IV shows intrinsic viscosities of the unfractionated polymer in acetone at a series of temperatures (20-40"). KO major change occurred in this temperature range. The actual values of the intrinsic viscosities, averaging out to 0.43 dl. /g., would generally belong to ordinary polymers with molecular weights about 2 X lo5. The abnormally small intrinsic viscosity, therefore, also indicates that the micelles are taking up very little volume for their molecular weight. Butanone Data. I n Fig. 1, the intrinsic viscositymolecular weight data of the block copolymer fractions are compared with those of the azeotropic copolymer fractions of Stockiiiayer and eo-workers' and with literature data for polystyrenell and for polymethyl methacrylate12 in butanone solution. Stockmayer's random copolymer fractions contained about 54 wt. yo styrene while the block copolynier fractions varied from 7 to 83 vol. % styrene (see Table I). Figure 1 shows that the intrinsic viscosities of all the random copolymer fractions were higher than those of either hoinopolymer of comparable niolecular weight while
L
I
/ o o
O
I
1
I
I
1
the intrinsic viscosities of the block copolyiner fractions were all lower than those of the homopolyiners. Stockmayer, et al., showed that the high intrinsic viscosities of their random copolymer fractions were caused by the therrriodynaniic repulsion between unlike monomers in each polynier molecule. Although the same repulsions are certainly operating in the block copolymer molecules, their intrinsic viscosities have decreased, not increased. Before continuing the discussion, it is necessary to show that this decrease in intrinsic viscosity is a property of the polymer molecules and not an experimental artifact of some sort. For example, low intrinsic viscosities are often the result of a broad molecular weight distribution. Since very little is known about the fractionation of block copolymers, it would seem reasoiiable in the absence of other data to assume that the fractions might have a very broad molecular weight distribution. I n that case, the radii of gyration would be expected to be abnormally high, since radii of gyration of polydisperse polymers are higher averages than weight averages. In Fig. 2, the radius of gyration-molecular weight data of the block copolymer fractions are compared with those of the random copolymer fractions and
-
-.
I
A
t
RANDOM
I
I
( STO CKM AYER
1
I
I
I
I l l
ET AL.)
I
-
I
COPOLYMER F R A C T I O N S
0 BLOCK COPOLYMER F R A C T I O N S ( T H I S WORK)
/
I
I
I l l
io5
Ios
IO'
M Figure 2 . Log (?)'/z us. log M of methyl methacrylate : styrene copolymer fractions in butanone. I
I
I
l
5
l
I
I
t
Ios
M
Figure 1. Log [ v ] us. log M of methyl methacrylate : styrene copolymer fractions in butanone.
T h e Journal of Physical Chemistry
(11) P. Outer, C. I. Carr, and B. H. Zimm, J . Chem. Phys., 18, 830 (1960). (12) J. Bischoff and V. Desreux, Bull. 8oc. chinz. Belges, 61, 10 (1952).
DILUTESOLUTIOK PROPERTIES OF A BLOCK COPOLYMER
with data for polystyrenell and polymethyl niethacrylate13 in butanone solution. In the case of the random copolymer fractions, the actual experimental values were used, not the values that had been theoretically corrected to weight averages by Ytockniayer, et aE. As shown in Fig. 2, the radii of gyration of the random copolymer fractions fell between those of the homopolymers of comparable molecular weight, while the radii of gyration of most of the block copolymer fractions fell either i n line with those of the random copolymer fractions or below these in the range expected for polystyrene homopolymer fractions. The radii of gyration of fractions 1 and 16 seem quite high coinpared with the other block copolymer fractions; they are even a little higher than those expected for polymethyl methacrylate. Since these are the first and the second-to-last fractions of the copolymer, respectively, these two fractions might be expected to have rather broad molecular weight distributions. None of the other fractions of the block copolymer has an abnormally high value for the radius of gyration; some of the fractions can be considered to have abnormally low values for the radius of gyration. These data are, therefore, a strong indication that the low values of the intrinsic viscosities of the block copolymer fractions in butanone are not caused by molecular weight polydispersity. A further indication of the fact that there is something intrinsically different about the block copolymer fractions in comparison to the randoin copolymer fractions is given by the second virial coefficients as shown in Fig. 3. The second virial coefficients of the random copolymer fractions Eire quite high, in the same range as those of methyl nzethacrylate homopolymer, while
10I
-
1
1
1
I
I
I
1
I
I
l
l
-
A RANOOM COPOLYMER FRACTIONS ISTOCKMAYER El’ AL 1 0 BLOCK COPOLYMER FRACTIONS ( T H I S WORK1
-
I
--
IO-
-
I
-
e
01 2x10‘
f
1
1953
those of the block copolymer fractions are quite low, in the same range as those of styrene homopolymer. All these data indicate that butanone is not as good a solvent for the block copolymer fractions as it is for the random copolymer fractions. I n Fig. 4, the intrinsic viscosities of some of the block copolymer fractions are compared with the [v J-lk! relationships of the hoizz0p01yrner~~J~ in toluene. It
M Figure 4. Log [s] us. log M of methyl methacry1ate:styrene block copolymer fractions in toluene.
can be seen that in toluene as well as in butanone, the intrinsic viscosities of the fractions are below the values that would be expected from a weighted average of the homopolymer intrinsic viscosities. There were no data on the random copolymer in toluene solution that could be used for comparison. These data have shown that the lowered values of the intrinsic viscosities of block copolymer fractions of styrene and methyl methacrylate are not specific to one particular solvent. The lowered intrinsic viscosities are connected, at least in butanone solution, with lowered radii of gyration and lowered second virial coefficients. The same repulsioiis between monomers of different types that increase the intrinsic viscosities of the random copolymer fractions seem to decrease
1 ~~
M
Figure 3. Log rz us. log M of methyl methacry1ate:styrene copolymer fractions in butanone.
IO‘
~
~~
(13) F. W. Billmeyer, Jr., and C. B. DeThan, J . A m . Chem. Soc., 77, 4763 (1955). (14) W. Hahn, W. Rfueller, and R. V. Webber, Makromol. Chem., 21, 131 (1956).
Volume 68, >‘umber
7
Julv, 1964
SONJAKRAUSE
1954
rather than to incrdase the intrinsic viscosities and radii of gyration of block copolymer fractions. Magat and co-workers16,16have postulated intramolecular phase separation in solutions of block and graft copolymers, even in solvents in which micelles are not expected. That is, the blocks containing different monomers are expected to occupy different domains in all solvents. If such an effect occurs, it may lead ‘to a lower radius of gyration than that of a random copolymer molecule of equal molecular weight and composition. Assuming intramolecular phase separation, it becomes interesting to decide whether the block copolymer molecules have the approximate Gaussian coil conformation similar to that of homopolymer and of random copolymer molecules of styrene and methyl methacrylate. The universal constant, 4, from eq. 1, which depends both on the radius of gyration and on the hydrodynamic properties of the molecules, should be very sensitive to conformation. The values of 4 shown for the block copolymer molecules in butanone and in toluene in Tables I and I1 are mostly in the usual range for homopolymers. The values for the more polydisperse fractions, 1 and 16, are below the usual range, as expected for polydisperse fractions when the measured values of the radii of gyration are used in the calculation. The average value of 4 for the other fractions, 2-15, is 1.7 X loz1,while the average value of 4 for the random copolymer fractions of Stockmayer, et al., is 1.9 x loz1. (The reported value’ of Stockmayer, et al., is somewhat higher than this since they used corrected, not measured values of the radii of gyration in their calculations.) The average value of 4 given by Flory” for homopolymer fractions is 2.1 X loz1. The value for the random copolymer fractions is within 10% of this value for homopolymers, while the average value for the block copolymer fractions is within Z070. It is difficult to tell whether this slight change in 4 is significant. It looks, a t any rate, as if the mass distribution of the block copolymer molecules cannot be very different from those of homopolymers or of the random copolymer molecules. There is another way of using the intrinsic viscosity and molecular weight data, without using the radii of gyration, to find out whether the data for the block copolymer fractions adhere to the theoretical expressions which have been derived for honiopolymers and which have been found useful for homopolymers. Following Flory and Fox,18 a plot is made of [v]”~/ M”a us. M / [ q ] . The intercept of such a plot, a t vanishing M / [ q ] , should be equal to K”/’, where K is defined by The Journal of Physical Chemistry
K
=
+[6(s;;i)/~]”2
=
(4)
[q]/~1’*a3
where (s?) is the mean square unperturbed radius of gyration of the polymer fraction of molecular weight M , and cy is the expansion factor for this fraction in the solvent in which the intrinsic viscosity is measured. Figure 5 shows plots for [q]z”/M’’a us. M / [ q ] in butanone solution for fractions of polymethyl methacrylate,* polystyrene,” the azeotropic (random) copolymer of styrene and methyl methacrylate,’ and for 1
I
I
I
I
1
I
0 BLOCK COPOLYMER FRACTIONS 6-16
A RANDO M COPOLYMER F R A C T I O N S
e
POLY ( M E T H Y L M E T H A C R Y L A T E ) FRACTIONS
1.4
-
/’
9.41 0
-
00
1
1
1
I
2
4
6
8
1 IO
1
I2
M / CTJ x 10Figure 5 .
[VI 2/8/lM1’3us. M / [ T ~of] fractions in butanone.
those fractions of the block copolymer whose compositions were between 72 and 83% styrene. Such a plot was made previously by Stockmayer and co-workers’ for the random copolymer fractions. The intersection shown a t M / [ q ] = 0 for the random copolymer fractions was obtained from a plot like this one by Stockmayer, et al.’ The intersections shown for the homopolymer fractions were calculated from experimental values of K obtained in &solvents by in the case of polymethyl methacrylate and by Hahn, et a1.,14 for polystyrene. (15) M.Lautout and M. Magat, 2 . physik. Chem. (Frankfurt), 16, 292 (1958).
(16) J. Danon, M ,Jobard, M. Lautout, M. Magat. M. Michel, M. Riou, and C. Wippler, J . Polymer Sci., 34, 517 (1959). (17) P. J. Flory, “Principles of Polymer Chemistry,” Cornell University Press, Ithaca, N. Y., 1953. (18) P.J. Flory and T. G Fox, Jr., J . Polymer Sci., 5, 745 (1950). (19) T.G Fox, Polymer, 3, 111 (1962).
1955
DILUTESOLUTION PROPERTIES OF A BLOCK COPOLYMER
It can be seen on Fig. 5 that all the points for the block copolymer fractions fall in a little cluster below the points and lines corresponding to the homopolymers and the random copolymer fractions. The two points that are situated a t some distance froni the others correspond to fractions 8 and 10 of the block copolymer sample and are in the middle of the composition range of the fractions used for this plot. The deviation of these points from the straight line which might otherwise be drawn through the other seven points cannot, therefore, be ascribed to a major difference in composition. If a line containing the nine points can be considered a t all, jt is not probable that it should have an intercept a t M / [ r ] = 0 which is equal to or greater than that of the niethyl methacrylate homopolymer. That is, the value of K , or of (?)/M as calculated from, K in eq. 4, of the block copolymer fractions would be much lower than those of the homopolymers. This is rather hard to believe when the significance of (g)/M, or rather, the derived quantity ( G ) / M , is considered. The constant, ( G z ) / M ,is a measure of the polymer chain dimensions under those circumstances in which the polymer chain has no net interaction with its environment. The only factor that influences chain dimensions under those conditions is the conformation entropy, that is, the polymer chain will have that particular end-to-end distance which allows the rest of the chain to exist in the largest possible number of conformations. These chain dimensions are influenced by the length of the chain, by the bond angles along the polynier backbone, and by the steric interactions between different portions of the chain. The constant ( $ ) / M already takes into account the length of the chain. Therefore, the variations in this constant between different polymers should depend only on differences in the polymer backbones and in the steric character of the chains. Polystyrene and polymethyl methacrylate have the same backbone, so the difference between the ( Q ) / M , as reflected in the intercepts on Fig. 5 , depends only on the steric character of the chains (plus a small correction for the monomer molecular weights which does not amount to much in this case). h copolymer of these, as long as it is unbranched, and as long as it exists in the same conformation as the homopolymers (the Gaussian coil),
should have a steric character intermediate between those of the homopolymers. This was found' for the random copolymer. The derivation of a value of ( g ) / M for some of the block copolymer fractions which is well below that of either homopolymer implies that there is something wrong with the derivation. I n the simplest theory, the slopes of the lines in Fig. 5 are proportional to (0.5 - xl), where x1 is the interaction parameter between polymer and solvent. I n order for the extrapolation to M / [ q ] = 0 to give a valid K , i.e., ( r T ) / M , this x1 must be reasonably independent of molecular weight. The interaction parameters between block copolymers and solvents are probably extremely molecular weight dependent even at constant composition of the block copolymer molecules if intramolecular phase separation occurs, since the amount of intramolecular phase separation is expected to be molecular weight dependent. If therefore looks, a t least qualitatively, as if the data on the block copolymer fractions in Fig. 5 can be explained using the assumption of intraniolecular phase separation. Putting this together with the conclusion which was drawn from the observed values of 4, we can conclude that the block copolymer niolecules of styrene and methyl methacrylate probably exhibit intramolecular phase separation even in a solvent which dissolves both homopolymers, but that each molecule, as far as the total mass distribution is concerned, can still be considered similar to a random coil. Admittedly, the data in butanone solution are very tenuous evidence for intramolecular phase separation when taken alone. If these data, however, are considered together with the evidence for micelle formation in acetone and in triethylbenzene, an intramolecular phase separation, at least a partial one, in butanone solution becomes much more credible. Polymer blocks which are incompatible enough to form micelles in some solvents can be expected to show some phase separation in all solvents.
Acknowledgment. Thanks to Mr. Joseph Bonafiglia, who obtained all the light scattering data, and to Mr. John J. Begley and Mr. Karl Macon, who obtained the intrinsic viscosities.
Volume 68, Number 7
J u l y , 1964
