782
SHIH-YENCHANGAND HERBERT MORAWETZ
-0.6 .d
Y
4 3
- 1.0
When both alcohol and electrolyte are added to a soap solution, mixed micelles are formed in which the alcohol partially replaces the ~ o a p . ' ~ ~The '~ schemes given by equations 1 and 2 must now be replaced by sM+
and yM +
+ rA- + tL
M,A,Lt-(r-8)
+ x( MsArLt)-~r-s))
(6)
MV(MIA,Lt)Z-(Z(r-*)-")
(7)
where M + is the alkali metal cation, A- is the long chain paraffin anion, L is the un-ionized alcohol and II: > y > T > s > t . Employing exactly similar reasoning to that for the soap-electrolyte system, i t may be shown that a t a particiilar activity of the soap 21 log a&f = IC' (8) y 5s log aL ~
+
On equating activities to concentrations this leads (13) H. R. Kleveas, Chem. Reus.,47, 1 (1950). (14) W. D. Harkins, R. Mittlemann and M. L. Corrin, THIS JOURNAL, SS, 1350 (1949).
Vol. 60
appears the logarithm of the concentration of the alcohol should be a linear function of the logarithm of the concentration of the cation. As before the cation concentration is obtained by summing the contributions of the soap and of the electrolyte. Relevant data are included in Table 11,and plotted in Fig. 3. It is seen that for alcohol concentrations between about 0.0012 and about 0.0075 M (depending on the solubility of the alcohol) the
whichubothsoap and alcohol are present. Conclusions It may be concluded, therefore, that over a limited region of concentrations the experimental results, both with and without alcohol present, are consistent with the assumption that viscoelasticity in soap-electrolyte systems develops as a result of a change in micelle shape. At low concentrations of electrolyte the soap is thought to be in the form of small spherical micelles but a t higher concentrations these pack together into cylinders which are then able to interlink giving rise to viscoelasticity. The change from spherical to cylindrical micelles is brought about mainly by the added cation but there is also an anion effect as well as an effect due to the presence of un-ionized alcohol. The change obeys a simple form of the Law of Mass Action, but this is only true for a rather limited range of concentrations. Acknowledgments.-The author wishes to thank Professor Sir Eric Rideal, F.R.S., for his interest and encouragement, and the Ministry of Supply for financial assistance.
POLYMER ASSOCIATION. 111. MOLECULA;lK AGGREGATION AND INTRAMOLECULAR GR.OUP ASSOCIBTION I N DILUTE SOLUTIONS OF STYRENE-METHACRYLIC ACID COPOLYMERS'*' B Y SHIH-YEN CHANG3 A S D HERBERT MORAWETZ Contribution from Department of Chemislr,y, Polytechnic Inslitule of Brooklyn, Brooklyn, N . Y . Received November 18, 1966
Seven styrene-methacrylic acid copolymers were studied in tetrachloroethane and carbon tetrachloride solution. The dcgree of molecular aggregation was determined by osmometry with and without added amine. The extent of carboxyl dimerization was measured by infrared spectroscopy and was found to be independent of the concentration of dilute polymer solutions, indicating that most of the carboxyl dimers form within single polymer coils. Two theoretical approaches to the degree of intramolecular group association in solutions of chain molecules carrying widely spaced interacting substituents are in satisfactory agreement with the experimental data. For any given degree of carboxyl association intermolecular aggregation was higher in the better solvent. The data indicate that the molecular chain configuration is independent of concentration in the dilute solution range.
Introduction Carboxylic acids are known to be largely dimer(1) Presented at the Meeting of the American Chemical Society, Minneapolis. September 15, 1955. (2) Support by the Office of Naval Research is gratefully acknowledged. Reproduction in whole or in part is permitted for any purpose of the U. S. Government. (3) Abstracted from a Ph.D. thesis submitted by 9.-Y. Chang to the Graduate School of the Polytcclinic Institute of Brooklyn, June, 1955.
ized by hydrogeri bonding in non-polar so1veiits4 and, thus, polymers carrying carboxyl groups tend to form aggregates in suitable solvent media. ,4 methyl methacrylate copolymer with 5 mole per cent. methacrylic acid was found to have an osmotic molecular weight of 181,000i n benzene solution a t 49.7", while in pyridine, which would be es(4) a. Allen and E. F. Cdldin. Q e o i l . R P P .7, , 255 (1053)
June, 1956
STYRENE-METHACRYLIC ACIDCOPOLYMERS
783
pected to suppress carboxyl dimerization, a value of 0.005 p in wave length. The optical densities were measured maxima of the carbonyl stretching vibra32,300 was obtained.6 Osmotic and light scatter- at theatabsorption 5.70-5.75 p and 5.85-5.88 p for monomeric and diing data indicated that the aggregates retained a tion meric carboxyls, respectively.* The effective resolution a t constant size over the entire concentration range these two bands was 0.051 and 0.063 p . The pair of sodium accessible to measurements. Interpretation of this chloride cells employed had an optical path length of 1 mm. surprising phenomenon suggested that only a small The blank cell contained the solvent when studying the of pjvalic acid solutions; for studies of copolymer fraction of the carboxyl groups participate in in- spectra solutions, it contained a polystyrene solution of a concentermolecular association, while the remaining car- tration such as to compensate for the absorption due to boxyls are either engaged in intramolecular group styrene residues in the copolymer. Osmotic Pressure Measurements.-Zimm-Myerson osassociation or hidden in the interior of the polymer mometers with Teflon gaskets and stainless steel plates were coil.6 thermostated at 29.6 f 0.005'. The height of the meniscus The present investigation is concerned with the was located with a cathetometer reading to 0.01 cm. Wet balance between intramolecular group association regenerated cellulose membranes type 300 (Sylvsnia DiAmerican Viscose Co.) were conditioned by succesand molecular aggregation in solutions of polymers vision, sive immersion, for 24 hours, in 50/50 water-acetone, 100% carrying varying densities of strongly interacting acetone (twice) 50/50 acetone-solvent, 25/75 acetonegroups. Copolymers of methacrylic acid were solvent, 100% solvent (4 times). Solvents employed for used, since their carboxyl association equilibrium the osmotic pressure measurements were 1,1,2,2-tetrachlorohas been studied extensively and may be followed ethane and carbon tetrachloride, with and without the addiof 1.6 volume yo N,N-dimethylbenzylamine (Eastmati conveniently by infrared spectroscopy. Styrene tion Kodak, b.p. 179-180") and a trace of t-butylcatechol to stawas chosen as the comonomer because its copoly- bilize the amine. Combined capillary and membrane mers are soluble in non-polar media and neither dissymmetry corrections were less than &0.02 cm. Osmotic equilibrium was attained in 24 hours with carbon tetrachlothe solvent nor the styrene residues absorb ride and in 48 hours with tetrachloroethane. Only with the strongly a t wave lengths used for following car- lowest molecular weight copolymers was it necessary to boxyl dimerization. As spectroscopic data do not allow for diffusion by extrapolation to zero time. The redifferentiate between intEamolecular and intermo- duced osmotic pressure plots were linear with slopes and lecular group association, the extent of molecular intercepts calculated by le@ squares. The true number average molecular weight M, of the copolymers was obaggregation was followed by osmometry. I n addi- tained from osmotic data in solvents containing amine. I n tion, solution viscosity data were obtained to show the absence of amine, higher apparent molecular weights the e f f c t of strongly associating groups, spaced at were measured, giving a degree of aggregation D, defined varying intervals along the molecular chain, both as the ratio of the apparent to the true molecular weighL6V6 Viscosity Measurements.-Ostwald type viscosimeters on the molecular configuration at high dilution and with large wells for dilution of the solutions were used. on molecular interaction a t higher solution con- Kinetic energy corrections were applied in calculating solucentrations. tion viscosities. Experimental Results and Discussion Preparation of Copolymers.-Methacrylic acid (Rohm When a polymer solution is sufficiently dilute so and Haas), dried by sodium chloride and calcium chloride, and styrene (Dow Chemical Co.) were distilled at reduced that there is little interpenetration of the individual pressure under nitrogen. Polymerization of the mixed chain molecules, association equilibria involving monomers a t 65', after thorough degassing, in the presence groups attached to the macromolecular backbone of 0.025 to 1.84 weight per cent. azo-bis-isobutyronitrile will be governed by their local concentration in the (Eastman Kodak) was carried to roughly 10% conversion. The copolymer was precipitated twice from butanone solu- swollen molecular coil, rather than the stoichiometion into a large volume of methanol and dried in vacuo at tric concentration in the body of the solution. This 50' for 48 hours. principle is strikingly illustrated in Fig. 1, which Analysis of Copolymer Composition.-Copolymer solutions in henzene containing 10 volume per cent. ethanol were titrated under nitrogen with sodium ethoxide in the same solvent mixture, using phenolphthalein as indicator. The sodium ethoxide was standardized against benzoic acid, recrystallized from ether (m.p. 122'). The methacrylic acid content of the copolymers was 3-4 times as high as that of the mixed monomers. 1,1,2,2-Tetrachloroethane (Eastman Kodak) was shaken with cold sulfuric acid until there was no discoloration, followed by washing with water until neutral to litmus. After drying over calcium chloride, the solvent was distilled twice under nitrogen a t reduced pressure through a column equivalent to 20 theoretical plates (dt = 1.5807, b.p. 145.9-146.3', %*OD 1.4954). Carbon tetrachloride (Eimer and Amend, reagent grade) was dried over phosphorus pentoxide and distilled through a 40 cm. packed column (b.p. 76.7 i0.2",d4301.5622). Pivalic acid (Eastman Kodak, "white label") was purified by six fractional freezings.? The material, m.p. 35.4", was distilled under reduced pressure before use, to free it f r o n dissolved air. Infrared Absorption Measurements.-A Perkin-Elmer Model 21 double beam spectrophotometer was used with the instrument settings recommended for quantitative analy~is. The rcpraduc:il)ility in 0.5gb in transmission and ~
( 5 ) H. Illorswetz and R. H. Gobran. J . Pol$,mer.Sci.. 1.2, 133 (1904). (0) H. Rlorawetz and R. 11. Gobran, .ibid., 18, 455 ( 1 9 0 5 ) ( 7 ) If. L. Rittrr and J . H. Silttons. J . A rn. Chsnr. S o r . , 67, 757 (194.5).
2.5
B -
I 1.0 05
\
1
I I
\
- - -
.-
4
h
5 10 15 20 25 30 35 Carboxyl conrn. X lo3 (cquiv./l.). Fig. 1.-Carboxyl association of pivalic acid and styrenemethacrylic acid copolymers in tetrachloroethane. 0
compares the dependence of the carboxyl association equilibrium on the solution c.onc.entration of pivalic. acid and varioiis styrene met,hncrglir wid (8) I). Fltrdzi aiid N . SIierq~ard,I'ror. Rnu. S u r . ( / , n d o u ) , A.216, 247 (1953).
SHIH-YENCHANGAND HERBERT MORAWETZ
784
copolymers. The extent of carboxyl association is characterized by dl/d2, the ratio of the optical densities a t wave lengths corresponding to free and dimerized carboxyls, respectively. As would be expected, this ratio decreases with increasing concentration of pivalic acid. However, with the methacrylic acid copolymers, dr/d2 depends merely on the copolymer composition and the nature of the solvent, remaining constant over the investigated range of concentrations. A slight decrease of d1/d2 with increasing solution concentration of the copolymer with lowest acid content was probably due to the very high solution concentrations (up t o 8 g./100 ml.) used to obtain adequate absorption at wave lengths characterizing the cai boxyl groups; interpenetration of molecular coils must have affected significantly the carboxyl association equilibrium. Table I lists the mole fraction of methacrylic acid, FA, and the true osmotic molecular weight of seven styrene-methacrylic acid copolymers with their degree of aggregation, D ,the second osmotic virial coefficient, B , the optical density ratio, dl/d2, and the intrinsic viscosities [ q 1 in tetrachloroethane or carbon tetrachloride solution. The extinction coefficients el and €2 of the free and dimerized carboxyl are required to obtain the degree of
an,
TABLE I SOLUTION PROPERTIES
O F STYRENE-METHACRYLIC
COPOLYMERS AT 29.6' co-
POLYmer no.
tion in carbon tetrachloride and chloroform has been reported by Barrow and Yerger.g TABLE I1 APPARENT DISSOCIATION CONSTANTS OF PIVALIC ACID DIMERIN CARBON TETRACHLORIDE AND 1,1,2,2 TETRACHLOROETHANE
IOZFA
C2H2C14 0 . 7 9 CzHzC14 6 . 5 CzHzCl4 7 . 3 CzHzC14 8 . 9 C2H2CI4 1 1 . 7 CzH2Cl4 1 5 . 2 CCl4 0.79 ccl4 4.5 ccl4 8.9 a In g.-l cm.7 sec.-2. tration of 2 g./100 ml. 1 3 4 5 0 7 1 2 5
Mn
26 108 57 102 40 142 26
17
The dimerization equilibrium of carboxyls attached t o a macromolecular chain may be represented formally by 2CeflcY2 = Kd
-
dddt
(6)
[rll
(1) (2) (3)
€1 and e2 may be obtained as the intercept of a plot of dl/c against dz/c. The experimental results led to values (l.-equiv.-'-mrn.-') of el = 37, € 2 = 41 in 1,1,2,2-tetrachloroethaneand el = 57, e2 = 70 in carbon tetrachloride. The apparent dimer dissociation constant Kd, given by
-2ca2 1 - a - Kd
= 25z/M[rll
where z is the number of carboxyl groups per chain 8 . 7 1.42b 0.207 of molecular weight M and Cleffis the equivalent 5 . 3 0.58 .773 concentration in equivalents per liter. 5 . 8 .48 ,525 (2) I n a second approach to the problem of esti-2.2 .48 ,732 mating Ceff,z carboxyl groups are assumed to be -4.1 .35 .480 attached at a constant spacing along the chain mole-4.3 .32 ,380 cule. For flexible chains, the probability distribu3 . 5 .49 .162 tion of the end-to-end displacement T is l@Ea
78 3 . 3 .20 .390 102 -2.6 ,127 .356 * Obtained at a solution concen-
d1 = C ~ E , ~ ( l a)ez
(5)
1-CY
C'eii
D 1.07 1.41 1.46 1.51 1.65 1.80 1.08 1.39 3.62
10 11 14
where Ceff is the "effective concentration" of carboxyls in the swollen polymer coil and K d is the dimer dissociation constant of a suitable monocarboxylic acid analog. Two approaches to an estimation of Ceffwere considered. (1) The Ceff of interacting groups attached to a flexible chain molecule may be approximated by a uniform distribution of these groups within a rigid sphere which is hydrodynamically equivalent to the ACID polymer coil. Since [q]/0.025 is the volume in ml. of the equivalent sphere per gram of polymer'O~"
dissociation CY of the carboxyl dimer. Assuming that pivalic acid has the same extinction coefficients as carboxyl groups of the copolymer, we have dp
0.47 .52 .61 .81
3.16 6.32 12.64 19.0 32.4
10-1
Solvent
Vol. 60
(4)
tended to increase with rising acid concentration, as shown in Table 11. A similar drift in the apparent equilibrium const,ant for acetic acid dimeriza-
W(r)dr = ( 3 / 2 ~ ) ~ / 1 ( P ) - 'exp h ( -3ra/27)4nr2dr
(7)
Kuhn12has pointed out that, for r2
