MOLECULAR AND GROUP ASSOCIATION EQUILIBRIA IN POLYMERS CONTAINING WIDELY SPACED INTERACTING GROUPS BY H. MORAWETZ Polymer Research Institute, Polytechnic Institute of Brooklyn, Brooklyn, N.Y. Received 16th December, 1957 Mixtures of methyl methacrylate copolymers containing about 5 mole % of methacrylic acid or dimethylaminoethyl methacrylate, respectively, form molecular association complexes in butanone solution which remain stable up to the highest dilutions accessible to osmotic or light-scattering measurements. In benzene solution, molecular association of the acidic polymer molecules with each other is also observed and the dependence of the size of the molecular aggregates on the concentration of cosolvents can be used to estm ate group association equilibrium constants. With styrene + methacrylic acid copolymers infra-red spectroscopy can be used to determine the extent of carboxyl dimerizationi and this is found to be independent of the solution concentration of the copolymer, being governed by the local carboxyl concentration in the isolated polymer coil.For a fixed degree of carboxyl dimerization, the extent of molecular association is higher in thermo- dynamically better solvents. In bulk samples of the copolymers the carboxyl dimerization equilibrium becomes frozen in the neighbourhood of the second-order transition tem- perature. While fairly extensive studies have been carried out on molecular association equilibria of low molecular weight species, little is known about the principles governing molecular association of high polymers.Yet it is clear that for each type of association known to exist with small molecules, analogous complex formation should be observed with polymers carrying the appropriate interacting groups. In non-polar media, typical examples comprise the hydrogen-bonded association complexes of hydroxylic 1 9 2 and carboxylic 3 compounds or the ion- pair formation of amines with carboxylic acids.4~ 5 When the solvent molecules form strong hydrogen bonds with one another as in the case of water, solutes may aggregate for three different reasons. (i) Particles carrying large charges of opposite sign will tend to associate particularly at low salt concentration. (ii) Molecules with bulky non-polar residues will be drawn to each other so as to minimize the number of broken hydrogen bonds between the solvent molecules (" the hydrophobic bond ").6 (iii) Hydrogen-bonded solute complexes map persist even in aqueous solutions provided the hydrogen bonds between solute molecules are sufficiently strong.7 Consider a chain molecule soluble in a given medium.If we now modify the polymer by introducing strongly interacting groups at a wide spacing along the macromolecular backbone, groups attached to the same polymer chain as well as groups attached to different chains will participate in complex formation. The intermolecular association persists frequently to the highest dilutions accessible to osmotic and light-scattering studies and leads to a dependence of the apparent molecular weight on the properties of the solvent medium.899 At higher con- centrations at which the polymer molecules may form a continuous network throughout the system, intermolecular group association may result in gelation. Such gels are thermally reversible, liquefying at temperatures at which the group association is reversed.10 Although molecular association of polymers and thermally reversible gel formation have been investigated by a number of workers in the past, no attempt 122H.MORAWETZ 123 seems to have been made to study systematically the dependence of these phenomena on the variables of polymer structure. The present report summarizes some initial observations made on polymers prepared specifically to illuminate the effect of the type and spacing of interacting groups and the length of the molecular chain on the properties of polymers both in solution and in bulk.EXPERIMENTAL The preparation of the methyl methacrylate copolymers and the styrene copolymers as well as their characterization has been reported previously.ll.12 Zimm-Myerson osmo- meters with wet regenerated cellulose membranes type 300 (Sylvania Division, American Viscose Co.) were employed for determinations of the apparent number-average molecular weights. The true number-average molecular weight of polymers carrying carboxyl groups was determined, employing as a solvent either pure pyridine, or any other solvent to which had been added 1.6 volume % of N,N-dimethylbenzylamine with a trace of t- butyl catechol stabilizer. Jnfra-red absorption spectra were determined with a Perkin-Elmer double- beam spectrophotometer, and the ratio of the optical densities at the absorption maxima of the 5.70-5-75 p and 5.85-5.88 p bands (corresponding to the carbonyl stretching vibration for monomeric and hydrogen-bonded carboxyl)13 was used as an index of carboxyl dimerization.Concentrations were calculated from the optical densities using molar extinction coefficients (1. equiv. -1-mm -1) obtained from pivalic acid solutions as 37 and 51 for monomeric carboxyl, 41 and 70 for dimerized carboxyl in 1 : 1 : 2 : 2-tetrachloroethane and carbon tetrachloride, respectively. Spectra of carboxyl-containing polymers in bulk were obtained by the pressed potassium bromide disc technique using an electrically heated cell 14 for holding the sample in the spectrophotometer.The molar extinction coefficients of monomeric and dimeric carboxyl in the solid polymers was estimated as equal to pivalic acid values in benzene, 65 and 63 1. equiv. -1-mm -1. RESULTS AND DISCUSSION MOLECULAR ASSOCIATION OF METHYL METHACRYLATE COPOLYMERS CARRYING CARBOXYL AND AMINO GROUPS In this study 11 a methyl methacrylate copolymer with 4.9 mole % methacrylic acid (no. av. mol. wt. MA = 32,300) and a copolymer containing 5.8 mole % dimethylaminoethyl methacrylate (no. av. mol. wt. MB = 135,000) were employed. Reduced osmotic pressure plots of mixtures of the two copolymers in any given ratio were strictly linear, but the apparent average molecular weights 2 obtained from the intercept were much higher than calculated from the molecular weights of the components of the mixture, indicating extensive molecular association.A degree of association D defined as the average number of molecules associated to an osmotically active particle is given by D = [aA/MA + (1 - .A) /MB] (1) where O ~ A is the weight fraction of the acidic polymer in the polymer mixture. Fig. 1 shows the dependence of D on aA for butanone solutions at 30.2"C and 50.1 "C and for benzene solutions at 49-7°C. It may be seen that in butanone D rises to a sharp peak for mixtures of equal weights of the two polymers, while in benzene solution the association of acidic and basic polymers is complicated by the associa- tion of acidic polymer molecules with each other. The nature of the association complexes involving a tertiary aliphatic amine and a carboxyl group has been investigated by Barrow and Yerger in their spectroscopic study of solutions containing triethylamine and acetic acid in carbon tetrachloride or chloroform.4 The evidence showed that the amine associates both with the monomeric acetic acid and with acetic acid dimer, and led to a hydrogen-bonded ion-pair structure for these species.The 1 : 1 complex was found to be more stable in the more polar chloroform and this was explained by solvation of the ion pair. It should be noted that the present data obtained at around 50°C show stronger association of the basic and acidic copolymers in benzene than in the more polar124 MOLECULAR AND GROUP ASSOCIATION EQUILIBRIA IN POLYMERS butanone. This is all the more significant since butanone was found to be the thermodynamically better solvent for the non-associating basic copolymer (the slopes of the reduced osmotic pressure plots were 1.6 X 10 7 and 1.0 x 10 7 ergs cm 3/82 for butanone and benzene respectively) so that more strongly associating groups would be required for the formation of molecular aggregates in this medium.At any rate, the dependence of the stability of ion-pairs on the nature of the medium is relatively slight compared with the very large effect on the formation of association complexes which depend entirely on hydrogen bonding. It is thus clear that the molecular aggregates of the carboxyl-bearing copolymers will rapidly dissociate as the hydrogen-bonding capacity of the interacting groups is being saturated by the solvent medium. b s - W c n 0 0 1 4 .b 8 1.0 "A FIG.1 .-The molecular association of mixtures of an acidic acid and a basic copolymer of methyl methacrylate. 0 - butanone at 30-2"C, 0 - butanone at 50.1"C, 0 - benzene at 49.7"C. MOLECULAR ASSOCIATION OF METHYL METHACRYLATE + METHACRYLIC ACID COPOLYMER IN BENZENE CONTAINING BASIC OR HYDROGEN-BONDING COSOLVENTS In agreement with previous investigators, we have found no indication of incipient dissociation of the molecular aggregates formed by polymer molecules on diluting solutions in the range accessible to osmotic measurements (from 1 g/100 ml to 0.1 gll00 ml). In fact, light-scattering measurements showed that the association complexes remained stable 15 down to a concentration of O.Olg/ 100 ml. These observations, suggesting that the degree of association of these molecules carrying large numbers of interacting groups remains constant over a wide range of solution concentration, are not easily interpreted in terms of a physical model.Let us consider for simplicity a solution of a polymer containing a single type of interacting group. We may then explain the constant size of the molecular aggregates by assuming that (i) most of the interacting groups are associated intramolecularly or else hidden within the polymer coil so that the "effective functionality "f'of the polymer (i.e. the number of sites available for intermolecularH . MORAWETZ 125 association) is less than two. (ii) The intermolecular association of the available sites proceeds practically to completion. This requirement may necessitate the cooperation of two or more favourably spaced interacting groups in each " site ".This model relates the degree of association D to the effective functionality f of the average polymer molecule by f = 2 ( 0 - l)/D, in analogy with the treatment of the condensation of poly-functional monomers 16 and it satisfies the condition that D be independent of solution concentration. If a cosolvent B is now added which may form complexes with the interacting group A of the polymer according to the equilibrium [ABl/[Al [BI = K, 4 I 1 4 I I I I I (3) 9 FIG. 2.-Molecular association of methyl methacrylate + methacrylic acid copolymer at 294°C in benzene containing: 0 dimethylaminoethyl acetate, methyl acetate, 0 acetic acid and 8 butanone. the effective functionality will be reduced to f' which determines the new degree of association D' by a relation analogous to (2).Assuming that f' is proportional to the number of free A groups, i.e. flf' = ([A] + [AB])/[A], we have then fly-'= (0 - l)D'/(D' - l)D = 1 + K(B). (4) Experimental data have been obtained17 on the effect of cosolvents on the molecular association in benzene at 29.8"C of a methyl methacrylate copolymer containing 4-9 mole % methacrylic acid. The copolymer had an osmotic molecular weight of 34,500 in pyridine and its degree of association in pure benzene at 294°C was 6.86. The cosolvents methyl acetate, acetic acid, dimethylaminoethyl acetate and butanone were chosen for study so as to obtain information on the relative stability of carboxyl complexes with the different types of groups which may have determined the extent of molecular association in the solutions of mixed acidic and basic polymers described in the previous section.The results plotted in fig. 2 show that acetic acid is much less efficient than methyl acetate in reducing the molecular association of the copolymer. This is undoubtedly due to the fact that very little of the added acetic acid is in the monomeric form which would associate with the carboxyl groups of the polymer, while all of the carbonyl groups of the ester are available for such association. It follows that this acidester copolymer must be assumed to associate largely due to intermolecular interactions of a carboxyl126 MOLECULAR AND GROUP ASSOCIATION EQUILIBRIA I N POLYMERS with an ester group rather than the formation of carboxyl dimers.The plots of f/f' against [B] are linear as required by (3) for the ester and the amine and the slopes correspond to association constants of 6.2 and 86 l./mole, respectively. (The latter figure is appreciably lower than the reported value of 800 l./mole for the association of triethylamine with acetic acid in carbon tetrachloride,4 but part of the discrepancy may be accounted for by the lower acidity of the carboxyl groups in the copolymer). The acetic acid data cannot be interpreted in this simple manner, because of the dimerization equilibrium of the cosolvent and the interaction of its monomeric form with both ester and carboxyl groups of the polymer. It should also be noted that the results point to much stronger hydrogen bonding to methyl acetate than to butanone ; this is contrary to the conclusion of Gordy and Stanford 18 who found that the infra-red OD absorption band of deuterated methanol was shifted more strongly in ketone than in ester solutions. However, this apparent discrepancy with our results may be due to the fact that in Gordy and Stanford's experiments the hydrogen-bonded acceptor varied at the same time as the solvent medium, while in our studies the group interactions were all studied in dilute benzene solution.0 INTRAMOLECULAR GROUP ASSOCIATION The study of the solution behaviour of styrene copolymers with methacrylic acid lends itself to a more detailed interpretation since only one group association A _ - ;7 I I I I 1 I I 5 10 I 5 2 0 I S 3 0 3 5 I .0 I \ 0 Pivolicocid refer tocopolymer deriqnotion equilibrium-the dimerization of carboxyl groups-must be taken into account and since in addition to the osmometric determination of molecular association, infra- red spectroscopy can be used to determine the fraction of carboxyl dimerized. An extensive study of this system has been carried out 12 and it was found that the extent of carboxyl dimerization has a value determined by the copolymer composi- tion and the solvent medium but is, within wide limits, independent of solution concentration. This is illustrated in fig. 3 in which the extent of the carboxylH. MORAWETZ 127 association is characterized by dl/d2, the ratio of optical densities at the absorption maxima of the carbonyl stretching vibration at 5.70-5.75 p and 5-85-5.88 p cor- responding to monomeric and dimerized carboxyl, respectively.The result is understandable for polymer solutions which are sufficiently dilute so that the individual molecular coils are far from each other and intermolecular group association is improbable compared with complex formation involving groups attached to the same molecular chain. Under these circumstances, the degree of group association should be goverened by the " effective local concentration " of the interacting groups within the space occupied by an individual polymer chain.19 The data obtained to date also seem to indicate that dl/d2 depends only on the density of the associating groups along the chain and is independent of chain 3.5- 3-0 D 2.5- FIG.4.-Molecular aggrega- tion and carboxyl dimeriza- tion in styrene + methacrylic acid copolymers. 2.0 0 C,H,Ci, Solutions 0 C CI, Solutions - - length.19 Moreover, the constancy of the extent of carboxyl dimerization seems to hold even up to concentrations at which there is appreciable interpenetration of the molecular coils. These observations suggest that most of the complexes form between groups spaced relatively close to one another along the polymer chain. A comparison of the fraction of dimerized carboxyl with the osmotically determined degree of molecular association D is given in fig. 4. In all cases D was remarkably low considering the large number of dimerized carboxyl carried by the copolymer. A typical case was a copolymer with zn = 102,000 carrying 90 carboxyls.Although 70 % of these groups were dimerized in tetrachloroethane solution, only 1.5 chains were associated, on the average, to an osmotically active unit. It can also be seen from the data in fig. 4 that for any given degree of group association, the molecular association of the polymer is higher in tetrachloroethane than in the poorer solvent carbon tetrachloride. It is understandable that the better solvent medium, in which the polymer chain is more highly extended, should favour intermolecular as against intramolecular group association. CARBOXYL ASSOCIATION OF STYRENE + METHACRYLIC ACID COPOLYMERS IN BULK The extent of carboxyl association in bulk samples of styrene + methacrylic acid copolymers has also been measured by infra-red spectroscopy.20 The results128 MOLECULAR AND GROUP ASSOCIATION EQUILIBRIA I N POLYMERS given in fig.5 show the variation of a, the degree of dissociation of the carboxyl dimer, with the temperature of the sample. During the first heating cycle (dashed line), o! remained unchanged up to a temperature of around 100°C; on further heating o! decreased, but on cooling down to room temperature it assumed a lower value than that observed originally. In subsequent heating cycles the samples behaved quite reversibly. The temperature dependence of a above 100°C corresponds to a heat of dimerization of 8-10 kcal in good agreement with values reported for low-molecular- weight carboxylic acids.3 At lower temperatures the dimerization equilibrium is effectively frozen due to the very high viscosity of the system.The freezing of the equilibrium occurs close to the second-order transition temperature of 82°C for polystyrene 21 and it would be interesting to ascertain whether the coincidence of a I -4.6 Mole$ Mathacrylic acid Mole% Methacrylic acid ------------- FIG. 5.-Dissociation of car- boxyl dimers in bulk samples of styrene 3- methacrylic acid copolymers. 0.4 - 0.t I I I I I I I 4 0 6 0 8 0 100 11L 140 Tcmp.[OC) discontinuity in the temperature coefficient of thermodynamic polymer properties and the freezing of chemical equilibria of groups attached to the polymer backbone is a general phenomenon. Such a correlation has been suggested previously by Zhurkov and Levin 22, 23 who studied hydrogen bonding in polymers carrying hydroxyl groups.The fact that cc was higher in the polymer samples as prepared by precipitation from dilute solution than after the first heating cycle shows that the polymer was originally even further from equilibrium than after the annealing operation. This may well be a general effect to be taken into account whenever one deals with polymer samples prepared in this manner. Financial support of this investigation by the Of€ice of Naval Research is gratefully acknowledged. 1 Wolf, Dunken and Merkel, 2. physik. Chem. B, 1940, 46,287. 2 Huckel and Schneider, 2. physik. Chem. B, 1940,47, 227. 3 Allen and Caldin, Quart. Rev., 1953, 7, 255. 4 Barrow and Yerger, J. Amer. Chem. SOC., 1954, 76, 5211. 5 Barrow and Yerger, J. Amer. Chem. SOC., 1955,77,4474, 6206.H . MORAWETZ 129 6 Kauzmann in The Mechanism of Enzyme Action, ed. McElroy and Glass (The Johns 7 Arshid, Giles, Jain and Hessan, J. Chem. SOC., 1956, 72. 8 Trementozzi, Steiner and Doty, J. Amer. Chem. Soc., 1952, 74, 2070. 9 Nord, Bier and Timasheff, J. Amer. Chem. SOC., 1951, 73,289. 10 Ferry, Adv. Protein Chem., 1948, 4, 1. 11 Morawetz and Gobran, J. Polymer Sci., 1948, 12, 133. 12 Chang and Morawetz, J. Physic. Chem., 1956, 60, 782. 13 Hadzi and Sheppard, Proc. Roy. SOC. A, 1953,216,247. 14 Longworth and Morawetz, Chem. and Ind., 1955, 1470. 15 Gobran, Ph. D. Thesis, (Polytechnic Institute of Brooklyn, 1954). 16 Mark and Toboisky, Physical Chemistry of High Polymeric Systems, (Interscience, 17 Morawetz and Gobran, J. Polymer Sci., 1955, 18, 455. 18 Gordy and Stanford, J. Chem. Physics, 1940, 8, 170. 19 Morawetz, J. Polymer Sci., 1957, 23, 247. 20 Longworth and Morawetz, J. Polymer Sci., 1958, 29, 307. 21 Williams and Cleereman, Styrene, its Polymers, Copolymers and Derivatizv, ed ., 22 Zhurkov and Levin, Doklady Akad. Nauk. S.S.S. R., 1950, 72, 269. 23 Zhurkov and Levin, Vestnik Leningrad. Univ., 1950, no. 3,45. Hopkins Press, Baltimore, 1954), p. 71. New York, London, 1950), p. 368,387. Boundy and Boyer, (Rheinhold Publ. Co., New York, 1952). p. 478. E