PROTON-TRANSFER REACTIONS OF POLYACRYLIC AND POLYMETHACRYLIC ACID shows or a t least suggests the role of the critical solution temperature. As for the generality of these new results, it would be desirable to expand the current range of temperature and one can expect that the actual equations, e.g., eq l and 6, are of limited validity. However, there is no reaslon to presume a restriction of the basic correspondence principle to the particular polymersolvent system studied here. I n many instances it is not convenient, if not actually impossible, to establish the thermodynamic critical coordinates. Provided a good solvent over a sufficiently wide range of temperatures is available, the
267
function -y(M,T) can be expressed in terms of an arbitrarily chosen M Oand To. If, by varying Mol the parameters of this function change in an expected manner, an estimate of Tc(Mo)may then be obtained from the temperature coefficientsof viscosity. Finally, we recall the persistent deviations of the lowest molecular weight at elevated concentrations from our superposition scheme, based on higher molecular weights, and analogous departures in respect to [q] and y. These results suggest separate studies of low molecular weight series with A4 < IO6 as a function of concentration and temperature.
K inetics of Paoton-Transfer Reactions of Polyacrylic and Polymethacrylic Acids with an Indicator by Shmuel Weiss,"' Hartmut Diebler, Max-Planck-Institut far Physikalische Chemie, Gdttingen, West Germany
and Isaac Michaeli Weismann Institute of Science, Rehovot, and the University of the Negeu, Beer-Sheva, Israel
(Received July 2, 1970)
Publicaition costs borne completely by The Journal of Physical Chemistry
'The kinetics of proton transfer between polyacrylic acid and the pH indicator phenol red and between polymethacrylic acid and phenol red have been studied by the temperature-jump relaxation technique in the pH range 6-8.5. I n every case only a single and well defined relaxation time was observed. The rate constant for direct proton transfer from the polyacid to the indicator was found to be (2 f 1) x lo7 J4-1 sec-1 (acid concentration expressed in terms of monomeric units) for both systems, essentially independent of pH in the pH range studied. No evidence 'was found from these kinetic studies and additional ones a t pH 5-6 for conformational transitions of the polyacids. Possible effects of the macromolecular nature of the polyacids on the prloton-transfer kinetics are discussed.
Introduction A great deal of information is now available concerning the kinetics of proton transfer reactions in aqueous solutions.2a,b This information, however, has been obtained from experiments with low molecular weight materials. The pimrlpose of the present investigation was therefore to obtain some information about protontransfer reactions involving polyelectrolyte reactants. When passing from low molecular weight to polyelectrolyte systems one might expect to find new patterns of behavior in the kinetics of proton transfer, due to the macromolecular nature of the polyelectrolyte. More specifically, in the case of polyelectrolytes the question arises whether all the acidic sites are equally available to proton exchange; evidently conditions can be envisaged in which some of the acidic groups may be
more exposed while some others are "buried" within the coiled polymeric matrix. Also, the affinity of a given acceptor group for a proton will depend on whether the neighboring groups are in the ionized or in the protonated form. Under such circumstances a whole series of proton transfer processes may be expected. Moreover, the binding of protons to a polyanion usually brings about conformational transitions in the macromolecule. Such transitions are known to affect the acidic strength of the molecule3 and thus will lead to a (1) On leave from Nuclear Research Centre, Negev, Israel Atomic Energy Commission. (2) (a) M. Eigen, Angew. Chem., Int. Ed. Engl., 3 , 1 (1964); (b) M . Eigen, W. Kruse, G. Maass, and L. De Maeyer, Progr. React. Kinet. 2 , (1964). (3) J. C. Leyte and M. Mandel, J . Polymer Sci. Part A , 2 , 1879 (1964); I. Michaeli, J . Polymer Sci. Part C,16, 4169 (1968).
The Journal of Physical Chemistry, Vol. '76,No. 2 , I971
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distribution of reaction rate constants for proton transfer; they also could give rise to the observation of additional time constants, typical of the conformational tranfitions themselves. The present investigation deals with the study of the relaxation processe,s in a system containing a polyacid and a low molecular weight p H indicator over the pH range 64.5. Two weak polyacids were chosen, polyacrylic acid (PAA), and polymethacrylic acid (PMA). The two are k.nown t o differ in the run of their potentiometric titratnon curves: unlike PAA, PMA has an “anomalous” titration curve which has been attributed to a cooperative conformational transition. (However, see also ref 4.) I3ecause of its suitable dissociation constant (pK = 7.7 at 20”) phenol red was used as indicator. The indicator is negatively charged (- 1 and -2) both in its acidic and basic forms. Experimental Section PA.A was obtained by polymerization of the distilled monomer in rsqueous solution in the presence of HzOz (3%).5 The system was kept for 4 hr at 90”. The polymer was subsequently precipitated in &So4 and redissolved in water. A low degree of fractionation was obtained by fractional reprecipitation with HzSO4. The fractionst thus obtained were dialyzed and dried by lyophilization. PMA was prepared from the monomer by polymerization with rzzobisisobutyronitrile initiator in aqueous solution at 6O”. The polymer was dialyzed and freeze dried. The degree, of polymerization of both PAA and PMA was estimated from light scattering t,o be of the order of 1000. The kinetic studies were carried out using a commercially available T-jump apparatus with spectrophotometric detection.6 Polyacid concentrations were 0.2 X 10-3 M to 5 X M (in monomeric units); all solutions contained 0.1 N Na~SOe (to provide sufficient electricd conductivity) and 4 X M phenol red. The solutions were thermostated a t 15.0 ( f0.2)O prior to il temperature jump of 5.0”. The chemical relaxation was followed spectrophotometrically at 560 mp, close to the absorption maximum of the basic indicator species. Time constants were evaluated as the mean of 4 or 5 individual measurements; the average deviation was within 10% of the mean.
Resdts and 1)iscnssion As outlined in the Introduction, the acidic and basic sites of the polycarboxylic acids are expected not to be equivalent with regard to their acidities or basicities, due to differing local environments. Proton transfer between indimtar and polyacid sites of different reactivities may then lead to a series of relaxation times, which may appear as a discrete set or as a close distribution, depending on the distribution of the acidic and basic groups and on their interactions. However, The Journal of Physical Chemistry, Vol. 76, No. 8, 1071
S.WEISS, H.DIEBLER,AND I. MICITAELI carboxylic groups of different reactivities are certainly capable of interconversion. Such in terconversion processes may be brought about by local changes in conformation and/or by proton exchange between different pplyacid molecules or between different parts of the same molecule (perhaps via a system of hydrogen bonds along the chain).8 If the rate of interconversion is high as compared to the rate of reaction with the indicator, the differences in reactivity will average out and the polyacid will behave as if all the protonated (or dissociated) carboxylic groups were equivalent. I n this case proton transfer will evidently give rise to a single re1axation time, whereas the interconversion process will not be detected by the applied technique. From studies of equilibrium properties it has been shown that, a t least in the case of PMA, the behavior of the polyacid can be formally interpreted in terms of the existence of two conformations. Under our experimental conditions these two conformations differ in acidic strength by close to two pK units. The existence of two such distinct forms would suggest that a t least two time constants appear in the relaxation spectrum (one of which being due to the change in conformation) unless the rate of the conforniational transition is high as compared to the rate of proton transfer. Another possibility, not ruled out by the equilibrium studies and favored by a recent report19is that the polyacid really exists as a mixture of a multiplicity of structures (except a t very low and a t very high degrees of ionization). I n this case a distribution of relaxation times would be expected unless, ag&n, the structural changes are too fast. Experimentally it was found that over the pH range studied both systems are characterized by a single and well defined relaxation process. Its time constant varied between 20 and 250 psec, depending on polyacid concentration and pH. A summary of the observed time constants is given in Table I. The dependence of the relaxation time on polyacid concentration a t constant pH is evidence against its being related Lo conformational transitions. To further check this point, the investigations were extended to pH values a t which the ratio of the two eonformations of PMA should be close to l.3 Using chlorophenol red and bromocresol green as indicators, the pH could be decreased to 5.1 (degree of dissociation of PMA LY = 0.1g3) (as a check similar experiments were performed (4) A. R. Matheson and J. V. McLaren, J . Polymer Sci. Part A , 3 2555 (1965). (5) Z. Alexandrowics, J . Polymer Sci., 40, 91 (1959). (6) Messanlagen Studiengesellschaft m.b.H., Gottingen, W. Germany. (7) The same medium had been used by Michaeli (ref 3 and unpublished data) in his equilibrium studies. (8) See A. Silberberg, J. Eliassaf, and A. Katchdsky, J . Polgmer, Sci., 2 3 , 259 (1957). (9) J. L. Koenig, A. C. Angood, J. Semen, and J. B. Lando, J . Amer. Chem. Soc., 91, 7250 (1969).
PROTON-TRANSFER REACTIONS OF POLYACRYLIC A N D POLYMETHACRYLIC
Table I: Dependence of the Reciprocal Relaxation Time X
----
PAA
~I-------
0.2
x
PH
10-8 M
6.20 6.70 7.10 7.50 7.90 8.30
24 13.3
0 5 x 10-a M
1x 10-8 M
:3 1
14.9 (7.8)" (4.5)"
36 17.9 9.7 (8.1)" (5.3)" (5.2)"
2 X 10-8 M
22 13.2 8.7 6.8 6.7
5x 10-8 M
18.5 12.0 11.3 11.4
ACID
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(sec-1 ) on Polyacid Concentration and pH
-PH
6.23 6.58 6.85 7.30 7.73 8.10 8.48
0.2 x 10-8 M
43 17.6
0.5
x
PMA
10-8 M
33 17.8 11.5 (6.3)" (5.1)"
1x io-' M
45 24 16.9 9.5 (7.4)" (8.0)" (9.8)"
2x 10-8 M
27 19.2 12.7 11.0 11.2 11.8
5x
io-SM
29 21 17.5 17.9 15.2
Values given in parentheses correspond to instances where polymer concentrations were so low that the condition C m - , CHW > k~ than that of k ~ due CHIn- not being sufficiently fulfilled. Both PAA and PMA are stronger proton donors than the acidic indicator species, the apparent pK values ( = -log CH+ * cr/l -- a> of the former varying approximately between 6.8 and 6.4 in the pH range studied, whereas ~ K H =I 7.'7. ~ Because of these differences in pK it would be expected' that k 3 8N ~ 2 X lo7mol-' sec-l represents the rate constant for a diff usion-controlled proton-transfer process. It should be borne in mind, however, that hydrogen bonding between the carboxylic groups of the polyacids may lead to a rate constant for proton transfer same what below the diff usion-controlled limit12 (the same mEty apply to h3,,the rate constant for the reaction of WI'A with OH-). For the analogous reactions of the monomeric acids ATPH3- and ADPH2with phenol red, difl'usion-controlled rate constants of 7 X lo8 mol-' have been reported.'O These values are not fit for direct comparison, however, since there is no theory available yet to predict rate constants for diffusion-controlled reactions in which the reactive sites of a polyelectrolyte chain represent one of the reactants. I3
27 1
The values for kasj do not show a significant dependence on CH+in the pH range within which a reliable determination can be accomplished. The slight increase in the rate constant for the reverse reaction, kat3,with increasing pH therefore mainly reflects the variations of the apparent pK values of the polyacids. Apparently the variations in charge and conformation of the macromolecules between a, rv 0.65 and a N 0.99 are not so severe as to have an appreciable effect on has). More pronounced effects may show up a t small values of a,but proton transfer will be difficult to study under these conditions by the present technique.
Acknowledgment. The authors wish to express their appreciation to Dr. L. De Maeyer for helpful discussions and to Dr. F. Eggers for help with the sound absorption experiments. (12) Reference 2, Table IV. (13) If the concentration of the polyacids is expressed in terms of polymeric species, the rate constant for proton transfer from the polyacid to the indicator has a value of about 1 X l O l o M-1 sec-1 0.6. For particles of spherical symmetry (which is not fulat a filled here) and with negligible electrostatic interaction, a diffusioncontrolled rate constant of 1 X 1O1O M-1 sec-1 corresponds to a distance of reaction of -30 -&a (taking 0.5 X om2 sec-1 as the sum of the two diffusioncoefficients). Obviously use of concentrations expressed in terms of polymeric species does not affect the validity of the derivation of eq 2 since indicator species concentrations still remain small relative to polymer concentrationin terms of equivalents per unit volume.
The Journal of Physical Chemistrv, Vol. 76, No. 9, I071
