2144
G. TORRENCE, S. AMDUR,AND J. A. MARINSKY
The Mean Molal Activity Coefficient of Polymethacrylic Acid at Various Degrees of Neutralization by G. Torrence, S. Amdur, and J. A. Marinsky*' Department of Chemistry, State UnCersity of N e w York at Buffalo, Buffalo, New York
14614
(Received June 69, 1970)
Publication costs borne completely by T h e Journal of Physical Chemistry
The osmotic and potentiometric properties of polymethacrylic acid, neutralized with standard sodium hydroxide to provide several fixed degrees of neutralization, CY, have been measured over a moderate concentration range at each selected CY value. The osmotic data have been employed in the Gibbs-Duhem equation to compute the ratio of mean molal activity coefficients of a reference solution and a sample solution. This has been compared with the change in the corresponding deviation from ideality that is identified by the difference, ApK, between pH - log a / ( l - CY)and pK, the negative logarithm of the intrinsic dissociation constant of its repeating monomer unit. The deviation term computed from the osmotic data and the deviation term obtained from the potentiometric data are in reasonable agreement in almost every experimental situation tested.
Introduction Much effort has been expended in an attempt to interpret potentiometric titration2-s and osmotic data719 that have been obtained for polymethacrylic acid, PMA (I). A most informative examination of this
where e is the charge of the proton and #(a) is the electrostatic potential at the surface of the polyion.'O I n this model the solution of polyelectrolyte is assumed to exhibit ideal behavior in the absence of macroion-counterion forces, the partial free energy of a mole of polyelectrolyte, d,, being expressed as
6, or
6,' (1) problem is provided in the approach used by Amoldla where potentiometric titration data are plotted as pH - log a/(l - a) (or pK) us. a. Ideally pH log a / ( l - a) = pKo and any distortion from a straight line of zero slope is believed to provide a quantitative estimate of the deviation from ideal behavior of the system as the polyion is progressively dissociated. Representative plots intercept the ordinate a t a value of 4.55.3 Since there is 110 ionization of the polymer at a = 0, this number should correspond to the negative logarithm of the intrinsic dissociation constant of the repeating acidic group of PMA. This intercept value, indeed, is in reasonable accord with the dissociation constant of the basic monomer unit, isobutyric acid, which is reported as 4.84at 2 j o . 3 As a is raised the pK value for the polyelectrolyte deviates increasingly from that of the monomeric acid unit. This discrepancy (ApK) is attributed to the change in electrostatic free energy of the molecule accompanying the ionization process a t the polyion surface due to group-group interactions3 and has been expressed as 0.434 [c#(a)]/(kT) The Journal of Physical Chemistry, Vo2. 7 6 , N o . 14, 1971
=
6,
(ideal)
+ A6, (el)
+ RT In yf, + RT In mp = dPo+ RT In mp + Ad, (el)
(1)
(2)
m p being the molality of the polyelectrolyte, y=ktp,its mean molal activity coefficient, and dPoreferring to its hypothetical standard state. At any a value the deviation from ideality should then correspond to the mean molal activity coefficient of the polyelectrolyte according to eq 3.
(1) Department of Chemistry, McGill University, Montreal, Quebec, Canada. (2) (a) A. Katchalsky and P. Spitnik, J . Polym. Sci., 2, 432 (1947); (b) A. Katchalsky and J . Gillis, Red. Trao. Chim. Pays-Bas, 68, 879 (1949). (3) R.Arnold and J. Th. G. Overbeek, ibid., 69, 192 (1950). (4) A. 0th and P. Doty, J . Phys. Chem., 56, 43 (1952). (5) H.Gregor and M. Frederick, J . Polym. Sci., 23, 451 (1957). (6) E. E.Kern and D. K. Anderson, ibid., Part A-1, 6,2765 (1968). (7) Z.Alexandrowicz and A. Katchalsky, ibid., Part A , 1,3231 (1963). (8) H. P. Gregor, M. J. Hamilton, J. Becher, and F. Bernstein, J . Phys. Chem., 59, 874 (1955). (9) Z.Alexandrowicz, J . Polym. Sci., 40, 98 (1959). (10) J. A. Marinsky, "Ion Exchange," Vol. 1, Marcel Dekker, New York, N. Y.,1966, Chapter 9.
MEANMOLALACTIVITY COEFFICIENT OF POLYMETHACRYLIC ACID This concept can and should be tested by employing the Gibbs-Duhem relation. For electrolyte solutionsll
Here y f is the mean molal activity coefficient of the electrolyte at its molal concentration m and C$ is the osmotic coefficient for the system. The value of yf, is obtained directly from graphical integration of the integral of eq 4,values of C$ in the dilute concentration range unaccessible to experiment (
