TRANSFERENCE PROPERTIES OF POLYMERIC ACIDS
979
were discovered with oxygen added, nor by changing the reaction temperature, except that at an optimum intermediate temperature the fibers are smaller and more friable. Their fine structure is described from shadow-cast specimens. Compound fibers are seen and a transverse, macroscopic periodicity is measured. REFEREYCES (1) CALHOUN, J. M.:Can. J. Research 16, 208 (1937). (2) DEVINS,J. C., AND WINKLER, C. A , : Can. J. Research B26, 356 (1948). (3) GRAHAM, W., AND WIKKLER,C. A , : Can. J. Research B26, 564 (1948). (4) OCELLET,C., AND L ~ G E R E., A . : Cnpublished results. (5) WATSON,JOHN H . L.: J. Phys. b- Colloid Chem. 61, 634 (1947). (6) WATSON, JOHN H. L.: J. Phys. b- Colloid Chem. 62, 470 (1948). (7) WATSON, JOHN H . L., . ~ N DKAUFMANN, K . : J. Applied Phys. 17, 996 (1946).
T H E ELECTROLYTIC TRASSFERESCE PROPERTIES OF POLYMERIC ACIDS' FREDERICK T. WALL, GUNTHER S. STENT,* AND J O H S J. OKDREJCIN Soyes
Chemical Laboratory, Vniversity of Illinois, Urbana, Illinois Receined October 3, lQ4Q THEORY
1 . Introduction
Kumerous investigations have shown that polymeric electrolytes possess properties which are strikingly different from those of either nonionic polymers or simple electrolytes. For example, it has been shown by Staudinger (7) and by Fuoss and Strauss (4) that the viscosities of polyelectrolyte solutions have an abnormal dependence on concentration. Moreover the conductance and ionization of solutions of such substances do not obey the laws valid for ordinary electrolytes, such as Ostwald's dilution law (3, 9). To characterize further the behavior of polymeric electrolytes, we undertook the study of the electrolytic transference properties of polymeric ions. Conductance measurements by Wall and deButts (9) on polymeric acids indirectly indicated that the mobility of a slightly ionized polymeric anion is very small compared to that of hydrogen ions. The purpose of the investigation here reported was to determine the actual magnitude of such mobilities by transference studies and to use electrolytic means for the fractionation of polymeric ions. 1 This work was carried out under sponsorship of the Office of Rubber Reserve, Reconstruction Finance Corporation, in connection with the Synthetic Rubber Program of the United States Government. * Present address: Kerckhoff Laboratories of Biology, California Institute of Technology, Pasadena 4, California.
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F. T. WALL, G. S. STENT, AXD J . J . ONDREJCIN
2. Ionic mobility To provide a basis for deriving theoretical formulas relating to mobility, we shall assume that a polymer molecule can be represented by a string of beads, as in Debye’s simple viscosity theory (2). The present theory will, of course, be subject to the limitations inherent in Debye’s theory, since identical assumptions are made with respect to the viscous interactions of “beads” with the solvent. A polymer molecule of the type assumed, consisting of N beads and moving through the solvent with constant velocity v, will experience a total frictional resistance
Q
=
Nfv
(1)
where f is Debye’s frictional force coefficient per bead. We shall identify the beads with monomeric units and N with the degree of polymerization and assume that j remains the same whether or not a monomer unit is ionized. Let us define the mobility p of an ion moving with velocity v under the influence of an electrical potential gradient 6 by the relation: =
P6
(2)
Substituting equation 2 in equation 1, one obtains:
Q = h’ffi6 (3) But if the ion carries a charge z , then the electrical force acting on it will be
Q
=
26
(4)
Equating equations 3 and 4 we obtain the mobility of a polymeric anion: p
= z/h7f
(5)
But if s is the number of ionizable groups per monomer unit and a the degree of ionization, then z = Nsa
(6)
and equation 5 becomes
(7) Thus it appears that the mobility of a polymeric anion is a function only of the ratio of the degree of ionization to the molecular friction coefficient, and not of the degree of polymerization, except implicitly as the latter affects the degree of ionization (9). P = as/f
S. Transference numbers
Let us consider a solution of one species of cation and k species of anions of degrees of polymerization N 1 , K 2 , . . . Nk in molar concentrations e+ and c1, c g , . . . c h , respectively, such as would be encountered in a mixture of polymeric acids. Let us further assume that there correspond to each species electrical charges of z+e and -zle, -z2e, . . .--zke. When an electric current is passed
TRASSFERENCE PROPERTIES OF POLYMERIC ACIDS
981
through this solution, the different species will, in general, carry different fractions of the current, and these fractions are the transference numbers of the constituent species. If we now assume that these ions move independently of each other, the current carried by the ithspecies in a cell of cross-sectional area A filled with such an electrolytic solution is
I,
Ap,c,z,eF+ (8) where I.(, is the ionic mobility of that species and F is the number of coulombs per faraday. The total current, I , flowing through the solution will be given by =
+ p+c+z+}
I = AeF+{&c,z,
,
(9)
where p+ is the cationic mobility. From equation 9 it will be seen that the fraction of the current carried by the jthspecies, i.e., the transference number, t,, is
and the total transference number of negative ions mill be t-
=
Cti i
But since the solution is electrically neutral, it follows that
CC,Zi = I
c+z+
(11)
In the special case of a homogenous polymer solution, Le., where k = 1, substitution of equation 11 into equation 10 gives the ordinary equation: t- =
+
I.(-/b+
IJ-)
(12)
Actually, it turns out that the mobilities of polymeric anions are very much less than that of the hydrogen ion, Le., pi
