1834
COMMUNICATIOKS TO THE EDITOR 0.
I
(COOMeCF2CF2)2N
coupling mechanisms, this interpretation seems less probable.
A“ = 9.4 A F = 13.8
(20) Fluorine p-T interaction has been previously proposed for pfluorine coupling18 (P. J. Scheidler and J. R. Bolton, J . Am. Chem. Soc., 88, 371 (1966)).
I11
(21) The second-order splitting obtained from a cyclic radical having rapidly exchanging conformations is shown in Figure 33, ref 10.
0.
AN = 22.8 A F = 5.9
IT‘
Acknowledgment. This work was supported by AFOSR(SRC)-OAR U. S. A. F. Grant S o . 1069-66. DEPARTMENT OB CHEMISTRY THEUNIVERSITY O F GEORGIA ATHENS,GEORGIA30601
JOHN L. GERLOCK EDWARD G. JAKZEN
RECEIVED DECEMBER 26, 1967
0.
I
C~-CFZ-CFZ-N-O-C(CH~)~
A N = 21.8 AF = 9.5
v
Cl-CFz-CF2-N02-*
Polyelectrolyte Adsorption,” by D. IC. Chattoraj
AN = 17.53 AF = 33.80
VI1 Because the dihedral angle for the p-fluorines is greater than 45” in I11 and VI2 (and VIIlS), it has been suggested that maximum fluorine coupling may occur when 0 = 9O”.l2 Available data in fact suggest that minimum fluorine coupling may occur at some angle between 0 and 90” ; an increase in this angle in either direction may lead to an increase in fluorine coupling. y-Fluorine coupling in I is usually large compared to y-coupling in other radicals; e.g., A H = 1.12 G for cyclobutyl10 radical and A” = 1.88 G for V.’* This may be due to p-T interaction between the y-fluorines and the carbonyl p orbital.z0 Although the y-fluorine coupling observed should be large enough to make second-order coupling detectable, none was found. Rationale for lack of secondorder y-coupling can be found in any mechanism which causes the y-fluorines not to be completely equivalent. Since the p-fluorines are completely equivalent, the y-fluorines alone must be experiencing time-dependent perturbations or the y-fluorine coupling is more sensitive to small perturbations than the p-fluorine coupling. As a source of the perturbation, rapidly exchanging solvent and/or ion complexes or very small planarity fluctuations of the cyclobutarle ringZ1can be suggested. A special case of second-order coupling arises when two nuclei (I = 1/2) have equal coupling of opposite sign.’ In this case an apparent first order 1:2: 1 triplet is predicted. Since an opposite sign for the two yfluorine couplings is inconsistent with usual hyperfine T h e Journal o j Physical Chemistry
Comments on “Gibbs Equation for
Xir: In a recent paper, Chattoraj’ suggested an equation for the adsorption of polyelectrolytes in the presence of salt with a common ion. His erroneous substitution for the electrochemical potential of individual ions in the Gibbs equation and his definition of surface excess led him to reach incorrect conclusions. In this criticism we shall constrain ourselves only to the most fundamental points. Equation 2 given by Chattoraj -dy = rpdpp
+ rire+dPire++ rx-dpx-
is correct only if the pi’s are the respective electrochemical potentials.z I n this equation r stands for surface excess, p for the electrochemical potential, and subscripts p, Me+ and X- stand for polyelectrolyte, cation, and anion, respectively. For adsorption of polyacids on a polarized surface, the Gibbs equation assumes the form3 -dy
=
rpdpp
+ rx-dpu,+ qdEvI,+
(1)
where pp and ps are the chemical potentials of the neutral polyelectrolyte and salt, and the surface charge density q divided by the charge of the electron is balanced by the surface excess of the ionic components rYe+ - rx-and --rP; v is the charge of the polyacid molecule. For a nonpolarized surface, the last term of eq 1 vanishes leaving an expression which can be obtained directly from Chattoraj’s eq 2. However, his eq 3
(1) D. K. Chattoraj, J . Phys. Chem., 70, 3743 (1966). (2) R. Parsons and M. A. V. Devanathan, Trans. Faraday SOC.,49, 404 (1953). (3) I. R. Miller and A. Katchalsky in “Proceedings of the 4th Inter-
national Congress on Surface Active Substances,” Vol. 11, “Physics and Physical Chemistry of Surface Active Substances,” J. Th. G. Overbeek, Ed., Gordon and Breach Scientific Publications, New York, N. Y., 1967, p 275.
COMMUNICATIONS TO THE EDITOR
1835
and his eq 7
-dr
-- =
d In C,
r,kT[l
+ u + CdC, Y2
1
obtained by his erroneous substitution, for the electrochemical potentials, are incorrect. I n these equslr tions C designates bulk concentration. The expressions obtained in ref 3 for the variation of the surface tension with polymer and salt concentration are
and if the osmotic factor in the surface +pu equals that in the bulk. It will be shown in a forthcoming publicationa that the negative surface excess of the co-ion may result in no change of surface tension despite strong polyelectrolyte adsorption. (4) Z. Alexandrowica, J. Polymer Sci., 56, 97 (1962). (5) Z. Alexandrowicz and A. Katchalsky, ibid., A I , 323 (1963). (6) M. A. Frommer and I. R. Miller, submitted to J. Phys. Chem.
POLYMER DEPARTMENT WEIZMANN INSTITUTE OF SCIENCE ISRAEL REHOVOTH,
I. R. MILLER
HYDRONAUTICS ISRAEL LTD. M. A. FROMMER REHOVOTH, ISRAEL RECEIVED OCTOBER 11, 1967
v4,cs rpcs + V4PCP
+
Reply to the Comments on “Gibbs Equation for Polyelectrolyte Adsorption”
where 4, is the osmotic factor of the polyelectrolyte measured in the absence of salt.4 In the derivation of eq 2 and 3 the experimentally justified additivity rule6 given in eq 4 and 5 was employed for expressing the chemical potentials of the neutral polyelectrolyte and the neutral salt in the mixed polyelectrolyte solution.
+ dp, = kT d In C,(v4,CP + C,)
dpp = kT d In C,(v4,CP
(4)
Cs)y$p
(5)
I n the corresponding expressions for the chemical potentials used by Chattoraj, the important osmotic factor which varies usually between 0.1 and 0.5 is missing. For a salt-free solution eq 7 of Chattoraj reduces t o -dr/d In Cp = kTI’(1 u), whereas our eq 2 assume the form -dy/d In C, = k T F ( 1 4,~). Experimentally , one can never achieve “ideal” polyelectrolyte solutions 11 here the osmotic factors and activity coefficients would approach unity. The more serious error follows from eq 10 of his paper which postulates rx- > 0. The Boltzmann distribution presented in Chattoraj’s eq 11 and 18 imply proportionality between the concentrations in the bulk and the corresponding surface excess. His replacement of surface excess by surface concentrations excludes the possibility for the surface excess to be negative. The requirement for rx- < 0 if X- is not surface active follows from the Donnan equilibrium which can be written as
+
CS(C,
+ Y+PC,)
+
Sir: Recently, hiiiller and Frommerl have criticized the use of the Gibbs equation (2) in deducing our expression for the kT coefficient in the case of the polyelectrolyte adsorption.2 I n our treatment for the adsorption of RNa, in the presence of NaCl, the implicit assumption is that the surface like the bulk behaves as a distinct macrophase. The phase concept of the liquid surface has been discussed by Guggenheime8 At distribution equilibrium between two such phases, it is legitimate to writea PRNav
PNaCl
It is evident from eq 6 that,for any arbitrary thickness rpis positive
6 of the surface phase, I’x- is negative if
S
= NRNav
(22)
=
(23)
PNsCl
Here p: and pz stand for the chemical potentials of the ith component in the surface and bulk phases, respectively. As in the case of the nonelectrolyte^,^^^ we can obtain the Gibbs relation for the present case in the form - d r = dn =
+ n,v,ci dpNaci
~ R N dpRNav ~ ”
(24)
Let us now assume that the polyelectrolyte concentration in each phase is ideally dilute and both RNa, and NaCl are completely dissociated so that ~ R N and ~ ” TLNeC1 become equal to n R and ncl-, respectively. Further, the bulk chemical potentials of the electrolytes can be written in the usual forms PRNaV PXaC1
=
S
= PR =
PNa’
+ +
VPNat
(25)
PCl-
(26)
(1) I. R. Miller and M. A. Frommer, J . Phys. Chem., 7 2 , 1834 (1968). (2) D. K. Chattoraj, ibid., 70, 3743 (1966). (3) E. A. Guggenheim, “Thermodynamics,” North-Holland Publishing Co., Amsterdam, 1950, pp 46, 345, 367. (4) J. T. Davies and E. K. Rideal, “Interfacial Phenomena,” Academic Press Inc., New York, N. Y . , 1961, p 197.
Volume 78, Number 6 May 1068
