Environ. Sci. Technol. i g ~ g , 2 3 747-748 ,
function of a)was given in ref 5, but omitted in ref 1 and 2. Marinsky and co-workers conducted a thorough study of ionic strength effects on FA protonation equilibria, and their results are important and interesting. However, reanalysis indicates that neither the permeable Donnan gel model nor the impermeable small acid model describes these effects for the FAs studied. The mechanism of the salt effects is still unresolved, and the field awaits development of a useful predictive and explanatory model. Literature Cited (1) Marinsky, J. A.; Ephraim, J. Enuiron. Sci. Technol. 1986, (2)
(3) (4) (5) (6) (7)
20,349-354. Ephraim, J.; Alegret, S.; Mathuthu, A.; Bicking, M.; Malcolm, R. L.; Marinsky, J. A. Environ. Sci. Technol. 1986, 20, 354-366. Marinsky, J. A. J. Phys. Chem. 1985,89,5294-5302. Paterson, R.; Rahman, H. J. Colloid Interface Sci. 1983, 94, 60-69. Alegret, S.; Escalas, M.; Marinsky, J. Talanta 1984, 31, 683-681. Nagasawa, M.; Murase, T.;Kondo, K. J. Phys. Chem. 1965, 69, 4005-4012. Olander, D. S.; Holtzer, A. J. Am. Chem. SOC.1968, 90, 4549-4560.
Stephen E. Cabaniss’
Department of Chemistry University of North Carolina Chapel Hill, North Carolina 27599-3290 Francois M.M. Morel
Ralph Parsons Laboratory Department of Civil Engineering MIT
Cambridge, Massachusetts 02139
SIR: Cabaniss and Morel are quite correct in much of their criticism of our two articles (1,2). Uniqueness of plots of pKaPP(~A), versus (pH pX) that are resolved at different ionic strengths does not imply absolute rigidity of the polyelectrolyte (cross-linked or linear) under investigation nor does it provide a test for its permeability to salt as we implied. (A) Rigidity of Polyelectrolytes (Gels). We have examined two hypothetical cases to provide an estimate of how faulted the rigidity criterion is. In both examples an intrinsic pK of 5.0 has been assigned to the repeating monomer unit of the weakly acidic linear polyelectrolyte. In one set of computations the polymer has been assumed to be quite flexible, increasing in water content from 1.3 kg of H20/mol (monomer basis) at a = 0.1 and I = 0.1-9.1 kg/mol at a = 0.9 and I = 0.0010. In the other set the weakly acidic polyelectrolyte has been assumed to be absolutely rigid at 1.0 kg/mol. The results of these computations are presented in Figure la,b. With the flexible polyelectrolyte (Figure la), the points diverge right from the start. For the rigid case (Figure lb), the points at each ionic strength define a single straight line with a slope of 0.5, as they must, before they begin to diverge at a = 0.6. Cabaniss and Morel, in their critique, presume this slope of 0.5, which characterizes the curves in Figures 5-8 of ref 1, to be coincidental and partly responsible for their accidental uniqueness, but they are wrong. In order for all the points to resolve a single line over the complete a range as shown in Figure IC, the hypothetical rigid polyelectrolyte has to be reduced in water content by a factor of 3 from its value at a = 0.6 by the
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0013-936X/89/0923-0747$01.50/0
time an a value of 0.9 is reached. The fact that uniqueness of this kind was obtained throughout our plots of pKaPP(~)v versus (pH + pX) (I,2) for poly(acry1ic) (Figure 4; ref 3) and poly(d,l-glutamic) acid (Figure 1,ref 4) would seem to indicate that significant loss in volume occurs in these polyelectrolytes after an a of 0.6 is reached. From the above we see that the criterion for rigidity that was claimed in our earlier articles (1,2) is only partially valid. However, the results of our computations still seem to suggest that some insight with respect to the flexibility or rigidity of a weakly acidic polyelectrolyte with only one functional unit repeated Y times in each molecule is gained from a plot of pKaPP(HA).versus (pH pX). With more than one acid group repeated in the polyelectrolyte, the curves separate as shown in the figure presented by Cabaniss and Morel in their critique (5). The most useful approach to flexibility or rigidity estimates is provided, however, by plots of (pH - pX) versus a for a polyanion ( 5 , 6 )or by plots of (pH + pX) versus a for a polycation (5, 7). Even though the uniqueness of such plots only shows, as Cabaniss and Morel point out, that volume of the polyelectrolyte phase at a particular a is unaffected by ionic strength while the volume may or may not vary with a, these data can be easily manipulated to obtain estimates of Vp, the water content of the polyelectrolyte phase as a function of a (8). (B) Donnan Model Test for Salt Permeability. The claim by us that the characteristics of P K * P P ~versus ) ~ (pH pX) plots at different ionic strengths, when presented for polyanions (linear, gel), provide real insight with respect to their permeability or impermeability to simple salt is wrong, as Cabaniss and Morel have declared in their critique (5): But so is their counterclaim that plots of a versus (pH - pX) for polyanions and (pH + pX) for polycations serve this function instead. The fact that such a plot is unique as ionic strength is varied with the PFeO(OH),NaC1, HC1 system (7) attests to this. Diffusion of NaCl and/or HC1 into the narrow 5-w channels of this gel together with the C1- and OH- ions that neutralize the positively charged matrix of this polycation is very unlikely, and this result shows that salt permeability is not a prerequisite for such uniqueness. (C) The Test for Salt Permeability. I have to agree with Cabaniss and Morel that the uniqueness of a plot of pKaPP(HA).versus pH at different salt concentration levels is not a test for salt impermeability and rigidity. Actually, the small but real separation of pKaPP(HA).versus a plots at sizably different ionic strengths (varying by factors of lo), the reason for such apparent uniqueness, is the only valid clue to the true nature of the system. It tells one immediately that the system is heterogeneous-but no more than that. Any conjecture beyond this point has to be based on chemical clues. Such a reconsideration of the fulvic acid, simple salt system, has led once again to its earlier description. The separate microphase that the molecule effects is still considered to be hydrophobic and salt impermeable (9). My colleagues and I are grateful to Cabaniss and Morel for their useful criticism.
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Literature Cited
0 1989 American Chemical Soc:iety
(1) Marinsky, J. A.; Ephraim, J. Enuiron. Sci, Technol. 1986, 20,349-354. (2) Ephraim, J.; Alegret, S.; Mathuthu, A.; Bicking, M.; Malcolm, R. L.; Marinsky, J. A. Ibid. 1986, 20, 355-366. (3) Nagasawa, M.; Murose, T.;Kondo, K. J.Phys. Chem. 1965, 69,4005-4012. (4) Olander, D. S.; Holtzer, A. J. Am. Chem. SOC.1968, 90, 4549-4560. Environ. Sci. Technol., Vol. 23, NO. 6, 1989 747
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(5) Cabaniss, S.; Morel, F. M. M. Environ. Sci. Technol., preceding comments in this issue. (6) Alegret, S.; Marinsky, J. A.; Escalas, M. T. TQlQntQ 1984, 31, 683-687. (7) Paterson, R.; Rahman, H. J . Colloid Interface Sci. 1983, 94, 60-69. (8) Miyajima, T.; Muhammed, M.; Marinsky, J. A., submitted for publication in J . React. Polym.
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Environ. Sci. Technol., Vol. 23, No. 6, 1989
(9) Marinsky, J. A.; Reddy, M. M.; Ephraim, J.; Mathuthu, A.,
submitted for publication in Enuiron. Sci. Technol.
Jacob A. Marinsky Chemistry Department State University of New York, at Buffalo Buffalo, New York 14214
