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for ribonuclease A. This research was supported in part by Grant No. GM 11762 from the Institute of General Medical Sciences, U.S. Public Health Service.
Supplementary Material Available: Tables 1M-5M (7 pages). Ordering information is available on any current masthead page.
References and Notes (1) D. R. Robinson and W. P. JenW, d A m Chem Sot, 87,2470 (1965). (2) E. E. Schrier and E. B. Schrier, J. Phys Chem., 71, 1851 (1967). (3) P. H. von Hippel and T. Schleich in ''Structure and Stability of Bidcgical Macromolecules", S. Timasheff and G. Fasman, Ed., Marcel Dekker, New York, N.Y. 1969. (4) P. K. Nandi and D.R. Robinson, d Am Chem S m ,94, 1299 (1972).
(5) P. H. von Hippel, V. Peticohs, L. Schack, and L. Karlson, Biochem&w,
12, 1256 (1973). (6) D. Talbot, Ph.D. Dissertation, Dartmouth College, 1968. (7) M. Y. Schrier, P. J. Turner, and E. E. Schrier, d Phys. Chem., 79, 1391 (1975). (8) C. Tanford and J. D. Hauenstein, d A m Chem Soc, 78, 5287 (1956). (9) E. E. Schrier and R. A. Robinson, d Biol. Chem., 245, 2432 (1970). (10) M. Y. Schrier and E. E. Schrier, Biochemistry, 15, 2607 (1976). (11) See paragraph at end of text regarding supplementary material. (12) M F. Gibbard and G. Scatchard, J. Chem €ng Data, 18, 293 (1973). (13) H. D. Ellerton and P. J. Dunlop, J. Phys. Chem., 7 0 , 1831 (1966). (14) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions", 2nd ed, Butterworths, London, p 478. (15) V. E. Bower and R. A. Robinson, d Phys. Chem., 67, 1524 (1963). (16) C. N. Pace, CRC Crit. Rev. Biochem., 3, 1 (1975). (17) C. Tanford, Adv. Protein Chem., 23. 121 (1968). (18) M. Noelken, Biochemistry, 9, 4122 (1970).
Properties of Organic-Water Mixtures. 11. Self-Diffusion Coefficients of Na' in Polyethylene Glycol-Water Mixtures at 25 0C1i2 Harold 0. Phillips,3aArthur E. Marcink~wsky,~~ S. Baruch S a ~ h s , ~and ' Kurt A. Kraus* Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830 (Received October 18, 1976) Publication costs assisted by the U.S. Energy Research and Development Administration
Self-diffusion coefficients, D, of Na' (NaCl, m = 0.1) were measured by the radiometric porous frit method for water mixtures of polyethylene glycol (PEG, molecular weight ca. 20000) at 25 "C. As the organic fraction cm2/s in 48 vol % PEG. cmz/s in water to 0.15 X of the solution increases, D decreases from 1.28 X The diffusion coefficient-viscosity product increases rapidly with increasing fraction of organic component in solution. At an organic volume fraction of 0.48, the relative diffusion coefficient-viscosity product is over 700 times larger than in water. A plot of the logarithm of the relative diffusion coefficients against logarithm of the volume fraction of water is essentially linear, with slope 3.3. This large slope implies that for self-diffusion of small ions the PEG solution behaves like an assembly of oblate ellipsoids of revolution with an axial ratio substantially different from unity.
In this series of papers, we have been concerned with obtaining information on the equilibrium and kinetic behavior of water-organic-electrolyte mixtures largely because of their possible pertinence to membrane processes such as hyperfiltration. An earlier paper4 dealt with diffusion in glycol- and glycerol-water solutions. In these low molecular weight viscous systems, diffusion is largely determined by viscosity. The present paper deals with self-diffusion of a small ion in a highly viscous (neutral) polymer-water system. One would expect that in this case diffusion and viscosity would not be closely related. A number of workers have measured conductance and diffusion of small particles in polymer-water mixtures and in non-Newtonian fluids: Matsumoto5 and Edelson and Fuoss' have measured the conductance of salts in polyvinyl alcohol (PVA)-water systems and found that the conductance is not decreased by the polymer to nearly the degree to which the polymer increases viscosity. Hoshino and Sato7showed that the diffusion of small molecules in polymer solutions was much less sensitive to the solution viscosity than expected from similar studies on low molecule weight organic-water solutions. Nishijima and Oster,* Biancheria and Ke eles: Astarita," and Clough, Read, Metzner, and BehnlEi have also found that the diffusion of small particles or molecules in polymer solutions is much larger than could reasonably be expected from bulk viscosity considerations.
Although considerable work has been carried out on the conductance and gradient diffusion of small molecules and particles in polymer solutions, apparently little work has been devoted to the measurement of self-diffusion coefficients of small ions in high molecular weight polymerwater solutions over a wide composition and viscosity range. This study utilizes the radiometric porous frit method, which is a rapid and versatile method for measuring self-diffusion coefficients, D, to determine the effect of polymer (polyethylene glycol, PEG) concentration on D of Na' ion in solutions. Measurements were carried to polymer concentrations of 48 vol 9% and to relative viscosities (compared to 0.1 m NaC1) of ca. 6100.
Experimental Section Method. The radiometric porous frit method" was used for measuring self-diffusion coefficients. In this method the rate of removal ("decay") of tracer from an equilibrated and ~alibrated'~ frit is measured as the same solution, not containing tracer, is pumped past it. The diffusion coefficients are computed from the exponential portions of the decay rates (corrected for background) obtained in a plateau region where the rate is essentially independent of flow velocity past the frit. For polymer concentrations of 48.2,22.6, and 12.6%, the half-time, T, of tracer removal was obtained over a wide range of flow rates and the plateau region established by The Journal of Physical Chemistry, Vol. 8 I, No. 7, 1977
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Kraus et al.
TABLE I: Self-Diffusion Coefficients of Na+ Obtained with Porcelain and Gold Frits at 25 C
TABLE 11: Self-Diffusion Coefficients ( D ) of Na' in NaCl ( m = 0.1)-Polyethylene Glycol-Water Mixtures at 25 "C
O
Material Porcelain Gold
Frit thickness, cm 0.047 0.066
r
,
~
(for 1 void M volume NaCl) 58 37.2 45 28.7 %
105~~,, cm2 s-l (in 22.6% PEG)
%
105~, cm2 s'' 1.28 0.98 0.90 0.85 0.59 0.53 0.39 0.147
PEG 0.0 7.0 10.8 12.6 21.5 22.6 31.1 48.2
0.526 0.529
plotting T against flow rate. In the remaining cases at least two measurements a t different flow rates in the plateau region were carried out; results were considered representative of the diffusional half-times when the decay rates agreed within ca. f2%. All measurements were carried out at 25 f 0.1 "C. Materials. Two porous frit materials were used porcelain slabs (Selas) with nominal pore diameters ca. 0.5 and 3.0 ym, and gold compacts prepared from gold powder " O O of 1, such as in our case where (a,- a d ) 31 20, Walden’s rule is not obeyed and the diffusion coefficient is strongly dependent on viscosity. For describing conductivities of suspensions, Fricke” computed values of a d for prolate and oblate ellipsoids of revolution; a similar computation for self-diffusion coefficients of small ions in the presence of macromolecules was carried out by Wang.” The coefficients are numerically equal for these systems. While linear equations of the type of eq 2 and the more elaborate equation of Fricke apply principally to dilute suspensions, equations have been developed for conductance in heterogeneous systems with very much higher volume fractions of the dispersed phase by Bruggeman’l and more recently by Meredith.17b These equations when evaluated at zero conductance of the dispersed phase imply that the relative conductivity (and presumably also the relative diffusion coefficient) varies with the volume fraction of the continuous phase raised to an appropriate power. We shall consider eq 23 of ref 17b which for our case may be written as
(1- $) = f ,
=
K,“
= (D/Do)”
(6)
or
1% D/Do = U / a )1% f v (7) where K , is the conductance ratio defined by Meredith and Tobias (MT). Equation 7 is formally the same as our empirical 1. The (form-sensitive) slope a = 1/23 is given by a = (1+ /3 + y), where /3 and y are numerical coefficients, defined and tabulated by MT, which are obtained from integrals whose values depend on the axial ratios of the ellipsoids of revolution which are models for the dispersed phase. Using their values of /3 and y and our observed value of the slope S = 3.3, one concludes that the polymer solutions of Figure 2 behave from the point of self-diffusionof small ions as assemblies of oblate ellipsoids of revolution with axial ratios somewhat smaller than 0.1. References and Notes (1) Research Jointly sponsored by the Office of Saline Water, U.S. Department of the Interior, and the US. Atomic Energy Commission under contract with the Union Carbide Corporation. (2) Previous paper in series: W. H. Baldwin, R. J. Raridon, and K. A. Kraus, J. Phys. Chem., 73,3417 (1969). (3) (a) Present address: EBASCO, New York, N.Y. (b) Resent address: Union CarbMe Corp., South Charleston, W.Va. (c) Visiting scientlst from Weizmann Institute of Science, Israel. Present address: Israel Desalination Engineering, Tel-Aviv, Israel. (4) A. E. Marcinkowsky,H. 0. Phillips, and K. A. Kraus, J. Phys. Chem,
72, 1201 (1988). (5) T. Matsumoto, Koleunshi Kagaku, 13,86 (1956). (6)E. Edelson and R. M. Fuoss, J. Am. Chem. SOC.,72,306 (1950). (7) S. Hoshino and K. Sato, Kagaku Kogaku, 31, 961 (1967).
(8)Y. Nishijima and G. Oster, J. Po/ym. Sci., 19, 337 (1956). (9) A. Bancheria and G. Kegeles, J. Am. Chem. Soc., 79,5908(1957). (IO)G. Astarita. Ind €ng. Chem, Fundam, 4,236 (1965). (11)S.B. Clough, H. E. Read, A. B. Metzner, and V. C. Behn, AIChEJ., 8, 347 (1962). (12) A. E. Marcinkowsky, F. Nelson, and K. A. Kraus, J. Phys. Chem., 69, 303 (1965). (13)A. E. Marcinkowsky,H. 0. Phillips, and K. A. Kraus, J. Phys. Chem, 89, 3968 (1965). (14)F. E. Bailey, Jr., and J. V. Koleske, “Surfactant Science Series”, Vol. I, “Nonionic Surfactants”, M. J. Schick, Ed., Marcel Dekker, The Journal of Physical Chemistry, Vol 81, No. 7. 1977
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New York, N.Y., 1967, Chapter 23, p 794. (15) We thank Mr. John Csurny for making these viscosity and density measurements. (16) R. H. Stokes and I.A. Weeks, Aust. J. Chem., 17, 304 (1964). (17) See, for example, (a) R. H. Stokes and R. Mills, “Viscosity of Electrolytes and Related Properties”, Vol. 3, Topic 18 of ‘The International Encyclopedia of Physical Chemistry and Chemical
(18) (19) (20) (21)
physics”, Pergamon Press, New York, N.Y., 1965. (b)R. E. Meredkh and C. W. Tobias, “Advances in Electrochemistryand Electrochemical Engineering”, Vol. 2, Interscience, New York, N.Y., 1962, p 15. R. Simha, J. Phys. Chem., 44, 25 (1940). H. Fricke, Phy. Rev., 24, 575 (1924). J. H. Wang, J Am. Chem. Soa, 76, 4755 (1954). D. A. G. Bruggeman, Ann. Phys., 24, 636 (1935).
Properties of Organic-Water Mixtures. 13. Self-Diffusion Coefficients of Na’ in Glycerol Triacetate-Water Mixtures’i2 Harold 0. Phlllip~,~ Arthur J. Shor, Arthur E. Marcinkow~ky,~ and Kurt A. Kraus” Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, pnnessee (Received November 9. 1976) Publication costs assisted by the U.S. Energy Research and Development Administration
Self-diffusion coefficients,D, of Na” in water solutions of glycerol triacetate (GTA) were obtained at 25 O C as a function of water fraction, f,,and sodium perchlorate concentration. The latter was used to produce miscibility of water and GTA over the composition range studied. At constant NaC104concentration,D decreases rapidly with water content, qualitatively as expected from the viscosity of the solutions. A plot of log D vs. log f,is essentially linear, with a slope of 1.5. The diffusion coefficient-viscosity products are not quite constant but have a shallow maximum near f,= 0.5. A t constant organic volume fraction of 0.97, an increase in NaC104 concentration causes a large increase in the viscosity of the solutions and a somewhat smaller increase in diffusion coefficients.
Our earlier thermodynamic studies of glycerol triacetate (GTAI-water mixtures5 were carried out because we believe that this system, as well as similar ones, are reasonable models for the thermodynamic (equilibrium) properties of cellulose acetate membranes. While one would not expect a water-organic mixture containing a low molecular weight organic compound to be a good kinetic model for a membrane, it seemed nevertheless of interest to examine the diffusional properties of the GTA-water system and, perhaps, even to establish how large the difference between it and a membrane system is. GTA and water are not miscible in all proportions. This immiscibility makes it impossible to examine the diffusion properties over a broad composition range. Since GTA and water can be made miscible in all proportions through addition of modest quantities of certain salts: we elected to make most of our measurements in GTA-water mixtures containing 1.4 M of NaC104 (moles per liter of the GTA-H20 solvent). Since sodium perchlorate has a significant effect on the viscosity of these systems, we have also carried out some measurements as a function of NaC104concentration in GTA solutions of very low water content.
Experimental Section Method. The radiometric porous frit method which was used for measuring the self-diffusioncoefficients has been previously described.’ Briefly, the method consists of saturating a porous frit with the solution of interest containing a radioactive isotope of the ion of interest and measuring the rate of removal of the radioisotope as a solution of identical composition (not containing the tracer) is pumped past it. The diffusion coefficients can then be calculated from the diffusional decay half-times obtained in a flow regime where the measured half-times of removal are essentially independent of flow rates past the frit. Corrections for radioactive decay are made when necessary. The Journal of Physlcal Chemistry, Vol. 81, No. 7, 1977
TABLE I: Self-Diffusion Coefficients of Na’ in Glycerol Triacetate-Water-NaC04 Mixtures at 25 C (1.4M NaC0,) Volume lo”, fraction H’O (f”) shob cm’ls DslD,s, 0.934a 0.844 0.721 0.469 0.291 0.148 0.045
aNoGTA.
1.00 1.61 2.38 4.94 10.3 25.3 111.6
1.26 1.03 0.756 0.415 0.196 0.074 0.016
1.00 1.32 1.43 1.63
1.60 1.49 1.42
b q = 0.952 CPfor 1.4 M NaClO,
solution.
Porous gold frits with about 45% void volume were used and calibrated as described earlier.’,’ In separate experiments, it was shown that the gold frit did not adsorb sodium ions significantly from the GTA-water mixtures. The temperature of the measurements was 25 i 0.1 “C, except for the more viscous solutions where variations were f0.2 “C. Materials. The tracer 24Na(TI,, = 15.05 h) was obtained from the Isotopes Division of ORNL and used without further purification since examination of the y-energy spectra showed no detectable impurities. Use of the tracer was discontinued after several half-lives as a precaution against significant relative buildup of possible long-lived contaminants. The solutions were prepared from reagent grade NaC104 and Eastman Kodak glycerol triacetate. Each solution was checked for water content by Karl Fischer titration. Viscosities were measured by standard techniques (Cannon-Ubbelohde viscometer). Results and Discussion The self-diffusion coefficients of Na” were measured in GTA-H20 solutions as a function of solution composition.
