J. PhyS. Chem. 1981, 85, 2843-2851
-
graphs of Alms et al., will give a vanishing intercept for D-I as q/T 0. The viscosity dependence of the motion of small ions and intermediate-size molecules has been studied by measuring both their diffusion coefficients and their limiting conductances A,, at zero concentration. Berner and Kivelson4used paramagnetic enhancement of nuclear spin relaxation to determine the translational diffusion coefficient of di-tert-butyl nitroxide in ethylene glycol, water, and other solvents, confirming the Stokes-Einstein equation (eq 1)to within a factor of 4 as q varied over 4 orders of magnitude. For simple ions and small molecules moving in a solvent whose molecules are bigger than those of the solute, at high viscosity a relation for the drag coefficient f of the form f a qa for 0.63 < a < 0.70 has long been s~ggested.'~This form is found both for A,, of simple electrolytes in sucrose16and mannitol1' solutions and for the diffusion coefficient of n-hexane and naphthalene in compound oils with q > 10 c P . ~We have studied the motion of macromolecules, finding for q > 10 cP that a = 1.0 to within experimental error. The Stokes-Einstein equation (eq 1) is properly obtained for a single Brownian particle, not for a solution in which interactions between Brownian particles are significant. Conventional theories18indicate that corrections to eq 1 take the form D(c) = D ( l + aC#J), where for hard spheres a is a constant of order 1 and C#J is the volume fraction of the solute. For the polystyrene suspensions, (15)W.Heber Green, J. Chem. Soc,, 98,2023 (1910). (16)Jean M. Stokes and R. H. Stokes, J. Phys. Chem., 60,217(1956). (17)Jean M. Stokes and R. H. Stokes,J. Phys. Chem., 62,497(1958). (18)B. U.Felderhof, Physica A (Amsterdam),89,373 (1977);B. U. Felderhof,J. Phys. A , 11, 929 (1978).
2843
on which the bulk of our discussion rests, 9 = 4 X W ,so D for these systems should be indistinguishable from its infinite dilution limit. The concentration dependence of
D for polystyrene spheres in plain water solution has been examined experimentally; if multiple scattering is suppressed by means of homodyne coincidence techniques,l8 D is independent of concentration for 4 as large as 0.01.20 The diffusion coefficient of isoionic serum albumin in solutions of moderate ionic strength is only weakly dependent on concentration.21 While it is sometimes said that glycerol tends to stabilize protein conformations, there do not appear to be any data on conformational changes of serum albumin in concentrated glycerol. Such changes, if they exist, would obscure any interpretation of the results presented here on BSA diffusion. Our discussion therefore emphasizes measurements made on the polystyrene-sphere suspensions, since no polar, hydrogenbonding solvent seems likely to affect the size of the spheres. In conclusion, it seems unlikely that interactions between the macromolecular probe molecules have a significant effect on the results presented here. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. Additional support was provided by Grant Che-79-20389from the National Science Foundation. We thank Mr. Richard Finegold, Mr. Larry Chin, Miss Katie MacNamara. and Mr. Todd Werner for their technical assistance a t various steps in this research. (19)G. D. J. Phillies, J. Chern. Phys., 74, 260 (1981). (20)G.D. J. Phillies, Phys. Rev. A, in press. (21)G. D. J. Phillies, G. B. Benedek, and N. M. Mazer, J. Chern. Phys., 65,1883 (1976).
Small Ionic Clusters of LiC104 in Low Dielectric Constant Media from Conductivlty Data at 293 K M. Nlcolas" and R. Relch Laboratoire de Physique des Solhles. Universlt6 Paris-Sod, Centre d'Orsay, 9 1405 Orsay, France (Recelved: March 11, 1980; In Final Form: February 13, 1981)
The molar conductivity of LiC104,AM,is measured in various solvent systems, over a wide range of concentration (lov55 c 5 saturation) and dielectric constant (2.20 5 e 5 33). The influence of the solvent mixtures (POlar-nonpolar, protic-aprotic) on ion pair and triple ion formation is investigated. The KT variations are found to be linear functions of ( c - ~ ) ~for , the four studied systems, provided e R 3.00. The sharp rise of AM d c 5 1M) is attributed to small ionic cluster formation. For a given solvent system, all tangents to the log Awlog c curves converge to the same point, W. The model suggested by the authors leads to the conclusion that the maximum number, n,of LiC104-neutral pairs, bound to a free ion Li' or ClO, to give a cluster, is determined by the dielectric constant of the medium, for a given solvent system.
Introduction In the last few years, there has been renewed interest in the nature of ionic species present in low dielectric constant solvents. The use of various organic mixtures allows the effect of the dielectric constant on the solute behavior to be studied. In particular, for dilute solutions of salts in high dielectric constant solvents, ion-solvent interactions take place, which depend strongly on the 'Laboratoire associ6 au CNRS. 0022-3654/81/2085-2843$01.25/0
nature of the solvent: polar or nonpolar, protic or aprotic; the cations and/or the anions may be more or less solvated depending on the case. If the dielectric constant of the medium is sufficiently low, complex ions may be formed. New studies of cluster formation have recently been carried out, especially for very small charged1p2 or uncharged3t4 (1)T.P. Martin, J. Chem. Phys., 69,2036 (1978). (2)T.P. Martin, J. Chem. Phys., 72,3506 (1980). (3)J. W.Brady, J. D. Doll, and D. L. Thompson, J. Chem. Phys., 71, 2467 (1979).
@ 1981 American Chemical Society
2044
The Journal of Physical Chemistry, Vol. 85, No. 19, 1981
aggregates. The first experiments on the conductivity of electrolytes in very low dielectric constant media were Kraus, et al."' Since these papers, carried out by FUOSS, few extensive studies have been made on this topic. Our previous work6 on the conductance of LiC104 in methanol-tetrahydrofuran mixtures has shown triple ion formation for dielectric constant values of 6 5 e 5 12. We present here an ionic aggregation study of this salt over a wider range of conditions, namely: (i) a larger permittivity scale (2.20 < E < 33), (ii) different solvent systems (polar-polar but protic-aprotic, methanol-ethyl acetate; polar-nonpolar and protic-aprotic, methanol-dioxane; finally polar-nonpolar and aprotic-aprotic, ethyl acetate-dioxane); (iii) ionic cluster formation more complex than triple ions. All these systems show characteristic behavior, but also possess common properties as we shall see below.
Nicoias and Reich
3.15
3.05 3.10
285 3'00
2.85 2.90 1.39
138 137 1.36
Experimental Section Methanol was purified in a closed system in a flask containing magnesium turnings and iodine, then distilled, and used immediately after. The other solvents were very pure (E. Merck, Darmstadt, Germany); ethyl acetate and dioxane contained less than 0.01% water. Their specific conductances were very low (
