NOTES
July, 1958 the one used by Smyth and others.6 The X-12 KlystronGused by us as the source of microwave power had very little frequency drift over long time intervals (8 to 10 hours). The use of two slide screw tuners one to match the reflection from the dielectric window and the other to match the reflection from the crystal detector did insure a voltage standing wave ratio of 1.02 f 0.01 with the liquid cell empty. It was found advisable to use a mechanically driven plunger in conjunction with a sensitive linear d.c. recorder as this meant a great saving in time while at the same time providing an accuracy in the wave length measurements comparable to the hand driven micrometer plunger. The position of the plunger could be read to 0.0005”. The error in the determination of the loss factor ( E ” ) is about 2%. The temperature of the thermostatic liquid cell was co2trolled by suitable temperature regulators to within 0.5 , and the temperatures below room temperatures down to about -30” (the lowest used in our measurements) were obtained by circulating an appropriate mixture of antifreeze and water cooled by a hermetically sealed ’/* h.p. compressor.
Results and Discussion
889
perhaps be appropriate to mention that variable temperature curves are more difficult to interpret than variable frequency ones, especially if the change of relaxation time with temperature is small as in the case of the present investigation. Measurements with variable frequency have the advantage that the static permittivity of the polar constituents is not varied during a set of measurements at one concentration. Acknowledgments.-The author is grateful to the National Science Foundation for the award of a grant in support of the above investigation. The author also wishes to thank Dr. A. Schallamach for many helpful suggestions during the course of this investigation. Thanks are also due to Dr. D. H. Whiffen for valuable comments concerning the results. Part of the experimental work was done by Eugene A. Bradley.
Loss Factor-Temperature Curves of Solutions in n-Heptane of i. Nitrobenzene and Nitroethane and ii.-Nitroethane and o-nitrotoluene are shown in Fig. 1. In each mixture the concentrations of the individual dipolar components were adjusted to be the same and are given in mole fraction. As t,he results at these comparatively low concentrations did not seem to indicate any clear trend as regards the separation of the peaks with change in concentration it was thought desirable to study the mixtures at substantially higher concentrations of the dipolar solutes. As the solvent, n-heptane, would not retain the dipolar solutes a t lower temperatures at these higher concentrations, solvents of higher viscosity were used so as to bring the loss factor peaks to higher temperatures. A high viscosity solvent like Nujol was found unsuitable because the ,solubility in it was rather poor. The solvents used in these measurements were cyclohexane and ndodecane. Loss factor-temperature curves at higher concentrations using these solvents are shown in Fig. 2. As before in each mixture the concentrations of the individual dipolar constituents were adjusted t o be the same and are given in mole fraction. The measurements in both the low concentration range as well as the high concentration range were carried down to as low a temperature as possible before there is any visual separation of the mixture. It is rather surprising to note the distinctness of the two maxima in all the mixtures and particularly in the case of very similar nitrobenzene and onitrotoluene. The results thus seem to indicate that the mixtures chosen do not tend to one relaxation time, but that each polar liquid retains its own. From a comparison of the present curves with the corresponding curves for two component mixtures with only one polar component present it would be possible to determine how much the maximum is changed by the addition of the third component. The indication from the curves, however, is that such change as does occur is to be described as due t o change of solvent, rather than cooperative motion of the dipoles. In conclusion it would
SURFACE CONDUCTIVITY OF AN ANIONEXCHANGE RESIN BY NORMAN STREET University of Illinoia, Urbana, Illinois Received April B4.1968
Recently several reports of investigations on surface conductance have been published, one by Watillonl on glass capillaries and another by van Olphen2 on bentonite gels. Street* has reported measurements on the surface conductance of kaolinite suspensions, and O’Connor, Street and Buchanan4 on some few measurements made on various minerals. These latter were carried out on plug packings concurrently with streaming potential measurements. One advantage of using packed plugs for the determinations is that the hydraulic radius ( A I S ) can be measured simultaneously. Thus knowi.ng the flow rate of the electrolyte solution through the plug during the application of a known pressure drop, then, as shown by O’Connor, Street and Buchanan4 AIS = 0.00184(C&)’/:
where AJS
hydraulic radius (Le., ratio of, cross-sectional area available to flow, to wetted perimeter) C = measured cell constant of the plug 7 = viscosity of flowing fluid (poise) Q = rate of flow (cc. min.-l cm.-l Hg) =
Experimental The resin was Amberlite IR-4, a weak base anion-exchange resin which was purified6 by washing with water at 80’ for eight weeks, regenerated with 0.1N ammonia sohtion for four weeks, then washed free from alkali and finally air dried. The streaming potential and conductance measurements were made in a cell essentially similar to that described by Buchanan and Heyman8 except that a U bend with sealed-in electrodes was fitted to the outlet tube so tha! conductivity measurements could be made more readlly during the course of a run. Streaming potential and resistance measurements (1) A. Watillon, J . chim. phys., 6 4 , 130 (1957). (2) H. van Olphen, THISJOWRNAL, 61, 1276 (1957). (3) N. Street, Australian J . Chern., 9, 333 (1956). (4) D. J. O’Connor, N. Street and A. S. Buchanan, ibid., 7 , 245
(1954).
’
( 5 ) See for example the paper by W. M. Heaton, Jr., E. J. Hennelly and C. P. Smyth, J . A m . Chem. Soe., TO, 4093 (1948).
(61 Manufactured by the Varian Associatea, Palo Alto, California.
(5) I. J. O’Donnell, M.Sc. Thesis, University of Melbourne, 1948. (6) A. 8. Buckanan and E. Heyman, Proc. Roy. SOC.(London), A196, 150 (1948).
NOTES +5
I
-5t
5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Fig. 1.-Zeta-potential in millivolts (open circles), and surface conductivity in ohm-' (closed circles) against
PH. were made as described by Buchanan and Heyman. Electrolytes were HC1 and KOH, and AIS was calculated for each plug packing following measurements of C and &. The surface conductivity (ha) was calculated by ha = ( A / S ) K where K is the difference between the conductivit of the electrolyte solution when filling the pores of the pLg, and the bulk conductivity of the solution.
Results and Discussion Figure 1 shows both surface conductance (A,) and zeta-potential (calculated by the HelmholtzSmoluchowski equation) plotted against pH. Table I gives values of zeta and X. a t higher pH's. TABLE I PH 8.7 10.3 10.7
Zeta-potential (mv.)
-17.9 -22.8 -22.2
Surface conductivity (ohm -I),
x
109
2.35 2.74
2.67
Generally, AIS was of the order of 5-6 X The surface conductivity calculated from the zetapotentials is lower than the measured values, being of the order of 10-lo ohm-1 rather than ohm-'. On the other hand, the surface conductivity calculated from the exchange capacity (6.3 meq./g. of air-dried resin) is much greater than the measured value, being of the order of lo-' ohm-I. One can conclude that the Stern layer ions a t least, and probably also a swollen gel layer, contribute t o the surface conductance of this resin. Nevertheless, there is correspondence between measured zeta and A, in that the surface conductance shows a minimum a t approximately the isoelectric point. Rutgers and De Smet' also observed a minimum of surface conductance at the zero of zeta-potential when using thorium nitrate solutions on a glass surface. (7) A. J. Rutgers and M. De Smet, Nat. Bur. Standards (J.S.) Circ. No. 524, 263, 1953.
T H E LENNARD-JONES POTENTIAL FOR SPHERICAL MACROMOLECULES1 BY ANDREWG.DEROCCO~ The Harrison M . Randall Laboratory of Physics, University of Michigan, A n n Arbor, Michigan Received M a y 16, 1058
De Boers and Hamaker4 mem t o have been of the
responsible for the earliest ealealwtiQns
Vol. 62
intermolecular potential between spheres of uniform composition. More recently Atoji and Lipscomb,6 and Isihara and Koyamas have performed similar computations. The results of Atoji and Lipscomb depend on a series approximation valid for molecular distances fairly large in comparison t o molecular radii, while those of Isihara and Koyama appear to be valid a t all distances of approach. In this note we shall demonstrate that the original method of Hamaker may be employed t o obtain results equivalent t o those of Isihara and Koyama but having the feature of a notation more easily associated with recognizable molecular parameters. In general the forces between macromolecules may be of several kinds, and for spherical macromolecules having static charge distributions, the interaction energy a t values of pH well-removed from the isoionic points of the molecules may be described very nicely by a simple coulombic potential. Another related energy develops when a molecule has sites to which, for example, protons may be attached, and is determined by the excess of available sites over the average number of bound protons. Such a condition leads t o a great many configurations which differ only slightly in free energy, and the consequent mobility of the protons over the sites results in an induced polarization leading a t fairly long ranges t o a potential decreasing as R-2. This potential was described by Kirkwood and Shumaker' and shown by them t o play an important role in the interaction of proteins a t the isoionic points of the molecules, where, certainly, structure sensitive electrostatic forces play n serious role. In addition t o the energies mentioned above, a macromolecule also exhibits a considerably weaker kind of interaction, perhaps best described as a kind of Lennard-Jones potential. We mean by this, that part of the interaction energy for macromolecules which is analogous to the use of a Lennard-Jones (12:6) potential for, say, argon atoms. Clearly some kind of integration process is needed if we are t o go from the 12:6 potential to its corresponding form for a macromolecule and one such procedure is described below, but before passing over t o this consideration it should be emphasized that we are dealing with a strictly special case, uix., a spherical macromolecule for which any static or fluctuating charge distributions are completely ignored. We are dealing with weakly interacting macrospheres or a small part of the interaction for the usual case. Consider two macrospheres of radii R1 and Rz, having atomic distribution functions PI and p2 (taken as constants) and separated by an intermolecular distance R. We generalize the Hamaker formalism and write (1) Aided by a grant from the American Cancer Society. (2) Department of Chemistry, University of Michigan, Ann Arbor,
Michigan. (3) J. H. De Boer, Trans. Faraday Soc., 82, 10 (1936). (4) H. C. Hamaker, Physicu, 4, 1058 (1947). (5) M. Atoji and W. N. Lipscomb, J . Chem. Phys. 21, 1480 (1953). ( 6 ) A, Isihara and R. Koyama, J . Phys. Soc. Japan, 12, 32 (1957). (7) J. G. Kirkwood and J. B. Shumaker, Proc. Null. Acad. Sci., 3 8 , 863 (1952).
