COMMUNICATIONS TO THE EDITOR
1792
VOl. 64
The anchored fractions p found in the present experiments are considerably higher than the fraction of anchored segments postulated by the theory of Simha, Frisch and E i r i ~ h . A ~ later theoretical treatment4 for the case of appreciable adsorption energies shows much better agreement with our experimental results. The order of magnitude of the adsorption energy EO can be estimated roughly by analogy with corresponding monomeric substances, a t least for the case of un-ionized polymers near the electrocapillary maximum. The estimated eo per methacrylic acid residue is 4-5 kT and per lysine residue is about 8-10 kT. The effective range of the forces R under these conditions is narrow and the approximate solution of eq. 14 in reference 4 which gives ( p ) = const. X (1. - 0 ) a / R seems only of limited validity. Here CY is the probability of a successful contact between segment and surface, and 0 is the fraction of the surface covered. Close to the adsorption potentials, EO is of the order of kT. ( p ) , as postulated in reference 4 for this case, is 2 4 1 - 0) (1 eo/kT)/ (~.fZ)'/n. The p's found in our experiments under these conditions are considerably higher and they depend very little on the molecular weight.
labeled PbCG as tracer, the two ions experience identical environments during the experiment and the measurement should be ideal for comparing the coefficients of the two species. This fact, together with the generally improved accuracy, leads us to prefer the present results, which are presented in Table I.
POLYMEB DEPARTNENT
and
+
WEIZMANN INSTITUTE OF SCIENCE REHOVOTH, ISRAEL
I. R.
hIILLER
TABLE I THEDIFFUSION COEFFICIENTS OF PbeloAND C1" IN MOLTEN PbClp Temp., DI;b x io5 op x 105 OC.
cm.
510 518 533 546 556 566
8ec.-1
0.997i0.02 1.05 f0.004 1.12 f0.07 1.13 f O . O 1 1.26 f0.03 1.37 f0.02
cm.
seo.-1
1.80 i0.05 1.90 z k 0.03 1.92 f 0.07 2.09 f 0.07 2.26 f 0.03 2.34 f 0.03
It will be seen that a plot of log D us 1/T for these data does not give the apparent discontinuity found in the earlier work1 These data fit very well a relationship of the form D = A exp( - AH*/RT), with Dpb
= 7.73
x
eXp( -6777 k 643/RT)
DCI= 8.95 X IO-'exp(-6099
f 483/RT)
AH is the energy of activation for diffusion, which shows no significant difference for the two ions (3) R. Simha, 13. L. Frisch and E. R. Eirich, J. Phys. ChPm., 57, within experimental error. This corresponds to the 584 (1953). results reported for other system^.^ However, (4) H. L. Frisch, ibid., 69, 633 (1955). there is no immediately apparent correlation between the diffusion coefficient and either the ionic radius or the ionic weight, as has been reported SELF-DIFFUSION I N RilOLTEN PbC12 variously for other systems. As was the earlier Pir: experience, and as is usual in molten salts, neither We have had occasion recently to repeat an the Kernst-Einstein nor Stokes-Einstein relations earlier measurement of the self-diff usion coefficients hold for this system. We are, a t present, investiof Pb21*and Cl36 in molten PbCl,. The original gating the influence of a variety of factors on the paper' reported anomalous results for these quan- diffusion coefficient and this work will be published tities. The present results, although generally within the coming year. We gratefully acknowlsimilar, are more nearly what might be expected edge the continuing financial support given this for this system in the light of corresponding data work by the Robert A. Welch Foundation. for other systems. The experimental procedure GERALD PERKINS, JR. R. B. ESCUE employed in this work is described in detail in an NORTHTEXASSTATECOLLEGE TEXAS JANESF. LAMB earlier paper.* Since this procedure uses doubly DENTON, J . ~ ~ A Y NKIMBERLEY E RECEIVED JULY7, 1960
(11 G. Perkins. Jr., R. B. Escue, J. F. Lamb and T. H. Tidwell, THISJOURNAL,64,495 (1960). (2) G. Perkins, Jr., R. B. Escue, J. F. Lamb. T . H. Tidwell and J. W. Wimberley. T H I S JOURNAL, to be published.
RECEIVED AUQUST 26, 1960 (3) A. S. Daorkin, R. B. Escue and E. R . VanArtsdalen, JOURVAI.,64, 872 (19ti3.
THIS
