It. L. CLELAND, J. K.
27%
have brcn calculated as shown in Table I. A benzene nionolayer on silica gel has been estiinatedii to have a thickness of about 4 .k., corresponding to A*/A, = 2.3. ‘l’hc quantitative catiiiiates of I),, DI2* provided by Fig. 5 are very rough in view of the crudcncss of the equivalent capillary model. the soniewhat arbitrary choice made for (cos e)*, *, the obvious diffcrenccs (Fig. 2 ) in DaPP for diffeient porous specimcns, and uncertainties in the quantity dclq/dcl*. The> conclusion that L>,/DIL* is less than one seeins justified, honevcr. A t A*/iZ, = 2 . 5 our estimate indicates that I ) , values a t nost concentrations are of the order of one-third to one-half the free diftusion coefficient. I n order to discuss the friction cocfficients of solution coinponcnts with the boundary, it is convenient to define a “niolccule” of the pore boundary as that amount of inatcrial occupying the avcragc niolecular volume in the solution, so that the “molar” concentration cg of boundary “molecules” is equal to c*. The fraction zo which such L‘nioleculw’’contribute to the nearest-neighbor shell of a moleculr in the nionolayer s would be estiinatcd at I/,$ for a close-packed lattice, as would the fractions zq and z * . We niay write R,o’ = IZ,,goco,where Rlo is a friction coefficicrit analogous to thc K,,in the interfacial region. We now substitute this definition of R,o into the fiist equation of (9) and solvc for ZJ3/llj2* with use of (18) and (19) and the approxiiiiatiori 7 : = V2*to obtain (h,/k,)/(dci’//dci*)
I)SlDls* =
h.
ks 1/12
=
z*
=
=
1/12
+
c ~ ~ c Z ~ / C ~ * C ~ *
+ cpzay1 +
Z’(C~’C*),
PlSY2
(21)
1/, = Rlgo/R12
The quantities h, and dcls/dcl* have been estimated in Table I froin solution adsorption datal3 a t 25’. The values of thc parameter k, given in Table I have bccii calculated a t various A * / A , from (21) and the data of Fig. 5 I t is interesting to not(. that the values of k , so calculated, except at pi(’ = 0 for niost A * / A , , arc relatively indrpcndcnt of composition. Thc decrease in I>rl/Illz* at high p20 does not lead to high values of k,. This decreasc is thus evidently ascribabit. to conccntratiori clffects rather than to resistance effects. ‘t‘h(k tcnii y12 in (21) should be concentrationindcpcndcnt, sin(.(. the ratio cq,’c* iiiay he taken as unity to a good approxiniation. IYith our prwious cstiiiiates of thr z factors we tlicn have 1/12 = 2 / j , 3y, = R,O/lZl* The expcrjmcntal \ d u m of y defined by y =
cpZsy1
+
BItISCK, AKD
R. K. SHAW
Table I : ICstirnation of Surface Diffusion Parameterso
0 . 0
0.78
0.25 0.50 0.75 O.!M 0.95
0.81 0.04 1.:30 1.91 2.46
0.64 0.64 0.64 0.9 1.6 2.3
2.2 1.8 1.9 2.2 2.0 1.9
&A. I/ a
4.1 2.5 2.3 3.1 2.7 2.5
7 . 6 39 3.1 4.0 2.5 2.9 3.9 5 . 1 3.3 4.3 3.0 3.6
7.6 4.8 4.0 1 . 3 1.9 2 . 5
3.5 3.3
Data are tiased on disk 4 a t 25”.
given in Table I were obtained from an average value of k, at all compositions, with the exception of the high values a t pio = 0. It is of interest in this connection that rough estimates of y1 and y2 can also be made from viscous flow data for the pure components. The estimates, bascd on a hydrodynaniic treatincant of a slipping film m ~ d e l which , ~ ~ ~resembles ~ in iiiany resperts thc model used in this work, are yl = 0.7 and y r = 0.8 when r l * / A S is taken to be 2.5. These estimatcis are subject to uncertainties similar to those in the present work. The values of the Rlocan thus be estiniatcd to bc from 2 to 10 times larger than R12, the friction coeficic3nt for the two liquid components. The integrand of the integral expressions for the molecular friction coefficientI5 is pi*oportional, among other things, to the gradient of intcrniolccular potential energy. We expect this gradient, equal in magnitude at a given point to the attractive force, to be greater a t a given distance of separation for an i, 0 interaction (z = 1, 2) of an i inolecule with a boundary (or 0) “niolecule” than for a n i, J interaction (i, j = 1, 2 ) , when the boundary is a material which adsorbs positively. Our result is thus in qualitative agreement with theory.
Discussion 15. HI.TCHINSON (Stanford 1-niversity, California). You mentioned, in the inforrnal disrussion of your experiments, ttlitt, diffusion expcrirnents of this type are well mired t,o study in midergr:tdii:it,c physicaal chernistry laboratory courses. Would you care t,o comment on the conditions under which the experiments m r ~ yhe c-wried out in a reasonable lengt>h o f tirnc i n such B course; r . g . , how Itrng should one wait to get “infinite time” values? ~
cPlS‘/i
The Journal of l’hysiral ChemistrU
=
h, -
YlZ
(2.3) B. 11. Smith and .J.
JI. Thorp. J . P h y s . Chem., 67, 2017 (1903)
It. I,. C I X ~ A X I )This . expcririit%rittias tieen used for 3 ye:irs i n tliis
good rtwilts following the inst,rricdioris of (;:trlantl (ref. I2 of the paper). Acicwrdiiig t o
dcpiirtiiic~ritwith
Shocmakor
:irid
\\‘oultl it riot lie druirtltile t.0 corisitier possible interchange effects :ind snrfiwe Iay(:rs? Cj. A. TI. I3loksnr:t, J . Colloid Sci., 12, 4 0 (1057). t i e t c ~ c i ~lirilk ii
