NOTES
702
dK/dr is positive. As the transition is made from a linear polymer to a compact spherical molecule, a drops to zero and the K constant rises to 2 3 / p where p is the density of the compact molecule and the intrinsic viscosity is expressed in units of g./ cc. These values of a and K for compact spherical molecules follow from the hydrodynamic theory of solution viscosity of Einstein.15 Thus, on the basis of Price, Nartin and Bianchi’s experimental results and of the Einstein theory, it would appear that dK,’dr is positive and that the A of eq. 15 will always be positive in contradiction to the conclusions of Saito4 and Inokuti.j6 It should be pointed out, however, that this conclusion is academic aiid without practical importance inasmuch as dn, dr is negative; i.e., it appears to be impossible to have K change without a also changing. Furthermore, in many vinyl type polymers, b is significantly greater than 2 initially so that the term ao/bo (db/dr)!,s, of eq. 12 must be negative and far from negligible. For illustrative calculations let us consider data of Shultz, Roth and Rathmanng and of Kilbl on polymers assumed initially to have a random molecular weight distribution. Kilb measured the intrinsic viscosity of polydimethylsiloxane; from his data a rough estimate of A equal to 29 X g.,/e.v. can be made. From rg equal to 10.3 X 1019 e.v./g. and a. equal to 0.79, ao/rg is 77 X 10-22g./e.v. By difference In M,,o*
dr
1 dK + KO = -58 dr
X
g./e.v.
From the data of Price, Martin and Bianchi13 quoted above, (l/Ko)(dK/dr) appears to be about one tenth the magnitude of In M,vo(da/dr); neglecting it, we can estimate Aa to be about -0.04 t o the gel point. X similar calculation from the data of Shultz, Roth and Rathmanng on polystyrene yielded an estimated Aa of -0.03, the same order of magnitude as the result of Iiilb. In both cases these are estimates of the total change in a up to the gel point. Thus, the change in intrinsic viscosity beyond that due to the increase in molecular weight on irradiation up to the gel point can be explained on the basis of a decrease in a of about 0.03 to 0.04 unit. We conclude that this method of analyzing the intrinsic viscosity data in the cabe of polymers ultimately undergoing gelation on irradiation and possessing initially a random molecular weight distribution can yield a first approximation of the extent to which the 1-iscosity exponent a should change with the irradiation. Exact estinintrs would require a knodedge of dK’dr and, in general, dbjdr. (15) 4. Einstein Ann. P h y s z k , (41 19, 288 (190b), 3 4 , 781 (1911).
1-01. 65
Acknowledgments.-The work of this note stems from a project sponsored by the Air Research and Development Command, U.S.A.F. Grateful acknowledgment is expressed to R. IT.Kilb and 11. Inokuti for helpful comments.
ERRATUM TO THE PAPER O S THE KINETICS OF ETTAPORAITIOS1 BY 8.S.PENAER Diu of Engineering, Cali/. Inst a/ Tech. Pasadena, Calaf. Receiaed January ID, 1961
Professor A I . Boudart of Princeton University has kindly called my attention t o an error in the derivation of the rate equation for the kinetics of evaporation from absolute reaction rate theory. He has pointed out that, if consistent estimates are made for the free volume in the equation for the partition function per molecule in the liquid. ab well as in the vapor pressure equation, then the Hertz-Knudsen equation is obtained n ith or without the assumption that the communal entropy has its full d u e R. Thus the free volume i f in the expression for the partition function = ( 2 am
. W 3 ’ 2
h3
2’1
should not be z’f but2 rather ezf when the communal entropy is R and the usual expression is used for the vapor pressure, z zz., p
h 2’
= - exp( 61
- I€€.JRT)
Introduction of the specified changes makes it unnecessary to assume that the fundamental equilibrium assumption of absolute reaction rate theory must be abandoned in order to obtain a theoretical relation that is in accord with the experimentally verified Hertz-Kiiudsen equation. The result obtained from u straightforit ard application of absolute reaction rate theory, using a model in which the actirated voniplex moves freely a t the surface, is identical svith the nonequilibrium theory of hlortenseii and Eyring. Professor Boudart qtates in a private communication that it is gratifying to note that all difficulties have been removed froin a theory possessing “the beautiful simplicity of absolute rate theory n ith a transmisiioii coeffihcicnt equ:il to unity and the usual cquilihriuni asbumptioil.” (1) 6 8 Penner, J P h / s Chem 56, 475-479 (19.52) (2) See, for example IC. F.Herzfeld and T -4 Lito\it7, i b s o r j i t i u n a n d Dispeision of UltrrLaoniL Wales ” i c d d t i i ~ i c Press, Inc Yen York, N. Y , 1959 p . 378 (3) E 31 l l o i t c r sen rLn I I1 L511ng. J f’iiya Cherri , 64, 84b (1900).
