I’RU:)HOXI~II~: Bull. S O P . c h i i n . [ 2 ] 17, 253 (18721. Rose: Pogg. .41111. 112, 164 (1861). \vErsl.:n: J . Phj.s. Chcm. 26, 654 (1923). WEISER .4xn L ~ I L I . K . \ ~J-.: Phys. Chem. 40, 1075 (1936). J~:EISER. I S D ~IILLIG.IS: J . Phys. Chem. 44, lOSl (1940).
31ELTISG -AS11 ET7APOR;1TIOS -4s RAYYEPROCESSES S. S. PESSER .JPt
Z’ropulEioia
Laborniorg, California Institute of Technology, Pasadena, Calijornia
Received January 26, 1948 IXTR ODUCTI 05
Throries of melting ( 1 , (i,14, 17) and evaporation (7, 10, 13j for a number of models of t,he liquid ant1 solid states have been revien-ed by Lennard-Jones 112) ‘The kinetics of fusion has been discussed by Lindemnnn (13) and the rat.es of evaporation 1,- Frenktl 1.3). Hon-ever, neither melting nor el-aporation appears t o have been considered from the point of view of Eyring’s rate theory ( 2 , 5 ) . Tt is the purpose of this paper to show that Eyring’s rate theory leads to useful iywilts for the rates of fusion and evaporation if reasonable assumptions are made conctrning the nature of the activated comples formed during fusion arid evaporation. The results obtained for the rates of evaporation are of the same order of niagnitutle ;is thosc predicted from the Knudsen equation (8, 11). I
TEIE KISETICS O F FCSION
Aiccmdingt o the itati-tical theory of reaction rates ( 2 , :)> the rate of fuqion is
\rliere F* is the partition function of the activated complex formed during melting, F is the partition function of the original solid, EY is the activation energy for fusion per molecule, 1,. is the gas constant per molecule, T represents the absolute temperature, and h is Planck’s constant. If the solid consists of Einstein oscillators with vibration frequency Y , then, except for the factor corresponding t o the internal partition function, since near the melting point. If the activated complex also consists of Einstein oscillators, then F* = (1 - e--hv*/kr)--? - ( / ; y l / / z y * ) ? (3) I
*.
950
S. PESSER
where v* is the vibration frequency of the Einstein solitl in the activat’ed stat(:. In view of Lindemann’s work (15) it is not unreasonable to expect that
(~4)
v* zk v
With this assumption the precrtling expressions lend t o the lesiilt j = vc7C/’J[
(,j)
If t’lie solid at the melting point may he approximated by particles moving freely wit,hin a potent’ial box, then F* and F can he expressed in ternis of liquid partition fiinctions 112). In this case and where 1‘1 represents the free volume per molecule and Equations 1, 0. and 7 lead to the relation: I =
>TI
is the mass per niolecule. (81
@71‘’(/
