Determination of self diffusion coefficients using the radial distribution function
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2 exp ( - a j ) ]
[1]
where s r e p r e s e n t s the bond d i s s o c i a t i o n e n e r g y , j is the fluctuation d i s t a n c e and a is r e l a t e d to the c u r v a t u r e of the p o t e n t i a l v s the fluctuation d i s t a n c e c u r v e . F r o m q u a s i - c h e m i c a l t h e o r y ED was e s t i m a t e d as the e n e r g y n e c e s s a r y to b r e a k o n e - h a l f of the n e a r e s t n e i g h b o r bonds and is e x p r e s s e d a s : 2a//v s
-
ZN ~
[2]
where Z is the n u m b e r of n e a r e s t n e i g h b o r s , ~ H v is the heat of v a p o r i z a t i o n , and N o is A v o g a d r o ' s n u m b e r . Swalin a s s u m e d that the fluctuation d i s t a n c e , j , r e s u l t ed f r o m the s t r e t c h i n g of four of the eight n e a r e s t n e i g h b o r bonds by w r i t i n g the fluctuation e n e r g y in t e r m s of the M o r s e function a s E(j) = 4e. In s i m i l a r m a n n e r Hines, W a l l s , and A r n o l d 2 a s s u m e d that the fluctuation e n e r g y should be E(j) = (Z/2)E but r e d e f i n e d the n u m b e r of diffusion paths. The m e a n fluctuation d i s t a n c e c a l c u l a t e d by Swalin is: _2
J
3 kT
= 4g
[3]
and the value c a l c u l a t e d by Hines, W a l l s , and A r n o l d is: -2 J
-
6 kT ZK
[4]
where k is the B o l t z m a n constant and K is the W a s e r P a u l i n g 4 force c o n s t a n t . Reynik 3 p r e s e n t e d a fluctuation model a l o n g the s a m e ANTHONY L. HINES is Associate Professor, Department of Chemical Engineering,Colorado School of Mines, Golden, CO 8040 I. HUGH A. WALLSis Professor, Department of MechanicalEngineering, University of Texas at Austin, Austin, TX 78712. Manuscript submitted July 19, 1978. METALLURGICAL TRANSACTIONS A
l i n e s as the one p r o p o s e d by Swalin except that he a s s u m e d the fluctuation e n e r g y could be r e p r e s e n t e d by a q u a d r a t i c equation E ( } ) = K j 2 where K is the force c o n s t a n t . In his work, the fluctuation d i s t a n c e was shown to be the d i s t a n c e f r o m where E(j) is a m i n i m u m to where the e n e r g y curve c r o s s e s the a x i s , E(j) = 0. Calculated fluctuation d i s t a n c e s a r e p r e s e n t e d in the work of R e y n i k for the a s s u m e d q u a d r a t i c r e p r e s e n t a tion of the fluctuation e n e r g y . D e s p i t e the f u n d a m e n t a l a p p r o a c h of these m o d e l s , diffusion coefficients a r e not p r e d i c t e d with a g r e a t deal of a c c u r a c y . T h i s p a p e r r e p r e s e n t s a n a t t e m p t to extend the fluctuation m o d e l s a s applied to the diffusive p r o c e s s by u s i n g fluctuation d i s t a n c e s obtained f r o m RDF c u r v e s . II. FORMULATION OF DIFFUSION MODEL A new diffusion model is d e r i v e d by r e l a t i n g the diffusion p r o c e s s to the s t r u c t u r e of liquids as des c r i b e d by the r a d i a l d i s t r i b u t i o n function. T h i s is a c c o m p l i s h e d by s t a r t i n g with the E i n s t
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