The Journal of Physical Chemistry, Vol. 82, No. 13, 1978
Permeation and Sorption in Laminated Medium
stitution of eq 7 and such an excited state into eq 9 gives c2 - acS
AgL = -2h(E,p - E , ) where S represents the overlap integral between the qbM(np,) and qbA (5s) orbitals. Using the values of the coefficient a an$ Eo determined earlier in the calculation of the isotropic coupling constant to Ag, letting E,, = -EIp AEs+p where EIPand AE,,, are the ionization potential and the s p transition energy of the atom M, respectively, and assuming a reasonable value for the overlap integral S, the magnitude of the coefficient c may be assessed from the observed &L. For S = 0.2 the magnitudes of c2 thus estimated were in the range of 0.10 f 0.02 for AgM of group 2A, and 0.04 f 0.02 for AgM of group 2B. In view of the approximations employed the values of c2 assessed from the g tensors are regarded as being in reasonable agreement with those evaluated from the hyperfine coupling tensors. The present study amply demonstrated the feasibility of generating heteronuclear polyatomic molecules by
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co-condensation of atomic beams in rare gas matrices. The results obtained strongly warrant extension of the effort to include other metals, and examination of the intermetallic molecules thus generated by other spectroscopic methods.
References and Notes (1) F. A. Cotton, Acc. Chem. Res., 2, 240 (1969). (2) K. A. Gingerich, J . Cryst. Growth, 9, 31 (1971). (3) W. A. Cooper, G. A. Clarke, and C. R. Hare, J . Phys. Chem., 76, 2268 (1972). (4) E. P. Kundig, M. Moskovits, and G. A. Ozin, Angew. Chem., Int. Edit. fngl., 14, 292 (1975). (5) Preliminary result obtained for AgZn, AgCd, and AgHg had been communicated earlier. P. H. Kasai and D. McLeod, Jr., J . Phys. Chem., 79, 2324 (1975). (6) P. H. Kasai, E. B. Whipple, and W. Weltner, Jr., J . Chem. Phys., 44, 2581 (1966). (7) P. H. Kasai and D.McLeod, Jr., J . Chem. Phys., 55, 1566 (1971). (8) See, for example, M. W. P. Strandberg, “Microwave Spectroscopy”, Methuen, London, 1954, p 11. (9) M. Wolfsberg and L. Helmholz, J . Chem. Phys., 20, 837 (1952). (10) See, for example, H. Kopfermann, “Nuclear Moments”, Academic Press, New York, N.Y., 1958, p 123-138. (11) M. H. L. Pryce, Proc. Phys. SOC.(London) Ser. A , 63, 25 (1950). (12) C. E. Moore, Natl. Bur. Stand. Circ., No. 467, 1 (1949), 2 (1952), 3 (1958)
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Permeation and Sorption in the Linear Laminated Medium H. t. Frlsch Department of Chemistry and Center for Bioioglcal Macromolecules, State University of New York at Albany, Albany, New York 12222 (Received January 13, 1978) Publication costs assisted by the National Science Foundation
In this paper we interrelate the results of permeation and sorption measurements on membranes of thickness 1 composed of a linear, laminated medium. In particular, we demonstrate the equality of flow in a “desorption” permeation at the high activity membrane surface ( x = 0) to the “absorption” permeation at the low activity membrane surface ( x = I). In the concluding section we present initial and long time estimates for the penetrant activity in these diffusion problems based on WKB asymptotics. 1. Introduction In recent years a large number of papers have appeared1-l1 dealing with diffusion-controlled permeation and sorption of vapors and simple gases in microporous powder compacts or similar inhomogeneous materials. The simplest situation occurs if there is no time or concentration dependence of the basic coefficients describing this flow: These coefficients are all spatially dependent and are the penetrant partition coefficient h (in many references this is simply taken to be the solubility coefficient S ) ,the diffusion coefficient D , and the local permeability coefficient P = Dk. In most cases investigators have treated the spatial dependence of k, D , and P as arising solely from a dependence on the distance in the direction of flow, x
k = k(x)
D
= D(x)
P = Dk = P(x)
(1.1)
Thus the material is treated as a linear, laminated medium.1° We will also in this paper restrict ourselves to this limiting, idealized situation, recognizing though a t the outset that this may be more a matter of mathematical expediency than a fully realistic physical description. The purpose of this paper is to interrelate the basic experiments which are ubiquitously performed in studying diffusive flow through such membranes. These are4z7 (1) “absorption” permeation (subscript a) for which the penetrant activity will be denoted by a ( x , t ) = a , ( 2 ) “desorption” permeation (superscript d) for which the penetrant activity will be denoted by b(x,t) = b, and (3) 0022-3654/78/2082-1559$01 .OO/O
penetrant desorption (say via a sorption balance or similar experiment) for which the activity will be taken to be A(x,t)= A. In all of these cases the penetrant activity is the local penetrant concentration divided by the partition coefficient, k ( x ) . Mathematically these activities satisfy the following boundary value problems: aa a k-=inO
