2111
MEDIUM EFFECTS IN NUCLEAR MAGNETIC RESONANCE respectively, whereas for silver nitrate it is 2.85 cal/gion deg,8and for the solid AgI transition at 147” to the high-conducting form, the A S is 3.48 cal/mol deg.lJ (It is assumed that in a-AgI the Ag+ ions also resemble those in the molten state.) Taking an entropy of fusion per g-ion of Ag+ between 2 and 3 cal/deg, we find an entropy contribution for R/IAg41aof 8-12 cal/mol deg, in good agreement with the measured values. Thus the silver ions in the conducting compounds are highly
disordered and can be considered to behave as if they were in the fluid or molten state. Achmowledgments. The authors wish to thank Dr. H. Wiedersich of the Science Center of North American Rockwell Corp. for his aid in calculating the configurational entropy contribution of the silver ions and Mr. L. Hermo for preparation of the materials used in this study.
Medium Effects in Nuclear Magnetic Resonance. V.
Liquids Consisting of
Nonpolar, Magnetically Isotropic Molecules’ by F. H. A. Rummens,2 W. T. Rapes,$ and H. J. Bernstein Division of Pure Chemistry, National Research Council, Ottawa, Canada (Received Noaember 6, 1967)
The binary collision gas model for interpreting the pressure dependence of chemical shifts in gases has been extended to liquids by using the appropriate liquid density and an empirical factor. To account for the different medium shifts of the peripheral CHa groups and inner CH2 groups of Si(CHzCHa)4in various solvents, it is necessary to introduce a site-factor correction which recognizes that the probe nuclei are not at the center of the molecule under investigation. It is possible then to estimate almost quantitatively the medium shift and its temperature dependence of nonpolar solutes in magnetically isotropic solvents. iinother model which considers only the cage of nearest neighbors has also been investigated. Some comments have been made about the effect of formally including a repulsion term in the intermolecular shielding.
1. Introduction The medium shift in nonpolar, magnetically isotropic liquids urn (Le., the chemical shift in the liquid state minus that in the gas phase at zero pressure) is assumed to consist of two parts4 urn = ub
+
uw
(1)
where Q b is the classical magnetic susceptibility effect, which for cylindrical sample tubes is equal to6
where xv and XM are the volume and molecular magnetic susceptibility, respectively; M is the molecular weight; and p is the density. The van der Waals contribution uw is the only other term present in inert liquids of magnetically isotropic nonpolar molecules. Calculation of this uw term has met with considerable difficulties. Bothner-By6 was the first to recognize the dispersion forces as the probable cause for these “excess shifts.” His estimates lead to the correct sign and nearly the
right order of magnitude for the downfield Bothner-By’s model result’sin
uWshifts.
(3)
where B is a bond parameter (Marshall and Pople’ calculated B = 0.74 X 10-l8 esu for the hydrogen atom) ; a2and I2 are the polarizability and ionization potential of the perturbing solvent molecule, while r is the intermolecular distance between the centers of solute and solvent molecules. Howard, Linder, and Emerson8 used a “continuous(1) National Research Council Communication No. 10088. (2) National Research Council Guest Scientist, 1963-1964; National Research Council Postdoctoral Fellow, 1964-1 965. (3) NRC Postdoctoral Fellow, 1969-1961. (4) A. D. Buckingham, T. Schaefer, and W. G. Schneider, J . Chem. Phys., 32, 1227 (1960). (5) W. C. Dickinson, Phys. Rev., 81, 717 (1951); C. Lussan, J . Chem. Phys., 61, 462 (1964). (6) A. A. Bothner-By, J . Mol. Spectrosc., 5, 52 (1960). (7) T. W. Marshall and J. A. Pople, Mol. Phys., 1, 199 (1958). (8) B. B. Howard, B. Linder, and M. T. Emerson, J . Chem. Phys., 36, 485 (1962).
Volume 78, Number 6 June 1968
F. H. A. RUMMENS, W. T. RAYNES,AND H. J. BERNSTEIN
2112 dielectric” model previously described by Linderg and found
for an infinite dilute solution of solute 1 in solvent 2. Here n is the refractive index of the solvent, and a is the “cavity” radius of the solute molecule, where the hv’s are mean excitation energies. The same model has been applied by Lumbroso, Wu, and Dailey.lo Yet another model has been proposed by Bernstein and Raynes.ll The solvent effect is regarded as due to the “cage” of the nearest neighbor solvent molecules. Thus the value for uw is given by uw = Za,(pair), where 2 is the number of nearest neighbor solvent molecules in the cage and u,(pair) is the same as in ref 12: vix., rw(pair) = -3BazIz/r6. 2 is obtained by dividing the area of the spherical surface through the centers of the molecules in the first coordination layer, 4 ~ ( r l Y Z ) ~ , by the effective cross section of a 2 = r(rl solvent molecule, ( 2 ~ ~ )Therefore, ~. rz)2/r22,where rl and r2 are the radii of solute and solvent molecule. It is interesting to note that for neat liquids (rl = rz), 2 = 4 ~ close , to the theoretical 2 = 12 for close packing, while for rl .
+
+
+
Acknowledgment. F. H. A. R. is indebted to Niels Stensen Stichting for financial support during the period 1963-1964. We thank Dr. Schafer for sending us a set of blueprints of this probe design.
Volume 78, Number 6 June 1968
