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Communications to the Editor TABLE I: Formation Constants of Heteroconjugates of l,l-Dihydroxy-2,2,2-trichloroethane with Some Inorganic Anions in Nitrobenzene at 37" Anion K, M-l c104-
M06019~PM0120403SiMo120404 pwizo403-
2.55 f 0.39 1.76 It 0 . 4 1 3.11 i 0 . 6 3 24.7 f 2 . 7 1.30 f 0.45
anions are of two types, terminal and bridging.l2 It seems likely that protonation or hydrogen bonding would take place a t the bridging oxygen atoms, since the terminal oxygens are strongly polarized toward the interior of the anion by x bonding to the metal atoms.13 The differences in stabilities of the molybdate complexes cannot simply be accounted for in terms of electrostatic (-4 us. -3) arguments, but also show influences of the central atom upon the surface charge density. The central atom has elsewhere been shown to affect reduction potentials and spectroscopic properties of 1:12 heteropoly anions.14 Finally we note the variation between the complexes of PM012O4o3- and PW120403-. We have pointed out elsewhere15 that, other things being equal, heteropoly molybdates are somewhat stronger Br4nsted bases than the corresponding heteropoly tungstates, and the present results are consistent with this.
Acknowledgments. The support of this research by AFOSR, through Grant No. AF70-1833, is gratefully acknowledged. References and Notes (1) (2) (3) (4) (5)
Author to whom correspondence should be addressed.
L. Barcza and M. T. Pope, J. Phys. Chem., 77, 1795 (1973).
L. Barcza and M. T. Pope, manuscript in preparation. L. Barcza and M. T. Pope, J. Phys. Chem., 78, 168 (1974). S. Kondo and I. Nitta, X-Sen, 6, 53 (1950) [Chem. Abstr., 45, 3237 (1951)]. (6) K. Ogawa, Bull, Chem. SOC.Jap., 36, 610 (1963). (7) S. R. Jain-and S. Soundararajan, Tetrahedron, 20, 1589 (1964). (8) P. Greenzaid, A. Luz, and D. Samuel, J. Amer. Chem. SOC., 89, 749 (1967). (9) L. C. Gruen and P. T. McTigue, J. Chem. SOC., 5217 (1963). (10) Upon heating the solutions of motybdates and pyrocatechol, reduction of the polymolybdates occurred. In the case of hexamolybdate a stoichiometric reaction produced 1,2-benzoquinone(ref 3). (1 1) Earlier results with pyrocatechol led us to state that 12-molybdosilicate and -phosphate anions were less subsceptible to hydrogen bonding than was perchlorate anion (ref 2). The present results show that this statement is not necessarily valid for chloral hydrate complexes. (12) In the Keggin (1:12 heteropoly anion) structure there are two types of bridging oxygen atom. (13)'A referee has pointed out that Strandberg interpreted long Mo-0 distances in H e P M o ~ 0 3 ~as ~ - evidence for protonated terminal oxygens (Acta Chem. Scand., Sect. A, 26, 217 (1974)). This seems reasonable. but the molybdenum atoms in question each have two terminal oxygen atoms. In the Keggin and Mo60& structures each metal has a single unshared oxygen. Reduction of charge density on the oxygen by T bonding is expected to be more efficient in the latter case. (14) M. T. Pope, Polym. Prepr., Amer. Chem. Soc., Div. Polym. Chem., 13, 787 (1972). (15) E. Papaconstantinouand M. T. Pope, lnorg. Chem., 6, 1152 (1967).
COMMUNICATIONS TO THE EDITOR
Evaluation of Dielectric Permittivity by Time Domain Spectroscopy Publication costs assisted by the Materials Science Program, Brown University, with support from the National Science Foundation
Sir: We present here simple formulas for evaluating complex permittivity e * ( ; ~a)t frequencies u = w / 2 x from Laplace transforms of voltage pulses V O( t) and R ( t ) incident on and reflected from a dielectric sample in coaxial lines, as observed by time domain spectroscopy (tds).' From transmission line and network theory,2 the input admittance y IN of a dielectric sample in length d of coaxial line terminated by an admittance Y d is Y I N = ( y o + y d ) / ( l Z a d ) , where y o = iwC.d((tanh x ) / x ) and 2 , = i w L cd ((tanh x )/x ) are the open-circuit admittance and short-circuit impedance of the dielectric section, C, and L, are the geometric capacitance and inductance per unit line length, x = i o €*ll2d/c,and c = (LcCc)-1'2.y IN is related to the transforms u o ( i w ) and r ( i w ) of V , ( t ) and R ( t ) by
+
+
= Gc(uO r ) / ( u g - r ) , as the input voltage is u g - r for our sign convention and the input current is G, ( u o r ) , where G, = (Cc/Lc)1/2. For a sample inserted in a matched line, Y d = G,, and combining the preceding equations gives
YIN
+
The approximation x coth x = 1 - 3/3( w d / c ) * c * gives an explicit solution for € * valid for ( 1 / 4 5 ) ( ~ d / c ) %
