Cp2)

NOTES

950

limitation on frequency coverage makes intensity considerations more difficult when reorientation times are broadly distributed.6 Ifolecular mechanisms for mechanical relaxation in polymers are not so well established for secondary transitions although many workers have contributed in important ways to the proper appreciation of the factors involved. On the other hand, a very successful theory has been developed for the interpretation of sonic absorption in liquid^.^ We propose that this model is appropriate for the interpretation of many secondary transitions in mechanical loss studies of polymers. If a polymer has a side group that can reorient between two sites the mechanical loss can be shown to have a maximum given by7 tan 6,

=

(RT/2)(AHo/RT)2(M~2~2/Cp2) X exp( - AHo/RT)exp(AXo/R) (1)

where cr is the expansion coefficient, C, the molar heat capacity, c is the speed of sound, and AH" and AS" are the enthalpy and entropy difference between the two sites. Thus, AH" can be determined by analysis of the temperature dependence of the mechanical loss intensity. (Equation 1 is a simplified form valid when A H " / R T is greater than 2 or 3. More general forms are given by Lamb.7 A plot of T X tan ,6 us. 1 / T will often yield a straight line with slope proportional to AH".) Let us now consider the /3 transition of poly(methy1 methacrylate) in the context of the foregoing discussion. This transition is evident in dielectric, nmr, and mechanical results and the frequency-temperature map shows excellent correlation between the various experiments, The resultant activation energy is about 20 kcal/mole. Analysis of the dielectric loss intensitp yields an effective dipole moment that increases from about 1.4 D. a t room temperature to 1.7 D. a t 130". This compares favorably with -1.9 D. found for ethyl acetate in ~ o l u t i o n . ~Nuclear magnetic resonance TI results make it clear that both the ester and main chain methyls are rotating rapidly at temperatures well below the p region.'O The depth of the TI minimum corresponding to the p transition is consistent with rotation of the ester side group but only an approximate analysis has been made. Analysis of the mechanical loss yields, for the enthalpy difference between sites, AH" g 3.4 kcal/ mole. This is close to the value AH" 3 kcal/mole found for ethyl acetate liquid by ultrasonic relaxation' We might suggest, on the basis of this comparison, that the energy difference has an intramolecular origin. The theory of Lamb7 reveals that the activation energy

-

T h e Journal

of

Physical Chemistry

measured is the lower of the two; ie., the barrier is -20 kcal/mole in one direction and -23 kcal/mole in the other. AS" must be 3 or 4 eu. These considerations make it quite obvious that the /3 transition in polymethyl methacrylate corresponds to a reorientation of the ester side group. In addition, parameters characterizing hindrances to thiq motion have been evaluated. I t will be of interest to see how widely detailed interpretations such as these can be applied. In any case, relaxation intensities are a relatively untapped resource. Intensity analyses will lead to a more secure understanding of the mechanisms by which electric, magnetic, and elastic energies are converted to heat and clearer pictures of molecular motion. Acknowledgment. It is a pleasure to acknowledge the assistance of W. P. Slichter in the development of this material. Helpful discussions were provided by D. C. Douglass, A. A. Bondi, and S. Natuoka. (6) T. 11.Connor, Trans. Faraday Soc., 60, 1574 (1964). (7) J. Lamb in "Physical Acoustics," 11, A, W. P. Mason, Ed., Academic Press, New York, N. Y., 1965, p 203. This chapter by Dr. Lamb contains a beautifully clear exposition of the theory and experimental documentation of its successes in liquids. (8) W. Reddish, Pure A p p l . Chem., 5 , 723 (1962). (9) C . P. Smyth, "Dielectric Behavior and Structure,'' McGrawHill Book Co., Inc., New York, N. Y., 1955. (10) J. G. Powles, B. I. Hunt, and D. J. H. Sandiford, Polymer, 5, 505 (1964). (11) G. W. Becker, Kolloid-Z., 140, 1 (1955). (12) J. Heijboer, ibid., 148, 36 (1956).

Free Energy of Formation of LizTe at 798°K by an Electromotive Force Method' by M. S. Foster and C. C. Liu Chemical Engineering Division, Argonne National Laboratory, Argonne, Illinois (Received October $1, 1966)

The thermodynamic properties of the binary lithium-tellurium system have been studied using electromotive force measurements of a concentration cell without transference. Very little information pertaining to this system was found in the literature. The lattice constant of LizTe was reported by Zintl, Harder, and Danth.4 A semiconductor character was predicted for LizTe by Mooser and P e a r ~ o n . ~ (1) Work performed under the auspices of the U. S. Atomic Energy Commission. (2) E. Zintl, A. Harder, and B. Danth, 2. Elektrochem., 40, 588 (1934).

95 1

NOTES

The complete phase diagram for the sodium-tellurium system is given by Hansen and Anderko4 and shows both N:tzTe (1326°K) and NaTea (709OK) as congruently melting compounds, while NaTe reportedly dissociates at 628°K.

I

I

I

I

I

l

I

l

I 1

1.08

2

1.06

VI

1.04

1

2 1.02 -I

Experimental Section The cell used in this investigation was contained in a furnace well attached to the floor of an inertatmosphere box. The helium atmosphere was continuously purified by recirculation through an activated charcoal trap immersed in liquid n i t r ~ g e n . ~ The cell configuration was similar to that described previously.6 The electrode contacts were tungsten rods. The chromel-alumel thermocouple used to monitor the cell temperature was contained in a small tantalum tube, closed on one end, which was immersed in the electrolyte. The reference electrode (anode) consisted of a two-phase mixture of LisBi(s) and a bismuth-rich liquid alloy of lithium and bismuth. The over-all composition of this electrode varied from 60.3 to 56.0 atom yo lithium during the experiment as lithium was coulometrically removed (initial quantities of lithium and bismuth were 5.4702 and 107.3808 g, respectively). The lithium metal used was obtained from Foote Mineral Co., Philadelphia, Pa.. in the form of 1-lb ingots sealed in cans under an argon atmosphere. The impurity analysis supplied by the Foote Mineral Co. was 0.003% S a , 0.0028% K, 0.003% C1, and 0.0031% N,. No further purification of the lithium metal was attempted, but only bright metal pieces were used. Bismuth metal was obtained in shot form from United Mineral and Chemical Corp., Sew York, N. Y. The impurity analysis furnished by United Mineral and Chemical Corp. showed 0.0004% Ag, 0.0001% Cu, 0.0002% Pb, and 0.0001% Fe. This metal was melted under helium and filtered to remove oxide impurities prior to use. The voltage of this electrode was previously determined against lithium.6 The second electrode in this study was an alloy of lithium and tellurium contained in a porous B e 0 crucible. A total of 14.6935 g of tellurium was added initially. Elemental tellurium was obtained from American Smelting and Refining Co., Sew York, N. Y. Impurity analysis furnished by American Smelting and Refining Co. showed 0.0001% Mg, 0.0001% Fe, and 0.0001% Cu. This material was melted under helium and filtered before use. The electrolyte was the eutectic composition 30 mole Yo LiF, 70 mole yo LiC1.’ This composition was made up in air, using reagent grade chemicals, and purified by the method of RiIaricle and Hume,* i.e.,

E

6 a

LOO

5 0.98

0’94

005

0.10

015 020 0.2s a30 035040 ATOM FRACTION Li IN To

050

OS0

Figure 1. Voltage-composition behavior of the cell: Li(in Bi(1) saturated with solid LiaBi) LiC1-LiF Li ~ over-all atom fraction Li in Te) in Te ( X L = a t 798’K.

I

1

chlorine gas was passed through the molten eutectic, after which the excess chlorine was removed by bubbling helium through the melt. The melt was sealed in Pyrex under vacuum and transferred to a heliumfilled drybox where all subsequent operations were performed. Lithium was added coulometrically to the tellurium from the reference electrode a t a constant current of 0.5 amp. Sufficient coulombs were used to change the composition of the lithium-tellurium electrode by -0.5 atom 70each time. After each increment of current was passed, the lithium-tellurium alloy was stirred and the cell potential read with a Leeds and Sorthrup Type K-3 potentiometer a t 5-min intervais until constant to +0.5 mv (usually -20 min). Results The concentration of lithium in the tellurium was calculated directly from the number of coulombs used and the assumption of 100% current efficiency. The behavior of the observed cell potential us. the computed concentration of lithium in the tellurium is shown in Figure 1. The discontinuity at 0.39 atom fraction is believed to be the point a t which the cathode alloy at 798°K becomes saturated with LLTe. The (3) E. Mooser and W. B. Pearson, J . Electronics, 1, 629 (1956). (4) M. Hansen and K. Anderko, “Constitution of Binary Alloys,” McGraw-Hill Book Co., Inc., New York, N. Y., 1958. (5) M. S. Foster, C. E. Johnson, and C. E. Crouthamel, “Helium-

Purification Unit for High-Purity Inert-Atmosphere Boxes,” ANL6652 (1962). (6) M.S. Foster, S. E. Wood, and C. E. Crouthamel, Inorg. Chem., 3 , 1428 (1964). (7) H. M. Haendler, P. S. Sennett, and C. hi. Wheeler, Jr., J. ~ l ~ ~sot., t 106, ~ 264 ~ ~(1959). h ~ ~ . (8) D. L. Maricle and D. N. Hume, ibid., 107, 354 (1960).

Volume 70, Number S

March 1066

COMMUNICATIONS TO THE EDITOR

952

absence of breaks in the curve at atom fractions 0.25, 0.33, and 0.50 indicates the absence of LiTee, LiTez, and LiTe, respectively (see corresponding phase diagram of Sa-Te), in the system. If the data could be obtained through the 0.66 atom fraction, a sharp drop in emf would appear, the emf approaching -0.7 v on the plot in Figure 1 or 0 v with respect to a liquid lithium anode. The observed cell potentials were converted to those for the cell

I

Li(1) LiC1-LiFI Li in Te ( X L ~= atom fraction Li in Te)

(1)

by adding 0.7055 v a t 798°K (see ref 6). The standard states are taken to be Li(1) and Te(1) in the cell environment (saturated with electrolyte). Therefore, the excess chemical potential of Li in Te a i the cell temperature (T = 798 f 1°K) may be calculated ApLiE

=

-FE - R T In XLi

(2)

where F is the value of the Faraday and R the gas constant, These results are shown in Table I. The , average excess chemical potential, A ~ L is~-~37,145 135 cal/mole. A least-squares fit of the data to a quadratic function of XLi resulted in the equation A p ~= i ~-36,568

+

- 5736X~i 11,676X~i~ (cal/mole) (3)

The standard deviation of this equation is 29 cal/mole. The cell reaction (1) may be written Li(1)

+ l/zTe(l) (saturated with solid LizTe) + '/~LizTe(s) (4)

for an over-all electrode composition of X L ~2 0.39. For this reaction we may write

AG = -FE = '/zAGr"

- '/zRT In X T ~ '/2ApTeE

(5) where XTe is the atom per cent Te in the Li-Te liquid saturated with LizTe(s), A ~ is Tthe ~excess ~ chemical potential of Te in the same liquid, and AGro is the standard free energy of formation of Li2Te(s) from the elements. The value of A ~ was T calculated ~ ~ from the Gibbs-Duhem relationship. A constant value of A p ~ gave i ~ A ~ =T 0, ~while ~ eq 3 yielded A ~ =T -50 cal/mole. Using either value, the standard free energy of formation of LizTe(s) a t 798°K was calculated to be -77.9 kcal/mole. The standard deviation of this value is estimated as 0.4 kcal/mole. Table I : Calculated Excess Chemical Potential of Li in Te Cumulative total coulombs added

Calculated over-all concentration of Li in Te (atom fraction)

Observed cell potential, v

660 1260 1860 2460 3060 3660 4460 5260 6060 6860 7860 8860 9860 12060

0.056 0.10 0.14 0.18 0.22 0.25 0.29 0.32 0.35 0.38 0.41 0.44 0.47 0.52

1,0912 1.0573 1.0392 1,0244 1,0175 1.0075 0.9966 0.9854 0.9756 0.9686 0.9666 0.9644 0.9646 0.9644

-APLF! cal/mole

36860 37025 37 150 37181 37300 37289 37263 37190 37112 37075

. . .a

. . .a . . .a

. . .a

' Two-phase region existed at this over-all composition (see Figure 1 and text). Acknowledgment. The interest of Dr. J. A. Plambeck in this work is gratefully acknowledged.

C O M M U N I C A T I O N S T O THE E D I T O R The Mechanism of Ketene Photolysis

Sir: The photolysis of ketene has often been used as a source of methylene radicals,1*2yet the mechanism of the photolysis is still in some doubt.* Any proposed mechanism must account for the following facts. (a) At short the formed in the photolysis are almost entirely singlet, The Journal of Physical Chemietry

whereas a t long wavelengths they are predominantly tri~let.~ At an intermediate wavelength, 3200 A, (1) T. Terao and S. Shida, Bull. Chem. SOC.Japan, 37, 687 (1964). (2) F. Casas, J. A. Kerr, and A. F. Trotman-Dickenson, J . Chem. Soe., 1141 (1965). (3) W. A. Noyes, Jr., and I. Unger, Pure A p p l . Chem., 9,461 (1964). (4) S. Ho, I. Unger, and W. A. Noyes, Jr., J. Am. Chem. &c., 87, 2298 (1965).

~

~