1354
ROBERT C. MILLERAND CHARLES P. SMYTH
An alternative explanation of some of these discrepancies has been offered by Turnbull31 for the case of grain growth, namely the presence of impurities, which may lower the free energy difference between the phases. If this lowering is temperature dependent, then the apparent values of the energy and entropy of activation are increased. Although it is quite possible that inclusions are present, these are not in a sufficient concentration in the solid reactions studied to give a variation in transition temperature between the different samples, and it seems unlikely that this effect could be large. The influence of inclusions and of strain on the free energy will be most noticed near to the transition temperature and may give rise to an “indeterminacy thickening” of the type digcussed by Ubbelohde. Summing up, although the application of transition state theory is suggestive it does not seem to take the subject of solid-solid reactions much fur(31) D. Turnbull, J. Metals Trans.,191,3 (1951).
Vol. 60
ther, since the difficulties are thrown back on to the properties of an unknown transition phase, but neither are the other attempts a t a solution free from criticism. It appears that most progress could be made by studies on single crystals. It would also be interesting to test the vapor transport theory on a system such as claudetite-arsenolith (As2O3),for which the phase with the higher vapor pressure evaporates slower than the other phase, owing to the anomalous nature of the evaporation coefficients. The writer would like t o put in a plea for the determination of activation energies wherever possible and believes that chemists and metallurgists would profit greatly by pooling their ideas. However, it should be remembered that metals have high surface energies, are often alloyed, and are often studied a t temperatures a t which diffusion readily occurs. It is a pleasure to acknowledge my indebtedness t o Dr. N. H. Hartshorne of the University of Leeds for valuable discussions and permission to refer to some of his work prior to publication. ~
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MICROWAVE ABSORPTION AND MOLECULAR STRUCTURE IN LIQUIDS. XVI. DIPOLE DIRECTION AND RELAXATION TIME IN PYRIDINE, TRIOXANE AND THEIR SYMMETRICAL TRIMETHYL DERIVATIVES1 BY ROBERTC. MILLER^ AND CHARLES P. SMYTH Contribution from the Frick Chemical Laboratory, Princeton University, Princeton, X . J. Received February 49 1966
Measurements of dielectric constant and loss have been carried out at wave lengths of 1.24, 3.22 and 10.4 cm. and 300 m. and temperatures from 20 to 80” upon collidine, or 2,4,6-trimethylpyridine, sym-trioxane and paraldehyde. The viscosities and densities have also been measured. The results are combined with those previously published for pyridine to investigate the effect of dipole orientation in the molecule upon dielectric relaxation. 2,4,6-Trimethylpyridine and paraldehyde, in spite of much larger molecular size, have virtually the same viacosity as pyridine. However, the critical wave length, at which the dielectric loss is a maximum, has a value for 2,4,6-trimethylpyridine approximately 4 times that for pyridine, probably because of close-packing of the triangular 2,4,6-trimethylpyridine molecules in the liquid and, also, because of their arger size. Paraldehyde, which has a molecule similar in size and shape to that of 2,4,6-trimethylpyridine, has a critical wave length about twice as large, presumably, because the dipole is perpendicular to the molecular triangle instead of parallel to it as in 2,4,6-trimethylpyridine,thus requiring the triangular slabs to turn over instead of rotating in their plane when orientation occurs in the applied field.
An earlier paper3 of this series has discussed ten flat, rigid molecules such as those of pyridine and quinoline, which have the permanent dipole in the plane of the ring. It is the purpose of this paper to compare the dielectric relaxation times of two such molecules with those of two similarly shaped molecules in which the dipole axes are perpendicular to the planes of the rings. The previously studied pyridine3 and the newly investigated 2,4,6-trimethylpyridine, or collidine, 2,4,6-(CH3),C5HzN, will be compared with sym-trioxane, (CH20)a,and paraldehyde, (CH3CH0)3. (1) This research was supported by the United States Air Force through the Office of Scientific Research of the Air Research and Development Command. Reproduction, translation, publication, use or disposal in whole or in part by or for the United States Government is permitted. (2) Supported by a Grant-in-Aid to the Chemistry Department, Princeton University, from E. I. du Pont de Nemours and Company. (3) R. 8. Holland and C. P. Smyth, THISJOURNAL, 69, 1088 (1955).
Experimental Methods and Results Trioxane from Brothers Chemical Company waa fractionally distilled; m.p. 60.5’; lit.* 61-62”. U.S.P. paraldehyde w p washed Tith water and fractionally distilled; m.p. 12.3 ; lit.6 12.5 ; b.p. 123.8’; lit.b 124’. Collidine from the Brothers Chemical Company was dried o v y barium oxide and fractionally distilled; b .p. 170.0-170.2 , lit.6 172”. Dielectric constants e’ and losses e” a t wave lengths of 1.24, 3.22 and 10.4 cm., and the so-called static dielectric constant EO at a wave length of 300 meters were measured by methods described or referred to in earlier papers of this series.* The values obtained at each temperature of measurement are given in Table I. The values of the critical wave length Am, at which the loss is a maximum, and of the empirical constant CL for the distribution of the relaxation (4)J. F. Walker, “Formaldehyde,” Reinhold Publ. Corp., New York, N. Y.,1953, p. 146. (5) J. Timmermans, ”Physico-Chemical Constants of Pure Organic Compounds,” Elsevier Publishing Co., New York, N. Y., 1950, p. 500. (6) “International Critical Tables,” McGraw-Hill Book Co.. New York, N. Y.
MICROWAVE ABSORPTIONAND MOLECULAR STRUCTURE IN LIQUIDS
Oct., 1956
1355
O'Dwyer and Sack8 and P o ~ l e s the , ~ molecular relaxation times for these four liquids are 0.70 t o 0.75 of the macroscopic relaxation times3 7 . It is evident, therefore, that the critical wave length values provide a means of comparing the relative behaviors of the molecules. Examination of Stuart-Briegleb models for the four molecules under consideration shows that the shape of the pyridine moleule is approximately that of an oblate spheroid, that of the collidine and paraldehyde molecules a triangular slab with flatTABLE I tened corners and slightly indented sides, and that DIELECTRIC CONSTANTS AND LOSSES of the trioxane intermediate between the other two ;.24 om. g.22 cm. 1 0 . 4 cm. forms. The dipoles of the pyridine and collidine t, oc. f f" E' f" f0 molecules lie in the planes of the rings. The dipole Collidine, 2,4,6-(CHs)C6H2N moment of sym-trioxane indicates that the mole20 2.71 0.77 3.37 1.67 6.15 2.07 8.00 cules are largely in a chair form and the same is .95 3.75 1.80 6.06 1.71 7.46 40 2.75 probably true of the paraldehyde molecules. l o ~ l l 1.40 6.94 60 2.85 1 . 0 3 4.09 1.90 5.95 I n this form the molecular dipole moment is perpendicular to the ring. I n the paraldehyde molesym-Trioxane, ( C H Z O ) ~ cule, steric repulsion makes the three equatorial 65 8.51 6.80 13.11 5.27 15.75 2.16 15.55 positions appear to be the most probable locations 80 8.00 5.97 12.29 4.36 15.04 1.62 14.20 for the three methyl groups and the closeness of Paraldehyde, (CH$H0)3 the molar volumes of paraldehyde and collidine in 20 2.43 1.00 2.87 2.08 5.14 4.78 14.70 Table I1 supports this supposition.ll The pre40 2.42 1.09 3.21 2.26 6.54 4.24 12.25 viously described models for these two molecules 60 2.53. 1.15 3.74 2.56 7.26 3.36 10.30 have been constructed on the basis of these con8.70 80 siderations. The approximate dimensions of the 7.46 100 molecules (Table 111) obtained by measuring these 6.42 120 models may be expressed in terms of the thickness of the spheroidal or triangular slab, the length of TABLE I1 the side of the triangle, and the diameter of the CRITICALWAVE LENGTHS,DISTRIBUTION COEFFICIENTS, circle described when the slab is rotated about the VISCOSITIES A N D MOLAR VOLUMES axis of symmetry perpendicular to it.
times calculated by the usual methods' are given in Table 11. Although the collidine and paraldehyde dielectric constant and loss values fitted the Cole and Cole arc plots, the critical wave length values calculated a t different frequencies did not agree with one another. The critical wave lengths were, therefore, taken from the values measured a t the nearest wave length. The slightly revised values included in Table I1 for pyridine differ from those previously published by no more than the probable error. Table I1 also gives the values measured for the viscosities of the liquids and the molar volumes calculated from the measured densities.
f
1,
OC.
1 20 40 60 20 40 60
f"
Xm (cm.)
1.74 1.40 1.09 0.91 7.6 6.2 4.4
a
Pyridine 0.04 0.02
0 0
Collidine 0.08 -09 .IO
11 (CPS.1
1.31 0.95 .72 .58
v (CC.) 79.5 80.6 82.2 84.0
0.98 .73 .58
131.9 134.6 137,O
0.94 0.73
76.9 78.5
sym-Trioxane
60" 80
1.55 1.36
0 0
Paraldehyde 20 20 0.05 1.186 .07 0.816 40 12.6 60 8.2 .10 0.606 a Extrapolated from values at 65".
133. 65 136.56 139.75
Discussion of Results The dielectric or macroscopic relaxation time, T = h , / 6 ~ X 1O1O,differs from the molecular relaxation time because of the effect of the internal field of the liquid. It is greater than the molecular or microscopic relaxation time because, when a given molecule in a polar liquid turns, its neighbors must assume new orientations, thus increasing the macroscopic relaxation time. In terms of the very approximate internal field factor derived by (7) C. P. Smyth, "Dielectric Behavior and Structure," McGrawail]Book Co., New York! N. Y., 1955, pp. 69-70,
TABLE I11 APPROXIMATE MOLECULAR DIMENSIONS (i.) A N D DIPOLE MOMENTS ( X 10'8) Pyridine Collidine sym-Trioxane Paraldehyde
Thickness
Side
3.2 3.6 3.6 3.9
8.3 5.9 8.0
..,
Diameter
Moment (in soln.)
6.7 8.6 6.6 8.6
2.2312 1.93Ia 2.WZ 2.03lz
When the viscosities of these four liquids a t 60" are compared, it is evident that collidine and paraldehyde, in spite of their much larger molecular sizes, have virtually the same viscosity as pyridine. This suggests the possibility that viscous flow in these liquids may involve primarily the slipping of molecular layers over one another with little rotation of the individual molecules. The higher viscosity of trioxane as compared to pyridine is consistent with the closer packing of the molecules indicated by the smaller molar volume and the larger dielectric constant. The critical wave length of trioxane a t 60" is 1.70 times that of pyridine as compared to a viscosity ratio 1.62 for (8) J. J. O'Dwyer and R. A. Sack, Australian J . Sci. Research, AS, 647 (1952). (9) J. G. Porvles, J . Chem. P h v s . , 21, 633 (1953). (10) A. A. Maryott and 6. F. Acree, J . Research Natl. Bur. Standards 33, 71 (1944). (11) See also R. J. W. Le FBvre, J. W. Mulley and B. M. Smythe, J . Chem. Soc., 290 (1950). (12) C. P. Smyth, ref. 7, pp. 299,343. (13) M. A. G. Rau and B. N. Narayanaswamy, 2. physik. Chem., B26, 23 (1934),
1356
A. G. KEENAN
the two liquids. There is no proportionality between critical wave length and viscosity for the other two liquids which have practically the same viscosity as pyridine a t 60", paraldehyde increasing more rapidly with decreasing temperature than collidine and pyridine. The critical wave length of collidine is approximately 4 times that of pyridine, although its greater diameter should make it only 1.6 times as lar& Probably, the additional difference may be attributed to close packing of the triangular collidine molecules in the liquid, which necessitates a considerable amount of displacement of the neighboring molecules when rotational orientation occurs, while the pyridine molecules can orient by rotation in the plane of the ring with very little displacement of neighboring molecules. The critical wave length of paraldehyde is 2.6 times that of collidine a t 20" and 1.9 times it at 60°, although the viscosities and the molecular sizes and shapes of the two are very nearly the same. I n paraldehyde, however, the axis of the molecular dipole is perpendicular t o the triangular slab instead of parallel to it as in collidine. Con-
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sequently, dipole orientation involves the turning of the triangular slabs out of their planes with consequent greater displacement of neighboring molecules than is required for rotation in the plane of the slab and resultant longer relaxation time and critical wave length. I n other words, the collidine critical wave length is lower because its molecules can orient by rotating in the plane of the triangular slab, although they may do so by turning out of the plane as well, while the paraldehyde molecules have to orient by turning out of this plane. The paraldehyde critical wave length a t 60" is about 5 times that of trioxane at the same temperature, just as that of collidine is about 5 times that of pyridine, and for similar reasons. The approximately zero values of CY, the coefficient of distribution of relaxation times, for pyridine and trioxane are consistent with their molecular symmetries, while the small but appreciable values for the other two molecules are about what is often found for molecules of this somewhat lower symmetry.
THE CRYOSCOPIC HEAT OF FUSION OF AMMONIUM NITRATE1 BY A. G. KEENAN Department of Chemistry, Illinois Institute of Technology, Chicago 16, Illinois Received February 18, I068
Freezing point depression data have been measured for fused salt systems with Li, Na, K, Rb, Cs, T1 and Ag nitrates as solutes and NH4N03as solvent, in thz concentration range 0 . 5 4 0 mole and temperature range 160-170". The re roducibility of the data is within 1 0 . 0 2 . The results show interesting correlation with ionic radii and structure. The Xata are interpreted to indicate that there is no solid solution formation in the case of the Li, Na and Ag nitrates, without recourse to actual analysis of the solid phase. These solutions are, in fact, very close to ideal and the data yield a value of 1.53 kcal. mole-' for the latent heat of fusion of ammonium nitrate.
I n preparation for other work, the freezing-point depressions for a number of solutions of alkali nitrates in fused ammonium nitrate as solvent were determined in an apparatus developed for this purpose. The results proved to be of sufficient interest t o warrant a more systematic study. A series of cryoscopic measurements was, therefore, carried out using the nitrates of Li, Na, K, Rb, Cs, Ag and T1 as solutes in the concentration range of 0.5 to 4.0 mole yo. Most of these systems have been covered in the extensive phase-rule studies of the past12but neither the accuracy nor the range of concentrations have, in general, been comparable with the present work. The interpretabion of cryoscopic data at elevated temperatures is seriously complicated by the prevalent occurrence of solid solutions under these conditions. Precision in the direct analysis of the
solid phase is usually very difficult experimentally. * The extensive phase-rule studies, in which no solid solution formation is reported, are usually of limited accuracy so that the existence of such solutions to the extent of several per cent. concentration is not precluded by the data. It is believed that the present results can be interpreted in such a way as to exclude the possibility of solid solutions in certain systems without recourse to a direct experimental analysis of the solid phase. It has, therefore, been possible t o calculate unequivocally a value for the heat of fusion of ammonium nitrate from the data for these systems. The apparatus and technique are relatively simple and give freezing points which are reproducible to a few hundredths of a degree within the temperature range studied so far, namely, 160 to 170". Experimental
(1) This research was supported by the United States Air Force through the Office of Scientific Research of the Air Researoh and Development Command under contract No. AF 18(600)-1148. (2) Some of the more recent and pertinent references are: E. 0. Holmes, E. O'Connell and F. Hankard, J. A m . Chem. Soc., 1 3 , 2885 (1951); E. 0.Holmes and D. Revinson, ibid., 66,453 (1944); J. Whetstone, Can. J. Rea., B26, 499 (1948); H. M. Glass, K. Laybourn and W. M. Madgin, J . Cham. Soc., 199 (1933); R. G. Early and T. M. Lowry, ibid., 121, 963 (1922); E. P. Perman and W. J. Howells, dbid., lZ3, 2128 (1923).
A diagram of the freezing point cell is shown in Fig. 1. The inner tube containing the sample was made of 20 mm. P rex tubing, and the outer wall of the vacuum jacket was oP40 mm. tubing. The complete assembly shown in the diagram was 45 cm. high. The jacket was evacuated to the ultimate vacuum of a conventional two-stage mercury (3) H. Flood, T. Forland and A. Nesland, Acta Chem. Scand., 6, 1193 (1951); E. P. Permqn and D. R. Dawkina, J. Chem. Soc., 126, 1239 (1924).
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