DIELECTRIC BEHAVIOR O F MIXTURES O F HEPTANOL-1 AND
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HEPTANOL-4
The Dielectric Behavior of Mixtures of Heptanol-1 and Heptanol-4 and the Fluid Structure of the Monoalcohols by P. Bordewijk, F. Gransch, and C. J. F. B6ttcher Chemical Laboratories of Leiden University, Department of Physical Chemistry II,Leiden, The Netherlands (Received February 11, 1969)
The dielectric properties of mixtures of heptanol-1 and heptanol-4 were determined in the frequency range b e tween 1 kHz and 3 MHs at temperatures between -60 and 0”. The results of the measurements indicate that, although the two alcohols have different activation enthalpies, the dielectric properties of their mixtures can nevertheless be described by means of a single principal relaxation range. From this it follows that the theory of Bauer, Magat, and Brot concerning the dielectric relaxation of the monoalcohols, which theory states that breaking of the hydrogen bond is the ratedetermining step, must be rejected. A possible explanation for the experimental results could be that the liquids under study contain one kind of cyclic multimers with a high dipole moment, and that these multimer units are retained during the reorientation process.
Introduction Since Mizushima published his measurements on a number of alcohols in 1926,’ it has generally been found that the relaxation behavior of the monoalcohols can mainly be described with one relaxation time. Although Girard and Abadie2 found a second relaxation range and Cole and DavidsonS even a third one, the amplitude of the first relaxation range of pure compounds with a high value of the Kirkwood correlation factor g is large as compared to the amplitude of the subsequent relaxation ranges. Mizushima interpreted his observations on the basis of Debye’s model for the r e l a ~ a t i o n ,and ~ Girard and Abadie tried to take into account the deviations of the spherical shape, basing themselves on Perrin’s theory.6 However, it is just for the alcohols that a microscopic viscosity deviating strongly from the macroscopic viscosity must be assumed if the Debye-Perrin theory is to be reconciled with the facts. A theory based on Kauzmann’s conceptiona rather than on that of DebyePerrin, was developed by Bauer, Magat, and Brot;l-1° the latter theory was accepted by Cole’l and Smyth12 and has recently been defended by Raczy, et aZ.l3 This theory is based on the assumption that monoalcohols have a wide distribution of multimer sizes, due to linear association, because addition of a new molecule to a chainlike multimer must always yield about the same amount of energy. If the dielectric relaxation were caused by rotation of the multimers as a whole, this would lead to a distribution of relaxation times, which is not found experimentally. The dielectric relaxation must therefore be caused not by the rotation of the multimers as a whole, but by rotation of single molecules, which could only be brought about by breaking of the hydrogen bonds. This breaking would then be the rate-determining step, the required energy being inter-
preted as the activation enthalpy of the dielectric relaxation. An objection to this theory has been put forward by Sagal,14 who found the relaxation frequency to be influenced by dilution of the alcohol with an apolar compound, which is not in accordance with the theory of Bauer, Magat, and Brot. Another difficulty offered by this theory is that it cannot explain that the activation enthalpies of the various monoalcohols differ greatly, as has been pointed out in particular by MiddelhoekI16Je who determined activation enthalpies varying between 7.9 and 15.5kcal/mol for the straight-chain heptanols. The values found so far for the activation enthalpies of the monoalcohols range from 3.5 kcal/mol for methanol” up to 19.4 kcal/mol for 2,2-dimethylhexanol-l and 2,2-dimethylo~tanol-l.~* The activation enthalpy (1) 8.Mizushima, Bull. Chem. Sac. Jap., 1, 163 (1926),and references therein. (2) P. Girard and P. Abadie, Trans. Faraday SOC.,A42,40 (1946). (3) R. H.Cole and D. W. Davidson, J . Chem. Phys., 20, 1389 (1952). (4) P.Debye, “Polar Molecules,” Chemical Catalog Co., New York, N.Y.,1929. (5) F.Perrin, J. Phys. Rad. (7),5,497 (1934). (6) W.Kauzmann, Rev. Mod. Phys., 14, 12 (1942). (7) E.Bauer, Cahiers Phys., 20,l (1944). (8) E.Bauer, ibid., 21,21 (1944). (9) P. C. Brot, Ann. Phys., 13-2,714(1957). (10) C.Brot and M. Magat, J . Chem. Phys., 39,841 (1963). (11) F.X.Hassion and R. H. Cole, ibid., 23,1756 (1955). (12) S.K. Gargand C. P. Smyth, ibid., 46,373 (1967). (13) L. Raczy, E.Constant, and A. Lebrun, J . Chim. Phys., 64, 1180 (1967). (14) M. W.Sagal, J. Chem. Phys., 36,2437 (1962). (15) J. Middelhoek and C. J. F. Bottcher, “Molecular Relaxation Processes,” Special Publication No. 20,The ChemicalSociety, London, 1966,p 69. (16) J. Middelhoek, Thesis, Leiden, 1967; see p 61. (17) D.W.Davidson, Can. J . Chem., 35,458 (1957). Volume 73, Number 10 ’ October 1969
P. BORDEWIJK, F. GRANSCH, AND C. J. F. BOTTCHER
3256 increases with the length of the carbon chain, and furthermore is usually greater the more central the position of the hydroxyl group in the molecule. The theory of Bauer, Magat, and Brot would imply that the energy necessary to break the hydrogen bond increases in the same manner. The point of departure for the present investigation was the consideration that if the differences in activation enthalpies are caused by differences in the energies necessary to break the hydrogen bonds, this would appear from measurements on mixtures of monoalcohols with different activation enthalpies. I n such mixtures, there are different kinds of hydrogen bonds, each requiring its own energy to break. Therefore mixtures of monoalcohols with different activation enthalpies would show a distribution or a superposition of relaxation times. For the present study we chose heptanol-1 and heptanol-4, which are known from Middelhoek's investigations to show strongly different activation enthalpies. We preferred a mixture of isomers to a mixture of components such as methanol and decanol-1 for the following reason. For methanol and decanol-1 the differences in the energies necessary to break the hydrogen bonds might be explained by the great differences between the static dielectric constants of these compounds. In that case the breaking of all the hydrogen bonds in the mixture should require the same energy.
Experimental Section Dielectric constants and losses were determined between l kHZ and 3 MHz and between -60 and 0" in a dielectric cell described e1se~here.l~The capacitance and conductivity of the cell were determined with two bridges: in the frequency range from 1 to 100 kHz a General Radio bridge Type 1615-A was used; in the frequency range from 100 kHz to 3 MHz, a Wayne Kerr bridge Type B 201 was used. Materials were supplied by Fluka and purified by careful distillation afber drying on CaS04. The investigated mixtures contained 74.85,50.68,and 24.34 wt % heptanol-1. The pure compounds were also examined.
Figure 1. Cole-Cole plot for mixture of heptanol-1 and -4 at T = 55.4'.
E"
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Figure 2. Cole-Cole plots: heptanol-1, -31.9'; 0 , mixture of heptanol-1 and -4, -28.0'; 0, heptanol-4, -30.9".
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cuts a length S,/R log e log ek'2sh from the axis. These lines are given in Figure 3 for both the mixtures and the pure compounds, whereby for the pure compounds also points determined by M i d d e l h ~ e k ' ~a t~20 '~ and 30" with a coaxial line have been added. Values of E, and S, are given in Table I. Table I Wt % heptanol-1
100 74.85 50.68 24.74 0
Ea
Sa.
kcal/mol
oal mol-1 deg-1
7.9 8.9 11.0 13.1 15.4
9.0 11.3 18.5 25.8 34.9
Results Measured values of E' and E" can consistently be described by one relaxation time. Typical Cole-Cole plots are shown in Figures 1 and 2. Deviations from the semicircle are not greater than for the pure compounds, as shown especially by Figure 2. To calculate values of Ea and Safrom the relation
log ( v O / T )was plotted against 1/T. The straight line fitting best with the points obtained in this manner was computed according to the least-square criterion. The slope of this line amounts to -Ea/R log e, and this line The Journal of Physical Chemistry
Discussion Since our results show that mixtures of heptanol-1 and heptanol-4 have a principal dispersion range with a single relaxation time, although these heptanols are characterized by strongly divergent activation enthalpies, the breaking of the hydrogen bond cannot be the rate-determing step for the dielectric relaxation. Denney and Cole,2owho measured mixtures of methanol (18) W. Dannhauser, L. W. Bahe, R. Y. Lin, and A. E'. Flueokinger, J . Chem. Phys., 43,257 (1966). (19) P.Bordewijk, Thesis, Leiden, 1968. (20) D. J. Denney and R. H. Cole, J . Chem. Phys., 23,1767 (1955).
DIELECTRIC BEHAVIOR O F MIXTURES O F HEPTANOL-1 AND HEPTANOL-4
20 320
340
360
,
I
I
380
400
420
--, I
440
105
460
T('K)
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heptanol-1; 0, Figure 3. R a t e plots of log vo/T us. 1/T: mixture of heptanol-1 and -4 (3 :1); 0, mixture of heptanol-1 and -4 ( 1 : l ) ; A, mixture of heptanol-1 and -4 (1:3); X , heptanol-4.
and propanol-1, found for these mixtures also a principal dispersion range with a single relaxation time. They considered this not inconsistent with the viewpoint that changes in hydrogen bonding are an essential element in the relaxation process, because the necessary energy and configurations must first be realized from interactions with the surroundings. We cannot agree with this argument, because the point a t issue is not the manner in which the energy is supplied by the surroundings, but the question of how much energy has to be supplied. When the breaking of the hydrogen bond is the rate-determing step, the fact that different bonds need different energies to break must lead to a superposition of relaxation times. Therefore, the theory of Bauer, Magat, and Brot cannot be valid. I n the latter theory the step from linear association to a distribution of multimer sizes cannot be assailed. It is possible, however, to criticize the supposition that if the relaxation were caused by rotation of the multimers, a distribution in multimer sizes would result in a distribution of relaxation times. This supposition would follow from Debye's relaxation theory, which uses the model of a particle with the dimensions of the molecule imbedded in a continuum with the viscosity of the
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liquid. Preference must be given to Kauzmann's model, in which the relaxation is caused by a process disturbing the order in a microcrystalline area of the liquid. As a result, an alcohol with a distribution of multimer lengths representing a mixture of different particles need not show a distribution or a superposition of relaxation times. Nevertheless, one must reject the assumption of linear multimers maintained during the reorientation process, because the mean length of the multimers would strongly increase with decreasing temperature. This temperature dependence of the mean multimer length would lead to a temperature dependence of the activation .enthalpy, which is not found experimentally. As a model in which the size of the multimers is not dependent on temperature to such a large extent, we prefer the model of cyclic multimers. We assume these multimers to be retained during the reorientation. The model of cyclic multimers is also the only one that can explain the infrared data obtained by Kuhn and Bowman.21 Measurements in the gas phase suggest that these multimers are built up for molecule^.^^-^^ To explain the static dielectric behavior, it must be assumed that these cyclic tetramers have a high dipole moment. A possible explanation of this high dipole moment is that the oxygen and hydrogen atoms lie in two different planes parallel to each other, and that the hydroxyl group in such associates is more polar than the monomer. From the static dielectric behavior of solutions of a monoalcohol in an apolar so1vent,26-28it follows that dimers with a low dipole moment must also be assumed. The principal relaxation range is then caused by reorientation of the tetramers. According to Kauzmann, the activation enthalpy of the dielectric relaxation depends on the size of the area in which the microcrystalline order must be disturbed to make reorientation possible. If the probability that two molecules reorientate at the same moment decreases slowly or rapidly with distance, this area is called large or small, respectively. The area to be activated increases with increasing size of the particles (multimers or molecules), which is the reason why the activation enthalpy increases from methanol to tetradecanol. The area to be activated, however, also depends on the structure of the particles. Its size is especially influenced by the way in which the carbon atoms of the (21) L. P. Kuhn and R. E. Bowman, Spectrochim. Acta, 17, 650 (1961). (22) R. G. Inskeep, J. M. Kelliher, P. E. ,McMahon, and B. G. Somers, J. Chem. Phys., 28, 1033 (1958). (23) C. B. Rretsohmer and R. Wiebe, J. Amer. Chem. Soe., 76, 2579 (1954). (24) W. Weltner and K. 8. Pitrer, ibid.,73, 2606 (1951). (25) N. 9. Berman and J. J. McKetta, J. Phys. Chem., 66, 1444 (1962). (26) G. Oster, J. Amer. Chem. Soc., 68,2036 (1946). (27) R. LiBbaert, Thesis, Lille, 1962. (28) P. I. Gold and R. L. Perrine, J.Phys. Chem., 71,4218 (1967).
Volume 73, Number 10 October 1969
J. C.SHIEHAND P. A. LYONS
3258 aliphatic rest are connected with the cyclic system of associated hydroxyl groups. I n the series heptanol-1, -2, -3, and -4, the carbon atoms are bound increasingly rigidly to the system of hydroxyl groups, on the average, so that the probability that neighboring multimers must reorientate at the same moment will increase in the same way. Therefore, in this series the activation enthalpy and entropy also increase, as has been demonstrated experimentally. 'The relaxation behavior of the mixtures of heptanol-1 and heptanol-4 can be explained qualitatively with this model; in these mixtures the relaxation is also caused by the activation of an area in the liquid, and this area is larger the more heptanol-4 the mixture contains. The problem of why the monoalcohols show a principal relaxation range characterized by one relaxation
time is reduced in this way to the same problem as that of why compounds like bromobenzene show one relaxation time. According to Anderson and Ullman,2esuch relaxation behavior must be expected if the environment fluctuates rapidly as compared to the reorientation. The reason for this difference between the various movements in the liquid is not clear, however. Nonetheless, we can explain the most important aspects of the dielectric relaxation of the monoalcohols by assuming that these compounds associate to dimers with a low dipole moment and to cyclic tetramers with a high dipole moment, the latter being retained during the reorientation.
(29) J. E.Anderson and R. Ullman, J. Chem. Phys., 47,2178 (1967).
Transport Properties of Liquid n-Alkanes by J. C. Shiehl and P. A. Lyons Department of chemistry, Yale University, New Haven, Connecticut 06680 (Received February 19, 1969)
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Mutual and tracer diffusion coefficients supplementing existing data are presented for the systems n-C6Hlr n-ClzH26, n-C&6 n'C16H34, n-CsHl8 n-CleHar,and n-CloHzz n-Cl6H34 deriving from Gouy interferometric and diaphragm cell measurements. Based upon these and other reported data, the transport behavior of n-alx2D1* kanes can be summarized as follows. (1) The Darken equation holds; Le., D12 = (xlDZ* d In fIxl/d In x1 (This is consistent with Van Geet and Adamson's finding for the system n-CsH18 n-Cl~H26.~) (2) The activation energy for the tracer diffusion of any n-alkane is the same in any n-alkane medium at a given density. In a medium of a given density, the size of the moving segment is independent of the chain length. (3) For all binary n-alkane mixtures, Dlz/(dlnflxl/d In xl) is a linear function of density, p , All these lines extrapolate to zero mobility at p = 0.84, corresponding to a supercooled melt of an n-paraffin of very high molecular weight. The slopes of these lines are linear functions of 1/G2, where nl, n2 are the numbers of carbon atoms in the two components. (4) The tracer diffusion coefficient of any linear alkane C, in any n-alkane medium (either pure liquid or mixture) is determined only by n and the density of the medium at a given temperature. ( 5 ) Deviation from linearity of plots of DI2against p can be used to determine the thermodynamic terms, d In flsl/d In xl, hence also activity coefficients and excess free energies. (6) Viscosities of n-alkanes (pure liquids or mixtures) are simple monotonic functions of density. These rules describe accurately the transport behavior of those n-alkanes which have been studied and should define those properties for any liquid n-alkane system or melt. Rules 2 and 4 are slightly modified versions of the application of the principle of congruence first used in this fashion by Van Geet and Adamson.2
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Introduction This study was started to supplement the meager information on transport phenomena in systems with negative deviations from Raoult's law. As the work developed, the aim reduced to an attempt to answer a few specific questions. Is it possible to completely describe transport phenomena for simple n-alkane systems? Seen as a class, can their transport properties be rationalized? The Journal of Physical Chemistry
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Experimental Section Mutual diffusion coefficients were measured over the entire range of concentrations for the system n-C6H14 n-CizHz6 a t 25 and 35" and for the system n-CloHzz n-CieHad a t 25". The Gouy results (with an expected
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(1) Chemistry Department, Wesleyan University, Middletown, Conn. 06467. (2) A. L. Van Geet and A. W. Adamson, J. Phys. Chem., 68, 238 (1964).
