1814
WALTERDANNHAUSER AXD ARTHUR F. FLUECKINGER
Dielectric Constant and Intermolecular Association of Some Liquid Nitriles
b j Walter Dannhauser and Arthur F. Flueckinger Department of Chemistry, State University of New Y o r k , Bufalo 14, N e w York
(Receiued January 9.9, 1064)
Densities and equilibrium dielectric constants of propio-, acrylo-, pivalo-, benzo-, and 2,6-dimethylbenzonitrile have been measured from near their melting points to about 200 ', The Kirkwood-Frohlich correlation factor is less than unity in each case and generally increases with increasing temperature. The dielectric data are analyzed on the basis of an equilibrium between monomer and an antiparallel dipole pair dimer, and the nature of the association is discussed.
Introduction There is convincing evidence from a variety of experimental investigations that nitriles associate with polar molecules in solution or in the pure liquid (self-association). What is not clear is the nature of the interaction. In some instances, where a good proton donor is present, the interaction is described in terms of hydrogen When the proton donor is weak or absent, the discussion has involved electrostatic dipole-dipole interactions4i5 or actual chemical bond formation6,' involving the lone pair on the nitrogen atom of the nitrile group. Since the distinction between these types of interaction is not a t all sharp, we hardly can expect that any one experimental approach will resolve the question unambiguously. It is therefore desirable to study this problem with as many different techniques as possible. This paper reports the results of an investigation of the temperature dependence of the dielectric constant of several pure liquid nitriles and the interpretation of the data in terms of specific dipole interactions. Experimental Materials. Acrylonitrile (Eastman P5161), propionitrile (Eastman 528), pivalonitrile (K and K Laboratories Lot 36830L), and beneonitrile (Matheson Coleman and Bell 1205) were fractionally distilled in an 80 x 1 cm. glass helix-packed column operated a t high reflux. The middle fractions were retained, were stored in a desiccator until required, and were injected into the cells with a syringe in order to minimize exposure to the atmosphere. Density, index of refraction, and analysis by gas chromatography served as criteria of sample purity. The Journal of Physical Chemistry
2,6-Dimethylbenzonitrile (E( and K Laboratories Lot 39600) was recrystallized twice from petroleum ether. The resulting white crystalline material melted a t 89-90' (lit.* 90-91'). Bridge and Cells. The transformer ratio-arm admit-; tance bridge has been described before.' A glass-" jacketed cell' was used at temperatures below the normal boiling points and a stainless steel autoclave-type cell9 was used for superheated liquids. The stray capacity of the glass-jacketed cell, and thus its geometric capacity, has been more precisely determined since our previous paper and the agreement between dielectric constants obtained in both cells was excellent. Dilatometry. The dilatometers and method have been described el~ewhere.~
Results Dielectric constants were measured at several frequencies as a function of temperature and these values were plotted on a large scale graph. Data interpolated from these curves are presented in Table I. Propionitrile degraded noticeably at the higher tempera(1) W. Dannhauser and A. F. Flueckinger, J . Chem. Phys., 38, 69 (1963). (2) S. S . Mitra, ibid., 36, 3286 (1962). (3) A. Allerhand and P. von R. Schleyer, J . Am. Chem. Soc., 8 5 , 8 6 6 (1963). (4) J. D. Lambert, et al., Proc. Roy. Soc. (London), A196, 113 (1949). (5) A. M. Saum, J . Polymer Sci., 42, 67 (1960). (6) F. E. Murray and W. G . Schneider, Can. J . Chem., 33, 797, (1955). (7) C. D. Ritchie and A. Pratt, J . Phys. Chem., 67, 2499 (1963). (8) R. Scholl and F. Kacer, Bey., 36, 327 (1903). (9) W. Dannhauser and L. W. Bahe, J . Chem. Phys., 40,3058 (1964).
DIELECTRIC CONSTANT
AND
tures, and acrylonitrile polymerized and degraded, so that the results for these compounds a t temperatures above 150’ are somewhat uncertain. The other materials were thermally stable, and it was possible to obtain consistent dielectric data on both the heating and cooling portion of %t run. No dispersion was noted for any of the compounds. Table I : Dielectric Confitants of Liquid Nitriles t , “C.
-80 -60 -40 -20 0 20 30 40 60 80 100 120 140 160 180 200
Acrylonitrile
(55.2)” 49.8 44.5 40.2 36.3 33.0 31.5 30.0 27.3 24.8 22.5 20.4 18.3 16.1 (14.0)“
..
’ Slight extrapolation
Benzonitrile
2,B-Dimethylbenzonitrile
..
..
.. ..
..
.. ..
f’ropionitrile
Pivalonitrile
.. 41.6 38.3 35.1 32.2 29.7 28.6 27.5 25.2 23.0 21.0 19.2 117.4 15.7 14.0 12.4
,.
.. 21.1 20.2 19.4 17.8 16.4 15.1 13.9 12.8 11.8 10.9
..
.. .. 27.8 25.9 25.1 24.4 22.9 21.3 20.0
18.7 17.5 16.3 15.0
..
.. .. ..
.. .. ..
.. .. 16.8 15.3 14.1 13.0 12.1 11.2
of data.
There appears to be only one previous determination of the dielectric constant of acrylonitrile. The reported value,’O E = 38 a t 25’ and 30 Mc., is so much larger than our results that we wonder if it may be a misprint. In the vicinity of room temperature, where a comparison with literature values is feasible, our results for propionitrile are about 7% higher than previous work,” which all dates to about 1900. Our results for benzonitrile check well with the very care-. ful work of and Sugden13 while Davies14recently reported dielectric constants for pivalonitrile are slightly lower than ours but have exactly the same temperature dependence. The dielectric constant of 2,B-dimethylbenzonitr[le has not been reported before. The densities of acrylonitrile, propionitrile, and benzonitrile are related to the centrigrade temperature by the equation p == po
1815
ASSOCIATION O F LIQUIDNITRILES
-
at
- bt2
Values of the constants, obtained by graphical analysis of our data, axe presented in Table 11.
Discussion The most general theory of the dielectric constant of polar liquids is that due to Kirkwoodl6 and Froh-
Table 11: Parameters of the Density Equation: p = PO - at - btz
Acrylonitrile Propionitrile Benzonitrile Pivalonitrile“
PQ
a X lo*
0.828 0.802 1.025 0.7423
11.1
0
10.0 9.16 9.75
5.8
b X
Temp. range
lo7
0 0
-60-170” -65-260” 0-220° 20-60
a Data of M. Davies, Trans. Faraday SOC.,58, 1705 (1962). We have extrapolated densities to 180” with these constants.
lich.16 Cole” has recently presented a lucid analysis of the approximations that are required to transform their formally correct, but experimentally untestable, formulations into the working equation Eo
=
E,
+
+2
$- ___ 3Eo 260
6,
~
)
4nNppo2 ~
3MkT 9
(1)
Here eo is the equilibrium dielectric constant, E , is the high frequency dielectric constant characteristic of induced polarization (which we have approximated by e, = l . l n 2evaluated ~ a t each test temperature by the Clausius-Mossotti equation), po is the dipole moment of the molecule under vacuum, M is the molecular weight, N is Avogadro’s number, p is the density, and kT is the thermal energy. The correlation factor, g, first introduced by Kirkwood,16 is a measure of those short range intermolecular forces that lead to specific dipole-dipole orientations. I n the absence of such forces, g = 1, eq. 1 reduces to the formulation deduced by OnsageP from a purely macroscopic model. According to the Kirkwood-Frohlich theory, g values greater than unity are explained as being due to a predominantly parallel alignment of neighboring dipoles; g values less than unity to an antiparallel alignment. The temperature variation of the correlation factor may then be analyzed in terms of equilibria ~
(10) H. S. Davies and 0. F. Wiedeman, I n d . Eng. Chem., 37, 482 (1945). (11) A. A. Maryott and E. R. Smith, “Tables of Dielectric Constants of Pure Liquids,” National Bureau of Standards Circular 514, U. 9. Govt. Printing Office,Washington, D. C . , 1951. (12) A. 0. Ball, J . Chem. Soc., 570 (1930). (13) S. Sugden, ibid., 768 (1933). (14) C. Clement and M. Davies, Trans. Faraday Soc., 58, 1705 (1962). (15) J. G. Kirkwood, J . Chem. Phys., 7, 911 (1939). (16) H. Frohlich, “Theory of Dielectrics,” 1st Ed., Oxford University Press, New York, N. Y., 1949. (17) R. H. Cole, “Progress in Dielectrics,” Vol. 3, J. B. Birks, Ed., Heywood and Co., London, 1961, p. 47 ff. (18) L. Onsager, J. Am. Chem. Suc., 58, 1486 (1936).
Volume 68, Number 7
J u l y , 1964
1816
WALTERDANNHAUSER AND ARTHUR F. FLUECKINGER
involving the intermolecular forces which cause the specific alignment. However, Buckley and Maryottlg have suggested that g values differing from unity, and also the temperature variation of g, may be interpreted by means of a simple modification of the Onsager equation without recourse to a molecular model involving specific intermolecular forces. Their proposed modification consists of assuming a spheroidal, rather than a spherical, shape for the molecular cavity which contains the dipole (the cavity has the molecular volume) and in maintaining the volume of the cavity independent of the temperature. Buckley and Maryott tested their theory with numerous examples, including propionitrile and benzonitrile. They expressed their results in terms of a deviation factor
G, =
po2 (calcd.)
(expt1.1 where PO (calcd.) is the dipole moment calculated from their eq. 2 and p0 (exptl.) is the experimentally determined dipole moment under vacuum. Over a limited temperature range (50’ for propionitrile and 70’ for benzonitrile) they found that G, remained substantially constant and that the values of the cavity eccentricity required for a reasonable fit correlated well with those obtained from molecular models. We have repeated their calculations over the much wider temperature range of our experiments with the following results: the deviation factors do remain essentially constant with temperature and they can be adjusted to unity for each compound by a suitable choice of the cavity eccentricity. However, we were not consistently able to use eccentricities obtained from molecular models for this adjustment. For example, acrylonitrile and pivalonitrile deviate from Onsager’s (unmodified) equation by about the same amount but their eccentricities vary greatly (acrylonitrile = 0.89 ; pivalonitrile = 0.56 from Stuart models). These values, when used in Buckley and Maryott’s equations, lead to deviation factors of about 1.3 and 0.87, respectively. Xevertheless, in view of the constancy of the deviation factor that Buckley and hfaryott’s modification provides, we must admit that dielectric data alone would provide inconclusive evidence for molecular association in these nitriles. But the evidence for association is varied and does not depend on dielectric theory for its validity. Thus, we were interested in trying the Kirkwood-Frohlich theory, which specifically introduces intermolecular forces, and comparing the results of such an analysis with those of other workers using other techniques. pO2
The Journal of Physical chemi8tru
Experimental correlation factors, gexptl,were calculated from eq. 1 with our dielectric constant and density data. (We have assumed that the density and index of refraction of 2,6-dimethylbenzonitrile are equal to those of benzonitrile and we used Davies’14 data for pivalonitrile.) The dipole moments of acrylonitrile (3.9 D.), propionitrile (4.0 D.)? and benzonitrile (4.42 D.) are those quoted by SmythZ0from vapor phase measurements. We assumed the dipole moment of pivalonitrile to be identical with that of propionitrile since its moment in benzene solution is essentially the same as propionitrile’s in benzene, and it is generally observedz0 that the moments of isomeric aliphatic molecules are identical. Davies14 quoted po = 3.6 D. for piralonitrile from measurements in the pure liquid (assuming g = l ) , but we believe that this value is too low. 20a The dipole moment of 2,6-dimethylbenzonitrile was estimated to be 4.0 D., the vector sum of the benzonitrile and m-xylene moments. 2o In Fig. 1 we have plotted gexptlagainst temperature. All the curves are similar in showing correlation factors less than unity and, excepting that of 2,gdimethyl-
1.0
c
0.9
. 0.8 D
2 0.7 0.6
0.5 I
-80
I
-40
I
I
0
I
I
I
40 t,
oc.
I
80
I
I
120
I
I
160
I
I
200
Figure 1. Experimental correlation factors a8 a function of Centigrade temperature. Data points are: 0, acrylonitrile; 8, propionitrile; 0 , pivalonitrile ; 0 , benzonitrile; Q,
2,6-dimethylbenzonitrile.
benzonitrile, with a positive temperature coefficient. This behavior is to be contrasted with that observed for hydrogen cyanide and cyanoacetylene, where the g’s are greater than unity and decrease with increasing temperature. From these qualitative observations we conclude that the intermolecular association that is suggested in this (19) F. Buckley and A. A. Maryott, J . Res. Natl. Bur. Std., 53, 229 (1954). (20) C.P.Smyth, “Dielectric Behavior and Structure,” McGraw-Hill Book Co., Inc., New York, N. Y., 1957. (20a) NOTEADDEDIN PROOF.-L. J. Nugent, D. E. Mann, and D. R. Lide, Jr., J . Chem. P h y s . , 36, 965 (1962). have measured the dipole moment of pivalonitrile by Stark effect microwave studies. They report PO = 3.95 i 0.05 D.
1817
DIELECTRIC CONSTANT AND ASSOCIATIOX O F L I Q ~ I NITRILES D
study, indicative of an antiparallel orientation of near neighbor dipoles, differs in type rather than degree from the hydrogen bonding which was assumed to account for the head-to-tail association in HCN and HCE-C-CN. Recent spectroscopic investigations have shown that nitriles are generally excellent proton acceptors with such donors as alcohols and phenol. Mitra2interpreted his results to indicate that the OH. . . N bond is even stronger than the O H . . . O bond, but Allerhand and von Schleyer3 have criticized his technique of using small concentrations of the donor in pure acceptor media. In any event, since the only nitriles that have been reported to hydrogen bond in the pure liquid are HCN and HCCCN, and these have uniquely acidic hydrogens, we conclude that the lack of self-hydrogen bonding of most nitriles is due to their weakness as proton donors. Thus, even in the case of 2,B-dimethylbenzonitrile where hydrogen bonding through the relatively acid parahydrogen would lead to colinearity of the dipole moments, there is no evidence from our dielectric data to indicate any head-to-tail association. The second virial coefficient of acetonitrile vapor has been interpreted4 in terms of a monomer-dimer equilibrium. The dimer was assumed to have the antiparallel dipole configuration and from the temperature dependence of the second virial coefficient Lambert obtained -5.2 kcal./mole for the enthalpy of association. The electrostatic energy of an antiparallel dipole pair relative to the separated monomers, choosing reasonable values for M~ and the distance of closest approach, is of this order of magnitude and was cited as corroboration of thLe model. The nature of the interactions in liquid is much more difficult to explain than that in the gas phase, of course. S a ~ m from ,~ a copparative analysis of viscosities, boiling points, and most particularly the enthalpies of vaporization of alkanes, esters, and nitriles, has suggested that in the pure liquid phase nitriles form dimers through a specific antiparallel dipole-dipole interaction that he called dipole-pair bonding. By assuming that the only specific intermolecular interaction is the dipole-pair bond, Saum estimated the energy of this bond to be about -8 kcal./mole, which is amazingly close to the value deduced from the temperature dependence of the second virial coefficient and that calculated by electrostatics from the antiparallel model. Saum’s analysis seems highly speculative, however : and it leads to the conclusion that propionitrile is about 70% associated into dimers a t room temperature. If as many as 70% of the dipoles were associated into antiparallel pairs, whose net dipole moment would be zero, we would hardly expect the dielectric constant of
nitriles to be as large as is found. The fact that the correlation factors are only slightly less than unity also suggests that the extent of dimerization may be much less than that calculated by Saum and we were interested to see if an analysis of our dielectric data in terms of a dipole pair was reasonable. Let the equilibrium between monomers and dipolepair bonded dimer be represented as 2 A , @ Az. The equilibrium constant (mole fraction units) is then given by
K =
=
s(Az)/(z(Ai))2
(24
(nzn)/ni2 = (n/ni)(n/ni - 1)
(2b)
where nl is the number of moles of L‘monomer,”n2 is the number of moles of dimer, and n = nl nz. Our operational definition of monomer is a molecule whose correlation factor, gl, is unity, ie., one whose dipole moment is correlated on the average only with itself. The average correlation factor per molecule in the dimer, 92, is zero because of the assumed antiparallel alignment. If the experimentally determined correlation factor is identified with the weighted average of g1 and 92, we have
+
Qexptl
= zlgl
+ 2x292
= 21 =
(3)
n1/n
so that we can substitute into eq. 2b and obtain =
( l / d ( l / q - 1)
(4)
Finally, from standard thermodynamics, we have the result that a plot of log K against l/T°K. should yield a curve whose slope is - A H 0 / 2 . 3 R . Such curves are shown in Fig. 2, and the calculated thermodynamic functions are given in Table 111.
Table I11 : Thermodynamics of Antiparallel Dipole-Pair Formation a t 298°K.
-AF”, koal./mole
-AHo, koel./mole
Acrylonitrile Propionitrile Pivalonitrile Beneonitrile
-0.64 -0.47 -0.65 0.07
0.73
2,6-Dimethylbenzonitrile
-0.88
-0
1.00 1.11 1.18
-A P , e.u./mole
4.63 4.94 5.90 3.72 2.92
We note, first of all, that this simple model appears to be valid over the entire temperature range. (The upsweep of the acrylonitrile curve a t high temperatures is presumed to be due to degradation and/or polymerization.) The equilibrium constants are generally less than unity, and the mole fraction of the nitrile Volume 68,Number 7 July, 1964
1818
WALTERDANNHAUSER AND ARTHUR F. FLUECKINGER
0.2
0.1 2.2
1 2.6
I
I
3.0
3.4
I
3.8 1000/T,OK.
I 4.2
I 4.6
5.0
Figure 2. Equilibrium constant for dipole-pair dimer formation (mole fraction units) as a function of reciprocal absolute temperature. Data points are: 0, acrylonitrile; 9, propionitrile; 8, pivalonitrile; a, benzonitrile; @,
2,6-dimethylbenzonitrile.
present as dimer a t room temperature is about 0.25 (0.40 for benzonitrile) in contrast to 0.7 estimated by Saum. The significance of the thermodynamic data depends on what is meant by the “monomer” and “dimer” state. Saum6 suggests that the dimer is the specific dipole-pair, and he calculated the potential energy of the antiparallel configuration of two CN dipoles separated by the van der Waals distance of closest approach. This is -8 kcal./mole relative to the isolated dipoles. However, in the pure liquid the monomer is not the isolated dipole, but merely one whose potential energy relative to any specific orientation of a near neighbor(s) is less than kT. If we consider two point dipoles and ask at what separation their potential energy, averaged over-all relative angular orientations2I and neglecting interactions with other neighbors, becomes equal to kT1 this turns out to be 6.8 8. at 300°K. for dipoles of 4.0 D. The average distance of separation in liquid njtrjles as deduced from the molar volume is between 5 and 6 8. The potential energy of two antiparallel dipoles (4 D.) separated by 6 8. is also just about to kT (which imp1ies that if there is a stable antiparallel orientation the dipoles must be closer together than 6 i.), and it is not difficult to visualize a model where the difference in energy between the “random” and the dimer state is about 1kcal./mole. The Journal of Physical Chemistry
Some additional evidence for this conjecture may be deduced from D a ~ i e s ”investigation ~ of the dielectric relaxation of pivalonitrile and other symmetrical, polar molecules. He finds that the activation energy for relaxation is very small, characterjstically about 1 kcal./mole, which indicates that there is very little potential energy difference between various orientations in the liquid. This is in general agreement with our conclusions. Additional insight on the extent of association in the liquid has been obtained by applying Hildebrand’s rulez2to nitriles and corresponding hydrocarbons and alcohols. According to Hildebrand, the slope of a log-log plot of vapor pressure against absolute temperature evaluated at equal vapor volumes is a measure of the entropy of vaporization to an ideal gas. Such a plot, with data from the literaturelZ3shows that AS,,, of nitriles is only slightly greater than that of the corresponding hydrocarbons, for which we expect essentially no liquid association, and considerably less than that of the corresponding alcohols, which are generally acknowledged to be highly associated. The conclusion that the degree of association in pure liquid nitriles is slight must be tempered by the fact that the entropy of dimerization in the liquid would probably be small and that this technique is rather insensitive. Murray and Schneider6 have suggested k h a t the dipole-pair configuration is unreasonable because it places the nitrile groups, which are regions of high aelectron density, in close proximity. They prefer to picture the interaction as having a skewed-T configuration as
R-C=N N
4
C
R in which the lone pair interacts with the relatively positive carbon of a neighboring nitrile. We suspect that such a configuration would become increasingly unlikely as R becomes large and bulky. Along these lines we note that our results for pivalo- and 2,6-dimethylbenzonitrile are essentially the same as for propio- and benaonitrile, for example. Furthermore, the fact that the correlation factors are less than unity (21) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids,” John Wiley and Sons, Inc., New York, N. Y . , 1954. (22) J. H. Hildebrand, “Regular Solutions,” Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962, p. 59. (23) J. Timmermans, “Physico-Chemical Constants of Pure Organic Compounds,” Elsevier Publishing CO., Inc., New York, N. Y., 1950.
DIELECTRIC CONSTANT AND ASSOCIATION OF LIQUIDNITRILES
is a strong indication that the prevalent configuration must be generally antiparallel. However, if the dimer is not exactly antipairallel it will have a finite dipole moment and our thermodynamic calculations would then have to be revised in the direction of greater extent of association. We conclude that the antiparallel dipole pair is a reasonable model which accounts for the dielectric properties of these nitriles. However, the stability of the dimer is probably not as great as suggested by Saum and the extent of association is also correspondingly lower. Obviously, a great deal of work is still
1819
required to resolve the discrepancies and ambiguities mentioned above. A determination of the crystal structure of some of the simpler nitriles would be of particular value.
Acknowledgment. A. F. F. has been supported by B National Science Foundation Summer Fellowship for Secondary School Teachers (No. 71075). This work and its publication has been supported by the Directorate of Chemical Sciences, Air Force Office of Scientific Research, under Contract AF 49(638)-939 and Grant AF-AFOSR-271-63.
Volume 68, Number 7 July, 1964
