INTERMOLECULAR ASSOCIATION IN STERICALLY HINDERED OCTANOL ISOMERS
3273
Dielectric Study of Intermolecular Association in Sterically Hindered Octanol Isomers1 by Gyan P. Johari and Walter Dannhauser Department of Chemistry, State University of N e w York at Buffalo, Buffalo, New York 1421.4 (Received April 9,1968)
The equilibrium dielectric constant of %methyl-and 3-methyl-4-heptanoland also 2,bdimethyl-, 2,4-dimethyl-, 2,2-dimethyl-, and 3,4-dimethyl-3-hexanol has been measured over a wide range of temperature. All isomers have closely similar dielectric behavior quantitatively as well as qualitatively. The Kirkwood correlation factor is less than unity at all temperatures in each case. The results suggest the existence of a monomerdimer (ring) association and equilibrium constants for ring-dimer formation are deduced. AH” for H-bond formation in rings is estimated as -4.5 kcal/mol; AS” per mole of H-bond formation varies from -12 to - 16 eu.
Introduction The entropy of a dielectric is given2 by the expression
E2 be S=&+--8~ bT where So is the entropy in the absence of an applied electric field, E . Most polar liquids have a negative temperature coefficient of the dielectric constant, and the field thus decreases the entropy by partially aligning the dipoles. If be/bT > 0, the field increases the entropy, implying a randomization superimposed on the alignment due to the field, and this in turn implies that the zero-field “structure” must be highly ordered in a very specific manner. (For this reason, be/bT of crystals may be positive.) I n a previous p a p e P of this series, we presented dielectric data pertaining to some isomeric octyl alcohols that exhibited both types of behavior mentioned above. Also, for some of the compounds of that study, de/bT changes sign as a function of temperature, implying a temperature-dependent fundamental change in the liquid structure. The alcohols exhibiting this behavior are all characterized by a sterically hindered environment around the -OH group; i.e., they all have an alkyl group@) on the same or the carbon atom neighboring that to which the -OH is attached. We concluded that such alcohols associate intermolecularly to form essentially planar, nonpolar ring-dimers a t high temperatures and thah these species were transformed to linear chain n-mers as the temperature decreased. As part of our continuing study of liquid structure by dielectric methods, we wanted to examine several more examples of compounds which might show this interesting and rather unusual behavior. We have continued to use jsomeric octanols as test samples in order to compare their behavior with those compounds studied previously. In this paper, we report dielectric
data for six isomeric octanols and demonstrate that intermolecular association into nonpolar ring species is common to them all and is easily predictable for other species.
Experimental Section Materials. 3-Methyl-4-heptanol (3 ;4), 2-methyl-4heptanol (2;4), and 2,5-dimethyl-3-hexanol (2;5;3) were obtained from Chemical Samples Co., Ohio. These samples have a quoted purity of better than 98%. 3,4-Dimethyl-3- (3;4;3), 2,4-dimethyl-3- (2;4;3), and 2,2-dimethyl-3-hexanol (2;3;2) were “Baker” grade. All samples were refluxed over CaHz and fractionally distilled a t 50 :1 reflux ratio. The samples were identified by their boiling point, density, and refractive index. See Table I. Bridges and Cells. A General Radio Type 1615 A bridge was used for the capacitance measurements. Readings of capacitance were taken a t several frequencies to ensure that the calculated dielectric constants are free from dispersion or polarization errors. A three-terminal, guarded, parallel-plate cell, which has been described earlier,abwas used. Because of the very small dielectric constant of these liquids, the cell with a nominal geometric capacitance of 15 p F was used. The cell constant was determined before each run. Corrections were applied for the small stray capacitance, which was determined by calibration with cyclohexane and CC14, and the temperature coefficient of the cell constant. Temperatures were measured with a calibrated thermocouple inside the cell. Densities were measured a t 25” with a pycnometer. These values are summarized in Table I. Densities a t (1) Supported by the Office of Saline Water, U. S. Department of the Interior, via Grant 14-01-0001-604, (2) H. Frohlich, “Theory of Dielectrics,” 1st ed, Oxford University Press, New York, N. Y.,1949. (3) (a) W. Dannhauser, J. Chem. Phys., 48, 1911 (1968); (b) W. Dannhauser and A. F. Flueckinger, ibid., 38, 69 (1963).
Volume 7.2, Number 9 September 1068
GYANP. JOHARI AND WALTERDANNHAUSER
3274 Table I : Physical Properties of Octanol Isomers Properties
Density (25') /ml Boiling point,'& n26D
2;2;3
2;4;3
3;4;3
2;6;3
2 ;4
3;4
0.8213 154.5 1.4250
0.8311 159 1.4285
0.8409 159.5 1.4325
0.8132 157.5 1.4212
0.8103 165 1,4328
0.8331 166.5 1,4223
other temperatures were calculated by the equation determined p1 = p o - at. The value M = 7 X dilatometrically for 3;4, was taken to be the same for all isomers. 3.6
Results Equilibrium dielectric constants for 3;4, 2;4, 2 ;2;3, 2;4;3,3;4;3,and 2;5;3were measured from about 140 to -80", or until the sample froze. The measured equilibrium dielectric constants were plotted against temperature on a large scale. Interpolated values at integral temperatures for all the six isomer are summarized in Table 11.
3.2
2.9
PA
Table 11: Dielectric Constant of Octanol Isomers as a Function of Temperature t,
oc
-80 -70 -60 -50 -40 -20 0 20 40 60 80 100 120 140
2;4
3;4
2;2;3
2;4;3
4.350 3.982 3.712 3.522 3.388 3.301 3.344 3.476 3.661 3.754 3.759 3.678 3.539 3.336
...
... ...
...
2.600 2.598 2.601 2.618 2.702 2.878 3.123 3.376 3.550 3.618 3.541 3.386 3.280
...
... ...
2,653 2.779 3.005 3.284 3.487 3.563 3.524 3.376 3.251
2.480 2.448 2.443 2.480 2.613 2.816 3.125 3.461 3.624 3.655 3.572 3.435 3.321
2;6;3
3;4;3
2.475 2.425 2.396 2.384 2.384 2.520 2.715 2.965 3.240 3.445 3.534 3.540 3.414 3.271
2.486 2.500 2.519 2,541 2.564 2.664 2.852 3.115 3.355 3.497 3.528 3.467 3.336 3.236
Figure 1 shows the temperature dependence of the equilibrium dielectric constants of these isomers. Literature data,4 available for 2;4 and 3;4, are also plotted for comparison. We note that our data for 2;4 are uniformly higher and have a qualitatively diff erent temperature dependence than those of Smyth and stoop^;^ for 3;4, their data are so different, qualitatively as well as quantitively, that we suspect there was a mistake in the identity of their sample.
Discussion We reported in an earlier papera&that, according to their dielectric behavior, pure liquid octanol isomers can be grouped roughly into two categories: (1) isomers which show the ('conventional" dielectric behavior typical of most polar liquids (ie., the dielectric constant increases monotonically with decreasing temperature) ; The Journal of Physical Chemistry
Figure 1. Equilibrium dielectric constant of isomeric octanols aa a function of temperature. Filled circles and inset are data of Smyth and Stoops4 for 2;4 and 3;4, respectively.
these are the isomers in which the -OH group is relatively less sterically hindered; and (2) isomers in which the dielectric constant goes through a maximum with decreasing temperature; these are the isomers in which the -OH group is more sterically hindered because of the presence of an alkyl group close to it (within the chain). As seen in Figure 1, the six isomers under discussion all follow the behavior of the second category. Starting a t the highest temperature, the dielectric constant increases with decreasing temperature, there is a reversal near 70", and the dielectric constant then decreases with decreasing temperature. In 2;4, 2;5;3, and 2;4;3, there is another reversal of the temperature dependence of dielectric constant a t very low temperatures and the dielectric constant then increases rapidly with decreasing temperature. From the profile of the so-T plots of 3;4, 2;2;3, and 3;4;3, it appears that in these isomers the reversal in the temperature dependence of so would occur at temperatures below -80". As in earlier papers,3&we discuss the equilibrium dielectric polarization in terms of Kirkwood's theory2t6 which permits a specific representation of near-neighbor interactions. According to the Kirkwood-Frohlich theory, a correlation factor, g, is defined as (4) C.
P. Smyth and W. N. Stoops, J. Amer. Chem. Sac., 51, 3339
(1929).
(6) J. G.Kirkwood, J. Chem. Phys., 7,911 (1939).
INTERMOLECULAR ASSOCIATION IN STERICALLY HINDERED OCTANOL ISOMERS eo = e,,
+ 2eo 3eo+
+2
~
e,
24~Np~02 ___ (2) 3MkT
(',3 )
Here, eo is the equilibrium dielectric constant, M is the molecular weight, N is the Avogadro number, k is the Boltzmann constant, p is the density of the liquid, and bo is the molecular dipole moment i n vacuo, which we have taken as 1.68 D for all the isomers. The limiting high-frequency dielectric constant characteristic of induced polarization, e,, has been taken as 1.05 n2D, evaluated at each temperature by assuming the validity of the Clausius-Mossoti relation.6 The correlation factor, g, is EL measure of short-range intermolecular forces, such as hydrogen bonding, which give rise to specific dipole-dipole orientation. The magnitude of g depends on both the geometry and extent of association. A correlation factor greater than unity is interpreted as being due to ]predominantly parallel alignment of nearneighbor dipoles, less than unity to an antiparallel alignment. Values of the correlation factor calculated from eq 2 are plotted against temperature in Figure 2. For all isomers except 2;4, the correlation factor is less than unity and decreases with decreasing temperature. This decrease is relatively very small above 100". At low temperatures the correlation factor goes through a shallow minimum near -60" for 2;4;3 and 2;5;3 and a t -40" for 2;4. The correlation factor of 3;4;3 and 3;4 drops to less than 0.05 a t very low temperatures and becomes relatively insensitive to changes in temperature. In terms of the Kirkwood-Frohlich theory, the positive temperature coefficient of g indicates an increase in the predominantly antiparallel association with decreasing temperature in these liquids. We suggest that the extraordinarily small correlation factor of these compounds is due to intermolecular association into small rings where, as in carboxylic acid dimers, the molecular dipoles largely cancel each other. The upsweep in the g's of 2;4, 2;4;3, and 2;5;3 indicate the existence of at ring-chain equilibriumaa and that chain formation is favored at low temperatures. Using the $!&mespecific molecular model as earlier,aa we attempt to make the foregoing conclusions quantitative. For all isomers, at temperatures where the correlation factor is less than unity, we consider monomers in equilibrium with ring dimers of zero dipole moment.? For the monomer-ring dimer equilibrium AI
3275
+ AI * A2
(3)
where AI refers to a monomer and Az to a ring dimer, the equilibrium constant (using volume fraction units) is related to ithe correlation factor as3* (4) Equilibrium constants calculated from eq 4 are plotted 1ogarithmicall.y against reciprocal temperature in Fig-
0.4
0.0 193
2.33
273
413
453
493
Figure 2. Kirkwood correlation factor as a function of temperature.
IOC
(B
2;4 314
IC
0 212;s B 2i4;3 0 2;5;3
e
I
3;4;3
B
1000/To K
0.L
2
3
4
5
Figure 3. Equilibrium constant for ring-dimer formation (volume fraction units) plotted logarithmically against reciprocal absolute temperature. Dashed line corresponda to a slope of 9.0 X 103/2.3R.
ure 3. AH", AS", and AGO for ring-dimer association in the pure liquid were estimated from these plots and are listed in Table 111. We have also included our (6) The choice of e, is quite critical for liquids whose eo is very close We have chosen e, = 1.06 ~ Q asD a reasonable compromise to t,. between 1.1 nZD, which was found to be too large from our relaxation measurements, and 1.0 n%, which does not include atomic polariraD not affect tion. However, calculations of g based on 6, = 1.1 ~ Z do our conclusions. (7) We do not claim that dimers are the only ring species. In order to keep the model relatively simple, we have chosen dimers, It might be noted further that very large rings cannot account for the very low values of g. Because of the flexibility of H bond, the nearneighbor correlation in very large rings is not essentially different from that in long chains.
Volume 72, Number 9 September 1968
GYANP. JOHARI AND WALTER DANNHAUSER
3276 Table I11 : Thermodynamic Parameter for Ring-Dimer Formation in Pure Liquid Octanol Isomers, Based on Volume Fraction Units
Liquid
2-Methyl-4-hep tan01 3-Methyl-4-heptanol 2 ;2-Dimethyl-3-hexanol 2 ;4-Dimethyl-3-hexanol 2 ;5-Dimethyl-3-hexanol 3;4-Dimethyl-3-hexanol 2-Methyl-3-heptanol' 3-Methyl-3-heptanola 4-Methyl-3-heptanol' 5-Methyl-3-hep tanola a
-AHo, koal/ mol
- AGOaes,
8.7 8.8 9.6 9.7 9.6 8.8 8.6
7.7 9.0 10.5
ked/
- AS0zes,
mal
eu/mal
0.103 0.636 0.774 0.610 0.780 0.694 0.41 0.78 0.24 -0.35
28.9 27.3 29.5 30.7 29.7 27.3
27.2 23.2 29.4 36.6
Taken from ref 3a.
values3&of these parameters for 2;3, 3;3, 4;3, and 5;3 for comparison. The enthalpy per mole of H-bond formation in ring dimers ranges from 4.3 to 4.8 kcal in these isomers. These values are so closely similar that they can be approximated (within the experimental error) by a singly value of AHo = 4.5 kcal/mol. This is in contrast to the molar enthalpy of H-bond formation in chain species*a which is quite characteristic of the isomers and ranges from 6 to 9 kcal. The apparent identity of AH" values in all the isomers of this investigation confirms that association into rings is much less specific than association into chains. Furthermore, the AHo of ring formation is significantly less than that of chain formation. Evidently, the H bonds in rings are weak in comparison to those in chains. The molar entropy of H-bond formation in these sterically hindered isomers range from - 13.7 t o -15.4 eu. However, we do not see any correlation between the entropy of H-bond formation in rings and the amount of steric hindrance about the -OH group. It appears that the presence of a methyl group on the same or on a neighboring carbon atom makes the -OH
The Journal of Physical Chemistry
group so sterically hindered that causing further changes in the immediate structural environment by introducing more methyl groups does not significantly affect the dielectric properties. I n this respect, it is interesting to note the extreme sensitivity of the intermolecular association t o the position of the -OH group, as can be seen for example by comparing 2;2;3 and 2;2;1 (neooctanol) :8 the former appears to associate exclusively into rings in the temperature range accessible t o us; the latter, while possibly favoring rings at higher temperatures (the correlation factor is slightly less than l), definitely favors linear chain species at lower temperatures. We conclude that octanol isomers in which the environment about the -OH group is sterically hindered by an alkyl group on the same or on the next carbon atom tend t o associate into ring dimers, while those isomers whose -OH group is less severely hindered associate into linear chains. The relative population of ring and chain species is strongly temperature and pressure dependent so the octanols provide an ideal system with which to explore the subtleties of intermolecular association. With our experience so far as a guide, it is easy to predict other classes of compounds9 which might show similar behavior. Dielectric behavior of the type discussed in this paper is probably less exceptional than is usually supposed. (8) W. Dannhauser, L. W. Bahe, R. Y . Lin, and A. F. Flueckinger, J. Chem. Phys., 43, 257 (1965). (9) R. Perrin and P. Issartel, Bull. SOC.Chim. France, 1083 (1967), have determined dielectric constants of some methyl- and dimethyl phenols. They discuss their results in terms of a temperaturedependent "Onsager moment" which, in our notation, means a temperature dependent correlation factor. For highly hindered species, Le., 2,6dimethyl phenol, g is close to unity and almost independent of temperature. Their experiments are restricted to relatively high temperatures though, and so they find no evidence for antiparallel association. de/dT < 0 in all cases, but i t is close to zero for the hindered species, Carboxylic acids (with formic acid a notable exception) have long been suspected of associating in antiparallel ring dimers. A. E. Lutskii and S. A. Mikhailenko, Zh. Strukt. Khirn., 4, 14 (1963), have shown that dr/dT > 0 for acetic-valeric acid. However, they suggest that disruption of the ring dimer is only one aspect of the behavior and believe that a major change of the dipole moment upon formation of an H bond is the most important factor.
