J. Phys. Chem. 1983, 87, 1034-1038
1034
the most important variations are obtained by changing alcohol. The interactions are strongly attractive in the microemulsions containing pentanol and much less in hexanol and heptanol systems. Besides, for a given series, interactions increase with an increase of the micellar radius. The intensity data have been analyzed with the intermicellar potential discussed in paper 1. It appears that the behaviors of calculated and experimental virial coefficients are quite similar; moreover, considering experimental accuracy, calculated and experimental values are very close. In particular, the effects of alcohol chain length and micellar size are well represented. The calculation provides an approach for the understanding of the variations of the interactions. Indeed, in a schematic way, attractive energy results from the penetration of the aliphatic layer of the micelles and is proportional to the penetrated volume. Variations of this volume can be ob-
tained in two different manners: either in changing the alcohol chain length or in changing the micellar size. The alcohol effect corresponds to the principal effects; for a given micellar radius, as the alcohol chain length decreases, RHS decreases; hence, the thickness of the penetrated layer is increased and the interactions are stronger. The second effect relative to the micellar size is a secondary effect and can be explained in the same way. An increase of the micellar radius leads to an increase of the volume of interaction and also to variations of compositions of the continuous and dispersed phases.
Acknowledgment. We thank B. Lemaire for stimulating discussions and Mrs. M. Maugey for her technical assistance. Registry No. SDS, 151-21-3;dodecane, 112-40-3;1-pentanol, 71-41-0; 1-hexanol,111-27-3;1-heptanol,111-70-6water, 7732-185.
Experimental and Theoretical Approach to Molecular Dynamlcs of Pyridine Derlvatives and Related Molecules from Dlelectric Relaxation Measurements. 1. 2,3'-Bipyridyl in the Liquid State P. Freundlich, E. Jakusek, H. A. K W z l e j , A. Koll, M. Pajdowska, Instytut Chemii, Universytet W r d w s k i , 50-383 Wr&w
Poland
and S. Sorrlso' Istituto di Chimica Fislca, Universiti di Perugia, 06100 Perugia, Italy (Recelved Juiy 6, 1982; I n Final Form: October 27, 1982)
Dielectric relaxation measurements and theoretical calculations were performed on 2,3'-bipyridyl in the liquid state, in the frequency and temperature ranges of 1.8-40 GHz and 293-323 K, respectively. A complex dielectric absorption band was found that can be interpreted as being due to the presence of two rotations involving, respectively, the whole molecule and the heterocyclic rings about the C-C central bond. A particularly suitable computational method allowed us to divide the complex band into two simple ones. Theoretical calculations of the total interaction energy (as s u m of dipole-dipole interaction energy; strain and deformation energies, and the *-electron energy) between the two hexatomic moieties do not exclude the possibility of internal rotation around the C-C bond. Macroscopic dielectric relaxation times were also calculated for both rotations, giving the following results (temperature/K, T1/ps, ~ ~ / p s293,388,33; ): 303,271,28; 313,217,24; 323,195,21. Finally, the activation energy barriers for the two molecular motions were derived from dielectric and viscosity mea= 1.86 kcal-mol-'; M E * ( q ) = 7.88 surements, giving the following values: A H E * ( T ~ ) = 3.85 kcal-mol-', kcal-mol-'.
Introduction Among heterocyclic compounds, pyridine is quite important both for the great number of reactions in which its derivatives participate and for its very numerous practical applications.' This accounts for the interest of many researchers in this class of compounds from several points of view. Often, pyridines are studied together with the corresponding benzene derivatives, with the aim of showing the effect of the presence of a nitrogen atom in the heteroaromatic ring. (1) E. Klingsberg, Ed., "Pyridine and Ita Derivatives", Interscience, New York, part 1, 1960; part 2, 1961; part 3, 1962, part 4, 1964. R. A. Abramovich, Ed., 'Pyridine and Ita Derivatives", Supplement, Interscience, New York, parts 1-4, 1973. 0022-3654/83/2087-1034$01.50/0
As regards more particularly the molecular dynamics of the present class of compounds from dielectric dispersion measurements, there are some studies concerning compounds containing only one pyridine ring, but few about interesting molecules such as bipyridyls,2 bipyridylethylenes, stirylpyridines, and so forth. We have begun a large-scale research which foresees the analysis of the dielectric relaxation mechanism of many of this last group of molecules and of some related ones, with the aim of determining if there is a common dynamics that can explain the behavior of the single components of this class of compounds by means of a certain rationalization. (2) D. D. Klug, D. E. Kranbuhel, and W. E. Vaughan, J. Chem. Phys., 53, 4187 (1970).
0 1983 American Chemical Soclety
The Journal of Physical Chemistry, Vol. 87, No. 0, 1983 1035
Dielectric Relaxation of 2,3'-Bipyridy in the Liquid State 2 , 2 1 D ,f
2.21
D f
1.4 A x,,
0
-v,l
--
+
Flgure 1. Cis configuration of 2,3'-bipyridyl from which the calculation of the dipole-dipole interaction energy started.
The present paper describes the results obtained for 2,3'-bipyridyl in the liquid state. Nothing has been published until now regarding this molecule, either in the field of relaxation mechanism or in that regarding the conformational aspects in solid, liquid, and solution states.
Experimental Section Materials. 2,3'-Bipyridyl was a commercial product and was purified by means of threefold distillation under vacuum before use. Physical Measurements. Dielectric permittivity (E') and loss (e")were measured in the frequency range 80 MHz-18 GHz by means of coaxial slotted line Rohde-Schwarz 3916/50 for 80-300 MHz, Orion Type EZN-1 for 500 MHz-4 GHz, and HP Type 817 B for 1.8-18 GHz. The range 18-40 GHz was covered by two independent slotted lines; for the K band the Unipan K-100 laboratory system was used and for the Q band the PIT LPF-08 was used. Over the whole frequency range the value of the confidence interval obtained from a number of measurements was estimated to be f1.5% for E' and &3% for E". Dielectric relaxation measurements were made in the liquid state in the temperature range 293-323 K, sufficient for obtaining good values for some thermodynamic parameters. The static dielectric permittivity was measured at 1.592 kHz with a TESLA semiatomatic C-Bridge BM-84 type connected with the sample holder and controlled by means of an IDP temperature controller. The temperature of the sample was measured with a copper-constantan thermocouple to an accuracy of fO.O1 K. All calculations were made by means of computer systems. Energy Calculations The possibility of internal rotation about the C-C central bond was further ascertained by us by means of some theoretical calculations of the total energy involved between the two pyridine rings. It was assumed that the most important contributions to this interaction energy are the following: dipole-dipole interaction energy, strain and deformation energies, and ?r-electron energy. Dipole-Dipole Interaction Energy. This type of interaction energy (Edip,in kcal-mol-') has been calculated by starting from the cis configuration of Figure 1, using the following relationship:
.
E
[%I 9-
I 01 0
I 220°
1350
"'
'
40
1
80
1
'
120
1
'
160
"
200
'
"
240
'
280
I
"
'
320
4 @/"
Flgure 3. Interactlon energy between the two rings in 2,3'-bipyridyi as a function of the dihedral angle between the planes of the two moleties. The cis conformer has 9 = 0.
The contribution of dipole-dipole energy in 2,3'-bipyridyl appeared to be very small (in general less than 1% of the total energy) and practically can be neglected in the contrast to 2,2'-bipyrid~l.~p~ Strain and Deformation Energies. This contribution, which is of a steric nature, was calculated with Kitajgorodskij atom-atom potential6 between the H and C atoms laying at the center of the molecule according to Figure 2. To explore all possibilities concerning the conformation of the examined molecule, we considered the deformations of the D1-D4 bond angles which give rise to the greatest contributions to the interactions between the two moieties. For the same reason the C-C central bond distance was also minimized during the calculations. a-Electron Energy. This was calculated by means of the HMO method with the modified resonance integral (&?) of the central C-C bond according to eq 2, in which Bo is
.
where pk, p), and pi are, respectively, the components of the electric dipole moment on the x , y , and z axes; X12, Y12, and Z12 are, respectively, the projections of the r distances on the x , y , and z axes, with r = (X122+ YlZ2+ 2122)1/2.
D. Flgure 2. Configuration of 2,3'-bipyridyl showing the steric interaction between the two heteroatomic rings.
(3)P. Freundlich, E.Jakusek, H. A. Kolodziej, A. Koll, M. Pajdowska, and S. Sorriso, 2.Phys. Chem. (Frankfurt om Main), 131, 161 (1982). (4)A. Koll, H. A. Kolodziej, and S.Sorriso, J . Mol. Struct. Theochem., submitted for publication. ( 5 ) A. I. Kitajgorodskij, 'Molecular Crystala and Molecules", Academic Press, New York, 1973.
1036
The Journal of Physical Chemistry, Vol. 87, No. 6, 7983
p12 = Po exp[-4.l(r - 1.397)] cos 4
Freundlich et al.
(2) T:323
the resonance integral for the benzene bond with a length of 1.397 A; 4 is the dihedral angle between the planes containing the pyridine rings. The values of Po, the force constant, and the natural length of the C-C central bond have been matched by adjusting the structure of the biphenyl molecule in the solid and gaseous phase and for the configuration having perpendicular rings. The results reported in Figure 3 were obtained from these calculations for several conformers derived from the internal rotation about the central C-C bond.
Discussion Analysis of the experimental results can be made by taking into account the peculiarities of this molecule. In fact, it has two dipole moment components which may be active and contribute to the dielectric absorption. Assuming that several rotations take place, one sees that the component of the dipole moment parallel to the rotation axis may change its direction by means of overall reorientation of the molecule and the perpendicular component may also change its direction by means of both overall and internal molecular reorientation. When these two movements are stochastically independent, the Goulon-RivaiP treatment leads us to the conclusion that the sum of the two exponential terms should be observed, one of which may be characterized by 11
=
=
(3)
+ -1
(4)
T2
Tor
'K
A
6"-
T=303
C,
z:,
- 271 28
. E't
when 1 - -1 _ ,.int
lor
lC
In eq 3 and 4 TO' is the correlation time for the overall reorientation and 7 c is the "chemical relaxation time". Obviously when 70r >> rC,we can expect 71 = 70r and 7, = rC. Furthermore, if the internal rotation is dramatically hindered which means that the energy barrier is high, the asymmetry of the absorption curve may be due to wide angle vibrations. According to the Budo' treatment, when the shape of the potential energy is cosine-like or parabolic, the dipole moment correlation function is a sum of two or more exponential terms. From theoretical calculations it seems that this is roughly the situation present in 2,3'bipyridyl. On this basis, we decided to separate the obtained absorption curve into two independent Debye-like absorptions, which can be identified with and r2given in Goulon-RivaiP treatment, with the first and second term of the Budo7 relationship given for the case of hindered rotation. As we shall observe below, one can notice that the first relaxation time is very long for a molecule of such shape and volume in a solvent of low viscosity, and can be treated as an overall rotation affected by a large macroscopic viscosity. The results of the dielectric relaxation measurements are reported in Figure 4 as Cole-Cole arc plots.8 From this figure it may be seen that the picture of the dielectric absorption is rather complex and cannot be described by a simple Debye relation. There are two Debye regions, represented by two semicircles, in which the radius of each is proportional to the weight of the corresponding relaxation process. If we assume that there are two stochastic (6) J. Goulon and J. K. Rivail, 'Spectroscopic Consequences of Very Fast Chemical Processes"in 'Protons and Ions Involved in Fast Dynamic Phenomena", Elsevier, Amsterdam, 1978. (7) A. Bud6, J. Chem. Phys., 17,686 (1949). (8)K.S.Cole and R. H. Cole, J. Chem. Phys., 9,341 (1941).
Flgure 4. Cole-Cole arc plots for 2,3'-bipyridyl in the liquid state at various temperatures.
motions independent of each other, as has just been shown, the following relationships can be written:
-€' -- t, €0 -
--
Elf
€0
- 6,
-
C1
1
+
W27i2
C1
1
+
w27,'
+ 1 +C2
(5)
Z + 1 +Cw2r22
(6)
w27Z2
to is the static dielectric permittivity, t, is the optical dielectric permittivity; E'is the frequency-dependent dielectric permittivity; d' is the frequency-dependent dielectric loss; w is the angular frequency of the measuring electric field; C1 and C2 are, respectively, the weight fraction of the first and second absorption, (C,+ Cz = 1); and 1, and T~ are, respectively, the macroscopic relaxation times of the first and second process. A special computer program has been used to separate the total absorption band into two single bands, and the principle of this is shown in Figure 5. The values so obtained represent the most probable ones for relaxation parameters of the two absorptions so separated, and are reported in Figure 6 for temperatures of 293,303,313, and 323 K. Also in Figure 6 the calculated dielectric loss curves are compared with the observed ones at the same temperature. As may be seen from this figure, the agreement between calculated and observed curves is very good. Concerning the contributions of each absorption to the dielectric spectrum of 2,3'-bipyridyl, one sees that it is evident that one absorption clearly prevails over the other. With regard to the molecular motions associated with these relaxation processes, theoretically two situations might be present according to our results: (i) molecular
Dielectric Relaxation of 2,3'-Bipyridy in the Liquid State
I
r H I (,.J i
I 4
.
1.1
4 )
1037
i
l---
C l l c u l a t l o n of doriv8tl~es
The Journal of Physical Chemistry, Vol. 87, No. 6, 1983
Solution of
~
1
E=D*A
Flgure 5. Special computer program used In calculating the single dielectric absorption bands of the complex dielectric absorption observed for 2,3'-bipyrdyl in the liquid state.
relaxation about more than one axis; (ii) molecular relaxation for T~ and group relaxation for 72. The first possibility may very probably be ruled because it is well-known that for such small molecules the relaxation data cannot be analyzed into relaxation contributions about different axes. Therefore, if we accept that the second situation (molecular relaxation and group relaxation) occurs, there is the problem of assignment of the absorption bands. This can also be made by means of the average electric dipole moment values calculated from the intensity of the absorption bands, using the Onsager model modified by Collie, Hasted, and R i t s ~ n .The ~ values so obtained are first relaxation process ~1 = 3.05 D second relaxation process p = 1.05 D Obviously the first value is very close to the molecular dipole moment (see below) and consequently this band must be assigned to the orientation of the whole molecule about the axis perpendicular to the central C-C bond. From the electric dipole moment it seems also that the second absorption can be explained as an internal rotation of the pyridyl rings about the C-C central bond. On this basis, taking into account the average value of the dipole moment calculated from the intensity of the second absorption band, one can obtain the value of the dihedral angles between the two heterocyclic rings, which is shown to be 32 and 1 2 2 O , as a compromise among various energetic exigencies which often act in opposition to each other. This explains why the molecule is not planar. The results of the theoretical calculations of the total interaction energy between the two hexatomic rings (see Energy Calculations) are in agreement with this conclusion. In fact, it may be seen from Figure 3 that the minimum of the total interaction energy is found at dihedral angles of 35, 140, 220, and 325O. This agreement should be considered very good if one takes into account the fact that both calculations involve quite different assumptions and approximations. The energy difference between the absolute maximum and minimum values in Figure 3 is about 5.45 kcal-mol-l. (9)C.H.Collie, J. B. Hasted, and D. M.Ritaon, h o c . Phys. SOC.,60, 145 (1948).
8
9
6 -
10
11
T.323
K
10
11
4
8
9
log
v
Figure 6. Calculated and observed (0)dielectric absorptions for 2,Sf-bipyrMyl in the liquid state at various temperatures.
It is sufficient to render some rotamers preferred with respect to others. However, this energy barrier cannot prevent a rapid interconversion between various conformers in the presence of an electric field. The same thing very probably occurs as concerns the possibility of a rapid interconversion between rotamers having values of 140 and 220°, and 320 and 40' for the dihedral angle between the two heteroatomic rings. In fact, in the latter cases the energy barrier to internal rotation about the central C-C bond is about 2.55 kcal-mol-'. It is noteworthy that the observed value for the relaxation activation energy is about 1.85 kcal-mol-l in the pure liquid. The possibility of an equal distribution of the 2,3'-bipyridyl among the four energy minimum (with or without a rapid interconversion between them) can qualitatively be seen from a comparison between the observed dipole moment and the calculated one. In the present case, however, this method does not allow us to distinguish
1038
The Journal of Physical Chemistry, Voi. 87, No. 6, 1983
Freundlich et al.
between these two situations (interconversion or not). For this purpose, we can uselo J H : ( T , ) = ~8 5 k c a l m o l
(7)
when when pc&d, h0,and C p : are, respectively, the moment calculated for free rotation, the vector sum of all components of the rotating moments along their axes of rotation (C-C), and the sum of the squares of the components of the rotating moments perpendicular to their axes of rotation. Assuming for the moment of pyridine the value found in the liquid state (2.43 D)," we obtain a value of 3.a4 D for pcalcd,which is greater than the observed one (3.05 D). At the same time the latter is quite different than the theoretical moments calculated for the skew-cis form (4& D for 0 = 35O) and the skew-trans form (2.09 D for 0 = 140O). The comparison between calculated and observed moments seems to indicate that the pseudo-trans conformers slightly prevail over the corresponding cis ones. The small difference between these results and those obtained from theoretical calculations might be due to the intermolecular interaction. From a thermodynamic point of view, some information may be obtained about the relaxation process from the Eyring12relationship
where 7 is the macroscopic relaxation time; h and kF are, respectively, the Plank and Boltzmann constants; A H E * is the molar activation enthalpy barrier; A&* is the corresponding entropy variation. Recasting eq 8, we get the following: AHE* A&* h In (T7) = -- - In (9) k RT R So, if the AHE*and ASE*values are independent of the temperature, the plot in In ( T T )vs 1/T is linear. In Figure 7 both In (TT')and In ( T T ~are ) reported as a function of the temperature. Both these functions are practically linear indicating that the assumption made is perfectly correct. From this figure the following values were calculated: A H E * ( T J = 3.85 kcal.mo1-' and M E * ( 7 2 ) = 1.86
+
(10) M.Davies, "Some Electrical and Optical Aspects of Molecular Behaviour", Pergamon Press, London, 1965. (11) T. Hanai, N. Koizumi, and R. Gotoh, Bull. Inst. Chem. Res. Kyoto Uniu., 39, 195 (1961). (12) A. Chelkowski, "Dielectric Physics",Elsevier and Polish Scientific Publishers, Warzawa, 1980, p 126.
1651130
J H : ( ~ ~ ) = I8 5 k c a l m o l
31
3 2
3 3
34
35
Figure 7. Macroscopicrelaxation times as a function of temperature.
kcal-mol-'. For comparison the value of AHE(f) was measured and was found to be 7.88 kcal.mol-'. Such a large difference between AHE*(T) and A H E * ( q ) suggests some flexibility in the molecule examined here.
Concluding Remarks We have used dielectric relaxation measurements at various temperatures to study the molecular dynamics of 2,3'-bipyridyl in the liquid state. At all temperatures explored the dielectric spectrum consists of a complex absorption band which has been shown to result from two bands, which may be assigned to the molecular and internal rotation, respectively. Theoretical calculations of the simple bands of the dielectric relaxation absorption confirmed the information obtained from Cole-Cole arc plots. As concerns the interaction energy calculated theoretically, it has been found that its value does not prevent the interconversion. A sensible difference has also been observed between the molar activation energy determined from dielectric measurements and that obtained from viscosity measurements. This has been interpreted as an evidence of a certain flexibility of the molecular framework. In agreement with this, the ?r delocalization between the two aromatic systems is low, as is indicated by the fact that both the observed and calculated dihedral angles between the two heterocyclic rings are quite different from 0 or NO0, for the minimum energy conformation. Acknowledgment. S. Sorriso is indebted to Consiglio Nazionale delle Ricerche (Rome) for financial support. Registry No. 2,S'-Bipyridyl, 581-50-0.
