Dipole rotation in some substituted ferrocenes

13

Journal of Molecular Liquids, 59 (1994)13-25

ElsevierScienceB.V., Amsterdam

DIPOLE ROTATION IN SOME SUBSTITUTED

FERROCENES

STEPHEN W. FILIPCZUKtand LEONIDAS PHILLIPS TheSchool of Chemistry, The University of Sydney, Sydney, NSW 2006 (Australia) (Received 9 May 1992; in revised form 14 July 1993)

ABSTRACT The dielectric relaxation times (d) of dilute cyclohexane and benzene solutions of several mono-, di- and penta-substituted ferrocenes are determined. From these we derive the corresponding relaxation times (2) for intra- and overall molecular dipole rotation, as well as the associated thermodynamic parameters. Our analysis of the modes of dipole reorientation in l,l’-dichloroferrocene (DiClFc) takes into account the simultaneous operation of both intra- and overall molecular rotation, in accordance with standard theory. This was found necessary in order to account for the observation that the dielectric relaxation time of chloroferrocene (ClFc) in cyclohexane (14.4 ps) is greater than that for the larger molecule DiClFc (9.0 ps). We show that intra-molecular dipole rotation in DiClFc is less hindered than in ClFc.

INTRODUCTION In a previous publication [ll in this journal we derived the group- and molecular dipole moments of the following molecules: 1,2,3,4,5-pentachloroferrocene (PClFc), l;l’-dichloroferrocene (DiClFc), chloroferrocene (ClFc), 1,2,3,4,5_pentamethylferrocene (PMeFc) and 3,3’,4,4’-tetramethyl- 1,1’-diphosphaferrocene (TMePFc). We discussed evidence which suggested that group substitution had very little influence on the magnitude of the charge on the iron atom but a great effect on the distribution of molecular electronic charge. Herein, we complete our microwave dielectric absorption study on these interesting substances, by discussing the relaxation times and activation energies for various modes of dipole reorientation. We show that intramolecular dipole rotation of the cyclopentadienyl-chlorine (CpCl) group is much less restricted in DiClFc than in ClFc. The data of Jakusek et al. 121for DiClFc is re-analysed in order to estimate the activation enthalpy for intramolecular rotation of the Q-Cl ligand. + Deceased. 0167-7322/94/$07.00

0 1994- ElsevierScienceB.V. All rights reserved.

The process of central importance to this study is that of thermallyactivated dipole rotation. This can readily be detected in ferrocenes with polar side groups through appropriate dielectric polarization experiments. When employing low-frequency techniques to measure the ‘static’ dipole moments of derivatives such as the l,l’-dihaloferrocenes, a positive dipole temperature coefficient [3] indicates that the fraction of the more polar, but sterically less favourable, halogen-eclipsed forms increases with temperature (2’). The rate of dipole rotation in substituted ferrocenes can be probed through microwave dielectric absorption studies. The negative temperature coefficient of macroscopic relaxation times can be analysed in terms of (Eyring’s) rate theory involving activated or transition states [4,5], to yield enthalpies of activation for intramolecular rotation [2,6,71. In-plane ring motion in the ferrocenes involves thermal activation over a rotationally modulated five-fold potential barrier. The barrier heights are usually small [8] and often do not exceed a’few kBT (2 kBT in ClFc [3]). In the case of ClFc this barrier system is regular; but with DiClFc it is not-though it is symmetric about the halogen-eclipsed configuration. Hoffman and Pfeiffer [9] show that for molecules such as ClFc, the decay of orientation polarization associated with intramolecular (in-plane) CpCl rotation is characterized by a single relaxation time, 7int.However, for di-substituted DiClFc four relaxation times zFntmay be required [lo] (superscript 3 = 1,2,3 or 4 distinguishes the four rotational decay modes). EXF’ERIMEN’I’AL The substituted ferrocenes studied were prepared as reported previously [ill. All solvents were purified then dried by standing over sodium wire before use. Dielectric absorption measurements made at 1.14 GHz, 3.03 GHz and 8.54 GHz were carried out as described elsewhere [12], while those at 480 MHz were performed in a similar manner with equipment described by Williams [13]. For any particular ferrocene, loss tangents tan 6 were determined for a series of dilute solutions having solute weight fractions LO[l] .The slopes w at the limit of infinite dilution in plots of tan 6 versus w at the various frequencies (Table 1) were [l] converted to mean solute dipole moments l.~,dielectric relaxation times z’ and their associated uncertainties using the Debye equation [14] as adapted by Le F&vi-eand Sullivan 1151:

w=

I[ 1

NAP&1 + 2j2p2 27kBTq,qM

6d

1 + o2(Y)2

(1)

15

and &Iare respectively solvent density and static relative permittivity, Edis the permittivity of vacuum, M is solute molecular weight and NA, k, and w are Avogadro’s constant, the Boltzmann constant and the angular frequency, respectively. p1

TABLE 1 Experimental and best-fit (talc.) values of the dimensionless Debye absorption factor w for dilute solutions of several substituted ferrocenes at 298 K

Molecule

Solvent

Frequency (GHz)

vtiva

wale.

ClFc

Cyclohexane

0.48

0.0238ti.0046

0.0182

1.14

0.045OkO.0046

0.0430

3.01

0.1057kO.0053

0.1080

8.54

0.203lkO.0083

0.2055

ClFc

DiClFc

PClFc

PMeFc

TMePFc

TMePFc

Benzene

Cyclohexane

Cyclohexane

Cyclohexane

Cyclohexane

Benzene

1.14

0.0634kO.0063

0.0582

3.01

0.1454IkO.0057

0.1495

8.54

0.2981&0.0040

0.3011

0.48

0.0227kO.0106

0.0192

1.14

0.0472kO.0036

0.0468

3.01

0.1231iO.0057

0.1220

8.54

0.2877kO.0114

0.2884

1.14

0.0834kO.0069

0.0849

3.01

0.1657kO.0025

0.1661

8.54

0.1454kO.0027

0.1456

0.48

0.0145&0.0016

0.0133

1.14

0.0313M.0015

0.0301

3.03

0.060lkO.0008

0.0604

8.54

0.0584&0.0019

0.0571

0.48

0.0265kO.0048

0.0217

1.14

0.0500~0.0020

0.0516

3.01

0.136OkO.0072

0.1335

8.54

0.3239kO.0211

0.3180

0.48

0.0456kO.0080

0.0430

1.14

0.0990kO.0042

0.1020

3.01

0.2636&0.0022

0.2638

8.54

0.5551kO.0116

0.5560

“Av is the standard error in v taken at the 95% confidence level.

16 TABLE 2 The dielectric relation times < of several substituted ferrocenes at 298 K Molecule

Solvent

Y (PSI

ClFc ClFc DiClFc PClFc PMeFc TMePFc TMePFc

cyclohexane benzene cyclohexane cylcohexane cyclohexane cyclohexane benzene

14.4f1.7 13.okO.4 9.ozk2.3 36.0f1.2 33.3kO.4 8.7f1.2 11.9M.7

Literature values of? (ps)

37.6* -

aReference [21, T = 300 K.

RESULTSAND DISCUSSION Except for the solution-state relaxation time (7’) of DiClFc, those for the other ferrocenes listed in Table 2 are reported here for the first time. Measurements were performed near infinite dilution (w < 0.02) in order to minimize solute-solute interactions. Interesting relationships are immediately obvious in this table: (a) z’ for ClFc solutions is greater than that for solutions of the larger molecule DiClFc. This result is explained not by recourse to an analysis based on overall molecular rotation alone, but with the involvement of intra-molecular dipole rotation. (b) The relaxation times of the axially-symmetric ferrocenes are considerably larger than those in which intra-molecular dipole rotation is possible. The dielectric relaxation time of DiClFc reported by Jakusek et al. [2] far exceeds the value now found. This discrepancy cannot be explained in terms of different solvent viscosities according to Debye’s relationship (2). r=4x:r3q

(2)

kBT

where 71is the dynamic viscosity of the solvent and r is the ‘molecular’ radius. In ref. 121frequency v (Hz) has been used instead of angular frequency o (= 27~~radians/second) to calculate z’ (= I./a_). Applying this correction and the viscosity data of Timmermans [16] we estimate the corresponding value for cyclohexane solutions to be 9.1 ps, agreeing well with our measured value of 9.0f2.3 ps.

17

From [ 171the 2’ values of Table 2 reasonably equate to the corresponding molecular relaxation times in the limit of infinite dilution in non-dipolar solvents. Overall-molecular and intramolecular dipole rotation

The description of dielectric absorption for molecules whose structures are similar to phenol [181 and aniline t191 becomes complicated by the existence of two orthogonal component dipoles (y, parallel to and pL perpendicular to the long axis). In axial ferrocenes such as the penta-substituted PClFc and PMeFc, symmetry requires that there be only one component that contributes to (macroscopic) orientation polarization. In ferrocenes with more reduced symmetry other component dipoles and modes of re-orientation must be considered. Cole [18] and Williams 1191 have provided a rigorous analysis of dielectric relaxation based on dipole correlation functions for representative molecules capable of inversion, intramolecular and overall molecular rotation. Their models incorporate elements of the theory of Hoffian and Pfeiffer [91,which considers rotational transitions of dipoles between adjacent sites in a multi-fold energy barrier system. It was shown [l&19] that the orientation polarization associated with each component dipole in phenol and aniline relaxes with time constants z’,, and z’* given respectively by: 1 -=$1

1

(3)

%wl

_=l l+2z’.l

%m!

(4)

%t

zmo2and zint are respectively the relaxation times which characterize

overall-molecular and intra-molecular rotation. The total (microwave) absorption of solutions of these molecules will be a generalization of Eq. (1) for two overlapping Debye curves:

In the case of aniline, Williams 1191 describes Zintin terms of the elementary transition probability Kint(=1/4zi,t) for dipole rotation within

18

a two-site model [9]. With ClFc one must consider Cp-Cl rotation in a regular five-site energy barrier system. Hoffman and Pfeiffer [9] show that in this case 7int= 20 - 6)Kint ‘. For ClFc Eqs. (2) to (5) still apply however. From ref. [l], p,, (ClFc) is the molecular dipole component directed along the iron-cyclopentadienyl axis; p1 (ClFc) is the dipole component perpendicular to that axis. The latter coincides with the Cp-Cl bond direction. The component p,, (ClFc), arising through the inductive withdrawal of electrons by Cl from the ferrocenyl system, was evaluated in [l] as 1.16~10”~ C m. Possible molecular relaxation modes of ClFc are; overall molecular tumbling (zmol)and CpCl rotation about’ the metal-ring axis (%int)* That fraction of the total microwave absorption associated with l.$ClFc) is given by $/($ + &). But as 4, (ClFc) = 1.16~10”~ Cm [112 and cl,,(ClFc) =4.83x10 3o Cm [l] ,this fraction represents only 5% of the total absorption measured3. Given this, we can assume that the relaxation time of the measured absorption ?(ClFc) = 14.4 ps, may be taken as being equal to z’,(ClFc) given by Eq. (3). It is unfortunate that the component absorption due to l$ClFc) cannot be resolved, because this precludes the unique determination of the interesting quantity zm&CIFc) through Eq. (2) and thence zi,,(ClFC) via Eq. (3). Nevertheless, it would not be unreasonable to assume that z,JClFc) < zml(PCIFc) = 36 ps [z’(PClFc) = 36 ps = z’,,(PClFc) = z,,&PClFc) by symmetry and through Eq. (3)l. The low energy barrier of 2K,T quoted by Riemschneider and Wucherpfennig [3] for intramolecular ring rotation in ClFc implies relatively unhindered motion. This being so, it is very probable that Zint(ClFC)< z,,JClFc). By substituting this inequality together with the observation that YL(CIFc) = 14.4 ps into Eq. (4), it can be readily demonstrated that 29 ps < z,&ClFc) < 36 ps and 24 ps < Ti,,(ClFC)< 29 ps. We simplify the latter to obtain in an indirect and approximate way: zml(CIFc) = 32+4 ps

(6)

zi,,(ClFC) = 26+3

(7)

PS

1 Here, hint is strictly the probability for rotational transitions between adjacent sites according to a single-jump hypothesis [9]. Random jumps are also possible [20], but the form of Eq. (3) remains the same however. 2 In ref. [l] we labelled pl~(ClFc)as ~~I~‘. 3 The uncertainty in our measurements is also about 5%.

19

Unlike that situation in ClFc, the five-position energy barrier system in DiClFc is not regular, though it is symmetric about the halogeneclipsed conformation. As mentioned above, four relaxation times & [lo] may be required to characterize intramolecular Cp-Cl rotation in DiClFc. For single-axis rotors Hoffman and Pfeiffer [91have shown that although only one dipole may be involved in motion within a given (irregular) energy barrier system, the individual e,B,,values need not characterize the relaxation of equal amounts of orientation polarization. In the general case non-Debye behaviour is predicted, and depending on the relative magnitudes of the potential barriers separate absorptions may be resolved [21]. ‘The concept that a dipole occupies a definitely assignable site is strictly valid only when the local free-energy barrier between possible positions is considerably greater than k,T ’ [9]. As barriers decrease in magnitude the convergence of %Fnt values leads to Debye behaviour [9]. It has been shown that the average rotational energy barrier in DiClFc is about 2k,T 131.Since this falls well within the forementioned criterion [9] of Hoffman and Pfeiffer, relatively free intramolecular rotation is certain and we can conclude that all the $$ values in DiClFc lie within a narrow distribution. For our purposes, this can be substituted for by some average value denoted for convenience as ?&DiClFc). Williams [191 has shown that for molecules such as DiClFc (R,NC,H,Nl$ in his paper) the only other mode of polarization relaxation available is from overall molecular rotation4. Since by symmetry p,,is zero in DiClFc, the relaxation time of the observed dielectric absorption must be given by Eq. (4), where z’(DiClFc) = 9.0 ps = z’,(DiClFc). Although a unique value of zmz(DiClFc) cannot be obtained using the present technique, an indirect value can be deduced by imposing the following reasonable conditions on Eq. (4), namely zi,,(DiClFc) c zm&DiCIFc) c ~,~(PclFc). Using the data in Table 2, we obtain from these 18 ps < zml(DiCIFc) c 36 ps and 12 ps < Ti,,(DiCIFc) < 18 ps; which reduce to z,&DiClFc) = 27+3ps;

(3)

?&DiClFc)

(9)

= 15*3ps.

4 With regard to DiClFc solutions

considered in the present case, dipole rotation is constrained not to motion about a single axis, but to motion associated with the relatively free dynamics of a polar molecule in thermal equilibrium with a solvent. Equation (4) predicts that the polarization relaxation of DiClFc solutions is characterized by one relaxation time z’ = 1’1. This is confirmed by the simple Debye behaviour observed through our measurements and those of Jakusek et al. [21.

20

The magnitude of &(DiClFc) is significantly lower than that for ClFc. This is related to the fact that in DiClFc electron depletion in the Cp-Fe-Cp bond system induced by one chlorine substituent is enhanced by the presence of a second chlorine on the other ring. The associated increase in electron density in each Cp-Cl ring would tend to increase inter-ring repulsion more so in DiClFc than in ClFc. These effects will combine to produce a greater weakening of the Q-Fe bonds in DiClFc. The overall result will be a smaller steric interaction between rings in DiClFc and a lessening of the hindrance to intramolecular dipole rotation (compared to ClFc). Confirmation of a greater Cp-Fe bond weakening in DiClFc comes from an infra-red study by Phillips et al. [ill where it was shown that the (Cp-Cl)-Fe stretching force constants in ClFc and DiClFc are respectively 370 N m-l and 329 N m-l. As with DiClFc, the dielectric absorption of TMePFc solutions conforms to simple Debye behaviour. The relaxation time of this absorption [?(TMePFc) = 8.7f1.2 ps] will be given by Eq. (4), since no moment parallel to the metal-ring axis exists. In order to estimate the relaxation times for overall molecular and intramolecular dipole rotations in TMePFc, we adopt the same reasoning as applied to DiClFc: &(TMePFc) < Tml(TMePFc) < zml(PMeFc). From this we deduce 18 ps c rml(TMePFc) < 33 ps and 12 ps c &(TMePFc) < 18 ps, or z,&TMePFc) = 26+8 ps,

(10)

&(TMePFc)

(11)

= 15+3 ps.

Hoffman and Pfeiffer [9] have proposed a simple criterion (Eq. (12)) for distinguishing between free and hindered dipole rotation based on the time taken for a free rotor to turn 2x radians: 2xI -\I--’ ‘tie =2x k,T

(12)

I is the moment of inertia and ~~~ is the estimated relaxation time for free rotation. Given that I for Q-Cl rotations about the Cp-Fe-Cp axis is 7.1~10~~ kg m2, ~fiee(Cp-C1)= 20.7 ps. This approximate value compares favourably with the average of Ti,,(CIFc) and T&DiClFc) from Eqs. (7) and (9). It may be that a more appropriate expression for zfie should be (2d/kBT)%. This is because z (the reciprocal of o radians per seconds) has units of seconds per radian, not seconds per 2x radians as in Eq. (12). Applying our alternative expression results in a more realistic value of zfiee(3.3 ps) compared to both Eqs. (7) and (9).

21

Dipole rotation in the axially symmetric molecules PClFc and PMeFc, can only occur through overall molecular rotations according to Eq. (3): hence Y(PClFc) = z,&PClFc) = 36.0f1.2 ps;

(13)

Y(PMeFc) = z,&PMeFc) = 33.3k0.4 ps.

(14)

Thermodynamic parameters for dipole rotation

The rate equation for dipole rotation, as measured by 8, has been discussed by Eyring [41 in terms of the theory of absolute reaction rates [5] involving activated or transition states: (15) h and R are respectively Planck’s constant and the Universal Gas

constant. AG$is the molar free energy of activation for dipole rotation. At constant ,pressure and neglecting electrostriction, AGs is given by AG*=A.@-TAS*

(16)

AI$ is the molar enthalpy of activation representing the potential barrier separating equilibrium orientations of the dipole. AS* is the entropy change on formation of one mole of the activated complex. This may include a component associated with changes in the structure of the local solvation sphere, especially if the molecule is large [22,23]. AI@ is obtained from Eqs. (15) and (16) by differentiation of In z with respect to T1. Thus AZ$ = R(d In z/dTl) - RT

(17)

Eq. (15) solved for AG* yields

(18) Since dipole rotation can be treated as a rate process, the a priori expectation is that the AG# values characterizing the temperature de-

22

will be different. For molecules such as DiClFc, pendence of zmz and ~~~~ Eq. (4) requires that the observed AGs will be some mix of AGs values for the two modes of dipole rotation. Substitution of Eq. (151, expressed in terms of Tintand z,,,, into Eq. (4) shows that this combination is given by AGibs = -RT 1 exp

(19)

The activation enthalpies (and entropies) for each of the two processes will be different as well. Indeed, in an extreme case Davies and Edwards [23] have shown that with polystyrene solutions of P-naphthol, Mm, exceeds A& by a factor of 22. Using the data in Table 2, Eqs. (6) to (11) inclusive and Eqs. (13) and (14), we have calculated [using Eq. (1811 the various activation freeenergies for the intra- and overall rotational processes: these are presented in Table 3. In all cases AGL, > Act,,, but what is interesting is that AGtn,and AGL, are very similar in magnitude. It could be inferred that should AI& be smaller than &ml as is likely, LLsfnt would be more negative than AS;,,. We interpret this to mean that intramolecular motion in the ferrocenes studied is associated with a more ordered activated state than that for overall molecular rotation. This may not be surprising, considering that rotations of small groups would occur without significant disruption of the surrounding solvent milieu. Relevant to this point is the frequent observation that zmozresponds far more markedly to changes in viscosity than zint. These conclusions can be demonstrated by a re-interpretation of the dielectric absorption data of Jakusek et al. [21, for DiClFc in benzene. Their paper gives z’(DiClFc) as a function of temperature (theory shows TABLE 3 Molar activation free energies for overall molecular (mo2) and intramolecular (int) rotations for various ferrocenes in cyclohexane at 298°K Rotation mechanism

int mol

AGS(kJ mol-‘) ClFc

DiClFc

PClFc

PMeFc

TMePFc

12.6M.3 13.1f0.3

11.2k0.5 12.71to.7

13.4M.l

13.2k0.3

11.2k0.5 12.6k0.7

23 TABLE 4 Limiting values of the relaxation times ~~@iClFc) and &(DiClFc) (pa) set by Eq. (2) and the assumption 40 ps 2 zd(DiClFc) 2 20 ps. The a’(DiClFc) values are those of Jakusek et al. [21divided by 2rc(see text)

T(“K) 295

300 307 315 d In z/dT’l

z’(DiClFc) 6.24 5.98 5.73 5.28 757

~~1 43.57 40 35.64 31.38 1525

Cat

7.28 7.03 6.83 6.35 612

Gnol

21.78 20 17.82 15.69 1525

Snt

8.74 8.53 8.44 7.96 408

that z’ must here be given by Eq. (4) in which z’ = 2;). Given that zmoz cannot be ascertained directly from experiment we assume, reasonably, that it lies somewhere in the range 40 ps 2 z,l(DiClFc) 2 20 ps for dilute benzene solutions at 300°K. The temperature dependence ofz,[(DiClFc) must also be estimated and to this end we assume that it can be obtained from Eq. (2); a simplification found to be approximately true in many cases [24]. Using the latter inequality, Eqs. (2) and (4), the benzene viscosity data from Timmermans 1161and the dielectric relaxation times of Jakusek et al. [2], Table 4 can be constructed5. Table 5 lists values of & (obs, mol and int) calculated by insertion of the corresponding (d In z/dZ’+l) data from Table 4 into Eq. (17). Also presented are AG$ and AS*values which were determined using Eqs. (18) and (16) respectively. The relatively large AI$?, in Table 5 can be equated with the Eyring molar activation enthalpy for viscous flow [5] of benzene. This follows from the proportionality between z and q in Eq. (2). While viscous flow involves both the rotation and translation of molecules, microwave dielectric absorption arises only from the rotation of molecules. If AH$,,(DiClFc) is over-estimated as a result of the use of Eq. (2), then AH&,(DiClFc) as calculated in Table 5 would be under-estimated. To gauge the extent of this we refer to the calculations of Riemschneider and Wucherpfennig 131for DiClFc in n-hexane, in which the average height of the five intra-molecular rotational energy barriers was shown 5 In Table 4, zmOlis set initially to either 40 ps or 20 ps (the limits of the inequality 40 ps 2 zmoz2 20 ps). Equation (2) is then used to calculate rml at other temperatures and Eq. (4) to calculate the corresponding &,t.

24 TABLE 5 Thermodynamic parameters for dipole rotation in DiClFc as a solute in benzene at 300°K based on the data of Jakusek et al. 121 Rotation mechanism

AG’ (kJ mol-‘)

obs

9.0

mol int

13.0 9.6

AZ$ (kJ mol-l)

ASS &.I mol-l Kl)

3.8 10.2 0.9 to 2.6

-0.017 -0.009 -0.029 to -0.023

to be 5.2 kJ mol-‘. The latter is an Arrhenius activation energy A@. To compare it with our (average) intramolecular enthalpy estimate, we must calculate tint + RT. The resulting molar Arrhenius energy for internal Q-Cl rotation is 3.4 kJ mol-’ c AZ&, < 5.1 kJ mol-‘. The agreement between the two AZ& estimates is better than 0.7 Ft,T per molecule. It is clear that the potential barriers hindering intramolecular ring rotation in DiClFc, and by inference in ClFc and TMePFc also, are very small; lying somewhere between 1 K,T and 2 k,T. Overall molecular rotation of the ferrocenes studied appears to be somewhat more restricted, probably because of solute-solvent interactions of the type envisaged by Debye [14] in his formulation of Eq. (2). ACKNOWLEDGMENTS The authors are indebted to Professor M.J. Aroney for many helpful discussions, to M.D. Filipczuk for critically reading the manuscript and to Professor F. Mathey, Universit6 Louis Pasteur, France, for kindly providing a sample of 3,3’,4,4’-tetramethyl-l,l’-diphosphaferrocene.

REFERENCES 1 2 3 4 5 6

L. Phillips and S.W. Filipczuk, J. Mol. Liquids, 47 (1991) 261. E. Jakusek, H.A. Kolodziej, M. Rospenk and S. Sorriso, Adv. Mol. Relax. Int. Proc., 22 (1982) 167. R. Riemschneider and W. Wucherpfennig, Z. Naturforsch., 21b (1966) 929. H. Eyring, J. Chem. Phys., 3 (1935) 107; H. Eyring, Chem. Rev., 17 (1935) 65. S. Glasstone, K.J. Laidler and H. Eyring, The Theory of Rate Processes, McGrawHill, New York, N.Y., 1941. E. Jakusek, P. Freundlich, H.A. Kolodziej and S. Sorriso, Adv. Mol. Relax. Int. Proc., 24 (1982) 271.

25

7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

E. Jakusek, P. Freundlich, H.A. Kolodziej and S. Sorriso, Adv. Mol. Relax. Int. Proc., 24 (1982) 283. W.D. Luke and A. Streitwiesser Jr., J. Am. Chem. Sot., 103 (1981) 3241. J.D. Hoffman and H.G. Pfeiffer, J. Chem. Phys., 22 (1954) 132. J.I. Lauritzen Jr., J. Chem. Phys., 28 (1958) 118. L. Phillips, A.R. Lacey and M.K. Cooper, J. Chem. Sot. Dalton Trans., (1988) 1383. S.J. Pratten, M.K. Cooper, M.J. Aroney and S.W. Filipczuk, J. Chem. Sot. Dalton Trans., (1985) 1761. G. Williams, J. Phys. Chem., 63 (1959) 534,537. P. Debye, Polar Molecules, Dover Publ., New York, 1945. R.J.W. Le Fevre and E.P.A. Sullivan, J. Chem. Sot., (1954) 2873. J. Timmermans, Physico-Chemical Constants of Pure Organic Compounds, Elsevier, Amsterdam, 1950. N.E. Hill, W.E. Vaughan, A.H. Price and M. Davies, Dielectric Properties and Molecular Behaviour, Van Nostrand, New York, N.Y., 1969. R.H. Cole, J. Chem. Phys., 42 (1965) 637. G. Williams, Trans. Faraday Sot., 64 (1968) 1219. J.D. Hoffman, J. Chem. Phys., 22 (1954) 156. J.D. Hoffman, J. Chem. Phys., 23 (1955) 1331. D.L. Levi, Trans. Faraday Sot., 42A (1946) 152. M. Davies and A. Edwards, Trans. Faraday Sot., 63 (1967) 2163. E.J. Hennelly, W.M. He&on Jr and C.P. Smyth, J. Am. Chem. Sot., 70,4102 (1948).