the dielectric relaxation of some aliphatic chain compounds containing a polar group

39

Advances in Molecular Relaxation Processes, 6 (1974) 39-59 Q Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

THE DIELECTRIC RELAXATION OF SOME ALIPHATIC CHAIN

COMPOUNDS CONTAINING A POLAR GROUP

(Received July 24th, 1973)

JOHN CROSSLEY

Department of Chemistry, Lakehead University, Thunder Bay, Ontario (Canada)

CONTENTS

1. Introduction II. Ethers.

111. Ketones . . . IV. Amines . V. Bromoalkanes

VI. Alkenes . Summary . . References .

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39 40 40 46 47 54 58 58

1. INTRODUCTION

Dielectric absorption measurements at microwave frequencies have provided

an effective means of studying molecular structure in liquids and solutions’* ‘.

Aromatic molecules, especially those containing a rotatable polar group, have

been extensively investigated’, and it has often been possible to analyze their

absorptions in terms of two discrete relaxation processes: an intramolecular,

having a short relaxation time, and a molecular, with a relatively long relaxation

time. Aliphatic molecules are far more flexible and their dielectric dispersion is

usually characterized by a distribution of relaxation times, which is not always

symmetrical. The aliphatic alcohols have probably received more attention than

any other group of compounds4; however, a detailed molecular mode1 which

provides a satisfactory interpretation of pure liquid and solution measurements

is as yet unavailable5* 6. Unfortunately, apart from the early work of Smyth and

his students’ - lo, on n-alkyl bromides, no systematic studies of non-associated

aliphatic liquids have been reported. Furthermore, the interpretation and com-

parison of the existing relaxation data for pure liquids is complicated by uncer-

tainties regarding the effects of viscosity, internal field and molecular interaction.

These problems are largely eliminated in dilute solution with a non-polar inert

solvent, but it is only recently that any data have become available”- 14.

40 J. CROSSLEY

This article will review the dielectric relaxation for some aliphatic chain

compounds relevant to the author’s recent results”-‘4, which form part of a

systematic study of aliphatic molecules. Aliphatic alcohols and substituted ethanes

have been discussed in an earlier review4 and will not be mentioned here.

II. ETHERS

Table 1 summarizes the relaxation data obtained for some alkyl ethers in

n-heptane solution”* 16. The Cole-Cole distribution parameter, GL, for diethyl

ether is close to zero and the data cannot be represented by two relaxation times.

For the other ethers it was possible to analyze the data in terms of two discrete

relaxation times which were assigned to whole molecule rotation, ri, and intra-

molecular rotation, z2, by twisting about the C-O or C-S bonds.

TABLE 1

RELAXATION PARAMETERS FOR SOME ALKYL ETHERS IN II-HEPTANE

Data taken from ref. 15

Ether

Diethyl ether

Di-n-butyl ether

Di-n-hexyl ether

Di-n-dodecyl ether

Di-n-dodecyl sulphide

n-Dodecyl methyl ether

III. KETONES

T

(“C)

6 25

25

12 30 50

12 30 50

20 35 50

12 30 50

TO

hec)

1.9 0.03 1.3 0.06

16 3.4

18.6 0.14 14.8 0.11 5.9 0.01

42.5 8.0 30.7 7.1

42.4 0.35 204 9.3 28.6 0.25 119 7.7 10.6 0.12 41 6.2

45.1 0.35 213 11.9

29.2 0.26 122 10.3

13.3 0.13 47.7 8.5

9.5 0.34 46.4 4.4 7.0 0.25 36.1 3.7 5.5 0.18 28.4 3.2

G( t1

(t--c) T2

(psec)

_

C2

0.76

0.70 0.75

0.49 0.59 0.75

0.53 0.59 0.72

0.63 0.71 0.80

In contrast to aromatic ketones very few dielectric absorption measurements

have been reported for alkanones. Smyth and co-workers17*18 measured some

ketones as the pure liquids and their results are presented in Table 2. The mean

ALIPHATIC COMPOUNDS CONTAINING A POLAR GROUP 41

TABLE 2

RELAXATION PARAMETERS FOR SOME ALIPHATIC KETONES AS PURE LIQUIDS

Data taken from refs. 17 and 18

Ketone T to a 4 QlT (“C) (psec) (CP)

Acetone 1 4.0 0.03 0.40 10.0 20 3.3 0.0 0.33 10.0 40 2.8 0.0 0.27 10.2

2-Heptanone 1 15.3 0.12 1.10 13.9 20 10.8 0.07 0.81 13.4 40 8.2 0.06 0.62 13.1 50 7.8 0.0 0.56 13.9 60 6.1 0.05 0.50 12.2

4-Heptanone 1 17.3 0.09 0.98 17.7 20 12.5 0.07 0.74 17.0 40 8.9 0.08 0.57 15.6 60 7.2 0.10 0.46 15.7

I-Pentadecanone 50 32.9 0.11 1.85 17.8

9-Heptadecanone 50 35.0 0.09 2.5 14.0

relaxation times, q,, lengthen with increased molecular weight and the results

were interpreted in terms of dipole reorientation by whole molecule rotation and

an intramolecular process possibly involving twisting around the R-C and R’-C

bonds of the ketone

0 II /,

iCIR, R

Unlike the ethers, however, the ketone loss data did not separate into two dis-

persion regions.

Table 3 shows the relaxation data obtained for some ketones in cyclohexane

solution using a Cole-Cole distribution function. The T,, values for the 2-alkanones

and all the nonanones and 4-decanone are shorter than anticipated for molecular

rotation and are of the same magnitude as the relaxation time for acetyl group

rotation in aromatic molecules’s-20 (-7x lo-l2 set) and for acetone21S22

(3.2 x IO-l2 set) in dilute solution. For the 2-alkanones z. only slightly lengthens

as the alkyl group is increased from C4 to C,, , 5. for 2-octanone in n-heptane16

at 25 “C is 4 x lo-l2 set, and it is probable that dipole reorientation occurs

primarily by the intramolecular rotation of the terminal acetyl group. The location

of the carbonyl group on the hydrocarbon backbone has relatively little effect

42 J. CROSSLEY

TABLE 3

RELAXATION PARAMETERS FOR SOME ALIPHATIC KETONES IN CYCLOHEXANE SOLUTION AT 25 “C

Data taken from refs. 12 and 14

Ketone ro b:

(psec)

2-Hexanone 4.0 0.04 2-Nonanone 5.9 0.14 3-Nonanone 6.5 0.08 4-Nonanone 8.1 0.03 5-Nonanone 7.2 0.06 2-Decanone 6.1 0.08 4-Decanone 8.3 0.00 7-Tridecanone 13.8 0.07 2-Pentadecanone 6.8 0.15 4-Pentadecanone 11.0 0.17 S-Pentadecanone 17.1 0.13 2-Nonadecanone 8.3 0.18 IO-Nonadecanone 22.0 0.15 11 -Heneicosanone 22.2 0.11 Di-r-butyl Ketone 3.4 0.05 2,2-Dimethyl-3-heptanone 6.9 0.09 3-n-Butyl-2-heptanone 19.7 0.10 1,3-Diphenyl-2-propanone 12.5 0.10 Hexanophenone 18.8 0.11

on the relaxation time for the nonanones and decanones. In these molecules,

dipole orientation may occur either by overall molecular orientation or by

twisting around the R-C and R’-C bonds. The latter type of intramolecular

mechanism, which has also been invoked to explain the rapid relaxation of di-

phenyl ether’ 3, appears to make a large contribution to the absorption for these

ketones.

The relaxation times for the long-chain symmetrical ketones are signifi-

cantly longer than those for the 2-alkanones and detectably lengthen with increased

molecular size. Asymmetric loss curves have been obtained24 for 7-tridecanone

and lo-nonadecanone in cyclohexane at 22 “C. Relaxation times were not reported

but the loss curves indicate relaxation frequencies comparable with those in

Table 3. It appears that when both R and R’ are sufficiently long the intramolecular

process is restricted and the contribution from whole molecule rotation increases

with increased length of R and R’.

Aliphatic ethers and ketones have the structure

X

R’ ‘R’


with their resultant dipole moments approximately bisecting the RXR’ angle.

The mean relaxation time for n-dodecyl methyl ether in Table 1 (R’ = C,,

R = C,,) is very similar to those for several of the 2-alkanones (R = C,-C,, , R’ = C,). In addition the me values for di-n-hexyl ether and 7-tridecanone

(R’ = R = C,) are similar and for symmetrical ethers and ketones ~~ shows a

regular increase with increased number of carbon atoms. This suggests that whole

molecule rotation is a significant factor in their dielectric absorption. The results

given in Table 2 for pure liquid ketones are in agreement with the interpretation

of the cyclohexane solution results.

The work on ketones has been extended to include compounds in which

intramolecular rotation may be sterically restricted14. The mean relaxation time

for di-t-butyl ketone (Table 3) is quite short and the Cole-Cole c1 value is small,

thus it would appear that the t-butyl groups do not interfere with one another

in the intramolecular twisting mechanism which is the major process of dipole

reorientation. The relaxation time for 2,2-dimethyl-3-heptanone is quite similar

to those for the nonanones, also in cyclohexane solution. Thus the two methyl

groups adjacent to the carbonyl group of the former molecule are insufficient in

size to hinder intramolecular rotation to any significant extent. In contrast, the

n-butyl group in 3-n-butyl-2-heptanone appears to have a marked steric effect.

The relaxation time for this molecule in cyclohexane is considerably longer than

those for the 2-alkanones, and in the more viscous hexadecane (Table 4) it is longer

than that for lo-nonadecanone. It would appear that rotation of the whole mole-

cule makes an important contribution to the dielectric absorption of this sub-

stituted heptanone, the Cole-Cole distribution parameter c( is considerably greater

than zero; however, the data could not be analyzed in terms of contributions from

TABLE 4

RELAXATION PARAMETERS FOR SOME ALIPHATIC KETONES IN NON-POLAR SOLVENTS AT 25 “c


Ketone Decalin Hexadecane Parafln Oil-cyclohexane mixture

._

2-Hexanone 2-Nonanone 5-Nonanone 7-Tridecanone 8-Pentadecanone 2-Nonadecanone IO-Nonadecanone

1 I-Heneicosanone 3-n-Butyl-2-heptanone Hexanophenone

To (psec)

5.2 8.3 9.7

20.8 24.8 11.2 32.0

35.3

39.3

IX

0.09 0.09 0.06 0.08 0.12 0.17 0.11

0.09

0.08

to be4

4.8 8.5 9.6

19.4 24.0 12.8 31.9

36.9 41.2

GL

0.15 0.15 0.10 0.10 0.13 0.16 0.11

0.11 0.09

to We4

6.6 12.5 12.1 24.2 31.8 15.6 38.9

55.4

cf.

0.05 0.06 0.06 0.08 0.14 0.13 0.13

0.09

44 J. CROSSLEY

two reasonable relaxation times. The mean relaxation time for 1,3-diphenyl-2-

propanone is much shorter than that for benzophenone25, 19 psec in cyclohexane

at 25 “C, which has a somewhat similar shape and size. Benzophenone is an

essentially rigid molecule and thus intramolecular twisting about the benzyl-

carbonyl group bonds must make a significant contribution to the dielectric

absorption of 1,3-diphenyl-2-propanone. This is not unreasonable since the

resonance effects thought to be responsible for the high barrier to intramolecular

rotation in benzophenone are considerably reduced in the propanone. Unlike

the case of aliphatic ketones, segmental rotations are largely unimportant for

this aromatic ketone and the possibility of two overlapping Debye dispersions

due to whole molecule and intramolecular rotations is more probable. Although

the Cole-Cole plot for this compound in cyclohexane does not show any distinct

separation it is possible to obtain a good fit to the experimental E’ and E” data

using z1 = 18 psec, r2 = 5 psec and C, = 0.7, which are not unreasonable values

for the above processes. The mean relaxation times for hexanophenone, benzo-

phenone25 and acetophenone 26 in cyclohexane at 25 “C are 18.8, 19 and 10.2 psec

respectively, and the respective values in decalin also at 25 “C are 39.3, 34.6 (ref. 27)

and 17.5 psec. The resonance effects which restrict intramolecular rotation in

benzophenone are not as important for acetophenone. The mean relaxation time

for the latter is shorter than expected for molecular rotation and its dielectric

absorption data may be analyzed in terms of two relaxation times which can be

reasonably assigned to whole molecule and intramolecular rotation. Hexano-

phenone is similar in size to benzophenone and the mean relaxation times of these

two ketones in both cyclohexane and decalin are quite close. For hexanophenone

it would appear that the steric effect of the alkyl group together with the resonance

effect of the aromatic group gives rise to a high barrier to intramolecular rotation

and dipole reorientation is dominated by rotation of the whole molecule.

The relaxation time of a rigid molecule lengthens with increased solvent

viscosity, but experiments have shown2* that the viscosity dependence of the

relaxation time does not conform to a simple relationship, and is considerably

influenced by the shape of the solute molecule and the relative size of the solute

and solvent molecules. However, the ketones under investigation are non-spherical

in shape and although r0 will not be directly proportional to the macroscopic

viscosity it should detectably lengthen if the rotation of the whole molecule makes

any significant contribution to the dielectric absorption. Intramolecular rotation

occurs with relatively little displacement of surrounding molecules and the

relaxation times have generally been considered to be independent of viscosity.

Thus for a system in which dipole reorientation is achieved by both whole molecule

(7,) and intramolecular (TV) rotation the ratio t1/r2 would be expected to increase

with increased viscosity and give rise to a distortion of the Cole-Cole plot, which

should facilitate an analysis in terms of two relaxation times. The Cole-Cole

plots for the ketones in decalin, hexadecane and paraffin oil-cyclohexane are as

ALIPHATIC COMPOUNDS CONTAINJNG A POLAR GROUP 45

symmetrical as those obtained in the less viscous cyclohexane. The relaxation

times in Table 4 do lengthen with increased solvent viscosity however, i.e. cyclo-

hexane < decalin z hexadecane < paraffin oil-cyclohexane.

A comparison of the effect of increased viscosity on the relaxation time of

each ketone is given in Table 5, and, as expected even for rigid molecules, the

viscosity ratios are much greater than the corresponding relaxation time ratios.

The rp/cc value* for 2-nonanone appears to be anomalously high when compared

with the values for the other 2-alkanones; however, the viscosity of 2-nonanone

in paraffin oil-cyclohexane solution is greater than that of the others. In order

to partially correct for the difference in viscosity of the paraffin oil-cyclohexane

solvents the reduced relaxation time ratios are presented in the last column of

Table 5.

TABLE 5

RATIOS OF RELAXATION TIMES IN CYCLOHEXANE (Tc), DECALIN (TD), HEXADECANE (TV) AND PARAFFIN

OIL-CYCLOHEXANE (tp), AND REDUCED RELAXATION TIMES IN CYCLOHEXANE (TRC) AND PARAFFIN

OIL-CYCLOHEXANE (Qp) AT 25 “c (q&c = 3.5, r/&,Jc = 3.8)


Solute TDITC TWITC zdtc IlPh= k4TRC __~~~~___~~~ ~~ _____~~~ _ _ ~~_ 2-Hexanone 1.3 1.2 1.7 8.5 0.17 2-Nonanone 1.4 1.4 2.1 13.1 0.16 5-N onanone 1.4 1.3 1.7 8.4 0.18 7-Tridecanone 1.5 1.4 1.9 10.5 0.17 I-Pentadecanone 1.5 1.4 1.9 11.6 0.16 2-Nonadecanone 1.4 1.5 1.9 11.6 0.16 1 0-Nonadecanone 1.5 1.5 1.8 11.7 0.15 J I-Heneicosanone 1.6 3-n-Butyl-2-heptanone 1.9 Hexanophenone 2.1 2.2 3.0 12.1 0.43

Hexanophenone and 3-n-butyl-2-heptanone had previously been considered

to be rigid molecules and the ratios for these compounds in Table 5 are greater

than those for the other ketones in all the solvents. The values for the first seven

ketones in Table 5 are very similar, which is somewhat surprising in view of the

earlier interpretation of the cyclohexane data. In addition, the small differences

between the relaxation times of the 2-alkanones in cyclohexane are magnified in

the more viscous solvents, and it would appear that whole molecule rotation does

contribute to the absorption of the 2-alkanones, but the magnitude of this contri-

bution is less than it is for the symmetrically substituted ketones. However, it

was not possible to obtain sensible analysis in terms of two relaxation times,

probably because segmental rotations, which are not possible for the analyzable

* The symbols tp and tc are defined in Table 5.

46 J. CROSSLEY

aromatic ketones, also contribute to the absorption. In fact for a majority of the

ketones the distribution parameters listed in Tables 3 and 4 show no significant

increase with increased solvent viscosity, which might indicate that the intramolec-

ular and whole molecule relaxation times are lengthened. The effect of viscosity

on these processes for aliphatic molecules has not been investigated in any system-

atic studies and consequently there is little with which to compare the values in

Table 5. For n-octyl bromide, dipole reorientation is thought to occur by a

variety of segmental rotationsz9 and TH/TC at 25 “C is 1.2.

The TJTC value for anisole at 25 “C is about 1.2 and in solution the intra-

molecular relaxation process has a weight factor3’ of about 0.65. The T~/TC

values for both acetophenone and benzophenonez6* ” are about 1.7.

IV. AMINES

The relaxation times obtained for some aliphatic amines”, 31, 32 are shown

in Table 6. For the primary amines as pure liquids or in solution the TV values

are too short to be ascribed to whole molecule rotation and are of the magnitude

obtained for the intramolecular relaxation of small polar groups in aromatic

molecules3. No significant increase in z. with increased size of the alkyl group

TABLE 6

RELAXATION PARAMETERS FOR SOME ALIPHATIC AMINES

Data taken from refs. 11, 31 and 32

Amine

Ethyl- n-Propyl- n-Butyl- n-Amyl- n-Hexyl- n-Nonyl- 2-Nonyl- %Nonyl- n-Decyl- n-Undecyl- Diethyl- Di-n-Propyl- Di-n-Butyl- N,N-Dimethyl-n-octyl- N,N-Diethyl-n-octyl- N-Methyl-n-octyl-

Pure liquid, Cyclohexane,

0°C 25 “C

to u.

b-4

4.1 0.07 4.0 0.0 5.1 0.0 5.0 0.0

8.2 0.07 12.4 0.13 17.1 0.0

to Wee)

1.6

2.2 3.1 4.1 3.6 3.0 3.5

13.5 26.1

8.9


or with the location of the NH2 group in the nonylamines is apparent. These

results suggest that dipole orientation in primary n-alkylamines occurs pre-

dominantly by a fast intramolecular relaxation process, and rotational orientation

of the whole molecule makes little or no contribution to the absorption. In contrast

the mean relaxation times for the secondary and tertiary amines, which are much

longer than those for the primary amines, lengthen with increased number and

size of the N-alkyl groups. The lengthening of r,-, for the n-octylamines is greater

than would be expected if an intramolecular process dominated their absorption.

The relaxation time for N,N-diethyl-n-octylamine (R-N(C,H,),) is considerably

longer than that for pure liquid diethylamine (H-N(C,H,),). It would appear

that reorientation of the whole molecule makes a significant contribution to the

absorption of secondary and tertiary amines. The contribution apparently increases

with the size of the N-alkyl group.

The restriction of intramolecular relaxation is brought about with far

smaller R groups for amines, R-NR,, than for ketones RCOR. In ketones,

0

II C

/\ R R’

the carbonyl group is coplanar with the R-C and R’-C bonds. Steric hindrance

to rotation about these bonds only occurs with relatively large R and R’ groups.

The amines,

R

I N

/‘\ R’ R”

are pyramidal and the R’NR” angle is smaller than the RCR’ angle. This gives

rise to some steric restriction to rotation about the R-N bond for secondary

amines with a small N-alkyl group, and the effect is considerable for tertiary

amines. It is probable that intramolecular relaxation only makes a small contribu-

tion to the dielectric absorption of N,N-diethyl-n-octylamine.

V. BROMOALKANES

In their early microwave studies Smyth and co-workers’-” measured

twenty-seven organic halides, including twelve I-bromoalkanes, at three micro-

wave frequencies from 1 to 55 “C. The mean relaxation times and Cole-Cole

distribution parameters (Table 7) increased with increased chain length and

decreased temperature. Smyth’s group considered that the large distribution param-

eters for the long-chain bromoalkanes result from segmental reorientations about

48 J. CROSSLEY

TABLE 7

RELAXATION PARAMETERS FOR SOME BROMOALKANES, C.H2.+1Br AS PURE LIQUIDS AT 25 “C


n

2

3

4

5

6

7

8

9

10

12

14

16

to @xc)

3.8

5.8

8.7

12.1

15.7

19.2

21.8

28.5

33.7

48.9

53.8

69.6

a

0.06

0.09

0.10

0.14

0.17

0.20

0.23

0.24

0.25

0.26

0.27

0.29

TL TlJ

(psec) (psec)

1.8 8.0

2.2 15.2

3.1 24.6

3.3 44.5

3.6 67.8

3.7 99.8

3.7 128

4.3 187

4.9 231

6.9 348

7.0 413

8.1 597

C-C bonds. They also observed a close parallelism between the processes of di-

electric relaxation and viscous flow. Higasi et a1.33 represented the dielectric

data for these bromoalkanes in terms of a distribution of relaxation times, similar

to that given by Frijlich 34, between two limiting values. The lower limit TV was

attributed to the relaxation time for the rotational orientation of the terminal

CHzBr group. The upper limit ~~ was considered to represent the relaxation time

of the largest orienting unit, usually the end-over-end rotation of the molecule

as a whole. It was claimed that the numerical values given in Table 7 are consistent

with this physical picture, indicating the approximately correct nature of the

distribution function. The absorptions of a number of the liquid bromoalkanes

were further measured at millimetre wavelengths in order to obtain improved

accuracy for the CH,Br group relaxation times35. The results, when examined

together with the previous lower frequency data, revealed asymmetric complex

plane plots. Unexpectedly high losses were obtained at 2.2 mm and the arc plots

had left and right skews. They retained the concept of a distribution of relaxation

times between limiting values and used a more general form of distribution func-

tion.

Denney36 studied some isobutyl and isoamyl halides at low temperatures

(100 OK) in the frequency range 0.05 kHz to 2 MHz and obtained Cole-Cole

complex plane loci in a skewed-arc form with small deviations at the highest

frequencies. Further work37 on these halides in the supercooled liquid state

established a close similarity between viscous flow and dielectric relaxation.

Glarum3* reviewed both Smyth’s and Denney’s work on bromoalkanes

and pointed out that for isobutyl bromide the parameter /I, which occurs in the

skewed-arc function, varies from a low temperature value of 0.5 to nearly unity


at room temperature, in which case Smyth’s data are described by a circular arc

with a small distribution parameter. Glarum measured isoamyl bromide at 1, 3

and 9 GHz between - 75 and + 25 “C. The experimental points at all temperatures

fell reasonably close to a single curve on a reduced complex plane plot which could

be described by an asymmetric skewed-arc distribution function with fl z 0.7,

although a circular arc plot gave a better representation of the high frequency

data. A “defect diffusion model” was proposed to explain the behaviour in which

it is supposed that the skewed arc arises from cooperative relaxation. This model

implies that the relaxation of a molecule is most probable immediately after one

of its neighbours has relaxed.

Mopsik and Cole39 examined the dielectric absorption of n-octyl iodide

over a wide frequency range between - 40 and + 40 “C. The frequency dependence

of the loss was found to deviate only slightly from a Cole-Davidson skewed-arc

function at all temperatures. Mopsik and Cole suggested that if some of Smyth’s

data were experimentally in error then they could also be represented by skewed

arcs. The latter behaviour was attributed to a diffusion mechanism for which the

decay function is not exponential and is only formally expressed as a continuous

distribution of exponentials.

TABLE 8

RELAXATION PARAMETERS FOR SOME BROMOALKANE~, c~H~~+,BT. IN SEVERAL SOLVENTS AT 25°C

Data taken from ref. 13 and the author’s unpublished results

_ n Cyclohexane

70 cc

(psec)

8 16.2 0.24

10 20.0 0.21

12 23.1 0.21

14 24.3 0.23

16 25.5 0.24

18 26.6 0.22

Solvent I Soluent II Solvent III

70 a

(psec) 70 a

be4

20.8 0.21

26.0 0.27

34.4 0.27

38.7 0.29

47.1 0.31

27.1 0.21

31.6 0.25

36.8 0.26

38.8 0.27

42.0 0.29

44.3 0.28

70 c(

(we4

32.2 0.33

41.9 0.32

47.8 0.32

52.9 0.31

58.9 0.33

Table 8 shows the relaxation parameters for six monobromo-n-alkanes in

solution at 25 “C. In all cases the absorption data were well described by a Cole-

Cole distribution. Solvents I, 11 and III were prepared from various non-polar

saturated hydrocarbons in order to facilitate a discussion of viscosity effects.

Solvent I was prepared so as to give solution viscosities close to those of the pure

liquids. Solvents II and III have viscosities of about 5.5-7.5 and 14-20 CP respec-

tively. The CI values show no apparent solvent or solute dependence. The r0 values

for the bromoalkanes in cyclohexane solution’3 are much longer than those for

analogous ketones and amines (Tables 3 and 6 respectively). These results suggest

50 J. CROSSLEY

TO 70-

50-

30 -

10 n 5 10 15 20

Fig. 1. Plot of to (psec) against the number of carbon atoms n in the R group of n-bromoalkanes RCH,Br as pure liquids (O), in cyclohexane (v ), in solvent 1 (A), in solvent II (a), and in solvent III (0) at 25 “C. Data taken from refs. 13, 33 and author’s unpublished results.

0 e- 0 I I , n

5 10 IS

Fig. 2. Plot of to/q (psec/cP) against the number of carbon atoms n in the R group of l-bromoalkanes at 25 “C in the same notation as Fig. 1. Data taken from refs. 13, 33 and author’s unpublished results.


that polar end group rotation is not as dominant a mechanism of dipole reorienta-

tion for bromoalkanes as it is for primary amines and 2-alkanones. However,

the mean relaxation times for bromoalkanes in cyclohexane lengthen only slightly

with increased molecular size and the contribution from intramolecular rotation

is not negligible. The molecular size dependence of r0 for bromoalkanes in several

solvents and as pure liquids is illustrated in Fig. 1. The curves for cyclohexane,

solvent II and solvent III have a similar shape and show a decreased slope with

increased number of carbon atoms of the solute molecule. For each of these three

systems the macroscopic viscosity of the solvent is relatively constant and the

viscosities increase cyclohexane < solvent II < solvent 111. The viscosities of the

liquid bromoalkanes increase with increased molecular size and the viscosity of

each bromoalkane in solvent I is very close to the viscosity of its pure liquid. The

curves for the pure liquid and solvent I are steeper than the others and their slopes

increase with increased number of carbon atoms, which is undoubtedly a con-

sequence of the increase in viscosity. Figure 2 shows the molecular size dependence

of the reduced relaxation time, r&l, and is strikingly different from Fig. 1. How-

ever, it is again noticeable that the pure liquid and solvent I curves are quite

similar and differ only in the magnitude of r,,/q. The curves for the more viscous

solvents II and III are almost linear and horizontal in contrast with the cyclo-

hexane curve. Smyth and co-workers have reasonably explained6- lo the shape of

the pure liquid curve, and thus that for solvent I, by suggesting that the increasing

internal orientating power of the molecular chains causes the increase in relaxation

time with increasing chain length to fall farther and farther behind the increase in

viscosity. In addition, it has been shown 4o that even for rigid molecules, unless

the solute molecules are about three times the size of the solvent molecules then

the Debye equation is inadequate and the molecular relaxation time is not directly

proportional to the macroscopic viscosity. The viscosity dependence of r. for

five bromoalkanes is shown in Fig. 3; the curves are relatively smooth and flatten

off at the higher viscosities.

A comparison of the relaxation times and viscosities for the pure liquid and

solvents I-III with those in cyclohexane is shown in Table 9. The relaxation time

ratios are generally much lower than the viscosity ratios. The viscosity ratios for

each bromoalkane as the pure liquid and in solvent I are very similar since the

solvents were made up in order to produce this effect. However, the relaxation

times (Tables 7 and 8) and relaxation time ratios for the pure liquids are greater

than those for solvent I. There are two possible reasons for this behaviour: (i)

molecular dipole-dipole interactions in the pure liquid slow down the rotation

of the reorienting dipoles; such interactions will be minimal in dilute solution,

and (ii) the internal field effect, which is negligible for dilute solutions, will lengthen

the relaxation times for the pure liquid. The internal field correction has been cal-

culated for the liquid bromoalkanes using the Powles4i expression and the values

may be compared with ~O(liquid)/ZO(solvent I) in Table 10. It is evident, even allowing

52 J. CROSSLEY

0 4 8 I2 16

Fig. 3. Plot of r,, (psec) against viscosity for I-bromooctane (A), I-bromodecane (m), l-bromododecane (7 ), I-bromotetradecane (3) and 1-bromoctadecane (0) at 25 “C. Data taken from ref. 13 and author’s unpublished results.

TABLE 9

RELAXATION 1’IMES AND VISCOSITIES OF SOME BROMOALKANES IN VARIOUS SOLVENTS DIVIDED BY

THEIR RESPECTIVE RELAXATION TIMES AND VISCOSITIES IN CYCLOHEXANE SOLUTION AT 25 “C

Data taken from refs. 13, 33 and author’s unpublished results

”

8 10 12 14 16 18

Pure liquid

d%YC rll%YC

1.50 1.55 1.69 2.38 2.12 3.75 2.21 4.33 2.73 7.0

Solvent I Solvent II Solvent III

~l~cyc rhwc ~l~c,c rll%ve hyc rllrwc

1.28 1.52 1.67 5.38 1.99 14.4

1.30 2.23 1.58 5.77 2.10 15.2 1.49 3.70 1.59 7.64 2.07 15.8 1.59 4.29 1.60 6.57 2.18 18.7 1.85 6.62 1.65 6.83

1.67 7.53 2.21 19.4 _~~ _~____ ~~

TABLE 10

COMPARISON OF RELAXATION TIMES FOR I-BROMOALKANES As THE PURE LIQUIDS AND IN DILUTE

SOLUTIONS OF THE SAME VISCOSITY, WITH THE POWLES INTERNAL FIELD (E)

Data taken from ref. 33 and author’s unpublished results

I-Bromooctane 1.17 1.24

1 -%romodecane 1.30 1.21

l-Bromododecane 1.42 1.19

I-Bromotetradecane 1.39 1.17 I -%romohexadecane 1.48 1.17

ALIPHATIC COMPOUNDS CONTAINING A POLAR GROUP

TABLE 11

53

RELAXATION PARAMETERS FOR SOME DIBROMOALKANES

Data taken from refs. 42-45

Compound State a

1,4-Dibromobutane4’

48 34 27

T

(“(3

0.0 18.5 34.5

0.0 19.0 41.8

20.0 31.5 44.0

38 30 22

t1

(psec)

1,6-Dibromohexane4’

45 37 32

35 35

35 35

35 35

1,6-Dibromohexane4” 35 35

20 40 60

20 40 60

20 40 60

L L L

L L L

L L L

L B

L B

L B

L B

L L L

L L L

L L L

L L L

L L L

L L L L

L L L

L L L

20.7 12.9 7.3 6.4

33.0 22.2 12.3 9.1

37.5 23.0 15.0 11.2

47.4 26.4 20.7 14.4

24 19 16

26 19 16

24 19 15

1 ,4-Dibromopentane44 20 32 40 24 60 17

1,4-Dibromob~1tane~~ 1 66.2 40.4 25 33.1 23.0 40 21.4 17.1

1,6-Dibromohexane45 1 90.7 52.0 25 48.8 35.3 40 31.9 24.5 55 22.0 18.3

1,8-Bromooctar1e~~ 25 73.4 43.7 40 50.4 32.6 55 36.0 25.8

I,lO-Dibromodecan& 30 76.0 43.7 40 58.1 37.2 55 39.0 28.9

a L and B indicate pure liquid and benzene solution, respectively.

2.5 0.72 2.8

2.5 0.78 3.1

2.5 0.82 2.8

2.5 0.84 3.2

2.8 0.88 2.3 0.88 2.1 0.88

3.5 0.91 3.0 0.88 2.6 0.88 2.5 0.88

3.0 0.88 2.6 0.88 2.9 0.85

2.9 0.88 2.9 0.86 3.4 0.83

54 J. CROSSLEY

for any inadequacy in the Powles expression, that the internal field effect alone

does not account for the difference between the pure liquid and dilute solution

relaxation times. Dipole-dipole, or other, interactions apparently contribute to

the longer relaxation times in the pure liquids, and the effect would seem to increase

with increased molecular size. This of course does not necessarily imply stronger

interactions for the longer molecules.

In contrast to the Cole-Cole distribution shown by the monobromoalkanes

at 2.5 “C, a number of workers 42-45 have obtained Cole-Davidson skewed arcs

for some dibromoalkanes as the pure liquids and in dilute solution, and the

relaxation times are given in Table 11. The mean relaxation times for the dibromo-

alkanes are considerably longer than those for the analogous monobromo-

alkanes, and the distributions are quite small. It would appear that dipole re-

orientation by whole molecule rotation makes a large contribution to the absorp-

tion of the dibromoalkanes and that segmental rotations are much less important.

Anderson and Smyth44 suggested that the dielectric behaviour of the dibromo-

butanes and 1,Cdibromopentane was essentially that of rigid molecules. However,

the highest frequency they used was only about 9 GHz and they could not rule

out small contributions from CHzBr group rotation. Chandra and Prakash43 and

Garg et a1.45 made measurements at higher frequencies and their data could

be adequately represented by skewed-arc plots. In addition, both groups were

able to analyze their data in terms of a superposition of two non-interacting Debye-

type relaxations. The two relaxation times were reasonably assigned to end-over-

end molecular rotation, tI , and CH,Br group rotation, r2. The agreement between

the analyses given by Chandra and Prakash43 and Garg et al.45 is remarkably

good. However, the 71 values are generally shorter than the 7u values obtained

for the monobromoalkanes. It is evident that the mechanism of dielectric relaxa-

tion for dibromoalkanes is quite different from that for the monobromoalkanes.

These results are in sharp contrast with the behaviour of monosubstituted and

para-disubstituted benzenes46; the dielectric absorption of the latter is almost

entirely due to intramolecular relaxation and their relaxation times are much

shorter than those for the monosubstituted compounds.

VI. ALKENES

The mean relaxation times for some pure liquid I-alkenes4’ listed in Table 12

lengthen with increasing chain length up to 1-hexadecene. The slight decrease for

1-heptadecene is probably not significant and the t0 values for 1-hexadecene,

I-heptadecene and 1-octadecene are probably only accurate to + 10 % because

of their low losses. The results suggest that the dielectric dispersion of 1-alkenes

is not dominated by the polar end group rotation mechanism responsible for the

dielectric dispersion of primary amines” and 2-alkanonesl’ but involves larger


TABLE 12

RELAXATION PARAMETERSFORSOME I-ALKENESAT 25°C


Alkene ro a

(psec)

Hexene 5.2 0.13 Octene 10.4 0.25 Decene 17.6 0.24 Dodecene 21.6 0.34 Tetradecene 29.7 0.28 Pentadecene 35.3 0.24 Hexadecene 41.4 0.30 Heptadecene 36.7 0.35 Octadecene 39.8 0.37

Fig. 4. Plot of r. (psec) at 25 “C against the number of carbon atoms n in the n-alkyl R group of pure liquid alkenes (m), pure liquid I-bromoalkanes (O), I-bromoalkanes in cyclohexane solution ( x ), 2-alkanones in cyclohexane solution (7 ) and I-aminoalkanes in cyclohexane solution (A). Data taken from ref. 47.

species. Figure 4 shows a plot of z. measured at 25 “C against the number of

carbon atoms in the R groups of 1-bromo-alkanes RCH,Br, 1-alkenes RCHCH,,

I-aminoalkanes RNH, and 2-alkanones RCOCH, . For the latter two, which were

measured in cyclohexane solution, r. is relatively independent of the size of R.

56 J. CROSSLEY

The magnitude of the relaxation times implies that dipole reorientation occurs

primarily by rotation of the terminal NH, and COCH, groups respectively. It

has been mentioned that the r0 values for 1 -bromoalkanes in cyclohexane lengthen

with increasing chain length but the curve levels off as R increases, whereas the

chain length dependence of r0 for the pure liquid bromoalkanes is more

pronounced and the slope increases as R increases. The curve for the liquid

I-alkenes also shows that me has a marked dependence upon chain length. In

general, the comparison of r0 values for pure liquids requires some caution since

a number of largely unknown factors such as microscopic viscosity and molecular

interaction, which are constant in dilute solution, complicate the situation.

Analogous I-alkenes and I-bromoalkanes have a similar shape and size and it is

not unreasonable to compare the viscosity dependence of their TV values. Figure 5

shows a plot of the reduced relaxation times, se/q, which according to Debye

theory are proportional to the volume swept out by dipole reorientation, against

the number of carbon atoms in the R groups of the liquid I-alkenes, liquid l-

bromoalkanes and I-bromoalkanes in cyclohexane solution. The latter two

curves were discussed earlier. The curves for the pure liquids are similar but the

r&l values for the bromoalkanes are smaller than those for the corresponding

I 1 I t

0 5 n ‘O 15

Fig. 5. Plot ofz& (psec/cP) against the number of carbon atoms in the n-alkyl group R for pure liquid I-alkenes (a), pure liquid l-bromoalkanes (0) and I-bromoalkanes in cyclohexane solution ( x ) at 25 “C. Data taken from ref. 47.


alkenes. This is not unexpected since the bromoalkanes have the larger viscosities

and even for large rigid molecules the internal friction coefficient is smaller than

the macroscopic viscosity 4o It is noticeable that 1-hexadecene is the only com- . pound to show a marked deviation from the curve for the alkenes, which suggests

that its r. value may be the erroneous one amongst the larger alkenes in Table 12.

The z,/q values reach a maximum for five and seven carbon atoms in the R groups

of 1-bromoalkanes and 1-alkenes respectively instead of increasing continuously,

and this behaviour was discussed previously.

TO

30 - .

.

.

Fig. 6. Plot of the experimental x,, value for l-bromoalkanes (0) and the calculated to value for I-alkenes in cyclohexane solution (a) at 25 “C against the number of carbon atoms in the n-alkyl group. Data taken from ref. 47 and unpublished results.

Because of their small dipole moments, -0.4 D, molecular interaction and

internal field effects for 1-alkenes will be quite small and it may be reasonable to

compare their ~~ values with those for the I-bromoalkanes in dilute solution. By

making the assumption that the viscosity dependence of 7. for corresponding

bromoalkanes and alkenes is the same, the relaxation times for the alkenes in

cyclohexane have been calculated from the ~~ and viscosity values of the bromo-

alkanes in solvent 1 and in cyclohexane and for the liquid alkenes. Figure 6 com-

pares the measured relaxation times of the bromoalkanes with the calculated r.

values for 1-alkenes in cyclohexane solution. The curves are in quite good agree-

ment considering the approximations, and serve to indicate further that dielectric

relaxation in 1-alkenes and 1-bromoalkanes involves similar mechanisms.

58 I. CROSSLEY

SUMMARY

In the previous sections a relatively large number of relaxation data have

been presented for discussion. For the amines, ethers and ketones with polar end

groups dielectric relaxation is dominated by intramolecular rotation. However,

if the polar group is well removed from the chain end for ethers and ketones and

if the amines are N-substituted the intramolecular process may be restricted.

Segmental rotations seem to present a reasonable model for the relaxation of

I-alkenes and I-bromoalkanes, while the absorption of a,o-dibromoalkanes is

much more dominated by whole molecule rotation. The potential barrier to

rotation of the terminal NH, and COCH, groups in amines and ketones is less

than that for rotation about the skeleton C-C bonds48 and the dielectric absorp-

tion is dominated by terminal group rotation. In contrast, the potential barrier

to CH,Br group rotation is slightly greater than that for rotation about skeleton

C-C bonds, and the absorption may be interpreted in terms of segmental rotations.

However, the potential barrier for rotation of the CH: CH, group is similar to

that for NH2 and that for COCH, is considerably less than that for CH,Br, but

the dielectric behaviour of alkenes is similar to that of I-bromoalkanes. A barrier

height model cannot alone explain the differences in dielectric relaxation amongst

the various n-alkyl compounds. An additional factor to be considered is the

direction of the resultant electric dipole moment within the molecule. For aromatic

molecules it is quite simple to use group dipole moments and bond angles to cal-

culate the contributions from various modes of dipole reorientation’. The task

is obviously more difficult for aliphatic chain compounds.

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the dielectric relaxation of some aliphatic chain compounds containing a polar group

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