the behaviour of polar molecules in solid paraffin...

The behaviour of polar molecules in solid paraffin wax

By R. W. Sillars, D .Phil.

New College, Oxford

(Communicated by E. V. Appleton, —Received 25 July 1938)

Introduction

The idea tha t dielectric materials may contain minute electric dipoles, able to rotate under the action of an electric field, has been current for a very long time. Originally it provided simply a plausible explanation of the property which a dielectric has of increasing the capacity of a condenser into which it is introduced; later Hopkinson, Pellat, and others suggested tha t the “ anomalous ” after-effects of a condenser might be due to similar dipoles retarded by “ frictional” forces and able to rotate only slowly towards alignment with the external field.

The quantity of electricity concerned in these effects is often approximately conserved, so that the explanation was an attractively simple one. With a growing knowledge of the time-scale of molecular processes, however, the notion that a molecular dipole might take seconds or minutes to take up an equilibrium position lost favour, while a quantitative theory of dipole effects was developed by Debye. From this it appeared that, for dilute solutions of polar substances in simple light liquids, the times involved would be of the order of 10~9 sec.

Measurements of dispersion and absorption in such liquids at frequencies up to the present limits of electrical measuring technique have largely confirmed Debye’s quantitative conclusions. More viscous liquids, many of which contain molecules of widely differing sizes, and which may possess quasi-crystalline structures, do not show such a satisfactory agreement with the simple theory. More recently Debye and Ramm (1937) have published a treatment in which viscous and crystalline forces are regarded as acting simultaneously. This seems to fit the facts in some cases, but its application is somewhat limited because of the complexity of the analytical expressions involved.

I t is now generally accepted that dipole rotation may take place in solids, and there is a growing body of evidence that the time constant involved may be comparatively large; anomalous dispersion and absorption a ttributed to this cause have been observed at audio-frequencies and even at

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50 cycles/sec. These effects have been observed with such diverse substances as ice, glycerol a t low temperature, JZ-camphor, chlorinated diphenyls, and solutions of cetyl palmitate in paraffin wax. Although it may be debated whether these should all be regarded as solids in every sense, there is no doubt tha t the postulates of the original theory of Debye are not applicable to them.

In order to obtain more experimental information about effects of this sort, in the hope th a t it might help in formulating an adequate theory of them, it was decided to extend the experiments of Jackson (1935) with paraffin wax solutions. The long-chain paraffins are known to possess definite crystalline structures (Muller 1932) which are not likely to be seriously modified by the presence of a few per cent, of an ester of similar type. A preliminary experiment had suggested that the time constant depends to an enormous extent on the size of the ester molecule. The experiments of this paper were therefore directed to determining the time constants of 5 % solutions of different long-chain esters in a particular sample of paraffin wax at various temperatures below the solidification point.

For this purpose one may observe either changes of dielectric constant (dispersion), or changes of loss-angle (energy absorption). The former method is unsatisfactory with small concentrations of polar molecules, since the changes in capacitance due to changes in dielectric constant are of the same order of magnitude as those resulting from the changes of density and formation of voids in the wax on heating and cooling. The loss-angle method was therefore employed.

Methods and apparatus

The loss-angle of a condenser containing the material under test was determined at various temperatures and frequencies by the methods outlined below. The material was then removed and the condenser plates brought nearer together, so that the capacity was the same as before, and the loss- angle was again determined under the same conditions.

The difference between the two results, corrected for stray capacities in parallel with the specimen, was taken as the loss-angle of the material. The loss-angle of the empty condenser was found to be sensibly independent of temperature, so that it sufficed to measure this at room temperature only.

Radio-frequency measurements were carried out by the same method as Jackson employed. A suitable coil was connected to the terminals of the test condenser, forming a resonant circuit the power factor of which was found from the width of its frequency response curve (Moullin 1930, 1931).

The behaviour of polar molecules in solid paraffin wax 67



08 R. W. Sillars

Measurements at frequencies up to 25,000 cycles/sec. were effected with a bridge of the Schering type, using a Wagner earth.

The construction of the test condenser is shown in fig. 1. The sample is placed between two circular chromium plated brass electrodes. The upper electrode rests on the specimen unless the softening temperature of the latter is likely to be reached, in which case the electrode is supported from a brass block slung on quartz rods. The lower electrode is in good electrical

QUART 2

TINFOILUPPER ELECTROOt

LOW ER ELECTffOOl

Fid. 1

and thermal contact with the copper case which surrounds the whole condenser. This case is surrounded by, and is in good electrical contact with, a tinned sheet bath, filled with oil, water or methylated spirit, which can be heated electrically, or cooled by the addition of ice or solid carbon dioxide. An outer tinned sheet case is packed with powdered cork, as lagging. This is connected to the copper case for radio-frequency measurements, and to earth for bridge measurements.

Thermocouples are placed in the bath and in the upper electrode. The latter can be manipulated from outside the case and is withdrawn from the electrode before making a loss-angle measurement.

Connexion to the insulated electrode is made through a brass rod surrounded by a glass sheath protruding through the condenser case. I t was found that when low temperature baths were used it was difficult to prevent water and snow from accumulating on the glass sheath where it emerged




from the cold metal. As this lay in the stray field between the rod and the case, it gave rise to an indeterminate energy loss. To overcome this a strip of tinfoil was wound around the glass for about the first inch of its length, and connected to the case. This shielded the show from the stray field, and did not conduct away so appreciable a quantity of heat as to cause condensation farther out. Provided reasonable precautions were taken to wipe away moisture the leakage along the outside of the glass sheath was found to be insignificant, except for low audio-frequencies when it was eliminated by a further narrow strip of tinfoil connected to the earth of the bridge, using the familiar principle of the guard ring.

In order to prevent the entry of moisture into the condenser case all joints were packed with cork, and a supply of air, dried by passage through sulphuric acid and over phosphorous pentoxide, was pumped in through a side tube, a pressure of about 3 in. W.G. being maintained.

Presumably as a result of these precautions no trouble due to conduction by the surface of the specimen was encountered, and a guard ring was not employed. In one case a wax specimen which had been allowed to become damp showed a loss-angle a t low frequencies roughly proportional to the inverse of frequency, but this appeared to be a volume rather than a surface effect, for the provision of a guard ring did not diminish it appreciably.

Both radio- and audio-frequency measurements were sensitive to about 0*5 x 10~4 in phase angle, and the probable relative error between points on the same curve was estimated to be about 10~4. The absolute accuracy of the results depends on the accuracy of the determination of the loss-angle of the condenser, the accuracy of determination of stray capacities, and the absence of air gaps between the electrodes and the specimen. Errors due to the first two causes did not exceed 2 or 3 %, but it appeared that irregularity in the thickness of the specimen and more particularly the impossibility of ensuring that it lay perfectly flat, might give rise to errors as high as 7 % of the measured phase angle.

The difficulty of maintaining constant low temperatures in the bath gave rise to some uncertainty, particularly at temperatures far removed from that of the room. The procedure in taking readings was to observe the temperatures of the upper condenser plate and of the bath; when these were within half a degree of one another a measurement of loss-angle was made, and another pair of temperature readings taken immediately afterwards.

An uncertainty of about ± 1° C must be allowed in temperatures between 0 and — 30° C, and about ± 2° C in lower temperature readings.



70 R. W. Sillars

Materials

A refined wax melting over the range 57—60° C and known to have a negligible loss-angle was used as the solvent. Details of the esters employed are given below:

Ethyl stearate, C20H40O2: commercial supply, used as received.

Butyl palmitate, C20H40O2: synthesized from palmitic acid (Kahlbaum) which had been recrystallized from alcohol and benzene, and butyl alcohol of boiling point correct to C.

Butyl stearate (I), C22H440 2: commercial supply, used as received.

Butyl stearate (II): commercial supply, twice redistilled.

Butyl stearate (III): synthesized from stearic acid (Kahlbaum) and butyl alcohol, and further purified.

Octyl palmitate, C24H480 2: synthesized from palmitic acid and octyl alcohol.

Dodecyl palmitate, C28H 560 2: synthesized from palmitic acid and dodecyl alcohol.

Dodecyl stearate, C30H 60O2: synthesized from stearic acid (Kahlbaum) which had been recrystallized from alcohol and benzene, and dodecyl alcohol twice redistilled.

Cetyl palmitate, C32H640 2: spermaceti recrystallized three times from acetone and three times from ether.

To prepare a specimen for loss measurements, the molten wax containing about 5 % of ester was poured on to a pool of mercury contained in an iron pot about 8 in. in diameter, which had been warmed to a temperature of 70 or 80° C. This was allowed to cool and the edges of the wax sheet so obtained were cut off leaving a sheet whose thickness was about 0-08 cm. and did not vary by more than +0*001 cm.

The sheets so obtained were not all similar in appearance, although their preparation was as far as possible identical. Those containing cetyl palmitate, dodecyl stearate, octyl palmitate, and butyl stearate (III) were uniformly translucent. The sheet containing butyl stearate (II) showed occasional patches of white opacity, those containing dodecyl palmitate, butyl stearate (I), and butyl palmitate had similar patches covering about half their areas, and the ethyl stearate specimen was almost entirely opaque.




I t was suggested th a t these patches of opacity might be caused by the separation of some of the ester as a separate phase instead of remaining in solid solution. To investigate this point the solidification temperatures of solutions containing up to 20 % of butyl stearate (I) and of cetyl palmitate were observed. I t was found tha t the depression of the solidifying point varied linearly with concentration, the slope of the temperature-molar- concentration graph being the same for both esters.

Results and discussion

Observations were made on all the esters at two or more frequencies and over a range of temperature sufficient to delineate the curve of tan 8 down to values one-fifth of the maximum or less. A typical pair of curves, those for

OX<503

Tem perature °C

Fig. 2. 4-47% bu ty l stearate (III) in paraffin wax.

the specially synthesized butyl stearate, is shown in fig. 2. A set of similar curves covering five different frequencies is shown in fig. 3 for cetyl palmitate. The curves for the various esters were all fairly similar in shape with the exception of those of figs. 4 and 5 which will be discussed separately.

Observation of the variation of tan# with frequency at constant temperature of 0° C were made on the cetyl palmitate specimen and are shown in fig. 36. As it was more difficult to obtain accurate readings at constant temperature than at constant frequency, the constant temperature method was not employed again.



72 R. W. Sillars

F ig . 3 6. 4*92% cetyl palm itate in paraffin wax a t 0° C. x Points taken from constant frequency variable tem perature curves.

F ig . 4. 5-35% bu ty l stearate (I) in paraffin wax.




/4/" k c lse c

70 -60 -SO-40 S O S O - to O 10 SO 3 0

Tem perature °C

Fig. 5. 4*81% buty l stearate (II) in paraffin wax.

I t is proposed to discuss these results in terms of Debye’s equation

k ' tan 8 = k "4v (*q + 2)2 3 * 3

n/i*’M T ’ I + wV2’

where k'is the “ real component of dielectric constant” (i.e. dielectric constant in the ordinary sense) at any frequency.

k " is the “ imaginary component of dielectric constant” (corresponding to the conductivity or power loss),

d is the amount by which the phase-angle between current and e.m.f. is less than 90°,

x0 is the dielectric constant at a frequency so low that dipole effects are fully developed,

n is the number of polar molecules per c.c., a is their dipole moment,

o) is the angular frequency of the alternating e.m.f.,k is Boltzmann’s constant,-T is the absolute temperature,r is a constant with the dimension of time, corresponding to a relaxa

tion time, henceforward the “ time constant” .

I t will be assumed that the experimental curves are made up of a summation of curves of the type represented by equation (1). The use of this expression derived from consideration of rotation in a liquid finds more justification than appears at first sight, for any simple theory based on a relaxation



74 R. W. Sillars

mechanism leads to a similar form of equation. Debye, for instance, suggested the assumption that the ice molecule has two stable positions with a probability of transition from one to the other, and derived expressions of the same form as those of his liquid theory. The afore-mentioned trea tment of quasi-crystalline liquids by Debye and Ramm results in a series of terms of the same type. Gemant (1935) has also published an analysis in which the dipole is supposed to be affected by elastic as well as viscous forces, and concludes tha t the form of the equation again remains the same as in Debye’s original theory.

If for simplicity we write equation (1) as

K/ / Cn COT

T+ w ¥ ’ ( 2 )

and assume that there are several groups of dipoles a t work, the membeis of one group having time constants different from those of another group, but all having the same dipole moment, the total effect will be

c (n x (OTx ; + n9 ; +1 + co2t \ 21 o>2r |

In the more general case of a continuous distribution of the number of dipoles in any range of time constants such that

dn = F(r) dr,

we have at" = Cf — dnJ 1 -I-

- ° S i ^ F(T)dT-

I f the curve of k "is plotted against log co, the total area under the curve is

= c j - 2 F(T)dr = C ? jd n

= ^ Cn. (3a)

Thus this area is proportional to the total concentration of dipoles irrespective of the time constants associated with them. If the total concentration is known, then this area can be used to find the value of G, and hence the moment of the dipoles.




In the present experiments it is found tha t the curves are somewhat broader than equation (2) predicts, and this broadening is regarded as a spreading of the time constants about a central value. Such a spreading might be expected if the dipole molecules were not all identically situated. Whatever be the nature of the parameters controlling the value of r, they seem likely, a priori, to be affected by imperfections in the crystal of the wax solvent. Such imperfections would occur in any case in a pure solid unless extraordinary precautions were taken; they will be much more common in the mixtures employed for the present experiments. I t may be, indeed, th a t there exists no more than a certain orderliness in the arrangement of the molecules, not really meriting the description of a crystal. At any rate the existence of a range of time constants rather than a unique value is not surprising.

Equation (3 a) provides a means of calculating the dipole moment irrespective of this spreading. A similar integration with respect to logr can only be carried out strictly if the form of is known. I t can be shown, however, that provided F(t) approaches zero for all values of r outside a certain small range, i*.e. provided the range of spreading of r is small compared with r itself, its form is unimportant and

f k ". d(log r) = \ (36) Jo *

corresponding to (3a).The quantity k" is equal to k’ tan 8 The dielectric constant of the wax

alone was measured by Jackson (1935) and found to be 2-18. This value does not vary greatly with temperature below about 30° C, while variation due to dipole effects in the ester solutions is less than 1 %. In discussing the results of this paper, therefore, it will be assumed that

k " = 2* 18 tanwith sufficient accuracy.

From equation (2) the maximum value of (or tan 8) for varying w o r r

occurs when cot = 1, so that at this point we have r1 _ 1 co 27r /’ If, then, the

temperature a t which tan 8 is maximal is plotted against the logarithm of the inverse of the corresponding frequency, the resulting curve gives the relation between log 2nr and temperature. This is done in fig. 6, and a linear relation is found for dodecyl palmitate and for butyl stearate (I), while a slightly curved relation is found for cetyl palmitate. Most of the points of this figure are taken from curves of tan£ against varying temperature. According to equation (1) varying the temperature also varies the constant



76 R. W. Sillars

G of equation (2), so tha t maxima obtained in this way do not strictly correspond to m — 1. For the same reason the values of (tan £)max should decrease with increasing temperature. Examination of the various curves shows no particular systematic variation of this sort however, nor was such an effect found by Jackson. This factor has therefore been neglected and it is assumed that variation of temperature varies r only.

The relation between temperature and r can also be obtained by comparison of a curve of tan 8 against temperature at constant frequency with one against log(frequency) at constant temperature. If at temperature T0 tan 8 is ma ximal for oj = oj0, and if a change of temperature to Tx at constant frequency has the same effect as a change of to oj1 at constant temperature, then the change of temperature T0 to Tx corresponds to a change of r from 1 /(o0 to 1 Jo)v The points of fig. 7 are obtained in this way from figs. 3 and 36 for cetyl palmitate solution, the points of fig. 8 for the same ester are also sho wn as crosses on fig. 7 for comparison.

To determine the dipole moments, from the curves of tan against tem perature using equation (36), it was assumed that

log t — sT + constant,

where s is the slope of the appropriate line in fig. 8. The integral of equation (36) is then the area under the curve of tan 8 against temperature, multiplied by s. The moments calculated in this way are tabulated below. A value for the moment of cetyl palmitate calculated from the area under the curve of fig. 36, using equation (3a), is also included in the table.

E ster Dipole m om entE thyl stearate 130 x I0~8 e.s.u.

1*25 99

Butyl palm itate 1-56 99

B utyl stearate (III) 1-39 99

1-30 99

Octyl palm itate 1-22 99

1-22 99

Dodecyl palm itate 1-27 99

Dodecyl stearate 1-39 99

Cetyl palm itate 1-391-38 \ From tan

. 1-33 j tem perature curves9 ) J

1-36 „ From ta n in

frequency curves

The values obtained cannot be regarded as accurate, for in addition to the experimental errors already discussed the extrapolation of the curves to the



The behaviour of polar molecules in solid paraffin wax

ffthy! 'ptearate----- f------ fi°decyl

le&tX\f;rrZ a,‘

Tem perature (max.) °C

Fig, 6

Fig. 7. Correspondence of tem perature and log 2 deduced from fig. 9 b and the 141 kc./sec. curve of fig. 9 a.



78 R. W. Sillars

zero of tan 8 involves a rather indeterminate possibility of error. They are noticeably lower than the moment of esters determined by the usual methods, which are in the neighbourhood of 1-6-1-8.

In the discussion which follows (p. 79) it is concluded that rotation of the dipole can only occur by rigid rotation of the whole ester molecule about its long axis. In this case one would expect only the component of the moment perpendicular to this long axis to be effective, and since it is considered on chemical grounds that the electric axis is not perpendicular to the geometric one, a somewhat low value of effective dipole moment is rather to be expected. Unfortunately there does not seem to be sufficient certainty regarding the precise angle between the electric and geometric axes to make possible an accurate comparison of the moments in the above table with the values found for esters in solution in liquids.

The value calculated by Jackson from his results with cetyl palmitate is higher than the corresponding figures of the table above, although he did not take into account the “ spreading” effect. Jackson’s curves are, in fact, higher and sharper than the majority of those of the present work. Similarly the 3870 kc. curve of fig. 3 a is higher and sharper than those taken at lower frequencies. The cause of these differences has not been elucidated.

The majority of the curves are, however, of the general shape to be expected in view of the approximately linear relation between logr and temperature, and allowing for the “ spreading” effect already discussed. Exceptions are the curves of figs. 4 and 5, the former referring to a sample of butyl stearate as received from the supplier, the latter to a sample obtained from a different supplier and redistilled. The asymmetry of these curves might be attributed either to an abnormal and one-sided “ spreading” effect, or to a non-linear relation between log r and temperature*. The points for butyl stearate (I) in fig. 6 do not show any appreciable departure from linearity, so that this possibility is ruled out. I t was ascertained from the supplier that sample (II) had been prepared from commercial stearic acid containing about equal parts of stearic and palmitic acids. Butyl palmitate and butyl stearate were therefore synthesized from the pure acids and alcohol, and the curves obtained from them confirmed the suspicion tha t the curves of figs. 4 and 5 have two components, one corresponding to butyl stearate, and the other, somewhat larger, to butyl palmitate which displays

* D uring some prelim inary experim ents on sample (I) the la tte r explanation was considered the more probable and a theoretical discussion by F . C. F rank (1936) gave further grounds for believing it to be correct. Subsequent investigation, how ever, led to rejection of his explanation of the gross asym m etry of these curves in favour of the one given here.



a larger apparent dipole moment. The effect of redistilling sample (II) was probably to increase the proportion of palmitate. In fig. 8 is shown a composite curve obtained by summing the effects of 2*88 % butyl palmitate and 1*92 % butyl stearate calculated by simple proportion from the appropriate curves; the similarity to fig. 5 is apparent.

The elucidation of this point suggests that power factor measurements might provide a convenient means of identifying long-chain esters, ketones, etc. The separation and identification of mixtures of these compounds by ordinary chemical methods is extremely difficult (Piper and others 1931), but by dissolving the mixture in a hydrocarbon and plotting power factor

0-5

0 - 4

2 MX *0

g 02$

0-1


-70 -6 0 - SO-4 0 SO -20 -10 0 10 20 SO

Tem perature °C

Fig. 8. 2-88 % buty l palm itate and 1-92 % butyl stearate.

against temperature or frequency it should be possible to identify each chain-length from its contribution to the curve.

I t remains to enquire whether it is possible to elucidate the nature of the mechanism permitting rotation, and the physical significance of the time constant r. I t is known that pure hydrocarbon waxes form crystals in which the molecules lie side by side with their long axes parallel (Muller 1932). At low temperatures the packing is such that the molecules cannot rotate, but at temperatures near to the melting point the lattices of the higher waxes expand and rearrange themselves so that rotation of the molecules about their long axes can occur. I t is considered that the molecule is a rigid structure and rotate^ as a whole. X-ray powder photographs were taken at room temperature of the wax used in these experiments, and also of the wax containing 5 % of butyl stearate (III). In both cases sharp rings were obtained indicating a definite crystalline structure. The side spacings seemed to indicate that the wax molecules themselves are unable to rotate, at any rate up to room temperature, and one must suppose that the rotating ester



80 R. W. Sillars

“ fits loosely” into the lattice of fixed wax molecules. The proportion of ester molecules is not sufficiently great for a structural change in their immediate neighbourhood to show up on the X-ray photographs.

In fig. 96 the temperature for which tan <5 would be a maximum at a frequency of 3160 kc./sec. is plotted against the number of carbon atoms in the ester, the temperatures being obtained by interpolation in fig. 6. A smooth curve is obtained, from which it appears that the total length of the

N um ber of carbon atom s6

F ig . 9„ V ariation of time constant with chain length,

chain determines this temperature and tha t the position of the polar group in the chain is unimportant. Consider, for instance, butyl stearate having 22 carbon atoms. If we subtract two carbon atoms we can either take them from the long stearate chain leaving butyl palmitate, or from the short butyl group leaving ethyl stearate, and whichever we do the effect is the same, within the limits of experimental error. Similarly the point for dodecyl stearate in fig. 96 lies fairly between those for dodecyl and cetyl palmitates having two carbon atoms less and more respectively. I t seems safe to conclude, therefore, tha t the molecule behaves as a rigid whole, for if rotation of the dipole were allowed by a distortion of the molecule one would expect the nearness or otherwise of the polar group to the end of the chain to have a considerable influence.




In connexion with fig. 9 bit is perhaps worth remarking tha t the smooth curve provides additional confirmation that the effects observed are actually due to polar molecules and not to some spurious cause such as conduction effects arising from impurities. The processes of purification were by no means the same for all the esters and it is inconceivable that any spurious effects could give a smooth curve when plotted against the chain length of the ester.

As regards the significance of the time constant r, the simplest hypothesis to make would be that the molecule suffers a ‘ ‘ frictional ’ ’ restraint, somewhat analogous to that of a shaft rotating in a journal. In this case a theory similar to that of Debye for liquids could be constructed, where the viscous restraint on a rotating sphere would be replaced by tha t on a rotating cylinder. The constant would then be proportional to the length of the molecule, i.e. to the number of carbon atoms in it. That this is not so is apparent from the table below. The values of r shown are obtained by interpolation in fig. 6.

E sterE thyl stearate B utyl stearate Octyl paim itate Dodecyl stearate Cetyl paim itate

N um ber of carbon atom s

20 22 24 28 32

2irr a t — 20° C 2-0 x 10-7 sec. 3*3 x 10~6 „ 1*6 x 10- * „ 6*3x10-* „ 9*8 x 10- * „

I t is interesting to compare the results of Holzmliller (1937) who determined the time constants of a number of ketones ranging from acetone to nonyl acetyl ketone in solution in benzene and in hexane. He found that the time constants varied as a power of the molecular weight slightly greater than unity, and that the calculation of the time constant from Stokes’ equation became more valid the higher the molecular weight. This, incidentally, also implies a rotation of the molecules as a whole, for if distortion occurred the time constant would increase less rapidly than the molecular weight.

Another way of interpreting r is to regard it as inversely proportional to the probability that a dipole will rotate under the influence of the external field in a particular interval of time. This is the interpretation given to it by Debye in a tentative explanation of dipole effects in ice, to which reference has already been made. If, in the case of esters, we suppose each carbon atom to have an independent probability of moving, and if we further suppose that the dipole rotation can only occur if every atom of tbe molecule seizes an opportunity to move within a particular short interval of time, then the probability of rotation will vary exponentially with the inverse of

Vol. CLXIX. A. 6



82 R. W. Sillars

the number of atoms, in other words log r will vary as the number of carbon atoms in the ester. Fig. 9a shows log27rr plotted against the number of carbon atoms, and though the departure from linearity is not so wild as in the attem pt to correlate r itself with the number of carbon atoms, there is no sign of support for the above supposition.

I t seemed desirable to find out how the lengths of the wax molecules compared with those of the esters; to this end the long spacings were obtained from the X-ray photographs and found to indicate a chain length of about 26 carbon atoms. The influence of this magnitude on r cannot be discussed in the absence of a reasonably detailed hypothesis regarding the mechanism of rotation. There is not, however, any satisfactory theory of dipole rotation in solids which takes into account the time effects which are the subject of these experiments, and it must be reluctantly confessed that these experiments have not suggested any simple extension of existing theory.

To Mr E. B. Moullin, for his invaluable help and criticism, and to Mr D. R. Pelmore, who carried out all the chemical operations, as well as the X-ray measurements, the writer is greatly indebted.

He also has to thank the Metropolitan-Vickers Electrical Company, Ltd., for a scholarship enabling this research to be carried out a t the Engineering Laboratory of the University of Oxford, Dr A. P. M. Fleming, O.B.E., Director of the Company for his interest in the work, and the staff of the G.P.O. Research Station, Dollis Hill, for their help in connection with the X-ray measurements.

Summary

The experiments described constitute an extension of previous work by Jackson and were carried out on solid samples of paraffin wax containing small concentrations of various long-chain esters. The esters are of molecular type similar to the wax, but have a permanent electric moment in virtue of the ester group. Dipole effects similar to those found by Jackson are observed and the variations of. the characteristic time constants with temperature and with chain length of the esters are studied. Variation with temperature is approximately exponential, the exponent being about the same for each ester. I t is found tha t the time constant is a non-linear function of the total chain length of the ester molecule, but is relatively independent of the position of the ester group in the chain. I t is confirmed that the observed losses are due to dipole effects and not to some adventitious




cause. I t is concluded tha t the whole ester molecule contributes to the time constant, and therefore that it behaves as a rigid structure and does not simply become deformed in the immediate neighbourhood of the dipole group. This is in agreement with evidence from other sources. The results do not suggest any simple relation between chain length and time constant, and a satisfactory theory to relate them has yet to be found.

References

Debye, P . and R am m , W . 1937 A Phys., 28, 28. F rank , F . C. 1936 Trans. Faraday Soc. 32, 1634.Gem ant, A. 1935 Phil.Mag. 19, 746.Holzmiiller, W. 1937 Phys. Z . 38, 574.Jackson, W. 1935 Proc. Boy. Soc. A, 150, 197.Moullin, E. B. 1930 Wireless Eng. 7, 367.

— 1931 “ Radio-Frequency M easurem ents” , pp. 273 et seq. Griffin. Muller, A. 1932 Proc. Roy. Soc. A, 138, 514.Piper, S. H. and others 1931 Biochem. J . 25 , 2072.

Ionic recombination in air

By J. Sayers, Ph .D.*

Cavendish Laboratory and St John’s , Cambridge

(Communicated by E. V. Appleton, F.R.S.—Received 26 August 1938)

1. Introduction

The fundamental importance of the problem of recombination of ions in gases was appreciated almost as soon as the role of ions as carriers of electric charge in gas conduction was recognized. Indeed it was at one time believed that the greater part of the light emitted in the Geissler tube discharge had its origin in the energy resulting from ionic recombination.

Rutherford and Thomson were the first to show, and verify experimentally, that the rate of decay of ion population by recombination was proportional to the product of the numbers of ions of either sign. Thus, if we

* Musgrave Research Student, Queen’s University, Belfast.



the behaviour of polar molecules in solid paraffin...

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