Dielectric constants of dimethvl siloxane polymers M . J.'Hunter
E. B. Baker and A. J . Barry
DOW CORNING CORPORATION, MIDLAND, MICA.
THE DOW CHEMICAL COMPANY, MIDLAND, MICH.
Dielectric constants as a function of the temperature of the homologous series of pure trimethyl end-blocked dimethyl siloxanes having from one to seven oxygen atoms have been measured. From these constants, together with density-temperature data and optical refraction data, the effective dipole moments in the concentrated liquids, the infrared dispersion, and the dipole, atomic, and electronic polarizations have been calculated by meansof theonsagerKirkwood theory. A special procedure was devised in.order to apply this theory to the present case, where dipole moments are small and infrared dispersion is large. TWO of the compounds are anomalous since they have a temperature-dependent apparent dipole moment, and this dependence is ascribed to association. A causal relation between the infrared dispersion and the dipole moment is found such that the total polarization per gram of material is almost independent of the chain length, whereas the proportions of the individual electronic, atomic, and dipole polarizations may vary from one member to another.
I
SDGSTRIAL attention has been directed to the liquid polysiloxanes since the announcement in 1944 that silicones were in commercial production (1). An infinite number of these materials is possible, in which organo-substituted silicon atoms are joined through oxygen to other silicon atoms. The silicon atom always has a valence of 1 and is never doubly bonded t o oxygen. All of the valences of each silicon which are not occupied by oxygen-to-silicon linkages are satisfied by organic groups bonded directly through one of their carbon atoms t o silicon. The result is an extremely stable, inert structure. Perhaps the best known of the silicone fluids is the family of dimethyl siloxane polymers:
(1)
where z denotes the number of dimethyl siloxane-repeating units (8, 11). The members of this polymer homologous series are all liquids characterized by their stability to heat, resistance t o oxidation, chemical inertness and their nonsolvency for organic insulating materials. Their exceptionally l o x rate of viscosity change with temperature and their utility over the wide temperature range of -40" to 200" C. are also important to many industrial uses. These fluids are good dielectrics and have power factors of less than 0.0002 a t frequencies up to 10 megacycles ( 3 ) . ,4t higher frequencies some absorption occurs with rise in power factor above 100 megacycles ( 6 ) . They are insoluble in water and adhere tenaciously t o siliceous surfaces. A very thin surface film applied to glass or ceramic insulator bodies produces a water-repellent surface which maintains high surface resistance even in marine atmospheres and with moisture condensed on the surface (8).
The dielectric constants and power factors a-s a function of temperature of the nonvolatile members of t h e series were reported previously ( 5 ) . The present paper reports t h e dielectrio constants of the purified lower members over a similar temperature range. The individual compounds were separated by careful fractional distillation after chemical treatment t o remove polar impurities. Calculation of dielectric polarizations allows some interesting qualitative conclusions to be drawn regarding the structure of these liquids. Included for comparison is tetramethyl silane which could be considered as the lowest member of the series, although it contains no oxygen.
Experimental proeedare The apparatus used was a General Radio 716-BS2 audio-frequency bridge, with General Radio oscillator as source and wave analyzer as detector. Incidentally, the sensitivity and stability of this wave analyzer are such that the limit of accuracy is imposed only by the precision of the reference condenser, which limit is common t o heterodyne methods as well. In this work, measurements mere made a t 1000 cycles since the power factor of these fluids, except in special circumstances, was less than the sensitivity (0.003%) of the bridge. Figure 1 shows the cell used. The central electrode is supported on Vycor rings. This cell had good stability but an inordinately large thermal lag and it was necessary t o wait one hour for temperature equilibrium at each point measured. The dielectric constants of the individual linear methyl polysiloxanes from the hexamethyl disiloxane through the octamer (z = 6) and a few of the heavier oils are plotted against temperature in Figure 2. Some viscosities and boiling points are included. The constants are, in general, low, and progression is toward a limit a t high viscosities. The same progression toxard a limit is shown by the densities in Figure 3; in fact, most of t h e temperature change in dielectric constant is due t o simple density change. The progression toward a limit is more clearly shown in Figure 4 where the dielectric constants and densities, as measured at 25' C.. are plotted as a function of the number of silicon atoms in the chain. The densities were determined with a gravity balance for the actual samples used in the electrical measurements. (Previous results have been given by Hurd, 7 . )
Calculations The dielectric constants of these compounds are slightly larger than the squares of their refractive indices, principally as a result of contributions of the silicon-oxygen bonds which are partially ionic in character. These contributions are in the form of small permanent moments, together with infrared dispersion due t o the SiOSi bonds. Like quartz itself, the silicone fluids have very strong absorption bands in the infrared. There are two bands due t o the SiOSi bonds in the near infrared (12) at 9.5g and 12g, approximately. 1112
1118
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Vol. 38, No. 11
which is not known separately. I t could be determined by actual dispersion measurements in the infrared, in this case by measuring the refractive index a t about 15, by interferometric methods. Gnless n, is known separately for introduction in formlua 2, it iE not possible t o determine by plotting a function of E against 1/T and measuring the slope, because of the implicit dependence upon E and n:, which are both temperature dependent. Fuoss and Kirkwood (6) used a n approximate expression obtained by assuming the Onsager internal field to prevail even for atomic and electronic polarization. For very polar material such as they were concerned with, this is no doubt a very good approximation. It has the great advantage of removing the implicit dependence on e and n: and thus it is possible to plot directly without knowing nr. I n the present case, however, where the electronic contribution is SOTo of the total polarizat;on, the polarization values calculated are far too high, and the dipole moments are also incorrect. Their relation is:
4TN
g j p P :
Figure I .
Cell used for dielectric constant measurements
= -;i-
[“
9e
The sum of the molar atomic and electronic polarization is thup assumed to be (n: - 1)(2n? 1) Jf Pa P. = h a d
+
+
instead of the Clausius-Mosotti relation, using the Lorentz internal field, From the dielectric constant and density data as a function of temperature it is possible t o compute the dipole moments, the infrared dispersion, and the various contributions t o the polarization by means of the Onsager-Kirkwood (9, 10) theory. The relation between the dipole moment, go, and the absolute temperature, T is given by them as
where N is Avagadro’s number; k is Boltzmann’s constant, g is a factor depending upon the coordination of the neighboring molecules immediately surrounding a given molecule of the substance (g = 1 for completely uniform surroundings, reducing this equation t o Onsager’s) ; E is the dielectric constant a t low frequency; and n is the refractive index-, a t infinite frequency if there is no infrared dispersion, or n, at II frequency between dipole dispersion and infrared dispersion, if there is. It so happens that the infrared dispersion is about equal t o the dipole dispersion for the silicone fluidswe are concerned with here and is too important to neglect’. I n this case n becomes n,, 1 Since the present article was submitted for publication, some measurements a t one temperature for these polysiloxanes have been pubfished by R. 0. Sauer and D. J . Mead [J.A m . Chem. SOC.,68, 1794 (1946)l. They calculated dipole moments, assuming zero contribution from infrared dispersion, and their values are thus considerably higher than the values derived here. The neglect of the atomic polarisation places their conclusions seriously in doubt, since the SiOSi infrared absorptions are strong enough and a t long enough wave length to make the effect unusually prominent for these oompounds. This is to be expected theoretically [L. E. Button, A n n R e p t s . Progreaa Chem.. 37, 67 (1940) 1, in view of the large S i 0 bond moment of 2.8 D derived by Sauer and Mead i n their paper.
The data of the present work do not extend over a sufficient temperature range t o distinguish between the Fuoss-Kirkwood, the Onsager-Kirkwood, or the Debye ( 4 ) relations on the simple basis of whether they plot as straight lines against 1/T, for straight lines are obtained with all of them or none of them, depending on the substance. The Fuoss-Kirkwood relation is thus good enough to use in a preliminary treatment to detect departure from simple conditions. The data for the dimethyl siloxanes are plotted by means of this relation in Figure 5. It is apparent that all members of the series yield good straight lines except the dimer and the tetramer, iyhich are anomalouR
-
Figure 2. Dielectric constants of dimethyl polysiloxanes as a function of temperature
1
1
,Tetramethyl Silane
I
I
I--
I
t
i
i
~
although they seem t o approach straight lines a t low temperatmes. Deviations such as these are to be expected for concentrated liquids, and in this case we believe they are due t o molecular association. Having plotted the data by the Fuoss-Kirkwood relation, we may select two points on the regular straight-line portions of each curve and calculate both PO and n, from the Onsager-Kirkwood relation analytically. (For greater precision all points could be used by least square methods.) We took the two points specially designated on the curves of Figure 5. For the anomalous dimer and tetramer these are selected t o give low-temperature limiting values, of more doubtful accuracy. Using the Clausius-Mosotti relation for the temperature-independent atomic and electronic specific polarizations (polarization per gram of substance),
/---I 1
1
'
I
pde4+2p:d
gE
-p,[l;
4(Ec1)'] (6)
Equation 6 is now in useful form, with x and p , as unknown parameters, and E and d as known functions of T from the data. Using two points we obtain two quadratic equations in x and p,, which may be solved by first eliminating x and solving the resulting quadratic in p?. We then calculate p~ from x and p. from p , by difference, since p , is known from the Clausius-Mosotti relation and the optical refraction: pr =
aln',
-1
l e o - l m = -de, + 2
where nm and ern are the refractive index and dielectric constant extrapolated t o infinite frequency. The optical values were used without extrapolation.
Figure 5.
Fuoss-Kirkwood total specific polarizations plotted against 1/T
Thus p a , p e , and pd have been determined by independent means, using Equations 6, 4 , and 9 . The total specific polarip . 4- pd = pl pd. The infrared dispersion zation is p , = p . is A€ = e, - e m where E? is obtained from p , by means of Equation
+
+
4. 100
NUYaCR
OF
200 SILICON ATOMS
3 00
Figure 4. Dielectric constants and densities at 25' C. of dimethyl polysiloxanes as a function of the number of silicon atoms in the molecule
Molecular polarizations are obtained by multiplying the spec fic polarizations by the molecular weights. The results of the calculations are shown in Figures 6 and 7, and in Table I where sonie of the results for the dimer and tetramer are given in parentheses t o indicate that they are approximate low temperature limiting values.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1120
Vol. 38, No. 11
.4
Figure 6. Dipole moment, infrared dispersion, and Onsager specific polarizations plotted against number of oxygen atoms in molecule
.2
-€
0
h
>
- INFRA- RED
A
T L {
DISPERSION
.2
h
I
1
I
I
I
I
I
I
I
1
> Figure 5 . Onsager molal polarizations plotted against number of oxygen atoms in molecule 2 3 4 5 6 Number of Oxygen Atoms
7
Conelasions 1. The dipole moments of the dimer and tetramer are relatively small a t low temperatures, and thus cause an alternation in the values plotted against n, the number of oxygen atoms in the chain. The moments of the higher members approach a limiting value in a regular manner and even decrease somewhat. We conclude that in the concentrated liquids the dipole moments of the dimer and tetramer are reduced more than the others due to association, as mentioned previously. There is a t the same time an internal compensation of the individual moments due to geometrical inctors in the molecular structure ( 5 )T\ hicli v, o d d , of course, persist in the vapor or dilute solution. The internal compensation accounts for the approximate approach to a limit for the higher members. 2. The infrared dispersion varies from member t o member in almost exactly opposite manner to the dipole moment. This may be seen even more emphatically by comparing the specific atomic and electronic polarizations. Although determined independently they add up to a nearly constant value. Thus if the dipole moment of one member is low its infrared dispersion is high. This implies a direct causal relition between them, and a very simple one. Both effects have the silicon-oxygen bond as their common origin. B y swinging a p , us. 1/T line about a single point (pa, to) the dipole moment, which is proportional to the slope, and the polarization pr, which is the intercept a t T = -, must necessarily vary in inverse relation to each other, and are thus not independent. Removal of the assumed restriction,
Literature cited
T A B LI.~ RESULTSOF CALCVLATIONS hlember n
M X
Pr
Dimer
1 162 (7.2) (0.351) (0.43) (2.08) 1.890 (0.19) 0.3033 (0.048) (0.024) (0.375) (0.072) 49.2 (7.8) (3.9) (60.9) (7.8) (3.9)
Trimer 2 236 16.7 0.3210 0.799 2.058 1.910 0.148 0,2870 0.0340 0,0560 0.3770 0.0901 67.8 8.0 13.2 89.0 3.23 6.61
Tetramer 3 310 (3.8) (0.360) (0.43) (2.33) 1.922 (0.41) 0.2764 (0.084) (0.013) (0.373) (0.097) 85.4 (26.0) (4.0) (1 15.4) (8,6) (1.3)
Pentamer
4 384 14.0 0.3311 0.932 2.210 1,932 0.278 0,2732 0.0679 0,0472 0.3783 0.1047 104.9 22.2 18.0 145,P 5.56 4.49
Hexamer 5' 458 18.4 0,3209 1.167 2.184 1.938 0,246 0,2700 0.0509 0.0618 0.3827 0.1127 123,7 23.3 28.3 175,3 4.66 5.66
Heptamer 6
532 16.2 0.3305 1.143 2.267 1.941 0.326 0.2665 0.0640 0.0510 0.3815 0.1150 141.8 34.1 27.3 203.1 5.67 4.54
passage through (PO,t o ) , makes slope and intercept independent. The experimental data impose this constraint approximately and there is thus a physical reason for this restriction. 3. Not only do the specific atomic and electronic polariz4tions add up t o a nearly constant value, but almost all of the variation that remains is compensated by a corresponding and opposite variation in the specific electronic polarization, which causes the total specific polarization t o be quite constant. Accepting the results a t face value, this includes the deformation of the electronic shells in the conspiracy as well, although their involvement is relatively minor. The constancy of the total specific polarization means simply that the polarization per gram of material is practically independent of chain length, and that the polarizations are distributed over the various forms in such proportions as t o adhere to this rule. 4. The molar polarizations are added for completeness, although multiplication by a large factor linear in n obscures some of the features noted for the specific polarizations. The lines for pt and p , intersect at n = 0 as they should, and the average of po and p d becomes zero at n = 0, where no silicon-oxygen bonds are present (n = 0 is tetramethyl silane, indicated on Figure 7).
Octa-
mer ' 7 606 12.5 0.3388 1.106 2.329 1.947 0.382 0.2647 0.0741 0.0420 0.3808 0.1161 160.3 44.9 25.4 230.6 6.41 3.63
(1) Bass, S. L., Hyde, J. F., Britton, E. C., and McGregor, R. R . , M o d e r n PEustiw, 22, 124 (Nov., 1944). (2) Bass, S. L., Hyde, J. F., and McGregor, R. R., J. Am. Cerum. s o c . , 29, 66 (1946). (3) Bass, S. L., and Kauppi, T. h.,Proc. Inst. Radio Engrs. 33, 441 (1945). (4) Debye, P., "Polar Molecules", New York, Chemical Catalog Co., 1929. ( 5 ) Fuoss, R. M., and Kirkwood, J. G., J . Chem. Phys., 9, 329 (1941). (6) Hippel, A. von, Lab. for Insulation Research, M.I.T., private communication. (7) Hurd, C. B., J . Am. Chem. Soc., 68, 364 (1946). ( 8 ) Johannson, 0. K., and Torok, J. J., Proc. Inst. Radio Engrs., 34, 296 (1946). (9) Kirkwood, J. G., J . Chem. Phus., 7, 911 (1939). (10) Onsager, L.,J. Am. Chem. SOC.,58, 1486 (1936). (11) Patnode, W., and Wilcock, D. F., J. Am. Chem. SOC.,68, 358 (1946); H u n t e r , M. J., Warrick, E. L., Hyde, J. F., and Currie, C. C., I b i d . , t o be published. (12) Wright, N., Dow Chemical Co., unpublished work.
