Mechanism of Dielectric Loss in Paraffin Wax Solutions 197 An allowance is made for the fraction of the surface covered by adsorbed gas, by introducing the Langmuir isotherm, and the equation D = ^ ( r r b ) accurately represents the experimental results.
198 W. Jackson The composition of simple dielectric liquids can be specified precisely and varied in known manner without difficulty, and, under the stimulus of Debye’s work on polar molecules, knowledge of the behaviour of such media has advanced enormously in recent years. As yet, however, little progress has been made towards relating the properties of solid dielectrics to their chemical and physical constitution. The extent to which the Debye theory in its present form is applicable to these media remains therefore uncertain.
Mechanism of Dielectric Loss in Paraffin Wax Solutions 199 circuit remained in tune to a given frequency when the capacitance was changed from Cx to C by the change-over of switch S. (A description of these condensers and of the arrangements for their temperature variation has been given previously.* In the present work a thermionic voltmeter was employed as the recording device, and the circuit resistance determined by the Distuning Method (oscillator control).!) The loss in the loaded wax dielectric of was deduced from the difference between the total apparent circuit resistance when the circuit capacitance was formed by or by C. In order that this difference shall be appreciable, it is essential that the inherent resistance of the coil and of C should be as small as possible. After much difficulty coils were made, suitable for measurements over a wide range of frequency, Fig. 1—L, coil coupled to source of H.F. oscillations; C, air condenser; Cx> test condenser; S, change-over-switch; Y, thermionic voltmeter with which the total power factor of the circuit (ratio of apparent resistance to inductive reactance, viz., R/coL) was less than 2 x 10-3. With this circuit there was no difficulty in measuring an incremental power factor due to the presence of the wax dielectric of 10-4.
200 W. Jackson still molten, the movable plate was adjusted to bring the capacitance to the desired order of magnitude. There is considerable contraction on solidification and consequently a risk of void formation between the plates. This risk was minimized by cooling the adjusted condenser in such a manner as to ensure that the wax between the plates was the first portion to solidify. It was not possible to prevent the localized formation of minute voids in the later stages of cooling, but as the testing voltage across the condenser was only of the order of 1 volt, this was not a matter for concern. Indeed, it was found subsequently that deviation from the standard routine did not affect the power factor value to any recognizable extent.
Mechanism of Dielectric Loss in Paraffin Wax Solutions 201 With a view to obtaining this information, a small proportion of a known polar material, miscible in a manner analagous to that of the products arising in the cooking process, was added to a sample of the wax. The material chosen was an ester, cetyl palmitate, Cl5H32C02Cl6H33, a good supply of which was available in a highly purified condition. This molecule differs from those constituting the paraffin wax in that a polar group—C02—exists in the centre of the hydrocarbon chain. This a 3 o o <3 <3 £ o Cl Q melting 'point Temperature °C Fig. 2—Curve A, frequency 8-3 x 106 c.p.s.; during temperature decrease from room temperature; • during temperature rise from 2° C; X on regaining room temperature overnight. Curve B, frequency 9 0 x 105 c.p.s.
202 W. Jackson An important factor in the discussion of these results must be the effect of concentration on the height of the power factor maximum. This- is shown in fig. 5 for a range of concentration of cetyl palmitate extending from zero to 12-85%, and it is observed that the power factor maximum Normal paraffin axis of dipole moment Cetyl palmitate Fig. 3 X 4-0 C 3-0 & 1-0 Temperature °C Fig. 4—Frequency of measurement: A, 6-6 x 105; B, 2-8 x 106; C, 7 - 78 x 106;. D, 1-42 x 107 c.p.s. On curve C: © during temperature decrease; • during temperature rise; x on subsequent slow regaining of room temperature deviates more and more from proportionality to the concentration as the latter increases. The power factor per unit concentration is given by the slope of the curve at the origin as 1 -25 X 10~3.
Mechanism of Dielectric Loss i Paraffin Wax Solutions 203 It is also important to ascertain whether the height of the maximum for a given concentration of cetyl palmitate, and its position in the temperature range for a given frequency, are dependent on the particular type of paraffin wax medium employed, and also how these quantities are related to the type of polar molecule added.
204 W. Jackson The curve of fig. 6 shows the results obtained at a frequency of 9 • 7 x 106 c.p.s. on a 4 • 57% solution of a different type of polar molecule, «-hexadecyl alcohol, in the 57-60° C melting-point wax. The molecular weight of this material is about one-half that of cetyl palmitate; its polar group, «> 075 Oh 0-25 0 10 20 30 40 50 60 70 Temperature °C Fig. 6 —OH—, is located at the end of the methylene chain, and the axis of the dipole moment lies roughly perpendicular to the direction of the chain, fig. 7. By deduction from the subsequent calculations, the magnitude of the power factor maximum for this concentration of n- hexadecyl alcohol should be of the order of 10 x 10-3. The curve of axis of dipole moment/ i i i i /i-Hexadecyl alcohol Fig. 7 fig. 6 appears, therefore, as only the fringe of the downward slope of a complete curve similar to those of fig. 4 for the cetyl palmitate solutions, and the maximum would be attained at this frequency only by an appreci able further reduction in temperature.
Mechanism of Dielectric Loss in Paraffin Wax Solutions 205 Dielectric Constant Measurements It is well known that in the region of frequency (constant temperature) or temperature (constant frequency) in which a power factor maximum appears, an anomalous change of dielectric constant occurs. In the Debye theory of dipole orientation in particular, the important criterion for the magnitude of the power factor maximum is the factor (s0 — s*), where s0 and s* are the dielectric constant values at zero or low frequency and at very high frequency respectively. If it had been possible to obtain a complete curve of the variation of s with frequency at constant temperature, this would have provided a direct check on the power loss measurements. Instead it was necessary to be content with a study of the variation of dielectric constant with temperature, where, however, the same anomalous change occurs but where other factors—variable density and the temperature itself—enter to render this correlation less satisfactory. Further, the significant dielectric constant changes are only of second order since they are superposed on a relatively large residual value due to the solvent. For these reasons the measurements have been regarded rather as a qualitative than a quantitative check on the foregoing power factor determinations. Nevertheless, the quantitative agreement is found to be satisfactory.
206 W. Jackson for this frequency—compare curves C and D, fig. 4. The rapid decrease as the temperature approaches and passes the melting point of the wax solvent is due mainly to decreasing density.