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Pressure Dependence of the Dielectric Constant (for Water, Ethyl Alcohol, Methyl Alcohol, and Acetone).
(G. Falckenberg. Abhängigkeit der Dielektrizitätskonstante des Wassers, Äthylalkohols, Methylalkohols und Aceton vom Druck. Annalen der Physik 61, p. 145 — 1920).
The dependence of the dielectric constant on pressure has already been investigated by Röntgen¹), Ratz²), and Orlway³). These authors come to the conclusion that the increase of the dielectric constant, \(\Delta \varepsilon\), when the pressure is increased from 1 to 500 atmospheres, amounts to no more than \(1\%\) (for ethyl alcohol, methyl alcohol, water, ethyl ether, benzene, chloroform, etc.). The author of the paper under review believes that the methods of his predecessors were insufficiently sensitive and precise, and he determines the increase of the dielectric constant using the very sensitive method improved by Drude.
The liquid under study is poured into a small condenser included in the secondary oscillatory circuit. In the primary circuit the author places a spark gap and antennas, connected according to Rukop’s method⁴), which make it possible to obtain oscillations with weak damping and with a variable wavelength. The wavelength can be changed very finely by acting on a micrometric screw and, by means of it, increasing or decreasing the capacitance of the antenna.
The antennas of the secondary circuit can also be slightly lengthened or shortened, which already permits a coarser tuning of the systems into resonance. The energy of the oscillations in these antennas can be measured with the aid of a thermoelement included in the secondary circuit and connected to a sensitive Du-Bois-Rubens shielded galvanometer.
Plotting on diagrams, along the abscissa axis, the divisions of the micrometer that lengthens and shortens the primary antennas, and along the ordinate axis—the galvanometer readings, the author constructs resonance curves and from them determines the position of the micrometer screw corresponding to resonance.
By compressing the liquid enclosed in the condenser, he observes a displacement of the “resonance point” and from it determines the increment of the dielectric constant.
For this purpose the apparatus is first calibrated: a definite mixture of water and acetone is poured into the condenser (6, \(12^{1}/_{2}\), and 25 g of acetone per 100 g of mixture). The values of the dielectric constant for such mixtures the author borrows from Drude’s work⁵) and observes what displacement of the micrometer screw corresponds to a definite change of the dielectric constant of the liquid filling the condenser in one case or another.
Since the paraffin oil that fills the Caillete pump and compresses the liquid in the condenser is also in an electric field (though a weak one), and since in the final result a change may be reflected
¹) W. C. Röntgen. A. d. P. 52, p. 599. 1894.
²) E. Ratz. Z. f. phys. Chem. 19, p. 111. 1896.
³) R. Orlway. A. d. P. 59, p. 1. 1919.
⁴) H. Rukop. A. d. P. 42, p. 489. 1913.
⁵) P. Drude. A. d. P. 61, p. 496. 1897.
dielectric constant of paraffin oil, the author introduces the corresponding corrections.
Falckenberg’s results are as follows:
1) Water.
Column “A” corresponds to the initial pressure in the vessel, equal to 7 atmospheres. Column “B” corresponds to the pressure raised to 200 atmospheres (the observation is made after thermal equilibrium has been reached—after the temperature of the compressed liquid has fallen to its former value. The temperature in the room is kept constant throughout the experiment within the limits of \(16.3^\circ \pm 0.1^\circ\) C).
Column “C” corresponds to the pressure again reduced to the initial 7 atmospheres.
| Group of observations | Micrometer setting, mm: A | Micrometer setting, mm: B | Micrometer setting, mm: C | Mean difference, mm |
|---|---|---|---|---|
| 1 | 42,92 | 46,06 | 43,50 | 2,35 |
| 2 | 50,48 | 53,25 | 50,20 | 2,91 |
| 3 | 51,21 | 54,78 | 51,51 | 3,40 |
Mean: \(3.05 \pm 0.23\)
The calibration of the instrument indicated above makes it possible to conclude that, when the pressure is increased by 193 atmospheres, the dielectric constant increases by 0.764–0.775.
Introducing a correction for the change in the dielectric constant of the oil enclosed in the pump, the author finally obtains: for \(\Delta \rho = 193\) atm — \(\Delta \varepsilon = 0.722\), i.e. about \(0.88\%\).
2) Ethyl alcohol.
The values in column “B” were obtained under the same conditions as in the case of water. Columns “A” and “C” correspond to a pressure of 15 atm.
| Groups | Micrometer setting, mm: A | Micrometer setting, mm: B | Micrometer setting, mm: C | Mean difference, mm |
|---|---|---|---|---|
| 1 | 38,25 | 40,43 | 38,50 | 2,05 |
| 2 | 39,75 | 42,17 | 40,02 | 2,28 |
Mean: \(2.16 \pm 0.07\)
Taking into account the calibration of the apparatus and introducing the correction, the author finally obtains:
\[ \text{for } \Delta p = 185 \text{ atm.} \qquad \Delta \varepsilon = 1.8\%. \]
3) Methyl alcohol.
Similarly to the first two cases, one obtains:
Average displacement of the micrometer: \(3.09 \pm 0.04\) mm,
and finally:
\[ \text{for } \Delta p = 185 \text{ atm.} \qquad \Delta \varepsilon = 1.88\%. \]
4) Acetone.
Average displacement of the micrometer: \(2.98 \pm 0.03\)
\[ \text{for } \Delta p = 185 \text{ atm.} \qquad \Delta \varepsilon = 2.9\%. \]
Since for water, ethyl alcohol, methyl alcohol, and acetone the dependence between pressure and density has already been found with sufficient accuracy, the author uses his experimental material to test formulas expressing the relation between density and the refractive index \((n)\), taken as equal (for long waves) to the square root of the dielectric constant,
\[ n_{\infty} = \sqrt{\varepsilon}. \]
Of the three formulas expressing this relation:
\[ \text{a) } \frac{n^{2}-1}{d} = \mathrm{Const} \quad \text{b) } \frac{n-1}{d} = \mathrm{Const.} \quad \text{and} \quad \text{c) } \frac{n^{2}-1}{n^{2}+2}\cdot\frac{1}{d} = \mathrm{Const}, \]
the most accurate agreement is given, as it turns out, by the first. The last formula (Lorentz–Lorenz’s) gives unsatisfactory results.
To explain this the author attempts, following Wien1, to insert into this formula, instead of the number 2, a certain number \(u\), the greater, the more the shape of the molecule differs from spherical.
Proceeding partly from his own work and partly from the work of Ortvay2, he finds for \(u\) values that sometimes have absolutely no physical meaning (for ethyl alcohol, for example, \(u=\infty\)). The author explains the inapplicability of the Lorentz–Lorenz formula in these cases by strong polymerization of the molecules. He finds arguments in favor of such an assumption by comparing certain constants characterizing polymerization, namely the Eötvös constants (the temperature coefficient of the molecular energy of the surface layer) and the Trouton constants (the quotient obtained by dividing the molecular latent heat of evaporation by the absolute boiling temperature).
It turns out that liquids showing the greatest deviations from the Lorentz–Lorenz formula show similar deviations from the Eötvös and Trouton formulas.
V. Shuleikin.