Conductivity Measurements

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STUDIES ON GLASS VII. The Conductivities and Dielectric Constants of Glucose and Boron Trioxide Glassesi BY

s. BENSON

THOMAS?

In the preceding papers of this series3 considerable data have been presented on the physical properties of a number of substances in both the liquid and glassy states. A number of properties, such as specific heat, coefficient of thermal expansion, and dielectric constant, indicate that glasses more closely resemble the crystalline state than the liquid state, from which they are formed by cooling. However, when the logarithm of the viscosity is plotted against temperature a smooth curve showing no evidence of discontinuity between the glassy and liquid states is ~ b t a i n e d . ~ The present investigation is essentially a continuation of previous studies, and was undertaken with the hope that it might serve to extend our knowledge of the glassy state.

Conductivity Measurements The purpose of this study was to measure the changing conductivity of a number of substances as they are cooled from a temperature a t which they are definitely liquids to a temperature a t which they are hard glasses. Due to the wide range through which the conductivities vary, it was necessary to use two methods of measurement. The usual A. C. bridge method served for measuring resistances up to about two megohms, but a t higher resistances the condenser component of the current was so high that a satisfactory balance could not be obtained and a D . C. ammeter-voltmeter method was employed. By using a high-sensitivity Leeds and Korthrup galvanometer as the ammeter, this method was made very satisfactory, since the small current required, IO-^ amperes, caused no appreciable polarization if reversed every 20 or 3 0 seconds. In measuring high resistances by means of the bridge method an increased sensitivity is obtained by using a bridge of considerable resistance. For this reason a Leeds and Northrup student potentiometer having a slide wire resistance of I O O ohms was used in preference to the usual Kohlrausch bridge of but one ohm resistance. The alternating E. 11. F. was supplied by a These studies on glass are being carried on in the Chemical Lahoratory of Stanford University under the direction of Professor George S. Parks. Holder of the Shell Fellowship at Stanford, 1930-31. Parks and Huffman: J. Phys. Chem., 31, 1842 (1927); Parks, Huffman and Cattoir: 3. Phys. Chem., 32, 1366 (1928); Cattoir and Parks: J. Phys. Chem., 33, 879 (1929); Parks and Gilkey: .J. Phys. Chem.. 33, 1428 (1929); Parks, Thomas and Gilkey: J. Phys. Chem., 34,2028 (1930); Thomas and Parks: J. Phys. Chem., 35, 2091 (1931). An extensive, hut as get unpublished, investiqation of the viscxosity of liquid and glassy glucose has recently heen completed in this Iahoratory. See Master's Theses of Miss Lois Barton, Monroe Spaght, and Wilfred Rirhardson.


2104

S. B E S S O S THOAMAS

microphone huniiiier. .Is standard resistances Leeds and Sorthrup resistance boxes and calibrated grid leaks were used. Since they are entirely free from inductance arid capncity, the latter were found more satisfactory for resistances above 500,ooo ohms. The capacity of the cell was balanced out with a variable condenser across the standard resistance units. Three stages of transformer-coupled audio-frequency ariiplification were used in the output circuit. The cell used in measuring the conductivities of boron trioxide and sodium borate glasses consisted of two concentric platinum crucibles, the smaller of which had the bottom removed and x a ? suspended within the larger. The

TABLE I Resistance of a Sodium Borate-Boron Trioxide System Containing 2.4y0 Sodium Borate Temp., "C 674 660 571 548 j22

Results obtained using A. C. bridge method Specific Resistanre T e m p , "C Specific Resistanre

x x

104

4ii

104

46 7

3.16 X

10;

448

Ior'

44 1 43 9

3.92 5.01

5.54 1.24

x x x

IO'

5 00

2.39

484

4.40 X IO^

Temp., "C

IOfi

x

2.2

3 60

2.8 X io9 4.9 X 109 9.9 x I O 9

341 334

X IO^ X iofi X loi

x

107

X

107

x x

10s IO'

Results obtained using D. C. ammeter-voltmeter method Specific Resistante Temp., "C Sperific Resistanre

365 3.52

408 40.5

j.92 8.63 1.96 2.83 3.1 1.5 1.7

109

301

2.9 X 1oLo j . 9 x IO'i' 9.2 X IO'O

298

1.1

320

3 1I

x

101"

1 . 7 X Ioio

suspension w a s by means of platinum wires attached to nlundum rods, the rods being set in notches in the edge of the outer crucible. The cell was mounted in a large iron block lined with alundum cement. This block was equipped with a heating coil and imbedded in silocel so that it served aq a rough thermostat. The temperature of the cell was determined by a chrome1 alumel thermocouple in conjunction with a Leeds and Northrup thermocouple potentiometer. Since the relative positions of the crucible electrodes were subject to small changes, an accurate evaluation of the cell constant was not attempted. The value, however, is constant during each set of deterTherefore, minations and the total variations are probably not over 10%. the results are expressed in terms of specific resistances, and are of the correct order of magnitude. The several boron trioxide-sodium borate solutions were formed by heating the mixture in a platinum crucible for several hours a t the full heat of a blast


STCDIES O S GLASS

2105

lamp. A considerable amount of water was liberated during the first' hour of heating but during the latter stages the formation of bubbles in the melt was very slow, indicating that the water had been almost entirely removed. Table I present3 the data obtained for a solution of 2.4% of anhydrous sodium borate in boron trioxide. In Fig. I the logarithms of the specific resistances of a number of boron trioxide-sodium borate solutions are plotted against the corresponding temperatures. At the higher temperatures these mixtures are clear, viscous liquids. At the lower temperatures, they are hard, transparent glasses. It is thus evident that insofar as conductivity is concerned the transition between the liquid and what we choose to call the glassy state is gradual and continuous.

FIG I The Specific Resistances of Several Boron Trioxide-Sodium Borate Systems.

The conductivities of glassy and liquid glucose were measured using the cell previously employed by Cattoir and Parks in measuring the dielectric constants of the same material. The cell consisted of two coaxial copper cylinders hanging vertically in a large pyrex test-tube. The out,er copper cylinder had an internal diameter of 2 . I cm. and the inner cylinder an outside diameter of 1.6 cm.; they were both 4. j cm. in length. The relative positions of these two cylinders were maintained .by three small tightly-fit,ting glass rods placed in the space between them. The cell was introduced into a threeliter Dewar jar filled with transformer oil. Equipped with a stirrer, thermometer and electrical heating coil, it served as a small adjustable thermostat. Measurements of the resistances of pure glucose and a 1% solution of anhydrous sodium iodide in glucose were made by using the methods previously described. The sodium iodide increases the conductivity considerably above 50' C., but possibly goes out of solution below this temperature, altho there is no visible evidence of such an occurrence. When the logarithm


2106

6. BENSON THOMAS

of the resistance is plotted against temperature, a smooth curve is obtained similar to that shown by the boron trioxide and sodium borate glasses, thus supporting the previous statement that electrical conductivity shows only a gradual and uniform transition between the glassy and liquid states. A marked resemblance is to be noted between the curves obtained by plotting the logarithm of resistance against temperature and the logarithm

TABLE I1 Resistance of Liquid and Glassy Glucose Results obtained using A. C . bridge method Specific Resistance Temp. "C

132 129

123 117 I10

101.6 94.3 80.8

4.2 X 1 0 5 5.3 X 105 5.6 X 105 1.23 x 106 2.03 X IO^ 4.2 X 106 8.5 x I 0 6 4.5 X IO?

Results obtained using D. C. ammeter-voltmeter method Temp. "C Specific Resistance

8.7 X 10' 7.4 x IO8 8.1 X 109 9.0 X I O ~ O 5.8 X loll 3.8 X IO^*

78.5 63.7 52.2 42.2 32.9 23.3

Resistance of Liquid and Glassy Glucose containing Anhydrous Sodium Iodide Results obtained using A. C. bridge method Temp. "C Specific Resistance

117 I11

99.0

97.0 86.2 8.3.2 73.0 68.4 62.0

6.3 X 104 8.5 X 104 2.51 X 105 4.2 X 105

x 106 3.5 x I O 6 1.95 x IO'

Results obtained using D. C. ammeter-voltmeter method Temp. 'C Specific Resistance

68.3

61.8 52.5 40.0

2.00

38.0

4.4X

33.5 32.7 26.1

1.07

x

IO?

1%

6.8 X 2.1 x 1.8 X 8.5 X 1.4 X 4.5 x 6.1 X 2.4 X

IO? 108 108 IOIO

loll 1011 10ll

1oI2

I08

of viscosity against temperature. If the logarithm of resistance is plotted against the logarithm of viscosity, a curve is obtained that approaches very nearly to straight lines within the temperature intervals ioo C. to 145' C, and 30' C. to 45' C. The gradual change in slope occurring between 45' C. and 70' C. might be ascribed to variations in the dielectric constant which changes rapidly in this region. However, as will be shown later, the dielectric constant is by no means a well defined quantity and an attempt to take it into consideration would appear to be largely empirical.


STUDIES ON GLASS

2IOj

FIGz The Specific Resistance of Liquid and Glassy Glucose, and a I yo Solution of Anhydrous Sodium Iodide in Glucose

*

FIG. 3 Relation between the Electrical Resistance and the Viscosity of Liquid and Glassy Glucose.

Dielectric Constants Cattoir and Parks1 measured the dielectric constants of glassy and liquid glucose for the temperature range 200' K to 370' K a t a frequency of 1000 kilocycles per second. The dielectric constants for glassy glucose were found to vary uniformly from 3.8 a t zooo K to 5.4 a t 290' K. Between 290' K and 378' K the constant increased rapidly to a value of 23.9,after which it decreased to a value of 21.0a t 423' K. It has been shown by Mizushima* and others that this sudden change of dielectric constant is a property of polar 'Cattoir and Parks: J. Phys. Chem., 33, 879 (1929). Miaushima: Institute of Physical and Chemical Research, Tokio, 9,209 (1928);Kitchen and Muller: Phys. Rev., ( 2 ) 32, 929 (1928);Bock: 2. Physik, 31, 534 (1925);Graffunder: Ann. Physik, 70,225 (1923).


2108

S. BENSON THOMAS

liquids in general and that the temperature interval in which it occurs is dependent upon the frequency a t which the measurements are made. A further investigation of the dielectric constants of glassy and liquid glucose therefore seemed desirable. An electrical resonance method was used for the determination of the dielectric constants. Two Hartley oscillators were employed as shown in Fig. 4. The construction of these oscillators was such that the inductances were readily replaceable, thus permitting measurements to be made a t a number of different frequencies within a few minutes time. Circuit I contains in parallel with the usual inductance and variable capacity a calibrated variable resistance, R, and the dielectric cell, C,. The cell was used the same as that described in connection with the resistance measurements presented in the first part of this paper. The apparatus was calibrated using liquids of known dielectric constant and quoted as standards in the International Critical Tables.' The various frequencies of the oscillators were calculated from the

Circuit 1.

Circuit

IT.

FIG.4 Schematic Diagram of Oscillator Circuits

respective values of inductance and capacity, and were checked by comparison with a General Radio wave meter. The procedure used in making measurements was as follows: The sample was maintained a t constant temperature for about fifteen I. minutes in order to insure thermal equilibrium. The dielectric cell, C,, being connected and the resistance, R, dis2. connected, circuit I1 was tuned to approximately the desired frequency, and circuit I was tuned to resonance. The plate current was then read and recorded. 3 . The dielectric cell was disconnected and oscillator I adjusted to an initial setting that was always the same. The resistance, R, was then varied until the plate current was the same as in 2 . A final small adjustment of oscillator I1 was usually necessary to bring it to exact resonance with oscillator I. 4. The resistance, R, was then disconnected and the dielectric cell connected; circuit I was turned to resonance with circuit I1 and the plate current checked. 5 . Matched inductances of a different value were inserted in the oscillators and the process was repeated a t the new frequency. l

International Critical Tables, 6,

82.


STUDIES O K GLASS

2

109

Using the last setting of the variable condenser C1, the dielectric constant of the material may he read directly from the calibration curve. These results are given in Table I11 and Fig. 5 . Since the plate current of an oscillating vacuum tube is determined by the losses in the oscillating circuit, the resistance, R,must be equivalent to the losses in the dielectric cell. These losses occur as conductivity (which is negligible except a t the higher temperatures) and dielectric hysteresis which is due to a lag in the molecular dipole orientation. The latter loss may be regarded as equivalent to a power loss in a resistance, R,, in parallel with the condenser. Then,

-I -- _I - _1 Kx K. Rcc where R Dis~the direct current resistance of the cell. The conductivity of the

TABLE I11 Dielectric Constants of Glassy and Liquid Glucose Temp. "C 2.600

9.0° 32.2 50.0 64.0 76.0 84.0 97.0 110.0

123.0 140.0

kilocycles

5.3 6.I 8.3 11.4 15.3

23.0 -

Dielectric Constant 160 kilocycles

815 kilocycles

5.3 6.2 8.6 11.8 16.2 19.5 23.4 23.6

5.4 6.7 9.3 '3.3

92 kilocycles 5.6 6.8 9.5 14.2

20. I

22.2

23,s 24.2 23 ' 7

24.3 24.2 23.9

hypothetical resistance, R,, is equal to the dielectric losses of the condenser per unit of applied voltage. The dielectric losses occurring in liquid and glassy glucose a t frequencies of 1,300 kilocycles and 2,600 kilocycles have been calculated in terms of specific conductivities which would produce equal losses. The dielectric constants of abietic acid and boron trioxide were found to have the low values of 3.0 and 3.5, respectively. The values changed but slightly with temperature and frequency. The more polar sodium borate showed effects similar to those shown by glucose but the comparatively high conductivity prevented the complete investigation of this material with the present apparatus. The Debye theory' explains the anomalous effects exhibited by the dielectric constants of polar molecules by assuming that the dielectric properties of a polar molecule depend upon: I. An electric moment formed by the shifting of the electrons relative to the positive nucIeus due to the influence of an external electric field. Debye: "Handbuch der Radiologie," 6,p. j 9 7 (1925)


2110

S. BENSON THOMAS

2. The ability of the polar molecule to orient itself when under the influence of an electric field. Assuming the dipole moment to be constant, the ability of the molecule to orient itself will be determined by the restricting forces of other molecules, the frequency of the applied field, and the thermal agitation of the molecule which tends to break down any orientation produced. Considering only liquid or glassy materials it may be assumed that the restricting forces acting on the molecule are a function of the viscosity. At low temperatures where the viscosity is high the molecular orientation is negligible and the dielectric properties are due almost entirely to the electron

FIG.5 The Dielectric Constants and Dielectric Losses of Liquid and Glaasy Glucose. Curve I. Measurements made a t freqyency CII 92 Kilocycles '< (' 160 " Curve 11. " " Curve 111. 815 "

Conductivity Measurements

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