ELECTRICAL COXDUCTIOS I S TEXTILES. I The Dependence of the Resistivity* of Cotton, Silk and Wool on Relative Humidity and Moisture Content BY E. J . MIURPHY A N D A . C. WALKER
It is a well-known fact that textiles are very hygroscopic and that the resistance of a textile insulating material is very largely governed by the humidity of the air to which it is exposed. In 1914 S. Evershedl made an extensive investigation of the effect of moisture on the insulation resistance of a number of insulating materials, including cotton, from which he concluded that electrical leakage in such materials is practically entirely due to moisture condensed on their external and internal surfaces. Nore recently quantitative relationships between insulation resistance and relative humidity have been determined for cotton, silk and other fibrous insulating materials by Kujirai and AkaharL3 Measurements of the conductance of individual cotton fibers as a function of relative humidity have been made by Slater.3 His results show that in the range 4 0 - 8 0 q relative humidity the logarithm of the conductance of the fibers is a linear function of relative humidity. I n none of this work, however, does it appear to have been shown whether the relationship between resistance and relative humidity is chiefly an attribute of the fibrous structure4 of textiles or of some more fundamental structure such as that of cellulose in the case of cotton. An attempt to answer this question is one of the objects of the present investigat'ion. The present paper contains a discussion of data obtained in a study of the resistance-humidity and resistance-moisture content relationships for cotton, silk and wool. To determine bhe significance of these relationships the text,iles were studied in different forms, namely, as single fibers, as short threads, and as the covering of standard insulated wires. The effect of electrolytic impurities in the textile was also determined. Factors affecting the accuracy of the measurements on textiles are discussed. Other phases of the general problem of conduction in textiles will be considered in subsequent papers. Briefly, the results indicate that the insulation resistance of a textile sample is determined by its moisture content in such away that if the logarithm of the resistance is plotted against the logarithm of the moisture content a * IYhile the data iven in this paper are for the insulation resistance of sample of these textiles, it has been found that the insulation resistance of these samples does not differ significantly from their resistance and is proportional to the resistivity of the material. S.Evershed: J. Inst. El. Eng. (London), 52, j~ ( 1 9 1 4 ) . Iiujirai and Akahari: Sci. Papers, Inst. Phys. Chem. Res. (Tokyo), 1, 94 (1923). F. P. Slater: Proc. Roy. Soc., 96B,181 (1924). ' The conductance of a textile might be due chiefly to moisture adsorbed on the surfaces of the fibers or condensed in the interstices between them. H. L. Curtis (Bur. of Standards, Bull., 11, 3j9 (1914-15)) hasshown that the surface resistivity of a large number of materials is very sensitive to changes in relative humidity.
1762
E. J. MCRPHY AND A . C . WALKER
straight line is obtained whose slope is independent of the form of sample and of the amount of impurities contained in the textile, but is characteristic of the kind of material tested, Le., whether silk, wool, or cotton. That the resistance at a given relative humidity is also dependent on the amount of impurities indicates that the conduction takes place largely through water paths whose conductivity is dependent on the concentration of electrolytic matter. If these water-paths are pictured as forming a regular space-pattern, the elements of which change in dimensions with the moisture content in a way characteristic of the textile, the observed relationships may readily be explained.
Description of Materials Studied The samples used in this investigation are listed below with a brief description of the form in which they were tested. I . Cotton Threads 1.-Ash content, ber of threads in parallel, 2000.
1.0%.
Size of thread,
30/2.
2. Cotton Threads 11.-Ash content, 0.2676.~ Size of thread, Number of threads in parallel, 1600.
Num40/2.
3. Twisted Pairs2 I.-Ash content about the same as Sample I. Kind of wire, No. 18 double cotton covered tinned copper. Number of twisted pairs in parallel, 36. 4. Twisted Pairs3 11.-Ash content about the same as Sample 2 . Number of twisted pairs in parallel, I 5 .
5 . Silk Threads I. (Tussah)-Ash Number of threads in parallel, 360.
content,
2.1%.
Size of thread, 62/16.
6. Silk Threads' 11-Ash content, 0.287~. Size of thread, 62/16. Kumber of threads in parallel, 240. 7.
Wool Threads.-White
darning wool. Kumber of threads in parallel,
100.
8. Single Cotton Fibers.-Ash content, 1.07%. Number of fibers in parallel, 60. These samples were chosen so as to differ from each other in form, in dimensions, and in ash content, and therefore provide data regarding the influence of these factors on their electrical characteristics. Since the ash is largely composed of electrolytes, samples of relatively low ash content have also a relatively low electrolyte content. 1 Although this cotton was obtained commercially, it is probable that i t was washed during manufacturing operations, so that the water-soluble constituents of the ash were largely removed. * See description of experimental methods. 3 The insulated wire from which this sample was made was of the same stock as Sample 3, but was washed in boiling water for 30 minutes to reduce the amount of impurities. 4 This silk is from a lot of cultivated silk which vas washed to reduce the water-soluble content.
ELECTRICAL CONDUCTION IN TEXTILES
I763
Experimental Method The above described samples were prepared for test in the following three ways : Fibers.-The single fibers were pulled out of a thread of cotton with tweezers and mounted by means of a very thin glue solution on electrodes consisting of two concentric brass rings of 1.3 cm. difference in radius, supported on a well-insulated hard-rubber panel. It was necessary to mount 60 or more fibers in parallel to produce adequate galvanometer deflections for resistance measurements a t low humidities.
FIG.I
The Electrode-Fixture for measuring the Resistance of Threads
Threads.-The samples for making electrical measurements on threads were prepared by winding 30 to IOO turns of a continuous length of thread around two brass posts' 1.3 cm. apart between centers (Fig. I). Several units of this kind were mounted on a well-insulated hard-rubber panel and connected in parallel, forming a sample consisting of a large number of threads in parallel,* the separation of the electrodes being 1.3 cm. (e.g., sample I consisted of 2000 threads in parallel each 1.3 cm. in length.) The threads were held in place and in contact with the posts only by their own tension. Preliminary experiments were also made with posts fitted with bars by which the threads were clamped tightly to the posts to ensure good electrical contact. I t was found that both types of posts served equally well as electrodes, the contact resistance a t the electrodes being less than 57c, so the simpler type was adopted. * There was a distinct advantage in having a large number of threads in parallel both a t very low and a t very high humidities. The measurements could be extended to lower humidit;es than would have been possible with a smaller number of threads, and a t high humidities could be made with a milliammeter instead of a galvanometer, thus reducing the error due to polarization. Reducing the length of the threads is not as desirable as increasing their number for i t makes polarization and other secondary effects more prominent.
I764
E. J. MURPHY A S D A. C. WALKER
“Twisfed Pairs.”-This form of sample was chosen in order to simulate the conditions under which a textile is used in service, and consisted simply of two cotton insulated wires twisted together. No. 2 2 double cotton covered copper wire was used. Preliminary trials showed that by putting eight twists in a length of 5 cm., twisted pairs were obtained which were closely reproducible in insulation resistance and other electrical characteristics as well as convenient in size. The method of twisting may be understood by reference to Fig. 2 . The two ends of a piece of KO.2 2 cotton insulated copper wire 38 cm. long were fastened in two clips mounted j cm. apart, and a metal rod weighing about z kgm. was suspended from this loop of wire by means of two hooks also j cm. apart. The weight of the rod provided a constant tension during the twisting operation, which consisted simply in rotating the rod several times about its vertical axis. After cutting the wire at A, the sample consisted essentially of two copper conductors insulated from each other by four layers of cotton, two layers on each wire. Several samples of this kind were mounted on a hard rubber panel and connected in parallel to facilitate the measurement df the resistance of the sample a t low humidities. For all types of samples the electrodes were mounted on hard rubber panels which formed the lids of glass crystallizing dishes, or “humidifiers” ( 2 2 cm. diameter, 11 cm. deep), in which FIG.2 Diagram .showing LIeth:d of were put the sulphuric acid solut,ions used to propreparing Twisted Pairs duce the desired relative humidities. The electrodes were on the under side of the lids and electrical connection was made to them from outside the humidifier by means of the screws by which they were attached to the lids. To reduce surface leakage over the hard rubber toaminimum itwas covered with ozokerite, awaxof very low surface conductivity. The ozokerite was applied by melting it and pouring oyer the surfaces across which leakage might occur. When so prepared no detectable surface leakage took place between the electrodes except when exposed to relative humidities greater than about 99. jyc> where the leakage was still negligible. The humidifiers containing the samples were placed in an air-chamber maintained a t constant temperature t o within i . g D C ; the air-chamber was itself immersed in a water bath whose temperature was kept constant to .IT. The arrangement of the air-chamber was such that the leads necessary to make electrical connection to the samples were attached only while measurements were actually being made and a sufficiently long section of the leads was inside the chamber so that heat conduction to the samples during a measurement, due to the difference between the temperature of the room and the air-chamber, was negligible.
ELECTRICAL C O N D U C T I O r I N TEXTILES
I765
The relative humidities to which the samples were successively exposed were produced by sulphuric acid solutions.’ The specific gravities of these solutions and the relative humidities which they produced, as obtained from Wilson’s relative humidity-specific gravity curves,* are given in Table I. The samples were exposed to these humidities for 18 hours, after which time the rate of change of resistance with time is very slow and the samples could be regarded as substantially at equilibrium.
TABLE I Specific Gravity
Relative Humidity
W
Specific Gravity
Relative Humidity %
75.5 79. I 85.2 88.4 89.0 92.0 96.3 98.6
1.5465 I , 4785 1.4275 I . 3820 1,3297 I . 2924 I . 2412
IO 0
I .2200
19.5 30.0 38.8 50.5 59.0 70.8
I .
I . 2293
73 . O
I . 0300
1988 I . 1590 I , I395 1 ’ I345 I . 1080 I . 0642
ohms deThe resistance of the samples varied from 20 ohms to about pending on the humidity and type of sample. Because the range of resistance was so large four different methods of measurement were used, each better adapted for a particular range than the others. X few of the measurements at humidities lower than 1 0 5 were made by a leakage method, the circuit for which is shown in Fig. 3-1. The capacity C was charged through the sample R and then discharged through the galvanometer. The resistance of the sample is given by
where R is in ohms, t the number of seconds for which the voltage E was applied, 0 the ballistic t’hrow obtained on discharging the condenser, and Eil is the ballistic sensitivity of the galvanometer in coulombsl’mm., determined by charging the condenser to known voltages and discharging it through the galvanometer. The voltage to which the condenser C was charged by the leakage current mas small as compared with the applied voltage. For humidities between I O and 8 0 7 ~a direct deflection method was used (Fig. 3B). The resistance of t’he sample is given by
where D is the galvanometer deflection in mm., S a standard megohm (usually negligible in comparison with the first term), and K P the current sensitivity Saturated salt solutions were also used l o produce various relative humidities with results which agreed substnntially with those obtained with sulphuric acid solutions; but all of the humidities used in the data reported here were produced with the sulphuric acid solutions listed in Table I. * R. E. Wilson: J. Ind. Eng. Chem., 13, 326 ( 1 9 2 1 ) .
1766
E. J. MURPHY AND A. C. WALKER
in amperes/mm., determined by applying known voltages when the circuit contained only the standard megohm and the galvanometer. The calibrating voltages (provided by a potential divider) were chosen so that the calibration points corresponded within a millimeter with the scale deflections observed in the measurements and a calibration was made after each measurement for the scale deflection observed in that measurement. A sensitive
5H G
D
C
FIG.3 Electrical Circuits for the Measurement of Imulation Resistance A-Leakage
hlethod; B-Direct Deflection Method; C-Ohmmeter Method; D-Volt meter-hlilliammeter Method. R-textile sample, G-high sensitivity galvanometer, GI-pointer type galvanometer, S-standard resistance, C-air condenser, SH-Ayrton shunt, SW-discharging switch.
galvanometer is unsuitable for measurements a t humidities above 80-8 jyO because an appreciable increase in the resistance of the sample is caused by the measuring current during the 30 seconds to I minute required to obtain a reading. It was found that in the range 80-95y0 measurements could be made with sufficient rapidity with a Leeds and Xorthrup Ohmmeter to avoid error due to this cause. This instrument is a Wheatstone bridge with a single calibrated dial by means of which a measurement can be made in a few seconds (Fig. 3C). The resistance of the sample is given by R = KsS, where S is a standard resistance and Kt a calibration factor. At humidities above 95SGthe current through t h e samples was large enough to measure with a milliammeter, and the circuit shown in Fig. 3D was used. This had the advantage that a milliammeter reading could be obtained by an application of the measuring voltage for a second or so, and the resistance changes
1767
ELECTRICAL COSDUCTIOS I S TEXTILES
which occurred in this time were usually negligible.‘ The resistance is given 4 the resistance of by R = (ED) - A, where I is the current in amperes and . the milliammeter. Precision of Measurements The possible error in these methods of measurement due to insensitivity and errors of calibration is estimated to be less than *I% under the most favorable conditions and about ijrc under unfavorable conditions. It was frequently possible to use two or even three of these methods to measure the same resistance. The agreement of the different methods is illustrated by Table 11. This is a good indication that there arc no systematic errors of
TABLE I1 Sample and Conditions
Resistance (megohms)
Cotton Threads I, a t IO^, R. H. Cotton Threads 11, a t IoS;; R. H.
by dlrect deflection, by leakage, by direct deflection by leakage,
Cotton Threads 11, a t 96 3 7 K. H. by direct deflection, by ohmmeter, Cotton Threads 11, at 8gC; 1%.H. Cotton Threads 11, at 8 j . 2 5
by direct deflection, by ohmmeter,
2.49
x
2.17
X IO^
2.0
x
1.98X
I06
10’
10’
0,59 0.59
6.6 6.5 1.39 x
I0
by ohmmeter,
1.3
10
R.H. by direct deflection,
x
Cotton Threads I, at 76
R H.
by direct deflection. by ohmmeter,
1.98 I 56
Cotton Threads I, a t 96
R. H.
by ohmmeter, by milliamnieter
1.15
I . 06
x x
I O d 10-2
appreciable amount in the methods of measuring resistance, for the four methods involved the use of different apparatus and the measurement of several different quantities such as time, capacity and voltage in the leakage method, current and voltage in the direct deflection and milliammeter methods, and the ratio of two resistances in the Ohmmeter method. The factor which causes the greatest difficulty in making precise measurements on textiles a t humidities greater than about So:> is the increase in resistance with time of application of the riicasuring current, called hereafter “polarization.” By using rapid methods of measurement when necessary the 1 At very high humidities the initial reading of the milliammeter was sometimes in doubt on account of the rapidity of decrease of the current. In these cases a second measurement was made with the current flowing in the opposite direction. In the second measurement the current increased with time for a second or so and approached closely to the initial value. The measurements were also confirmed by repeating them aftrr the samples had been allowed about 30 minutes t o recover from the previous measuring current. The rapid changes of resistance which take place a t very high humidities are not always evident when a galvanometer of long period is used.
I 768
E. J. MURPHY A S D A. C . WALKER
error in the present data due to this cause was reduced to less than on the average, but at humidities very close to 100% the error may be as large as 20%. Comparison of the present results with preliminary measurements in which no measures were taken to avoid polarization shows that at humidities near 1007~ an error by as much as a factor of j o in the resistance might be caused by neglecting the effect of polarization. At humidities below about 10% the resistance of samples of small electrode separation also increases with time with sufficient rapidity to cause an error which may be as large as zoyc, but only two or three measurements were made under these conditions.
LOGlo TIME-MINUTES
FIG.4 Change of Resistance of Cotton Threads with Time of Exposure to 76% Relative Humidity a t Z j T . I . A sample of low electrolyte content. A sample of normal electrolyte content. 2. Resistances are for a single 1 . 3 em. length of thread.
Other possible sources of error in the measurements are: failure of the samples to reach equilibrium at a given humidity, uncertainty in the humidity corresponding to a given specific gravity of the sulphuric acid solutions, and fluctuations in temperature. The samples used in the present work were small and a large surface was exposed to the air relative to their volume; in the case of the thread samples it seems probable that the inner fibers were exposed to air of about the same humidity as the outer ones. This probably favored the rapid attainment of equilibrium. The rate of approach to equilibrium is illustrated by Fig. 4, which shows that after IOO to zoo minutes the rate of change is very slow. 4 period of 18 hours for equilibrium was adopted as a standard procedure. Tests made to determine how much further change
ELECTRICAL CONDUCTIOX IN TEXTILES
I769
in resistance would take place in several days showed an average change of less than 6 7 , and a maximum change of 147~. The relative humidity corresponding to a given specific gravity could be read to f.270; the percentage error corresponding to this deviation varies from *zYc a t 107~ relative humidity to f.270 a t 1007'relative humidity. The specific gravities of the solutions were the same Rithin the experimental error at the end of the investigation as a t the beginning.
TEMPERATURE- DEGREES C
FIG.5 Change of Insulation Resistance of Cotton Samples with Temperature a t 767, Relative Humidity Curve I is the insulation resistance ( X IO-I. The values so obtained are tabulated in Table VI along with the moisture contents obtained directly from the moisture content-relative humidity data. The average deviation is only 3.5YG. Since the moisture content data were not obtained under exactly the same conditions as the resistance data, this agreement is as good as could be expected. These results point directly to the conclusion that the moisture content of the cotton, and not the prevailing relative humidity, is the controlling
+
1 In making the resistance measurements the highest humidity to which the samples were exposed was 98.670, while the,cycle of humidities used by Urquhart and Williams in determining the moisture content included 10070 relative humidity. To correct for this difference the curve shown in dotted lines in Fig. 9 was used to obtain the logarithm of moisture content for relative humidities above 88%. This correction makes no change in the position of the curve.
I779
ELECTRICAL CONDUCTION IN TEXTILES
factor in determining its resistance, Le., the only significant effect of a change in relative humidity is the change which it produces in the moisture content of the cotton. Hence by making a single measurement of resistance and moisture content on a given sample of cotton, the resistance a t any other moisture content (or the humidity corresponding to it either for increasing or decreasing humidities) may be calculated with considerable accuracy.
TABLE VI Comparison of Moisture Contents calculated from Observed Resistances with those given by the Moisture Content-Relative Humidity Data H
6.0 10.0
19.5 30.0 38.8
50.5
R 3.28.10'~ 5 . 6 8 . I o9 4 . 4 6 , 108 4.74.10' 8 . 0 9 . 106 8 . 6 2 , 105 I . 6 2 .105
59 .'o 70.8 73.0 75.5 79.1 85.2 88.4 92.0 96.3 98.6 98.6 96.3 92.0 88.4
. 7 2 . IO4 I . I 5 , IO4 6.73.10~ 3 . 2 8,103 6 . 4 0 , IO? 2.76.10~ 9.90' I O 2.30~10 3.94 5.48 1.63.10 4.27'10
8 5 2
I ,55.102
79.1
4.44'102
75.5
I.51.10~
73.0 70.8 59.0 50.5 38.8 30.0 19.5
I ,516.103 2.30.10~ I . 56.10~ 6 . 0 3 . 104 4 . 6 2 .105 3.72.I 0 6 3.14.10' 2.92 108 4.96.10~ 3 , 3 2 ' 1011
10.0
6.0 2.0
I
I . 01 ' I 0 2
K a I
&fobs
AM
1.67
I
.62
-0.05
2.02
2.00
-0.02
-1.0
2.66 3.39 4. IO 5 . I9 6.24 7.94 8.26 8.79 9.48 11.30 12.36 13.49 16.22 19.59 18.88 16.83
2.82
$0.16 $0.30 s0.31 + O . 19
+6.0
13.80 13.15 11.80 10.28
3.69 4.41 5.38 6.17 7.66 7.98 8.41 9.04 10.60 11.56 13'19 16.40 19.28 19.28 17.78 15.48 1 4 . I3 13.03 11.3j IO. j z
I O . 00
10.00
9.84
9.59 7.76 6.70 5.37 4.47 3 ' 47 2.46 1.88
15.07
8.02
6.92 5 57 4.45 3 54 2.79 2.06 1.31
Average percentage deviation
=
I . 00
AM% -3. I
+8.8 $7.6 +3.7
-0.07
-1.1
-0.28
-3.7 -3.5 -4.5 -4.9 -6.6 -6.9 -2.2
-0.28
-0.38 -0.44 -0.70
-0.80
-0.30 $0.18 -0.31 + o . 40 + o . 95 $0.41 fo.33 -0.
I2
-0.45 24
+O.
0.00 -0.2
j
-0.26 -0.22
-0.20 +0.02
+I.I
-1.6 +2.I
+5.6 +2.7
$2.4 -0.9 -3.8 +2.3 0.0 -2.
j
-3,2 -3.2 -3,6 $0.4
-0.07
-2.0
-0.33 -0.18 -0,31
-11.8 -8.8 -31.0
3.547c (omitting 31 and 11.8).
.
1780
E. J. MURPHY AND A. C. WALKER
In order to explain the significance of the data just presented we may assume that cotton is a complex system of cellulose, water and impurities in definite ratios. Then the relationships shown by the resistance-humidity and resistance-moisture content curves for twisted pairs, threads and single fibers indicate that this complex system may be regarded as having a definite specific resistance which is determined by the values of the ratios of its constituents. This implies that the total resistance of a textile is not appreciably affected by the resistances of the contacts between the fibers of which it is composed or by the arrangement of the fibers relative to the direction of current flow. Further support for this conclusion has been obtained from the results of a large number of measurements of the resistance of single cotton fibers and of threads of the same material at a fixed humidity. These data have shown that the resistance of a single fiber is n times that of a thread containing n fibers in its cross-section. It has also been found that the resistance of a cotton thread increases in direct proportion to its length, even for lengths greater than that of any single fiber. This would not be expected if contact resistances between fibers formed a significant part of the total resistance. The discussion so far has been confined to the results of measurements made on cotton. Similar data were also obtained for silk and wool but for a smaller humidity range. These data are given in Tables VI1 and T'III. From the relations shown by cottons of different electrolyte content it would be
TABLE VI1 The Insulation Resistance of Silk Threads as a Function of Humidity and Moisture Content Silk Threads I (Tussah)
H
38.8 50.5 59.0
70.8 73.0
75.5 79.' 85.2
88.4 92.0 96.3 98.6
BI 7.57 8.77 9.91 11.89 12.36 12.91 '3.77 1578 1 7 . IO
19.28 23.99
Silk Threads I1 Sample I
Sample z
R
R
R I .60,IO*
.09.109
2 . 2 4 , IO7
I
6.37 , 1 0 6 2 .32 , 1 0 5 1.38.10~
4 . I j . IO* I . 41. 107
8 . 8 2 , 104
5 .65, 1 0 6
.86 IO' .96, I 0' 1.39'10'
8.57 ,103 5.58.1~' 1.69.10~ 7.06.10 8.I O
2.02'106
I
73.IO5 6 .I j , 1 0 4 6.87,1 0 3 6.60,IO? I .90.I o2
I .0 1 ' 1 0 5
2
I.
I
, 6 4 . I o6
3.50.io4 6.60.1 0 3 6 .j 3 . 1 0 ~ 2.16.10'
2.37 H is the relative humidity in percent. hf the moisture content of the silk in percent of the dry weight based on Schloesing's data. R is the insulation resistance of a single 1 . 3 em. length of thread measured with an applied voltage of 100.
1781
ELECTRICAL CONDUCTION I N TEXTILES
TABLE VI11 Insulation Resistance of Wool Yarn a t H
M
50.5 59.0 70.8 73.0
12.97 14.22
16.18 16.67 17.26 18.20
R 7.53.107 2.26.10~ 2.21.106
I . 35 , I O 6 75.5 6 . 9 7 . 105 2.40,105 79.1 H is the relative humidity in percent.
H 85.2 88.4 92.0 96.3 98.6
25'
C
JI 20. j I
22.28 24.83 30.06
R 2.96 I
.Ij
104 '
104
. 0 3 , 103 I , 7 8 , 102 3.10'10 2
hl is the moisture content of the wool in percent. R the resistance of a single 1 . 3 em. length of yarn. ripplied voltage 100.
expected by analogy that the curve for Silk Threads I1 would lie above that for Silk Threads I and be parallel to it since Silk Threads I1 have a lower electrolyte content than Silk Threads I. The curves in Fig. I I show that in this respect cotton and silk behave alike. In Fig. I Z the resistance data have been plotted as a function of moisture content. The logarithm of resistance vs. logarithm of moisture content curves are straight lines within the error in the moisture content data as applied to these samples. The moisture content data were taken from a paper by Schloesing.' His experimentally determined values for unbleached raw China silk and for wool a t 2 4 T were recalculated to 2 5 O C , using temperature coefficients based on his data. While only four points are given in the range 36y0 to 96yc humidity for the moisture content of this type of silk, these data are supported by similar measurements on three other kinds oi silk. The deviations of the points from the lines in Fig. 1 2 are of the order of magnitude to be expected from the small but appreciable variations in the hygroscopicity of silk with its source and treatment, as also shown by Schloesing's data, and from the long interpolations necessitated by the small number of points. I n our judgment the following equations best fit the curves for silk and wool and therefore express the insulation resistances of these sanples as functions of their moisture contents: For silk, Log R = - 1 6 . 0 log 11 C, or R = C' AI-16.0
+
where R is the resistance in megohms of a single silk thread 1.3 cm. long, 11 the moisture content of the silk in percent of its dry weight, and C( = log C') a constant which has the value 22.4 for Silk Threads I, and 24.5 for Silk Threads 11; ' T h . Schloesing: Bull. SOC. encour. indust. nat., 8, 717 (1893);Comptes rend., 116, 808 (1893); Text. World Record (Boston), Sov., p. 2 1 9 (1908).
I782
E. J. MURPHY AND A. C. WALKER
For wool, Log R
R
= - 1 6 . 4 log = D’ &I-16.4
M
+ D, or
where R is the resistance in megohms of a single 1.3 cm. length of wool yarn, RI the moisture content of the wool, and D = log D’ = 26.0. From the values of the exponents of M, it is evident that silk and wool are even more sensitive to changes in moisture content than is cotton since the resistance of silk increases by a factor of about 65,000, and that of wool by one of about 90,000, when their moisture contents are halved, whereas the factor for cotton is 600 or approximately I,’IOO that for silk and 11 150 that for wool.
RELATIVE HUMIDITY-PER CENT
FIG. I 1
Insulation Resistance as a Function of Relative Humidity for Kool, Silk and Cotton. I . Silk Threads I1 (0 Sample I , Sample 2 ) 2. V-ool Yarn 3. Silk Threads I 4. Cotton Threads I The resistances are for a single 1 . 3 cm. length of thread or for a single twisted pair
The curves in Fig. I I afford a comparison of the relative insulating qualities of cotton, silk and wool for humidities greater than 40 or 507.Comparison with the moisture content-humidity curves in Figs. 9 and 13 shows that the greater the hygroscopicity of the textile the greater the resistance of similar samples of the raw textile, which is directly contrary to what ~ o u l d be expected in view of t,he dependence of the conductivity of a textile on its moisture content. However, this unexpected result can bc readily explained by the relations shown in Fig. 1 2 from which it is evident that a given quantity of moisture distributed in cotton has a higher conductance than the same quantity of moisture in silk, and that a similar relation holds between silk
ELECTRICAL CONDUCTION I S TEXTILES
1783
and wool though the difference is smaller. These relations appear reasonable if, for example, we assume for textiles any model in which the conducting water-paths form a regular network or space-pattern which corresponds to some regularity in the structure of the textile (e.g., in the structure of cellulose), the form or dimensions of the elements of the network being different for different textiles. Then the conduction paths in any direction may be considered to consist effectually of elementary filaments of water containing
FIQ.1 2 Insulation Resistance as a Function of Moisture Content for Wool, Si!k and Cotton Wool Yarn Silk Threads I1 (0 Sample I , 0 Sample 2 ) Silk Threads I 4. Cotton Threads I The resistances are for a single 1.3 cm. length of thread or for a single twisted pair. I. 2.
3.
alternately expanded and constricted portions a t regular intervals along their length. Where these variations in cross-section are large, the resistance of such a filament is determined by the parts of the filament whose crosssectional area is least. The resistance of the whole filament is then practically independent of the amount of water in the expanded portions.’ Thus wool could have a higher resistance than cotton for a given moisture content if the structure of wool is such that the moisture is distributed in filaments having constricted parts of smaller cross-section than similar constricted parts in the elementary conduction filaments in cotton. It would also be expected that Cf. Evershed’s “dormant” and “resistance” water.-S.
Evershed: loc. cit.
1784
E. J. MURPHY AND A . C . WALKER
the narrower the constrictions in such filaments the more rapidly would the resistance of the filament vary with moisture content because the percentage change in cross-sectional area of the constricted parts, for a given increment of moisture, would be greatest for the filaments having the narrowest constrictions. That the behavior of these textiles is consistent with this explana-
RELATIVE HUMIDITY-PER CENT
FIG 13 The Moisture Content of Wool and Silk as a Function of Relative Humidity Interpolated to 25°C. from Schloesing’s data. I . Wool 2. Silk
tion is shown by the fact that the resistance varies with moisture content most rapidly for the textiles which combine relatively high hygroscopicity with relatively high resistance (Fig. 12). The relative insulating qualities of textiles, therefore, are determined not only by their hygroscopicities, but also by the resistance of the moisture as distributed within them, and by the rate of variation of resistance with moisture content.
Summary Data are given showing the variation of the insulation resistance of cotton, silk and woo1 samples with relative humidity and moisture content. The samples consisted of short threads, individual fibers and standard cotton insulated wires. Some of these samples contained more electrolytic impurities
ELECTRICAL CONDUCTION IN TEXTILES
1785
than others. The results therefore show the effect of differences in the form and electrolyte content of the samples on the resistance-humidity relationship. The insulation resistance of any cotton sample is about 10'~times greater a t 1 % relative humidity than at 997c, and in the range 20-8oyc is an exponential function of relative humidity. The rate of change of insulation resistance with relative humidity is independent of the form of the sample and of its electrolyte content. h decrease in the electrolyte content of the cotton causes an increase in the general level of resistance, Le., a displacement of the resistance-humidity curve parallel to itself. The conductance of a cotton thread is equal to the sum of the conductances of the fibers of which it is composed and the resistance of a cotton t'hread is directly proportional to its length. These facts indicate that in spite of its fibrous structure cotton has a fairly definite resistivity. When the resistance measurements are made both in the order of increasing and of decreasing relative humidity the resistancerelative humidity curve is a closed loop whose sides are almost parallel in the range 2 0 - 8 0 7 ~ . The logarithmic plot of t'he insulation resistance of cotton samples as a function of their moisture content gives a system of parallel straight lines, indicating that the resistivity of cotton is a power function of its moisture content. This shows also that in the resist,ance-humidity curve relative humidity are due to the the loop and the inflections a t 2 0 and relationship between moisture content and humidity rather than resistance and humidity. Equations are given by which the resistance of a cotton sample can be calculated for any moisture content (or the relative humidities corresponding to it) provided a measurement has been made a t a single moisture content. The regular dependence of the resistivity of cotton on its moisture and electrolyte content and the relatively small variation of resistance from one sample to another of the same material suggest that the distribution of moisture corresponds to some regularity in the structure of the textile, e.g., in that of cellulose in the case of cotton. The insulation resistance of silk and wool samples is also a power function of their moisture contents. The resistivity of silk depends on its electrolyte content in the same way as that of cotton. The rate of change of resistivity with moisture content is much greater for silk and wool than for cotton. For a given moisture content the resistivity of silk or wool is greater than that of cotton though silk m d wool are more hygroscopic than cotton. The investigation of cotton was not extended below about' 17~ relative humidity and that of silk and wool not below about 4 0 7 ~so it is not definitely known whether these relationships hold a t humidities lower than these. It is suggested that the conducting water-paths in a textile consist in effect of elementary filaments which have alternately expanded and constricted sections along their length, forming a regular space-pattern whose elements have different dimensions for different textiles. The resistivity of the textile is then determined by the cross-sectional area of the narrowest parts of the path rather than by the total moisture content; thus, by assuming that the constricted parts of the filaments are smaller in silk and wool than in cotton the higher resistivity of these materials for a given moisture
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E. J . MURPHY AND A. C. WALKER
content is explained. The rapidity of the variation of resistivity with moisture content can also be explained in this way. This work forms part of an investigation of the insulating properties of textiles which was initiated by Mr. R. R. Williams. We are particularly indebted to him for the suggestion of the study of the relation of the individual fibers to the textile as a whole and of the effect of humidity on insulation resistance. We also wish to take this opportunity to thank Dr. H. H. Lowry for his very helpful interest in the work and for valuable assistance in the interpretation of the results and the preparation of this paper. Bell Telephone Laboratories, New York, N . Y .
