Electroosmosis in Paper Electrochromatography with Electrode Vessels JOHN L. ENGELKE’, HAROLD H. STRAIN, and SCOTT E. WOOD* Argonne N a t i o n a l laboratory, Lemont, 111. A simplified apparatus has been designed for the study of electroosmotic and hydrostatic flow in filter paper. Under the conditions employed in electrochromatography and with the ends of the paper dipping into the electrolytic solution, there is a significant electroosmotic flow through the paper. This flow, determined with noncharged flow indicators such as hydrogen peroxide, varies with different lots of paper; i t increases with electrical field strength and dilution of the electrolytic solution; it varies little with the compression of the paper, the amount of the solution in the paper, and the duration of electrolysis; and it is uniform throughout the paper. The flow due to hydrostatic pressure is proportional to the head. It decreases with the compression of the paper and the amount of water in the paper. The hydrostatic pressure equivalent to the electroosmotic pressure at 7.55 volts per centimeter is only about 0.3 mm. of water per centimeter of the paper. Because of the difficulty in controlling these variable conditions, the electroosmotic flow could not be defined precisely in terms of these variable factors. In electrochromatographic separations, the electroosmotic flow is determined most precisely with flow indicators.
in terms of the electrical field, time, hydrostatic pressure, quantity of solution in the paper, concentration of the solution, and nature of the electroosmosis indicators. Because of the variability of the migration system, many observations were not precisely reproducible. The system varied, for example, with time and different lots of paper. Consequently, emphasis has been placed upon the determination of the variable factors rather than upon a precise physical chemical interpretation of the observations. APPARATUS
The apparatus (Figure 1 ) is a modification of earlier models (6, 8,9, 15, 16). It consists of three basic units: a water-cooled, electrically insulated cell, C, which encloses and compresses the moist paper, P; a pair of electrode vessels, R, with primary electrodes, E, and with secondary electrodes for determination of the electrical potential; and a leveling tube, L,and manometer, M . An electronic rectifier served a s the direct current power supply (11), and a milliammeter in the circuit measured the current with an accuracy of about l ma.
W
HEN mixtures of solutes are resolved by electrochromatography in moist porous media such as Celite (14 ) or paper (1-3, 6, 6, 8,9, 11-15), the components of the mixture are transported by electroosmotic flow of the solution itself as well as by electrical migration through the solution (6, 8, 9, 15, 16). As in the early studies of electrolysis (1), the electroosmotic flow of the solution through the paper has been ascertained by the transport of zones of noncharged, nonsorbed, easily detectable substances such aa sugars (2, 6, 8, 9, 15) or tritium-containing water, HTO (14). In moist paper, a significant electroosmotic flow has usually been observed when the electrolytic solution is present in electrode vessels a t the ends of the paper (9, 6, 8, 9, 15). Recently, however, the electroosmotic flow was reported to be very small or zero when the electrodes are attached to the moist paper without electrode vessels (12, 15). The early intensive studies of electroosmotic flow through tubes filled with cellulose and through membranes of paper ( 1 ) did not provide a basis for interpretation of these different effects observed in paper strips with and without electrode vessels. This earlier work did indicate, however, that the electrcosmotic flow through paper is a property of the system and 8j 9,11, that it is affected by many diRerent conditions (1,5,6, 16, 16).
A search for the conditions that affect the electroosmotic flow when electrode vessels are employed has now led to an examination of the electroosmosis in long sheets of filter paper. These electromigration systems employed in electrochromatography present countless possibilities for variation. Because many electrochromatographic separations have been performed with Eaton-Dikeman filter paper (Grade 301) moistened with 0.1M lactic acid solution (12, 13), most of the authors’ exploratory investigations of electroosmosis have been performed with this migration medium. The electroosmotic flow has been studied 1 Present address, Department of Chemistry, University of California, Berkeley 4, Calif. 2 Present address, Illinois Institute of Technology, Chicago, Ill.
d
Figure 1. Apparatus for Study of Electroosmotic and Hydrostatic Flow in Filter Paper C. Glass plates of cell R. Electrode veasels for electrolytic solution E . Primary electrode supports
P. Filter paper strip L. Leveling t u b e
M . Differential m a n o m e t e r The secondary electrodes on the edges of the electrode vessels, a n d the cooling tubes, rubber pads, a n d aluminum strips forming t h e cell plates are not shown’
The Cell. The insulated cell was constructed from two thick, polished glass plates (0.75 X 12 X 17.5 inches). One face of each plate was covered with a foam rubber pad, 0.25 inch thick. Two wide strips of aluminum foil, each 0.003 inch thick, were then placed over each of the rubber pads. The portions (about 3 inches) of these aluminum strips extending beyond the sides of the glass plates were wrapped around water-cooled glass (or copper) tubes (14 mm.), one of which was placed along each side of the glass plates. Each plate, rubber pad, two aluminum strips, and two cooling tubes along the sides were enclosed with a sheet of polyethylene, 0.005 inch thick. The lower plate of this cell was supported on a substantial level wooden base so that the top padded face was level with the edges of the electrode vessels, R. The cell is thus a rigid impervious insulated heat exchanger, which applies uniform pressure to the paper. Electrode Vessels. Two borosilicate glass oven dishes (2.25 X 9.75 X 15 inches) were used as reservoirs, R, for the electro-
1864
V O L U M E 26, N O . 12, D E C E M B E R 1 9 5 4 lytic solution. Platinum wire (0.021-inch diameter x 10 inches), attached to Lucite forms and suspended in the reservoirs, served as the primary electrodes, E. Similar platinum wires fixed to the edges of the vessels adjacent to the cell formed the secondary electrodes. A voltmeter attached to these secondary electrodes (46.3 cm. apart) measured the potential drop in the enclosed portion of the paper strip t o within 5 volts. Lucite strips held the ends of the paper in the electrolytic solution. Lucite covers reduced evaporation from the electrode vessels during the electrolysis. Leveling Tube and Manometer. The siphon or leveling tube, L , was of 14-mm. borosilicate glass tubing with an 8-mm. stoprock. A Rensitive differential manometer, M , of 14-mm. tubing n w attached to the leveling tube a t opposite sides of the stopcock with flexible connections. With chlorobenzene, specific gravity 1.107, and water as the manometric fluids, hydrostatic pressures from 0 to 3 cm. of water were measurable with an accuracy of about 0.01 cm. Paper. Filter paper proved to be an extremely variable product. Ita electroosmotic properties varied with the source, treatment, and time the paper was exposed to the solutions and to the electrolysis. Different lots of the same brand of aper Pometimes showed marked variation in the electroosmotic egecta. A s an example, several lots of Eaton-Dikeman filter paper (Grade 301, 0.03 and 0.05 inch thick) exhibited electroosmosis toward the cathode with 0.1M lactic acid a s the electrolytic solution. One lot exhibited electroosmosis toward the anode, and this effect was not altered by washing with acids. All the experiments described were performed with paper from a single lot of the Eaton-Dikeman product, Grade 301, 0.03 inch thick. With paper from this lot, the electroosmosis was ton.ard the cathode with lactic acid as the electrolytic solution.
1865 levels in the two reservoirs was adjusted j u t before application of the voltage. After the requisite time, usually 4 hours, the electrical current was turned off, and the stopcock was opened. The ends of the paper extending through the cell were cut off, and the top plate was removed. The wet central portion of the paper strip, enclosed in the polyethylene envelope, was weighed. The paper strip, while still wet, was sprayed with a freshly prepared mixture of equal parts of 0.1M silver nitrate in 8% ammonium hydroxide and 6 M sodium hydroxide. In a few seconds, three round light blue spots appeared. The distance of migration of the three spots was then measured. The sprayed paper and the ends that had been cut off were dried overnight and weighed. The weight of paper in the middle section, the amount of solution in this section, and the volume of flow were then calculated. The basic experiments were designed so that only one variable was changed a t a time. These variables were the electromotive force, the time, the concentration, the compression, the hydrostatic pressure, and the nature of the electroosmotic flow indicator itself. The compression due to the weight of the upper plate alone was 0.104 pound per square inch. For greater compression, lead bricks were placed symmetrically on the upper plate. For most experiments, hydrogen peroxide was the electroosmotic flow indicator. It was not sorbed by the paper, and within the experimental error, it gave the same flow values a s several unrelated organic indicator substances. As shown with thermocouples, the temperature of the paper was as much a s 2" higher than that of the cooling water. Most measurements were made at paper temperatures of 17' d= 2' C. Temperatures between 12" and 20" C. were without significant effect on the results.
PROCEDURE
RESULTS
Before electrolysis, the weighed filter paper (8 X 22 inches) was immersed for 10 minutes in a large porcelain tray containing 800 ml. of the electrolytic solution, removed, and allowed to drain for a short period. As an added precaution against short circuits! the central portion of the paper strip was enclosed in a 10 X 17.5 inch polyethylene envelope and placed on the lower plate of the cell. Each end of the strip extending about 2.25 inches beyond the cell was placed between two pieces of the moistened filter paper (2 X 10 inches) and hung over the secondary electrode and down the side of the electrode vessel. These added stripe decreased the resistance to electrical and hydrostatic flow.
Most experiments are summarized in the form of tables and graphs. The symbols that have been employed are described in Table I. Table I1 shows the dependence of the electroosmotic flow, F , on the voltage. In Experiments I1 1 and I1 2, the current waa held constant; in the others, voltage waa constant. For the former, the reported voltage is the time average of the voltage. As the values of F a t 5.62 volts per cm. are an integral part of the relationships tested in Tables 111, IV, and V, these F values have been calculated on the basis of a direct proportionality between the flow and the field strength. For Experiments I1 l and I1 2, F equals 1.30 and 1.13 ml. per hour a t 5.62 volts per cm. Table I1 shows that the electroosmotic flow increases with the field strength. Additional indications of this effect are obtainable by interpolation of the result in Tables VI1 and 19. The uncertainties of the results are so large, however, that only a qualitative statement is warranted. Table 111, Experiments I1 1 and I1 2, and Figure 2 show that the rate of osmotic flow increases with time, apparently exponentially. This effect can be caused by a change of the system during electrolysis and also by retarding forces which chsngc with
__
.
._~~___ -_
T a b l e I. Spill bo1
E F
I .If
P
d C t
1.
Units Voltpercm. M I . per hour Ma. Moles Dyne per sq. cm.
G. s o h . per g . paper Lb. per sq. inch Hours Cm. per hour G . paper
T a b l e 11.
~
~~
Nonienclature
Description Electrical field strength (d.c.) Flow of solution in the paper (positive values toward cathode) Current flowing through paper Molarity of lactic acid solution Hydrostatic pressure (980 dynes per sq. c m . = 1 om. water) Wetness of paper Compressive force on paper Duration of experiment Migration rate (positive values toward cathode) Weight of dry paper strip (8 X 22 inch)
Effect of Voltage, E , o n Electroosmotic Flow.. F
( L = 4 hours; M = 0.lM; C = 0.104 Ib./sq. inch: P = 0 dyne/sq. om.) d, G . Soh. r, I. E. F, w , Expt. G . Paper G. Paper Cm./Hr. Ma. Volts/Cm. hIl./Hr. 0.575 14.0 5.18 1,20 35.98 3.25 I1 1 0.508 14.0 5.31 1.07 36.14 3.26 I1 2 1.045 20.8 7.55 2.15 a6.40 3.16 11 3 1.448 21.2 7.55 2.96 37.43 3.05 I1 4
T a b l e 111. Effect of Time, t, on Electroosmotic Flow-, F ( E = 5.62 volts/cm.; M
P
w Expt.
G. Paier
Table IV.
Three liters of the electrolytic solution were added to each electrode vessel. The leveling tube was filled, and the stopcock opened. With the polyethylene envelope opened momentarily, three spots of 10 pl. each of the flow indicator, usually a 0.1~11 solution of hydrogen peroxide in the electrolytic solution, were evenly spaced on a line drawn a c r o ~ sthe middle of the paper strip. The upper plate of the cell was placed in position, the stopcock in the leveling tube was closed, and the desired voltage (about 3 to 7 volts per cm.) was applied. When hydrostatic pressure was to be employed, the difference between the liquid
(E
Expt' IV 1 IV 2 IV 3 IV4
= 0
d, G. S o h T P G r
= 0.1M; C = 0.104 Ib./sq. inch; dyne/sq. cm.)
I'.
Cm./Hr.
Effect of Concentration, Flow, F
r,
Ma.
1.
IIr.
F, hlI./Hr.
M,on Electroosmotic
volts/cm.: t = 4 hours, C = 0.104 Ib./sq. inch; P = 0 dyne/sq: om.) d. W, G.S& v, I, .u, All./Hr F, G' Paper GyPaper Cm./Hr. Ma. Moles/L. 36.92 3.14 0.890 4.7 0.01 1.85 0.868 4.7 3.17 0.01 1.76 35.72 36.55 3.21 1.315 2.0 0.001 2.76 1.355 2.7 3.19 0.001 2.82 36.43 = 5.62
ANALYTICAL CHEMISTRY
1866
Table V indicates the dependence of the electroosmotic flow upon the nature of the eleciE = 5.62 volts/cm.; t = 4 hours: C = 0.104 lb./sq. in.; P = 0 dyne/sq. em.) trolvtic solution and uuon the d, treatment of the paper. With *G lr, VI I. Electrolytic Treatment F, distilled water, the electroG Paper Cm./Hr. Ma. Expt. G . Paper Solution of PaDer lll./Hr. osmotic flow in washed paper 3 16 0 670 15.0 0 , 1.M lactic acid V1 37 42 Washed 1 42 2 97 3.095 1.5 36 75 Distilled water V 2 Washed li 04 was nearly twice that in un3 13 1.795 1.8 36 70 Distilled water v 3 Not washed 3 69 1.482 Distilled water 3 21 36.76 3 13 Not washed v 4 washed paper. I n lactic acid, 3 17 0 . 1 4 1 NHiOH 1.452 N o t washed 36 63 V5 02 by contrast (Tables I1 and V), 0.004.M Th(N0a)r 3 18 1.310 3.5 37 19 Washed V6 i8 0.600 17.8 0.OOl.M AlCh in 0.134 3 09 36 48 V7 there was only a small increase lactic acid Not washed 1.21 of the electroosmotic flow in the n-ashed paper. The untreated paper contained 0.12% time or with the rate of flow. I t is not possible to separate these ash composed largely of calcium. After being washed with 0.1M factors in the experiments. Because of this dependence of the hydrochloric acid and then with distilled water by downward electroosmotic flow upon time, all the rates of flow reported in percolation, the paper contained less than 0.01% ash. Solutions the tables are average values for the time interval. of thorium and aluminum salts, which might have reacted with Table I V demonstrates that electroosmotic flow in paper inthe paper, had little effect on the electroosmotic flow. creases with decrease in the concentration of lactic acid, a result in agreement with observations on electroosmotic flow in many I , I I 1 I I other systems ( 1 ) . A plot of the electroosmotic flow against the concentration of the lactic acid (Table IV and calculated values from Experiments I1 1 and I1 2) showed that between 0.1 and 0.001.11 the flow decreases linearly with the logarithm of the concentration. Table V. Effect of \-ariation of Electrolytic Solution and Treatment of Paper on Electroosmotic Flow, F
E!
-
~
0
I
I
I
I
I
1
I
I
I
01
02
03
04
05
06
07
08
09
COMPRESSION,
IO
PSI
Figure 3. Effect of Compression on Quantity of Solution Held by Filter Paper
Table VII. Effect of Hydrostatic Pressure, P , on Flow, F (C = 0.104 lb./aq. inch: t = 4 hr.; I = 0 ma.: E = 0 volt/cm.; 31 = 0 , distilled water; negative values indicate flow toward anode)
Expt.
-I/ 0
I
I
I
,
2
3 -.ME.
I
I
I
4
5
6
W, G . Paper
d,
G . Soln. G . Paper 3.06 3 37 3.43 3.16 3 14 3 09 3 02 3 09
J',
Cm./Hr. -2.242 - 1.880 -0.942 -0,527 0.00 1.262 1,524 2.068
p, Dynes/ Sq. Cm. -3196 - 3024 - 1687 - 716 0 1282 2241 2730
F lIl./kr. -4.67 -4.17 -2.16 -1.08 0.00 2.55 3.06 4.08
7
hodis
Figure 2. Effect of Duration of Experiment on Total Flow Due to Electroosmosis
~
Table VI and the calculated values from I1 1 and I1 2 reveal that the electroosmotic flow varies little with the compression of the paper. By contrast with these flow values, the wetness E. 5.62 volts per c m . M . 0.1 M of the paper, d, decreases linearly with the increased compression. C. 0.104 Ib./sq. inch This relationship is shown by Figure 3 which summarizes some P. 0 d y n e s per sq. em. 40 determinations. Under these circumstances. the migration rate, V , increases with compression. Table VI. Effect of Compression, C, on Wetness of Paper, d, and on Table VI1 shows that small differences in hydroElectroosmotic Flow, F static pressure (1 to 3 cm. of water) produce a flow ( t = 4 hours: M = 0.1 M ; P = 0 dyne/sq. cm.) of the solution equivalent to the electroosmotic d. C, flow observed in many experiments (Tables I1 ~pG. Soh. v, I. E, Lb,./Sq. F* Mi./Hr. Expt. G. Piper G . Paper Cm./Hr. Ma. V./Cm. Inch (5.62 and V). The flow is dependent upon the pressure VI 1 36.00 3.12 0.550 14 5.55 0.493 1.10 1.12 and independent of direction as long as no potential V 33 6 3 00 .. 56 97 20 14 6 .. 00 88 00 .. 48 97 37 11 .. 2 1 84 11 .. 01 58 is applied (E = 0). VII 23 7 .. 00 00 2 .. 0 80 8 14 6 VI 4 36.59 2.78 0.745 14 5.95 0.877 1.36 1.29 In Table VIII, compression reduces the flow due to hydrostatic pressure. I n connection with
V O L U M E 26, NO. 12, D E C E M B E R 1 9 5 4
.c -5000
1867
I
-4;CC
-3000
I
I
-2000
-1000
HYDROSTATIC
Figure 4.
1 0
,003
PRESSURE,
I 2000
I
I
3000
4000
I
50W
dynes/cmZ
Effect of Hydrostatic Pressure on Flow a t Three Levels of Compression t.
M.
E. I.
1.4 em. of water corresponds to 0.3 mm. of hydrostatic head per em. Electroosmotic flow in various parts of the paper was determined with zones of hydrogen peroxide (10 pl., 0.1M)placed in parallel rows: across the center, a t 5 inches toward the cathode, and a t 7 inches toward the anode. With E = 5.62 volts per em.; t = 4 hours, P = 0 dyne per sq. em., and M = 0.1Mlactic acid, the spots migrated an average distance of 4.2 f 0.3em. Electroosmotic flow under the conditions described was also ascertained with a variety of indicator substances (0.1M)placed in the three parallel lines: a t the center, at 5 inches toward the cathode, and a t 7 inches toward the anode. These substances and the average distance that each migrated were: hydrogen peroxide, 4.6 em. ; thioacetamide, 4.3 em. ; allylthiourea, 4.3 cm.; formaldehyde, 4.1 em.; and hydroquinone, 4.0 em. Separate chromatographic experiments with flow of solvent into dry paper showed that hydrogen peroxide and formaldehyde were not sorbed by the paper. The other indicators were but slightly sorbed.
4 hours 0, distilled water 0 v o l t per c m . 0 ma.
‘t
Table VII, the initial increment of compression causes the greatest decrease in the flow. At the different levels of compression Figure 4 shows that the flow is directly proportional to the hydrostatic pressure. These marked effects of compression upon flow due to hydrostatic pressure stand in sharp contrast to the small effect of compression upon electroosmotic flow. In Table IX, hydrostatic pressure may accelerate or retard the flow produced by the concurrent application of electrical potential. The net force causing the flow is the resultant of the hydrostatic pressure and the electrical force producing the electroosniotic pressure. For different levels of field strength, Figure 5 shows that the electroosmotic pressure is equivalent to the hydrostatic pressure when there is no flow. I n the preparation of this figure, the slope of all the curves was assumed to be the same as that with zero field strength. In the light of these results, the net electroosmotic flow is remarkably sensitive to variations of the hydrostatic pressure. From 3.24 to 7.55 volts per em., the hydrostatic pressure necessary to yield zero flow is equivalent to only 0.4 to 1.4 em. of water. In the 46.3 em. of paper bet ween the secondary electrodes, a pressure difference of
a C
\
E
i
s
o -2
-4
-6
t
I1
-2500
Figure 5.
I
I
I -201)O -1500
-1000 -500 nrDROSTnTlC
0 500 900 530 PRESSURE, d i . e s / ~ - ~
2000
2500
Effect of Hydrostatic Pressure on Flow a t F o u r Levels of Electrical Field t.
C.
4 hours 0.104 lh. per sq. inch
As a rule, the indicator spots were round and symmetrical when transported by electroosmotic flow alone. When transported by hydrostatic flow, they were often unsymmetrical and elongated in the direction of flow.
Effect of Compression, C, on Flow, F, Due to Hydrostatic Pressure, P 4 hours; E = 0 volt/cm.; I = 0 ma.: ilf = 0. distilled water; negative
Table VIII. (t
-
DISCUSSION
values indicate flow toxyard anode)
Electroosmosis and Electrochromatography. These studies of electroosmosis in moist paper reveal many conditions that JV, G . Soln. V, Lb./Sq. F, are significant for the resolution of mixtures by electrochroExpt. G. Paper G . Paper Cm./Hr. Inch hll./Hr. matography. The experiments with the flow indicators show -2.45 0.493 -1.272 36.93 2.92 VI11 1 1.78 0.493 0.930 36.24 2.95 VI11 2 that the electroosmotic flow occurs uniformly through the paper. -2.24 -1.170 0.877 36.85 2.90 VI11 3 The solution must, therefore, flow from one electrode vessel to 2.07 1.111 0.877 37.30 2.79 VI11 4 -1.138 0.877 -2.09 36.52 2.82 VI115 the other. Under the conditions emuloved - - here, 0.877 2.54 2.78 1.370 VI11 6 37.30 the solution a t the anode serves as a reservoir or source; the cathode vessel serves as the receiver. Table IX. Effect of Hydrostatic Pressure, P , on Electroosmotic The small amount of the transported Flow, F, a t Different Levels of Field Strength, E does not change the liquid level in the large (1 = 4 hours; M = 0.1 M; C = 0.104 lb./sq. inch: negative values indicate flow toward anode) electrode vessels. d, The electroosmotic flow must be due to a drivw, G . . V, I. P, E, F, Expt. G . Paper G. Paper Cm./Hr. hfa. Dynes/Sq. Cm. V./Cm. hZl./Hr. ing force generated in the moist paper, not to r e IX 1 36.60 3.06 -1.130 8.4 - 2061 3.24 -2.26 actions a t the electrodes. This force depends 1x2 37.27 2.96 1.952 8.3 2445 3.24 5,62 upon the electrical field, the treatment of the 1 x 3 36.55 3.11 -0.805 19.1 -2170 paper, and the concentration and nature of IX 4 37.07 3.04 2.617 14.9 2342 5.62 5.28 1 x 5 37.17 3.05 -1,000 20.0 -2417 7.55 -2.03 1x6 36.19 307 2.875 22.2 2326 7.55 5.72 the electrolytic solution. The marked difference between the effect of compression upon d,
C.
P, Dynes/ Sq. Cm. -3120 2104 -3294 2960 -3319 3162
-!::!
ANALYTICAL CHEMISTRY
1868 electroosmotic flow and hydrostatic flow indicates that diderent flow mechanisms are involved. This view is supported by the uniformity of the indicator zones after electroosmotic transport and by the irregularity of the zones after hydrostatic transport. Under the conditions employed in these experiments, the electroosmotic migration ( V in the Tables) exceeds the electrical mobility of many ions (8, 9, 12). The mobility and even the direction of migration of substances examined by electrochromatography cannot, therefore, be specified unless the electroosmotic transport is determined or controlled as by opposed hydrostatic pressure or by modification of the paper and the electrolytic solution (5, 16). The electroosmotic flow is a complex phenomenon dependent upon many variable conditions-the treatment of the paper, the nature and the concentration of the electrolytic solution, the electrical field, the compression or wetness of the paper, the hydrostatic pressure or levels of liquid in the electrode vessels, and the duration of the electrolysis. I n practical applications of electrochromatography all these conditions are difficult to specify and to control. Consequently, precise, reproducible values for the mobilities of ions will be difficult to obtain even if the values are corrected for the electroosmotic flow determined directly. Phenomenon of Electroosmosis. Because of the large number of variables in this electrical migration system and the difficulty in determining them precisely, the phenomenological aspects of the electroosmotic flow have been examined. The equations of Mazur and Overbeek ( 4 , 10) and of Lorena ( 7 ) have served as a basis for the considerations. These equations nre
I
=
CnE
+ CiiP
The quantities C11, C12, and C22, the phenomenological coefficients, are functions of the factors necessary to define the system. The other terms are defined in Table I. The flow rates are time averages. From Equation 1, Ohm’s l ~ should ~ x be obeyed when P equals zero. Two separate experiments, in which the voltage was changed from 150 to 350 volts (3.24 to 7.55 volts per em.) over a short time interval, showed this to be true. For the longer experiments listed in Tables I1 and 111, the average value of Cll is 2.60 with a root-mean-square deviation of zkO.17. When Cll is divided by d, the grams of solution per gram of paper, the average value is 0.82 with a deviation of jzO.06. The variation of Cll with compression may be obtained from Experiments VI 1 and 2, average value 2.41, and from Experiments VI 3 and 4, average value 2.33. The corresponding values of Cll/d are 0.79 and 0.83. Within the large limits of error, these values suggest that Cn decreases slightly with compression while Cll/d is nearly constant. It is believed that, within the accuracy of the measurements, the variation of the individual systems, the possible variation of a single system with time, and the uncer-
tainty of the temperature, these results illustrate a proportionality between the current and the voltage. From Equation 2, the flow rate should be proportional to the field strength. A plot of the field strength against th‘e values of F from Table I1 and a corresponding plot of the interpolated values obtained from Tables VI1 and I X revealed considexahle scattering of the points. These points approximate a direct proportionality between the voltage and the flow rate, although a t the higher voltages the flow rate is greater than expected. Again the variations between individual systems and the possible variation of a single system with time and with the field strength made precise determinations difficult. The average value of C12, assuming a direct proportionality, is 0.235 for all coinparuble experiments with a spread from 0.16 to 0.30. The value of Czz, the coefficient for hydrostatic flow, has been obtained from the data of Table VII, omitting VI1 6. At B compression of 0.104 pound per square inch, the value is 1.13 X 10-3 ml. sq. cm. dyne hour. From Table VI11 and Figure 3, Czz is not linear but decreases with compression. The electrical current caused by the hydrostatic flow, C‘,J’, is of the order of 10-6 ma. This value is insignificant relative t o the current producing the electroosmotic flow-namely, 2 to 22 ma. LITERATURE CITED
(1) Butler, J. A. V., “Electrical Phenomena at Interfaces.” S e w York, hlacmillan Co., 1951. (2) Collet, L. H., J . chim. phys., 49, C65-8 (1952). (3) Durrum, E. L., J . Am. Chem. Soc., 72, 2943 (1950). (4) de Groot, S. R., “Thermodynamics of Irreversible Processes,” pp. 94-140, Sew York, Interscience Publishers, 1951. (5) Jermyn, AI. A, and Thomas, P., NatuTe, 172, 728 (1953). (6) Kunkel, H. G., and Tiselius, A., J. Gen. Physiol., 35, 89 (1951). (7) Lorenz, P. B., J. Phgs. Chem., 56, 775 (1952). (8) McDonald, H. J., Lappe, R. J., JIarbach, E. P., Spitrer, I
