NELECTHC PROPERTIES AND HIGH FREQUEMCY CONDUCTANCE OF WYOMENG BEN?QNETE Hm: fer {Eva Degree emf pk. D. MRCHEGAN STATE WWW-W? Wilfred L. Polzer 1960 0-169 This is to certify that the thesis entitled fi¢mflboé [2”??? -‘Z""/Z:—“<" M11 ’Mfl/L FMff/Mg’ “1.4; karma/(«g tot/(,2, / 0 47 ét/mflw4 (4m 44 I‘Tux/é 'l/ presented 9 / has been accepted towards fulfillment of the requirements for I ([72! l ) degree in 5/ «‘40 SW 4M? /// //"”V"M Major professor / Date //Z“"“"”‘ {1/760 LIBRARY Michigan State University 4. A. *..=........ . do DIELECTRIC PROPERTIES AND HIGH FREQUENCY CONDUCTANCE OF WYOMING BENTONITE BY 0 Wilfred L'f Polzer 44:! A THESIS Submitted to the School for Advanced Graduate Studies of Michigan State University in partial fulfillment of the requirements ‘ ' ‘ 4; for the degree of «.2 ‘ ’! DOCTOR or PHILOSOPHY " Department of Soil Science it (1 -, \a 1960 ACKNOWLEDGMENTS The author wishes to express his appreciation to Dr. M.~M.‘ Mortland for his kind guidance and encouragement in the study undertaken. His thanks are expressed to Mr. Tung Ming Lai for his help and suggestions in the course of this study. He is also grateful to his wife,» Fran, for her unfailing support, help and encouragement in this undertaking. Acknowledgment is also due to Dr. A. Timnick and to the members of the guidance committee. ii DIELECTRIC PROPERTIES AND HIGH FREQUENCY ‘ ~ ‘ CONDUCTANCE OF WYOMING BENTONITE I 4‘ 1 '3 n. ‘ By - Wilfred L. Polzer 0‘- AN ABSTRACT " N “5. Submitted to the School for Advanced Graduate Studies ‘ ' of Michigan State University in partial 7 . N fulfillment of the requirements .1? for the degree of . ". DOCTOR OF PHILOSOPHY Department of Soil Science 1960 fiflaWwZ’J/ Approved ABST RAC T The purpose of this research was to study the dielectric behavior and high frequency conductance of Wyoming bentonite clay and to study the effect of the type of exchangeable cation on these electrical prOperties of the bentonite clay. Eight different kinds of base saturated clays of seven different concentrations were studied in this experiment. The cations associ- ated with the bentonite clays were aluminum, barium, calcium, magnesium, lithium, sodium and potassium. Electrolyte solutions of sodium, potassium and calcium chloride were also used as a means of comparing the results obtained from the clay suspensions. The range in frequency at which the measurements were made varied from one kilocycle per second to 192 megacycles per second. A General Radio Type 650-Aimpedance bridge was used to measure the capacitance of the clay suSpensions in the kilocycle frequency range. A high frequency oscillator was used to show the effect of frequency on the capacitance and the conductance of clay suspensions in the megacycle frequency range. All the results were interpreted on the basis of a parallel equivalent circuit in order to account for the effect of the measuring cell on the electrochemical results obtained. The results obtained showed that both the capacitance and the conductance are dependent on the frequency at which the measurements are made. The capacitance of the clay suspensions was found to decrease with an increase in frequency. When based on the specific .s.‘ '0‘ ., it"s-'7'. - '. >‘\ .I conductance of the clay suspensions the capacitance was found to'var‘y ' . I: with the kind of cation associated with the clay in the low megacycle ‘ . , frequency range. The order of difference was Li clay > Na clay > . K clay. The high frequency conductance of the clay suspensions was greater than the high frequency conductance of electrolyte solutions at similar specific conductances. A difference in high frequency cen- ductance was also obtained between the various kinds of base saturated clays. The order of response was as follows: Ba clay > Ca clay > Mg clay > Li clay > Na clay > K clay. 3 TABLE OF CONTENTS ' .'fC3HAPTER 'IV. V. LIST OF INTRODUCTION. . . . . . . . ‘ SAMPLE PREPARATION . . . ‘ DIELECTRIC PROPERTIES . Experimental Apparatus . Procedure. . . . . . . . . Reslflts ‘ O O I I O O O O 0 Discussion . . . . . . . . . O t 0 e C I I 0 I I O I O I O Q 0 I e C HIGH FREQUENCY CONDUCTANCE . Experimental Apparatus . Results.......... Discussion . . . . . . . . wMMARYO I O O C I I I O I I REFERENCES. "APPENDIX....... Procedure............. LIST OF TABLES TABLE Page 1. Dependence of pH and Specific Conductance on the Milli- equivalents of NaOH Added to Hydrogen Saturated WyomingBentonite...... ............. 74 11. Frequency Dependence of Capacitance of Wyoming i Bentonite Clays and Electrolyte Solutions. . . . . . . . . 75 111. Frequency Dependence of Resistance of Wyoming Bentonite Clays and Electrolyte Solutions. . . . . . . . . 79 IV. The Dependence of Specific Conductance on Concentration of Sodium Bentonite Clay and Electrolyte Solutions. . . . 83 V.‘ Negative Deflection (Volts) of High Frequency ReSponse to Potassium Chloride Solutions. . . . . . . . . . . . . . 84 VI. Negative Deflection (Volts) of High Frequency ReSponse to Sodium Chloride Solutions. . . . . . . . . . . . . . . . 85 VII. Negative Deflection (Volts) of High Frequency Response toSodiumBentonite.................... 86 VIII. The Dependence of Specific Conductance on Concentration of Wyoming Bentonite Clays and Electrolyte Solutions . . 87 IX. The Negative Deflection (Volts) of High Frequency Response to Electrolyte Solutions and Wyoming BentoniteClays...................... 89 X. Change in Re5ponse to Variation in Moisture of Clay- SandMixtures...................... 93 XI. Change in Response to Variation in Butanol Content of Clay- sand Mixtures. a e s s s s s e s s s o e e e s c s o 94 XII. Change in Response to Variation in Octanol Content of Clay-sand Mixtures. . o o o o s n a o s o s s s e e u e e 95 vii LIST OF FIGURES FIGU RE Page 1. Titration curves to determine the cation exchange capacity of Wyoming bentonite clay. . . . . . . . . . . . 6 | Z. Capacitance comparison bridge circuit diagram; R, - CRL rheostat, R2 — known resistance, R3 - D rheostat, C3 - known capacitance, Rx— unknown resistance, Cx- unknowncapacitance........... ...... .. 9 “VF-.1 3. Diagram of the capacitance cell; A — cell container with brass electrode, B - 3/4 inch thick wooden boards, C - wire connecting copper sheets, D - copper sheets, E - i bolts connecting wooden boards, F - cardboard im- pregnated with a mixture of beeswax and paraffin. . . . 12 4. The relationship of the change in parallel capacitance to the specific conductance of the clay suspensions at 300, 400, 500 and 600 kilocycles per second. . . . . . 15 5. The relationship of the change in parallel capacitance to the Specific conductance of the clay suspensions at 300, 400, 500 and 600 kilocycles per second. . . . . . l6 6. The relationship of the change in parallel capacitance ' to the concentration of the clay suSpensions at 100 kilocyclespersecond.................. 17 7. The relationship of the change in parallel capacitance to the concentration of the clay suspensions at 300 kilocyclespersecond.................. 18 8. The relationship of the change in parallel capacitance to the concentration of the clay suspensions at 500 kilocycleSpersecond.................. l9 9. The relationship of specific conductance to the concen- tration of the clay suspensions. . . . . . . . . . . . . Zl LIST OF FIGURES - Continued FI GU RE 10. 11. 12. 14. ISI 16. 17. 'w I Page Diagrams of (A) the fundamental equivalent circuit of the cell and the solution, and (B) the parallel equi- valent circuit of the cell and the solution; C1 - capaci- tance of beeswax-paraffin mixture, C2 — capacitance of the solution, R - the resistance of the solution, Cp- parallel capacitance of the circuit, Rp - the parallel resistanceofthecircuit.................. 22 Schematic diagram of the high frequency conductance apparatus. I O I I I I I I I I I I I I I I I I I I I I I I I ' 28 Schematic diagrams of the cell assembly of the high frequency conductance apparatus; A - banana jacks, B - glass container, C - shielding, D - plastic support, E - electrode, F - plastic wall, G - glass opening. . . . 30 Schematic diagrams of the cell assembly of the high frequency conductance apparatus, A- banana jacks, B - glass container, C - shielding, D- plastic support, E - electrode..... ..... . ...... 31 The relationship of high frequency response to the specific conductance of sodium chloride and potassium chloride solutions at thirteen and thirty megacycles per second........................... 34 The relationship of high frequency reSponse to the specific conductance of sodium chloride and potassium chloride solutions at forty-four and fifty- seven mega- cyclespersecond..................... 35 The relationship of high frequency response to the specific conductance of sodium chloride and potassium chloride solutions at seventy-nine and one hundred ninety-two megacycles per second. . . . . . . . . . . . 36 The relationship of high frequency re5ponse to the Specific conductance of Na clay susPensions and sodium chloride solutions at thirteen megacycles per second. . 37 LIST OF FIGURES - Continued FIGU-RES l8. 19. 20. 21. 22. 23. 24. 25. 26. The relationship of high frequency response to the specific conductance of Na clay suspensions and sodium chloride solutions at thirty megacycles per second. . . The relationship of high frequency response to the specific conductance of Na clay susPensions and sodium chloride solutions at forty—four megacycles per second. The relationship of high frequency response to the specific conductance of Na clay suspensions and sodium chloride solutions at fifty-seven megacycles per second........................... The relationship of high frequency response to the Specific conductance of Na clay susPensions and sodium chloride solutions at seventy-nine megacycles per second........................... The relationship of high frequency response to the specific conductance of Na clay suspensions and sodium chloride solutions at one hundred ninety-two mega- cyclespersecond..................... The relationship of high frequency response to the specific conductance of sodium chloride and calcium chloride solutions at thirteen megacycles per second. . The relationship of high frequency response to the specific conductance of sodium chloride and calcium chloride solutions at forty-four megacycles per second. The relationship of high frequency response to the specific conductance of sodium chloride and calcium chloride solutions at seventy-nine megacycles per second........................... The relationship of high frequency response to the specific conductance of sodium chloride and calcium chloride solutions at one hundred ninety-two mega- cyclespersecond..................... Page 38 39 40 41 42 44 45 46 47 I I. _ . \ LIST OF FIGURES - Continued ' FIGURE 27. 28. 29. 30. 31. 32. 33. 34. The relationship of high frequency response to the specific conductance of monovalent cation clay sus- pensions and sodium chloride solutions at thirteen megacyclespersecond. . . . . . . . . . . . . . . . . . The relationship of high frequency response to the Specific conductance of divalent cation clay suspensions and sodium chloride solutions at thirteen megacycles persecond......................... The relationship of high frequency response to the specific conductance of monovalent cation clay suspen- sions and sodium chloride solutions at forty-four mega- cyclespersecond..................... The relationship of high frequency reSponse to the specific conductance of divalent cation clay suSpensions and sodium chloride solutions at forty-four me gacycles persecond......................... The relationship of high frequency re3ponse to the specific conductance of monovalent cation clay suSpen- sions and sodium chloride solutions at seventy-nine megacyclespersecond. . . . . . . . . . . . . . . . . . The relationship of high frequency response to the specific conductance of divalent cation clay suSpensions and sodium chloride solutions at seventy-nine mega- cyclespersecond..................... The relationship of high frequency response to the specific conductance of monovalent cation clay suspen- sions and sodium chloride solutions at one hundred ninety-two megacycles per second. . . . . . . . . . . . The relationship of high frequency response to the specific conductance of divalent cation clay suspensions and sodium chloride solutions at one hundred ninety-two megacyclespersecond. . . . . . . . . . . . . . . . . . Page 48 49 50 51 52 53 54 55 LIST OF FIGURES - Continued FIGURE Page 35. The relationship of high frequency response to the concentration of Na clay susPensions and sodium chloride solutions at thirteen, forty-four and one hundred ninety-two megacycles per second. . .. . . . . . 63 ' 36. The relationship of the change in parallel capacitance ' to the Specific conductance of the clay suSpensions at 300 kilocycles per second. . . . . . . . . . . . . . . . . 96 37. The relationship of the change in parallel capacitance to the specific conductance of the clay suspensions at 400 kilocycles per second. . . . . . . . . . . . . . . . . 97 38. The relationship of the change in parallel capacitance to the specific conductance of the clay suSpensions at‘ i 500 kilocycles per second. ..... . . . . . . . . . . . 98 i 39. The relationship of the change in parallel capacitance to the specific conductance of the clay suspensions at 600 kilocycles per second. ........ . . . . . . . . 99 xii CHAPTER I INTRODUCTION All materials are generally classified into three main divisions; conductors, semi-conductors and non-conductors, which are based upon the conductivity or resistivity of the mate rial. The divisions may over- lap each other since the resistivities for these divisions are only arbitrary. The semi- and non-conducting materials are considered di- electrics which are characterized by a dielectric constant. However, all materials have dielectric properties even though they may be conductors. If an alternating voltage is applied across a material, whether it is a solid, liquid or gas, a current results depending upon the electrical properties of the material. The current which arises from the applied voltage may be derived from one or both of two types of electrochemical behavior. One type of electrochemical behavior results in electrical energy being converted into heat energy. This conversion is due primar- ily to migration of ions through a voltage gradient. The other type of electrochemical behavior results from a di5p1acement of charge which also takes place under the influence of a voltage gradient. However, no energy is converted to heat because a restoring mechanism is also present so that the energy which is used to displace the charge on one part of the alternating cycle is returned on the next part of the cycle. This current determines the capacitance of the material which, in turn, is a measure of the dielectric properties of the material. The amount of current which arises from the applied voltage is dependent on the frequency of the alternating voltage. When the dielectric behavior of a colloidal susPension is measured at high frequencies, factors other than dielectric constants of components of the colloidal suspension have far more influence which results in an increased "apparent dielectric. " Curtis and Fricke (1937) measured the "apparent dielectric constants" of suspensions, including kaolin, in a frequency range from 0. 25 to 2000 kilocycles per second. The values obtained reached as high as 40, 000 at the low frequencies, but decreased rapidly as the frequency increased. These workers (1935) also measured electrical conductance up to 16, 000 kilocycles per second of colloidal suspensions and found an increase in conductance with an increase in frequency. Smyth (1955) with reference to dielectric constants, and Overbeek (1952) with reference to both dielectric constants and conductance, re- ported the results of various workers, showing that over certain ranges of frequency the dielectric constants of colloidal solutions are much larger than that of water, but that these values decrease with an increase in frequency. The large dielectric constants of colloidal solutions were attributed by Overbeek (1952) to either a permanent dipole moment or to the electric double layer of the colloids, more probably the latter. A rise in conductance was found to result with an increase in frequency. This was attributed to the oscillating movement of the particles being so rapid that the asymmetry of the double layer did not have time to develop to its full extent. Soil scientists have been interested in capacitance measurements from a practical as well as from a theoretical point of view in the field of soil water. Edlefsen (1933) and Aleksandrov (1934), as reported by Thorne and Russell (1947), found an almost linear relationship between capacitance and soil moisture in the dry range of soil moisture up to moisture equivalent. Fletcher (1939) also found that soil colloids had an effect on the capacitance. Anderson and Edlefsen (1942) using Bouyoucous blocks, but measuring capacitance instead of resistance, found very large values between the moisture equivalent and the permanent wilting point. Using the theory of Fricke and Curtis (1937), Anderson (1942) based the high range of values on polarization at the interfaces of a dielectric dispersed in water. Thorne and Russell (1947) concluded that their results of capacitance measurements could be qualitatively based on the fact that there is a high degree of orientation of the dipolar water molecules at the solid-liquid interfaces within the system. The purpose of this research was to study the dielectric behavior and high frequency conductance of Wyoming bentonite clay and to study the effect of the type of exchangeable cation on these electical proper— ties of the bentonite clay. “—— CHAPTER II SAMPLE PREPARATION The Wyoming bentonite used in this experiment included seven concentrations of eight different cation— saturated clays. The concen- trations ranged from 0. 00176 to 0. 04526 grams of élay per milliliter of suspension. The cations used for clay saturation included sodium, potassium, lithium, magnesium, calcium, barium, aluminum and hydrogen. The clay was put into susPension with a Waring blend mixer. The susPension was diluted to approximately one percent clay and allowed to settle over night at which time the < 2 micron clay particles were separated. The <2 micron clay suSpension was then passed through a column of Amberlite Resin IR-4B in order to exchange any anions present in the clay susPension. The clay was then tested for chloride and sulfate ions. Sulfuric acid was added to a small portion of clay, the clay flocculated and then the supernatant solution tested for chlorides. If no white precipitate formed from the addition of silver nitrate the clay was considered free of chlorides. Conversely, hydrochloric acid was used to replace any sulfate ions from the clay and calcium nitrate was used as the testing reagent for sulfates in the supernatant solution. The clay was then electrodialyzed to approximately pH 5. 5. It was felt that this pH value was high enough so that the hydrogen ions would not cause lattice decomposition of the clays, yet low enough so that the cation exchange resin would be more efficient in replacing the cations associated with the clay with the desirable kind of cations. w I . The cation exchange capacity of the bentonitewas determined by hydrogen saturating a sample of clay with Amberlite Resin IR- 120. The sample was immediately titrated with a standard sodium hydroxide. The exchange capacity was determined both potentiometrically and conductiometrically as shown in Figure l. The clay used for sodium saturation was passed through hydrogen saturated Amberlite Resin IR-120 and the proper amount of sodium hydroxide (87. 6 milliequivalents per 100 grams of clay) was added to neutralize the clay. The lithium and potassium saturated clays were prepared by pass- ing the anion free clay suspensions through a column of lithium and potassium saturated Amberlite Resin .IR-120, respectively, instead of hydrogen saturating the clay first. The calcium saturated clay was prepared by taking anion free clay and saturating it with tenth normal calcium chloride. The ratio of added calcium chloride to the number of exchange sites on the clay was approxi- mately fifty to one. The chlorides were washed free with the use of suction. Silver nitrate was used to test for chlorides. The aluminum saturated clay was prepared in the same manner as the calcium saturated clay. In addition, the pH of the susPension was kept below neutral in order to keep the aluminum chloride from precipitating on the clay. Similarly the barium and magnesium saturated claysl were prepared from clays that had been removed of free anions and hydrogen saturated. Barium chloride and magnesium oxide were used to saturate the clays with barium and magnesium, respectively. The barium saturated clay was then washed free of chlorides. lThe barium and magnesium saturated clays had been prepared by Dr. H. Jacobs for use in his Ph. D. Thesis work. 12.00- 1o.ooL— _1200 8 00 e ~800 I l l I L I l O 20 40 6O 80 100 120 140 160 Millequivalents NaOH per 100 grams clay Figure 1. Titration curves to determine the cation exchange capacity of Wyoming bentonite clay. Specific Conductance (,U mhos cm“) - Duplicate samples of quartz sand-Wyoming bentonite mixtures were prepared for determining high frequency response to (moisture in the range from one-third to fifteen atmospheres of pressure. ' Samples of five, ten and fifteen percent clay by weight were used in thisproblem. Water, butanol and octanol were also used as solvents in a range from zero to approximately seven percent solvent. Duplicates of only five and ten percent clay were used. No special treatment was given to the Wyoming bentonite in the experiment. CHAPTER III DIE LEC TRIC PROPERTIES Experimental Apparatus The method used to determine the dielectric properties of bentonite was that of measuring the capacitance of the clay suSpensions with a General Radio type 650-A impedance bridge. A diagram of the capacitance comparison circuit of this bridge is found in Figure 2. The condition of balance for the bridge is that ZIZx : 2223 (1) where 21, 22, 2:, and Zx are the complex impedances of the four arms. Since the impedances of the four arms are complex, two require- ments must be met in balancing the bridge. One requirement is that the magnitudes of the impedances must satisfy equation (1). Secondly, the sum of the phase angles of one pair of opposite arms must equal the sum of the angles of the other opposite arms. If the impedance values of the bridge circuit in Figure 2 are substituted into the impedance values in equation (1) where Zl : R1 ; Z2 : R3 (2) and (3) , 1 [ ZS _ R3 _ J (a) c;3 (4) , _ . 1 2X - RX " J 0.) Cx (5) i then R R ' 1 ‘ R R '—1—- (6) 1(x'Jwa)- z( 3’-J“°C3) Exte rnal Detector D Figure 2. Capacitance comparison bridge circuit diagram; R1 - CRL rheostat, R2 - known resistance, R3 - D rheostat, C3 — known capacitance, Rx- unknown resistance, Cx— unknown capacitance. Frc diti the 10 ‘1 where R, and R2 are known resistors; R3 is a known resistor plus the resistance of capacitance, C3; C3 is a known capacitance; Cx is an unknown capacitance; Rx is the unknown resistance of Cx. and w is 2 1r times the frequency in cycles per second. By separating into real and imaginary numbers and equalizing the real parts on the two sides of the equation, as well as the imaginary terms, the following equations result: Rle = RzRa 01' RX = %1 R3 (7) l l 1 R R1 wcx R2 LOC3 01' CX C3 R2 (8) From these two equations, it is shown that there are two balance con- ditions which requires two variables. Cx is determined by adjusting the CRL rheostat, R1, the values being calibrated in capacitance readings. Rx is determined by adjust- ing R3. The R3 values are calibrated in the dissipating factor, D, which is defined as RwC where R is the total resistance of arm three at a frequency of one kilocycle, w is 2 n times frequency in cycles and C is the capacitance of arm three. If so is assumed to be one, then D = RC or R = €— (9) If Rx and R3 of equation (7) are substituted for R in equation (9), then _Dx_Rz' __Rz D3 Rx‘—cx ‘ R. R“ R. C. ‘10) R c = ..z .2; DK R1 D3 c, (11) ll Cx is then substituted by equation (8) R C R = ..L .1. __1 Dx R1 D3 C3 R2 (12) or therefore D3 = Rx Cx (13) Rx can then be calculated from equation (13). An oscilloscope, Model 130A, made by the Hewlett-Packard Company at Palo Alto, California, was used to determine the balance point. A sensitivity of 0. 05 volts per centimeter was used throughout the experiment for the oscilloscope. An audio oscillator Model 200CD also made by the Hewlett-Packard Company was used as the external frequency generator with an output voltage of 90 volts. The capacitance cell was made up to two 12 inch x 16 inch and two 12 inch x 18 inch copper sheets, and one 1 3/4 inch x 2 1/4 inch brass plate. The four copper sheets were connected in series with one another, while the brass plate was connected in parallel with the copper sheets. Cardboard, impregnated with a mixture of beeswax and paraffin was used as insulation between the copper sheets. Boards, 3/4 inch thick, were bolted on the outside of the copper sheets to keep the distance between the sheets constant. A mixture of beeswax and paraffin was applied to the edges of the cell in order to keep the humidity between the sheets as constant as possible. A diagram of the cell is shown in ‘ Figure 3. The distance of 1 1/4 inches between the brass plate and the copper sheet was kept constant with the use of plastic material. The plastic also served as a containerfor the material to be measured. The brass plate was covered with a thin film.of beeswax-paraffin mixture {Ct U 111-- $1.9- 12 .Gfludndm pad ands/moon. mo engende— 6 Sum? usugmoumfim Undonpumo u .m .mpudon. GopooB wnfloocsoo 9:03 I m .302? Monaco .. Q .3023 nommoo 95300530 0.53 I D Jackson. sumac? Mega god“ ¢\m u m .oponuuoao mango. fig Hogan—Goo doc I 4 ”Zoo oosdfiodmdu 93 mo Emuwswfl .m oudwwm 3mH> ”An—Hm 3MH> .HZOMh o_ l I. I l I lo _ _ mlld _o _ Elm _ _ 0 Lo _ _ o_ o < r-Q- Th Th( wit? acr N0 1 -‘——-— 13 in order to prevent passage of direct current between the electrodes. The purpose of such a large cell was to obtain a capacitance for both the cell and the clay suspension in the range of the impedance bridge. Procedure In this experiment six different concentrations of NaCl and CaClz were used along with the eight cation-saturated clays of seven different concentrations. A sample was placed into the cell and readings of both capacitance and the dissipation factor were recorded. Readings were taken at nine frequencies; one, ten, fifty, 100, 200, 300, 400, 500, and 600 kilocycles per second. The resistance of the suspensions was calculated from the D factor through equation; D = R to C where D = dissipation factor R = resistance in ohms o.) = 2 1r time frequency in cycles per second C = capacitance in farads. The apparatus and the suspensions to be measured were kept in a constant temperature room at a temperature of 25 i 0. 5 degrees centigrade. The humidity was kept in a range from 50 to 65 percent relative humidity with the drying agent, silica gel. Each time a suspension was placed in the cell the d. c. leakage across the electrodes was tested with aTriplett ohmmeter Model 630-A. No d.c. leakage was encountered. A11 capacitance and D factor readings were taken in duplicate and the average of the two was considered the correct value. P511 the: It. ()1 14 Results The results for the capacitance measurements are given in Tables 11 and III. Figures 4 and 5 show the dependence of capacitance change on the specific conductance of the clay suspension at eight dif- ferent frequencies. In Figures 36, 37, 38 and 39, of the appendix, the deviation of measurements from the drawn curves given in Figure 5 is presented. Curves showing the dependence of capacitance change on concentration of clay suspension are found in Figures 6, 7 and 8. The change in capacitance is based on the capacitance of the pure solvent, '. water. Instead of absolute capacitance the change in capacitance was used in order to explain the results on a theoretical basis. Greater deviation occurred at the higher frequencies employed. This was attributed to error in obtaining the true null point on the impedance bridge. The null point was increasingly more difficult to obtain as high frequencies were used because of the limitations of the oscilloscope. Another source of error could have been due to a fluctuation of humidity. The relative humidity could only be kept within a range of 50 to 65 percent. The capacitances of sodium chloride and calcium chloride solutions were also measured. There was essentially no difference in the capacitance change of the electrolyte solutions and those of the clay sus- pensions at similar specific conductances. Since the conductance of these electrolyte solutions was not in the lower range of conductance of the clay suspension the results were not plotted. The following relationship were observed from the data in Figures 4, 5, 6, 7 and 8. l) Capacitance is dependent on the frequency at which the measure- ments are made. 15 .9336 Hum mofiohoofix cow was ooH .om .oH Hm msommsommsm >20 08. mo monouoaucoo oflmoomm 23 cu oocmfiommdo 32.2mm a: smudge 05 mo mfiAmGofldHoh 08H. .w ouswwh $-80 moss \5 ooGduodpsoU omfioomm ooh: co: oomfi 003 com ooo cow com . _ _ _ . _ _ F _ m oaofnoofix 0H .N. mongoose om. J. 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(spare; n/fi’) do V 20 2) The change in capacitance varies with the specific conductance of the clay susPensions. 3) The change in Specific conductance of the clay suspensions is a linear function of the concentration of these suspensions, however the slope of the change varies with the type of cation associated with the clay as seen by Figure 9. Discussion The capacitance measurements are interpreted in terms of a parallel equivalent circuit. According to Curtis (1950) a great deal of erroneous thinking relative to electrical problems in biology has resulted from failure to use an equivalent circuit, either the parallel or the series type, in making measurements and in interpreting the results of these measurements. The parallel equivalent circuit is used instead of the series equivalent circuit because Reilley (1954) has described this type more completely than could be found for the series equivalent circuit. In Figure 10 a diagram of the cell is given in terms of the fundamental equivalent circuit and one in terms of the parallel equivalent circuit. The admittance of the parallel equivalent circuit is given as taken from Reilley (1954). 31'; Q)2 C12 _ w: + 003 (C1C12+C2C12) Y = 1 z z + J 1 2 z (1) 7312+ w (C1+Cz) i2 + co (C1+C2) Y G P+J Bp (2) where Y is the net admittance of the circuit in mhos. Gp is the con- 1 ductance term which is equal to —R—p-, the reciprocal of the parallel resistance in mhos. It is also the real part of admittance. Bp is the /o .wnofimsommdm >30 05 mo Goflmnudoonoo 03.0 no 00:303.:00 03:009.“ mo mEmcofldfiwu 04.3. .o 005mmh 21 :33 non 093qu Gomudnucvoaoo adv o.mm 0.0m o.m~ o.o~. o4: o4: c.m T _ H _ _ _ 3‘ Lryth'HVbi \‘l’l‘! >30 .mm \1 x >30 m2 >30 so I >30 34 >30 02 COM 0 O fi‘ 0 O \O O O Q pooos (rum soquz /V) soueionpuog 33;:st 22 AAAAA vyvv :cz , Figure 10. Diagrams of (A) the fundamental equivalent circuit of the cell and the solution, and (B) the parallel equivalent circuit of the cell and the solution; Cx - capacitance of beeswax-paraffin mixture, Cz - capacitance of the solution, R - the resistance of the solution, Cp - parallel capacitance of the circuit, RP - the parallel resistance of the circuit. Z3 susceptance term (0) Cp) which is the imaginary part of admittance in mhos. w is equal to 2 1r f. f is the frequency in cycles per second. R is the actual resistance offered by the solution in ohms. R is equal to-ll; where k is the actual low-frequency conductance of the solution. C1 is the capacitance due to the paraffin-beeswax mixture in farads. C2 is the capacitance due to the solution in farads. j is the operator (-l)%. Since parallel capacitance was measured in this experiment the discussion is limited to the equivalent parallel capacitance term. c,10C0ioouw hmE ofi mo >380mmm :00 0,5 mo mgmumdfip ofiuwcfioflom .NH ounmwm 3MH> QZH «s—I’ ~._l I I lln --.-1.1 III--@ m _ _ a _.___ @. 3HH> nHOH. 31 I I 1 -—-—’~__.. I 9:: .._-__._:-_-+.; ...... -E I I I. i SIDE VIEW Figure 13. Schematic diagrams of the cell assembly of the high frequency conductance apparatus; A - banana jacks, B - glass container, C - shielding, D - plastic support, E - electrode. 32 su8pensions without hindering the reproducibility of the cell. The cell box was bolted into place to allow more rigidity when measurements were taken. Procedure Thirteen different concentrations, 0. 01 to 1. 00 normal, of sodium chloride and potassium chloride were used to show the response of the high frequency oscillator to the conductance of strong electrolytes. Also, eight concentrations of sodium clay, ranging from O. 0116 grams to 0.1344 grams Lper milliliter were used to compare the response of bentonite to that of strong electrolyte solutions. Response was measured at six frequencies; 13, 30, 44, 57, 79 and 192 megacycles per second. The R; resistor of the oscillator was set at 936 ohms for each response. The student potentiometer was standardized with a Weston cell before each series of measurements. The results were based on the difference in re3ponse with suspensions in the cell and with conductivity water in the cell. In another part of the high frequency conductance experiment the reaponse to sodium chloride and calcium chloride was recorded in addition to the response to the seven concentrations of eight different cation- saturated clays used in the capacitance measurements. In this case only four frequencies; 13, 44, 79 and 192 megacycles per second were used. The R; resistor was set at 1000 ohms. A different glass container was used in this series of measurements. All readings were taken in a constant temperature chamber at 25 i O. 5 degrees centigrade. ‘ An experiment was also set up using percent moisture and percent clay as variables in quartz sand- Wyoming bentonite clay mixtures. High frequency reaponse was measured at all six frequencies. 33 Three levels of clay, 5, 10 and 15 percent, were studied. The moisture content was varied in part of the experiment by using the pressure plate and the membrane methods. The atmOSpheric pressure ranged from 1/3 atmOSphere to 15 atmospheres. A lower range of moisture was obtained by adding water to the mixtures in small amounts, then allowing them to equilibrate for seven days. The percent moisture was determined by oven drying a small portion of the sample. Butanol and octanol were also used as solvents in this range of liquid variation. Only 5 and 10 percent clay mixtures were used for the lower range of moisture and alcohols . Re salts The results for high frequency conductance are given in three parts. In the first part the results show the effect of electrolyte solutions on high frequency reSponse as compared to results obtained by Reilley and McCurdy (1953). The results also show the effect of sodium saturated Wyoming bentonite on high frequency reSponse. The data are presented in Figures 14 through 22 and are eXpressed as negative deflection in volts. The negative deflections in volts represent an increase in the deflections of high frequency conductance. This can be explained on the basis of Ohm’s Law. Voltage is directly related to resistance, but re- sistance is inversely related to conductance; therefore voltage is inversely related to conductance. If a decrease in voltage is obtained, an increase in conductance would be observed. The pure solvent, water, represents zero deflection. Deflection was used because the absolute voltage could not be reproduced, due mainly to voltage fluctuations. In attempting to standardize the voltage with a Weston cell the galvanometer showed a very slow but continuous change in voltage with time. 34 .9835 com moaohommog 15.33“ pad Goouufiu um mGoUdHOm mcmnoEo Edammwuom can ovmnogo EdmuOm mo mocmuospaoo 3:0on or? on omcommou twosofivoum gwE mo mEmaofimHou 93.. .mL oudmwm :qu mogg \vJ mocmuofipcoo 0&3on oooooa cocoa oooH A , n H pcooom mom moaocnommoe om allollo paooom pom moaocnodmoa ma Tloll oomo . oouvo . coco . oomo . (9110A) Honoaueo GADRBQN .950me com mmfiorwommog Go>mmu>nwfl can 9.98.35qu 5 as mcoEHSOm opwnogo Edflmmemeom paw. opmuoEo 8560.,“ mo moamuodpcoo 0&3on mg» on omcoamou cwocosvcuw Am“: mo mEmcoflmHmu oQH. .mH ohsmfim :qu moan \\v oocmuofipcoo oflfiommm ooo.oo~ 000.0“ ooogn 1 _ ‘ n @cooom Mom mofiucwommoe hm oléllo cqooom Mom mofiocnommog we. 1 l L .ooHo. oomo . oomo . oowo . oomo. 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(9110A) museum eAmfiaN 40 .35000 n0m m30>00m0§ C0>0mu>uwfl 00 0:03:30 03.0330 83000 050 3030000050 >30 02 00 032303500 03030000 030 o» 0mcomm0n >0c0dv0nw fiwfi mo mw£0G0330u 0:8 .0N 0udmrm $180 moan SJ 00cmuoquo0 03300mm 0000 000» 0000 0000 000w 000m 000M 0003 4 _ _ _ _ a _ _ UQO000 u0m m30>00m02 >0 >30 .02 II... 30.02 0030. 00N0 . 00m0 . 00¢0 . 00m0 . (sitoA) uotioagsq cAti'eScoN 41 0000 .000000 009 030>0mw0§ 0GEu>HC0>00 00 0003300 003030 53000 000 0003003500 >30 02 00 0003050000 0030000 000 00 0300000.” >0c0sw0um £03 00 020003.30n 00H. .HN 0.“.meh A750 0005 \\v 0003050000. 033009.01 oooo oooo ooom oooe ooom ooom oooH A w _ _ _ _ _ >030 dz Illo 30.02 000000 000 m30>00w0§ 0N. 0030. 00N0 . 00m0 . 0000 . (8110A) 110009090 aAneBeN 42 0000 .000000 00m 0300300000 03013000 0000000 000 0.0 0003.300 0000030 003000 00.0 00000000000 >03 .02 m0 00000000000 0030000 000 0» 00000000 >000000um 003 .«0 930003200 00% .NN 0003M $1000 0050 53 0003000000 030025 ooh: 080 83. ooow ooom ooom 82 4. . _ . _ _ _ >30 02 0'16 030030002 mod #002 III 00H0. [floomo . 400m0 . 40°00. (8110A) 1100991330 eAmfiaN 43 Six frequencies; 13, 30, 44, 57, 79 and 192 megacycles per second were used in this experiment. ’ Sodium chloride and potassium chloride were the electrolytes used. The results show that the electro- lyte solutions behaved similarly to those that Reilley and McCurdy (1953) used. In plotting high frequency response as a function of Specific conductance all electrolytes fall on the same curve. However, the clay suspension curves varied from those of the electrolyte solutions. The clay susPensions showed greater reSponse with respect to Specific conductance than did the electrolyte solutions. At the lower frequencies the maxima of the clay suSpension curves fell below those of the electro- lyte curves. However, as the frequency was increased, the difference in the maxima became less until there was essentially none. The results obtained for the second part of high frequency con- ductance measurements are presented in Figures 23 through 34. These data show the effect of the type of cation associated with the clay on the reSponse of high frequency conductance. The electrolyte solutions, sodium chloride and calcium chloride, were also used in order to check the previous results. The Wyoming bentonite clays included those saturated with sodium, potassium, lithium, calcium, barium, magnesium, hydrogen and aluminum. In these interpretations the hydrogen clays were not used because of the combination of aluminum and hydrogen ions in the suSpensions due to changes in the mineral composition of the hydrogen clays. It was found that the Specific conductance measurements of the aluminum clays were extremely erratic due to the effect of floccu- lation. Therefore, the aluminum clays were also not included in the interpretations of high frequency conductance measurements. The 13, 44, 79 and 192 megacycles per second frequencies were employed for this part of the experiment. The results showed a difference between 44 .000000 00& 0000030000000 000000.00 0.0 0003.300 0000020 00000000 000 0000030 0000000 00 0003000000 00000000 000 00 00000000 030000000 0mg 00 0000000000000 00H. .mm 0003M A7000 0008 \\v 00000000000 000000n~m 000000.0m04 ooo .8 000 .3 ooom 82 com _ _ _ _ 00000w 00m 00~0>00w0§ m0 «H000 .Illb H002 . 00N0 . 0000 . 0000 . 0000 . 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(8110A) Honoauaa 9AD'939N .000000 00m 0000>00m000 03015000 0000000 000 0.0 0003.300 0000030 0000000 000 00000000000 >30 00300 00000.30 00 0003000000 00000000 000 00 00000000 >0000000m 0mg 00 0000000000000 008 .wm 000m?“ 55 A7000 00000 \\0 00000000000 00:00am of 3: OE 2: cm 3 0 0 _ _ 0 _ 00000m 00% 0000030002 N00 1 00a (9110A) Homauaa 9101128901 56 the different types of clays used. The response in decreasing order to these different types of clay was as follows: Ba clay > Ca clay > Mg clay > Li clay > Na clay > K clay. The third part of the high frequency conductance involved the reSponse to a change in moisture, butanol, and octanol in clay-sand mixtures containing five and ten percent clay. The results, obtained over a low liquid range, zero to six percent by weight, may be found in Tables X, XI and XII. The liquid was added to the clay- sand mixtures and allowed to equilibrate for one week, at which time percent liquid and high frequency conductance measurements were taken. The assump- tion was made that one week was time enough for the liquid to equilibrate in an unsaturated condition, which is not strictly true. The results show that the reSponse was different at different clay contents for both the water and the alcohols, the five percent clay mixture giving a greater reSponse than the ten percent clay mixture. A maximum was reached in all cases, though the alcohols gave much greater variability than did the water. No explanation is given for this variability. The reSponse to changes in amount of water was much greater than the response to changes in alcohol content. An attempt was made to measure the reSponse of high frequency conductance to moisture changes for clay-sand mixtures of five, ten and fifteen percent clay over the range of moisture which is considered available to plants. The porous plate and pressure membrane methods were used to obtain the moisture in this range. The variability of the results was such that no conclusions could be drawn. f2 CE tc 57 Discus sion The relationship of high frequency conductance to Specific con- ductance of the clay suspensions was found to differ from the response of the ordinary electrolyte solutions. This deviation can be explained on the basis of the dependence of capacitance and conductance of colloidal systems on frequency. References are given by Kortiim and Bockris (1951) on the dependence of conductance, and by Overbeek (1952) on the dependence of capacitance on frequency. At high frequencies, as the frequency is increased, the capacitance or measured dielectric constant decreases. This phenomenon can be eXplained on the basis that as the frequency is increased the charged particles have less time to complete their diSplacement before the a. c. frequency cycle reverses its field; thus less polarization takes place causing a decrease in the capacitance or measured dielectric constant of the suSpension. The asymmetry of the double layer may not develop to its fullest extent in this frequency range, which, in turn, would decrease the amount of polarization. The dependence of conductance on frequency is known as the disPersion of conductance or the Debye effect. This effect can be attributed to the change in f X , "Conductance Coefficient, " with a change in the frequency of the applied field. The "Conductance Coefficient" which is defined as the ratio of the measured equivalent conductance to the ideal value which according to Kortiim and Bockris (1952) was introduced by Bjerrum into equation (1) where Av is the measured equivalent conductance,_/L°O is the equivalent conductance at infinite dilution, and a. is the degree of 58 dissociation. This coefficient was introduced to take into consideration the effect of concentration on the ionic mobility of electrolyte solutions. The mechanism of the Debye effect can be explained by considering the ionic atmosPhere in an electrolyte solution. In an a. c. field a central ion of an ionic atmOSphere changes its direction of motion with the change in the direction of the cycles of the applied field. At low frequencies the mobility of the ion is retarded because of its ionic atmOSphere. When the frequency becomes very high the central ion changes direction so quickly that there is little chance for the ionic atmosPhere to retard the motion of the central ion. Thus an increase or dispersion of conductance occurs. In the case of clay susPensions the retarding force on exchangeable cation may be expected to vary as the distance of these cations from the surface of the clay particles varies. The closer the exchangeable cation is to the clay particle, the greater the force of attraction of the ion to the clay. Another possible explanation of retarding forces may be on the basis of increased viscosity of water near the clay particle, thus creating a greater frictional force for the exchangeable cations to over- come. A discussion of this point of view is made by Low and Lovell (1959). The electrical potential exerted by the clay mineral on associated ions is described in terms of an exponential function. As the distance from the clay particles increases the force which retards the movement of ions decreases exponentially. A differential in the mobility of the ions in the double layer thus occurs. This differential in the mobility of ions gives a measured conductance at low frequency which is much lower than would be expected if all the ions were free of any retarding force. If the frequency is increased to a point where the ions move only a very short distance in following the alternating field, then these ions 59 do not have to overcome the retarding force or at least only a portion of it. This causes an overall increase in the mobility of the ions; thus increasing the conductance of the suSpension. The high frequency conductance measurements are interpreted in terms of the parallel equivalent circuit. Since the equivalent circuit is the same as that used in the capacitance measurements, the admittance is also the same. Thus, the high frequency conductance term is given as 1 k 0)" C12 (2) RP - kz ‘1" (02 (C1 + C2)2 O *0 II I where the symbols are the same as those found in the discussion in Chapter 111. However C1 refers to the capacitance of the glass walls instead of the paraffin—beeswax mixture. By differentiating equation (2) and setting the results equal to zero, Reilley (1954) found that the position of the peak is dependent on the frequency, the capacitance of the cell walls and capacitance of the solu- tion in the following manner. k peak or k minimum '= 0 (01+ 0,) (3) where k peak refers to the Specific conductance at the peak of the high frequency conductance curve and k minimum refers to the specific conductance at the minimum of the high frequency parallel resistance curve. Furthermore; Reilley (1954) found that Q.) C12 2 (C1+ C2) G peak = (4) 01‘ Z (CL+ C3) 0 C12 R minimum = (5) by substituting equation (3) into equation (2) where G peak is the high 60 frequency conductance value at the maximum and R minimum is the high frequency resistance value at the minimum. The relationship of high frequency conductance to Specific con- ductance of the electrolyte solutions follows the theoretical and experi- mental results of Reilley and McCurdy (1953). Since the voltage measured is directly related to the input resistance of the oscillation circuit, results obtained should follow equation (4) and equation (5). Figures 14, 15 and 16 Show that as the frequency increases the low frequency con- ductance (Specific conductance) at the peak or at the minimum also in- creases, which bears out equation (3). Equation (5) shows a decrease in high frequency resistance with an increase in frequency. This is also shown to be true in Figures 14, 15 and 16. Even though the clay suSpenSion curves deviate from those of the electrolyte curves, they can be explained on the basis of equation (3) and (5). From equation (5) it can be seen that if the clay curves are compared to the electrolyte curves for the same frequency, then any difference between the minima will be due to the capacitance, C2. Since the minimum of the suSpenSion curves falls below (more positive) that of the electrolyte curves, the capacitance of the clay suspension is indicated to be greater than that of the electrolyte solutions. This would be eXpected on the basis of an added polarization due to the asymmetry of the double layer of the colloidal particles at high frequencies. At the higher frequencies the minima of the clay curves are as great or slightly greater than the minima of the electrolyte curves. This suggests that as the frequency is increased further the double layer loses its asymmetry because of the rapid reversal of the alternating field. In comparing the clay susPension curves to the elecurolyte curves on the basis of equation (3) the results indicate that the capacitance of the clay suSpensions is less than that of the electrolyte solutions because the 61 k minimum of the clay curves is to the left of the k minimum of the electrolyte curves. This is apparently contradictory to equation (5). However, if the dependence of conductance on frequency is taken into consideration, then the data should follow both equation (3) and equation (5). This can be eXplained on the basis that the high frequency field sees more apparent free ions in the clay suspension than does the low frequency field. Therefore, if the Specific conductance could be measured for the same number of apparent free ions as seen by the high frequency field, then the k minimum of equation (3) would be greater than that actually observed. This indicates that the k minimum Should be at a high k value than is actually Shown in Figures 17 through 22. Since equation (3) predicts that the k minimum value for the clay suSpensions should be to the right of the k minimum value for the electro- lyte solution on the basis of the capacitance of the clay systems, this suggests that the increase in conductance at high frequency is actually greater than that which is shown in comparison of the clay system with pure electrolytes. The results of the different kinds of cation saturation of the clay Show that the high frequency conductance compared to the specific conductance differs with the kind of cation associated with the Wyoming bentonite. These responses are all based on the deviation from high frequency-low frequency conductivity curves of electrolytes. Figures 27 through 34 show the following response in decreasing order: Ba clay > Ca clay > Mg clay > Li clay > Na clay > K clay. It was observed that the difference in high frequency reSponse between the kinds of cation-saturated clays increased with an increase in frequency. However, the ratio of the difference in high frequency response between the kinds of cation— saturated clays stayed approximately the same. 62 In order to explain this phenomenon, high frequency conductance reSponse was plotted against concentration (equivalents per liter) for the sodium chloride solutions and for sodium clay suspensions. Thus, as indicated in Figure 35, as the frequency increases, the difference between the electrolyte curve and the clay suSpension curve decreases. This is assumed to be due to a reduction of the diSplacement of ions. The calculated distance traveled by the ions at a frequency of one mega- cycle per second, is 0. 00194, 0. 00260 and 0. 00381 K per half cycle for lithium, sodium and potassium, respectively. This might suggest that all the retarding force encountered by ions at low frequency should be negligible at one megacycle per second. However, as the distance from the surface of the clay decreases to a small value the force with which the cations are held by the clay should be quite strong. Anderson and Low (1958) estimated the force near the clay surface to be of large magnitude. Therefore, it does not seem improbable that some of the ions are retarded at very high frequencies even though the movement of ions is very small. Since this experiment was not designed to explain why a difference in high frequency response occurred for the various cation-saturated clays, several explanations are given based on various concepts of the structure of clay and its environment. The sequence of the high frequency response of the different kinds of cation- saturated clays may be explained on the basis of the viscosity of the water near the surface of the clay. It was postulated in a review by Low and Lovell (1959) that the structural development in the adsorbed water near the clay surface is enhanced by increased ionic dissociation from the clay. The disruptive effect of the ions is less when they are distributed through a relatively large volume than when they are concen- trated at the surface where the structure is "anchored. " 63 .000000 000 0000>00w000 03730000 0000000 000 000 0:00:3000 .00000000 00 000000000 00.000000 005.0000 000 00000000000 >000 .070 00 000000000 0000 000 00 0000000000 00000000000 0m? .00 0000000000000 00.0. .mm 000m0h 000000 0000 000000.,»00000 0000000000000 0000. 0mm0. 00m0. 0mm0. 00N0. 00.000. 0000. 0m00. _ _ 4 _ _ . _ _ ‘0 00000m 0000 0000,000m030 \\\.\\\\\\)\ 00000m 00m 0000>00m00>0 00‘ \\ 00000w 00m 000000000030 m0 00.070 IIIO >000 070 all 00N0 . 000.0 . 0000 . 0000 . 0000 . (9310A) “0099090 eAneSSN 64 Based on activity measurements,Marshall (1949) found the fraction of the ions active to be potassium > sodium > calcium for Wyoming bentonite clay. Therefore, the potassium was considered to be the most dissociated while calcium was considered to be the least dissociated. Thus the vis- cosity of the adsorbed water would be greatest for the K clay and least for the Ca clay, if the argument in the preceding paragraph is accepted. This difference in viscosity coincides with the difference found for high frequency conductance measurements. Davis (1955) reported mean ionic activities of various cation saturated Wyoming bentonite clays as related to the molality of the chloride of the different cation Species associated with the clay. The order of mean ionic activities for the different cation Species was found to depend on the particular sample of Wyoming bentonite used. For one set of monoionic clays the order of mean ionic activities was potassium > sodium > lithium. For another set of monoionic clays the order of mean ionic activities was just the reverse. The order of mean ionic activities for the first set of monoionic clays follows the order for the high frequency conductance measurements if the response is based on the viscosity of water as postulated by Low and Lovell (1959). It is assumed that the mean ionic activities are a measure of the relative dissociation of the cations adsorbed by the clays. The order of the mean ionic activities of the divalent cations associ- ated with Wyoming bentonite as reported by Davis (1955) did not follow the order of divalent cation clays obtained by the high frequency reSponse. The difference in high frequency reSponse for the various cation- saturated clays may also be based on the concept of mobility. The order of mobility at high frequencies would be different from the order of mobility of cations in electrolyte solutions. Work by Low (1958) indicates that the order of mobility of cations associated with clays do differ from the order of mobility of cations in electrolyte solutions. 65 A possible reason for the greater high frequency re Sponse in the case of divalent cation—saturated clays as compared to monovalent cation clays is that at the same Specific conductance a larger number of di- valent ions are present in the suSpensions than monovalent ions because of a greater concentration of divalent cation-saturated clay. Therefore the high frequency reSponse would be expected to be greater. Another possible exPlanation for the difference in high frequency response for the various cation-saturated clays may be based on the thickness of the double layer of the clay particles. The thickness of the double layer of the clay particles may be estimated from the electro- kinetic or zeta potential (:5), which is defined as the work done in moving a unit charge from the inner boundary of the double layer to a remote point in the bulk of the solution. Marshall (1949) gives the relationship between the zeta potential (I) and thickness of the double layer by the following equation: _ 1TdO" ”‘6 ‘ ‘75—— ‘7’ where I is the zeta potential, d is the thickness of the double layer, o’is the surface density of charge and D is the dielectric constant. Work by Baver (1929) showed that the order of zeta potential for different cation saturated clays was Li clay > Na clay > K clay. If the surface density of charge and the dielectric constant are assumed to be constant, then the Li clay would have the greatest double layer thickness while the K clay would have the least double layer thickness. On this basis the micelle of the Li clay would contain the greatest number of ions and the micelle of K clay would contain the least number of ions. Therefore, the high frequency reSponse of the Li clay would be greater than the high frequency reSponse of K clay. On this same basis the 66 thickness of the double layer of the divalent cation saturated clays would be Ba clay > Ca clay > Mg clay. It is also observed from the high frequency reSponse of the dif- ferent kinds of monovalent cation- saturated clays that there are slight but definite differences in the capacitance of the kinds of cation-saturated clays. » Equation (5) indicates that the conductance at the peak is determined by the magnitude of the capacitance; the greater the conductance, the smaller the capacitance. The experimental curves in Figure 27 when applied to equation (5) indicate that the capacitance of the monovalent cation- saturated clays follow this decreasing order: Li clay > Na clay > K clay. Work by Marshall (1956) indicates that the clay particles themselves possess a certain mobility and so contribute to the specific conductance measurements of clay susPensions. The effect of high frequency on the conductance of the clay particles themselves can not be explained on the basis of this investigation. However, it seems reasonable that as the frequency increases an increase in the conductance of the particles would occur until a critical frequency is reached where the particles can no longer follow the alternating field because of their large mass. The clay particles would be expected to contribute very little to the high frequency conductance in the megacycle range. The results for the clay- sand mixtures show that the high frequency reSponse depends on variations in water, butanol and octanol contents. The results for the clay- sand mixtures also show that the high frequency response is greater for the five percent clay mixtures than for the ten percent clay mixtures at the same liquid concentration. A minimum was obtained in all cases; however, water gave the greatest deflection while octanol gave the least deflection. 67 The fact that a difference in reSponse was obtained for the five percent clay mixtures compared to the ten percent clay mixtures indi- cates that the amount of clay has an effect on high frequency conductance measurements, but the reason for this effect is not known., The specific conductance of the mixtures would have to be known, but this could not be measured at such low liquid concentrations. Since the minimum does not depend on the Specific conductance, equation (5) predicts that the water mixtures have the largest capacitance while the octanol mixtures have the lowest capacitances. The dielectric constants of the pure liquids are 3.4, 7.8 and 78. 5 for octanol, butanol and water reSpectively. Therefore, the results obtained for capacitances are as expected. The following conclusions can be drawn from the high frequency conductance data: 1) The capacitance and conductance of clay suspensions as com- pared to those of electrolyte solutions is dependent on the frequency of the applied electric field. 2) At the lower frequencies employed (13, 30, and 44 megacycles per second), the capacitance of the clay suspension is greater than the capacitance of electrolyte solutions. At the higher frequencies employed (5?, 79, and 192 megacycles per second) the capacitance of the clay suSpensions is Similar to that of the electrolyte solutions. In the case of the monovalent cation saturated clays the order of capacitance is Li clay > Na clay > K clay. 7 3) The high frequency reSponse based on Specific conductance is greater for the clay suspensions as compared to that of the electrolyte solutions. The high frequency reSponse based on 68 Specific conductance also differs with the kind of cation saturated Wyoming bentonite clay. The order of high frequency response is as follows: Ba clay > Ca clay > Mg clay > Li clay > Na clay > K clay. 4) At low concentrations of liquids in clay- sand mixtures the capacitances of water, butanol and octanol in clay- sand mixtures follow the same order as the dielectric constants of the pure liquids. The order is as follows: water > butanol > octanol . CHAPTER V SUMMARY The results obtained for the dielectric prOperties and high frequency conductance of Wyoming bentonite may be summarized as follows: 1) The capacitance of the clay suspensions was found to be dependent on the frequency at which the measurements were made. 2) In the kilocycle frequency range the capacitance of all the base saturated clays showed the same relationship to the Specific conductance of the clay suSpensions. 3) In the megacycle frequency range the capacitance of the monovalent cation clays followed this order: Li clay > Na clay > K clay. 4) The capacitances of the clay suSpensions were greater than those of the electrolyte solutions in the low megacycle frequency range. This difference between the capacitances of the electrolyte solutions and the capacitances of clay su3pensions diminished as the frequency was increased. 5) The high frequency conductance of the clay suSPensionS was found to be dependent on the frequency at which the measurements we re made . 69 7O 6) The high frequency conductances of the clay suspensions were greater than those of the electrolyte solutions at similar Specific conductances (low frequency). 7) The high frequency conductance varied with the cation associated with the clay and was found to follow this order: Ba clay > Ca clay > Mg clay > Li clay > Na clay > K clay. 10. 11.. 12. LIST OF REFERENCES Anderson, A. B. C. A method of determining soil moisture content based on the variation of the electrical capacitance of soil at a low frequency with moisture content. Soil Sci. 56:29-41. 1943. Anderson, A. B. C., and Edlefsen, N. E. The electrical capacity of the 2 electrode plaster of paris blocks as an indicator of soil moisture content. Soil Sci. 54:35-46. 1942. Aleksandrov, B. P. Measurement of soil moisture by electro- static capacity. Trans. Int. Soc. Soil Sce., Soviet Sec., First Comm. 147-153. 1934. Baver, L. D. The effect of the amount and nature of the exchangeable cations on the structure of a colloidal clay. Univ. of Miss. Agr. Exp. Stat. Res. Bul. 129. 1929. Blaedel, W. J. , it 3:}. Theory of chemical analysis by high frequency methods. Anal. Chem. 24:1240-1244. 1952. Brotherton, M. Capacitors, Their Use in Electronic Circuits. D. Van Nostrand Co. , New York. 1946. Childs, E. C. A Note on Electrical Methods of Measuring Soil Moisture. Soil Sci. 55:219-233. 1943. Curtis, H. J. Chap. VIII. Bioelectric Measurements. Alber, F. M., Editor. BiOphysical Research Methods, Interscience Publishers, Inc., pp. 233-270. New York, 1950. Curtis, H. J. , and Fricke, H. The ,dielectric constant and resistance of colloidal solutions, Phys. Rev. 48(2): 775. 1935. Curtis, H. J. , and Fricke, H. The electrical conductance of colloidal solutions at high frequencies. Phys. Rev. 47:974. 1935. Davis, L. E. Ion pair activities in Bentonite suSpensions. Proc. Third Natl. Conf. on Clays and Clay Menerals, NAS-NRC 395:282-289. 1955. Debye, P. Polar Molecules. The chemical Catolog Company, Inc., New York, 1929. 71 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 72 ' Edlefsen, N.‘ E. A review of results of dielectric methods for measuring moisture present in materials. Agr. Eng. 14:243- 244. 1933. Fletcher, J.‘ E. A dielectric method for determining soil moisture. Soil Sci. Soc. Am. Proc. 4:84-87. 1940. Frbhlick, H. Theory of Dielectrics. Clarendon Press, Oxford, 1949. Fricke, H., and Curtis, H. J. The dielectric prOperties of water-dielectric interphases. J. Phys. Chem. 41:729-745. 1937. Fujiwara, S., and Hayashi, S. Mechanism of high-frequency titration. Anal. Chem. 26:239-241. 1954. Hall, J. L. High-frequency titration, theoretical and practical aspects. Anal. Chem. 24:1236-1240. 1952. Husted, R. F. , and Low, P. F. Ion Diffusion in Bentonite. Soil Science. 77:343-353. 19.34. Kortiim, C., and Bockris, J. O'M. Textbook of Electrochemistry, Vol. I. Elsevier Pub. Co., New York. 1951. Low, P. F. The apparent mobilities of exchangeable alkali metal cations in bentonite-water systems. Soil Sci. Soc. of Am. Proc. 22:395-398. 1958. Low, P. F., and Lovell, Jr. C. W. Joint Highway Research Project No. 5. The Factor of Moisture in Frost Action. Purdue Univ. , Lafayette, Indiana. January 1959. Marshall, C. E. The Colloid Chemistry of Silicate Minerals. Academic Press Inc. , New York. 1949. Marshall, C. E. Thermodynamics, quasithermodynamic, and nonthermodynamic methods as applied to the electro-chemistry of clays. Proc.: Fourth Natl. Conf. on Clays and Clay Minerals, NAS-NRC 456: 288-300. 1956. Overbeek, J. Th, G. Chap. V. Electrokinetic Phenomena. Kruyt, H. R.,‘ Editor. Colloid Science, Vol. 1, Elsevier Pub. Co., New York. pp. 238—244. 1952. Reilley, C. W., and McCurdy, W. H. Principles of high- frequency titrimetry. Anal. Chem. 25:86-93. 1953. 27. 28. 29. 30. Ryder, J. D. Electronic Fundamentals and Application. Prentice-Hall, Inc., Englewood Cliffs, New Jersey. 1954. Smyth, C. P. Dielectric Behavior and Structure, Dielectric Constant and Loss, Dipole Moment and Molecular Structure. McGraw-Hill Book Co. , Inc. , New York. 1955. Stout, M. B. Basic Electrical Measurements. Prentice-Hall, Inc., Englewood Cliffs, New Jersey. 1950. Thorne, M. D., and Russell, M. B. Dielectric Pr0perties of Soil Moisture and Their Measurement. Soil Sci. Soc. Am. Proc. 12:66-72. 1947. APPENDIX TABLE I ' DEPENDENCE OF pH AND SPECIFIC CONDUCTANCE ON THE MILLIEQUIVALENTS OF NaOH ADDED TO HYDROGEN SATURATED WYOMING BENTONITE Meq. NaOH Sp. conduct-“ Meq. NaOH Sp. conduct- per 100 gms. ance (102/1/ per 100 gms. ance (102/0' of clay pH mhos cm‘l) of clay pH mhos cm”) 0.00 3.50 3.10 80.83 6.20 1.02 8.12 3.55 2.95 84.04 6.71 1.03 16.24 3.60 2.67 87.25 7.63 1.20 24.36 3.62 2.35 90.46 8.70 1.40 32.48 3.66 2. 10 93.67 9.40 1.75 40.60 3.88 1.80 96.88 9.70 2.20 48.73 4.00 1.53 100.09 9.90 2.65 51.94 4.18 1.42 103.31 10.00 3.05 55.15 4.27 1.33 106.52 10.12 3.45 58.36 4.30 1.21 109.73 10. 19 4.05 61.57 4.53 1.09 112.94 10.28 4.55 64.78 4.95 0.98 121.06 10.40 5.70 67.99 5.40 0.98 129.18 10.50 7.05 71.20 5.55 0.98 145.33 10.65 9.70 74.41 5.72 0.98 161.47 10.80 12.50 77.62 6.00 0.98 75 podcficoo mm mo ms ow mp m.0> m.0~. mp mo 0 om mo mos mos mm. m3: m4; ms 00 b 00 om Hm mm. mm m.m> m0» méh mo 0 m m0 00 mo 00 mos. m .05 NF 00 m mm 00 Ho mm moH mm m.0~. m.:. mo 0 mm 00 0m m» 03 mm mm M» 00 m mm m0 0m 00 oi ow ms: m .2. 00 N 5:0 mo 00 om mm mo on m .0» ms 0m. 00 Zoo .H 00 om mm mo 0N. m.0N. mu. 0N. mo ZoH . o0 om mm mo 0N. m.0~. ms 0N. 00 Z00. 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SOLUTIONS AND WYOMING BENTONITE CLAYS Thirteen Megacycles per Second Sample Sample NaCl CaClz Number H Clay A1 Clay .005N .0963 .0916 2 .0165 .0339 .OlN .0811 .0847 3 .0420 .0172 .02N .0540 .0577 4 .0600 .0177 .04N .0298 .0336 5 .0773 .0246 .06N .0205 .0237 6 .0841 .0277 .08N .0193 .0195 7 .0825 .0396 . lON .0165 .0164 8 .0398 .50N .0043 .0035 — 1.00N .0037 .0022 Sample Number Na Clay K Clay Li Clay Ca Clay Ba Clay Mg Clay 2 .0249 .0288 .0222 .0088 .0075 .0125 3 .0404 .0486 .0377 .0068 .0132 .0178 4 .0559 .0728 .0574 .0150 .0175 .0193 5 .0742 .0838 .0746 .0244 .0290 .0292 6 .0769 .0763 .0750 .0319 .0333 .0401 7 .0750 .0691 .0690 .0556 .0408 .0455 8 .0647 .0573 .0538 .0475 .0517 Continued TABLE IX - Continued Forty-four Megacycles per Second Sample _ Sample NaCl CaClz Number H Clay Al Clay .005N .0275 .0265 2 .0038 .0059 .OlN .0399 .0392 ,3 .0093 .0030 .02N .0439 .0438 4 .0148 .0030 .04N .0349 .0358 5 . 0235 .0056 .06N .0270 .0281 6 .0291 .0070 .08N .0228 .0230 7 .0346 .0102 .10N .0190 .0196 8 .0115 .50N .0060 .0062 1.00N .0038 .0036 Sample Number Na Clay K Clay Li Clay Ca Clay Ba Clay Mg Clay 2 .0056 .0075 .0046 .0002 .0014 .0020 3 .0105 .0118 .0090 .0010 .0028 .0033 4 .0164 .0207 .0161 .0020 .0050 .0044 5 .0271 .0320 .0269 .0056 .0090 .0060 6 .0326 .0379 .0341 .0093 .0123 .0097 7 .0354 .0407 .0364 .0156 .0145 .0123 8 .0401 .0408 .0175 .0180 .0147 Continued TABLE IX - Continued Seventy-nine Megacycles per Second Sample .Sample NaCl CaClz Number H Clay Al Clay .005N .0111 .0103 2 .0013 .0020 .OlN .0179 .0172 3 .0035 .0010 .02N .0257 .0253 4 .0065 .0008 .04N .0279 .0279 5 .0105 .0017 .06N .0246 .0251 6 .0138 .0027 .08N .0214 .0220 7 .0174 .0047 .10N .0190 .0196 8 .0054 .50N .0058 .0055 "" 1.00N .0034 .0033 Sample Number Na Clay K Clay Li Clay Ca Clay Ba Clay Mg Clay 2 .0025 .0025 .0024 .0006 .0010 .0010 3 .0042 .0050 .0042 .0002 .0017 .0016 4 .0072 .0085 . 0076 .0012 .0029 .0024 5 .0127 .0150 .0139 .0032 .0046 .0038 6 .0172 .0202 .0191 .0052 .0062 .0057 7 .0197 .0240 .0232 .0085 .0080 .0073 8 .0242 .0250 .0098 .0103 .0087 Continued TABLE IX - ~ Continued One hundred ninety-two Megacycles per Second Sample ‘ . 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