Dielectric Method for Analysis of Water in Particulate Solids Seymour
Katz, Willard W. Bach, and William A. Reiche
General Motors Research Laboratories, Warren, Mich. A direct reading, multi-range dielectric instrument was developed to augment the dielectric analysis of water in porous and particulate solids by techniques which extract the moisture from the solid into a solvent with low dielectric constant, usually dioxane. By programming the instrument for a dioxane-water range (04% to &lo% water) using two reference solutions prepared with the practical grade solvents used in the analyses, solvent impurities are effectively blanked and subsequent analyses within the defined range are made with a single measurement. The instrumental portion of the analysis can be performed in as little as 15 seconds with an accuracy of approximately 2 1% of the full scale reading. THENEED FOR a general, laboratory method for rapid and accurate analysis of water in a wide variety of porous and particulate solid materials led to an investigation of dielectric methods ( I , 2). Particular consideration was given to a method based on the extraction of moisture from the solid with dioxane (1,Cdiethylene dioxide), a low dielectric constant (e), water miscible solvent, and the subsequent determination of the change in E of the solvent ( 3 , 4 ) . This was considered best suited for a general method because dielectric measurements are simpler and more rapidly performed on liquids than directly on particulate solids. In addition, one cell can be employed for all analyses ; and, for solvent insoluble materials, the method is insensitive to sample-to-sample variations in e. Direct determination of E can be employed for these analyses (5); however, solvent contaminants, particularly water, are sources of error. Wolfe (4) showed that measuring the difference in dielectric constant between an unknown and the solvent blanks solvent impurities, water in particular, making the use of well characterized solvents unnecessary. Since water is a major contaminant in dioxane, the differential technique for blanking water is valid as long as a linear relationship exists between water concentration, C, and E. A summary of available information on the dielectric constant of dioxane-water solutions, plotted in Figure 1 as the increase in dielectric constant, E~~~~~~~~ - €dioxane, as a function of water concentration (wt %) indicates that linearity probably does not extend above 2 %. The range of concentrations over which water can be effectively blanked can be extended to include the nonlinear portion in Figure 1 if it is assumed that over a concentration range of interest, C,,,, bounded by the water contamination level in the solvent, C,, at the low end and by the concentration, C C,, at the high end, the dielectric constant varies linearly with concentration. This is represented by the straight line A B in Figure 2. Using this assumption, the increase in the water concentration, C, arising from the ex(1) J. Mitchell, Jr., “Treatise on Analytical Chemistry,” Part 11, Volume I, I. M. Kolthoff and P. J. Elving, Eds., Mack Publishing Co., New York, N. Y., 1961, p 155. ( 2 ) F. Oehme, Dielektrische Messmethoden, Monograph NO. 70,
for Angew. Chem. and Chem.-Ing.-Tech.,Verlag Chemie, 1962. (3) F. Oehme, Angew. Chem., 68,457(1956). (4) W. C. Wolfe, ANAL.CHEM.,35, 1884 (1963). (5) A. R. Von Hipple, Ed., “Dielectric Materials and Applications,’’ Technology Press of M.I.T. and Wiley, New York, N. Y., 1954. 1270
ANALYTICAL CHEMISTRY
4.0
I
I
I
I
I
I
X
I
Weight Percent Water
Figure 1. Change in dielectric constant of dioxane-water solutions with water concentration, 22 “C 0 Reference 4 (interpolation) 0 Reference 6 (interpolation) x Reference 7 (interpolation) 0 Reference 8 (extrapolation)
traction of water from a solid sample into dioxane having a water contamination level, C,, can be determined from the equation of the straight line:
where, as shown in Figure 2, C < C,,,, A€ is the difference in dielectric constant of solutions C, and C C,, and Aemaxis the corresponding difference for solutions C, and C,,, C,, where the value of C,,, is known. This equation is valid for
+
+
(6) G . Akerlof and A. 0. Short, J . Amer. Chem. Soc., 58, 1241 (1936). (7) F. E. Critchfield, J. A. Gibson, Jr., and J. L. Hall, ibid., 75, 1991 (1953). (8) A. R. Tourky, H. A . Rizk, and Y. M. Grigis, J . Phys. Chern., 65, 40 (1961).
VI
Weight Percent Water
Figure 2. Analysis is based on the near-linearity of the Esolution - €dioxane us. concentration curve over a limited but useful range of concentration small ranges; C,,, = 1 - 2 z . However, even for relatively large ranges, (C,,, = 5 % ) where the assumption of linearity is not strictly valid, the function CmaxAe/Aemax has a characteristic value which is proportional to C and which is much less sensitive to the magnitude of C,,than is Ae. The function Ae/Aemaxcan be determined from independent measurement of A E and A E m a x . However, considerable speed and simplification were achieved through the development of a multi-range, meter reading instrument whose response was characteristic of AE/Aemax. EXPERIMENTAL Apparatus. The instrument (Figure 3) employs a capacitor type measuring cell (CX) as part of a resonant circuit which is coupled to a 456-kc crystal oscillator. The instrument is set to measure any range of moisture concentrations between 0-1 % and O-lOz by adjusting tuning capacitors C10 and C12 so that the resonant frequency of the circuit is slightly higher than the oscillator frequency when the measuring cell contains the dioxane solution with the highest water content to be C,). Substitution of dioxane solutions measured (C,,, with lower water content shifts the resonant frequency to higher values and produces correspondingly lower voltages across the detector circuit and meter (Ml). In order to obtain values that represent Ae/Aemnx,the meter is adjusted to give full scale deflection for a dielectric constant change Acrnax. This is done by setting the meter, using potentiometers R7 and R1 l , to read zero and 100, respectively, C, occupy the cell. Subsequent when solutions C,and C,,, introduction of a solution of intermediate concentratione.g., C C,-gives an intermediate response which is proportional to At/Aemsx. During operation of the instrument, the solvent slowly absorbs moisture from the air which increases its dielectric constant and thereby increases the dielectric constant of all solutions made with the solvent.
+
+
+
TI
I/* V L
Figure 3. Circuit diagram. Oscillator (left), detector (upper right), normalizing controls (lower right) I.F. transformer (455 kc), James Millen No. 61455 T1 Crystal oven 6.3 V a.c. at 75 "C, Bliley No. TCO-14 ov1 456 kc crystal, Valpey CT-cut, HC-6/U mount, CR1 75 "C operation temperature 6134 electron tube, G.E. 5 star v1 v2 6H6 electron tube 4P6P rotary switch, Centralab No. PA2011 sw1 1150H-2 microammeter, Simpson No. 4282, 2 z , M1 e 1 5 fia L1 5.0 mh RF choke, Miller No. 6304 10.0 mh RF choke, Miller No. 6306 L2 c1, c7, c11 0.1-pF paper capacitor, 400 V 10-pF silver mica capacitor, 500 V c2 900-pF silver mica capacitor, 500 V c3 0.01-fiF silver mica capacitor, 500 V c4, c 5 0.05-fiF paper capacitor, 400 V C6 C8 10-pF electrolytic capacitor, 450 V c9 20-pF silver mica capacitor, 500 V c10 5.5-20 pF tuning capacitor, Hammarlund No. MC20S, modified by adding calibrated knob, Johnson 116-222-1 c12 8-80-pF tuning capacitor, Hammarlund No. MC7543, modified by adding calibrated knob, Jol-nson 116-222-1, and by removing 5 rear stator and 4 front rotor plates C13 75-pF silver mica capacitor, 500 V for T1 secondary fixed capacitor C14 100-pF silver mica capacitor, 500 V for T1 primary fixed capacitor cx Detector cell; replaceable air capacitance 1.8 pF R1 4-MR resistor, 1 %, 0.5 watt R2 2.9-MR resistor, 2%, 1 watt (2 MI1 and 0.9 MQ in series) R3 400-KR resistor, 1%, 0.5 watt R4 100-KRresistor, 1%, 0.5 watt R5 60-KQresistor, 1%, 1watt R6 20-KQresistor, 5 %, 2 watt R7 IO-KQ potentiometer, Beckman 10-turn Helipot, Model A RS 2-KR resistor, 1%, 1watt R9 50-KQ resistor, 1%, 1watt R10 IO-MR resistor, 1%, 0.5 watt R11 450-KQ potentiometer, Beckman 10-turn Helipot, Model A R12 6-MQresistor, 1%, 0.5 watt
These changes are small, however, and do not appreciably affect the value of Atmax. These changes are compensated for by removing sufficient capacitance from the system, using C12, so as to re-zero the meter when solvent is in the detector cell. The electronic circuit is temperature sensitive with an dA E apparent - = 1 X lo-* OC-'. This is large compared to a
dir
precision of A E = 1 2
x
10-3 which is desired for analyses in
VOL. 41, NO. 10,AUGUST 1969
1271
h
~
K
l
T 30CC Syringe o
l
l
l
l
l
l
l
l
l
l
Cmax.(wt. '10 water)
Figure 5. Meter values for tuning procedure
Figure 4. Detector cell system 1. Sample 2. Filter ("Pipe Cleaner" 1.5-cm length, 3-mm dia) 3. Beaker 4. Inlet tube (2.4-mm i.d.) 5. Copper electrode (9.5-mm dia, external dimensions 26-mm X 51 mm X 51 mm) 6. Brass electrode(6.2 mm dia) 7. Teflon gasket 8. Copper cover plate (3.2 mm thick) 9. Kovar-glass electrical feed-through 10. Stainless steel tube (2 mm 0.d.) 11. Teflon tubing 12. Glass reservoir (5 cc) 13. Three-way stopcock
the 0-1 range. To minimize this effect, the electronics are housed in an insulated cabinet which is maintained at least 10 "C above ambient (usually 50 "C) with the temperature held constant t o 1 0 . 1 "C. The detector system, Figure 4, consists of a replaceable filter, a n inlet tube, a two-terminal detector cell, and a reservoir, mounted outside of the cabinet in a vertical arrangement. By means of suction provided by a syringe, solution is drawn vertically through the cell until the 5-cc reservoir is filled. In the process, solution remaining in the cell from the previous analysis is flushed into the reservoir where it does not influence the measurement. The dilution error incurred by successively filling the cell with solvent and the C,,, C, solution is about 1 % of the full scale reading. In this study, a n added flushing was performed; however, it is not considered necessary under ordinary conditions. The time required for this portion of the analysis is about 20 seconds. The cell operated a t ambient temperature (22 f 0.05 "C) in all of the experiments. For field work, however, the cell is maintained at constant temperature by using the temperature controlled cabinet as a heat source. Because the cell was was not designed to be leak proof, it is kept outside of the cabinet to prevent possible ignition of dioxane vapors by the electric heater in the cabinet. Heat is provided t o the cell
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ANALYTICAL CHEMISTRY
by its intimate contact with the face of a finned copper heat sink which is exposed through a rectangular passage in the cabinet wall. By covering the capacitor portion of the detector system with a 5-cm thickness of polyurethane foam insulation, the cell temperature is held constant to 1 "C for ambient changes of 10 "C. When the cell is operated a t elevated temperatures, 1 to 2 minutes must be allowed for temperature equilibration of the water-dioxane solutions being analyzed. The instrument was designed for continuous, drift-free operation. Instrument drift of *0.003 p F was observed over a period of two weeks. This high degree of stability is achieved through the use of crystal oscillator circuit, a military type RF transformer, and regulated power supplies (power supply voltage is constant to better than 0.5 % under normal load and line variations). Materials. The dioxane used was of technical (Union Carbide) and purified (Matheson) grades. The solvent was dried (less than 0.01 water detected by Karl Fischer titration) by allowing it to stand in contact with Linde 4A molecular sieves for several days. For analytical purposes, this treatment is not necessary when the instrument is set for a range of 0-2% or greater. No differences were found in the use of the technical and purified grade solvents. Distilled water was used in this investigative work. However, no differences were found with the use of tap water. The dioxane-water solutions were prepared by weight. Procedures. The primary (C14) and secondary (C13) 130 p F fixed capacitors supplied with the 61455 Millen R F transformer (Tl) must be changed to 100 p F in the primary and 75 p F in the secondary. The following procedure must be followed t o prepare the instrument for operation: Place a milliammeter in series with transformer T1 a t pin 1, with the negative milliammeter lead connected to pin 1. Set the range selector (SW1) t o one of the equivalent 1, 3, or 5 positions. Turn the primary coil variable tuning capacitor slightly past (low capacity side) the minimum current position (-1.8 mA). Switch the instrument off and then on again. If the oscillator fails to start and the ammeter does not return to its previous value, turn the primary coil tuning capacitor to a slightly lower capacitance setting and repeat the procedure until the desired response is obtained. Remove the ammeter, and restore the circuit. Set the dials of C10 and C12 to 30 and 50, respectively. Fill the cell with a dioxane solution containing 10% added water and adjust the secondary coil, variable tuning capacitor for maximum deflection on meter scale (Ml).
look-l
I
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I
* 0.2
I
04 0.6 C / C max.
0.2
0.8
1.0
13
+
0.8
ID
Figure 7. Data for present method, showing insensitivity to water contamination. Cell temperature 22 "C
= 1.0% Cm,, = 2.9% C m a x = 3.8% C m a x = 4.8% c,,, = 7 . 4 2 C m a x = 9.1% cm,,
A X
06
C/C max.
Figure 6. Instrument response to water concentration ranges varying between 0-1 % to 0-9%. Cell temperature 22 "C. 0
04
X
+ 0
A
Adjust the transformer coupling capacitor so that M1 reads 80. Lock the coupling capacitor with lacquer cement. The instrument is set for a particular moisture range as follows: Turn range selector (SW1) to one of the equivalent tune positions (1, 3, or 5). With a dioxane solution containing the concentration of added water desired for full scale deflection (1-10 Z ) in the cell, rotate coarse tuning capacitor, C10, clockwise to get maximum meter deflection, then rotate counterclockwise, stopping within the range of values designated in Figure 5 . Using C12, set the meter needle precisely on a meter division line within this range. T o set the instrument to give full scale deflection for a dielectric constant change, Aemax,turn SW1 to position 2, 4, or 6 according to whether the tuning value was taken from the first, second, or third curve, respectively, in Figure 5. With solvent (C,) in the cell, rotate the zero adjust, R7, so the meter reads zero. Replace C, with ,C ,, C, and set the meter to read 100 with the range adjust potentiometer, R11. Repeat the zero adjust and range adjust operations. The instrument is now set for reading in terms of Ae/Aemax. Switching the instrument to different scales is facilitated by noting, for each scale, the setting of potentiometers R7 and R11 and the precise meter value used in tuning with C12. In this study, meter readings of 5 and 95 were used for the C,and Cmax C, solutions, respectively, because it was necessary at times to take precise readings slightly above and below the desired range.
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C, = O.O%, ,,C , C, = 4.62%, ,,C , = 4.62% C , = 0.48%, Cmax C, = 5.07%, Cm,, = 4.59% C. = 0.96%, Cm,, C. = 5.50%, C,,, = 4.54% C m a x = 4.45 Cs = 1.90 %, C m s x Cs = 6.35 Cs = 2.82 %, C m a x Cs = 7.20 %I Cmax = 4.38 %
For this investigation, the instrument response to dioxane water solutions was determined with a series of prepared solutions. No corrections for change in water content due to absorption of moisture from the air were necessary. Under ordinary circumstances, such corrections are made by periodically introducing samples of the dioxane being used for analyses into the cell and setting the meter needle at zero by rotating the fine tuning capacitor, C12, with the range selector in one of the SW1-B positions. RESULTS
The instrument response to series of solutions covering water ranges of 0-l.OX to 0-9.1z are given in Figure 6 as meter readings vs. relative concentration, CjC,.,. The response of the instrument is seen not to be linear, with nonlinearity increasing with increasing values of C,,,. The insensitivity of the method to water contamination of the solvent is illustrated in Figure 7, which gives data for five series of solutions having a relatively constant value of C,,, (4.50 =k 0.1273 but with varying values of C. (0-2.8z). Each set of data was obtained by standardizing the instrument with the appropriate C,and C,,, C. solutions. Thus the meter readings in each case were proportional to AE/AE,~,. In contrast to this, Figure 8 shows data for four of the series of solutions used in Figure 7 (C.between 0 and 1.973 in which the instrument was used to obtain differential measurements.
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VOL. 41, NO. 10,AUGUST 1969
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3
4
5
C (wt. Ole water 1
Figure 8. Effect of water contamination of dioxane on differential dielectric measurements. Cell temperature 22 OC 0
c. = 0.00%
X
C, = 0.48z C, = 0 . 9 6 z 0 C . = 1.90%
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0.5
1.0
I .5
'c tcs'
DISCUSSION
The relative insensitivity of the described method to water contamination in the solvent is clearly shown by a comparison of Figures 7 and 8. However, the operationally simple differential technique is insensitive to water levels of less than 0.5% (Figure 8), and thus it is employed to blank small increases in moisture resulting from the exposure of the solvent to air. The differences in the differential curves in Figure 8 are consistent with the nonlinear relationship between dielectric constant and the concentration of water in dioxane, shown in Figure 1. This is illustrated in Figure 9 which replots the data in Figure 8 as meter reading vs. E ~ -+ tCS ~ using ~ the curve in Figure 1 for conversion. The progressive increase in nonlinearity of the calibration curves with increasing C,,, as shown in Figure 6 can only be 1274
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ANALYTICAL CHEMISTRY
cs
Figure 9. Data from Figure 7 replotted as meter reading us. EC + cS - f C s 0
c, = 0.00%
x c, = 0.48%
+ 0
In this case, the regular standardization procedure was performed only for the series with C, = 0. This fixed the covered by the meter. Curves for subsequent series (C,# 0) were obtained without restandardization. However, for each of these series the capacitance of the tuned circuit was decreased by a fixed amount, using capacitor C12, so that the C, solution read 5 on the meter. By operating the instrument in this manner, the meter readings for each series were proportional to AE.
8
1
2 .o
C , = 0.96% C . = 1.90%
accounted for in part by the nonlinearity in the AE vs. C relationship for dioxane-water solutions. As indicated by Figure 9, instrument nonlinearity also exists. Because this paper was primarily concerned with the instrumental portion of the analysis, consideration of the water extraction step of the analytical procedure was circumvented by generating the data with prepared water-dioxane solutions. In practice, however, two aspects of the extraction, reproducible extraction efficiency for water (water extracted/ water contained in the original sample), and reproducible extraction of materials other than water, largely determine whether this technique can be successfully employed. Since the water detected by the instrument must be related to the concentration of water in the original sample, a knowledge of the extraction efficiency is required. This is often obtained implicitly by calibrating the instrument response with samples containing known amounts of water. For systems in which the extraction efficiency is not very close to unity, it is also necessary to ensure that variations in the factors which influence efficiency-e.g., large changes in temperature or C,-are minimized. The extraction of sample constituents other than water must be considered because they contribute to E of the final solution. These materials can raise or lower the apparent concentration of water depending on whether E for the ex-
tracted species is, respectively, higher or lower than e for the water-dioxane solution being analyzed. Since the values for e for the water-dioxane solutions under consideration are relatively low, ranging from e = 2.2 (pure dioxane) to e = 6.0 (10z water), the most pronounced changes are produced by extracted sample constituents with high e. For systems in which the type and quantity of extractable material remains constant, calibration curves which relate instrument response to moisture content can be obtained, using samples of known moisture content, as long as the e of the final solution does not exceed the range of the instrument (e = 6.0). As a result of the method’s relative insensitivity to solvent contaminants and the speed of analysis made possible by cell design and direct reading features of the instrument, the
technique has been successfully employed in the analysis of water in a wide variety of materials including iron, alumina, graphite, lead dioxide, silica gel, paper, molecular sieves, foundry sand, soil, vinyl plastisols, and automobile transmission fluids. Through the use of devices to rapidly dispense a fixed volume of dioxane, complete analyses, including extraction, were frequently performed in 2-3 minutes, with an accuracy of f1 to =t2% of full scale reading, making the instrument particularly valuable for routine analysis.
RECEIVED for review January 29, 1969. Accepted May 19, 1969.
Study of Thermal Effects Observed by Differential Thermal AnaIysis Theory and Its Application to Influence of Sample Parameters on a Typical DTA Curve R. Melling, F. W. Wilburn, and R. M. McIntosh R & D Laboratories, Pilkington Brothers Limited, Lathom, Ormskirk, Lancashire, England
A mathematical model has been developed in order to study the effects of sample and block parameters on the transfer of heat in a DTA apparatus. The model is used to investigate the effect of differing sample radius and physical properties on the area, shape, and peak temperature of a typical DTA peak. I n this paper, it is assumed that the block has an infinite conductivity and the periphery of the sample is heated so as to rise in temperature at a linear rate. The influence of heat leakage along the thermocouple wires is also studied. THE TECHNIQUE of differential thermal analysis (DTA) has been extensively used for the qualitative study of the processes which occur as a substance is heated or cooled. In order to use the technique as a quantitative tool, many workers have made a mathematical analysis of the system. The shape of a DTA curve wilfbe influenced by the transfer of heat from the source to the samples and by the rate of internal generation or absorption of heat by the test sample as it undergoes a physical or chemical change. The difficulties inherent in solving mathematical equations which completely describe the system have forced previous authors to introduce restrictive simplifying assumptions. Heat transfer equations have been developed by various authors (1-I]), without introducing a specific reaction equation. Further, some of these authors (1-6) use a lumped parameter model of heat transfer, in which the separate parts of the apparatus, namely holder and sample materials are assumed to have no thermal gradients within themselves. This assumption will be true in stirred samples but not apply in static powdered samples. By manipulation of a reaction equation, e.g. the Arrhenius equation, other authors (12-17) have shown that various relationships exist between the heating rate and peak temperature, and between the difference temperature and actual temperature at a fixed time, from which activation energies,
and “orders of reaction” may be derived. Whether such relationships are valid when heat transfer equations are introduced was not considered. One of the present authors (18) has investigated, using a lumped parameter model, the influence o f the thermal properties of the holder and sample materials on the general shape of a DTA curve. This paper showed the important role played by these thermal properties in determining the shape of a DTA curve. In this present paper the authors have, by the use of a finite difference scheme, been able to take account of the thermal gradients within the samples and to generate or absorb heat ~
~
(1) M. J. Vold, ANAL.CHEM., 21, 683 (1949). (2) H. J. Borchardt and F. Daniels, J . Amer. Chem. Soc., 79, 41; (1957). H. J. Borchardt, J. Iitorg. Nucl. Chem., 12, 252 (1960). (3) A. A. Blumberg, J. Phys. Chem., 63, 1129 (1959). (4) D. M. Speros and R. L. Woodhouse, J . Phys. Chem., 67, 2164 (1963). (5) V. M. Padrnanabhand et ul., J . Iizorg. Nucl. Chem., 12, 356 (1960). 36,2162 (1964). (6) D. J. David, ANAL.CHEM., (7) P. L. Arens. “A Study on the DTA of Clays,” Druk, Excellors Foto-Offset, S. Gravenhage, Holland, 1951. (8) S. L. Boersma, J. Amer. Ceram. Soc., 38, 281 (1955). (9) E. Sturm, J. Phys. Chem., 65, 1935 (1961). (10) P. Pacor, Anal. Chim. Acta, 37, 200 (1967). (11) G. de Josselin de Jong, J. Amer. Ceram. SOC.,40, 42 (1957). (12) H. E. Kissinger, ANAL.CHEM., 29, 1702 (1957). (13) G. 0. Piloyan and 0. S. Norikova, Russ. J. Inorg. Chem., 12, 313 (1967). (14) L. Reich, J. Inorg. Nucl. Chem., 28, 1329 (1966). (15) E. S. Freeman and B. Carroll, J. Phys. Chem., 62, 394 (1958). (16) R . L. Reed, Leon Weber, and B. S. Gottfried, Ind. Eng. Chem. Fund, 4, 38 (1965). (17) P. Murray and J. White, Trans. Brit. Ceram. Soc., 54, 204 (1955). (18) F. W. Wilburn, J. R. Hesford, and J. R. Flower, ANAL.CHEM., 40, 777 (1968). VOL. 41, NO. 10, AUGUST 1969
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