1402
Ind. Eng. Chem. Res. 1994,33, 1402-1404
A Piezoceramic Bender as a Force Transducer for Surface Tension Measurements Ruozi Qiu and Robert C. MacDonald' Department of Biochemistry, Molecular Biology and Cell Biology, Northwestern University, Evanston, Illinois 60208
When connected to the appropriate electronic circuit, an inexpensive ($10) piezoelectric ceramic bender is a sensitive force transducer for accurate surface tension measurements. Although these devices are not suitable as steady-state transducers, they do function as sensitive transducers when used in the detachment m d e of the Wilhelmy method. Under such conditions, the voltage output of the transducer is linearly related to the applied force with an output of millivolts or more per dyne. Tension measurements with a Wilhelmy plate of a centimeter or less perimeter have a precision of 0.5 dyn/cm over the observed range of surface tension from 23 to 72 dyn/cm. Because of the low cost, dozens of measurements can be done simultaneously using common computer multiplexing interface boards.
Introduction The Wilhelmy plate m e t h d is a common technique for determining the surface tension of liquids in which the force on a plate which penetrates the surface is measured with a sensitivebalance or force transducer (Gaines, 1966). Electrobalances are widely used, but are sufficiently expensive to discourage multiple simultaneous measurements. Another transducer that has been employed for monitoring surface tension by the Wilhelmy method is the linear variable differential transformer (LVDT) (Albrecht, 1983). Although less expensive than electrobalances, these devices require special electrical circuitry as well as custom mountings of a spring of appropriate Young's modulus to operate properly. A variation of the Wilhelmy method involves separating the plate from the liquid/air interface and measuring the maximum change in force (Gaines, 1966;MacDonald and Simon, 1987).In this mode, the measurement is dynamic and inexpensive force transducers may be used. Ceramic piezoelectric elements represent such devices which have been used in a wide variety of force and displacement measuring instruments (Pallas-Areny and Webster, 1991). We describe here the use of a piezoceramic transducer for surface tension measurement. This device is not only sufficiently inexpensive to allow economical monitoring of the surface tension of a large number of samples, but it also has a large enough voltage output that minimal amplification of the signal is needed. Simultaneous measurement of dozens of samples is readily performed using a personal computer equipped with a multiplexed analog-to-digital, digital-to-analog converter interface board. Another advantage is its small size. The sensor may be mounted in places where it would be difficult to accommodate an electrobalance or even a LVDT.
Principle of Operation of a Piezoceramic Bender as a Force Transducer When a piezoelectric element is polarized by applying a voltage, its dimensions change. Conversely, when it is stressed mechanically, it produces an electrical charge, which generates a potential difference between two isolated electrodes. The charge generated depends on the material of the element, its size and shape, and how the force is applied to it. For a long, thin piezoceramic element, mounted as a cantilever, the voltage due to a downward force F applied at the free end such that it causes the
piezoceramic bender A
Figure 1. Diagram of the apparatus for measuring surface tension with a piezoceramic force transducer. The eccentric on the motor shaft causes the trough containing the sample to oscillate in position along the vertical axis so that the probe, a platinum wire or plate, alternately dips into and is pulled from the surface of the sample. The voltage appearing across the electrodes at the upper and lower surfaces of the bender is sensed by an analog-to-digital interface board and transmitted to the computer.
element to bend is given by
v=3&
4 WlF
where L, W, and Tare the three dimensions of the ceramic element (length, width, and thickness) andg is its voltage coefficient. The bender we used is a bilayer element; the polarization directions of the two layers are parallel to the plate normal but antiparallel to each other. Under an external force causing bending along the long axis, one layer will be in tension while the other is in compression, hence the electrical output of the bender will be twice the output of each layer. Within wide ranges, these devices exhibit linear relationships between output voltage and applied force.
Apparatus for Measurement of Surface Tension Figure 1 is a diagram of the apparatus we constructed for measuring surface tension with a piezoceramic bender. It is similar to the apparatus used previously for measuring surface tension of monolayers with the detachment variation of the Wilhelmy method (MacDonald and Simon, 1987)and consists of a sample platform, force probe, and force measurement unit. Samples are contained within Teflon wells on the platform. The latter is driven in vertical oscillation with an eccentric shaft on a 4 rpm
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synchronous motor. The probe (plate or wire of platinum) hanging from the piezoceramic bender enters the water when the platform moves upward. At the end of the cycle, when the platform moves downward, the probe detaches from water surface. The force applied to the probe thus produces mechanical stress in the bender and generates a voltage across its electrodes. This voltage is measured using a personal computer equipped with ASYST software and an interface board (analog-to-digitalinput and digitalto-analog output) of 10l2ohm input resistance (Labmaster, Scientific Solutions Inc., Solon, OH). The computer was programmed to control data acquisition as well as data analysis. A signal from the digital-to-analog (D/A) converter turns the motor on and off for one or a series of cycles, as appropriate for measurement a t hand. Within one revolution of the motor, 60 data acquisitions are completed. After saving and/or printing the results, the instrument is ready for the next measurement. The piezoceramic benders were purchased from Piezo Electric Products, Inc. Metuchen, NJ (G-1195,nickel electrode). Their dimensions are 2.5 in. long by 0.1 in. wide by 0.018 in. thick. A small hook for hanging the probe was glued to one end with epoxy cement. The other end was attachedto an adjustable acrylicplastic mounting, again using epoxy. Two wires, soldered to the two electrodes at this end, were connected to the input of the analog-to-digital (A/D) converter section of the interface board for voltage monitoring. To prevent environmental electromagnetic perturbation, the connection wires and part of the bender were electrically shielded by enclosing them in a grounded metal box. As a result of the stress due to contact with and detachment from aliquid surface, the output of the bender is essentially a distorted square pulse, as shown in Figure 2. The sharp rise in the signal on the left side corresponds to contact between plate and liquid, and the sharp fall on the right side corresponds to the detachment of the plate from the liquid. The signal of interest, which is proportional to the surface tension, is the maximum voltage change due to the drop in force upon probe detachment. Under our experimental conditions, the time for generating this voltage jump is well under 1 s. The bender is a capacitiveelement and the time constant (RC)of the circuit
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Figure 3. Plot of weight added to bender vs voltage output.
may be set using a resistance R connected directly across the two electrodes. With our bender, the maximum signal was obtained with a 1O1Oohm input resistance. There was no advantage in increasing the input resistance above 1O1O ohm, since its only effect was to increase noise and drift. On the other hand, a lower resistance loaded down the device and reduced the signal.
Performance of the Piezoceramic Bender in Surface Tension Measurements The proportionality coefficient between electrical and mechanical variables was determined by adding small weights which had been calibrated with an electrobalance (RTL, Cahn Ventron Instrument Corp.) to the bender and measuring its voltage output. The linear coefficient was 2.0 mV/dyn according to the results shown in Figure 3. With full scale of the 12 bit D/A converter set at 10 V and with a gain of 10,the resolution is hence 0.49 mV, which corresponds to 0.25 dyn. Given data acquisition circuitry so configured, surface tension of liquids such as water can be determined with good precision using a probe having a perimeter of 1 cm. In order to determine the standard deviation of a series of repeated surface tension measurements, the surface tensions of water and of methanol at room temperature were measured with a platinum plate probe (6mm wide X 0.05mm thick). The measurement was performed using the piezoceramic bender system described here as well as with the electrobalance mentioned previously. The same computer and interface were used with both transducers. The values acquired by the computer, which correspond to the maximum change in force experienced by the probe, are converted to values in dynes per centimeter with their mean value representing that of the surface tension of water (72.6 dyn/cm) and of methanol (22.6 dyn/cm), respectively. As shown in Table 1,the standard deviations are 0.55 dyn/cm in the case of the water surface and 0.41 dyn/cm in the case of the methanol surface. They are similar to the standard deviations of the measurements made with the electrobalance. To further test the suitability of the transducer for surface tension determinations, we compared the surface tension measured with the bender to that measured with the electrobalance, over a wide range of tensions. Different tensions were obtained by delivering surfactant onto a water/air interface. The surface tension of the resultant
1404 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 Table 1. Comparison of Results of Surface Tension Measurements Using an Electrobalance and a Piezoceramic Force T r a n s d u c e r electronic balance piezoceramic bender sample no. water methanol water methanol 72.9 23.1 1 72.6 22.9 12.2 22.4 2 72.9 22.2 72.2 22.4 3 72.9 22.6 72.1 22.7 4 12.8 22.7 73.3 22.6 5 73.0 22.9 22.7 22.6 72.7 6 72.6 12.3 22.0 7 72.4 22.4 73.7 23.0 8 72.4 22.6 72.8 22.8 9 72.4 22.6 21.9 22.6 12.9 10 72.2 71.9 23.1 11 72.5 22.5 22.6 22.6 72.6 av 72.6 0.41 0.2 0.55 SD 0.25 A 6-mm X 0.05-mm platinum plate was used as probe to measure the surface tensions of water and of methanol at room temperature. Units are dynes per centimeter. a
monolayer varies with molecular density, so simultaneous measurement of surface tension using the two transducers furnished an appropriate set of data for their comparison. It also provided a test of the device under common laboratory conditions, namely that of determining the surface tension of a monolayer at the aidwater interface. The surfactant, dioleoylphosphatidylcholine,was dissolved in chloroform at a concentration of 10m g / d and delivered to the surface of water contained in a 100-mm by 20-mm Teflon trough. A plot of the results is displayed in Figure 4. As may be seen, the electrobalance and the piezoelectric transducer gave essentially the same values over a range of tensions from 23 to 72 dyn/cm.
Summary The use of piezoceramic benders as force transducers for surface tension measurements is described. The piezoceramic transducer, when used in the detachment mode of the Wilhelmy method, provides sensitivity and precisionthat are comparable to those of an electrobalance. Although an advantage for some applications is the small size of the piezoelectrictransducer, its principal advantages are low cost, simplicity of mounting, and relatively large electrical signal. The device used for the experiments described here currently costs about $10, has no moving parts, being simply a rectangular bar, and generates millivolt outputs under typical conditions. It thus becomes
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Surface tension (mN/m) measured by piezoceramic bender
Figure 4. Comparison of surface tension measurementa made with an electrobalance and the piezoceramic bender system.
economical to monitor the surface tension of large numbers of samples simultaneously with piezoelectric transducers.
Acknowledgment We thank Dr. B. M. Abraham for his attentive reading of the manuscript. This work was supported by NIH Grants 1 R01 GM 38244 and 1 PO1 HL 45168. Literature Cited Albrecht, 0. The Construction of a Microprocessor-Controlled Film Balance for Precision Measurement of Isothermsand Isobars. Thin Solid Films 1983,99, 227. Gaines, G. L. Experimental Methods. In Insoluble Monolayers at Liquid-Gas Interfaces; Interscience: New York, 1966; pp 4-50. MacDonald, R. C.; Simon, S. A. Lipid Monolayer States and Their Relationships to Bilayers. h o c . Natl. Acad. Sci. USA 1987,84, 4089. Pallas-Areny, R.; Webster, J. G. Generating Sensors. In Sensorsand Signal Conditioning; John Wiley & Sons Inc.: New York, 1991; pp 247-251. Received for reuiew November 15, 1993 Accepted February 25,1994. Abstractpublishedin Aduance ACSAbstracts, April 1,1994.
