Abstract:
An oxygen sensor includes a solid polymer electrolyte, e.g., on an acid treated Nafion membrane and uses a diffusion-limited fuel cell type reactions. The sensor avoids electrolyte leakage and avoids consumption of electrodes. In different configurations, a counter or reference electrode can be on the same or the opposite side of the electrolyte as a sensing electrode. An insert limits and controls oxygen diffusion into a sensing chamber containing the sensing electrode that catalyzes reduction of oxygen. Applying appropriate bias voltages to the reference and sensing electrodes causes an output current of the sensing electrode to be proportional to the rate of oxygen consumption based on Frick&#39;s law under a diffusion-limited mode. The output current can be measured, e.g., using a resistor to convert the current to a voltage signal.

Description:
BACKGROUND 
   Solid electrolyte oxygen sensors and galvanic cell oxygen sensors are currently the most widely used sensors for monitoring gaseous oxygen. Solid electrolyte oxygen sensors typically include an electrolyte body made of an oxygen-ion-conductive ceramic such as zirconium (ZrO 2 ) doped with traces of metal oxides (e.g., Y 2 O 3 ). Porous electrodes on opposite faces of the body permit the diffusion of oxygen ions through the electrolyte body. Thus, when one electrode is exposed to a reference gas (e.g., air) and the other electrode is exposed to a sample gas (e.g., engine exhaust), a difference in oxygen partial pressure at the electrodes causes diffusion of oxygen ions that results in a corresponding voltage difference between the electrodes. A limitation of these solid electrolyte oxygen sensors is that the ceramic electrolytes used in the sensors only conduct oxygen ions when heated to temperatures above 400 to 600° C. Accordingly, the solid electrolyte sensors generally require time to heat up before becoming responsive, and an auxiliary electrical heater may be needed in the sensor as described in U.S. Pat. No. 4,175,019 to Michael P. Murphy. 
   Galvanic cell oxygen sensors using liquid electrolytes are generally simple, cheap, and operable at room temperature. U.S. Pat. Nos. 4,132,616 and 4,324,632 to Tantram et al., U.S. Pat. No. 4,495,051 to Fujita et al., U.S. Pat. No. 4,775,456 to Shah et al., U.S. Pat. No. 4,988,428 to Matthiessen et al., and U.S. Pat. No. 5,284,566 to Cuomo et al. describe some configurations for known galvanic cell oxygen sensors. Galvanic cell oxygen sensors operate on the same principle as a battery and generally include a cathode and an anode in contact with a liquid electrolyte. The cathode is typically made of a metal such as platinum, gold, or silver that is an effective catalyst for the electrolytic reduction of oxygen, and the anode is generally made of lead. The reduction of oxygen at the cathode produces oxygen ions that flow through the electrolyte to the anode and react with the lead anode. The resulting current between the cathode and anode is linearly proportional to the oxygen concentration, so that oxygen concentration measurements are easily determined from measurements of the current between the anode and cathode. 
   Galvanic cell sensors have several significant disadvantages. In particular, their life expectancy is a function of usage and the resulting anode consumption. Leakage of liquid electrolyte can also reduce sensor life and damage surrounding components. Furthermore, galvanic cell sensors have a tendency to read low due to loss in sensitivity as the sensors age. For most process control applications, false low oxygen readings can produce dire consequences. As a result, galvanic cell sensors must be frequently recalibrated, sometimes as often as once per day, depending on the criticality of the application. Another major drawback of galvanic cell sensors is their susceptibility to oxygen shock that results when galvanic cell sensors are exposed to a high concentration of oxygen. The high oxygen concentration can cause local variations of electrolyte composition that may take hours to equalize. 
   Polymer electrolytes have found applications in many areas of electrochemical technology. Nafion, for example, is a solid polymer electrolyte that has been widely used in the development of sensors and fuel cells. Nafion has an excellent ionic conductivity, outstanding chemical and thermal stability, and good mechanical strength. Additionally, Nafion, modified with a variety of noble metals, can create composite materials with ionic and electronic conductivity characteristics that are desirable for gas sensing. Galvanic cell sensors based on the solid polymer electrolyte (SPE) have been used to detect carbon monoxide (CO) and toxic gas with good performance as described in U.S. Pat. No. 4,227,984 to Dempsey et al. and U.S. Pat. Nos. 5,573,648, 5,650,054, 6,179,986, and 6,200,443B1 to Shen et al. 
   U.S. Pat. No. 4,227,984 to Dempsey et al. describes a gas sensor using three electrodes on the surface of a solid polymer electrolyte mounting membrane to detect toxic gas such as carbon monoxide (CO) or nitrogen dioxide (NO 2 ). U.S. Pat. Nos. 5,573,648, 5,650,054, 6,179,986, and 6,200,443 B1 describe an SPE gas sensor with a two-electrode or three-electrode system for measuring carbon monoxide and other toxic gases in the environment. These toxic gas sensors generally are low cost and accurate and have a long useful life but have not been suitable for oxygen detection. 
   U.S. Pat. No. 6,080,294 to Shen et al. discloses a galvanic oxygen sensor including a solid polymer electrolyte and liquid electrolyte electrically connected in series between a cathode and an anode. This sensor is similar to the traditional galvanic cell oxygen sensor but uses the solid polymer electrolyte to control the rate of the electrochemical reaction. This can improve the useful life of the sensor, but the sensor still has many of the same problems as the more conventional galvanic cell oxygen sensors. In particular, using the liquid electrolyte still presents leakage problems. Another drawback is that a permeable membrane that controls oxygen diffusion can introduce larger temperature effects. Further, the lead (Pb) anode is consumed over time, changing the available surface area of the lead anode as lead (Pb) is converted to lead oxide (PbO and PbO 2 ). As a result, the electrochemical activity and current output eventually falls to zero, at which point the sensor must be rebuilt or replaced, causing a lead pollution problem. 
   Another problem in galvanic oxygen sensors is the use of an alkaline electrolyte, which can be affected by prolonged exposure to acidic gases such as CO 2 . Most of these sensors should not be used continuously in atmospheres containing more than 25% CO 2 . In some cases, prolonged exposure to acid gas damages the basic sensor electrolyte. In other situations, high concentrations of acid gas produce a current flux that alters the normal expected output of the sensor at a given concentration of oxygen. 
   In view of the current state of sensor technology, an easily manufactured oxygen sensor having a long operational lifespan, fast response, low cost, no leakage, and a compact size would be highly desirable. 
   SUMMARY 
   In accordance with an aspect of the invention, an oxygen sensor uses fuel cell type reactions and a solid polymer electrolyte to sense or measure oxygen in a sample gas. In comparison to other electrochemical oxygen sensors, the oxygen sensor has a relatively low resistance, a fast response, and a long operating life, without requiring liquid electrolytes, lead electrodes, or consumed parts. The sensor is also operable at room temperature. 
   In operation of an oxygen sensor in accordance with an exemplary embodiment of the invention, a sensing electrode catalyzes a reaction in which oxygen captures the electrons and combines with hydrogen ions from the solid polymer electrolyte to form water. To compensate for the loss of electrons at the sensing electrode and hydrogen ions in the polymer solid electrolyte, a counter electrode is biased to a voltage that cause electrolysis of water, producing the hydrogen ions and offering electrons. A reference electrode attached to the solid polymer electrolyte can provide a reference voltage relative to the counter and sensing electrode. The electrons from the counter electrode form an output current that flows to the sensing electrode. The resulting current of electrons depends on the rate of oxygen consumption at the sensing electrode and can be measured to determine the oxygen concentration at the sensing electrode. The hydrogen ions created at the counter electrode move to the sensing electrode through the polymer electrolyte, which is a good protonic and electronic conductor. 
   An important advantage of this type of sensor is that the sensor does not consume electrodes or other materials when sensing oxygen, unlike Galvanic cell sensors that typically consume a lead electrode when detecting oxygen. Moisture required for and generated by the sensor can be introduced through the humidity in the gas being measured and is recycled and preserved in the solid electrolyte and in an optional sealed reservoir. The sensor is thus capable of an operational lifespan of over two years even when used in dry conditions. 
   One exemplary embodiment of the invention is a gas sensor including a reference electrode, a counter electrode, and a sensing electrode in electrical contact with a block or membrane of a solid electrolyte. A suitable biasing of the sensing electrode relative to the reference electrode permits a reaction of oxygen with the hydrogen ions at the sensing electrode to produce water and in the process draws electrons through the sensing electrode. To supply the electrons to the sensing electrode and hydrogen ions in the polymer electrolyte, the counter electrode can be biased for the electrolysis of water to release hydrogen ions and electrons. The hydrogen ions enter the polymer electrolyte, and the electrons flow to the sensing electrode. The resulting current through the sensing electrode from the counter electrode indicates a measured oxygen concentration. 
   The sensor can further include an insert or restriction between the sensing electrode and a source of a gas being measured. The insert includes a capillary pore or some other diffusion barrier that controls a flow of oxygen to the sensing electrode. With the diffusion barrier, the diffusion rate limits the reaction at the sensing electrode, so that the reaction rate and the output signal are proportional to the oxygen content of the gas outside the sensor. 
   A housing of the detector can include a reservoir that contains water that maintains humidity in or around the solid electrolyte. In the reservoir, a moisture-retaining agent such as a polymer material containing H 2 SO 4  can maintain a suitable moisture level in the solid electrolyte for a long useful lifetime of the oxygen detector. 
   The solid electrolyte is generally a protonic conductive electrolyte membrane. The solid electrolyte can be a perfluorinated ion-exchange polymer such as Nafion or a protonic conductive polymer such as poly(ethylene glycol), poly(ethylene oxide), poly(propylene carbonate). When used, a Nafion membrane can optionally be treated with an acid such as H 3 PO 4 , which improves the moisture retention characteristics of Nafion and the conductivity of hydrogen ions through the Nafion membrane. The sensing, counter and reference electrodes can be hot-pressed onto the Nafion membrane to provide a high conductivity between the electrodes and the solid electrolyte. 
   The electrodes and particularly the sensing electrode are preferably made of a porous conductive material. The sensing and counter electrodes are preferably made of a material that catalyses oxygen reduction and may include platinum, gold, ruthenium, palladium, iridium, platinum/ruthenium, platinum/iridium, platinum/palladium alloy, carbon, and platinum/carbon. The reference electrode can contain a noble metal such as platinum and gold or a high conductivity metal/salt combination such as Ag/AgCl. 
   The sensing electrode is on a side of the solid electrolyte that is exposed to the gas being measured. However, in various alternative embodiments of the invention, either the counter electrode or the reference electrode can be on the same side as the sensing electrode or on the side opposite to the sensing electrode. Additionally, the shapes of the sensing, counter, and reference electrodes can vary. In one embodiment, all of the electrodes are circular. In another embodiment of the invention, the sensing electrode and the counter electrode include a disk and a concentric ring surrounding the disk. 
   Another embodiment of the invention is a miniature or button-type solid polymer. Generally, very small sensors for sensing oxygen have not been possible because common galvanic oxygen sensors need an anode containing a lot of lead for consumption. Galvanic sensors thus could not be reduced to button size (e.g., about 1 cm 3  or less). However, an oxygen sensor using a solid polymer as a support electrolyte and a fuel cell reaction for sensing can be made quite compact. 
   One button-type oxygen sensor in accordance with and embodiment of the invention includes a first electrode as sensing electrode, a solid polymer as support electrolyte, and a second electrode as a counter/reference electrode. A gas permeation membrane, which can be made of polypropylene and polyester, replaces the diffusion pore to control the oxygen diffusion rate. Pieces of glass fiber, which permeated with H 2 SO 4 , can be used to adjust humidity. The basic operating principles the button-type oxygen sensor is the same as those of a larger fuel cell oxygen sensor, but the second electrode in the button-type oxygen sensor functions as a counter electrode to balance the reaction at a sensing electrode by providing hydrogen ions and electrons and as a reference electrode for measuring a relative bias to the sensing electrode. The gas permeable membrane that limits oxygen diffusion to a sensing electrode surface limits the reaction process. The reaction process therefore should be described by Fick&#39;s diffusion equation, making the output signal proportional to the oxygen content. 
   Another exemplary embodiment of the invention is a method for sensing oxygen in a sample gas. The method includes controlling a rate of diffusion of oxygen from the sample gas into a sensing chamber; and measuring a current through the sensing electrode that results from a catalyzed reaction of oxygen in the sensing chamber. A bias voltage between the first and second electrodes (e.g., sensing and reference electrodes) that are in electrical contact with a solid electrolyte causes the sensing electrode to capture ions and electrons, which were respectively provided by the counter electrode and the polymer electrolyte. The counter electrode is driven to create the hydrogen ions and electrons from water to supply to sensing electrode. The net reaction is water to water. Accordingly, the sensing method does not consume material in a sensor and can be used in a sensor having a long useful life. The control of the diffusion, which can be implemented using a capillary pore that limits the diffusion rate and the reaction rate so that the measured current is proportional to the chemical content of the gas diffusing into the sensing chamber. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a solid polymer electrolyte (SPE) oxygen sensor in accordance with an embodiment of the invention. 
       FIG. 2  shows the operating circuit of a three-electrode system sensor for the sensor of  FIG. 1 . 
       FIGS. 3A ,  3 B, and  3 C respectively show top, bottom, and side views of a solid electrolyte membrane having an electrode pattern in accordance with an embodiment of the invention. 
       FIGS. 4A ,  4 B, and  4 C respectively show top, bottom, and side views of a solid electrolyte membrane having another electrode pattern in accordance with an embodiment of the invention. 
       FIGS. 5A and 5B  respectively show top and side views of a solid electrolyte membrane in accordance with an embodiment of the invention having three electrodes on the same side of the membrane. 
       FIGS. 6A and 6B  respectively show top and bottom views of a solid electrolyte membrane in accordance with an embodiment of the invention where sensing and counter electrodes are a disk and a surrounding ring. 
       FIG. 7  illustrates a button-type oxygen sensor in accordance with an embodiment of invention. 
       FIG. 8  is a graph showing the response of the sensor of  FIG. 1  to different concentrations of oxygen. 
       FIG. 9  illustrates the linear response of the sensor of  FIG. 1  to oxygen concentration. 
       FIG. 10  shows the influence of the ambient temperature on the sensor of  FIG. 1  or  7 . 
       FIG. 11  shows the results of a stability test for the sensor of  FIG. 1  or  7 . 
   

   Use of the same reference symbols in different figures indicates similar or identical items. 
   DETAILED DESCRIPTION 
   In accordance with an aspect of the invention, an oxygen sensor uses a solid polymer electrolyte (SPE) and a fuel cell reaction to measure the oxygen concentrations in a sample gas. A SPE oxygen sensor in accordance with an embodiment of the invention avoids electrolyte leakage and has a significantly improved life and response time when compared to the galvanic cell oxygen sensor. The sensor also permits detection and measurement of oxygen at room temperature and has a structure that can be easily miniaturized. 
     FIG. 1  illustrates an oxygen sensor  100  in accordance with an embodiment of the invention. As illustrated, oxygen sensor  100  includes a solid electrolyte membrane  110  bonded to a sensing electrode  112 , a counter electrode  114 , and a reference electrode  116 . Housing  120 , which can be made of a rigid chemically inert material such as Teflon, includes a bottom housing  122  and a cap  124  that enclose solid electrolyte membrane  110  and electrodes  112 ,  114 , and  116 . 
   In sensor  100 , an inlet system includes a dust cover  126  on housing cover  124 , an inlet hole  128  through housing cover  124 , and a diffusion capillary  132  through a restrictor  130 . Dust cover  126 , which can be made of a material such as polypropylene or polyester, prevents dust and other particulate contaminants from entering sensor  100  and thereby protects electrolyte membrane  110  and sensing electrode  112  from contamination. 
   Capillary  132  controls the gas diffusion rate to sensing electrode  112 . In an exemplary embodiment, capillary  132  is less than about 0.1 μm in diameter and about 0.5 mm long. More generally, the diameter and length of capillary  132  limit the rate of diffusion of oxygen into a sensing chamber  140  and can be adjusted for the specific geometry and reaction rate of sensor  100 . An oxygen permeable membrane such as a polytetrafluoroethylene could alternatively be used to control diffusion, but would typically suffer from greater temperature variations. By controlling the diffusion rate, capillary  132  also controls the availability of oxygen at sensing electrode  112 , and as described further below, the diffusion rate becomes the limiting factor that controls the reaction rate for the reduction oxygen at sensing electrode  112 , the mass transport, and the resulting measurement current. 
   An oxygen permeable membrane  142  and a glass micro-fiber paper  144  are between capillary  132  and sensing chamber  140 . Membrane  144 , which can be made of Teflon or another suitable material, protects capillary  132  from water or other substances from inside sensor  100  that might otherwise block capillary  132 . Glass micro-fiber paper  144 , which can be treated with sulfuric acid, helps adjust the humidity in sensing chamber  140 . 
   A reservoir  150  containing a moisture-retaining material  152  such as a cotton or glass fiber paper permeated with sulfuric acid, silicon gel, or polymers (e.g., a polyethylene glycol or polypropylene carbonate) are in bottom housing  122 . Moisture retaining material  152  releases water as required to maintain a suitable humidity or moisture level in electrolyte membrane  110 . O-ring gaskets  146  are above and below solid electrolyte membrane  110  to prevent moisture from reservoir  150  from leaking past membrane  110  and to prevent the gas from entering into sensing chamber  140 . 
   A key part of sensor  100  is the assembly including solid electrolyte membrane  110  and electrodes  112 ,  114 , and  116 . Many factors such as the composition and treatment of membrane  110 , the interfaces of electrodes  112 ,  114 , and  116  to membrane  110 , and the arrangement of electrodes  112 ,  114 , and  116  in sensor  100  influence the performance of the membrane/electrode assembly. In an exemplary embodiment of the invention, solid electrolyte membrane  110  is made of Nafion, which a hydrated copolymer of polytretafluoroethylene and polysulfonyl fluoride vinyl ether containing pendant sulfuric acid groups. Other protonic conductive polymers such as polyethylene glycol, polyethylene oxide, or propylene carbonate could alternatively be used. 
   A low bulk ionic resistance through membrane  110  is desired for a fast response. An important factor influencing the bulk ionic resistance is the interface resistance between solid electrolyte membrane  110  and electrodes  112 ,  114 , and  116 . Accordingly, a good contact between the electrodes and membrane  110  is important, and in accordance with an aspect of the invention, a hot-pressed method is employed to attach electrodes  112 ,  114 , and  116  to membrane  110 . In one specific fabrication process, a Nafion membrane, which is about 0.18 mm thick, is coated with liquid Nafion or a Nafion solution. The coated membrane and platinum or noble metal electrodes/catalysts are then heated to about 120° C. while being pressed together at a pressure of about 2000 BL for 20-30 seconds, then moved to ambient air for cooling. 
   The bulk ionic resistance also depends on the resistance or resistivity of solid electrolyte membrane  110 . To lower the resistance of a Nafion membrane, a Nafion membrane can be acid treated before pressing electrodes  112 ,  114 , and  116  on membrane  110 . One specific acid treatment applies sulfuric acid (H 2 SO 4 ) at a concentration of 0.5 to 1 mol/L to the membrane. However, combining phosphoric acid (H 3 PO 4 ) additives with Nafion can improve Nafion&#39;s high temperature electrochemical performance. In one specific acid treatment, a Nafion membrane is immersed in concentrated phosphoric acid (85% wt.) and heated to about 150° C. for 1 hour, after the membrane is immersed in boiling water and 3% hydrogen peroxide. The membrane is moved to deionized water for washing off dissociation acid. A report in Mat. Res. Symp. Proc. 1998, vol. 496, p. 217, also describes some treatment processes for Nafion. 
   Three pins  162 ,  164 ,  166  are respectively connected to electrodes  112 ,  114 , and  116  via platinum wires (not shown) inside sensor  100 . The wires can be soldered to electrodes  112 ,  114 , and  116  and to pins  162 ,  164 , and  166  using conventional techniques. Pins  162 ,  164 , and  166  thus enable connection of external sensor electronics for current output and bias input. 
     FIG. 2  is a circuit diagram illustrating the operation of sensor  100  and the connections of pins  162 ,  164 , and  166  to electrodes  112 ,  114 , and  116  in sensor  100  and to electrical components such as differential amplifiers  210  and  220  and a resistor  230  on a printed circuit board. Alternatively, the electrical components illustrated in  FIG. 2  could all be integral parts of the oxygen sensor. 
   During operation, sensing electrode  112  catalyzes a reaction in which the oxygen that enters into sensor  100  and diffuses to sensing electrode  112  captures the electrons and combines with the hydrogen ions from the polymer solid electrolyte  110  to form water as indicated in Equation (1).
 
½O 2 +2H++2e − →H 2 O  (1)
 
   Differential amplifier  210  has input terminals coupled to reference electrode  116  and to a reference voltage Vin and an output terminal coupled to counter electrode  114 . Differential amplifier  210  thus drives counter electrode  114  to cause electrolysis of water that creates hydrogen ions and offers electrons to compensate for the hydrogen ions and the electrons consumed at sensing electrode  112  in the reaction of Equation (1). The electrolysis operation is shown in Equation (2).
 
H 2 O→2H++½O 2 +2e −   (2)
 
   The electrons flowing to sensing electrode  112  form an output current that depends on the rate of oxygen consumption, and the output current can be measured to determine the oxygen concentration at sensing electrode  112 . The hydrogen ions created at counter electrode  114  flow to sensing electrode through polymer electrolyte  110 . The oxygen created at the counter electrode  114  partly diffuses out of sensor  100  through a hole  154  through reservoir  150  and hosing  122  or is kept in the reservoir  150 . 
   The reactions of Equations (1) and (2) balance, so that the overall reaction converts water to water, and oxygen at sensing electrode  112  into oxygen at counter electrode  114 . The electrons liberated at counter electrode  114 , the electrons captured at sensing electrode  112 , and the hydrogen ions migrating from counter electrode  114  to sensing electrode  112  via the solid polymer electrolyte  110  flow at rates that depend on the reaction rate for the reaction of Equation (1). Differential amplifier  220  drives an output voltage Vout to a level such that a current through resistor  230  matches the flow of electrons required for the reaction at sensing electrode  112 . Voltage Vout is thus proportional to the reaction current, and the resistance of resistor  230  can be adjusted to control the proportionality constant between voltage Vout and the oxygen concentration. 
   The configuration of terminals  112 ,  114 , and  116  on membrane  110  can control the efficiency of the reduction of oxygen at sensing electrode  112  and therefore the level of the measurement current.  FIGS. 3A ,  3 B, and  3 C respectively show top, bottom, and side views of an electrode/membrane assembly  300  in accordance with an embodiment of the invention having sensing electrode  112  on one side of electrolyte membrane  110  and counter and reference electrodes  114  and  116  on the other side of electrolyte membrane  110 . 
   In an exemplary embodiment of the invention, electrolyte membrane  110  is a disk of acid-treated Nafion having a diameter of about 1.5 mm and a thickness between about 0.1 mm and about 0.2 mm. Sensing electrode  112  is preferably made of a catalyst material for the reaction of Equation (1) and can be, for example, platinum, gold, ruthenium, palladium, iridium, platinum/ruthenium, platinum/iridium, platinum/palladium alloy, carbon, or platinum/carbon that is porous and preferably about 0.2 mm thick. Counter electrode  114  and reference electrode  116  can be made of the same material as sensing electrode. Accordingly, reference electrodes can also be made of a noble metal such as platinum or gold or a high conductivity metal salt combination such as silver/silver chloride. 
   The electrodes are circular in the illustrated embodiment for ease of manufacturing. In the exemplary embodiment of the invention, each of sensing electrode  112  and counter electrode  114  has a diameter of about 0.5-0.8 mm, and reference electrode  116  has a diameter of about 0.3-0.4 mm. 
   For electrode assembly  300 , reference electrode  116  is on the side of membrane  110  opposite to sensing electrode  112  and is relatively isolated from the environment. The reference potential is thus more stable against changes in oxygen concentration in the environment, and also avoids a potential shift that could lead to a measurement error. Counter electrode  114  is also on the side of membrane  110  that is opposite to sensing electrode  112 . This prevents the reaction products (e.g., freed oxygen) at counter electrode  114  from interfering with the sensing electrode reaction. 
     FIGS. 4A ,  4 B, and  4 C respectively show top, bottom, and side views of an electrode/membrane assembly  400  in accordance with an embodiment of the invention having sensing and counter electrodes  112  and  114  on one side of electrolyte membrane  110  and reference electrode  116  on the other side of electrolyte membrane  110 . Membrane  110  and electrodes  112 ,  114 , and  116  in assembly  400  can have the same chemical composition and dimensions as corresponding structures in assembly  300  described above. 
   Electrode/membrane assembly  400 , like assembly  300 , has the advantage of isolating reference electrode  116  on the opposite side from sensing electrode  112  and thus has good reference voltage stability. Additionally, having counter electrode  114  on the same side as sensing electrode  112  can speed up the rate of mass transport by reducing the distance that hydrogen ions must travel through solid electrolyte membrane  110 . With assembly  400 , higher sensitivity is expected because of high mass transport rates in the absence of a membrane or significant liquid film barrier. Electrodes  112  and  114  can also share the same sample gas and humidity, giving the two electrodes  112  and  114  the same reaction condition. However, a suitable distance between sensing and counter electrodes should be considered because a short distance can result in the reaction products of counter electrode  114  affecting the reaction at sensing electrode  112 . 
     FIGS. 5A and 5B  respectively show a top view and a side view of a electrode/membrane assembly  500  in accordance with an embodiment of the invention having electrodes  112 ,  114 , and  116  all on the same side of solid electrolyte membrane  110 . This configuration has the advantage of a high mass transport rate and may also simplify the structure of the electrical connections to electrodes  112 ,  114 , and  116 . 
     FIGS. 6A and 6B  respectively show top and bottom views of an electrode/membrane assembly  600  having a ring-disk type configuration where a ring-shaped counter electrode  114  surrounds a circular sensing electrode  112 . The concentric electrode configuration of assembly  600  provides a low ionic bulk resistance between sensing and counter electrodes  112  and  114  and provides a high stability for reference electrode  116 . 
   An exemplary fabrication process for assembly  300 ,  400 ,  500 , or  600  starts with a Nafion membrane  110  that may be acid treated as described above. Top and/or bottom faces of the Nafion membrane are then coated with liquid Nafion, before a heat-pressure device presses electrodes  112 ,  114 , and  116  on the face or faces of the Nafion membrane to form a three electrode system. 
     FIG. 7  shows a button type of oxygen sensor  700  in accordance with an embodiment of invention. Button sensor  700  includes a series of substantially flat elements that can be stacked in contact with each other to provide a very compact sensor configuration. As an electrode system, sensor  700  includes a solid polymer electrolyte membrane  710  bonded to a first electrode  712  and second electrode  714 . Each of membrane  710 , electrode  712 , and electrode  714  can be disk-shape, and electrodes  712  and  714  are generally smaller than membrane  710  to provide spaces for gas around electrodes  712  and  714 . 
   A rigid thin housing made of a metal such as stainless steel includes a lower housing  720  and a cap  722  that enclose the electrode system. A hole  724  in housing  720  and a gas permeable membrane  730  and a paper element  740  inside housing  720  permit gas flow to electrode  712 . Gas permeable membrane  730 , which can be made of material such as polypropylene and polyester, controls the gas diffusion rate from outside sensor  700  to electrode  712 . Paper element  740  can be a glass microfiber paper that is permeated with sulfuric acid (e.g., 6 mol/L H 2 SO 4 ) contacts first electrode  712  and serves to adjust reaction humidity. Paper  740  of the same type is also placed on the second electrode  714  as a micro-reservoir to keep humidity in solid polymer electrolyte membrane  710 . Rubber O-rings  750  are respectively placed on the two sides of the solid polymer electrolyte membrane  710  to prevent gas or moisture leakage. 
   Housing  720  and cap  722  can be made of metal or another conductive material to act as electric contacts for supplying a bias voltage and outputting a current signal. Accordingly, housing  720  is electrically connected to electrode  712 , and cap  722  is electrically connected to electrode  714 . Conductive bands or similar structures (not show) can be used to provide the electrical conductivity through intervening elements such as gas permeable membrane  730  and paper layers  740 . An insulation material  760  such as plastic or rubber electrically insulates cap  722  from housing  720 . 
   The basic operating principle of oxygen sensor  700  are the same as for oxygen sensor  100  of  FIG. 1 , but in sensor  700 , second electrode  714  serves as the counter electrode for generation of hydrogen ions and free electrons and as the reference electrode relative to sensing electrode  712 . To function as a counter electrode, second electrode  714  is positively biased (e.g., to about 0.6 V) to cause the reaction of Equation (2) that provides electrons to sensing electrode  712  and protons or hydrogen ions to solid polymer electrolyte  710 . Sensing electrode  712  can be connected to the input of an amplifier in the same manner as sensing electrode  112  in  FIG. 2  so that an output voltage depends on a rate of oxygen reduction reaction at sensing electrode  712 . 
   Gas permeation membrane  730  limits oxygen diffusion to sensing electrode  712 , so that the reaction rate and output signal are proportional to the diffusion rate. According to Fick&#39;s diffusion equation, the diffusion rate is proportional to the oxygen content outside of gas permeation membrane  730 , so that the output signal is proportional to oxygen content. 
   The button type oxygen sensor  700  can provide a compact sensor configuration. In one exemplary embodiment, sensor  700  has an overall diameter of about 20 mm and a thickness of about 3 mm for a total volume of about 1 cm 3 . 
   The sensing processes in sensor  100  and  700  generally include four steps that could potentially limit the overall reaction rate and therefore the measurement signal. The steps are: gas diffusion to sensing electrode surface; the sensing electrode catalytic reaction; transfer of electrons and ions to the sensing electrode; and the removal of electrode reaction products from the electrode surface. The slowest of these steps creates a bottleneck that will control the reaction rate for the whole process. If the whole process is controlled by gas diffusion to the sensing surface, in other words, if the diffusion is the bottleneck, the gas concentration has a linear relation with the reaction rate and the output signal because the Fick&#39;s equation indicates that the diffusion is proportional to the oxygen content. 
     FIG. 8  shows a plot  800  of the output signal of a sensor such as illustrated in  FIG. 1  or  7 . For plot  800 , the oxygen concentration remains constant until a time T 1  when the oxygen concentration in the target gas suddenly drops. In response, the output signal drops and reaches 90% of the full response at a time T 1 ′ that is less than 10 seconds later. Similarly, at time T 2 , the oxygen concentration returns to the initial level, and the output signal rises to 90% of the full response at a time T 2 ′ that is less than 10 seconds later. The fast response time of sensor  100 , which is impressively faster than that of currently available commercial oxygen sensors may be attributed to high electrocatalytic activity of sensing electrode  112 , and a reaction rate that is diffusion limited. The small volume of sensing chamber  140 , which is between sensing electrode  112  and capillary  132  in sensor  100  of  FIG. 1 , quickly reaches equilibrium where the diffusion rate and sensing reaction rate are the same. In an exemplary embodiment, sensing chamber  140  has a volume less than about 0.01 mm 2 . 
     FIG. 9  shows a plot  900  of the output signal from sensor  100  as a function of oxygen concentration outside sensor  100 . For plot  900 , sensing electrode  112  has a fixed potential of about −0.6 V with respect to reference electrode  116 . Plot  900  illustrates a suitably linear relationship is obtained for oxygen content in the range of 0 to 30%. The measurement signal of plot  900  shows that the oxygen diffusion rate through capillary  132  is satisfactorily described by Fick&#39;s diffusion equation (i.e., is proportional to the oxygen content) over a range of 0-30% oxygen. Accordingly, the reading from sensor  100  represents the percentage of oxygen in the gas sample, and is independent of total gas pressure. 
   An oxygen content above about 30% oxygen presents additional complications for measurement in sensor  100 . In particular, if the oxygen content is above about 30%, the diffusion rate may no longer be proportional to the oxygen content, requiring a non-linear conversion of the output signal to an oxygen content value. Further, if the diffusion rate becomes too high, the reaction rate at sensing electrode  112  becomes the limiting factor of the overall process and the resulting measurement signal, and sensor  100  cannot distinguish higher oxygen content levels. 
     FIG. 10  shows a plot  1000  of the measurement signal as a function of temperature for a gas sample containing a fixed oxygen content. The output signal of sensor  100  varies slightly with gradual changes in temperature as shown in  FIG. 9 . The temperature effect may arise from thermal changes in gas diffusion rates, electrode reaction rates, and membrane resistance. When exposed to a step change in temperature, sensor  100  exhibits a transient response, which is a decrease in the measurement signal for a drop in temperature and an increase in the measurement signal for a rise in temperature. 
     FIG. 11  shows a plot  1100  illustrating the long-term stability test of the measurement signal from a sensor  100  for a sample gas having a fixed oxygen content, e.g., in ambient air sensed over several months. No large signal change is found after the long time testing. The uniformity of the measurement arises from the ability of sensor  100  to measure oxygen without consuming an electrode or other material. In particular, oxygen is reduced on sensing electrode  112  into water, and that water is consumed to produce hydrogen ions and oxygen at counter electrode  114 . The net reaction is no change in the constituents of sensor  100 . Therefore, sensor  100  can provide consistent measurements as long as the material and structure in sensor  100  are unchanged. 
   Although the invention has been described with reference to particular embodiments, the description is only an example of the invention&#39;s application and should not be taken as a limitation. Various adaptations and combinations of features of the embodiments disclosed are within the scope of the invention as defined by the following claims.