A FLEXIBLE, MICROFABRICATED IMPEDIMETRICFLUID TEMPERATURE SENSOR
Alex Baldwin, Trevor Hudson, Eugene Yoon, and Ellis Meng
University of Southern California, Los Angeles, USA
ABSTRACT
A novel impedimetric temperature sensor which utilizes theelectrochemical impedance between two electrodes exposed to an
aqueous solution to transduce temperature is presented. The solution
resistance between electrodes is highly temperature dependent sinceionic mobility increases with temperature. High-frequency
electrochemical impedance can be used to accurately measuresolution resistance, and therefore transduce fluid temperature. A
temperature sensor composed of two platinum electrodes on a thinfilm Parylene C substrate exposed to fluid was designed, fabricated,
and tested. Fluid temperature was transduced with high sensitivity(-59.33 Ω/°C) by measuring the impedance magnitude between
electrodes at an appropriate frequency where phase was minimized.
Compared to conventional platinum resistance temperaturedetectors (RTDs), our sensor achieved over 4× higher sensitivity andresolution (±0.02°C). Furthermore, the sensor is specificallydesigned for use in liquids, and features flexible, biocompatible
construction for biomedical or microfluidic applications.

dependent due to increased ionic mobility at higher temperatures.
This sensitivity exceeds the temperature coefficient ofsemiconductor materials (Table 1), with a reported temperature
coefficient of -1.98%/°C for human cerebrospinal fluid [7].
Measuring solution resistivity using high-frequency electrochemical
impedance enables highly sensitive fluid temperature transduction.
Impedance spectroscopy was used to transduce the internal
temperature of lithium ion batteries [8, 9]. However, until now, no
one has demonstrated the use of impedance measurement totransduce temperature in bulk solution.
Table 1. Temperature coefficient of resistance (TCR) of metals andsemiconductors which have been used in resistive temperature
sensors, as well as several ionic solutions including humancerebrospinal fluid (CSF).

Material

Temperature
Sensitivity (%/°C)

Platinum
CopperPolysilicon

0.392
0.430
-2.5 to 0.1

Germanium-2.0

1.32M (5%) NaOH
7.9M (30%) NaOH

-2.01
-4.50

2.95M (20%) KCl-1.68

Human CSF

-1.98

INTRODUCTION
State-of-the-art methods for measuring fluid temperature include
thermocouples and resistance temperature detectors (RTDs) [1, 2].
Thermocouples utilize the Seebeck effect, in which a temperaturedependent voltage occurs at the junction of two dissimilar
conducting elements [3]. They are generally made using nickel
alloys, though occasionally platinum and rhodium are used toenhance stability, and have temperature sensitivities up to 60 µV/°C.
However, thermocouples have low accuracy and precision, andgenerally cannot distinguish temperature changes less than 2°C.
Semiconductor junctions can also be used as thermocouples, withsensitivities up to 110 mV/°C and resolutions as good as ±0.8°C [1].
Thermocouples require packaging to protect conducting elementsfrom water intrusion and to act as a barrier shielding the body fromnon-biocompatible sensor material.
RTDs are conductive or semiconductive elements whose
resistance changes with temperature. The most common commercial
RTD (PT100) is made of bulk platinum wire and defined by aresistance of 100 Ω at 0°C and a temperature coefficient of
0.385%/°C [2]. Platinum RTDs can also be microfabricated on thinfilm substrates, though the temperature sensitivity of thin-film
platinum is lower than bulk material. Most metal RTDs use platinum
due to its high linearity, but other metals such copper and nickel canbe used as well. Laboratory-grade RTDs operate between -200°C
and 1000°C with precision approaching ±0.001°C, althoughcommercial RTDs are closer to ±0.03°C. The main drawbacks ofplatinum RTDs are low sensitivity and the need for encapsulation
when used in aqueous solutions.
Semiconductor materials, such as silicon, germanium, and metaloxides, exhibit lower electrical resistance when operating at higher
temperatures [1, 4]. These semiconductor RTDs, also known asthermistors, possess temperature coefficients exceeding -2%/°C andhave comparable precision to metal RTDs. However,semiconductors corrode and disintegrate under chronic soaking inphysiological fluid [5, 6].
An alternate approach to measure temperature changes inphysiological fluid via measurement of the fluid’s resistivity isinvestigated. The resistivity of an aqueous solution is temperature

THEORYThe impedance between two electrodes exposed to solution canbe approximated by a Randles circuit [10] (Figure 1). This circuit
consists of a charge transfer resistance Rct and a double layer
capacitance Cdl at each electrode-electrolyte interface, as well as thesolution resistance Rs between the electrodes.

Figure 1: The electrochemical impedance between two electrodesconsists of the solution resistance RS, as well as a charge transfer
resistance Rct and double layer capacitance Cdl at each electrodeinterface. At high frequencies, the electrode-electrolyte interface is
bypassed and impedance can be approximated as RS.

Rct describes the relationship between an electrode’s
overpotential v0 and the resulting current due to faradaic reactions at
the electrode surface. Assuming surface and bulk reactant
concentrations are equal, the relationship between v0 and the net
current across the electrode-electrolyte interface inet is given by the
Butler-Volmer equation:
𝑖𝑛𝑒𝑡 = 𝑖𝑜 {𝑒 −𝛼𝑐 𝑛𝑓𝑣0 − 𝑒 (1−𝛼𝑐 )𝑛𝑓𝑣0 }(1)

where αc is a transfer coefficient which can range from zero to unity,
n is number of electrons transferred, i0 is the exchange current
density, and f is equal to F/RT, where F is Faraday’s constant, R is
the gas constant, and T is temperature in Kelvin. At low
overpotentials, the linear approximation of an exponential can beapplied to equation 1, resulting in the following expression forcharge transfer resistance:−𝑖𝑜 𝑛𝐹
𝑖𝑛𝑒𝑡 =
𝑣
𝑅𝑇 0
𝑑𝑣0
𝑅𝑇
𝑅𝑐𝑡 =
=
𝑑𝑖𝑛𝑒𝑡 𝑛𝐹𝑖𝑜

(2)

This result implies a direct correlation between Rct andtemperature. Previously, charge transfer resistance was used totransduce the internal temperature of lithium ion batteries [8, 9].
However, the byproducts of faradaic reactions can be toxic [11], andmany microelectrodes are too small for accurate measurement ofcharge transfer resistance. Therefore, electrochemical impedance
measurement depends on Cdl and Rct.
A double layer of electrostatically bound ions builds up at anelectrode-electrolyte interface, leading to the formation of acapacitance Cdl [12]. Helmholtz, Gouy-Chapman, Stern, Graham,and others modeled this phenomenon, but the precise relationships
between Cdl and temperature remains under active investigation andhas not been fully characterized [13, 14].
Solution resistance RS follows from a solution’s conductivity,
which is highly sensitive to changes in temperature. Electrolyte
conductivity results from the movement of dissolved ions in
response to an applied electric field. Bulk conductivity is
proportional to ionic concentration, but a molar conductivity 𝛬 =𝐺/𝑐 can be defined, where G is the bulk conductance and c is themolarity of ions [15]. As ionic concentration goes to zero, interionicforces disappear. This is known as a state of ‘infinite dilution’ andis useful for modeling conductivity in an aqueous solution. If an ion
is modeled as a spherical charged particle within a continuous fieldof water and ionic mobility is defined as the limiting velocity perapplied force, the conductivity at infinite dilution can be derived
from Stoke’s Law as
𝜆0 =

𝑞𝐹
4𝜋𝜂𝑟

(3)

where λ0 is conductivity at infinite dilution, q is ionic charge,  iswater’s viscosity, and r is ionic radius [16]. Only viscosity varies
significantly with temperature; therefore, the temperature
coefficient of a solution’s conductivity at infinite dilution isinversely proportional to water’s viscosity. Theoretical models forwater’s viscosity are generally inaccurate, but the following
equation fits to empirical viscosity measurements within 1%
accuracy for temperatures between 0 and 100°C and atmosphericpressure (0.1 MPa):
4

𝜂
𝑇 𝑏𝑖
=
∑
𝑎
(
)
𝑖
10−6 𝑃𝑎 𝑠
300
𝑖=1

(4)

i

a

b

1
2

280.68511.45

-1.9
-7.7

3
4

61.1310.45903

-19.6
-40.0

where  is in Pa·s and a and b are dimensionless, experimentally
determined constants [17]. Using this formula, the infinite dilution
temperature coefficient of conductivity can be shown to vary from 3%/°C to -1.5%/°C, with a value of -1.95%/°C at 37°C [18].
The Stoke’s Law model of infinite dilution conductivity can be
improved by including dielectric losses which occur due to the
movement of charged particles. This results in the following:
𝜆0 =𝑞𝐹
3 2 𝜀0 − 𝜀∞4𝜋𝜂𝑟 + 𝑞𝜏8
𝜀02 𝑟 3 0

(5)where 0 and  are the high frequency and low frequency limits ofthe solution permittivity and 𝜏0 is the Debye relaxation time [19].
Both the Debye relaxation time and water’s permittivity aretemperature dependent [20, 21], but changes in viscosity still drive
the temperature sensitivity of ionic solution conductivity.
Interionic forces must be considered at concentrations above
infinite dilution. These can be modeled by the Debye-HuckelOnsager equation, leading to the following relationship between
concentration and conductivity:

Λ = λ0 −𝑧 2 𝑒𝐹 2
2
3𝜋𝜂 (
)
𝜀𝑅𝑇
(

𝑥𝑧 3 𝑒𝐹3+2
24𝜋𝜀𝑅𝑇√

2
𝜀𝑅𝑇

λ0 √𝑐

(6)

)

where Λ is conductivity, c is electrolyte concentration in moles perliter, z is the valency number of each ionic species, e is the electron
charge, and x describes the symmetry of an ionic species [22]. The
temperature sensitivity of a solution decreases as ionic concentration
increases, but this decrease remains negligible in most cases. For
example, cerebrospinal fluid (CSF) has an ionic concentration of
295 mM, but there is only a 0.19% difference in its temperature
coefficient compared to a solution at infinite dilution.
The above equations are valid for ionic solution composed ofstrong electrolytes. Weak electrolytes are much more complex, but
in general their temperature coefficients will be much higher at highconcentrations and approach that of strong electrolytes at low
concentrations. This is due to the temperature dependence of a weakelectrolyte’s disassociation constant, leading to large changes inionic concentration when temperature is altered. Intuitively, one
would assume that ultrapure water would be either non-conductive
and thus insensitive to changes in temperature or would have asensitivity similar to an ionic solution at infinite dilution. However,despite resistivities greater than 18 M∙cm at room temperature,
pure water does indeed conduct electricity. This conduction ismediated by a small fraction of water molecules spontaneously
disassociating into hydroxide and hydronium ions. Ultrapure water
acts similar to a very weak acid or a very weak base and exhibits amuch higher sensitivity to temperature changes than ionic solutions,with a temperature coefficient ranging from 7.4%/°C at 0°C to
2.3%/°C at 100°C [23]. However, the addition of ppb levels of
impurities will cause baseline conductivity to change by a muchhigher factor than changes in temperature, and the solution will soon
resemble a typical ionic solution.

The predictable and highly sensitive relationship between RS andtemperature suggests the possibility of temperature transduction. By
measuring electrochemical impedance at high frequencies, theelectrode-electrolyte interface is bypassed and impedance consists
only of RS. Therefore, fluid temperature can be transduced using
high-frequency electrochemical impedance (Figure 2). Solution
resistance measurement is at its most efficient when phase isminimized.
Measurement Frequency

PBS), a common physiological fluid analog. 1× PBS is isotonic withcerebrospinal fluid and has a resistivity of 50 Ω∙cm.
For electrochemical impedance spectroscopy (EIS) testing,sensors were sealed in glass vials filled with 1× PBS and placed ina water bath, which was heated to temperatures between 30 and
50°C. A Gamry Reference 600 potentiostat was used for EIS
measurement (1 Hz – 1 MHz, 10mVPP). For single-frequency
impedance tests, solution was heated from room temperature(~20°C) to 50°C using a hot plate while a thermocouple/multimeter(Newport TrueRMS Supermeter, ±2°C accuracy) was used tomonitor fluid temperature. Data was collected from impedance
electrodes using an Agilent E4980A precision LCR meter at 0.1 VPP
and from the RTD using a Keithley SourceMeter with 10 µA bias
current. Impedance and resistance data was simultaneously
collected and analyzed using a custom LabVIEW program.

RESULTS

Figure 2. The magnitude and phase of temperature sensing
electrodes, measured in 1×PBS. By measuring electrochemical
impedance at the frequency where phase is minimized, solution
resistance can be transduced.

EIS from 1 Hz to 1 MHz was measured from 30 to 50°C at 5°C
temperature intervals (Figure 4). The results demonstrated a clear
temperature dependency of impedance at frequencies from 1 to 100
kHz. The temperature coefficient was approximately -2%/°C, whichmatches reported temperature coefficient measurements in
cerebrospinal fluid [7]. The discontinuities in the EIS graphs werelikely a result of inadequate shielding by the chicken-wire Faraday
cage. Although 10 kHz appeared to be the optimal measurement
frequency due to its position in the center of the resistive range,
single-frequency benchtop testing showed that measuring
impedance at 100 kHz provided more consistent results.

EXPERIMENTAL DESIGN
We performed several experiments to demonstrate temperaturetransduction via high-frequency impedance. The temperature sensor
used in these experiments consisted of a pair of platinum electrodes
and a platinum resistor on a Parylene C substrate (Figure 3). The
electrodes had exposed areas of 150 x 250 µm2 with centers 750 µm
apart. A platinum resistor, located 1 mm away from the electrodeson the same Parylene C substrate, was used as an RTD for
benchmarking. The RTD consisted of a 25 µm wide serpentine trace
and had a nominal DC resistance of ~450 Ω.

Figure 4: Electrochemical impedance spectroscopy of a pair of
platinum electrodes at temperatures between 30°C and 50°C. As
temperature increases, the impedance magnitude within theresistive range decreases.

Figure 3: Impedimetric temperature sensing was tested using a pairof platinum electrodes on a Parylene C substrate. A microfabricatedplatinum RTD, fabricated on the same substrate, was used forbenchmarking.
Sensors were primarily tested in phosphate-buffered saline (1×The platinum RTD was calibrated by comparing its resistance tothermocouple measurements in 1× PBS, revealing a temperature
coefficient of resistance of 1.21 Ω/°C. Temperature was then cycled
between 20 and 50°C while simultaneously measuring impedance
magnitude at 100 kHz and temperature using the RTD. The
impedance magnitude correlated extremely well with temperature,with a temperature coefficient of -59.33 Ω/°C (Figure 5). Minimal
hysteresis was observed over multiple cycles. Based on noise, 3σresolution of impedance-based temperature sensing was measured
to be ±0.02°C, compared to ±0.08°C for the platinum RTD.

[6]

[7]

[8]

[9]

Figure 5: Impedance magnitude at 100 kHz was roughly linear withtemperature, with a temperature coefficient of -59.33 Ω/°C andresolution of 0.02°C. This compared favorably to the RTD, whichshowed a temperature coefficient of 1.21 Ω/°C and a resolution of
0.08°C.

[10]
[11]

[12]

CONCLUSION
A novel method of measuring bulk fluidic temperature via
electrochemical impedance was tested using a flexible,
biocompatible temperature sensor. Results confirm theoreticalpredictions, and the impedimetric temperature sensor was able tomeasure sub-degree temperature fluctuations at a higher resolution
than platinum RTDs, which are considered the gold standard fortemperaturetransduction.
Electrochemical
impedancemeasurements are substrate-independent, and temperature
measurement via electrochemical impedance can be implemented inany device with exposed electrodes in an aqueous solution. Future
work will evaluate repeatable sensing in physiological fluids
towards achieving chronic temperature monitoring in vivo, as well
as exploring this technique’s sensitivity to changes in ionicconcentration and composition.

[13]
[14]

[15]
[16]

[17]

ACKNOWLEDGEMENTS
We would like to thank Dr. Brian Kim, Dr. Donghai Zhu of the Keck
Photonics Lab, and all the members of the Biomedical
Microsystems Lab for their help and support. This work was fundedby the National Science Foundation under award EFRI-1332394.

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CONTACT
Ellis Meng, ellis.meng@usc.edu