Measurement Science and Technology
Meas. Sci. Technol. 00 (2015) 000000 (8pp)
UNCORRECTED PROOF
Temperature sensing of micron scale
polymer fibers using fiber Bragg gratings
J Zhou1, Y Zhang1,2, M Mulle1 and G Lubineau1
1
King Abdullah University of Science and Technology (KAUST) Physical Sciences and Engineering
Division, COHMAS Laboratory, Thuwal, 23955-6900, Saudi Arabia
2
Shanghai Jiao Tong University, School of Mechanical Engineering, State Key Laboratory of Mechanical
Systems and Vibration, 800 Dongchuan Road, Minhang District, Shanghai 200240, People’s Republic of
China
E-mail: [email protected]
Received 18 February 2015, revised 8 April 2015
Accepted for publication 16 April 2015
Published
Abstract
Highly conductive polymer fibers are key components in the design of multifunctional textiles.
Measuring the voltage/temperature relationships of these fibers is very challenging due to
their very small diameters, making it impossible to rely on classical temperature sensing
techniques. These fibers are also so fragile that they can not withstand any perturbation from
external measurement systems. We propose here, a non-contact temperature measurement
technique based on fiber Bragg gratings (FBGs). The heat exchange is carefully controlled
between the probed fibers and the sensing FBG by promoting radiation and convective heat
transfer rather than conduction, which is known to be poorly controlled. We demonstrate our
technique on a highly conductive Poly(3,4-ethylenedioxythiophene)/poly(styrenesulfonate)
(PEDOT/PSS)-based fiber. A non-phenomenological model of the sensing system based on
meaningful physical parameters is validated towards experimental observations. The technique
reliably measures the temperature of the polymer fibers when subjected to electrical loading.
Keywords: fiber Bragg grating, conductive polymer, fiber, temperature, sensors
AQ1
(Some figures may appear in colour only in the online journal)
1. Introduction
these sensors do not provide good thermal contact with the
probed surface. Their cooling surface may also be very large,
which may induce significant measurement errors. RTDs and
thermistors may be subjected to self-heating effects that may
be detrimental if corrections are not made. These conventional
electrical temperature sensors are reliable and accurate when
they are fully surrounded by the environment they are supposed to sense. Although contact may be improved by using
thermal conductive pastes, these sensors are more suitable for
measurements of liquids and gases than for measurement of
solids. In measuring the temperature of small objects, optical
methods have been developed. This development stems from
the progressive miniaturization of electronic components
and the need to characterize their thermal behaviors. Optical
methods have three major advantages: they do not require
contact with the object, they provide a spatial distribution
of the temperature measurements and they have a high spatial resolution. Using liquid crystal imaging, Aszodi et al
During the last decade, significant developments in electrical
conductive polymers have taken place [1–3]. Polymer fibers
made of conductive polymers may be doped or de-doped with
adequate solvents to tailor their conductive properties in such
a way that they deliver significant joule effects when subjected to low current [4, 5]. These conductive polymer fibers
can be used in wearable heating textiles as they are flexible
and non-costly compared with carbon or metallic fibers [6].
Characterizing the thermal response of such heating fibers
is important but remains very challenging because the small
diameters (a few micrometers) of the fibers.
The most prevalent technologies used to perform temperature measurements today are thermocouples, resistance temperature detectors (RTDs) and thermistors. Their size may be
as small as a few tenths of microns and they allow high resolution measurements. However, with their typical bulbous ends,
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managed to obtain temperature maps with 5 μm separated
isothermal lines [7]. Clayes et al used a thermo-reflectance
method that allowed a lateral resolution of 1 μm [8]. Dohkkar
et al demonstrated the capacity of a near-infrared thermography device to provide 1 μm resolution in both steady and
transient states [9]. Infrared thermography is widely used in
industry for thermal characterization, although due to the diffraction limit of infrared imaging, the spatial resolution is on
the order of 5 μm.
An alternative solution is to use optical fiber Bragg grating
(FBG) devices. Such devices have been successful in thermal
characterization under cryogenic conditions [10] or at very
high temperature (up to 1000 °C) [11, 12]. FBGs have been
embedded in composite materials to measure in-core temperatures during manufacturing processes [13, 14]. FBGs
also have intrinsic advantages for sensing the temperature of
small resistive polymer fibers subjected to current. They have
a small size and a linear geometry; they are passive sensors
and immune to electromagnetic interference. However, there
is limited research on the use of FBGs to measure temperature
on the micro-scale. An attempt was made by Antunes et al to
measure the temperature of a copper wire [15]. The smallest
tested wire had a diameter of 100 μm. The sensor was placed
in contact along the wire and bonded with a thermal conductive compound to promote heat transfer. The acquired data
was used in a model to predict the real temperature of the
wires as a function of incident electrical current. This study
included both conduction parameters and global radiation/
convection parameters that were identified by fitting a global
single dimension equation. Because it was a very macroscopic
model and the physical parameters were retrofitted to match
the experimental results, it could not give reliable measures of
the wire temperature.
Motivated by the above considerations, we developed a
new experimental approach and a related numerical model,
in which we investigate the response of an FBG subjected
to the joule effect produced by a 10 μm-diameter polymer
fiber under current loading. This approach is guided by the
idea that uncontrolled environmental parameters have to be
minimized as much as possible. Direct contact between the
polymer fiber and the FBG was avoided because the efficiency
of the thermal transfer at the contact could not be determined
with accuracy. We could partially solve this problem by using
additional thermal paste but this solution would likely damage
the polymer fiber and introduce a thermo-mechanical stress
mismatch during heating. We therefore placed the FBG sensor
as close as possible to the polymer fiber without contact and
in the ambient air. Our model is based on a two-heat transfer
mechanism: radiation and convection.
The changes in temperatures can be detected at different
voltages. We also run the measurement at different distances
between the polymer fiber and the FBG sensor and investigate the dynamic thermal response. We then compared
experimental results with the numerical model developed in
COMSOL Multiphysics. Here we discuss the capability of the
model to reproduce both the dependency of the measured temperature on voltage and the variation in the FBG temperature
with respect to its distance to the heating source (the polymer
fiber to be probed). These two observations are used to
directly validate the model without tuning the model parameters. We finally discuss the validity of the overall approach to
probing changes in the temperature of micro-sized and sensitive systems.
2. Experimental
2.1. Preparation of poly(3,4-ethylenedioxythiophene)/
poly(styrenesulfonate) (PEDOT/PSS) microfiber
PEDOT/PSS microfibers were fabricated via wet-spinning
as described in a previous study [5]. The fiber was wet-spun
from a 22 mg mL−1 PEDOT/PSS dispersion (using a Clevios
PH1000) followed by a vertical hot-drawing process. Wet
fibers were pulled out from an acetone/isopropyl alcohol
(acetone/IPA) coagulation bath. The resulting fibers had an
average diameter of 10 μm and an electrical conductivity of
340 S cm−1. The fibers were prepared and fixed on a paper
card to avoid fiber damage while handling the samples.
2.2. Preparation of FBG and calibration
An FBG reflects a part of the incident light signal that is represented by a spectrum of wavelength [12, 13], it characterized
by Bragg wavelength, λB, which corresponds to the spectrums
peak. When the FBG is subjected to axial strain, ε, or temperature changes, ΔT, the peak shifts proportionally with these
thermo-mechanical loadings. The Bragg wavelength variation
can be expressed as [16, 17]:
ΔλB
= KTΔT + Kεε
(1)
λB
where KT and Kε are related to the sensors sensitivities to temperature and strain, respectively. In this study the strain component was neglected as tests were carried out under stress-free
conditions. The FBGs used here were 5 mm long and written
on SMF28e standard fibers. The coating was removed along
the FBG. The Bragg wavelength of the sensor was 1530 nm at
room temperature.
The temperature sensitivity (KT/λB) of the FBG was calibrated by immersing it together with a thermocouple in a
beaker filled with water. The temperature of the water was
increased gradually from 20 to 70 °C. The temperature and
Bragg wavelength measurements were recorded at 1 Hz. The
FBG sensitivity was determined to be 9.9 pm °C−1.
2.3. Experimental set-up and procedure
The experimental set-up is shown in figure 1(a). The optical
fiber and the polymer fiber were placed parallel to each other
on a micro-manipulator, on the mobile and fixed part, respectively. The distance between the fibers could be controlled at a
resolution of 5 μm. The micro-manipulator was placed inside
a protective chamber to avoid environmental disturbances.
Two conductive silver paste electrodes, spaced 20 mm
apart, were connected to copper wires used to apply the electrical field. The effective length of the polymer fiber between
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Figure 1. (a) Experimental setup for the temperature measurement of the polymer fiber using FBGs. (b) Microscope images of the optical
fiber and the polymer fiber at different distances.
Figure 2. (a) FBG spectra recorded at different voltages. The distance between the polymer fiber and the FBG is 100 μm. (b) Change of the
wavelength versus voltage for different distances between the polymer fiber and the FBG.
the two electrodes was 20 mm. To generate Joule heat on the
polymer fibers, the electric field was applied to the fiber with a
DC power supply (EXTECH instruments 382 280) and a pulse
functional generator (Agilent Technology 81 150 A). The first
instrument was used to investigate the thermal response under
steady conditions and the second under cyclic conditions. The
current flow in the fibers was monitored by using an U1252B
digital multimeter. A Micron Optics sm125 unit was used for
the acquisition of Bragg peak shifts and reflected spectra.
The minimum distance between the polymer fiber and
the optical fiber was set to 100 μm. It was then gradually increased to 6000 μm. The distance and the parallel
placement between the fibers were controlled using a
Leica DM2500 optical microscope. Images are shown in
figure 1(b). For each distance, the voltage was applied to
the polymer fiber with incremental steps of 2 V from 0 to
28 V. Electrical current data were captured at 1 Hz and FBG
measurements at 2 Hz. The tests were conducted three times
to evaluate repeatability and stability. In another series of
tests, the dynamic thermal response of the polymer fiber was
investigated at a distance of 100 μm. A cyclic square wave
voltage was applied from 0 to 15 volt at frequencies of 0.02,
0.1, 0.25 and 0.5 Hz.
3. Experimental results and discussion
3.1. Raw measurement
We first studied the raw data provided by the optical sensor.
FBG spectra were recorded at each voltage step. Figure 2(a)
presents these results for a distance of 100 μm between the
polymer fiber and the FBG. The spectra from 0 to 28 V present
a clear peak, indicating that the peak shits are reliably related
to voltage change. Figure 2(b) shows changes in the Bragg
peak wavelength for different distances between the polymer
fiber and the FBG as a function of voltage steps. At the closest
position (100 μm), the wavelength change from one voltage
level to another is clearly pronounced. The sizes of wavelength steps reduced as the distance between the polymer fiber
and the FBG increased. At 6000 μm, the FBG delivered a constant signal, indicating that at this distance the sensor was not
able to detect any change.
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Figure 3. (a) Temperature variation and current versus time for the polymer fiber placed 100 μm from the FBG. The voltage increased in
steps of 4 volts from 0 to 28 V. (b) Changes in temperature versus voltage for increasing distances between the polymer and the FBG.
Figure 4. (a) Dynamic thermal response of the polymer fiber at a distance of 100 μm from the FBG. A cyclic voltage was applied from 0 to
15 V at frequencies of 0.02, 0.1, 0.25 and 0.5 Hz. (b) The temperature and current changes with respect to time at 0.1 Hz.
and the voltage affect the change in temperature as detected
by the FBG.
3.2. Key experimental results
In section 3.1, we presented raw measurements that were
obtained for a certain voltage level and for a certain distance
between the FBG and the polymer fiber. Here, we present
the experimental observations to which the predictions of the
numerical model presented in section 4 are compared.
FBG data were transformed into temperature information
according to equation (1). Curves of temperature variation to
current are plotted with respect to time in figure 3(a). Results
are given for the polymer fiber placed 100 μm from the FBG.
Due to the current and the resistivity of the fiber, a joule effect
was generated. This heat was transmitted by convection and
radiation to the FBG. The temperature change (ΔT) detected
by the optical sensor follows the current profile very closely.
The maximum value of ΔT is 55.6 °C at 28 V. The response
of the FBG to a voltage change took less than one second.
Because heat is generated, transmitted and detected during
this short delay, we can consider that this optical sensor is
very sensitive. Figure 3(b) shows change in temperature as a
function of voltage at different distances between the polymer
fiber and the FBG. These results show how both the distance
3.3. Dynamic response
We analyzed the dynamic response of the sensor/polymer
fiber system by applying square wave voltage at different frequencies (figure 4(a)). The detected thermal response is stable
and repeatable at each given frequency. From one frequency
to another the temperature variation differs. The higher the
frequency, the lower the temperature variation. This indicates
that either joule heat is not generated to its maximum or that
its transmission to the temperature sensor is not completed
before another cycle takes place.
Figure 4(b) presents details of temperature and current
changes with respect to time at 0.1 Hz. The profile of the
detected heat does not follow the square wave of the current.
There is a small delay before reaching the steady state during
both the heating and the cooling phase. The average delay is
approximately 2.5 s. This represents the responsive limitation
of the sensor/polymer fiber system under which the measured
value will not be representative of the voltage input.
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(a)
Destination
face
m
20 m
tion
irec
ep d
Swe
Source
face
variable distance
(100 to 6000µm)
y
z
x
(b)
Figure 5. (a) The geometry for the numerical model and the meshed polymer fiber and optical fiber. (b) The surfaces where boundary
conditions are applied.
4. Modeling of the sensing set-up
and it would be a totally arbitrary parameter to be identified
by fitting experimental observations. This would make the
model questionable from a physical point of view and we
chose to eliminate the conduction mechanism by systematically making non-contact measurements.
Two heat transfer mechanisms thus have to be included in
the model: convection (which can still take place as all the
experiments presented here were made in air) and radiation.
Our model describes such exchanges between three elements:
the polymer fiber, the FBG fiber and the environment.
A major challenge in any sensing application is to resolve the
physical quantity to be probed (here for example, the temperature of the polymer fiber or the heat flux it dissipates) as
a function of the measured physical quantity (here, the temperature of the FBG). In other words, how can the physical
quantities that are not directly measured by the sensor be evaluated if the FBG temperature is known? Answering this question requires a physically accurate model of the measurement
system. This forward model can then be used to resolve the
targeted physical quantity by solving the associated inverse
problem.
The first step is to model the heat transfer between the electrically loaded polymer fiber and the FBG. Among the three
well-known heat transfer mechanisms (conduction, convection and radiation), conduction has been made impossible by
avoiding contact in the experimental set-up. Indeed, modeling
any conductive heat transfer that comes from direct contact
between the polymer fiber and the FBG would be very challenging. Thermal conductivity of contacts is poorly defined
4.1. Model geometry, meshing and boundaries definitions
The model geometry is shown in figure 5(a). The lengths of
the polymer fiber (Ω1, diameter 10 μm) and the optical fiber
including the 5 mm FBG (Ω2, diameter 125 μm) are both 20
mm. The distance between the surface of the polymer fiber
and the surface of the FBG ranges from 100 to 6000 μm
depending on the simulated experimental conditions.
Quadrilateral elements are used for free meshing of the
cross sections of both the FBG and polymer fibers. The plane
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mesh is then extruded to create a three-dimensional mesh from
this meshed cross section via a swept mesh method. We used
20 elements between the source and the destination faces.
−
+
∂Ωiz and ∂Ωiz are the start and end cross sections for the Ωi
domain. ∂Ωil is the cylindrical surface of each domain (i = 1
or 2). ∂Ωi is the complete boundary for each domain (figure
5(b)).
Table 1. Physical parameters selected for simulation of the
electrical and thermal behaviors of the system.
Property
Symbol
Unit
Value
σ1
k1
ε1
h1
S.m−1
W.m−1.K−1
—
W.m−2.K−1
34000
0.22
0.9
85
k2
ε2
h2
W.m−1.K−1
—
W.m−2.K−1
1.38
0.95
5
Polymer fiber
Electrical conductivity
Thermal conductivity
Surface emissivity
Convection coefficient
4.2. Formulation of the multiphysics problem
FBG
A coupled electrical/thermal problem is solved on the geometrical model described in figure 5 using the heat transfer
and radiation capibilities of COMSOL Multiphysics.
Electrical behavior. The start and end cross sections of the
polymer fiber are subjected to ground and operating voltages
(equations (2) and (3)). Flux conservation is assumed in the
volume (equation (5)) and electrical insulation is assumed on
the lateral surface (equation (6)). We assume a constant isotropic electrical conductivity, σ1 (equation (7)).
Thermal conductivity
Surface emissivity
Convection coefficient
− q ⋅ n = 0,
∀ M ∈ ∂Ωiz − ∪ ∂Ωiz +, i ∈ [1, 2]
(12)
•Thermal constitutive equations
q = ki Φ,
∀ M ∈ Ωi, i ∈ [1, 2]
(13)
•Electrical potential equations:
−
V = 0,
∀ M ∈ ∂Ω1z
(2)
q con = hi(Troom − T ),
∀ M ∈ ∂Ωil , i ∈ [1, 2]
(14)
+
V = Vmax,
∀ M ∈ ∂Ω1z
(3)
E = −∇V ,
∀ M ∈ Ω1
(4)
q rad = αi(Gim + Giam ) − εi(σSBT 4 ),
∀ M ∈ ∂Ωil , i ∈ [1, 2]
(15)
Thermal conductivity is isotropic (equation (13)). The
convective exchange (qcon) is assumed to be, at every point
of the lateral surfaces, ∂Ω1l and ∂Ωl2, proportional to the difference between the temperature and the temperature of the
environment (Troom) (equation (14)). An important point is
the choice of the convection coefficients. The convection
coefficient of the FBG, h2, is set to the classical value for
silica glass in air (table 1). For the polymer fiber, a higher
value, h1, is selected because the water content in PEDOT/
PSS is relatively high and is progressively released during
the heating process [5, 18]. This can then largely modify the
moisture content in the vicinity of the surface of the polymer
fiber, which classically yields to higher convection coefficients [19, 20].
The radiative flux, qrad, on each lateral surface is decribed
by equation (15). In details:
•Electrical equilibrium equations:
∇ ⋅ J = 0,
∀ M ∈ Ω1
(5)
J ⋅ n = 0,
∀ M ∈ ∂Ω1l
(6)
•Electrical constitutive equations:
J = σ1E ,
∀ M ∈ Ω1
(7)
Thermal behavior and thermal transfer. The polymer fiber and
the FBG are both initially at room temperature (Troom) (equation (8)). The thermal flux, Φ, is classicially defined as the
gradient of the temperature scalar function (equation (9)).
A classical internal heat transfer equation is assumed
(equation (10)). Qi is the internal heat source density (i = 1
or 2). The start and end cross sections are thermally insulated
(equation (12)). The lateral surfaces of the polymer fiber, ∂Ω1l
and of the FBG, ∂Ωl2, can exchange heat (equation (11)) by
radiation (qrad) or by convection with their environment (qcon).
•Each surface receives an inward flux, (Gim + Giam ), modulated by the absortivity of the continuum, αi. Gim is the
mutual boundary-to-boundary irradiation. Giam is the irradiation received from the environment, which is assumed
to behave as a black body. As such, Giam can be defined as:
•Thermal potential equations
T (t = 0, M ) = Troom,
∀ M∈Ω
(8)
4
Giam = F amσSBTroom
(16)
Φ = −∇T ,
∀ M∈Ω
(9)
where σSB is the Stefan–Boltzmann constant
(σSB = 5.670 400 · 10−8 W.m−2.T−4). Fam is the ambient
view factor whose value is equal to the fraction of the
field of view that is not covered by other boundaries
(0 ⩽ Fam ⩽ 1 must hold at all points). Fam is a geometrical
quantity estimated by the finite-element package based
on the model definition.
•Thermal equilibrium equations
∂T
ρi Ci
= −∇ ⋅ q + Qi,
∀ M ∈ Ωi, i ∈ [1, 2]
(10)
∂t
− q ⋅ n = q rad + q con,
∀ M ∈ ∂Ωil , i ∈ [1, 2]
(11)
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Figure 6. (a) Experimental and modeling results of different distances at 28 V. (b) Experimental and modeling results of different voltages
at a distance of 100 μm.
•Each surface loses an outward flux, (σSBT4), assuming the
Stefan–Boltzmann law, which is modulated by the emissivity of the continuum, εi.
Figure 6(a) compares the experimental and modeling
results at different distances from 100 to 6000 μm with a
fixed applied voltage of 28 V. Figure 6(b) compares experimental and modeling results at different voltages from 0 V
to 28 V with a fixed distance of 100 μm. We observe that
the experimental measurements and more importantly, their
changes with distance and voltage, are well predicted by
the model without introducing numerous phenomenological
parameters. The fact that the change with distance is well
predicted demonstrates that the introduced heat transfer
mechanisms are correct and that the model can reliably
reconstruct quantities of interest that are useful for design
purposes.
To simplify the process, each continuum (either the polymer fiber or the optical fiber) is assumed to behave as a grey
body with equal absortivity and emissivity (αi = εi) [21, 22].
Heat source. The coupling between the electrical and thermal
behaviors is generated by the Joule effect that produces the
body heat source in the polymer fiber. As such, Q1 is defined
by equation (17). Of course, no heat source is assumed in the
FBG so that Q2 is taken to be equal to zero.
Q1 = E ⋅ J , ∀ M ∈ Ω1
(17)
Both transient and steady-state models have been developped.
Because the stabilization of the measured temperature is very
quick (figure 3), we prefer to rely only on the steady-state measurements. Then, the above set of equations can be simplified
by assuming it is independent of time. A stationary solver is
(
∂T
used by assuming that terms ρi Ci ∂t
5. Conclusion
Temperature measurements have been conducted at the
micron scale to probe changes in temperature of conductive
polymer fibers when electrically loaded. Such fragile fibers
can be probed only by non-contact measurement systems.
The ability and efficiency of FBGs to supply such measurement has been demonstrated in this framework. This is a step
toward better understanding of the response of such fibers and
their use in heating devices.
A key point is that unreliable heat transfer mechanisms
have been carefully removed. It was possible to simulate the
whole sensing configuration without extensive calibration or
assumptions in the modeling part. We demonstrated that a
model directly based on both radiation and conduction that
utilizes the classical material parameters that characterize
involved materials provides very pertinent results. This model
can now be used to extract, depending on the information
needed for each application, any quantity of interest that is not
directly measured in the experiments such as the temperature
of the polymer fiber, the heat flux dissipated by the polymer
fiber and the relative fractions of the radiated and convective
heat flux. Future work will focus on the optimization of such
conducting fibers that is possible thanks to the accuracy of this
measurement technique.
)) in equation (10) vanish.
This choice leads to a more robust model as it reduces the
number of material parameters to be identified (knowing that
any mistake in the material parameters introduces errors in
the reconstruction of the measured temperature of the polymer
fiber). A transient model would also need to characterize the
heat capacity, Ci and the density, ρi, for both domains Ω1 and
Ω2. These parameters are not needed when solving the steadystate equations.
All physical parameters used for the simulation are listed
in table 1. These are either very classical values for glass or
have been identified in previous publications about conductive
fibers [5].
4.3. Modeling results and comparison with experiments
The experimental results presented in figures 2 and 3 are simulated by varying the applied voltage from 0 to 28 V and the
distance, l, between the polymer fiber and the FBG from 100
to 6000 μm.
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Acknowledgments
AQ2
intensified CCD camera and frame integration Meas. Sci.
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Research reported in this publication was supported by K
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Authors are grateful to KAUST for its continuous support.
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