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Sensors and Actuators A 189 (2013) 195–203 Contents lists available at SciVerse ScienceDirect Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna Fiber Bragg Grating sensors to measure the coefficient of thermal expansion of polymers at cryogenic temperatures Marco Esposito a,h , Salvatore Buontempo a,f , Angelo Petriccione b , Mauro Zarrelli b , Giovanni Breglio c,f , Andrea Saccomanno c , Zoltan Szillasi d,f , Alajos Makovec e,f , Andrea Cusano g,f , Antonella Chiuchiolo g,f , Marta Bajko h,f , Michele Giordano b,f,∗ a INFN – National Institute of Nuclear Physics, Sez.NA, Italy CNR-IMCB – Institute for Composites and Biomedical Materials, National Research Council, Italy c DIBET – University of Napoli Federico II, Italy d ATOMKI – Institute of Nuclear Research of the Hungarian Academy of Science, Hungary e University of Debrecen, Hungary f CERN – European Organization for Nuclear Research, Switzerland g Engineering Department – University of Sannio-Benevento, Italy h DSF – Physical Sciences Department, University of Naples Federico II, Italy b a r t i c l e i n f o Article history: Received 3 May 2012 Received in revised form 3 September 2012 Accepted 14 September 2012 Available online 25 September 2012 Keywords: Thermal expansion Cryogenic temperature Fiber optic sensor FBG Epoxy PMMA a b s t r a c t One of the fundamental advantages in the employment of the Fiber Bragg Grating (FBG) sensors lies in their capability to allow measurements in extreme environmental conditions with also very high immunity toward external electromagnetic interference factors. The behavior of a polymer-coated FBG sensor, tested in cryogenic conditions at the laboratories of the European Organization for the Nuclear Research (CERN) in Geneva, has been analyzed and will be discussed in this paper. Magnets used in the Large Hadron Collider (LHC) for the High Energy Physics Researches at CERN need in fact extreme cooling conditions to preserve the internal superconductivity highly crucial for their performances. The magnets, built with NbTi based superconductors, are cooled with liquid helium and they operate at 1.9 K. The aim of the present work is to estimate the thermal expansion coefficient of two polymers based on epoxy and methacrylate (PMMA) used as coating of FBGs, in the temperature range from 4 K to 300 K and to check their suitability for the use in temperature monitoring of the superconducting magnets. A standard numerical derivative method has been employed to estimate thermal expansion coefficients; moreover the correlated fluctuation analysis (CFA) based procedure is proposed, as a reliable alternative, to overcome numerical derivative drawbacks at very low temperatures within the range of 4–20 K. The calculated values of thermal expansion coefficient for both systems are in agreement with literature data on similar material. © 2012 Elsevier B.V. All rights reserved. 1. Introduction The measure of the linear thermal expansion coefficient (CTE) of a material is generally obtained by the experimental data relative to the strain or length changes due to the temperature variations. In fact, it is well known that this material property is defined as the derivative of the free thermal strain in respect to the temperature. There are many different kinds of sensors which can be used to measure thermal strain or equivalently material elongation, such as resistive strain gauges sensors, capacitive strain gauges sensors, laser interferometers, optical sensors, linear variable ∗ Corresponding author at: CNR-IMCB – Institute for Composites and Biomedical Materials, National Research Council, Italy. E-mail address: [email protected] (M. Giordano). 0924-4247/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sna.2012.09.016 differential transformers (LVDT). Many of these sensors have found applications also in cryogenic conditions, as the resistive strain gauges [1–4], the LVDT [5] or the capacitance dilatometers, this latter based on the capacitance changes due to the distance variations between armatures. For example, Escher [6], by using an highly sensitive capacitance dilatometer, has obtained CTE values from 0.12·10−6 K−1 (at 9.8 K) to 71.9, 68.4 and 61.9·10−6 K−1 at 278 K, depending on the cross-link densities of the examined epoxy system. Schwarz [7], by an inductive dilatometer, has found the CTE in cryogenic conditions for both an epoxy (2.9·10−6 K−1 at 16.6 K, 90.6·10−6 K−1 at 289 K) and a PMMA (2.0·10−6 K−1 at 12.2 K, 61.4·10−6 K−1 at 276.9 K); other studies on the CTE of epoxies with different ZrW2 O8 filler content were also performed by Chu et al. [1], employing resistive strain gauge sensors. The aim of this work is the evaluation of the thermal expansion coefficient within the temperature range from 4 K to 300 K, 196 M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203 for two polymeric materials (i.e. an epoxy and a PMMA) by using coated FBG sensors. In this way, the suitability of the epoxy and the PMMA for use in cryogenic sensors has been also checked. The FBG sensors have several and well-known advantages: compactness, intrinsic multiplexing, lower cost of the devices for the data acquisition, noise immunity (especially with respect to the electromagnetic fields), low attenuation of the optic signal; but free FBG sensors also present very low sensitivity to the temperature in cryo temperature conditions. Epoxy and PMMA have been chosen and preferred to other coating materials not only for their large thermal expansion coefficients but mainly for their excellent adhesion to the surface of the fiber which can assure an optimal stress distribution at the fiber-coating interface. Many authors have studied the FBG sensor behavior in cryogenic condition, mainly for strain, temperature and structural health monitoring. Rajinikumar et al. [8] have evaluated the physical properties influencing the Bragg response (thermo-optic coefficient, photo-elastic coefficient, glass thermal expansion coefficient) as function of temperature in the wide range 4–300 K. In his work FBGs were tested at cryogenic conditions and coated with metal materials to enhance the sensor sensitivity at low temperature. The calculated values of the sensitivity resulted anyway lower than the sensitivity achievable through polymer coating due the difference between the CTE of the tested metals and the CTE of an epoxy or PMMA. Mizunami et al. [9] measured at low temperature the temperature sensitivity of FBG sensors fixed on a Teflon substrate, which have showed a higher sensitivity compared to other substrate materials. It was found that the temperature sensitivity was even higher than the sensitivity achievable by using a PMMA substrate; however the main inconvenience relies on the epoxy adhesive layer required to fix the FBG to the Teflon substrate. James et al. [10] evaluated the temperature sensitivity of the nude FBGs down to 2.2 K. Habisreuther et al. [11] analyzed instead the response at cryogenic temperatures of Ormocer (an hybrid polymer material synthesized by a sol–gel process) coated FBG sensors: at 10 K, the thermal expansion coefficient for the Ormocer coated fiber resulted 1.5·10−6 K−1 . Tanaka et al. [12] tested FGB sensors at cryogenic conditions under high magnetic fields confirming the magnetic field immunity. Latka et al. [13] showed the negligibility of the thermo-optic and magnetooptic effects in cryogenic environments for FBG strain sensors employed for the structural health monitoring of superconductors when subjected to significant forces generated by strong magnetic fields. The present paper has been organized as follows. The onedimensional thermo-mechanical model of coated FBG has been illustrated in Section 2 to present the governing equations. The samples manufacturing and the experimental set up have been detailed in Sections 3 and 4. Raw data from thermal cycling have been presented in Section 5. The CFA method has been introduced in Section 6, evaluating the thermal expansion coefficients within the range 4–300 K. Main results regarding the effectiveness of the coated FBG as a sensor for the evaluation of the thermal expansion coefficient of the coating material have been presented in Section 7. 2. Coated Fiber Bragg Grating (FBG) The structure of the FBG is formed by a periodic refractive index modulation within the fiber core, which results in a series of grating planes formed along the fiber axis. If the Bragg condition is met, light signal is coupled into the device and reflected by each of the grating planes to form a reflected signal substantially characterized by a wavelength commonly known as the Bragg wavelength (). The Bragg wavelength of a FBG is dependent on the effective refractive index of the fiber core (n) and the period of the grating plane () and can be expressed by the well-known equation [8]: = 2n (1) Any strain variation, dε = d/ or temperature perturbation, dT, experienced by the FBG results in a shift in Bragg wavelength, which is given by [9]: d = (1 − pe )dε + dT (2) In Eq. (2) the photo elastic constant is pe = −(∂n/n∂ε) ≈ 0.23 [8] and the thermo optic coefficient is = ∂n/n∂T ≈ 8 ppm/K for silica at room temperature [8]. Detailing the mechanical constraints acting on the fiber optic, it is possible to evaluate the effective deformation experienced by the FBG sensor. As an example, in the case of free FBG subjected to a temperature variation dT the deformation of the fiber is determined by the thermal expansion coefficient of the optical fiber constituent material, ˛glass : dε = ˛glass dT (3) and the shift is obtained from Eq. (2): d = [(1 − pe )˛glass + ]dT (4) In the case of a temperature variation dT applied to the coating (having radius R, Young modulus Ec and coefficient of thermal expansion ˛c ), a difference in tension with respect to the fiber (having radius r, Young modulus Eglass and coefficient of thermal expansion ˛glass ) is generated due to the thermal expansion coefficient mismatch between the different materials. The balancing of the resulting thermal forces along the fiber axis allows the determination of the common deformation of the coating and the fiber, i.e. dεFBG = dεcoating = dε and, thus, the evaluation of the effective thermal expansion coefficient of the coated fiber system: dε = ˛coated dT FBG = ˛c Hc + ˛glass Hglass (5) Hc + Hglass where H is the longitudinal stiffness, respectively of the coating, Hc = (R2 − r2 )Ecoating , and glass, Hglass = r2 Eglass . The model of the coated FBG subjected to the only thermal variation dT is then derived: d = (1 − pe ) ˛c Hc + ˛glass Hglass Hc + Hglass + dT (6) The approximation of considering constant the properties of different materials with temperature leads to a description of the coated FBG behavior with respect to the temperature starting from a reference status, i.e. (T0 , 0 ), according to the following expression: ln 0 = (1 − pe ) ˛c Hc + ˛glass Hglass Hc + Hglass + (T − T0 ) (7) 3. Samples preparation Fiber Bragg Gratings have been provided by Welltech Instrument Company Limited (Hong Kong) with the following specifications: grating length 10 mm; Bragg wavelength tolerance ±0.5 nm; reflectivity >90%; FWHM (full width at half maximum of the spectrum) <0.3 nm. 3.1. Coating materials Polymeric coatings around FBGs were produced using two classes of polymeric precursors: epoxy and acrylic. For the epoxy based polymer, precursors are DGEBA high purity liquids with M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203 197 which facilitates the casting process but, conversely, it allows air inclusions during premixing operation. To overcome this inconvenience, mixing stage was performed by using a planetary mixer under vacuum (10 kPa abs) at room temperature. For the epoxy based system, all components were premixed in the right proportion (100:14, according to supplier data sheet) to obtain a reactive mixture and, then, degassed to prevent gas entrapment in the final product. After degassing the casting was performed very quickly. The curing profile was then divided in two steps: a preliminary curing stage at room temperature for 12 h and a post-curing stage at 100 ◦ C for 4 h. For the acrylic systems, the premixing stage was slightly different, due to both the presence of the solid component to dissolve in the liquid one and the long lasting degassing stage not suitable for such a quick reactive system. For these reasons, the component mixing was a very critical operation; however, by adding the solid component into the liquid and mixing very carefully it was found that air entrapment sensibly reduce allowing to abbreviate the degassing stage. For the acrylic system the first polymerization stage was very fast, as gelation occurred in a few minutes and solidification in less than 1 h. Post curing stage was the same as for epoxy system. Fig. 1. Mould set up for manufacturing of polymer coating on FBG fiber. an EEW of 170–175, multi-functional aliphatic amine as hardener and a tertiary amine as catalyst. The employed epoxy system was supplied by Elantas Camattini (Italy) under the label, EC-170 + IG 824-K24. PMMA precursors were arranged in a two-component system: a very fine PMMA powder mixed with a peroxide catalyst and a liquid mixture, characterized by the presence of methylmethacrylate monomers, crosslinking agent and initiator. The acrylic system was supplied by Heraeus (Paladur). The powder and the liquid mixture were premixed in the right proportion and then quickly used due to its rapid reaction time (within a few minutes). 3.2. Coating methods Epoxy based and acrylic polymers were obtained starting from its liquid precursors by in situ polymerization, and then reactive casting was employed as most suitable manufacturing process to realize the coated FBG samples. This solution allows producing an interface between polymeric material and fiber cladding, which ensures an efficient strain transfer from the polymer system to fiber. Polymer precursors are liquid and highly compatible with silica, which represents the main constituent of the fiber cladding, and thus a good surface wetting could be achieved before polymerization. After the fiber was cleaned with isopropylic alcohol, the polymeric material was casted around the cladding section near the Bragg grating. The final nominal dimensions of coating of the fiber containing the Bragg grating were 2.5 mm height, 5.0 mm width, and 25.0 mm length. To carry out the manufacturing process by reactive casting, an optimized mould was realized (the inferior half mould is reported in Fig. 1). In the manufacturing setup, a constrain system was accurately designed in order to induce pre-alignment and pre-stress to the FBG sensor and at the same time to control the chemical shrinkage due to the polymerization reaction during the first curing stage. An extra post-curing stage was considered for both reactive systems by using a constrain-free configuration; this was to allow the natural rearrangement of the system and to reduce the local interfacial stresses between polymer coating and cladding near the FBG grating. For each polymeric coating, four different specimens were prepared at once, in order to obtain fully comparable items. Both systems exhibit a very low viscosity at room temperature, 4. Experimental set up The samples were positioned in a dedicated sample holder and then inserted into the cryostat as shown in Fig. 2(a). The FBG sensor holder consists in a small copper box assuring a good thermal stability among the FBG fibers and the reference temperature sensors. Two temperature sensors, one of a type CERNOXTM and another thermo resistive Platinum thermocouple (PT100), previously calibrated, where used to monitor the ambient temperature. The cooling down of the system was performed by using liquid helium pumped into the cryostat until the final temperature reached 4.2 K. Due to this pumping operation, the cool-down turned to be too rapid and later analysis proved that the thermal equilibrium could not be reached within the sample holder. In contrary, the warmup could take sufficiently long time, since the liquid helium was allowed to boil away in the cryostat. In order to control the warm-up, resistors were placed at the bottom of the sample holder; however, since no further helium was pumped into the holder, this setup did not allowed a suitable temperature stabilization and thus only a slow and poor controlled warming-up stage could be achieved. The two temperature sensors were connected electrically in series and powered by a Keithley 2400 source meter operating in a constant current source mode. Voltage readouts were performed by a Keithley 2000 and a Keithley 2001 precision DMM devices. In order to reduce the bias on the measured temperature associated to the Seebeck-effect, voltage drops on both temperature sensors were read out at different polarities and the voltage drop readouts were averaged to compute temperature values. This temperature value then served as an input for the proportional warm-up control. The resistors were connected to a TTi TSX3510 power supply. All three Keithleys and the TTi devices were connected to a GPIB bus that controlled by customized software through a Prologix GPIB-ethernet controller. A schematic diagram showing all the instruments used in the experimental set up for the data acquisition is reported in Fig. 2(b), where the optical measurement (a), the readout of the reference temperature sensors (b) and the heater with the PR 4116 Universal transmitter – DSS (c) are drawn. Four different FBG sensors were located in the sample holder. In order to increase the reliability of the sensors, two epoxy coated FBGs were spliced together and both ends were brought out from the cryostat. The same setup was built for the PMMA coated sensors. 198 M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203 Fig. 2. (a) Experimental setup. (b) Schematic drawing of the DAQ: the optical measurement (a), the readout of the reference temperature sensors (b) and the heater with the PR 4116 Universal transmitter – DSS (c). This configuration, allowed the readout on all sensors from both sides, so data were assured to be recorded even in case of optic fiber break. One end of the epoxy sensors array and one end of the PMMA sensors array were connected to a Micronoptics sm125 interrogator. Fig. 3 shows the reflected spectra of the sensors at room temperature. 5. Experimental results Data acquisition has been performed for several cooling down and warm up cycles. The experimental dataset consists of two types of signal: voltage from the thermal resistive sensors (PT100 and CERNOXTM ) and central reflected wavelength signals from FBG sensors. The experimental data from the cryogenic test-bench was stored in a Network-attached Storage unit (NAS) situate at CERN and off-line processed. Fig. 4(a) shows the temporal evolution of the Bragg wavelength for all the FBG sensors. The letter A represents the epoxy-coated sensor while the letter B represents the PMMAcoated sensor. The two digits indicate the sensors reference Bragg wavelength in nanometers at room temperature (e.g. 62 stands for 1562 nm). Fig. 4(b) shows the time evolution of the temperature, as measured by the CERNOXTM sensor. In total 16 different warmup and 16 cool-down steps were performed. Raw data related to the Bragg wavelength and temperature evolution, as reported in Fig. 4, were computed according to Eq. (7) normalizing the sensor responses to the room temperature and to the reference Bragg wavelength. Fig. 5 reports the normalized sensors output as a function of the temperature (only warm up test were analyzed). Epoxy-coated sensors present in general a smaller change of the Bragg wavelength compared to the PMMA-coated sensors within the range 4–300 K. Fig. 6 shows the normalized sensors outputs in the low temperature range. Fig. 6(a) and (b) reports the normalized sensors outputs, relative to the epoxy and PMMA coated sensors, respectively. All the thermal cycles are reported. Fig. 6(c) and (d) shows the values averaged among all the warming up cycles. The sensitivity of the FBG sensors decreases at low temperatures for both the polymers. 6. Evaluation of the thermal expansion coefficient 6.1. Methodology The thermal expansion coefficient of the coating system, ˛coating (T), can be easily found starting from Eq. (6): ˛coating (T ) = Hglass + Hc 1 d Hc (1 − pe ) dT − − Hglass Hc ˛glass (8) Fig. 3. Spectral distribution of the reflected light from the FBG sensors on room temperature. Blue line refers to epoxy coated FBGs array. Black line refers to PMMA coated FBGs array. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203 199 Fig. 4. (a) Bragg wavelength of the FBG sensors vs. time. The blue and the red lines represent the epoxy-coated FBGs (A55 and A65), the green and the black line represents the PMMA-coated FBGs (B52 and B62). (b) Reference sensor temperature vs. time. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) The thermal expansion coefficient of the coating material is not only dependent on the thermo and elasto optical properties of the FBG sensor but also on thermo-mechanical properties of the fiber itself and its coating material. Therefore the more accurate analysis of the terms in Eq. (8) is needed. At room temperature (RT), 300 K, the Young modulus of the glass and the polymers, are Eglass = 77 GPa and Ecoating = 3 GPa, respectively, according to Takeda [14]. These values lead to the following relative stiffness for the tested sensors: Hglass /Hc = 0.015 @ RT. On the other hand, at very low temperature the polymers Young modulus, Ecoating , increases more than the Young modulus of the silica, Eglass , with a further arising of the relative stiffness of coating. In particular, at cryo temperature (CT), 4 K, the Young modulus of the glass and the polymers are respectively Eglass = 83 GPa, Ecoating = 9 GPa [14] and thus relative stiffness is Hglass /Hc = 0.005 @ CT. Furthermore at RT, according to Rajinikumar et al. [8], James et al. [10] and Habisreuther et al. [11], the physical properties of the FBG silica are: ˛glass = 2.6 ppm/K, = 8.59 ppm/K, pe ∼ = 0.23, while at low temperatures (4 K), the physical properties of the FBG silica are: ˛glass = 1.0 ppm/K, = 1.02 ppm/K, pe ∼ = 0.23 [8,10,11]. Table 1 summarizes all the properties at cryo and room temperature of the fiber and the coating. Based on these values, the following engineering assumptions have been set: Hglass /Hc ∼ = 0 and pe (T) ∼ = 0.23 independently of the temperature. Substituting in Eqs. (5) and (6), these assumptions give back: k(T ) ≡ d ln(/u ) = ˛coating (T )(1 − pe ) + (T ) dT (9) (with u = 1 nm), or equivalently: ˛coating (T ) = 1 (k(T ) − (T )) 1 − pe (10) Fig. 5. Normalization to room temperature and reference Bragg wavelength of FBG sensors outputs vs. temperature (only warm-ups). Solid lines are averaged over different warm ups, dotted lines are individual warm-ups outputs. 200 M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203 Fig. 6. Zoom plot for normalized sensor outputs from 4 K to 15 K. (a) Epoxy-coated sensors. All the warm-ups. (b) PMMA-coated sensors. All the warm-ups. (c) Epoxy-coated sensors. Average sensitivity curves. (d) PMMA-coated sensors. Average sensitivity curves. Table 1 List of all the properties at cryo and room temperature of fiber and coating. Temperature (K) Eglass (GPa) Ecoating (GPa) ˛glass (ppm/K) (ppm/K) pe 4 300 83 77 9 3 1.0 2.6 1.02 8.59 0.23 0.2 The evaluation of the thermal expansion coefficient of the coating material can be obtained by the estimation of the temperature derivative of the logarithm of sensor outputs, (T). A standard procedure to perform numerical temperature derivative has been applied to the outputs of FBG and temperature sensors. The numerical derivative method needs a continuous monotonic temperature variation to reconstruct the function and thereof its temperature derivative. Due to the poor temperature control in very low temperature range, the numerical derivative algorithm inevitably fails. An alternative method should be implemented to overcome such drawback. 6.2. Correlated fluctuation analysis (CFA) u (t) = ki · T (t) + c (11) where i indicates the i-th interval and ki is provided by Eq. (9). Under this hypothesis, for the i-th set of points, for the expected value E{} and variance Var{}, it results: E ln u i = ki E{T }i + c u i = ki2 · Var{T }i (13) or, equivalently: ki = ln(/u )i Ti (14) where ln(/u ) and T are, respectively, the logarithm of Bragg wavelength shift and temperature standard deviations relative to the i-th interval. The time duration of each sub interval i, was chosen such as the corresponding temperature variation within the sub-interval was less than 0.3 K. 7. Results and discussion Hereafter, an alternative methodology is proposed to evaluate the CTE based on correlated fluctuation analysis (CFA) of the two time signals, namely the Bragg wavelength shift, ln(), and temperature, T. The fluctuation analysis has been performed by dividing the temperature history in short temporal intervals, I, in which the temperature is almost constant. In these conditions the relationship between temperature T and ln(/u ) can be considered linear, thus it can be written: ln Var ln (12) The thermal expansion coefficients of coating polymers were obtained by computing both methods, i.e. by evaluating the temperature derivative and by performing the CFA based procedure. Fig. 7 shows the estimated CTE values (averaged over the all warm-ups) accounting the sensor raw data (different for coating material employed and reference Bragg wavelength) according to the numerical temperature derivative method without considering the thermo-optic effect. Analysis performed on different FBG sensors coated by the same material gives CTE values substantially identical. Similar results have been obtained with the fluctuation analysis procedure. Fig. 8(a) and (b) reports respectively, for each of the indicated material and employed algorithm, the mean and the standard deviation. These latter values were computed by taking into account all curves (one for each warm-up step from 4 to 300 K) of the thermal expansion coefficient as function of the temperature achieved M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203 201 Fig. 7. Thermal expansion coefficient obtained through numeric derivative from sensors with different reference Bragg wavelength data averaged on all the warmups. Fig. 9. Thermal expansion coefficient (zoom at low temperatures). without considering the thermo-optic effect. On the same graph, literature data for similar material systems were reported as dotted points [15]. Good agreement was found between the two methods for the estimation of the thermal expansion coefficient in the temperature range between 50 and 300 K, while remarkable discrepancies were found in the very low temperature range between 4 and 50 K. Estimated values of the thermal expansion coefficients for epoxy and PMMA systems used in this study have been compared with literature data regarding similar material systems [15] showing an excellent agreement. Very interestingly, the numerical derivative method provides a worse estimation of the CTE values within the low temperature range. In the range 4–20 K the standard deviations are of the same order of magnitude of the estimated CTE values. This effect is probably due to the fact that numerical derivative method needs a continuous monotonically temperature variation to reconstruct the function and thereof its temperature derivative, while fluctuation analysis do not require this constrained conditions. In particular, correlated fluctuation analysis method has been proposed, in this work, to overcome limitations arising from a not “ideal” temperature and Bragg wavelength signal synchronicity (from diffusive time lags and analog signals synchronization) and a “not monotonic” temperature variations (due to the not perfectly controlled temperature ramping). It is worth noting that correlated fluctuation analysis is well performing also in the temperature range where a numerical derivative method results ineffective. Fig. 9 shows a close up of the thermal expansion coefficients in the low temperature range 4–50 K. In this range the two methods provide significant difference in the thermal expansion coefficients estimates. Most relevant is the concavity of the function ˛coating (T). CFA analysis registers a level off of the thermal expansion coefficients just below 10 K, while numerical derivative method suggests a sharp decrease of the thermal expansion coefficient within the same range. In particular, CFA analysis suggests a strong non linearity within the range 4–10 K. In this range, defined as Debye temperature range, maxima of the thermal expansion coefficient have been already reported [15]. The 4–10 K range will be matter of further and dedicated experimental investigations. Finally, Fig. 10 shows thermal expansion coefficient predictions obtained by using Rajinikumar et al. [8] measurements of the temperature dependent thermo-optic coefficient. As a matter of fact, neglecting the thermo optic coefficient will introduce a maximum 20% overestimation of the CTE values, as showed in Fig. 10 by the ratio between the Fig. 8. (a) Thermal expansion coefficients of epoxy and PMMA (averaged on all the warm-ups) without considering thermo-optic coefficient. (b) Standard deviation of the thermal expansion coefficient for the epoxy and the PMMA thermo-optic coefficient without considering thermo-optic coefficient. 202 M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203 correlated analysis of the FBGs outputs and the temperature sensors to evaluate the thermal expansion coefficient extending the data interpretation in the Debye temperature range (4–10 K) and (c) the suitability of the epoxy and PMMA coatings to be employed for cryogenic temperature monitoring, since they can guarantee adequate level of the sensitivity to the sensor as assured by their thermal expansion coefficient values in the wide range 4–300 K. References Fig. 10. Ratio between the thermal expansion coefficients obtained considering and not the thermo-optic effect. CTE values obtained considering thermo optic effect and those achieved without taking into account this effect. 8. Conclusions FBGs have been used to evaluate the thermal expansion coefficients of two coating polymeric materials: namely, an epoxy and a PMMA resin. In general, the response to a temperature change of a coated FBG depends on the physical properties of the fiber (thermo-mechanical, thermo-optical and elasto-optic properties), on the thermo-mechanical properties of the coating material and on the geometry of the assembly, i.e. fiber radius and the coating thickness. Such a complex interplay between these factors makes very complex the response of the coated FBG sensor to the temperature variations. The potential application of this sensor system for the evaluation of the thermal expansion coefficient of the coating material requires an appropriate design. In particular, the thickness of the coating could be chosen in order to set the stiffness of the coating in respect to that of the sensor. In fact, when Hc Hglass , the temperature response of the coated FBG is dominated by the thermal expansion coefficient of the coating. Based on this engineering approximation, the thermal expansion coefficients of an epoxy resin and a PMMA have been evaluated accounting for both the elasto-optic coefficient and thermo-optic coefficient of the optical fiber in a wide range of temperature, i.e. 4–300 K. Results for the two polymers have been compared with literature data for similar polymeric systems resulting in an excellent agreement. Thermal expansion coefficient requires the evaluation of sensor output variation due to the temperature variation. The standard numerical temperature derivative method suffers of serious drawbacks due to the phase mismatch between the two experimental signals, mostly in the very low temperature range where temperature control is difficult. To overcome such problems a method based on the analysis of the fluctuations of the two signals has been proposed such as a correlated fluctuation analysis based procedure. Comparison between the direct calculation from the sensors output of the numerical temperature derivative and the CFA method have showed that thermal expansion coefficients evaluation are consistent and in the very low temperature range, the so-called Debye temperature range (4–10 K), the CFA produces better estimates. Main results of the present work are: (a) the demonstration of the efficiency of FBG sensor in the measurement of the coating material thermal expansion coefficient down to cryogenic temperatures, (b) the proposal of a methodology based on the [1] X. Chu, R. Huang, H. Yang, Z. Wu, J. Lu, Y. Zhou, L. Li, The cryogenic thermal expansion and mechanical properties of plasma modified ZrW2 O8 reinforced epoxy, Materials Science and Engineering A 528 (2011) 3367–3374. [2] P. Ifju, D. Myers, W. Schulz, Residual stress and thermal expansion of graphite epoxy laminates subjected to cryogenic temperatures, Composites Science and Technology 66 (2006) 2449–2455. [3] J.B. 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Willsch, Fiber-optic Bragg gratings as magnetic field-insensitive strain sensors for the surveillance of cryogenic devices, Cryogenics 49 (2009) 490–496. [14] T. Takeda, Y. Shindo, F. Narita, Three-dimensional thermoelastic analysis of cracked plain weave glass/epoxy composites at cryogenic temperatures, Composites Science and Technology 64 (2004) 2353–2362. [15] G. Hartwing, in: G. Hartwig (Ed.), Polymer Properties at Room and Cryogenic Temperatures, Plenum Publishing Corporation, New York, 1994. Biographies Marco Esposito got the Master degree in Mechanical Engineering in 2006 at the University Federico II of Naples – Italy. From 2007 to 2010 he collaborated with the Institute for Composite and Biomedical Materials of the National Research Council, CNR – IMCB Italy, in the fields of structural and fluid dynamic analysis on components in composite materials. After the 2nd Level Master degree in Automotive Engineering got in 2010, he started in 2011 the PhD in Fundamental and Applied Physic. Current fields of interest: simulations/numerical analysis, optical sensors, high energy physic. Salvatore Buontempo got the degree in Electronic Engineering in Naples University in 1989 with an experimental thesis at CERN. He specialized in Particle Physics Detectors and he got a permanent position as researched in INFN Naples in 1993. In 2000 he got the level of INFN Senior Researcher and INFN Research Director in 2004. In 2001-2002 he was CERN Scientific Associate. In 2003-2005 he was CERN Project Associate. In 1991-1998 he participated in CHORUS experiment at CERN as Project Manager of Electromagnetic Calorimeter. In 1998-2008 he participated in OPERA experiment in CERN and LNGS as Technical Coordinator. Since 2008 he is Technical Coordinator of the RPC detector in CMS Experiment at CERN and member of CMS Central Technical Coordination Office. Fields of Interest: Construction and R&D on Particle Physics Detectors, their Instrumentation and Technology Transfer. Angelo Petriccione graduated in Materials Engineering and received the Ph.D. degree in Materials and Structures Engineering from the University of Naples “Federico II”, Naples, Italy, respectively in 2006 and 2011. He is currently working as Post-doc fellow at Institute for Composite and Biomedical Materials of the Italian National Research Council (IMCB-CNR). His current research interests include the study of carbon nanoparticles composites and advanced thermoplastic PMCs made by rective processing. M. Esposito et al. / Sensors and Actuators A 189 (2013) 195–203 Mauro Zarrelli is permanent researcher at Institute for Composite and Biomedical Materials (IMCB) of the National Research Council (CNR). He obtained an Undergraduate Degree in Materials Engineering at University of Naples “Federico II” in 1998. He defended his PhD at Cranfield University in 2002 working on novel polymer composite matrix for aerospace application, receiving an AUDI Foundation grant (2001) as young researcher. Major area of expertise are: polymer composite for aerospace application, nano-composites, electrical mechanical and thermal property, degradation and fire behavior, delamination and residual stress, fire resistance. He took part to several EU and National projects and he has published 25 scientific papers, 3 book contributions and more than 40 contributions to international conferences. Giovanni Breglio was born on 1965. He graduated in electronic engineering cum laude at University of Naples Federico II on 1990. On 1994 he took the PhD degree. From 1996 to 2001 he was as Permanent Researcher at Electronic Department at University of Naples. Since 2001 he is Associate Professor at the Faculty of Engineering of Federico II. Since 2006 he is the Coordinator of the Electronic Engineering Courses at the University of Naples Federico II. The actual scientific activities of Giovanni Breglio are manly in the areas of Power Electronic Devices development and characterization, and the design and optimization of optoelectronic devices and Fiber Optic Sensor systems. On these topics he is author or coauthor of more than 150 among journal and proceedings articles. He is owner of six international patents. He contributes as reviewer or TPC component to the most important Journals and Conference of the cited topics. Andrea Saccomanno was born on April 7, 1982 in Benevento, Italy. In 2009 he received the M. S. degree in Telecommunication Engineering from University of Sannio, Italy, defending an experimental thesis on the fabrication of photonic quasicristals. In 2010 he joined the University of Napoli “Federico II” as PhD student. His main research interests are in monitoring system based on Fiber Bragg Grating sensors and Photonic Crystals for sensing applications. Zoltan Szillasi got the MSc in 1996 in Physics at the Kossuth University, Debrecen, Hungary. Between 1999 and 2008 he was an assistant lecturer of the same University (which in the meantime became University of Debrecen). In 2008 he obtained his PhD in Physics. Since then he is an associate researcher of the Institute of Nuclear Physics of the Hungarian Academy of Sciences (ATOMKI) in Debrecen. Since his MSc he have worked on the Charged Higgs Boson search in the L3 experiment at LEP, then he joined the CMS collaboration in 2000 where he participated in the development of the Hardware Muon Barrel Alignment System of which he is presently the project coordinator from the Hungarian side. In 2009 he joined the FOS4CMS collaboration. His principal interests are the measurement development and large scale integration of the measurement technologies. Alajos Makovec got the MSc at the University of Debrecen in 2011 where he continued his work as a PhD student. Presently, he is working on data acquisition and measurement automation. Andrea Cusano was born on May 31, 1971, in Caserta. He received his Master degree cum Laude in Electronic Engineering on November 27, 1998 from University of Naples “Federico II”, Italy and his Ph.D. in “Information Engineering” from the same University. He is actually Associate Professor at the University of Sannio in Benevento. From 1999 his activity is focused in the field of optoelectronic and photonic devices for sensing and telecommunication applications. He was cofounder in 2005 of the spin-off company “OptoSmart S.r.l.” and in 2007 of the spin-off company “MDTech”. He published over 120 papers on prestigious international journals and more than 150 communications in well known international conferences worldwide; he has 4 international patents currently in charge of prestigious industrial companies (Ansaldo STS, Alenia WASS, Optosmart and MdTEch) and more than 10 national patents. He is Editor-in-Chief of the journal Optics & Laser Technology (Elsevier), and associate editor of Sensors and Transducers Journal, Journal of Sensors (Hindawi), The Open Optics Journal (Bentham), The Open Environmental 203 & Biological Monitoring Journal (Bentham) and the International Journal on Smart Sensing and Intelligent Systems. He is also referee of several scientific international journals. He is a member of the technical committee of several international conferences such as IEEE Sensors, ICST, EWSHM, EWOFS. Andrea Cusano was principal investigator and scientific responsible of several national and international research projects. He is coauthor of more than 10 chapters published in international books and invited papers in prestigious scientific international journals. He is coeditor of 2 Special Issues (Special Issue on Optical Fiber Sensors, IEEE Sensors 2008, and Special Issue on “Fiber Optic Chemical and Biochemical Sensors: Perspectives and Challenges approaching the Nano-Era”, Current Analytical Chemistry, Bentham, 2008, and of 3 scientific international books. He is also consultant for big companies of the Finmeccanica group such as Ansaldo STS and Alenia WASS. He has also collaborations with CERN in Geneva where he is working on the development of innovative sensors for high energy physics applications. Antonella Chiuchiolo was born in Benevento on April 1983. In 2006 she obtained the first level degree in Computer Science Engineering at University of Sannio (Benevento). For her thesis about the structural monitoring with fiber optic sensors, she has been working with the Optoelectronic Division of University of Sannio in collaboration with CIRA (The Italian Aerospace Research Centre). Then she started her studies in Automation Engineering at University of Sannio. During her master thesis activities, from January to June 2011, she has been involved with a stage of 5 months at CERN (European Organization for Nuclear Research) in Geneva, in the project devoted to the development of new temperature sensors based on Fiber Bragg Gratings technology. On July 2011 she obtained the master degree with mark 110/110 cum laude and the thesis “Feasibility study of the use of Fiber Optic Sensors in cryogenic environment for superconducting magnets at CERN”. Marta Bajko is MS. Mechanical Engineer from the Technical University of Budapest where she got her degree in 1994. From 1994-1996 she worked in Spain as engineer in the Physics department of the CEDEX Laboratory on superconducting technology. From 1996-today she is employed by CERN where she is presently leading the superconducting magnet test facility after having worked on the design and development of the LHC superconducting magnets <correctors and main dipoles> and having followed as project engineer the production of 1/3 of the main dipoles of the LHC. Current fields of interest: superconducting technology, cryogenics, instrumentation at low temperature for superconductors. Michele Giordano, born in 1968, he received his Master degree cum Laude in Chemical Engineering at the University of Naples “Federico II” in 1992. In the same year he started a Ph.D. course in Materials Engineering. Ph. Doctor in 1995. Up to 1998 he completed the formative track within the Institute for Composite Materials Technology ITMC of the National Research Council CNR. In 1998 he acquired a definite time position as a Researcher at ITMC CNR where he become a Permanent Research in 2001. From 2003 to present he has been selected as a Lecturer at the University of Naples “Federico II” giving the “Composite Materials Technology” course. Since 2005 Senior Scientist at the Institute of Composite and Biomedical Materials IMCB CNR. In 2005 he has also been cofounder of the research spin-off company “OptoSmart”, focused on the development of fiber optic sensor systems. Since 2006 he has designed as the Responsible of the Composite Technology unit of IMCB-CNR coordinating the corporate CNR project “Polymers, composite and nanostructures technologies”. Since 2010 he is adjunct researcher at CERN. In 2007, he has cofounded a new research spin off company, MDTech, acting in the field of optical systems for biomedical applications. In 2011, he has cofounded a new research spin off company, Optoadvance, acting in the field of applications of optical sensors systems in music. Research activities are within the area of engineering and materials science. In particular the main research focuses are nano and macro composite materials, mainly polymer based, including multiscale design and processing of multifunctional composite materials, structural health management systems and thin films engineering for sensing and optoelectronic applications. He is author of more than 120 peer reviewed (ISI indexed) scientific papers and seven book chapters.