Assessment and applications of magnetoelastic resonators as platforms for remote real-time mass detection

D O C T O R A L T H E S I S Assessment and applications of magnetoelastic resonators as platforms for remote real-time mass detection Beatriz Sisniega Soriano Supervisors: Prof. Alfredo García Arribas Prof. Jon Gutiérrez Etxebarria 2025 (cc) 2025 Beatriz Sisniega Soriano (cc by-nc-sa 4.0) Agradecimientos Las primeras personas a las que quiero dar las gracias son mis directores, Alfredo y Jon. En primer lugar, por haberme apadrinado durante estos años, por todo lo que generosamente me habéis enseñado, por haberme iniciado en el mundo de la ciencia y enseñarme a desenvolverme en él, animándome a publicar y dándome la oportunidad de participar en conferencias. También por haber confiado en mí y haberme dado libertad para tomar decisiones y trabajar autónomamente; creo que he aprendido mucho de eso. Quiero agradecer a Jon su labor como intermediario facilitándome recursos, gestiones y contactos (conseguir materiales, cortar muestras, visitar otros laboratorios...), y su ayuda con el papeleo de la tesis. Y a Alfredo, su disposición y su cercanía, gracias por darme siempre los mejores consejos científicos, profesionales y también personales; valoro mucho tu opinión, tu gusto por las cosas bien hechas y tu buen ojo. Por supuesto, también quiero dar las gracias a Roberto Fernández de Luis por su gran ayuda con una parte de esta tesis. Para mí has sido un ejemplo de generosidad y de trabajo. Gracias por tu paciencia, por enseñarme tantas cosas sobre MOFs, por poner a mi disposición todos los equipos, por ayudarme siempre que te lo he pedido y por mostrarme una forma de trabajar que me voy a llevar conmigo. Otra persona a la que quiero agradecer su ayuda es Manu Barandiaran, por lo amable que ha sido siempre y porque siempre que se ha implicado mucho más de lo que era razonable esperar cuando le hemos pedido ayuda. Gracias por compartir conmigo tu saber y tu intuición. También quiero darle las gracias a Jorge Feuchtwanger, que sabe de todo y que me ha ayudado genuinamente con todo tipo de cosas, con el taller, con el diseño y la impresión de piezas, con el montaje de equipos, con dudas científicas, informáticas, o de la vida. Casi cada vez que me lo encuentro, me ayuda con algo. Muchas gracias por tu predisposición a ayudar siempre. I would also like to thank Professor Ong for his warm welcome to his group in the Knight Campus. Thank you for giving me the opportunity to work with you and sharing with me your knowledge and expertise, it has been a pleasure. I also want to mention Will and Jeff, who spent the days teaching me how to work with the cells, and were very kind to me from the very first day. Those months in Oregon were a very good experience both professionally and personally, which I think I will always keep in my mind, thank you guys! También tengo que mencionar a las personas (amigos) que han andado por este camino conmigo, los demás estudiantes de doctorado y compañeros que han pasado por el departamento, Danny, Guille, Nerea, Jon Ander, Carmen, Alain, Ander, Mikel, Andoni, Asier, Eider, Martín, Alba..., y a los doctorandos de arriba (física). Gracias por haber hecho estos años mucho más divertidos. A los que habeis acabado, enhorabuena! Y a los que aún os queda, mucho ánimo! Gracias a mi familia, y a David, que son siempre el mejor apoyo. Por último, gracias al Gobierno Vasco por concederme la beca del Programa Predoctoral de Formación que me ha permitido realizar esta tesis. A la gente del departamento de Electricidad y Electrónica y del Grupo de Magnetismo y Materiales Magnéticos por acogerme. También quiero dar las gracias a la gente de BCMaterials por dejarme usar sus instalaciones, y a los servicios generales de la universidad. Abstract Magnetoelastic Resonance sensors (MER sensors) have attracted the attention of the sensor community over the past decades as they have, besides their sensitivity, versatility and low cost, the potential to operate remotely thanks to their magnetic excitation and detection. MER sensors are based on the mechanical resonance phenomenon that can be excited in ferromagnetic materials (typically amorphous) via their exposition to alternating magnetic fields. This is possible due to the magnetostriction, which is a property of these materials that couples mechanical deformation with magnetization, and allows to excite magnetoelastic waves within them. Specific frequencies of that excitation (matching the dimensions of the material) give rise to the magnetoelastic resonance behavior, which can be magnetically detected. MER sensors developed in recent years are based on the changes of this resonance behavior (and more specifically, of its resonance frequency) related to changes on different external factors affecting the material (as temperature, viscosity, pressure, magnetic field, mass loads…), and their potential is still being explored to find new applications. In particular, their use as mass sensors (response to changes on their mass) is one of their most versatile uses, as the functionalization of their surface with different active materials provides them with adsorption capacities of different nature (which transforms the interaction with the target into a mass change). Magnetoelastic resonators have been used as mass sensors to detect nanoparticles, different gases, bacteria, pH changes...,etc. The present Thesis, focuses on the study of the performance and applicability of these magnetoelastic sensors operating as remote real-time mass sensors. Different strategies to improve the detection of these sensors and the evaluation of some limitations have been studied. Then, the subsequent application to different real-time mass detection experiments have been performed. First, in order to characterize the MER sensors and perform a real- time tracking of the resonance curves, a measurement system based on impedance measurements was developed and controlled with LabVIEW. Then, the numerical fitting of the resonance curves of the sensor to analytical expressions has been evaluated as a post-processing strategy to improve the detection. It was found that the fitting improves significantly the resolution of the sensors, by improving the accuracy in the determination of the main resonance parameters (especially the resonance frequency). On the other hand, the influence that the magnetic relaxation suffered by these materials has on the sensing performance has been investigated. It was found that under the effect of the bias magnetic field, magnetoelastic materials experience a relaxation phenomenon that greatly affects the sensor performance and limits its accuracy, as it causes a time drift of its resonance signal (and resonance frequency). This effect and different approaches to avoid its negative impact (selecting the conditions of the experiment and post-processing the sensing data) have been studied. It was found that the amplitude of the excitation field has a great influence on this relaxation behavior and can significantly reduce its effects. Besides that, it was found that the time-drift of the resonance frequency associated with this phenomenon can be corrected by modeling the relaxation behavior and subtracting its effect. Regarding the application of these MER sensors, first they have been applied to monitor the progress of the precipitation reaction of calcium oxalate crystals (one of the most common minerals that forms calcifications on the urinary tract). A ribbon of a corrosion resistant amorphous ferromagnetic alloy (Fe73Cr5Si10B12) was selected as the resonator material. This magnetoelastic platform was successfully used to monitor in real-time the formation of these salt crystals, allowing to study the quantity of calcium oxalate formed in different conditions and the dynamics of the reaction. In order to obtain a valid mass sensitivity calibration of the sensor, a detailed study of its sensitivity in the experimental conditions was performed. The effect of the surrounding medium and the elastic properties of the coating material (analyte) on the mass sensitivity was analyzed. It was found that the medium, although affects the resonance, does not affect the mass sensitivity. Instead, the coating material’s properties have a significant impact on the mass sensitivity, and should be taken into account when calibrating the sensors. The numerical fitting of the resonance curves and the correction of the relaxation behavior were performed in these precipitation reaction experiments to improve the resolution of the sensor and lower its limit of detection. Finally, the Thesis explores the functionalization of the magnetoelastic platforms with MOF (Metal Organic Framework) active layers, in order to develop wireless humidity sensors. Metal organic frameworks are highly porous materials, built by metallic ions linked by organic molecules. They hold high adsorption capacity values (adsorption per gram of material) and can be designed to absorb specific molecules, so they result in a very promising active material to combine with magnetoelastic detection. Different water-adsorbent MOF materials were synthesized, characterized and integrated onto the MER platforms. The sensors developed with these active layers present good sensitivity, selectivity and competitive response times, resulting in very promising gas sensors based on magnetoelastic detection to monitor in real-time the relative humidity. Besides, MER sensors have proven to be a tool with great potential to characterize the dynamic adsorption capacity of MOFs, and in extension, porous materials. Contents 1 Introduction 1 1.1 Sensors based on magnetoelastic resonance . . . . . . . . 2 1.1.1 Magnetoelasticity . . . . . . . . . . . . . . . . . . . 2 1.1.2 Magnetoelastic resonance . . . . . . . . . . . . . . 4 1.1.3 Effect of mass loading . . . . . . . . . . . . . . . . 8 1.1.4 Quality of the resonance signal . . . . . . . . . . . 11 1.1.5 The ∆Eeffect . . . . . . . . . . . . . . . . . . . . 12 1.1.6 Magnetostrictive material . . . . . . . . . . . . . . 15 1.2 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . 16 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 MER detection instrumentation and data processing 25 2.1 Magnetoelastic resonance detection system . . . . . . . . 27 2.1.1 Induction-based measurement system . . . . . . . 28 2.1.2 Impedance-based measurement system . . . . . . . 30 2.2 LabVIEW control . . . . . . . . . . . . . . . . . . . . . . . 35 2.2.1 DC field control . . . . . . . . . . . . . . . . . . . 35 2.2.2 ∆Eeffect measurements . . . . . . . . . . . . . . . 37 2.2.3 Time-evolution measurements of the resonance . . 38 2.3 Numerical fitting of the resonance curves to improve the detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 i This chapter gives a brief introduction about a property of ferromagnetic materials, magnetostriction, and how we can use it to develop very versatile magnetic sensors based on these materials. The basis of this phenomenon and the subsequent phenomenon of magnetoelastic resonance will be described and analyzed focusing on the application of these materials as mass detection platforms. Throughout the chapter, the most important parameters of magnetoelastic resonance-based sensors will be pointed out, as well as some applications and details about the material used. The versatility, sensitivity and especially, the remote operation of these sensors make them particularly interesting to be applied to a wide range of detection fields. Transducers are devices that convert one form of energy into another [1]. In this context, sensors (which are a form of transducers), convert an input physical quantity into a measurable or processable output quantity (usually into an electrical signal), as their purpose is to detect and measure that physical quantity. The other form of transducer is the actuator, which receives an input (usually an electrical signal), and converts it into some physical output (usually mechanical), as they are intended to transform energy. So transducers enable various systems to interact with the physical world by either sensing changes or generating responses based on inputs (Figure 1.1). Environment Sensor Actuator Controller Measure/Generation of elecrical signal Physical stimulus Physical action Output Input Figure 1.1: Scheme of operation of transducers (sensors/actuators). Transducers, and particularly sensors, are fundamental to our society as they are key in many technologies [2]: from the sensors that control our vehicles (cars, planes...), to the biosensors able to detect infectious diseases, passing through water or air quality control, diagnostic instrumentation in hospitals, the electrical-based technology, the Internet of Things (IoT) devices, etc. The great variety of sensors that exist and the diverse fields to where they are applied, make it difficult to establish a unique way of classify them. Sensors are differentiated from different perspectives: the basis of their operation (chemical, magnetic, optical...), the conversion principle they use (piezoelectric, magnetoresistive...), the physical quantity they measure (viscosity, temperature...) or their application (biosensors, position sensors, environmental sensors...) [1]. In particular, the family of magnetic sensors have enabled us 1 Chapter 1. Introduction to control and develop thousands of functions for centuries. From the invention of the magnetic compass to detect the geomagnetic field for navigation purposes, to the magnetic memories of computers [3, 4]. Different magnetic sensors have been developed based on different physical phenomena: electromagnetic induction, Hall effect, tunnel magnetoresistance (TMR), giant magnetoresistance (GMR), anisotropic magnetoresistance (AMR) or giant magnetoimpedance (GMI). This Thesis focuses on the study and application of a kind of magnetic sensors which are based on the magnetoelastic resonance (MER) phenomenon. These sensors are made of magnetostrictive materials, which can convert between magnetic and elastic energy. 1.1. Sensors based on magnetoelastic resonance 1.1.1. Magnetoelasticity In 1842, J. P. Joule [5] observed that the length of a ferromagnetic specimen changes as a result of magnetization, he cataloged this phenomenon as a new class of magnetic force and found a relative change of length of 1.4×10−6on a bar of iron upon magnetization. This phenomenon is nowadays known as magnetostriction, and it is a magnetomechanical property that ferromagnetic materials have. Figure 1.2: Pages of the James Joule publication on magnetostriction effect. In 1865, E. Villari [6] described the reverse of this effect, known 2 1.1. Sensors based on magnetoelastic resonance as Villari effect or inverse magnetostrictive effect, which describes the change in the magnetic properties of the material due to the application of mechanical stress. The fundamental origin of magnetostriction is related to the spinorbit coupling [7, 8], that transmits the spin orientation to the electronic orbitals causing a physical deformation; but its mechanism at a macroscopic level may be understood by the magnetization process that takes place in the material in the presence of an external magnetic field. In absence of a magnetic field, the magnetostrictive material has a magnetic domain distribution which minimizes its magnetic energy (with zero net magnetization). When the material is exposed to a magnetic field, the magnetic domains are reoriented (minimizing its energy again) by both the migration of domain walls and the rotation of the domains [7]. This process allows the material to rearrange the domains, which in turn causes a dimensional change according to its magnetostriction (materials with positive magnetostriction elongate, materials with negative magnetostriction shrink). This mechanism is represented in Figure 1.3. Since the deformation is isochoric (the volume remains constant) there is an opposite dimensional change in the orthogonal direction. L DL L DL Joule magnetostriction Villari effect H=0 s=0 H Hs s Figure 1.3: Representation of the mechanism of magnetoelastic effects on a magnetostrictive material with positive magnetostriction. This effect is quantified with the fractional change in length (denoted as λ) exhibited by the material when it is exposed to a magnetic field 3 Chapter 1. Introduction and it is given by: λ=∆L L,(1.1) where Lis the initial length of the material in the direction of the applied field and ∆Lits deformation. This mechanical deformation is related to the magnetization process, so it depends on the applied bias field, as it can be observed in Figure 1.4 [7]. The maximum deformation or saturation magnetostriction (λs), corresponds to the magnetic saturation state (saturation magnetization (Ms)), and it is characteristic of each material. Its magnitude is generally small, of the order of some parts per million. M Msls l HH Figure 1.4: Variation of magnetization (M) and magnetostriction (λ) with the applied bias field (H) for a material with positive magnetostriction. 1.1.2. Magnetoelastic resonance The dynamic behavior of this process, when we apply an alternating magnetic field to the magnetostrictive material, results in magnetoelastic waves propagating along it. Thanks to the strong coupling between the elastic and magnetic properties of these materials, the magnetoelastic waves can be generated (and detected) either mechanically or magnetically. When these waves are excited in a material of a given length (for example, in a ribbon of magnetoelastic material of length L), standing waves can be achieved if the wavelength of the induced magnetoelastic waves matches the dimensions of the ribbon (fulfilling the relationship L=n(λ/2), where nis an integer), causing a magnetoelastic resonance. 4 1.1. Sensors based on magnetoelastic resonance At this resonant condition, the strains, the changes of magnetization and the susceptibility of the material reach a maximum. This magnetoelastic resonance phenomenon is the basis of the use of magnetostrictive materials as sensor platforms, as this resonance condition can be measured (as will be described in Chapter 2) and is highly sensitive to several external factors (as will be explained in the following). For a free-standing rectangular-shaped magnetostrictive ribbon (which is the shape usually used for sensor applications), the induced longitudinal wave along the length direction (here taken as the x-axis, Figure 1.5) can be described by the following equation of motion [9]: ∂2u(x, t) ∂t2=E ρ(1 −ν2) ∂2u(x, t) ∂x2,(1.2) where Eis the Young’s modulus, ρis the density, and νis the Poisson’s coefficient of the magnetoelastic material, and u(x, t)is the displacement function of the longitudinal elastic wave. x=0 x u(x) L Figure 1.5: Scheme of the free standing magnetostrictive ribbon. This equation can be solved by using harmonic solutions [10]: u(x, t) = u0cos nπ Lxei2πfnt,(1.3) where u0is a constant and fnis the resonance frequency of the n-th harmonic mode. The term u0cos nπ Lxrepresents the oscillation amplitude. That is, all points in the sensor oscillate at the same frequency, but with different amplitudes. The solution to this equation gives the expression of the longitudinal resonance frequency, which depends on the dimensions and the elastic properties of the ribbon: 5 Chapter 1. Introduction fn r=n 2LsE ρ(1 −ν2).(1.4) So, selecting the frequency of the alternating magnetic field with which we excite the material to match the resonance condition, we can excite a magnetoelastic resonant behavior in it. The different resonance frequencies that can be excited in the ribbon are described by equation 1.4. In most sensor applications only the fundamental mode (n= 1) is considered because it presents the higher signal amplitude (as can be seen in Figure 1.6a), although some studies have also used higher harmonics to improve the sensitivity [11]. Frequency Amplitude n=1 n=2 n=3 n=4 n=5 fr1fr2fr3fr4fr5 (a) Maximum amplitiude Resonance Frequency fr Anti-Resonance Frequency fa (b) Figure 1.6: (a) Magnetoelastic resonance modes of a free magnetoelastic ribbon showing the fundamental resonance (n= 1) and the subsequent harmonics. (b) Detail of a resonance curve and the main resonance parameters. Figure 1.6b shows an example of a resonance curve and its main parameters: the maximum amplitude and the corresponding frequency, which is the resonance frequency. This resonance frequency is the parameter which is mainly used for sensor applications since, as it will be shown below, it is highly sensitive to changes of several external factors affecting the material such as magnetic field, temperature, mass loading, pressure, etc. The curve also shows the anti-resonance frequency, which corresponds to the minimum amplitude (due to the out-of-phase coupling between the strain and the magnetization). 6 1.1. Sensors based on magnetoelastic resonance Figure 1.7 shows the displacements that take place in different modes of oscillation (red color indicates the maximum displacement and dark blue the null displacement). n=1 fr=109.61 kHz n=2 fr=218.91 kHz n=3 fr=327.53 kHz Displacement max Figure 1.7: Finite element method simulations of the first resonant modes of oscillation (n= 1,2,3) of a magnetostrictive strip of dimensions 20 ×2 mm and corresponding resonance frequencies. Red color indicates maximum displacement and dark blue indicates no displacement. The right side shows the normalized displacement along the length of the ribbon (taken as the x-axis). As it can be observed, for the n-th harmonic mode there are nnodes where the displacement is null (shown in blue in the figure). These nodes are located at x=L/2n(2m−1) (where mis a positive integer from 1 to n), and do not contribute to the sensitivity of the magnetoelastic sensor. As it has been studied, the most sensitive parts of the ribbon are 7 Chapter 1. Introduction those that suffer the greatest displacement (in the fundamental mode of a rectangular ribbon, those zones are the tips) [11]. 1.1.3. Effect of mass loading As we have commented on the previous section, the magnetoelastic resonant behavior is highly sensitive to different external parameters, which is the phenomenon that has led to the use of these materials in a wide variety of sensing systems. The effect that the mass loading on the resonator surface (a change on its total mass) has on its resonance frequency, is the most widely used mechanism for developing different sensors. A wide variety of analytes can be related to changes on the sensor mass and moreover, the resonators may be functionalized with different materials on their surface in order to provide them with specific adsorption capacities, making the mass detection a very versatile feature. Some examples of mass detection with these sensors can be found on Table 1.1. Analyte Functionalization Reference CO2Amide-functionalized polymer [12] Ammonia Poly(acrylic acid-co-isooctylacrylate) polymer [13] Humidity Honeycombed thin film ceramic TiO2[14] Fe3O4nanoparticles - [15] Cell growth Parylene-C [16, 17] pH Poly(acrylic acid) [18] Glucose pH-responsive polymer+ glucose oxidase (GOx) [19, 20] Toluene UiO-66-NH2Metal Organic Framework [21] Swine fever virus Antigen anti-CSFV IgG [22] Heavy metal ions Bovine serum albumin [23] Salmonella typhimurium Polyclonal antibody to Salmonella [24] Bacillus Anthracis Filamentous phage [25] Anti-Sars-Cov-2 antibody N antige N-nucleocapsid phosphoprotein of SARS-CoV-2 [26] Pb2+ - [27] Escherichia coli Gold+anti-E. coli O157:H7 antibodies [28] Table 1.1: Different applications of magnetoelastic sensors operating as mass sensors. To analyze the effect that a uniform mass increment (∆m) of the 8 1.1. Sensors based on magnetoelastic resonance resonator mass (m0) has on its resonance frequency (fr), we can assume the mass change as a change on the resonator density (ρ) as: ρ′=m0+ ∆m A·d,(1.5) where Ais the surface area of the sensor and dits thickness (as described in Figure 1.8). m0d Dm A m0 Dm Dfr Figure 1.8: Effect of the mass loading on the resonator’s resonance. Solving the equation of motion (equation 1.2) with this modified density (ρ′), we can obtain a new fundamental resonance frequency: f′ r=1 2LsE ρ′(1 −ν2)=1 2Ls1 1 + ∆m/m0 A·d m0 E (1 −ν2).(1.6) Note that in this expression, it is assumed that the coating does not change the elastic properties of the resonator (the elastic modulus of the system resonator + coating is considered the same as the resonator’s Young’s modulus, E). When the effect of the coating elastic constants is taken into account, the behavior is different [29], as will be explained in detail in Chapter 4. The new resonance frequency (f′ r) can be expressed in terms of the initial resonance frequency (fr) as: f′ r=frs1 1 + ∆m/m0 ,(1.7) since the initial density is ρ=m0/A ·d. For small mass loads relative 9 Chapter 1. Introduction the disordered state of the liquid phase (that is why they are also called metallic glasses). Usually, they are Fe-rich and partially alloyed with nickel or cobalt, as well as doped with other metals in smaller proportions (boron, molybdenum, silicon...), in order to stabilize them or give them particular properties [48]. When it comes to sensor applications, the most widely employed ferromagnetic amorphous alloy is the commercially available Metglas 2826MB (average composition Fe40Ni38Mo4B18 [52]), as it presents excellent magnetic and magnetoelastic properties. But in this work another composition was selected as the sensor material: an amorphous alloy of composition Fe73Cr5Si10B12 which was provided by Ana Catarina Lopes and manufactured in Vacuumschmelze GmbH & Co., KG, Germany [53]. This composition contains a small amount of chromium (5 % atomic) that allows the formation of a passivizing layer on the surface of the material when it is in contact with the air (consisting of oxidized chromium) [54]. This layer favors the corrosion-resistance behavior of the material without the need of a pretreatment (for example, with layers of gold, chromium or polymers [55, 56]). In addition, this alloy presents excellent magnetoelastic properties, which are collected and compared with Metglas 2826MB properties in Table 1.2. For the applications developed in this Thesis (described in the following chapters), where the sensor would be operating under water exposure, this corrosion resistant composition was selected as the magnetostrictive material. Table 1.2: Magnetic, magnetoelastic and electrochemical characterization of Fe73Cr5Si10B12 and Metglas 2826MB samples. Data taken from [53], ∆Eand k values compared for 30 mm ×3 mm samples. Composition µ0Ms (T) λs (ppm) ∆E (%) kCorrosion rate (µm/year) ρ (g/cm3) Fe73Cr5Si10B12 1.12 14 17 0.41 0.035 7.207 Fe40Ni38Mo4B18 Metglas 2826MB 0.88 12 2.5 0.16 23.4 7.900 1.2. Outline of the Thesis The objectives of this Thesis mainly divide in two directions. The first one, is the analysis of limitations and improvement of the performance of MER sensors when they are used for remote real-time mass 16 1.2. Outline of the Thesis detection, and the second one, is their application to different massdetection experiments, where we aim to take advantage of their wireless operation. Magnetoelastic detection, especially when there is a great damping influence or the measurements take place in aqueous media, may require some strategies to improve the resolution. And real-time detection specifically, as we will see, may have some things to deal with, as signal time-instabilities. So, the first part of the Thesis will be focused on analyze this drawbacks and find strategies to overcome them. Chapter 2 is dedicated in the first place, to the home-made experimental measurement system developed to study the magnetoelastic sensors and the different detection applications. In addition, the performance of numerical fittings of the resonance curves of the sensors will be explored as a post-processing tool for improving the detection resolution. Different fitting expressions will be tested both whit theoretical and experimental data, and their performance in obtaining the main resonance parameters (and especially the resonance frequency) will be compared with that of direct methods. Chapter 3 addresses a limitation we have found on the performance of these sensors when operating in real-time detection: the influence of the magnetic relaxation suffered by these materials on their sensing performance. It was found that under the effect of the bias magnetic field, magnetoelastic materials experience a magnetic relaxation that affects negatively the sensor performance and limits the accuracy of the detection, as it causes a time-drift of its resonance signal (and resonance frequency). This effect and different approaches to avoid its negative impact (selecting the conditions of the experiment or post-processing the sensing data) have been studied. The second part of this Thesis is focused on the application of these sensors to two different monitoring experiments. Chapter 4 presents the use of a corrosion resistant MER sensor for real-time tracking a chemical precipitation reaction: the formation reaction of calcium oxalate crystals (one of the most common minerals that forms calcifications on the urinary tract). These magnetoelastic platforms were successfully used to monitor the formation of the salt crystals as the reaction progresses, allowing the study of the dynamics of the reaction and the factors influencing it. To develop this application, an evaluation of the mass sensitivity of these sensors will be performed in terms of the effect that the 17 Chapter 1. Introduction operation media and the elastic properties of the coating material have on it. In addition, in these detection experiments, both the improvement of the detection by using the numerical fittings of the resonance curves (Chapter 2), and the evaluation and correction of the magnetic relaxation effect (Chapter 3) were carried out in order to improve the sensing performance. Finally, Chapter 5 will explore the functionalization of the magnetoelastic platforms with MOF (Metal Organic Framework) active layers in order to develop a wireless humidity sensor. MOF materials are highly porous materials that can be designed to absorb specific molecules within their pores, thus when used as active layers in MER sensors they can act as adsorbent layers which can transform the presence of the analyte to a change on the sensor mass. Different water-adsorbent MOF materials were selected and synthesized in order to functionalize the magnetoelastic sensors to achieve high sensitivity humidity sensors with tailored selectivity. The quality of the MOF materials will be analyzed, and their adsorption capacity will be carefully studied. With this, their overall performance when integrated as active layers in MER sensors will be analyzed in terms of adsorption capacity, response time, stability, repeatability and selectivity. 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Ong, “Magnetoelastic sensors for real-time tracking of cell growth,” Biotechnology and Bioengineering, vol. 118, no. 6, pp. 2380–2385, 2021. [18] Q. Y. Cai and C. A. Grimes, “A remote query magnetoelastic ph sensor,” Sensors and Actuators B: Chemical, vol. 71, no. 1-2, pp. 112–117, 2000. [19] Q. Cai, K. Zeng, C. Ruan, T. A. Desai, and C. A. Grimes, “A wireless, remote query glucose biosensor based on a ph-sensitive polymer,” Analytical Chemistry, vol. 76, no. 14, pp. 4038–4043, 2004. [20] X. Gao, W. Yang, P. Pang, S. Liao, Q. Cai, K. Zeng, and C. A. Grimes, “A wireless magnetoelastic biosensor for rapid detection of glucose concentrations in urine samples,” Sensors and Actuators B: Chemical, vol. 128, no. 1, pp. 161–167, 2007. [21] P. G. Saiz, R. F. de Luis, L. Bartolome, J. Gutiérrez, M. I. Arriortua, and A. C. 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Guntupalli, V. A. Petrenko, and B. A. Chin, “Detection of bacillus anthracis spores in liquid using phagebased magnetoelastic micro-resonators,” Sensors and Actuators B: Chemical, vol. 127, no. 2, pp. 559–566, 2007. [26] W. R. Silva, L. C. Monteiro, R. L. Senra, E. N. de Araújo, R. O. Cunha, T. A. d. O. Mendes, and J. B. Mendes, “A biosensor based on magnetoelastic waves for detection of antibodies in human plasma for covid-19 serodiagnosis,” Biosensors and Bioelectronics, p. 116456, 2024. [27] S. Sang, S. Gao, X. Guo, P. Cheng, and W. Zhang, “The detection of pb2+ in solution using bare magnetoelastic resonator,” Applied Physics Letters, vol. 108, no. 5, 2016. [28] C. Ruan, K. Zeng, O. K. Varghese, and C. A. Grimes, “Magnetoelastic immunosensors: Amplified mass immunosorbent assay for detection of escherichia c oli o157: H7,” Analytical Chemistry, vol. 75, no. 23, pp. 6494–6498, 2003. [29] S. Schmidt and C. A. Grimes, “Characterization of nanodimensional thin-film elastic moduli using magnetoelastic sensors,” Sensors and Actuators A: Physical, vol. 94, no. 3, pp. 189–196, 2001. [30] C. A. Grimes, D. Kouzoudis, and C. Mungle, “Simultaneous measurement of liquid density and viscosity using remote query magnetoelastic sensors,” Review of scientific instruments, vol. 71, no. 10, pp. 3822–3824, 2000. [31] I. Bravo, A. Arnaiz, and A. García-Arribas, “Damping of magnetoelastic resonance for oil viscosity sensing,” IEEE Transactions on Magnetics, vol. 55, no. 1, pp. 1–5, 2018. 21 Chapter 1. Introduction [32] P. G. Stoyanov and C. A. Grimes, “A remote query magnetostrictive viscosity sensor,” Sensors and Actuators A: Physical, vol. 80, no. 1, pp. 8–14, 2000. [33] L. G. Puckett, G. Barrett, D. Kouzoudis, C. Grimes, and L. G. Bachas, “Monitoring blood coagulation with magnetoelastic sensors,” Biosensors and Bioelectronics, vol. 18, no. 5-6, pp. 675–681, 2003. [34] D. Kouzoudis and C. A. Grimes, “The frequency response of magnetoelastic sensors to stress and atmospheric pressure,” Smart Materials and Structures, vol. 9, no. 6, p. 885, 2000. [35] M. K. Jain, S. Schmidt, K. G. Ong, C. Mungle, and C. A. Grimes, “Magnetoacoustic remote query temperature and humidity sensors,” Smart Materials and Structures, vol. 9, no. 4, p. 502, 2000. [36] D. Kouzoudis and C. A. Grimes, “Remote query fluid-flow velocity measurement using magnetoelastic thick-film sensors,” Journal of Applied Physics, vol. 87, no. 9, pp. 6301–6303, 2000. [37] T. Huber, B. Bergmair, C. Vogler, F. Bruckner, G. Hrkac, and D. Suess, “Magnetoelastic resonance sensor for remote strain measurements,” Applied Physics Letters, vol. 101, no. 4, 2012. [38] N. P. Oess, B. Weisse, and B. J. Nelson, “Magnetoelastic strain sensor for optimized assessment of bone fracture fixation,” IEEE Sensors Journal, vol. 9, no. 8, pp. 961–968, 2009. [39] K. Zhang, L. Zhang, L. Fu, S. Li, H. Chen, and Z.-Y. 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Introduction and corrosion resistant properties of (fe–ni)-based metallic glasses for structural health monitoring applications,” Materials, vol. 13, no. 1, p. 57, 2019. [54] M. F. López, M. Escudero, E. Vida, and A. Pierna, “Corrosion behaviour of amorphous fe� cr� ni�(si, p) alloys,” Electrochimica acta, vol. 42, no. 4, pp. 659–665, 1997. [55] S. Huang, J. Hu, J. Wan, M. Johnson, H. Shu, and B. Chin, “The effect of annealing and gold deposition on the performance of magnetoelastic biosensors,” Materials Science and Engineering: C, vol. 28, no. 3, pp. 380–386, 2008. [56] N. Bouropoulos, D. Kouzoudis, and C. Grimes, “The real-time, in situ monitoring of calcium oxalate and brushite precipitation using magnetoelastic sensors,” Sensors and Actuators B: Chemical, vol. 109, no. 2, pp. 227–232, 2005. 24 Chapter 2. MER detection instrumentation and data processing set and available in the laboratory (located at BC Materials). An example of a resonance curve of a magnetoelastic ribbon measured in this system is shown in Figure 2.4. DC Power Supply Digital multimeter Spectrum analyzer Figure 2.3: Scheme of the induction-based measurement set-up. Figure 2.4: Resonance curve of a ribbon of composition Fe73Cr5Si10B12 and dimensions 20 mm ×2 mm at Hbias = 14 Oe measured in the induction-based measurement system. 2.1.2. Impedance-based measurement system In this Thesis, another experimental set-up based on impedance measurements was design and developed (Figure 2.5). This system was the principal set-up used during this work (with some modifications or additional elements depending on each application case). The main advantage of this set-up compared to the induction-based one is its simplicity. Unlike the other system, this one only requires a single coil for the 30 2.1. Magnetoelastic resonance detection system excitation of the resonance and detection of the induced signal. This method is based on the effect that the magnetoelastic material has on the impedance of the pick-up coil. That impedance is given by: Z(ω) = R+jωL(ω),(2.5) being ωthe frequency, Rthe resistance of the coil and Lits inductance. The inductance of a coil is directly proportional to the permeability (µ) of the material inside it (in our case, the permeability of the magnetoelastic material when the ribbon is placed inside the pick-up coil): L(ω) = N2A lµ(ω),(2.6) being Nthe number of turns of the coil, Aits cross section and lits length. Since the permeability of the magnetoelastic material increases significantly at resonance [5], a sharp peak occurs in the coil’s impedance spectrum at that resonance frequency, and so that the resonance behavior of the sensor can be observed through the impedance spectrum of the coil. DC Power Supply Digital multimeter Impedance analyzer Setting Up the OSA Setting Up the OSA book.book Page 3 Monday, January 31, 2000 10:34 AM Setting Up the OSA Setting Up the OSA book.book Page 3 Monday, January 31, 2000 10:34 AM Figure 2.5: Scheme of the impedance-based measurement system. In the experimental system, the DC magnetic bias field is produced by a Helmholtz pair (16.2 Oe/A (1.289 kAm-1/A)) which is fed by a power supply (KIKUSUI PBZ40-10). A digital multimeter (Agilent 34401A) was used to measure the applied bias field (through the voltage drop on a resistance connected in series to the Helmholtz coil). The 31 Chapter 2. MER detection instrumentation and data processing impedance of the pick-up coil was measured with an impedance analyzer (Keysigth E4990A, 20 Hz - 10 MHz, see details in Appendix A.1). The self-resonance frequency of the pick-up coil (fr= 637.5 kHz), is above the operation frequencies of the magnetoelastic sensors used in this Thesis (around 100 kHz). A picture of the experimental set-up can be found in Figure 2.6. Figure 2.6: Impedance-based measurement system. In this case, there is no compensation coil, as there will be no parasitic read signal from the AC field (the excitation coil is the pick-up coil itself), in return, the magnetoelastic signal appears superimposed to the self-induction of the coil (Figure 2.8a). The background signal corresponding to the coil impedance can be observed in Figure 2.7. Moreover, the permeability of the sensor itself (just by placing it inside the pick-up coil) will contribute to increase the inductance (and impedance) of the coil and therefore, to further increase the background (see Figure 2.7). In order to obtain the sensor resonance signal with a flat baseline, the background corresponding to the pick-up coil with the sensor inside it (without any bias field applied) was measured before each measurement and subtracted from the resonance data. Since the resonance curves measured with this system were acquired in magnitude (module of the impedance), the background correction was performed directly by subtracting the background impedance magnitude. More precise background correction could be done by subtracting 32 2.1. Magnetoelastic resonance detection system Figure 2.7: Background impedance of the pick-up coil (pink), and the pick-up coil with a sensor inside it (green). the complex impedance (real and imaginary parts), but that would require measuring and processing the complex sensor resonance (real and imaginary parts), and that, in return, will increase the measurement time. Figure 2.8 shows an example of a resonance curve of a magnetoelastic ribbon measured with this system. (a) (b) Figure 2.8: Resonance curve of a ribbon of composition Fe73Cr5Si10B12 and dimensions 20 mm ×2 mm at Hbias = 14 Oe measured in the impedance-based measurement system (a) without background correction and (b) with background correction. Figure 2.8a shows the raw resonance curve, with a background slope 33 Chapter 2. MER detection instrumentation and data processing corresponding to the inductance of the pick-up coil, and Figure 2.8b shows the same curve after the background subtraction. As can be observed, as the impedance module is being measured directly with this method, both frand faare precisely obtained. The sensor is placed in a sample holder that locates the sample in the center of the pick-up coil and the coil system. All measurements were performed with this configuration, as the position of the ribbon with respect to the pick-up coil affects the amplitude of the signal, which decreases as the ribbon is moved from the center (see Figure 2.9). 0 mm 5 mm 10 mm 10 mm 0 mm 5 mm 0 mm 5 mm 10 mm Z fr Figure 2.9: Effect of the position of the sensor with respect to the center of the pick-up coil (and therefore also with respect to the center of the coil system) on the resonance frequency and amplitude of the signal. As can be observed, the position of the ribbon also affects the value of the resonance frequency, which increases as the ribbon is displaced from the center. This is probably due to the slightly different excitation fields to which the sensor is exposed in each position. The equal placement of the sample in the center of the system (0 mm in Figure 2.9) ensures that any variation of this frequency is not due to its position, but to the analyte being detected. 34 2.2. LabVIEW control 2.2. LabVIEW control Several LabVIEW-based programs were developed throughout the Thesis in order to control the measurement system and automate and synchronize all measurements. The different measurement programs were developed using VISA (Virtual Instrument Software Architecture) communication in order to communicate with the different instruments (via GPIB (General-Purpose Instrumentation Bus)). Labview software developed by the instrument manufacturers as well as custom-made software was integrated in the programs. The basic programs used to measure the magnetoelastic resonance are detailed in the following. 2.2.1. DC field control As the magnetoelastic sensor is sensitive to the static magnetic field (as illustrated with the ∆Eeffect), to ensure a reliable response of the sensor to mass changes, the bias field must remain stable during measurements. Compared to the induction-based measurement system, which had no control over the bias field, a bias field control feature has been added to the impedance detection system, which improves the detection accuracy. In this system, as we have seen, the Helmholtz coils are fed by a voltage-driven power supply. The self-heating of the coils can produce an increment of their resistance which traduces in less current passing through the coils (for a given voltage input from the power supply) and therefore less generated bias field. To compensate for this effect and maintain the bias field value constant, a PID (proportional–integral– derivative) controller [6] was developed to control the voltage that the power supply provides to the Helmholtz pair (see details of the PID controller in the Appendix A.2). The PID controller tries to minimize the difference (e(t)) between the desired bias field (set point) and the actual bias field by applying a correction with proportional (Kp), integral (Ti) and derivative (Td) terms: u(t) = Kpe(t) + 1 TiZt 0 e(t)dt +Td de(t) dt .(2.7) 35 Chapter 2. MER detection instrumentation and data processing The actual bias field produced by the Helmholtz coils is measured by a multimeter through the voltage drop in a series resistance (10 Ω) connected to the Helmholtz pair (which provides the current passing through the system that can be then converted to magnetic field using the calibration constant of the coils). This value of the bias field is constantly given to the PID controller as the feedback (see Figure 2.10). DC Power Supply Digital multimeter Helmholtz pair Input (H set point) PID Feedback Output (Voltage) 10 non-inductive resistance Figure 2.10: Scheme of operation of the PID controller. The controller output is continuously passed to the power supply as the desired output voltage to feed the Helmholtz coils. The resolution of the digital multimeter is 0.1 mV, which when using a resistance of 10 Ωtranslates to a control of bias field differences of the order of 0.1 mOe. The PID controller was developed in LabVIEW environment (Figure 2.11). The program communicates with the multimeter, to continuously read the actual bias field, and with the power supply, to control its output voltage. The application has the option to set the values of Kp, Tiand Tdto adjust the control behavior. In our case, after study the behavior of the controller with several gains, Tdwas set to 0 (PI control), as the derivative term did not improve the control. 36 2.2. LabVIEW control Figure 2.11: LabVIEW front panel of the PID controller. 2.2.2. ∆Eeffect measurements One important measurement that allows us to characterize the magnetoelastic ribbons and find the best point of operation of the sensors, is the measurement of the ∆Eeffect. Such measurement can be obtained by observing the resonance behavior (and specifically its resonance frequency) as a function of the applied bias field, as we have seen in the introduction chapter. A LabVIEW program was developed in order to measure the ∆Eeffect of the MER sensors. The program controls the applied bias field, performing a sweep of its value, and collects the corresponding resonance signal of the sensor. The program configures the impedance analyzer parameters (type of measurement, range of frequency sweep, number of sweep points, measurement speed...), and the bias magnetic field range: initial, final and step values. Then it saves the background trace (impedance magnitude of the pick-up coil with the MER sensor inside) before the measurement 37 Chapter 2. MER detection instrumentation and data processing Figure 2.12: Front panel of the LabVIEW program developed to measure the ∆Eeffect. starts and before the bias field is applied. The program subtracts the recorded background from the subsequent measured resonance signals using the built-in functions of the analyzer. For each bias field step (increment), the program waits for the field value to stabilize (this program runs simultaneously with the PID field controller) and then collects and saves the corresponding magnitude (module of the impedance) of the resonance curve (Figure 2.12). From the curves, the resonance frequency is obtained as the frequency at which the amplitude is maximum using the built-in analysis procedures of the analyzer. Both the maximum impedance and the corresponding frequency (resonance frequency) are saved in data files as a function of the bias field. 2.2.3. Time-evolution measurements of the resonance The principal measurement needed in the Thesis was a real-time recording of the resonance signal, since the objective of the Thesis was to study the operation and applications of these materials as platforms for real-time mass detection. 38 2.2. LabVIEW control Figure 2.13: Front panel of the LabVIEW program developed to measure the evolution of the resonance over time. The implemented LabVIEW program (time-measurement program, Figure 2.13) initializes the impedance analyzer (selecting the operational parameters), records the background (impedance magnitude of the pickup coil with the sensor inside it (taken without Hfield)) and performs sweeps of the excitation frequency over the selected frequency range. The program asks for a value of the bias field, which is maintained constant during the measurement by the PID field controller (which runs simultaneously with the time-measurement program). The trace (impedance magnitude of the resonance curve with background subtraction), and the corresponding resonance frequency and maximum impedance are obtained using the built-in analysis procedures of the analyzer, transmitted to the control computer and saved as a function of time. The values of the temperature (using a thermocouple) and the bias field are also recorded throughout the entire measurement. These are the main magnetoelastic measurement programs used in this Thesis. However, for the detection application explained in Chapter 5, some modifications of both the measurement system and the LabVIEW control will be needed in order to incorporate some additional elements (since, for example, a flow control unit was added to the main detection system). The measurement setup and modifications performed 39 Chapter 2. MER detection instrumentation and data processing Figure 2.16). Table 2.1 shows an example of the values of the main resonance parameters obtained from the fittings compared to those obtained by direct methods. Table 2.1: Comparison between the parameters used to generate the theoretical curves, those retrieved through the numerical fit, and those calculated from direct methods when the signal has a level of noise corresponding to a SNR = 20. Theoretical Direct method Fitted fr(kHz) 40.00 37.90 40.02 Q5.00 4.35 4.95 k20.70 0.84 0.69 In order to evaluate quantitatively the accuracy of each method, the error relative to the theoretical value (%) was analyzed (Table 2.2). The relative error (εr, in %) was calculated as: εr=|Xtheoretical −Xobtained | Xtheoretical ×100,(2.16) where Xtheoretical is the theoretical value of each resonance parameter, and Xobtained is the corresponding parameter obtained (through the fittings or direct calculations). Analyzing the error values, it was clear that the accuracy of the parameters was improved in all cases when numerical fittings were used compared to the results calculated by direct methods. Specially when there is noise or the peak is damped and has less quality, since direct methods are quite sensitive to noise, while numerical fitting of the whole curve reduces its effect significantly. For example, the determination of Qwith direct methods leads to errors up to 20%, as already reported in other works [11], whereas numerical fittings significantly reduce these errors. The improvement in accuracy is also, in general, more noticeable as the coupling parameter takes smaller values. Thus, numerical fittings will be useful to improve the resolution on the determination of the resonance frequency (and other resonance parameters) when the sensor has noise or it is damped (for example, when working in liquid media, or when a fast measurement is needed and the 46 2.3. Numerical fitting of the resonance curves to improve the detection frequency determination could not be very fine). εr(Q)(%) εr(k2)(%) εr(fr)(%) SNR Direct Fit Direct Fit Direct Fit Q=5 k2= 0.5 fr= 40 kHz 10 26.54 6.93 46.06 2.64 4.50 0.12 30 20.42 0.16 22.35 0.13 4.50 0.05 50 17.87 0.03 26.96 0.04 3.50 0.00 Q=5 k2= 0.9 fr= 40 kHz 10 8.33 1.27 5.30 2.39 2.50 0.42 30 3.46 0.29 11.60 0.13 2.25 0.04 50 4.15 0.01 5.12 0.01 1.75 0.00 Q=20 k2= 0.5 fr= 40 kHz 10 10.55 2.70 10.69 3.01 0.50 0.05 30 5.00 0.09 2.03 0.03 0.25 0.01 50 5.00 0.02 3.13 0.00 0.25 0.00 Q=20 k2= 0.9 fr= 40 kHz 10 10.55 0.94 1.39 1.11 0.50 0.03 30 5.00 0.09 1.48 0.06 0.25 0.01 50 5.26 0.01 0.49 0.01 0.00 0.00 Table 2.2: Comparison of the relative error in the determination of the parameters (Q,k2and fr) through both methods: calculated by the direct formulas and retrieved from numerical fittings. Results are shown for different values of the parameters and SNR. 2.3.2.2. Fitting of experimental curves In order to test the behavior of the fittings with some experimental resonance data, several experimental curves with different values of the amplitude, resonance frequency and damping were used (Figure 2.17). The figure also shows the numerical fitting of the curves to expression 2.10 (dashed-lines). The background term (aω +b) was added to the fitting expressions since it was found that it improved the fitting performance. In Figure 2.18, it can be seen that the fittings to expression 2.10 behave slightly better, with lower value of the residual (lower error between the experimental data and the values obtained through the model). This is probably due to the fact that expression 2.10 has one more degree of freedom (7 fitting parameters) than expression 2.8 (6 parameters). Nevertheless, both models fit the experimental data reasonably well. 47 Chapter 2. MER detection instrumentation and data processing Figure 2.17: Experimental magnetoelastic resonance curve signals (curves 1-5), and corresponding numerical fittings to expression 2.10. (a) (b) Figure 2.18: Example of the numerical fittings of a experimental curve (Curve 3) to (a) equation 2.10 and (b) equation 2.8, and the corresponding errors (residuals). If we compare the resonance parameters obtained through the fittings of the experimental curve shown in Figure 2.18, we found that, effectively, they are similar (Tables 2.3 and 2.4). 48 2.3. Numerical fitting of the resonance curves to improve the detection χ0a b frQk2δrδa 0.0750 -0.0004 0.0414 109.91 36.482 0.10340 0.013706 0.014319 Table 2.3: Resonance parameters obtained with the fitting of Curve 3 data to equation 2.8. δrand δawere obtained with the equivalence expressions 2.13 and 2.14. A a b frfaδrδa 0.0714 -0.0004 0.0433 109.89 115.04 0.013500 0.011300 Table 2.4: Resonance parameters obtained with the fitting of Curve 3 data to equation 2.10. Analysis of the fitted resonance frequency An important characteristic of the fitting procedure is that the obtained values of the frparameter do not correspond to the position of the maximum amplitude of the resonance curves (here called fmax). If we take a look at the curves and the parameters, especially in the cases with more damping, we observe that fmax is systematically lower than the resonance frequency obtained with the fittings (fr) (see Figure 2.19a). (a) (b) Figure 2.19: (a) Observed discrepancy between the resonance frequency taken as the frequency of maximum amplitude (fmax) and the one obtained with the fittings (fr). (b) Difference between the experimental resonance frequency (fmax) and the resonance frequency obtained through the fitting to Equation 2.10 (fr) as a function of the damping (δr). This tells us that what we usually take as the resonance frequency 49 Chapter 2. MER detection instrumentation and data processing (frequency of the maximum of the resonance curve), is not actually the natural resonance frequency of the sensor, fr, which can be obtained from the fitting to the analytical expressions. Instead, fmax is affected by the damping of the curve, which shifts it toward lower values (it is an effective resonance frequency). A similar effect applies to the frequency of anti-resonance (minimum of the curve), which, when affected by damping (due to the mass deposition for example), increases with respect to the value which is obtained from the fits, fa(see Figure 2.19a). In fact, this difference between frand fmax depends linearly on the damping of the curve, as can be seen on Figure 2.19b, getting greater for higher damping values. To better understand this, we can divide the frequency response of a magnetoelastic resonator as different transfer functions representing systems of: a pure resonance (G1), a pure anti-resonance (G2), and the combination of both (G3), which represents the observed resonanceantiresonance behavior: G1(s) = ω2 r s2+ 2δrωrs+ω2 r (2.17) G2(s) = s2+ 2δaωas+ω2 a ω2 a (2.18) G3(s) = G1·G2=ω2 r ω2 a·s2+ 2δaωas+ω2 a s2+ 2δrωrs+ω2 r (2.19) Figure 2.20 illustrates this discrepancy, showing the frequency response of the system, for ideal resonance (G1, in blue) and anti-resonance (G2, purple) separately, and for the entire curve affected by damping (sum of resonance and anti-resonance, G3, orange). The frequency values obtained for the resonance (maximum) and anti-resonance (minimum) of the respective curves (blue and purple), coincide with those obtained in the fittings (frFit and faFit in Figure 2.20). In the combined curve (orange), however, the maximum and minimum are shifted with respect to these values, resulting in the values of the resonance and anti-resonance frequencies (frDamped and fa Damped in Figure 2.20), which match the experimental data. 50 2.3. Numerical fitting of the resonance curves to improve the detection Figure 2.20: (a) Frequency response of the system for resonance and anti-resonance behavior, and the total response affected by the damping. When using numerical fittings to improve the determination of the resonance frequency in a detection experiment, the fitted parameter fr could be used, but it is also possible to use the value of the frequency which corresponds to the maximum of the fitting curve, which will be more comparable to the one we obtain experimentally. In this Thesis, when using the numerical fittings to improve the sensor resolution, the frequency of the maxima of the fitting curves will be used. Operation of the numerical fittings under reduced frequency range Finally, the behavior of the fittings when the frequency range of the data is reduced has been studied in order to test if they can still provide, under these conditions, a valid performance. As an example of this, Figure 2.21 shows the fitting of the resonance curve in a reduced frequency range (purple). It was found that the fittings still fit well the experimental data and give accurate values of the parameters when the frequency range is considerably smaller. Therefore, when using the numerical fittings of the curves, the frequency range can be reduced on behalf of a quick measurement. As an example, the Qvalue obtained with this reduced frequency fitting, Q= 17.4, is practically the same as the one obtained with the complete curve, Q= 17.5. This is specially interesting since the analysis 51 Chapter 2. MER detection instrumentation and data processing of Qvalue by direct methods (using the FWHM) is not even applicable in this reduced frequency case. Figure 2.21: Magnetoelastic resonance curve and corresponding fitting to Equation 2.10 (in dashed black line) for a reduced range of frequencies (in purple). 2.4. Conclusions In this chapter, the instrumentation developed to characterize the magnetoelastic resonators and detect their resonance signal has been detailed, as well as the software developed to perform all the magnetoelastic measurements done through this Thesis. The measurement systems consist of an induction-based and an impedance-based set-ups. The measurement programs allow us to characterize the magnetoelastic materials (∆Eeffect program) and to monitor the resonance signal in real time (time-evolution measurement program). Special emphasis has been given to the control of the bias field, whose stability is essential for real-time detection (since its variations can cause changes in the signal). As a data processing strategy to enhance the detection of these sensors, the numerical fitting of the resonance curves have been explored as a tool to retrieve the governing resonance parameters. The study has demonstrated that the fittings are more accurate in obtaining the resonance frequency (and other parameters describing the resonance, such as the coupling parameter or the quality factor) than the classical direct methods, in particular when signals have considerable noise or are highly damped. Therefore, they can be very useful when using these sensors in 52 2.4. Conclusions liquid media or when a rapid measurement (less quality) is needed, as we will see in the following chapters. The performance of two different fitting expressions was analyzed, and analytical relationships between the different parameters have been established . Both expressions performed well (with a very low residual in relation to the experimental data) and have proven to be suitable for improving the detection resolution. It was found that the frequency at which the resonance curve is maximum (fmax), does not coincide with the natural resonance frequency of the system, fr, as included in the analytical expressions used for the fittings. The difference is produced because the damping displaces the maximum of the resonance towards lower frequencies. Through this Thesis, when using these numerical fittings, the resonance frequency obtained will be the frequency corresponding to the maximum amplitude of the fitting curve (which will be more comparable to the experimentally obtained one, and yet its resolution will be improved). During this Thesis, the numerical fittings were performed as a postprocessing of the measurements once they were made. As future work, the numerical fittings could be integrated into the general measurement programs using the LabVIEW environment, so that the fittings would be performed simultaneously with the experimental measurements. 53 Chapter 2. MER detection instrumentation and data processing Bibliography [1] C. A. Grimes, S. C. Roy, S. Rani, and Q. Cai, “Theory, instrumentation and applications of magnetoelastic resonance sensors: a review,” Sensors, vol. 11, no. 3, pp. 2809–2844, 2011. [2] K. Zeng, K. G. Ong, C. Mungle, and C. A. Grimes, “Time domain characterization of oscillating sensors: Application of frequency counting to resonance frequency determination,” Review of Scientific Instruments, vol. 73, no. 12, pp. 4375–4380, 2002. [3] Y. Le Bras and J.-M. Greneche, “Magneto-elastic resonance: Principles, modeling and applications,” Resonance, vol. 2, pp. 13–34, 2017. [4] N. Ida and N. Ida, “Faraday’s law and induction,” Engineering Electromagnetics, pp. 515–563, 2015. [5] C. A. Grimes, C. S. Mungle, K. Zeng, M. K. Jain, W. R. Dreschel, M. Paulose, and K. G. Ong, “Wireless magnetoelastic resonance sensors: A critical review,” Sensors, vol. 2, no. 7, pp. 294–313, 2002. [6] A. Visioli, Practical PID control. Springer Science & Business Media, 2006. [7] A. C. Lopes, A. Sagasti, A. Lasheras, V. Muto, J. Gutiérrez, D. Kouzoudis, and J. M. Barandiarán, “Accurate determination of the q quality factor in magnetoelastic resonant platforms for advanced biological detection,” Sensors, vol. 18, no. 3, p. 887, 2018. [8] P. J. Petersan and S. M. Anlage, “Measurement of resonant frequency and quality factor of microwave resonators: Comparison of methods,” Journal of applied physics, vol. 84, no. 6, pp. 3392–3402, 1998. [9] H. Savage and R. Abbundi, “Perpendicular susceptibility, magnetomechanical coupling and shear modulus in tb. 27 dy. 73 fe 2,” IEEE Transactions on Magnetics, vol. 14, no. 5, pp. 545–547, 1978. [10] A. García-Arribas, J. Gutiérrez, G. V. Kurlyandskaya, J. M. Barandiarán, A. Svalov, E. Fernández, A. Lasheras, D. De Cos, and I. Bravo-Imaz, “Sensor applications of soft magnetic materials based 54 Bibliography on magneto-impedance, magneto-elastic resonance and magnetoelectricity,” Sensors, vol. 14, no. 5, pp. 7602–7624, 2014. [11] Z. Kaczkowski, “Piezomagnetic parameters of the magnetostrictive materials,” Archives of Acoustics, vol. 23, no. 2, pp. 307–29, 2014. 55 Chapter 3. Influence of magnetic relaxation on MER detection (χ) do not reach their final values immediately after the field is applied, but some time is needed for the material to relax into an equilibrium state (through a complex interplay between the internal structure, magnetic domains, and thermal fluctuations). This relaxation has been explained by some authors to have its origin in an ordering mechanism of structural defects (intrinsic to the amorphous state (shear stresses, free volume or density fluctuations) [6]) interacting with the local magnetization vector via the magnetostrictive coupling [3, 7–11]. This behavior arises after a sudden rearrangement of the magnetic domain structure (as it happens when a magnetic field is suddenly applied or suppressed). When the material is exposed to the bias field, the direction of the magnetization vector suffers a sudden change, producing small short-range atomic re-arrangements in the material (which are reversible). That interaction leads to a progressive hindering of domain-wall motion [12], which leads to a time-dependent magnetization (characterized by a long-term behavior, with considerably large relaxation times). Usually the characterization of this magnetic relaxation is performed by following magnitudes such as M,χor µafter demagnetization [13– 15], but any other magnetic-related property of these materials will also suffer this relaxation behavior. This effect was soon recognized as a drawback in applications of these materials that require stable properties to ensure proper performance. For example, the influence of the relaxation of amorphous magnetic alloys has been detected in some parameters used in sensing applications, such as the magnetoimpedance [9, 10, 16]. However, little information about this issue can be found in MER sensor applications, where, usually, magnetic relaxation is not taken into account. Nevertheless, as we will see, this magnetic relaxation can be noticed in the most important parameter when using amorphous materials as MER sensors, their resonance frequency. As the resonance frequency is related to the magnetic state of the material (through the ∆Eeffect), the time-evolution of Mwill be traduced to a time-evolution of the resonance frequency (fr). Therefore, a detailed study of this phenomenon is basic to assess the MER sensor performance and to avoid its negative effects on the detection capability of these materials. Such study will be described in the following sections. 62 3.2. Measurement methodology 3.2. Measurement methodology Sensor material The material used in the investigation was an as-quenched magnetoelastic ribbon with composition Fe73Cr5Si10B12, laser cut with dimensions 20 mm × 2 mm × 25 µm and a total weight of about 8 mg. The magnetization curve of the ribbon is shown in Figure 3.4 together with the dependence of its resonance frequency on the applied bias field H(or ∆Eeffect). As described in the introduction chapter, the field at which the resonance frequency is minimum, about 7.8 Oe, is considered the effective value of the anisotropy field of the ribbon [17–19]. Magnetic relaxation experiments were performed at different values of the bias field (H), represented with red dots in Figure 3.4: 4, 7.8 and 10 Oe. Figure 3.4: Hysteresis loop of the material (solid line) measured in an inductive loop tracer, and dependence of the resonance frequency on the applied bias field (dashed line). Dots indicate the bias field values (H) selected for the relaxation measurements. Blue lines are depicted to illustrate the estimation of the anisotropy field from the M(H)curve. Measurement set-up Relaxation measurements were carried out by continuously monitoring the resonance signal (and in particular, the value of the resonance frequency) of a magnetoelastic sensor during a time interval of 2000 s 63 Chapter 3. Influence of magnetic relaxation on MER detection while the measurement conditions and parameters (DC-bias field, excitation field, temperature, and, in general, all the measurement system configuration) remained stable, so that the changes observed in the sensor signal could not be attributed to variations in those parameters. The experimental setup used to carry out the magnetoelastic measurements (Figure 3.5), was the impedance-based measurement system described in Chapter 2. It consists of a pair of Helmholtz coils producing a constant field longitudinal to the ribbon axis which biases the material, and an interrogation coil that produces the alternating magnetic field (to magnetostrictively excite the sample) and, in turn, detects the magnetization oscillations induced in the material. Setting Up the OSA Setting Up the OSA 10:34 AM Setting Up the OSA Setting Up the OSA 00 10:34 AM Impedance Analyzer Power supply PID controller Thermocouple Gaussmeter Figure 3.5: Scheme of the experimental setup used to measure the relaxation on magnetoelastic resonance. The excitation magnetic field (h), is produced by an alternating current passing through the interrogation coil, which is fed by a voltage given by the impedance analyzer (which can be tuned by selecting its amplitude, OSC level in mV). In order to know the amplitude of the excitation field (h) that is generated by a given OSC level in the analyzer, the current flowing through the interrogation coil was measured with an inductive current probe (Tek CT-2) (the output of the current probe was collected using an oscilloscope). The measured current was then converted into magnetic field amplitude using the calibration constant of the coil (84.6 Oe/A (6.732 kAm−1/A)). The relaxation experiments 64 3.2. Measurement methodology were performed for different amplitudes of the excitation field h: 20, 42, 100 and 180 mOe. All the measurements were carried out at room temperature, which was monitored by a thermocouple (NI USB-TC01, type K) inside the measurement system (temperature variations during the measurements were below 0.1 ◦C). The constant bias field Hwas controlled with the PID controller and continuously monitored with a gaussmeter (Lakeshore, 475 DSP Gaussmeter). Numerical fitting of the resonance curves In order to improve the accuracy in the determination of frduring the relaxation measurements, the resonance curves were numerically fitted to the analytical expression 2.8, as explained in Chapter 2. Figure 3.6 shows the improvement in the determination of the resonance frequency and the reduction of noise when numerical fittings are used in an example of a relaxation experiment. Figure 3.6: Comparison of the resonance frequency obtained directly as the maximum of the experimental curves (black) and the resonance frequency obtained as the maximum of the numerically fitted resonance curves (red). Here the fitting expression is shown again in order to have it at hand: Z(f) = Z0"1−8k2 π21−f2 r f2+jQ−1fr f−1#+af +b, (3.1) where Zis the impedance (amplitude) of the signal, and the fitting 65 Chapter 3. Influence of magnetic relaxation on MER detection parameters are: fr(resonance frequency), Z0(amplitude of the signal at low frequency), k(magnetoelastic coupling coefficient), Q(quality factor), and aand b(background parameters). As explained in Chapter 2, the values of frobtained by the fitting were taken as the frequencies corresponding to the maximum of the fitted curves, so that they are comparable to the experimental resonance frequencies. 3.3. Relaxation measurements An example of the time evolution of the resonance signal of the magnetoelastic sensor under constant bias field is depicted in Figure 3.7a. At t= 0 s, the bias field is set to its desired value (H= 10 Oe in this case). After that, due to the relaxation of the magnetization towards the equilibrium value, the resonance curve experiences a frequency shift towards higher values in both, resonance (maximum) and anti-resonance (minimum) frequencies. The time evolution of frand fais represented in Figure 3.7b. (a) (b) Figure 3.7: (a) Changes produced in the resonance signal of the sensor due to magnetic relaxation during the measurement under a constant bias field of 10 Oe and excitation amplitude of 20 mOe (each curve corresponds to a different time, from t= 0 s (when the bias field is set), up to 2000 s). (b) Temporal evolution of the resonance frand anti-resonance fa frequencies during relaxation corresponding to the curves shown in (a), obtained from the numerical fitting of the curves to equation 3.1. Apart from the effect on frand fa, the magnetic relaxation can also be noticed in the impedance (amplitude of the signal), which also increases with time. 66 3.3. Relaxation measurements 3.3.1. Relaxation phenomenon under different biasing and excitation fields Figure 3.8 shows the relaxation measurements performed with different conditions of the bias field (H) and the excitation field (h). (a) (b) (c) Figure 3.8: Increment of the resonance frequency of the sensor (colored lines) and corresponding numerical fitting to expression (3.2) (dashed lines) for different excitation amplitudes (h= 20, 42, 100, 180 mOe) due to magnetic relaxation under the application of a constant bias field of (a) 4 Oe; (b) 7.8 Oe (effective anisotropy field); (c) 10 Oe. 67 Chapter 3. Influence of magnetic relaxation on MER detection In the figure, the increment (change with respect to its initial value) of the resonance frequency (fr) of the sensor during the measurement time (2000 s) is shown for the different values of hand H. Colored-lines correspond to the experimental resonance frequencies (obtained from the numerical fitting of the data such as the ones shown in Figure 3.6) and dashed-lines to the fitting of the relaxation behavior model (which will be described in the following section). As it can be observed, frincreases with time in all cases, up to 0.24 % of its initial value in the case of a bias field of H= 4 Oe and an excitation amplitude of h= 20 mOe. In a real-time detection device, this change of about 270 Hz in the resonance frequency would appear as a time-drift of the output, representing a considerable source of error that would affect the performance of the sensor, reducing considerably its limit of detection. The tendency observed is that the change in the resonance frequency due to the relaxation is greater in the cases in which the excitation amplitude is weaker. In addition, the phenomenon is more noticeable at lower bias fields (as also reported by other authors [20]), below the anisotropy field value, when magnetization occurs mainly due to domain-wall motion, the slope of the hysteresis loop is greater, and small changes of the applied field lead to great changes in magnetization (see Figure 3.4). For higher applied fields, where the magnetization process is governed by domain rotation, the relaxation effect decreases. This sensitivity of the relaxation amplitude with the type of magnetization process has already been observed in amorphous alloys, being the relaxation intensity reduced when magnetization reversal occurs mainly by rotation processes [21, 22]. 3.3.2. Modelization of the relaxation behavior In order to study in detail the parameters that characterize the relaxation in these materials, the temporal evolution of the resonance frequency was fitted to the following expression, which describes the relaxation behavior and is derived from the formalism of strongly correlated systems [15, 23]: fr(t) = fr0+I[1 −e−(t/τ)1−n],(3.2) where fr0is the resonance frequency of the magnetoelastic sensor at the initial time, Iaccounts for the amplitude (or intensity) of the relaxation, τis the relaxation time, and nis called the coupling parameter and 68 3.3. Relaxation measurements accounts for the correlation of the system. This function is also known in the literature as the stretched exponential, which was first introduced to describe relaxation processes in dielectric materials [24]. The numerical fittings to this expression were performed using a non-linear least squares fitting in MATLAB, and the results are in good accordance with the experimental data (as shown in Figure 3.8, dashed black lines). The evolution of the parameters fitted to equation 3.2 was then analyzed as a function of the excitation amplitude (Figure 3.9). (a) (b) (c) Figure 3.9: Evolution of the fitted parameters as a function of the amplitude of the excitation field h for different values of the applied DC-bias field (H = 4, 7.8 and 10 Oe): (a) relaxation amplitude I, (b) relaxation time τ, and (c) coupling parameter n. 69 Chapter 3. Influence of magnetic relaxation on MER detection The tendencies observed match the behavior previously observed in the experimental data (Figure 3.8). It was found that the relaxation amplitude parameter Iand the relaxation time τ, both decrease with the increase of the excitation amplitude h. The relaxation time decreases from values of up to 2300 s to values of over 300 s. This reduction of the relaxation times suggests that the energy supplied by the excitation (Table 3.1), competes with the thermal energy (κBT= 4.14×10−21Jfor Tamb=300 K), and helps the system to relax faster. As the temperature (and therefore the thermal energy) is the same in all the experiments, the energy provided by the bias and excitation magnetic fields drives the changes in the relaxation kinetics. h=20 mOe h=42 mOe h=100 mOe h=180 mOe H=4 Oe 3.26 ×10−10J6.89 ×10−10J1.66 ×10−9J3.04 ×10−9J H=7.8 Oe 5.51 ×10−10J1.16 ×10−9J2.78 ×10−9J5.04 ×10−9J H=10 Oe 6.44 ×10−10J1.36 ×10−9J3.24 ×10−9J5.85 ×10−9J Table 3.1: Magnetic energy (Emag) provided to the material by the bias and excitation fields (estimated as Emag =1 2RHTBdV , where Vis the volume of the ribbon and HTis the sum of Hand hamplitudes). In a similar manner, the relaxation amplitude Idecreases from a value of about 420 Hz to about 30 Hz when the excitation is increased (for the case of H= 4 Oe). This decrease of the after-effect intensity with higher amplitudes of the driving field has already been pointed out by other authors [25, 26]. The coupling parameter n, follows a similar trend, decaying as the excitation amplitude is increased. The characterization of this relaxation behavior, is fundamental to optimize the operational parameters of these sensors in order to enhance their real-time performance. For example, a proper selection of the excitation field amplitude (h) can significantly reduce the effect of the magnetic relaxation on the resonance frequency (in terms of its intensity and relaxation times). This optimization will be generally used in the following chapters of this Thesis. Apart from that, if the experiment allows it, a waiting time with the sensor under the Hfield can be set before the measurements to let most of the relaxation to take place. That waiting time would be determined by the relaxation time obtained through the relaxation behavior study. This strategy was followed in the application shown in Chapter 5. In the cases where the experimental procedure or the nature of the 70 3.4. Influence of the excitation amplitude on the resonance signal detection experiment do not allow to wait for the material to relax, the relaxation model (equation 3.2) can be used to correct the frequency drift in the measurements caused by the relaxation. If a control run is measured to collect the relaxation behavior of the sensor (change in its resonance frequency), it can be fitted to expression 3.2 to obtain the main relaxation parameters. Knowing these parameters, the sensor measurements of the analyte can be corrected by subtracting the fr relaxation from the sensor signal. This procedure was followed in the application shown in Chapter 4 and will be explained in detail in that chapter. 3.4. Influence of the excitation amplitude on the resonance signal As we have seen, the excitation amplitude (h) has an evident influence on the relaxation behavior and can be selected to minimize it. However, it also has a direct effect on the intrinsic value of the resonance frequency and the amplitude of the signal. As the excitation amplitude increases, both frand the resonance amplitude decrease. Figure 3.10 shows the value of both parameters as a function of the bias field Hfor different excitation amplitudes (h= 20, 42, 100, 180 mOe). Figure 3.10: Influence of the excitation field (h) on the resonance frequency (solid lines) and maximum amplitude (Z, dashed lines) of the resonance curves for different bias fields (H). Dots correspond to the relaxed values of the resonance frequency (calculated through the parameters fitted to equation 3.2 for the different excitation and bias field values). 71 Chapter 3. Influence of magnetic relaxation on MER detection [11] P. Allia, G. Soardo, and F. Vinai, “Magnetic permeability aftereffect and structural defects of amorphous ferromagnetic alloys,” Journal of Magnetism and Magnetic Materials, vol. 31, pp. 1527– 1532, 1983. [12] P. Allia and F. Vinai, “Kinetic aspects of magnetic relaxation in amorphous ferromagnetic alloys,” in Relaxation in Complex Systems and Related Topics, pp. 51–59, Springer, 1990. [13] J. Rivas, M. López-Quintela, D. Martínez, F. Walz, and H. Kronmüller, “Magnetic relaxation in amorphous metals,” Journal of Non-Crystalline Solids, vol. 131-133, pp. 1235–1239, 1991. Proceedings of the International Discussion Meetings on Relaxations in Complex Systems. [14] P. Kwapuliński and G. J. Haneczok, “Magnetic relaxation in iron based melt spun ribbons,” Acta Physica Polonica A, vol. 136, no. 5, 2019. [15] P. Kwapuliński and G. Haneczok, “Formation of the relaxed amorphous phase in iron-based amorphous alloys monitored by magnetic relaxation techniques,” IEEE Transactions on Magnetics, vol. 58, no. 4, pp. 1–7, 2020. [16] P. Allia, C. Beatrice, M. Knobel, P. Tiberto, and F. Vinai, “Relaxation of magnetoresistance and magnetization in granular cu90co10 obtained from rapidly quenched ribbons,” Journal of Applied Physics, vol. 76, no. 10, pp. 6817–6819, 1994. [17] A. Lasheras, J. Gutiérrez, A. Balza, J. Barandiarán, and A. R. Pierna, “Radiofrequency magnetoelastic resonators for magnetoelectric applications,” Journal of Physics D: Applied Physics, vol. 47, no. 31, p. 315003, 2014. [18] A. Lasheras, J. Gutiérrez, and J. Barandiarán, “Quantification of size effects in the magnetoelectric response of metallic glass/pvdf laminates,” Applied Physics Letters, vol. 108, no. 22, 2016. [19] A. Sagasti, J. Gutiérrez, A. Lasheras, and J. M. Barandiarán, “Size dependence of the magnetoelastic properties of metallic glasses for actuation applications,” Sensors, vol. 19, no. 19, 2019. [20] Y. Wang, C. Li, Y. Li, X. Zhou, W. Wu, R. Yu, J. Zhao, C. Yin, Y. Shi, C. Jin, J. Luo, L. Zhao, T. Xiang, G. Liu, and X. J. Zhou, 78 Bibliography “Long-time magnetic relaxation in antiferromagnetic topological material eucd2as2,” Chinese Physics Letters, vol. 38, p. 077201, jul 2021. [21] P. Allia, C. Beatrice, F. Vinai, M. Knobel, and R. S. Turtelli, “Suppression of the magnetic‐permeability relaxation in nanocrystalline fe73.5cu1nb3si13.5b9,” Applied Physics Letters, vol. 59, pp. 2454– 2456, 11 1991. [22] S. Cruz Filho, M. Knobel, J. Sinnecker, R. S. Turtelli, and M. Vázquez, “Disaccommodation measurements in amorphous wires,” Journal of Magnetism and Magnetic Materials, vol. 104, pp. 105–106, 1992. [23] G. Haneczok and J. Rasek, “Free volume diffusion and optimisation of soft magnetic properties in amorphous alloys based on iron,” in Defect and Diffusion Forum, vol. 224, pp. 13–26, Trans Tech Publ, 2003. [24] G. Williams and D. C. Watts, “Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function,” Trans. Faraday Soc., vol. 66, pp. 80–85, 1970. [25] P. Allia, C. Beatrice, and F. Vinai, “The role of magnetoelastic coupling on magnetic disaccomodation of amorphous and nanocrystalline alloys. in magnetoelastic effects and applications,” First Int. Meeting on Magnetoelastic Effects and Applications, pp. 47–55, 1993. [26] A. Rezende, R. Turtelli, and F. Missell, “Magnetic permeability after-effect and the transition from co-rich to fe-rich amorphous alloys,” IEEE Transactions on Magnetics, vol. 23, no. 5, pp. 2128– 2130, 1987. [27] A. Garcıa-Arribas, J. Barandiaran, J. Gutiérrez, and I. Sagastabeitia, “On the origin of the nonlinear and chaotic behavior of the magnetoelastic resonance,” Journal of applied physics, vol. 81, no. 8, pp. 5686–5688, 1997. [28] A. Hubert and R. Schäfer, Magnetic domains: the analysis of magnetic microstructures. Springer Science & Business Media, 1998. 79 Chapter 3. Influence of magnetic relaxation on MER detection [29] A. Lasheras, J. J. Saiz Garitaonandia, I. Quintana, J. L. VilasVilela, and A. C. Lopes, “Self-bias magnetoelastic resonance sensors with improved mass sensitivity performance: The effect of nanocrystallization induction by annealing,” Available at SSRN 4824115. [30] A. Lasheras, J. Garitaonandia, I. Quintana, J. Vilas, and A. C. Lopes, “Development of nanocrystallized magnetoelastic sensors with self-biased effect and improved mass sensitivity,” Sensors and Actuators Reports, p. 100251, 2024. 80 CHAPTER 4 Monitoring of precipitation reactions In this chapter, a magnetoelastic resonance sensor is used to monitor the precipitation reaction of calcium oxalate (CaC2O4) crystals in realtime, by measuring the shift of the resonance frequency caused by the mass increase on its surface as the reaction progresses. Calcium oxalate is one of the most common minerals which form the calcifications on the urinary tract, so the study of the reaction dynamics, triggers and inhibitors could be of special interest. In this sense, magnetoelastic sensors could be highly useful for the task as they exhibit a remote operation, which allows them to monitor the reaction while it is taking place. The detection of the precipitated mass was performed when oxalic acid and calcium chloride were mixed in different concentrations (from 1mM to 100 mM). The validity of the mass calibration of the sensors was carefully analyzed, as the sensors were designed to operate in liquid media. In addition, numerical fittings of the resonance curves were performed in order to improve the detection resolution in low concentration precipitation reactions. Also a correction of the magnetic relaxation was implemented to improve the detection limit. The results show that the sensor is capable of tracking the precipitation reaction of solutions of concentration as low as 1 mM, with the sensor being able to resolve a mass of precipitate of 2 µg. The work presented in this chapter has resulted in the following publications: • Sisniega, B., Sagasti Sedano, A., Gutiérrez, J. and García-Arribas, A. “Real time monitoring of calcium oxalate precipitation reaction by using corrosion resistant magnetoelastic resonance sensors”. Sensors, 20(10), 2802 (2020). • Sisniega, B., Gutiérrez, J. and García-Arribas, A. “Magnetoelastic resonance detection of calcium oxalate precipitation in low concentration solutions”.IEEE Transactions on Magnetics, 58(2), 1-5 (2021). 4.1. Introduction 4.1. Introduction As we have seen, the sensitivity of magnetoelastic sensors to mass changes, together with their ability to query and detect remotely, make these devices especially interesting for sensing biological and chemical agents (see Table 1.1). In particular, the remote monitoring of precipitation reaction processes with these sensors is especially interesting, as they can provide real-time tracking of the evolution of the reaction when they are placed inside the reactor where the process occurs. This monitoring can provide information about the reaction kinetics or the factors that influence it, for example the effect of some inhibitors or catalysts. Among the precipitation reactions, some of them are of special importance in biomedicine as they are related to biochemical processes that affect the human health. In the human body, there are essential inorganic salts for diverse metabolic activities, which are dissociated in solution into ions (or electrolytes). If some of these ions are not properly absorbed within the body, they will tend to crystallize and eventually, to form stones. One of these precipitation processes is the formation of calcium oxalate (CaC2O4) crystals, one of the most common minerals that form calcifications in the urinary tract (so-called kidney or bladder stones, Figure 4.1) [1]. Kidney stones, also known as renal calculi, are mostly calcium based [2], and in particular calcium oxalate is the most common component (approximately 70% of stones are calcium oxalate-based [3]). Figure 4.1: Calcium oxalate urolith. Under normal conditions, urine has a remarkable ability to inhibit calcium oxalate crystallization, which prevents most of the population from continuously forming such stones. But some disorders, such as 83 Chapter 4. Monitoring of precipitation reactions hypercalciuria or hyperoxaluria (urine supersaturated with calcium or oxalate), can contribute to increasing the risk of suffering this pathology. In a urine sample collected over 24 h from an average adult, a quantity of 100–250 mg of calcium is usually found. In conditions of hypercalciuria the urine calcium excretion can be greater than 275–300 mg/day [4, 5], which can be estimated as 5 mM concentration of calcium (taken a 24-hour standard urine volume of 1.5 L). Hyperoxaluria, on the other hand, is an increased excretion of oxalate in urine, and it is also related to the formation of stones in the urinary tract [6]. The normal values of oxalate excretion in urine are under 40 mg/day [7], which corresponds to approximately a concentration of 0.3 mM. The use of magnetoelastic sensors to remotely monitor these types of reactions can provide fundamental information about the precipitation processes in biological fluids. It can increase our understanding of these complex processes of bio-mineralization, since this technique allows, for example, to study precipitation systems under the influence of different factors (such as pH, or concentration and chemical composition of the urine [8]), in order to know which factors or substances favor or inhibit the formation of crystals in the urinary tract [9–11]. Information about the precipitate mass in real-time can complement the information (usually obtained by monitoring changes in pH or concentration [12]) of studies in artificial systems that mimic the human physiological conditions, like human urine. Previous works by Bouropoulos and co-workers [13] have used magnetoelastic sensors to monitor this kind of bio-reactions, but in the present study several factors were improved: • The amorphous ferromagnetic material (Metglas 2826 alloy) was substituted by a ribbon of composition Fe73Cr5Si10B12, which avoids the need for pre-treatment of the surface to protect it from the corrosion occurring in the biological medium. This simplifies the procedure and enhances the sensitivity and quality of the signals (of great importance when using these sensors in aqueous environments). • The numerical fittings of the resonance curves described in Chapter 2 were used to overcome the negative effect that the damping of the liquid media and the deposited mass have on the quality of the signal, and therefore on the frdetermination. 84 4.2. Calcium oxalate precipitation • The magnetic relaxation correction was applied to the measurements, specially to the low concentration reactions (near the solubility limit of calcium oxalate, which has been reported to be around 10−4M (0.1 mM) in pure water at 25 ◦C [14]), in order to explore the limit of detection of the sensors. 4.2. Calcium oxalate precipitation The monitoring of the precipitation reaction was carried out by placing the magnetoelastic sensor in a small vial (Figures 4.2 and 4.3) with a mixture of equal parts (0.6 mL) of oxalic acid (H2C2O4) and calcium chloride (CaCl2) solutions at the same concentration, leading to the formation of the insoluble calcium oxalate crystals (CaC2O4) according to the reaction: CaCl2(aq) + H2C2O4(aq)→CaC2O4(s)+2HCl(aq).(4.1) C Calcium oxalate crystals Magnetoelastic sensor Glass vial Figure 4.2: 3D representation of the experimental procedure, the sensor is placed in a glass vial with the reactants, and the changes in the sensor signal are tracked while the precipitate is formed and settled on the sensor. The precipitation reaction occurs after mixing the two reactants and the formation of the salt crystals was tracked in real-time by monitoring the changes in the resonant frequency of the magnetoelastic sensor, which shifts as the precipitate is deposited on its surface, as a direct consequence of the increase of its total mass. 85 Chapter 4. Monitoring of precipitation reactions Equation 4.9 Simulations Material β1 2(β2−1) s Chromium 1.36 + 0.42 + 0.41 Aluminium 1.15 + 0.16 + 0.16 Silver 0.63 - 0.30 - 0.29 Gold 0.45 - 0.39 - 0.37 Table 4.1: Comparison between the sensitivity coefficients obtained with the expression 4.10 and those obtained with Comsol simulations. The coefficient 1 2(β2−1) in equation 4.10 is equivalent to s of the simulations (slope of the ∆fr/fr-∆m/m0relation). itate crystals, so that the elastic modulus and the density affecting the resonator would be the same as in the actual experiment, and possible errors obtained when calibrating with other materials would be avoided. 4.4.2. Effect of the medium on the mass sensitivity of the sensor The medium in which the magnetoelastic sensor is immersed will influence the shape of the resonance curve. This effect is depicted in Figure 4.7, which shows the resonance of the same sensor placed in different media (air, distilled water and glycerol 50 %). Figure 4.7: Effect of the surrounding media on the resonance curve. Measurements performed with a Metglas 2826 ribbon of dimensions 12.7 ×5 mm in air, water and a glycerol solution at 50 %. 92 4.4. Sensor calibration As it can be observed, working in more dense and viscous media causes both the resonance frequency and the amplitude of the sensor to decrease, and the quality factor Qto drop (due to the higher damping suffered by the ribbon). Grimes et al. [19] already gave an expression for the observed decrease in the magnetoelastic resonance frequency when the vibrating sensor is immersed in a viscous liquid: ∆fr=−√πηρl 2πdρs (fr)1/2,(4.11) where ηand ρlare the viscosity and density of the liquid, and ρsand d are the density and thickness of the resonator, respectively. The ∆frvalues obtained with this expression are compared with the experimental ones in Table 4.2. For the calculation, the following values were used: η(Water) =0.89 ×10−3Pa·s, ρl(Water) = 1000 kg/m3, η(Glycerol 50%) =6.8×10−3Pa·s, ρl(Glycerol 50%) = 1130 kg/m3, d= 25 µm, ρs= 7900 kg/m3and fr(Air)= 174.8 kHz. It is clear that the theoretical expression underestimates the actual change that suffers frwhen the sensor is immersed in a liquid, which is systematically greater when it is experimentally measured. ∆frExperimental (kHz) ∆frExpression 4.11 (kHz) Water -0.89 -0.56 Glycerol 50 % -2.24 -1.65 Table 4.2: Comparison of experimental and theoretical value (calculated through expression 4.11) of the change in resonance frequency of the sensor (∆fr) produced by the different media (with respect to its value in air). In order to elucidate if this effect will also affect the mass sensitivity or it will remain the same independently of the medium where the sensor is working, a test of calibration under different media was performed. To do that, a magnetoelastic sensor (Metglas 2826MB composition, dimensions 12.7 x 5 mm) was coated with polystyrene several times and its resonance frequency was measured after each deposition while vibrating in different media (air, water and glycerol 50 %). The polystyrene coating was performed with a spin coating machine (using a dissolution of polystyrene in acetone of concentration 0.5 g/ml), and the mass of the coating was measured on each step on a high precision balance. The results are shown in Figure 4.8. 93 Chapter 4. Monitoring of precipitation reactions Figure 4.8: Mass sensitivity of the same sensor in different media (air, water and glycerol 50 %). It was found that the sensitivity remained almost the same when the sensor was working in different media even though its resonance was damped. Therefore, regardless of the fact that the precipitation reaction sensor will be operating in a liquid medium, its mass calibration in air provides a valid estimation of the mass of precipitate. 4.4.3. Mass sensitivity calibration Taking the above-mentioned study into account, the calibration of the sensor to monitor the precipitation reaction was performed following two conditions. On the one hand, calcium oxalate crystals were deposited on the sensor surface so that the Young’s modulus and density of the coating are the same as in the real measurement; On the other hand, the calibration was performed in air, since, as we have seen, the value of the sensitivity is independent of the surrounding medium. This air calibration facilitates the procedure since dealing with calcium oxalate layers in water would be very complicated. The calibration of the sensor sensitivity to added mass was performed by depositing, in successive steps, a known mass of calcium oxalate precipitate on the sensor surface and measuring the corresponding change of its resonance frequency in air. The measurements were performed at a bias field corresponding to the anisotropy field (Hk, in our case Hk= 6.5 Oe, see Figure 4.9a), which will be the operation point of the sensor. 94 4.4. Sensor calibration Hk (a) (b) Figure 4.9: (a) Dependence of the resonance frequency with the applied magnetic field for the ribbon measured in air and when it is immersed in distilled water. The anisotropy field (minimum resonance frequency) was measured as Hk= 6.5 Oe, and did not change when the sensor was immersed in water. (b) Magnetoelastic resonance curves measured in air and water at Hk. The deposition of calcium oxalate crystals on the sensor surface was performed by preparing a precipitation solution (described in section 4.2) and letting the crystals to form. Then, by using a pipette, the surface of the resonator was covered with this solution and left to dry. Afterwards, the sensor was weighed on a precision balance (Figure 4.10, 0.1 µg resolution), and its magnetoelastic resonance frequency was measured at the anisotropy field. This process was repeated several times in order to obtain different points for the mass calibration (shown in Figure 4.11). Figure 4.10: High precision balance (Sartorius SE2) used to calibrate the response of the sensor to mass loadings. As we have seen in the introduction chapter, equation 4.3 is a first order approximation of the more general expression [20]: 95 Chapter 4. Monitoring of precipitation reactions fr f0 = (1 + ∆m m0 )−1/2.(4.12) This approximation is valid for small mass loads, when the other therms of the expansion are negligible. But the mass changes suffered by the sensor during the calcium oxalate precipitation process can be greater than 5 % of the initial weight of the sensor (m0= 7.6063 mg), as we will see below. When mass loads are considerable, the relation between the resonance frequency and the deposited mass is not linear any more. Therefore, a second order expansion of equation 4.12 has been used to obtain an appropriate fit for the calibration curve (shown in Figure 4.11): ∆f=fr−f0≈ − f0 2m0 ∆m+3f0 8m2 0 (∆m)2=a1∆m+a2(∆m)2.(4.13) -14 -12 -10 -8 -6 -4 -2 0 00.5 11.5 ∆f*(kHz) ∆m*(mg) ∆f*=*-9.8*(∆m)+*1.1*(∆m)2* Figure 4.11: Calibration curve obtained from the changes in the resonance frequency of the resonator (measured in air), caused by different calcium oxalate mass depositions on its surface. Black dots represent the measured calibration points. The solid red line represents the fit to Equation 4.13, with coefficients a1= −9.8 kHz/mg and a2= 1.1 kHz/mg2. The obtained calibration constants are: a1=−9.8±0.4kHz/mg a2= 1.1±0.3kHz/mg2 96 4.4. Sensor calibration Comparing the sensor sensitivity reported by Bouropoulos et al. [13], −1.38 kHz/mg, with the main mass calibration constant (a1) obtained for the magnetoelastic resonator in this work, our sensor is about seven times more sensitive. The main reason that accounts for this fact is the better magnetoelastic coupling coefficient (k) of the magnetoelastic ribbon. This is directly related to the length-to-width ratio (R=L/w) chosen for the resonator used in our experiments (R= 10, instead of R∼3of the previous work [13]). We can compare the experimentally obtained calibration constants with the theoretical ones, which can be calculated to be a1=−f0 2m0= −7.3kHz/mg and a2=3f0 8m2 0 = 0.7kHz/mg2(the mass and resonance frequency of the bare magnetoelastic sensor are m0= 7.6063 mg and f0 = 111.85 kHz, respectively). It can be observed that the experimental calibration constants are both higher than the expected values (by 25 % and 36 %, respectively). In principle, we could estimate the properties of the coating material (E/ρ of calcium oxalate) through the experimental mass calibration, by comparing it to equation 4.10. Using the main calibration constant obtained in the experiments, a value of β2=−0.28 is obtained ((a≈1/2(β2−1), being athe dimensionless calibration constant a=a1m0/f0=−0.64). This incongruence of the negative value of β2indicates that this procedure to obtain the elastic properties of the coating is not valid in our case (although its validity has been reported by other authors with other coating materials (silver, aluminium) [17]). Actually, observing equation 4.10, we realize that calibration constants a < −0.5are not explained by this approximation (as they will lead to negative values of β2), so the effect of the coating density and elasticity explained in section 4.4.1 does not completely explain the experimentally obtained calibration constant with calcium oxalate. This may be due to the fact that the elastic properties and homogeneity of calcium oxalate coatings are not comparable to those studied in that section, therefore the application of the elastic theory may not be adequate to study the effect of this kind of coating materials. Or because there are still other factors affecting the sensitivity that are not being considered. We can conclude that the differences observed between the experimental and the theoretical mass calibration, may be partially due to the effect of the coating properties, but still not completely explained in some experimental cases, as it is this case, so this is still an open subject. 97 Chapter 4. Monitoring of precipitation reactions 4.5. Results of the monitoring of the precipitation process Monitoring of precipitation reactions at high concentration First, the sensor was tested with high concentrations of the reactants (30, 50 and 100 mM). The effect of the different concentrations in the sensor signal can be observed in Figure 4.12. 30 mM 50 mM 100 mM (a) (b) (c) Figure 4.12: Measured magnetoelastic resonance curves of the sensor at different times during the precipitation process for solutions of oxalic acid and calcium chloride with concentrations of: (a) 30 mM, (b) 50 mM and (c) 100 mM. 98 4.5. Results of the monitoring of the precipitation process In this case, the spectrum analyzer was set to perform a sweep over the frequency range (80 - 122 kHz) in 5 s, with a resolution bandwidth of 105 Hz. The amplitude of the excitation field was set to h= 162 mOe in order to reduce the magnetic relaxation. The measured resonance curves show, in the same time window of 500 s, how quickly both the magnetoelastic resonance frequency (in kHz) and the amplitude of the detected signal (in mV) decreased as the calcium oxalate crystals were formed in each reaction. The rate at which this decrease occurred was clearly higher for the 100 mM than for the 30 mM concentration solution. In addition, a decrease of the quality factor (widening of the resonance curves, and thus a decrease of the signal quality) was observed as the reaction progressed and the precipitate mass was settled on the sensor surface. Figure 4.13a shows the temporal evolution of the sensor resonance frequency corresponding to the different concentration reactions. (a) (b) Figure 4.13: (a) Temporal evolution of frmeasured during the precipitation process for different reactant concentrations (30, 50 and 100 mM) and for the control test (sensor in a vial with distilled water). (b) Temporal evolution of frobtained through the numerical fitting of the experimental curves (experimental data shown in light colors, and frfrom fittings shown in dark colors). As it can be observed, the change in resonance frequency is directly related to the kinetics of the reaction and the quantity of precipitate formed. Note that the results for the 100 mM reaction are quite noisy; that noise is due to the deterioration of the signal quality (low Q) as the precipitate settles on the resonator and dampens its vibration (see Figure 4.12c). A poor quality signal reduces the accuracy with which 99 Chapter 4. Monitoring of precipitation reactions we can determine the resonance frequency. Thus, in order to improve the resolution in determining the resonance frequency of the sensor, the experimental data (resonance curves) were numerically fitted to equation 2.10 as described in Chapter 2 (the frvalues obtained from the fittings are taken from the maximum amplitude of the fitting curves). As the fitting equation not only depends on the resonance frequency but on the hole resonance curve (characterized also by other factors such as damping or background parameters), the parameters obtained through it are not as affected by noise as if the resonance frequency is taken directly from the maximum of the experimental curve. This improvement can be noticed in Figure 4.13b. The noise in frdetermination in the control run was around 100 Hz (corresponding to an increase of the resonator mass of about 10 µg according to equation 4.13 and the calibration constants a1and a2), and increases as the resonator is damped with the precipitate mass reaching values up to 2-3 kHz in the 100 mM concentration reaction (raising the mass detection limit to 200-300 µg.). With the numerical fittings, that noise was reduced to 10 Hz (see Figure 4.14), which improves the mass resolution to 1 µg. Figure 4.14: Close up look at the control measurement (gray), and reduction of frnoise by the numerical fittings (black). In addition to the change in resonance frequency, the effect of the precipitate in the sensor signal is also noticeable on other resonance parameters, for example on its amplitude, which decreases as the reaction progresses (see Figure 4.15a). Moreover, the numerical fittings allow us to study the reactions through the evolution of other parameters, as the damping parameters δrand δa, which increase as the precipitate is settled on the surface of the sensor (see Figure 4.15). 100 4.5. Results of the monitoring of the precipitation process (a) (b) (c) Figure 4.15: Temporal evolution during the reactions (for concentration 30, 50 and 100 mM) of (a) the maximum amplitude of the signal (resonance amplitude in mV obtained through the numerical fittings), and the damping parameters (b) δrand (c) δa. Monitoring of precipitation reactions at low concentration In order to explore the performance of the sensor at low concentrations and therefore determine its limit of detection, reactant solutions of concentration 1, 3, 5 and 10 mM were next used. When reducing the concentration, the mass of precipitate formed is less, so the changes observed in the resonance are considerably smaller (see Figure 4.16); Also, the rate of reaction is reduced. Therefore, in this case, the reaction time monitored was increased to 2000 s. In addition, the bandwidth of the frequency sweep was reduced to 36 Hz in order to distinguish smaller frequency shifts. The frequency range was also reduced to 100 - 122 kHz, since small frequency changes are expected. With this configuration the sweep time was 36 s, enough for following these reactions, since they evolve slower than the previous ones. 101 Chapter 4. Monitoring of precipitation reactions netoelastic sensor in the reaction at this concentration. 100 mM (a) 10 mM (b) 1 mM (c) (d) Figure 4.22: Scanning Electron Microscopy images of the precipitated calcium oxalate crystals (A mixture of COM and COD crystals were found). The predominant morphology is the COM structure. Precipitate formed in the reaction with reagents of concentration (a) 100 mM (scale bar is 50 µm), (b) 10 mM (scale bar 20 µm), and (c) 1 mM (scale bar 20 µm). (d) Detail of both morphologies of the calcium oxalate crystals, the hexagonal plate-like shape of COM crystals, and the octahedral shape of COD crystals. In white, a schematic 3D view of both crystals is shown. Scale bar is 10 µm. 4.7. Conclusions The results presented in this chapter demonstrate the feasibility of using magnetoelastic sensors in those cases where remote and nondestructive detection is required, as it is the case of the precipitation reaction of physiological inorganic salts, such as calcium oxalate (CaC2O4). 108 4.7. Conclusions MER detection turned out to be a fast detection technique, which allow the monitoring of the precipitation process and the study of its dynamics (precipitate mass, rate of reaction). The corrosion resistant alloy (Fe73Cr5Si10B12) used in this experiment has demonstrated to be as capable as the commercial Metglas 2826 alloy in monitoring precipitation reactions, with the advantage that no pretreatment is required to prevent oxidation when used as a precipitation reaction sensor. In addition, the use of the numerical fitting of the sensor resonance curves has improved significantly the sensor resolution in the determination of fr, and therefore the resolution in mass quantification (the resolution was improved from 10 µg to 1 µg). On the other hand, the correction of the relaxation effect by fitting the relaxation behavior and subtracting it from the measurements has improved the limit of detection of the sensors, so that precipitate masses as low as 2 µg are discernible by our sensing system. To achieve a correct mass calibration sensitivity of the sensors, several factors have been analyzed in this chapter. It was found that the surrounding medium (aqueous), although it affects the resonance signal, does not affect the sensor sensitivity. This allows to perform air mass sensitivity calibrations which will be valid for the sensor operating in liquid. However, regarding the material used as coating for the mass calibration, its mechanical properties greatly affect the sensitivity; therefore, the mass calibration should be performed with the specific analyte material (whenever it is possible). The difference between the theoretically and the experimentally obtained calibration constants is not yet completely explained by the effect of the coating properties in some cases, as is the case of calcium oxalate. Further investigation could be performed to elucidate other factors affecting that mass sensitivity. 109 Chapter 4. Monitoring of precipitation reactions Bibliography [1] T. Alelign and B. Petros, “Kidney stone disease: an update on current concepts,” Advances in urology, vol. 2018, 2018. [2] A. K. Singh, “Kidney stones,” in Decision Making in Medicine (Third Edition) (S. B. Mushlin and H. L. Greene, eds.), pp. 364– 367, Philadelphia: Mosby, third edition ed., 2010. [3] D. B. Leusmann, R. Blaschke, and W. 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Nancollas, “Crystallization of calcium phosphates. a constant composition study,” Journal of the American Chemical Society, vol. 102, no. 5, pp. 1553– 1557, 1980. [13] N. Bouropoulos, D. Kouzoudis, and C. Grimes, “The real-time, in situ monitoring of calcium oxalate and brushite precipitation using magnetoelastic sensors,” Sensors and Actuators B: Chemical, vol. 109, no. 2, pp. 227–232, 2005. [14] F. Ibis, P. Dhand, S. Suleymanli, A. E. van der Heijden, H. J. Kramer, and H. B. Eral, “A combined experimental and modelling study on solubility of calcium oxalate monohydrate at physiologically relevant ph and temperatures,” Crystals, vol. 10, no. 10, p. 924, 2020. [15] A. Sagasti, J. Gutiérrez, A. Lasheras, and J. M. Barandiarán, “Size dependence of the magnetoelastic properties of metallic glasses for actuation applications,” Sensors, vol. 19, no. 19, 2019. [16] A. Sagasti, J. Gutierrez, M. San Sebastián, and J. Barandiaran, “Magnetoelastic resonators for highly specific chemical and biological detection: A critical study,” IEEE Transactions on Magnetics, vol. 53, no. 4, pp. 1–4, 2016. [17] S. Schmidt and C. A. Grimes, “Characterization of nanodimensional thin-film elastic moduli using magnetoelastic sensors,” Sensors and Actuators A: Physical, vol. 94, no. 3, pp. 189–196, 2001. [18] S. Schmidt and C. A. Grimes, “Elastic modulus measurement of thin films coated onto magnetoelastic ribbons,” IEEE transactions on magnetics, vol. 37, no. 4, pp. 2731–2733, 2001. [19] C. A. Grimes, C. S. Mungle, K. Zeng, M. K. Jain, W. R. Dreschel, M. Paulose, and K. G. Ong, “Wireless magnetoelastic resonance sensors: A critical review,” Sensors, vol. 2, no. 7, pp. 294–313, 2002. 111 Chapter 4. Monitoring of precipitation reactions [20] P. G. Stoyanov and C. A. Grimes, “A remote query magnetostrictive viscosity sensor,” Sensors and Actuators A: Physical, vol. 80, no. 1, pp. 8–14, 2000. [21] N. Bouropoulos, C. Bouropoulos, P. Klepetsanis, M. Melekos, G. Barbalias, and P. Koutsoukos, “A model system for the investigation of urinary stone formation,” British journal of urology, vol. 78, no. 2, pp. 169–175, 1996. [22] T. Jung, W.-S. Kim, and C. K. Choi, “Biomineralization of calcium oxalate for controlling crystal structure and morphology,” Materials Science and Engineering: C, vol. 24, no. 1-2, pp. 31–33, 2004. [23] J. A. Wesson, E. M. Worcester, J. H. Wiessner, N. S. Mandel, and J. G. Kleinman, “Control of calcium oxalate crystal structure and cell adherence by urinary macromolecules,” Kidney international, vol. 53, no. 4, pp. 952–957, 1998. 112 CHAPTER 5 Metal Organic Frameworks as active layers: wireless humidity detection In this chapter, the functionalization of the magnetoelastic resonators with Metal Organic Framework (MOF) active layers is studied with the purpose of detecting humidity. Metal organic framework materials are known for their high adsorption capacity, which is due to their high porosity and surface area, and for their tunable selectivity, which comes from the fact that their pore chemistry and volume can be engineered to absorb specific molecules. In the following, different water-adsorbent MOF materials were synthesized and integrated as active layers onto the MER resonators. Their water absorption capacity and overall performance when integrated into the sensors were evaluated in terms of response time, sensitivity, stability, and selectivity to water molecules. The selected MOFs showed promising water harvesting capacity, enabling a successful sensor response to humidity in a wide range of relative humidity (3 % – 85 %) with competitive response times. In addition, magnetoelastic resonators have emerged as a promising tool for the characterization of the dynamic adsorption capacity of MOF materials. The work presented in this chapter has resulted in the following publication: • Sisniega, B., Fernández de Luis, R., Gutiérrez, J. and García-Arribas, A. “Magnetoelastic resonators functionalized with metal–organic framework water harvesters as wireless humidity sensors”.APL Materials, 12(7) (2024). 5.1. Introduction 5.1. Introduction With the accelerated progress of different industries and the raising awareness about the necessity of sustainable and healthy lifestyles, the detection of the presence of different gases and vapors have become imperative. Among a wide variety of gases, the detection of humidity (or its quantifying parameter, relative humidity, RH) is of particular importance due to the ubiquitous presence of water vapor in our atmosphere. Relative humidity detection is key in many fields (Figure 5.1), as environmental control, monitoring of processing industries, food storage, agriculture, or many domestic applications, such as the automated control of living environments in buildings [1]. Humidity detection is essential even when it comes to the capture and detection of other gases (e.g. CO2detection) [2], as water is a common interfering molecule. AIR QUALITY MONITORING CONTROL OF PROCESSING INDUSTRIES AGRICULTURE AND METEOROLOGY FOOD STORAGE BIODETECTION ADVANCED FABRICATION Figure 5.1: Application of humidity detection in several fields. Humidity sensors transduce the amount of water to some measurable parameter and, up to date, are mostly based on resistance [3], capacitance [4, 5] or refractive index changes [6, 7]. The degree of selectivity, sensitivity, robustness, compactness, fast response and cost required for humidity sensors depend highly on the specific application. Ideally, 115 Chapter 5. MOFs as active layers: wireless humidity detection washes. Finally, the obtained white powder was dried for 24 h at 80 ℃. The structure of MOF-808 arises from the coordination of trimesic acid molecules with six atoms of zirconium each. The zirconium atoms are then organized in hexa-nuclear metallic clusters (Zr6(OH)4O4) (Figure 5.7). UiO-66-NH2 H C O Zr N BDC-NH2 z x y z x y z x y z y Figure 5.8: Formation process of the UiO-66-NH2material. In a glass jar, the linker, 0.362 g (2 mmol) of 2-aminoterephthalic acid (BDC-NH2(C8O4NH7)), was dissolved with 20 mL of ethanol (EtOH) and 7 mL of formic acid. In a beaker, ZrCl4(0.47 g, 2 mmol) was dissolved with 16 mL of water. Then the zirconium chloride solution was slowly added to the linker solution while stirring, and finally left in the oven during 24 h at 100 ℃. After that, the resulting precipitate was centrifuged (7000 rpm, 10 122 5.3. MOF synthesis minutes) and subjected to four washing cycles with water followed by four methanol washes. Finally, the obtained white powder was dried for 24 h at 80 ℃. Again, as in the other zirconium-based MOFs, hexa-nuclear zirconium clusters are formed and connected through the organic linkers (in this case, BDC-NH2) (see Figure 5.8). Al-Fum H C O Al z x z x y z x y z y Fumaric acid Figure 5.9: Formation process of the Al-Fum material. The synthesis of Al-Fumarate was rescaled from the work of Zheng et al. [32]. A mixture of NaOH (0.24 g, 6 mmol) and fumaric acid (C4H4O4, 0.232 g, 2 mmol) was dissolved in 2.6 mL of distilled water in a screw-capped glass jar. The resulting solution was stirred until the solids were completely dissolved. Then, in a beaker, AlCl3·6H2O (0.482 g, 2 mmol) was dissolved in 2.4 mL of distilled water. The aluminium 123 Chapter 5. MOFs as active layers: wireless humidity detection chloride solution was slowly added to the linker solution. The reaction was stirred for 24 hours in a 100 ℃ oil bath. After the synthesis, the sample was centrifuged (7000 rpm, 10 minutes) and washed with aqueous 70 % ethanol (EtOH) solution, and then centrifuged and washed again with EtOH. Finally, it was dried overnight at 80 ℃. The fumaric acid is coordinated with the aluminium atoms, which then form chains (see Figure 5.9). CAU-23 S H C O Al H2TDC z x y z x y z x z y Figure 5.10: Formation process of the CAU-23 material. The synthesis of CAU-23 was scale-down from the work of Zheng et al. [32]. A mixture of NaOH (0.24 g, 6 mmol) and 2,5-thiophenedicarboxylic acid (H2TDC, C6H4O4S) (0.334 g, 2 mmol) was dissolved in 3.8 mL of distilled water in a screw-capped glass jar. The resulting solution was stirred until the solids were completely dissolved. Then, 124 5.4. MOF Characterization in a beaker, AlCl3·6H2O (0.482 g, 2 mmol) was dissolved in 1.2 mL of distilled water. The aluminum chloride solution was slowly added to the linker solution and the precipitate formed instantaneously. The reaction was left for 6 hours in an oil bath at 100 ℃ while stirring. After the synthesis, the sample was centrifuged (7000 rpm, 10 minutes) and washed with aqueous 70 % EtOH solution, and then centrifuged and washed again with EtOH. Finally, the obtained white powder was dried for 24 h at 80 ℃. As in the case of Al-Fum, the aluminium atoms are configured in chains, which are interconnected with the organic linkers (H2TDC) (see Figure 5.10). 5.4. MOF Characterization Once the MOFs were synthesized, and before their integration as active layers onto the MER sensors, a detailed characterization of the resulted materials was performed with several techniques in order to study their crystal structure and assembly of the building blocks, the number of structural defects they present and their stability to water presence. Such study was performed by means of X-Ray Diffraction analysis, Infra-Red (IR) spectroscopy and thermogravimetric analysis (TGA). 5.4.1. X-Ray Diffraction analysis In order to evaluate the crystalline purity of the MOF materials, which would confirm their successful synthesis and quality, their crystal structures were studied by X-Ray Diffraction characterization. The powder X-Ray Diffraction (XRD) patterns of the MOF materials were measured with a Panalytical X’pert PRO diffractometer (general services of UPV/EHU, SGIker), with CuKαradiation (λ= 1.5406 Å) in the range of 5◦<2θ < 70◦, with a step size of 0.02◦(see details about the diffractometer and X-Ray diffraction technique in Appendix A.5). As it can be observed in Figure 5.11, the measured diffractograms coincide with the patterns simulated from the structural information obtained from the Cambridge Structural Database (Cambridge Crystallographic Data Center, CCDC) for these materials. The data coincide as well with the patterns previously reported in the literature [35–38]. 125 Chapter 5. MOFs as active layers: wireless humidity detection Figure 5.11: Normalized powder X-Ray Diffraction (XRD) patterns of the synthetized MOFs (measured with CuKαradiation (λ= 1.5406 Å), 5◦<2θ < 70◦with step 0.02◦), and comparison with the simulated profiles. Further analysis of the data by a full-profile pattern matching using FullProf Suite [39] (see details about the pattern-matching in Appendix A.5), confirmed the purity of the samples and the absence of additional phases (Figure 5.12). The final fittings of the pattern matching analysis allow to estimate the cell parameters of the samples, which are resumed in Table 5.1 and are very close to the ones reported in previous studies. The MOFs based on zirconium (MOF 801, MOF-808 and UiO-66126 5.4. MOF Characterization NH2) present a cubic unit cell (with a=b=cand α=β=γ= 90◦). Whereas Al-Fum and CAU-23, belong to the monoclinic (a=b=cand α=γ= 90◦=β) and orthorombic (a=b=cand α=γ=β= 90◦) systems respectively. (a) (b) (c) (d) (e) Figure 5.12: Powder X-Ray diffraction profile analysis of: (a) MOF801, (b) MOF-808, (c) UiO-66-NH2,(d) Al-Fum and (e) CAU-23. 127 Chapter 5. MOFs as active layers: wireless humidity detection The crystallographic space groups of the MOFs were also confirmed (Table 5.2). Table 5.1: Cell parameters estimated with the full-profile pattern matching of the XRD data. a(Å) b(Å) c(Å) α(◦)β(◦)γ(◦) MOF-801 17.8910 ±0.0004 17.8910 ±0.0004 17.8910 ±0.0004 90 90 90 MOF-808 35.462 ±0.003 35.462 ±0.003 35.462 ±0.003 90 90 90 UiO-66-NH220.778 ±0.003 20.778 ±0.003 20.778 ±0.003 90 90 90 Al-Fum 6.8344 ±0.0008 12.139 ±0.001 14.231 ±0.002 90 122.53 90 CAU-23 15.4538 ±0.0009 24.0200 ±0.0009 14.2044 ±0.0009 90 90 90 Table 5.2: Crystallographic space group of the MOF materials. Space Group Symbol MOF-801 Pn¯ 3 MOF-808 Fd¯ 3m UiO-66-NH2Fm¯ 3m Al-Fum P121/c1 CAU-23 P21212 5.4.2. Hydrolytic stability of the MOF materials There are two pathways for the degradation of MOFs in the presence of water: hydrolysis and linker displacement. Hydrolysis occurs when the metal-linker bond is broken by addition of hydroxyl groups resulting in the liberation of a free, protonated linker, while the linker displacement mechanism involves the insertion of a water molecule into the metal-linker bond, followed by the release of a free, deprotonated linker [40]. The MOFs synthesized are, in principle, water-stable, but in order to confirm their stability to the exposure to high humidity levels during long periods of time (and prove the correct behavior of the sensors under extreme humidity conditions), a hydrolytic stability test was performed. The degradation of MOFs in the presence of water is often accompanied by a partial loss of crystallinity, which is why the comparison of X-Ray Diffraction patterns collected before and after exposure to humidity is often used to assess their stability [40]. Unstable compounds typically show a broadening of the diffraction maxima or even complete 128 5.4. MOF Characterization amorphization upon exposure to moisture. Therefore, the hydrolytic stability of the MOFs was evaluated by analyzing their X-Ray Diffraction patterns before and after they were exposed to a water-saturated atmosphere during 1 week (Figure 5.13). (a) (b) (c) (d) (e) Figure 5.13: Comparison of the XRD patterns before and after 1 week of exposition to high humidity of:(a) MOF-801, (b) MOF-808, (c) UiO66-NH2,(d) Al-Fum and (e) CAU-23. 129 Chapter 5. MOFs as active layers: wireless humidity detection The XRD patterns of the samples before and after the water exposition have been compared qualitatively, and the results show that the MOFs have a good water stability, as the patterns coincide with the ones before the exposition. Only MOF-808 shows a slight loss of crystallinity as some of the reflections appear to be broaden, but still, it is not considerably degraded. Therefore, the MOF materials are suitable to be used as active layers with the purpose of water detection. 5.4.3. FTIR Spectroscopy analysis In order to confirm that the MOFs are well-formed, Fourier Transform Infra-Red (FTIR) spectroscopy can be used to study the main vibrational modes of the structure of the materials. The observation of the different modes of vibration can indicate the presence of specific bonds within the structure, which will confirm the successful bonding of the different structural units. The IR-spectra of the samples (Figure 5.14), were measured after drying the samples at 125 ◦C during 12 h in a Jasco FT/IR-6100 spectrometer (see details about the technique and measurements in Appendix A.6). Figure 5.14: FTIR spectra of the synthesized MOF materials after drying them at 125 ◦C during 12 h. 130 5.4. MOF Characterization The MOF materials, specially MOF-801, MOF-808 and UiO-66NH2show a broad signal at 3700 - 3200 cm−1associated to the water molecules adsorbed within the MOF which are not totally removed by drying the samples. Nevertheless, the signature of the structural hydroxyl groups are easily located within this region (stretching vibration peaks of O-H are located between 3700 and 3600 cm−1, marked with * symbol in Figure 5.14). The most important section of the IR spectra is the one that contains the typical bands around 1620, 1581 and 1380 cm−1(**), which correspond to the stretching modes of carboxylate groups coordinated with the Zr and Al-based metal nodes, suggesting the successful bonding of the linkers with the metal ions. Signals around 983, and 796 cm−1can be attributed to C-H and C=C-H out-of-plane bending vibrations (***). Particularly, for UiO-66NH2, the absorption band at 1258 cm−1is associated to the vibrational modes of amino groups (#) in the BDC-NH2linker, and the signals at 3500 cm−1and 3400 cm−1, correspond to the asymmetric and symmetric N–H stretching (+). 5.4.4. Thermogravimetric analysis Metal-organic frameworks, and especially zirconium-based ones, are widely known for their defective chemistry [41]. That is, depending on the synthesis conditions, different degrees of missing linker can be generated randomly within their long-range crystal structures. Some linkers can be missing or can be replaced by other molecules (such as water or solvent molecules). In fact, the defects can have a great impact on the adsorptive properties of the MOFs and therefore, on their water harvesting performance [42]. The estimation of this linker defect density of the materials was carried out by thermogravimetric analysis (TGA). In general, TGA curves present different weight loss steps in different temperature ranges associated with the evaporation or calcination of the different molecules forming the material. Therefore, the analysis of the different weight loss steps in the TGA curves gives information about the sample composition, and the comparison with the theoretical mass loss values allows us to estimate the number of structural defects of the material. TGA curves of the samples were measured using a NETZSCH-proteus STA 449 F3-Jupiter thermo-balance (details can be found in Appendix 131