## 2 Materials and Methods
Using the same adhesive, samples measuring 5 \(\times\) 5 \(\times\) 1 mm and containing 0, 5, 10, and 15 vol% of MENs were placed in an environmental chamber at 95% relative humidity and at an elevated temperature of 70 \({}^{\circ}\)C. The magnetic signatures were taken prior to environmental exposure. After a 4-week period, the samples were removed and again scanned. All magnetic signatures were taken using a vibrating samples magnetometer, which has a sensitivity of 0.01 \(\upmu\)emu [23]. The adhesive's glass transition temperature was obtained using a Q600 SDT from TA Instruments to determine its evolution as a function of the curing time during the first 24 hours of curing. The tests were run from room temperature (\(\sim\)22 \({}^{\circ}\)C) until 250 \({}^{\circ}\)C at a heating rate of 5 \({}^{\circ}\)C/min. Argon gas was used for the testing. To monitor the local physical properties of adhesives non-destructively and non-invasively, the magnetic properties of MENs dispersed into these materials were evaluated using a B-H looper setup. Specifically, this setup was used to characterize the local properties of adhesive samples, adhesively bonded composite panels, and bonded mini double-cantilever beam (DCB) samples. The principle of reciprocity states that local values of the magnetic fields B and H are reflected by the system's induced and applied voltages, respectively. The application of other techniques, such as vibrating sample magnetometry (VSM), is limited since the sample needs to be attached to a piezo-actuator, thus requiring a specific sample preparation. In contrast, the B-H looper setup allows for the evaluation of the sample's surface without physically damaging it. This setup takes advantage of the magneto-electric effect to non-invasively evaluate magnetic signature differences at a microenvironment level. Based on the reciprocity principle, the electromotive force (EMF) or measured signal, \(\epsilon\), in volts is obtained by using Equation (2) as follows:  
\[\epsilon=\frac{n\Delta\varphi}{\Delta t}=\mu_{0}\ \frac{n\Delta\ \int H_{img}M(r)d\
u}{ \Delta t} \tag{2}\]  
where \(\Delta\varphi\) is the change in the magnetic flux in volt-seconds, \(\Delta t\) is the change in time in seconds, \(n\) is the number of turns in a coil, \(M(r)\) represents how the magnetization is distributed throughout the sample, and \(H_{img}\) is the normalized reciprocal imaginary field representing the geometry of the B-H setup. It can be seen in the B-H looper setup in Figure 2 how it consists of a function generator equipped in a lock-in amplifier and three different coils. Two detection coils are located at either side (shown in blue) with the purpose of acquiring a balanced detection. To amplify the magnetic signal from the sample and to cancel any background noise, these two detection coils were connected in series. The source coil located in the middle (shown in orange) was connected to the function generator to generate an AC magnetic field. The lock-in amplifier connected the detection and source coils and was used to amplify only the signal at the detection frequency and phase and cancel out all the noise signals at all the other frequencies. The sensitivity of the setup was reduced down to the microvolt level, and it was limited by the inductance of the whole setup, which is frequency dependent. Fortunately, this is not a fundamental limit, and we can further improve it in the future by increasing the number of balancing coils and optimizing the geometry of the coils through numerical simulations. To test the curing process using the B-H looper of the adhesive containing MENs, an input voltage of 4 V and a frequency of 1.3 kHz were used, which is the critical frequency. To determine this frequency, the frequency was swept from 100 Hz to 10 kHz, and the value at which the signal due to the MENs reached its maximum was recorded. This frequency value was characterized by the net inductance of the whole system, which is influenced  
Figure 2: B–H looper setup diagram. by the sample's microenvironment [22].