Flexible and twistable free-standing PDMS-magnetic-nanoparticle-based soft magnetic films with robust magnetic properties

In this paper, we develop multifunctional, physically soft, mechanically compliant, and magnetically responsive PDMS films, with embedded Fe3O4 nanoparticles, that show robust magnetic properties over a significant range of mechanical deformation. First, we establish that the magnetic properties, namely the saturation magnetization (M s), remanent magnetization (M r), and intrinsic coercivity (H ci) of these PDMS films in highly deformed configurations, i.e. in folded, twisted (with different twist angles), and bent (flexed) configurations, show very little degradation compared to those obtained in undeformed configurations. Next, the films were subjected to repetitive cycles of zero-to-max deformation (R = 0) and the saturation magnetization of the films was shown to not exhibit any significant degree of progressive degradation as a function of cyclic deformation history. These findings confirm the excellent robustness and cyclic durability of magnetic properties shown by these magnetic and compliant PDMS films and point to their suitability for wearable electronics applications.


Introduction
A critical aspect necessary for designing and fabricating widely usable wearable electronics is to ensure that functional devices (e.g. an electronic patch or a microscale circuit), that are the integral parts of such wearable systems (or functional textiles), remain fully functional even after the host structure experiences a history of repetitive large deformations.Such a need for deformation-resilient functional devices has led to an extensive use of soft polymeric films engineered with embedded micro-nanoscale particles [1][2][3][4][5][6][7][8][9][10]: the presence of these particles or inclusions imparts the necessary functionalities to these films, while the intrinsic mechanical compliance of the films and the ability of these films to retain the distribution of the embedded micro-nanoparticles even in the presence of the large deformation, enables them to withstand severe deformations without significantly compromising their functionalities.One such example of a physically soft functional film is the mechanically compliant, soft-magnetic films that are fabricated by embedding magnetic nanoparticles (NPs), such as Fe 3 O 4 or carbonyl iron or NdFeB, inside mechanically compliant polymeric matrices (such as PDMS, PMMA, ST3866, RM257, etc).Such compliant, magnetic films have found extensive uses in applications such as electromagnetic shielding [1,2], fabrication of magnetically responsive actuators [3,11], RF electronics [4], pressure sensor [5,12], micropumps [13], etc.
Among the different types of NP-laden compliant magnetic films, perhaps the most extensively studied one has been the PDMS-based compliant magnetic films with embedded Fe 3 O 4 NPs [1][2][3][4][5][11][12][13].The overwhelming use of such PDMS-Fe 3 O 4 -NP soft magnetic films can be attributed to various factors, such as the low cost and the abundance of PDMS and Fe 3 O 4 NPs, relatively well-established methods for handling PDMS and fabricating nanocomposites of PDMS with embedded Fe 3 O 4 NPs, the 'soft' magnetic nature of the Fe 3 O 4 NPs that enables easy magnetization and demagnetization with small hysteresis losses, biocompatibility of PDMS that ensures the use of such PDMS-based compliant and responsive films for a multitude of bio-related applications, and many more.Despite such rapid and extensive progress on the fabrication and application of mechanically soft and magnetically responsive PDMS-Fe 3 O 4 -NP films, two key interrelated questions remain very weakly addressed: (1) What is the robustness of the magnetic properties of the free-standing compliant PDMS-Fe 3 O 4 -NP films under highly deformed configurations?(2) How does the magnetic responsiveness of such freestanding compliant PDMS-Fe 3 O 4 -NP films get affected after hundreds of cycles of deformations?Affirmative answers to these questions are necessary to ensure that the compliant PDMS-Fe 3 O 4 -NP films can become the material of choice for compliant magnetically responsive durable patches that can be integrated into wearable electronics applications.There have been only a handful of studies that have demonstrated the robustness of the functional properties of Fe 3 O 4embedded PDMS films specifically in flexed [5,14,15] and/or stretched configurations [12], and other studies have focused on characterizing their mechanical properties as a function of applied magnetic field [16,17].However, the robustness of the magnetic properties of such films in presence of other deformation configurations (e.g.twisted or folded configuration; figure 3 delineates these configurations) has not been thoroughly investigated.Note that the folding geometry refers to the 180 • flexing of the film about the y-axis (as per the XYZ coordinate system, shown in figures 3(a)-(d)) at the mid-plane.Also, there exists a complete lack of data on how the magnetic responsiveness of such Fe 3 O 4 -NP-embedded compliant PDMS films would be affected after being subjected to hundreds of zero-to-maximum deformation cycles.Such repetitive cyclic deformation history is inevitable in wearable electronics applications: therefore, the robustness of the magnetic properties of compliant PDMS films with embedded Fe 3 O 4 NPs, as a function of deformation cycles, is an essential attribute.
In this paper, we aim to fill this knowledge gap by studying the magnetic robustness of Fe 3 O 4 -NP-embedded mechanically compliant PDMS films under different deformation configurations (namely, folded configuration, twisted configuration with 90 • and 180 • twist angles, and flexed configuration; figure 3 shows these different deformed configurations of the magnetic film schematically) and as a function of deformation cycles.First, we fabricate the PDMS film with embedded Fe 3 O 4 NP inclusions that are coated with oleic acid.These multifunctional PDMS composite films are subjected to controlled magnetic fields using a Vibrating Sample Magnetometer (VSM) machine under undeformed and a selected set of deformed (as identified above) configurations.The desired deformations were achieved with custom 3D printed sample holder developed for this study.Measurement of the corresponding magnetization with the applied magnetic field reveals that the magnitude of film deformation causes very little degradation of the magnetic saturation levels.This confirms their excellent functional robustness under the set of deformations studied here.Next, we tested the saturation magnetization of these compliant, magnetic PDMS films as a function of several types of cyclic deformation, namely bending (flexing), folding, and twisting with twist angles of 90 • and 180 • (see figure 3 for a schematic representation of the magnetic film being subjected to such deformations).We designed and fabricated custom test setups to mechanize the cyclic loading process.Most remarkably, we find that saturation magnetization does not show any statistically significant degradation as a function of repetitive number of cycles of the deformation types used in our study.Such a finding is of great significance since this confirms the potential of use of such PDMS-Fe 3 O 4 -NPs compliant magnetic patches in wearable electronic devices that require undegraded functionality over a life cycle of cyclic deformations.

Fabrication of Fe 3 O 4 NPs embedded PDMS films
Different ratios (by weight percentage) of PDMS-A (Dow Corning USA) and Xylene X5-1(o-, m-, pisomers; Fischer Scientific) were mixed with constant stirring at room temperature for 30 min to create 8 different samples.To each sample different ratios (by weight percentage) of oleic acid coated Fe 3 O 4 NPs (particle size: 20-30 nm, 98% purity; US Research Nanomaterials Inc.) were added as indicated in table 1.The resulting mixture in each case was stirred for another 30 min on a hot-plate stirrer maintained at a temperature range of 60 • C-80 • C. Subsequently, each of the mixtures were transferred into a closed container and kept in an ultrasonication bath (47 kHz, continuous mode) for 12 h.Ultrasonication helps in breaking down the NP aggregates and in creating a uniform dispersion.Each of the dispersion samples were drop-casted on a glass or a metal plate to form a thin layer (thickness < 2 mm) of the dispersion on the surface and were cured using a hot plate at 120 • C for 6 h.Alternatively, curing can be done using an ultraviolet lamp (wavelength 345 nm) for 3 h or one can do selfcuring at room temperature for 24-26 h.Different  shape masks can be used as molds to obtain different shapes and thickness of the dispersion layer followed by curing to fabricate soft magnetic films of varying dimensions.The fabrication process has been schematically described in figure 1.
Out of all the samples listed in table 1, the sample P100X100F100 exhibits the maximum range of saturation magnetization, i.e.M s = 21 emu g −1 -23 emu g −1 (results shown later).As a comparison, oleic acid coated Fe 3 O 4 NPs exhibit M s = 60.44 emu g −1 for (see figure S2 in the supplementary material or SM).Considering its excellent magnetic properties, the weight concentrations of the different components that leads to this particular sample were used for further studies.

Film characterization
Optical and SEM images of the surface of the films show fiber-like structures that represent the PDMS matrix and the black/dark-brown inclusions that represent the aggregates of the oleic-acid-coated Fe 3 O 4 NPs (see figure S1).

Magnetic characterization and measurement methods
For the present study, the magnetic properties of these soft magnetic films, such as saturation magnetization (M s ), intrinsic coercivity (H ci ) and remanent magnetization (M r ), and M-H hysteresis loops were measured using a Lakeshore Model 7460 vibrating sample magnetometer (VSM).Samples of the size ranges with maximum length of 10 mm, maximum width of 5 mm, and maximum thickness of 1 mm were used for testing.It was observed that the magnetic saturation was achieved at an input magnetic field strength of 19 kOe.Thus, for obtaining the M-H hysteresis loops, a cyclic magnetic field of Hmax = + 19 kOe to Hmin = −19 kOe was employed with a magnetic field ramp rate of 304 Oe s −1 , a time constant of 0.3, and time per point of 5 s.Characterizations were done for both in-plane and out-of-plane directions of the films.
For measurement of the magnetic properties in deformed configurations, deformation-specific sample holders were fabricated as an add-on to the VSM and the same measurement profile was used.
The deformations of the films and respective sample holders are shown in figure 3.

Degradation testing methods
For tabulating the change in magnetic properties of the films on being subjected to multiple deformation cycles, unique micro-controller-based DIY setups, which are effectively tiny loading setups, were fabricated for each of the four types of deformations (folding, twisting with twist angle of 90 • , twisting with twist angle of 180 • , and flexing) (see the SI for details): for each type of deformation, the working set-up for one deformation cycle is shown in figure 6.Each deformation cycle took 7 s with a dwell time of 500 ms at both the undeformed and fully deformed states.For each type of the deformation cycle, the saturation magnetization values of the samples were recorded after every 100 cycles and the samples were tested for a total of 1000 cycles.Considering the effect of stress relaxation on these compliant magnetic films, a resting period of 60 min was allowed before testing the magnetic properties of these samples.

Magnetic properties of the undeformed soft magnetic film
Here we first report the quantification of the magnetic properties of the undeformed compliant PDMS-Fe 3 O 4 -NP magnetic films.These films were placed inside the VSM machine (see figure 2(b)) and the corresponding magnetic properties of the films were characterized in terms of the corresponding M-H hysteresis loop (here 'M' is the mass magnetization resulting from the applied magnetic field 'H') (see figure 2(a)).The corresponding quantifications of the magnetic properties include the saturation magnetization or M s having the units emu g −1 (M s = m/w with m being the magnetic moment in emu and w being the mass of the sample in grams), the remanent magnetization (M r in units of emu g −1 ), and the intrinsic coercivity (H ci in units of Oe) (see table 2). Figure 2(a) confirms that the fabricated samples exhibited M s values in the range of 21-23 emu g −1 for the Fe 3 O 4 -PDMS films.Commensurate with superparamagnetic nature of the Fe 3 O 4 NPs, these PDMS films with embedded Fe 3 O 4 NPs exhibit very small hysteresis loss (see figure 2(a)), small intrinsic coercivity (69-74 Oe), small remanent magnetization (1.5-3 emu g −1 ), (see table 2) and high saturation magnetization (see figure 2(a)).
Furthermore, the OOP (out-of-plane) M s is founds to be roughly 5% lower than IP (in-plane) M s for all the samples (see table 2), which corresponds to an observed anisotropy in the fabricated films.These in-plane and out-of-plane directions are considered to be along the y-axis and x-axis respectively with reference to the undeformed configuration as shown in figures 2(b) and (c).On further investigation, the saturation magnetization observed along different orientations about the z-axis (−90 to +90 • ) were recorded as shown in figure S3.This corresponds to an easy axis of magnetization along the in-plane direction of the sample.The anisotropy might have been caused during the bottom-up hot-plate curing process even in the absence of an applied magnetic field, and due to experimental errors during fabrication.

Magnetic properties of the deformed soft magnetic film
This section focuses on quantifying the magnetic properties of the soft Fe 3 O 4 -NPs embedded PDMS films with the film being in highly deformed configurations.We shall place these films inside the VSM machine in either folded, or twisted (with twist angles of 90 • and 180 • ), or highly bent configurations (these configurations have been schematically represented in figure 3) and measure the corresponding magnetic properties, namely, magnetic saturation (M s ), remanent magnetization (M r ), and the intrinsic coercivity (H ci ).If these properties show insignificant changes as compared to the case where the Fe 3 O 4 -NPs embedded PDMS film is undeformed, we can infer the significantly large robustness of the magnetic properties of the Fe 3 O 4 -NPs embedded PDMS film even against very large physical deformations.
Figures 3(a)-(c) schematically represent the manner in which these films are deformed into folded, twisted (with twist angles of 90 • and 180 • ), and flexed configurations.Twisting geometry refers to torsional displacement of the film about the z-axis at an angle α.Flexing geometry refers to the radial bending of the film about the y-axis at a radius of r = 3.18 mm.
The existing sample holder of the VSM machine cannot accommodate the films in these deformed configurations, so custom sample holders were designed and additively fabricated for this purpose (please see figures 3(d) and (e)).
We consider both the in-plane (IP) and out-ofplane (OOP) directions for measuring the magnetic properties of the compliant, magnetic films in highly deformed configurations.The magnetic properties were calculated for the samples in the deformed configurations using the same test profile, i.e. by subjecting the deformed samples to fully reversed cyclic magnetic fields from 19 kOe to −19 kOe.Also, for a given sample, the different types of deformations are not combined for simplicity.
Figure 4 shows the variation of the in-plane magnetization (M) for the deformed samples as a function of applied magnetic fields (H).Results are shown for different types of deformations (folding, twisting with different twist angles, and flexing) and these results are compared with the corresponding M-vs-H variation for the undeformed samples.We do not see any significant decay in the strength of magnetization for a given H variation for the deformed samples as compared to the undeformed samples.This confirms the excellent magnetic robustness of these fabricated Fe 3 O 4 -NP-embedded PDMS films against significant physical deformation.Interestingly, the magnetization improves in the deformed configuration.For example, for the sample in the folded and flexed configurations, the in-plane saturation magnetization increases by nearly 21% and 10%, respectively, compared to that in the undeformed configuration.
Figure 5 provides corresponding results in the out-of-plane direction.For these measurements as well, we find little degradation in the saturation magnetization value for the deformed samples as compared to that for the undeformed samples.In fact, in the bent (or flexed) configuration, the film exhibits nearly 55% increase in the M s and 82% increase in M r (see table 2).However, the sample reverts to its prior properties after being returned to the undeformed state.This again confirms the robustness of the magnetic properties of the Fe 3 O 4 -NP-embedded PDMS films against large physical deformations.
In table 2, we provide these comparisons of the magnetic saturation (M s ) values between the cases of deformed and undeformed samples in both the in-plane and out-of-plane directions.Additionally, we provide the values of the remanent magnetization (M r ) and the Intrinsic Coercivity (H ci ) for these different cases (i.e.magnetic films in undeformed-vs-deformed configurations and measurements conducted in the in-plane-vs-out-of-plane directions).
Any kind of deformation of the films, induces a change in the mechanical state of the NPs, which impacts the overall magnetization of the samples.This effect has been well established in literature as the inverse magnetoelastic effect or the Villari effect [18,19].The application of mechanical stresses modifies the magnetoelastic energy which in turn modifies the anisotropy of the material at the macroscopic level.At the microscopic level, the change in interatomic distances allows for a symmetry reduction, and thus can modify the magnetostriction coefficients of a material.Therefore, the effective magnetic moments measured for the samples in the different deformed configurations can be considered a function of the effective stress tensor, effective magnetostriction coefficient, and the direction cosines of the magnetization and the measurement directions with respect to the orthogonal axes.

Degradation of the soft magnetic films subjected to cyclic deformation-induced stresses
Once the magnetic properties (and the corresponding magnetic robustness) of the Fe 3 O 4 -NP-embedded PDMS films were characterized in deformed configurations, the capability of these films to sustain hundreds of cycles of such deformations (and the deformation induced stresses) was studied.As has been schematically represented in figure 6, one deformation cycle (for any type of deformation) corresponds to the state change of the film from the initial undeformed state to the specified fully deformed state and then back to the undeformed state.Supporting movies, M1-M4, provide videos of one such cycle for each type of deformation.In each of the sub-figures, the curve for the undeformed sample is also provided for comparison.In these sub-figures, lines in red represent the results for the deformed samples, while the lines in blue represent the results for the undeformed sample.deformation cycles.For example, the samples undergoing folding, twisting with a twist angle of 90 • , twisting with a twist angle of 180 • , and flexing deformation cycles exhibited an average saturation magnetization decrease of 3.16%, 1.41%, 1.55%, and 2.69%, respectively.Similar observations were recorded for out-of-plane magnetization under cyclic deformation (see figure S5 in the SM).This confirms the extreme robustness of magnetic properties of these mechanically soft and compliant PDMS magnetic films even when subjected to large number of deformation cycles.The robustness can be qualitatively defined as the ability of the material to maintain its original properties even after multiple cycles of usage.The magnetic film in our study is robust in the sense that the effective magnetic properties are mostly retained even after 1000 cycles of deformation.The very slight (1%-3%) degradation in the properties (as identified above) can be primarily ascribed to the formation of holes in the samples on being subjected to hundreds of deformation cycles; see figure 7(b) representing the case for a sample subjected to 1000 cycles of folding deformation.These holes were observed in the high stress region for each deformation type, and were found in the bulk of the sample, and no crease lines were observed on the surface of the films.SEM images depicting the surface topography of the cross-section of the samples after undergoing the deformation cycles are shown in figure S6 in the SM.

Conclusions
In this study, PDMS-based complaint, soft magnetic films embedded with oleic-acid coated Fe 3 O 4 NPs were fabricated, and their reliability for usage in flexible electronic devices was investigated.The magnetic properties of the samples were characterized in both undeformed and deformed states (i.e.folding, twisting, and flexing): the presence of deformation was found to cause very little degradation of the magnetic properties of the films.To check the performance of the samples under cyclic fatigue loading, the films were subjected to a thousand cycles of respective deformations, and it was observed that the films exhibited little variation in their saturation magnetization values over the test range, thus elucidating their robust magnetic behavior.
While there are several studies on fabricating functional, physically soft magnetic films, the robustness of their magnetic properties in the presence of large deformations (and a large number of deformation cycles) have rarely been studied [3].Such a lacuna means a complete lack of information on the repeatability (and robustness) of the magnetic function specific performance of such films when integrated in actual devices and systems (e.g.wearable electronic devices).Our study addresses this gap and stresses the significance of testing the reliability and robustness of magnetic properties of such functional and physically soft magnetic films.

Figure 1 .
Figure 1.Schematic of the fabrication process of PDMS-based Fe3O4 soft magnetic film.

Figure 2 .
Figure 2. (a) M-H hysteresis loop of the undeformed and physically soft PDMS-Fe3O4-NP magnetic film sample (the sample contains 33.33 t% by weight of Fe3O4 NPs) for in-plane and out-of-plane directions.(a)-inset: Enlarged view of the hysteresis loop as shown by the orange square.(b) 3D representation of the VSM machine and the magnetic film introduced inside the VSM machine using a sample holder; subfigure (c) provides for a detailed schematic representation of the sample holder].(d) Photographs of the fabricated Fe3O4-NPs embedded PDMS films.

Figure 3 .
Figure 3. Schematic representation of the deformation geometry that ensures the soft, magnetic film to be in a (a-i)-(a-iii) a folded configuration, (b-i), (b-ii) a twisted configuration (with twist angle, α = 90 • ), (b-iii) a twisted configuration twisting (with twist angle, α = 180 • ), and (c-i)-(c-iii) a bent (or a flexed) configuration (r = 3.18 mm, with r denoting the radius of curvature of the substrate on which the soft, magnetic film is placed for ensuring bending or flexing of the film; obviously, smaller the value of r greater is the degree of bending or flexing).(d) Schematic showing the sample placement on additively manufactured sample holders for (d-i) folding, (d-ii, iii) twisting (α = 90 • and α = 180 • ), and (d-iv) bending.(e) Pictures of the additively fabricated sample holders.

Figure 7 (
Figure 7(a)  shows that the in-plane saturation magnetization (M s ) of the Fe 3 O 4 NPs-embedded-PDMS soft magnetic films, measured after every 100 deformation cycles, shows negligible changes, for a total of 1000 cycles, for all the four types of

Figure 4 .
Figure 4. M-H hysteresis loops (measurements done in the in-plane directions) for the deformed samples for the cases when the soft, magnetic film is (a) folded, (b) twisted (twist angle, α = 90 • ), (c) twisted (twist angle, α = 180 • ), and (d) bent or flex (with r = 3.18 mm, where r denotes the radius of curvature of the substrate on which the soft, magnetic film is placed for ensuring bent or flexed configuration).In each of the sub-figures, the curve for the undeformed sample is also provided for comparison.In these sub-figures, lines in red represent the results for the deformed samples, while the lines in blue represent the results for the undeformed sample.

Figure 6 .
Figure 6.Schematic (upper row) and working set-up (bottom row) elucidating the procedure of subjecting the Fe3O4-NP-embedded PDMS films to cycles of stresses induced due to (a) folding, (b) twisting (with a twist angle of 90 • ), (c) twisting (with a twist angle of 180 • ), and (d) bending or flexing.

Figure 7 .
Figure 7. (a) Variation of saturation magnetization (Ms) as a function of the deformation cycles for different types of deformations (each type of deformation has been measured along the in-plane axis).(b) Optical images (10x) showing the cross-section surface structure of the compliant soft magnetic films (b-i) before folding, (b-ii) after folding deformation for 1000 cycles, (b-iii) SEM image adter folding deformation for 1000 cycles.In (b-ii) & (b-iii), the holes that appear near the surface of the film have been identified.

Table 1 .
Different ratios (by weight percentage) of constituents in the dispersion samples.