Real-time monitoring of hydrogel rheological property changes and gelation processes using high-order modes of cantilever sensors

Hydrogels are crosslinked polymer networks that contain high water content and are commonly employed in a number of industrial, environmental, and biomedical applications as well as consumer products.^1–5 In addition to control over mechanical, transport, physical, and optical properties, hydrogels are receiving considerable attention based on the ability to change their properties via externally applied stimuli, so-called stimuli-responsive hydrogels.^6–8 Across all applications, hydrogel rheological properties are critical signatures for assessing material processability,^9,10 quality,^11,12 and functionality (e.g., response to stimuli),¹³ making rheological characterization central to accelerated hydrogels research and discovery initiatives. Therefore, identifying new paradigms for the characterization of hydrogel rheological properties is central to accelerating the pace of gel-based materials research and discovery of hydrogel-based therapeutics and technologies.

The lack of online and high-throughput characterization techniques is a major bottleneck in accelerated molecular and material discovery workflow.^14–16 For example, advances in array-based high-throughput biosensing and bioanalysis techniques are now beginning to alleviate characterization bottlenecks within the experimental loops of accelerated molecular discovery workflows. Similarly, the integration of high-throughput characterization techniques with combinatorial chemistry processes is now leading to the discovery of novel molecules and materials at unprecedented rates.^17,18 While high-throughput bioanalytical and characterization platforms have emerged for the screening of protein–protein interactions,¹⁹ structure data,²⁰ and electrical¹⁷ and electrochemical²⁰ properties, the breadth of structure and property information that could be useful in assessing material performance and quality across different applications presents a barrier to future accelerated materials discovery initiatives.^21–23 In particular, the characterization of hydrogel rheological properties, phase behavior, gelation processes, and functionality presents significant rate-limiting steps within state-of-the-art hydrogel materials research workflows because of the requirement for manual sample preparation steps and the time-intensive nature of traditional mechanical tests, which lead to low throughput.²⁴ Alternatively, given their foundation on sensitive miniaturized transducers, sensors provide opportunities to improve the limit of detection and dynamic range for rheological property characterization as well as facilitate high-throughput, online, and real-time monitoring of rheological property changes of soft materials during synthesis and processing. For example, miniaturized mechanical testing devices, such as nanoindentation tools, are enabling novel combinatorial approaches for high-throughput characterization of mechanical properties.¹⁵ Huth et al. recently created an algorithm for automated mechanical characterization of hydrogels from microindentation testing data acquired using atomic force microscopy (AFM) cantilevers demonstrating the promise of cantilever sensors as platforms for automated and highly reproducible soft material characterization workflows.²⁵ Thus, sensor-based techniques for the characterization of hydrogel rheological properties could facilitate future high-throughput combinatorial approaches for eliminating characterization bottlenecks that currently limit the pace of soft materials research, development, and discovery.

Over the past 25 years, atomic force microscopy (AFM) cantilevers and nanoindentation testing techniques have been leveraged to characterize the viscoelastic properties of various materials,²⁶ including hydrogels.²⁷ While AFM-based nanoindentation techniques utilize micro-cantilevers, the characterization approach poses considerable challenges to process monitoring applications. For example, the real-time sensing of material viscoelastic property changes for process monitoring applications would benefit from submersion of the cantilever sensors in the material to achieve process integration, and thus, demand highly integrated transduction and readout systems that are difficult to achieve using optical techniques. Furthermore, the use of a micro- and nano-scale contact probe limits the sample characterization area, which can pose challenges to the rapid characterization of bulk material properties or analysis of materials that exhibit spatial heterogeneity in the material property. Mather et al. extended the use of submerged meso-scale cantilever sensors for characterizing the viscoelastic properties of liquids.²⁸ In that study, the theory of Sader,²⁹ Maali et al.,³⁰ and Belmiloud et al.³¹ was leveraged to calculate a surrounding material's shear storage and loss moduli from the cantilever resonant frequency and quality factor responses with consideration for the internal damping of the meso-scale cantilever.²⁸ While Mather et al. were able to characterize the viscoelastic properties of polyacrylamide solutions, fluid damping effects impeded applications to the characterization of more viscous or viscoelastic materials.²⁸ Haring et al. recently reported that the second mode of submerged piezoelectric milli-cantilever sensors near 30 kHz enabled the characterization of alginate, gelatin, and poly(ethylene glycol) diacrylate (PEGDA) hydrogel viscoelastic properties across a dynamic range of 0–26 kPa and detection limit of 260 Pa and real-time monitoring of gelation processes.²⁴ While this study established milli-cantilever sensors as potentially promising platforms for high-throughput characterization of hydrogels and real-time monitoring of hydrogel processing, it is useful to consider if high-order modes in cantilever sensors also facilitate real-time sensing of hydrogel viscoelastic property changes and, as such, could enable sensor-based hydrogel viscoelastic property characterization at levels that surpass the upper limit of state-of-the-art dynamic light scattering microrheology techniques (10 kPa³² and 10⁵ Hz³³)—a gold standard for wide frequency characterization of soft hydrogel rheological properties.

It is well established that the mass-change sensitivity of cantilever sensors increases with mode number,^34,35 which has driven research on the use of high-order modes for chemical sensing and biosensing applications based on mass-change sensing principles.^36,37 While the use of high-order modes provides various measurement advantages in biosensing applications, such as increasing mass-change sensitivity by increasing resonant frequency,³⁵ improving measurement confidence by simultaneous tracking of multiple modes,³⁸ and facilitating multi-analyte detection through spatially distributed biorecognition elements,³⁹ the effect of mode number on the dynamic range and limit of detection for the detection of changes in hydrogel viscoelastic properties based on cantilever response has yet to be investigated. For example, the relative measurement advantage of high- to low-order modes (if any) is unclear, given the strong frequency dependency of many hydrogel rheological properties across wide frequency ranges.^32,40

Here, we show that high-order modes in piezoelectric milli-cantilever sensors near 1 MHz persist in commonly used chemically crosslinked and photocured hydrogels and exhibit increased sensitivity, dynamic range, and limit of detection for the characterization of hydrogel viscoelastic properties relative to low-order modes (∼30 kHz). Sensor signal changes are compared with low-frequency viscoelastic properties obtained from DMA studies (1 Hz) to characterize the sensitivity, dynamic range, and limit of detection for changes in viscoelastic properties of alginate and polyethylene glycol dimethacrylate (PEGDMA) hydrogels over the 0.5–4 wt. % (alginate) and 8–18 wt. % (PEGDMA) concentration range. This work shows that high-order modes in millimeter cantilever sensors facilitate sensitive characterization of hydrogel viscoelastic properties and gelation processes. It also suggests that dynamic-mode milli-cantilever sensors can facilitate monitoring of various dynamic processes in hydrogels and other soft materials, such as their response to stimuli, restructuring, or cellular growth processes, via real-time sensitive detection of changes in viscoelastic properties. This work shows that PEMC sensors can provide potentially useful sensor-based characterization platforms to mitigate existing bottlenecks related to low-throughput characterization loops in accelerated soft material discovery workflows.

Alginic acid sodium salt, calcium chloride, ethylenediaminetetraacetic acid (EDTA), polyethylene glycol dimethacrylate (PEGDMA; M_n = 750 Da), and 2,2-dimethoxy-2-phenylacetophenone (DMPA) were purchased from Millipore Sigma. Lead zirconate titanate (PZT-5A; 72.4 × 72.4 × 0.127 mm³) with nickel electrodes was purchased from Piezosystems (Woburn, MA). Borosilicate glass was purchased from VWR. Glass cylinders and ethanol (200 proof) were from Fisher Scientific. Polyurethane (Fast-Drying) was from Minwax. Epoxy (EA 1C-LV) and cyanoacrylate (409 Super Bonder) were from Loctite.

Composite piezoelectric-excited milli-cantiliever (PEMC) sensors with a flush design were fabricated from lead zirconate titanate (PZT) as described in previous studies [see Fig. 1(a)].^24,41,42 Briefly, borosilicate and PZT sheets were diced into chips (2 × 1 × 0.16 mm³ and 5 × 1 × 0.127 mm³, respectively; American Dicing; Liverpool, NY). A borosilicate chip was first bonded symmetrically to one end of the cantilever using cyanoacrylate such that the front of both chips was aligned. Subsequently, 30-gauge copper (Cu) wires were soldered to the top and bottom faces of the nickel electrodes on the distal end of the PZT layer opposite to the glass layer. The cantilever was then potted in a glass cylinder (6 mm diameter) with a non-conductive epoxy resulting in a cantilever geometry (3 × 1 × 0.127 mm³). The sensors were then coated with polyurethane via spin coating (1000 rpm for 2 min), which was then allowed to cure at room temperature to improve the adhesion of parylene-c to the sensor. The sensors were then coated with parylene-c (10 μm thick) following vendor protocols (PDS 2010 Labcoter^® 2; Specialty Coating Systems; Indianapolis, IN). Following parylene-c coating, the sensors were annealed for 1 h at 75 °C.

The sensor resonant frequency (f_n), phase angle at resonance (ϕ_n), and impedance at resonance (Z_n), where n indicates the mode number, were continuously monitored with a vector-network analyzer with impedance option (E5061b-005; Keysight). The sensor's dynamic mechanical response, here, the frequency response, was obtained via electromechanical coupling effects using electrical impedance analysis, which provides electrical impedance magnitude (|Z|) and phase angle (ϕ) spectra of the piezoelectric layer [|Z| and ϕ vs frequency (f), respectively]. The technique provides resonant frequency, phase angle, and impedance tracking in applications that require analysis in complex fluids and materials that may present challenges to the use of optical techniques. Electrical impedance analysis was performed using a stimulus amplitude of 100 mV AC and zero DC bias across a frequency range f_n ± 10 or 100 kHz (for low- vs high-order mode tracking, respectively). Sensor signals (f_n, ϕ_n, and Z_n) were acquired using a custom MATLAB program.

Alginate solutions ranging from 0.5 to 4.0 wt. % were prepared by dissolution of alginic acid sodium salt in de-ionized water (DIW) at room temperature with continuous stirring as previously reported.²⁴ The solutions (5 ml) were chemically crosslinked by depositing a 500 μl droplet of saturated calcium chloride on the surface of the polymer solution approximately 5 mm from the submerged sensor. PEGDMA solutions ranging from 8% to 18% were prepared in de-ionized water (DIW), and 0.2% DMPA from a 20% DMPA stock solution was used as a photoinitiator. PEGDMA hydrogels were cured with exposure to 365 nm UV light (1200 μW/cm² at 2 in.; UVGL-58).

The resonant frequency, phase angle at resonance, and impedance at resonance in air (f_n,air, ϕ_air, and Z_air, respectively) were determined as described in Sec. II C. Experiments began by adding 5 ml of room temperature alginate or PEGDMA solution to a 35 mm Petri dish (Celltreat). The cantilever was then submerged and data collection was initiated. Following the stabilization of the sensor signals, the alginate solutions were chemically crosslinked by manual application of a 500 μl droplet of saturated calcium chloride to the surface of the solution approximately 5 mm from the anchor of the cantilever. The addition of a 500 μl droplet of DIW served as an in situ negative control. PEGDMA hydrogels were formed through a photocuring reaction by exposure to 365 nm UV light for 20 min (1200 μW/cm² at 2 in.; UVGL-58).

Characterization of hydrogel low-frequency viscoelastic properties was done using a dynamic mechanical analyzer (Q800; TA Instruments). Cylindrical test specimens of alginate hydrogels (diameter = 12.7 mm and thickness = 5 mm) were punched from 5 mm thick hydrogel sheets prepared using the same cross-linking technique as previously described for the sensor studies. PEGDMA hydrogels with diameter = 13 mm and thickness = 6 mm were also prepared for testing. All measurements were acquired by the application of a 15 μm periodic displacement at a constant frequency (1 Hz) and 5 mN preload force in the compression mode.

While it is established that increasing mode number can increase the mass-change sensitivity of cantilever sensors^34,35 (see the supplementary material), the effect of mode number, and thus, resonant frequency, on a cantilever's dynamic response in hydrogels is not clear, given the complex frequency dependence of hydrogel rheological properties that occur across a wide frequency range and the potential effect of shear rate. Thus, we next characterized the spectral characteristics of low- and high-order modes in PEMC sensors in air, water, and various polymer solutions and hydrogels.

As illustrated in Fig. 1(a), PEMC sensors are actuated and sensed using a single piezoelectric layer, which is referred to as a self-exciting and -sensing design.⁴³ This design enables the cantilever frequency response to be characterized by the electrical impedance response of the insulated piezoelectric layer. Thus, electrical impedance analysis enables real-time monitoring of the cantilever resonant frequency (f_n) and quality factor (Q_n) while submerged in various fluids. As shown in Figs. 1(b) and 1(c), electrical insulation of the PEMC sensors with parylene-c enables them to be submerged in liquids, including solutions of gel-forming polymers. In addition to providing a highly compact sensor form factor, the self-exciting and -sensing piezoelectric measurement approach facilitates the characterization of high-order modes in PEMC sensors near 1 MHz, which are otherwise challenging to resolve using conventional optical techniques given the high frequency, small displacement amplitude, and large number of nodal points present.

Recently, we showed that the resonance of low-order modes in PEMC sensors [see Fig. 2(a)] persists in a range of hydrogels, including alginate.²⁴ In that study, we found that resonant frequency tracking could be performed in alginate hydrogels ranging from 0.25 to 0.75 wt. %. The low-order mode exhibited a limit of detection of 260 Pa with respect to changes in the quality factor response and 1.6 kPa with respect to changes in the phase angle response.²⁴ As shown in Figs. 2 and S1 in the supplementary material, PEMC sensors express both low- (f_air = 38.1 ± 4.1 kHz and Q_air = 25.1 ± 1.8; n = 10 sensors) and high-order modes across the 0–1 MHz frequency range. Figure 2(b) highlights the high-order mode, which exhibits high coupling between mechanical deformation and impedance change in the piezoelectric layer due to a combination of transverse and longitudinal deformation⁴¹ (f_air = 836.9 ± 32.6 kHz; Q_air = 34.9 ± 3.3; n = 10 sensors). The resonant frequencies and quality factors agree reasonably with previous finite element simulations of the composite PEMC sensors.⁴¹ As shown by the comparison of Figs. 2(a) and 2(b), the high-order mode exhibited larger changes in resonant frequency than the low-order mode with respect to changes in surrounding fluid properties. For example, the low-order mode resonant frequency and quality factor decreased 8.1 ± 0.2 kHz and 5.3 ± 0.3 (n = 10 sensors), respectively, upon submersion in gel-forming polymer solutions (0.5 wt. % alginate solution) from air, while the high-order mode exhibited decreases of 63.8 ± 3.7 kHz and 4.1 ± 0.2 (n = 10 sensors), respectively.

Similar to our recent findings, the resonance of the low-order mode persisted in alginate hydrogels [see Fig. 2(a)]. As shown in Fig. 2(b), we also found that the high-order mode persisted after the gelation process. Examining the percent decrease in phase angle (resonant mode peak height) of the low- and high-order modes upon gelation of 0.5 wt. % alginate solutions relative to the initial peak height suggests that the high-order mode could have a wide dynamic range regarding the characterization of hydrogel viscoelastic properties. We also found that the high-order mode facilitated real-time monitoring of gelation processes via real-time monitoring of various sensor outputs. As shown in Fig. 2(c), the high-order mode exhibited a greater change in phase angle relative to the value prior to cross-linking than the low-order mode following gelation of the surrounding alginate solution (1.59° vs 0.54°, respectively). While a comparison of the low- and high-order mode responses associated with the chemical gelation of alginate solutions does not indicate an effect of frequency on the gelation rate, Carvalho et al. showed that increasing the shear rate from 1 to 1000 Hz both delayed the onset of moduli increase (often referred to as phase II of gelation) and depressed the slope of the increase in moduli.⁴⁴ We note that the delay of onset of moduli increase was also observed in previous studies using low-order modes of PEMC sensors for the rheological characterization of hydrogel properties.²⁴ 

Having established that high-order modes in PEMC sensors resonate in 0.5 wt. % crosslinked alginate hydrogels, we next investigated the dynamic range of the high-order mode with respect to the confident detection of viscoelastic property changes and resolution of gelation processes. Thus, we next characterized the impedance spectra of the sensor over a range of hydrogel concentrations [i.e., across a range of low-frequency hydrogel storage and loss moduli (E′ and E″)]. As shown by a comparison of Figs. 3(a) and 3(b), submersion of the cantilever sensor in 0.75–2.25 wt. % alginate solutions caused a relatively larger mass-damping effect on the low-order mode. The shoulder peak near 30 kHz is attributed to a torsional mode that is adjacent to the transverse mode used for tracking and rheological characterization.⁴⁵ The resonant frequency and phase angle at the resonance of the low- and high-order modes from 0.75 to 2.25 wt. % decreased by 0.15 kHz and 1.4° vs 1.1 kHz and 1.6°, respectively. The shift in resonant frequency and quality factor with the change in surrounding liquid density is an expected result associated with cantilever fluid-structure interaction mechanics [see Eqs. (9) and (10) in the supplementary material].^38,46

Figures 3(c) and 3(d) show the phase angle spectra of the low- and high-order modes corresponding to Figs. 3(a) and 3(b), respectively, following chemical cross-linking of the surrounding alginate solutions into hydrogels. The relationships among hydrogel concentration (polymer fraction) and low-frequency (1 Hz) viscoelastic properties obtained via DMA [E′, E″, and tan(δ)] are shown in Fig. 4. As shown in Fig. 4(a), while increasing the polymer content increased the hydrogel storage and loss moduli, it reduced the hydrogel loss factor [tan(δ)] (i.e., damping) [see Fig. 4(b)]. As shown by a comparison of Figs. 3(c) and 3(d), moduli changes of the surrounding hydrogel caused the largest relative changes in the low-order mode outputs. In comparison, the high-order mode was relatively less damped when surrounded by alginate hydrogels of 23.4 kPa (2.25 wt. %), suggesting they have a wider dynamic range than the low-order mode. Thus, we next investigated the changes in cantilever frequency response, specifically, changes in resonant frequency, phase angle at resonance, quality factor, and impedance at resonance over a wider range of hydrogel viscoelastic properties (e.g., storage moduli and loss factors) to identify the effect of mode number on the sensitivity, limit of detection, and dynamic range of dynamic-mode milli-cantilevers regarding detection of hydrogel viscoelastic property changes.

Given that applications may use hydrogels across a range of concentrations, we next examined the concentration at which resonance of the high-order mode could not be monitored with a suitable resolution for real-time characterization of gelation processes (similar to the concentration at which resonance no longer persists). As shown in Fig. 5, we found that high-order modes enable real-time monitoring of gelation processes in alginate hydrogels via resonant frequency tracking over a wide concentration range, spanning dilute to 4 wt. % polymer solutions. A comparison of the sensor responses of the low- and high-order modes, including resonant frequency, phase angle at resonance, quality factor, and impedance at resonance, indicates that both the modes and sensor outputs exhibit varying sensitivity, limit of detection, and dynamic range with respect to changes in hydrogel viscoelastic properties [composition (wt. %), E′, and tan(δ)]. The high-order mode exhibited a wider dynamic range, enabling resonance and measurement in hydrogels of storage modulus as high as 33.2 kPa (4 wt. % alginate), compared with 23.4 kPa (2.25 wt. % alginate) for the low-order mode. The upper limit of the dynamic range was defined as the concentration at which gelation processes could not be continuously monitored via resonant frequency tracking. Beyond this range, the dissipative effects of the surrounding material damp the resonant mode such that either resonance is no longer present or the quality factor present is not sufficient to facilitate reliable real-time resonant frequency tracking. This result suggests that the dynamic range and limit of detection regarding sensing of viscoelastic property changes are both material²⁴ and mode number dependent.

Considering the data shown in Fig. 5 that relate changes in sensor outputs (resonant frequency, phase angle at resonance, quality factor, and impedance at resonance) to changes in hydrogel viscoelastic properties exhibit various linear regimes, the sensitivity can be interpreted as the slope of the sensor response (output) vs property (input) data. As shown in Figs. 5(a) and 5(b), the resonant frequency response of the high-order mode exhibited a higher sensitivity than the low-order mode with respect to storage moduli changes (i.e., hydrogel concentration). The sensitivity of the high-order mode was 287.2 Hz/kPa, compared with 4.57 Hz/kPa for the low-order mode. As shown in Figs. 5(d) and 5(e), the phase angle response of the high-order mode exhibited a significantly higher sensitivity to storage moduli changes than the low-order mode. The sensitivities of phase angle response for the high- and low-order mode to storage moduli changes were 0.33 and 0.02°/kPa, respectively. While the resonant frequency and phase angle response of the high-order mode exhibited increased sensitivity to changes in the viscoelastic properties of the surrounding hydrogel, the low-order mode quality factor response was more sensitive than the high-order mode [see Figs. 5(g) and 5(h)]. As shown in Figs. 5(j) and 5(k), the low- and high-order modes exhibited similar sensitivity in terms of impedance response for detecting changes in the surrounding hydrogel's viscoelastic properties. The individual low- and high-order mode data are presented in Fig. S2 of the supplementary material. In addition to the ability to detect changes in hydrogel storage modulus, the cantilever resonant frequency, phase angle, quality factor, and impedance responses of high-order modes also exhibited a correlation with hydrogel tan(δ) [see Figs. 5(c), 5(f), 5(i), and 5(l), respectively]. In particular, the phase angle and impedance responses exhibited the highest sensitivity with respect to the detection of changes in hydrogel loss factor [tan(δ)] [see Figs. 5(f) and 5(l), respectively].

In addition to the effect of mode number on the sensitivity of the measurement, it is also useful to consider its effect on the limit of detection, which here is defined as the smallest detectable change in storage modulus of a surrounding hydrogel using any of the four sensor outputs. The limit of detection is dependent on the sensor sensitivity and noise level. Considering the sensitivities and noise levels of the low- and high-order mode phase angle responses were 0.02°/kPa and 0.002° and 0.33°/kPa and 0.01°, respectively, the limit of detection for changes in storage modulus of the surrounding hydrogel were 300 and 91 Pa, respectively. The limit of detection of the low-order mode (300 Pa) agrees reasonably with our previous result of 260 Pa.²⁴ In contrast, the quality factor response of the low- and high-order modes exhibited sensitivities of 0.32 and 0.15 kPa⁻¹, respectively, and noise levels of 0.01 and 0.02, respectively. Thus, assuming the limit of detection can be estimated as 3 N/σ, where σ is the sensitivity and N is the noise level, the smallest detectable change in storage modulus of a surrounding hydrogel using a quality factor for the low- and high-order modes was 93 and 400 Pa, respectively. Thus, both the low- and high-order modes can facilitate sensitive monitoring of hydrogel viscoelastic properties via real-time tracking of different features of the cantilever frequency response (specifically, quality factor and phase angle at resonance, respectively).

Thus, these results show that the sensitivity, limit of detection, and dynamic range of resonant milli-cantilever sensors for characterization of viscoelastic properties of surrounding hydrogels can be improved using high-order modes, which are potentially important factors associated with their application to sensor-based characterization of soft materials. The data in Figs. 2–5 show that the resonance of high-order modes in PEMC sensors persists in alginate hydrogels across a range of concentrations that have been used extensively in various applications^47,48 and can serve to complement rheological measurements provided by low-order modes with high-frequency data or achieve measurements in hydrogels of storage moduli that exceed the dynamic range of low-order modes.

The data in Figs. 2–5 show that resonance of high-order modes in PEMC sensors persists in alginate hydrogels across a range of concentrations that have been used extensively in various applications^47,48 and can serve to complement rheological measurements provided by low-order modes (e.g., with high-frequency rheological data) as well as facilitate sensitive rheological characterization of hydrogels at relatively extended dynamic ranges. Thus, having demonstrated that the high-order mode exhibit a wider dynamic range than the low-order mode (with an extended upper limit), we finally examined if the high-order mode enabled continuous monitoring of gelation processes in hydrogels that exhibit storage moduli that were beyond the dynamic range of the low-order mode.

The correlations between phase angle changes with hydrogel composition and low-frequency viscoelastic properties found in alginate hydrogels suggest that millimeter cantilever sensors provide useful signals for real-time monitoring of gelation processes and rheological characterization of sol-gel systems. As shown in Fig. 5, alginate hydrogels formed using 4 wt. % solutions were beyond the dynamic range of the low-order mode. For example, as shown in Fig. 6(a), it is challenging to distinguish the low-order mode from the baseline frequency response following gelation of 4 wt. % alginate hydrogels around the sensor. In contrast, as shown in Fig. 6(b), the high-order mode remained present when surrounded by 4 wt. % alginate hydrogels (Q_gel = 24.4).

Alginate solutions undergo a chemically reversible gelation process at room temperature by the addition of calcium ions.⁴⁹ As shown in Fig. 6(c), continuous tracking of the sensor phase angle response of the high-order mode enabled real-time monitoring of a chemical gelation process in 4 wt. % alginate hydrogels. As shown in Fig. 6(c), the sensor phase angle response remained initially stable while fully submerged in a 4 wt. % alginate solution. The addition of a 500 μl droplet of DIW at 200 s, which served as an in situ negative control for the chemical gelation process, caused no significant change in the phase angle response. In contrast, the addition of an equal volume droplet of a calcium ion-containing curing solution caused the phase angle to continuously decrease by 15° over the course of the next 10 min. The gelation time was consistent with previous reports.²⁴ 

The ability to perform resonant frequency, quality factor, phase angle, and impedance tracking in alginate hydrogels near 4 wt. % suggests that milli-cantilever sensors may facilitate in situ monitoring of engineered tissues, which commonly vary from 1 to 3.5 wt. %,^50–52 and characterization of local hydrogel and tissue structure–property data. In particular, high-order modes may be particularly useful for the characterization of bioprinted tissues and other engineered hydrogels, which typically utilize higher polymer content.^52,53

Having shown that high-order modes can extend the dynamic range and sensitivity for real-time sensing of viscoelastic property changes in alginate hydrogels, we next examined the behavior of another commonly used hydrogel system based on polyethylene glycol (PEG). PEG-based hydrogels have become widely utilized and investigated synthetic polymer-based materials for tissue engineering and regenerative medicine applications. As shown in Fig. S3 of the supplementary material, PEGDMA hydrogels across the 8–18 wt. % concentration range yield hydrogels that exhibit storage moduli ranging from 17.4 to 109.9 kPa. As shown in Fig. 7, high-order modes in PEMC sensors enabled the characterization of PEGDMA hydrogels across the 8–18 wt. % concentration range. We note that this is a significant increase in the dynamic range relative to the alginate hydrogel system, which ranged from 6.0 to 33.2 kPa (see Figs. 4 and 5). Similar to chemically crosslinked alginate hydrogels [see Figs. 5(d)–5(f)], the phase angle response of high-order modes of cantilever sensors also exhibited relatively increased dynamic range and detection limit compared to low-order modes in PEGDMA hydrogels [see Fig. 7(e)]. However, unlike the alginate hydrogel system, the frequency and impedance responses of the sensor did not exhibit a correlation with concentration or low-frequency material properties [see Figs. 7(a) and 7(k)]. Interestingly, although the storage modulus of the most concentrated PEGDMA hydrogel was greater than that of the alginate hydrogel (18 vs 4 wt. % and 109.9 vs 33.2 kPa, respectively), the net shift in the phase angle and quality factor for the PEGDMA system were relatively smaller. For example, while the chemical gelation of a 33.2 kPa alginate hydrogel led to a net shift in the phase angle of 30.5% for the high-order mode, the photocuring of a 109.9 kPa PEGDMA hydrogel led to a shift of 2.1%. It is useful to note that DMA studies of alginate and PEGDMA hydrogels (see Figs. 4 and S3 in the supplementary material, respectively) revealed that the alginate hydrogels were relatively more dissipative than the PEGDMA hydrogels over the associated concentration ranges examined. For example, tan(δ) of the alginate hydrogels ranged from 0.34 to 0.19 across the 0.5–4 wt. % concentration range, while tan(δ) of the PEGDMA hydrogels ranged from 0.10 to 0.21 across the 8–18 wt. % concentration range, respectively, suggesting that the PEGDMA hydrogels were relatively less dissipative. In fact, we observed that high-order modes persist in PEGDMA hydrogels as concentrated as 35 wt. %, above which it becomes challenging to remove the sensor from the photocured material following an experiment without fracturing the cantilever. Ultimately, these studies suggest that high-order modes of PEMC sensors exhibit a relatively increased dynamic range upper limit than low-order modes in commonly utilized hydrogels. They also reveal that the dynamic range and detection limit of the PEMC sensors for the detection of viscoelastic property changes exhibit dependency on the material system.

We showed here for the first time that the resonance of high-order modes in dynamic-mode piezoelectric-excited millimeter-sized cantilever (PEMC) sensors persists in hydrogels of storage moduli as high as 109.9 kPa (DMA at 1 Hz) that otherwise damp resonance of low-order modes. The phase angle response of high-order modes exhibited a limit of detection for storage modulus (E′) changes in the surrounding hydrogel of 90 Pa. Continuous tracking of the phase angle response of high-order modes was also shown to facilitate real-time monitoring of gelation processes of hydrogels that are beyond the dynamic range of low-order modes. Ultimately, this work suggests that high-order modes of dynamic-mode milli-cantilevers can facilitate sensitive sensor-based characterization of hydrogels and real-time monitoring of gelation processes across a wide dynamic range in commonly used hydrogel systems. This work also suggests that cantilever sensors may provide attractive measurement platforms for advancing the characterization of soft materials toward future automated, sensor-based high-throughput measurement formats.

See the supplementary material for an expanded discussion of cantilever sensor mechanics, the impedance spectra associated with cantilever sensor impedance spectra across the 0–1 MHz frequency range in air and water, and sensor responses associated with gelation of alginate hydrogel over the 0.5–4 wt. % concentration range.

B.N.J. is grateful for the generous support of the National Science Foundation (NSF) (No. CMMI-1739318) that provided funding for the reported work.

The data that support the findings of this study are available from the corresponding author upon reasonable request.