Keywords: Chirp, adhesives, UV, PDMS
RH159
Abstract
Fast frequency chirps are an innovative method to rapidly characterize the time- and rate-dependent mechanical characteristics of fluids, soft solids, and even highly stiff polymeric materials. It can be used to significantly reduce test times for appropriate tests, and unlock new measurement space, in cases where the sample’s mechanical properties change before a frequency sweep can be performed. Here, fast frequency chirps are utilized across several case studies for the application of various adhesive materials.
Adhesives are an important type of material that can either permanently or reversibly bond two interfaces together [1,2]. Adhesives span many applications and industries and there are different overall categories of adhesives based on the mechanism of bonding [1,2,3,4]. Some adhesives, such as hotmelt adhesives, are heated well past a softening point, dispensed, and then subsequently cooled to solidification to bond two interfaces together [5]. Other adhesive systems are activated using stimuli such as heat or light to initiate a reaction. For such adhesives, the liquid precursor can be dispensed into the interfacial bonding area and then exposed to the appropriate wavelength and intensity light, temperature, or some sequence of the two (light cure followed by subsequent heating) [1]. There are also solution or dispersion adhesive systems. These can contain a significant amount of solvent (which can include water) and once dispensed, the solvent phase can evaporate to form a stiffer more elastic adhesive film [3]. Lastly, there are pressure-sensitive adhesives, which do not cure or harden but rather tack, and instead rely on a combination of interfacial surface interactions and shear viscoelasticity to maintain long-term bonds [4,6].
In healthcare, adhesives are found in applications such as dental adhesives and medical patches, as well as in the assembly of medical equipment components [7]. Adhesives are also found in a variety of electronics applications, playing a role in chip bonding, bonding components to PCBs, and encapsulation and potting [8]. Construction adhesives can be used to bond wood, drywall tile, and other materials either together or to a substrate layer [9]. This can include gap filling and/or sealing of interfaces. Adhesives are also widely used for packaging purposes, bonding paper or cardboard boxes into shape, as well as labels to boxes, bottles, and cans [3]. Overall, adhesives play a critical role in all levels of life, and consequently the characterization of their complex mechanical properties is a necessity for some combination of reduced cost, performance, and lifetime.
Key to all these instances is the characterization of the mechanical viscoelastic properties of the adhesives, whether as a function of timescale/frequency, temperature, before and after some form of cure (thermal, UV, humidity), or as a function of time at a relevant temperature and/or humidity. Frequency sweeps in particular are a tool that allows for the determination of the linear viscoelastic structural relaxation profile from short timescales to longer timescales, thus quantifying the elastic-like and viscous-like contributions to the resistance of deformation and the resistance to deformation over time, and giving insights into how a material might respond to loads within the linear viscoelastic limit over time.
A limiting aspect of frequency sweep characterization is it can take some time for the test to complete; the test duration scales to the inverse of every frequency probed. This means that overall characterization throughput can be limited in industrial applications. A more limiting implication is that the sample itself may undergo some evolution such as thermal degradation at elevated temperatures, dehydration, or any form of mechanical change within the duration of the measurement. Fast frequency “chirps” are a method to characterize samples with a continuous waveform that sweeps through the range of desired frequencies. Rather than oscillating for several conditioning and sampling cycles at each frequency, which inherently increases test duration, the deformation or imposed stress is performed with a single waveform in a fraction of the time. In this application note, innovative uses of fast frequency chirps are demonstrated for the characterization of several adhesive materials.
UV-initiated adhesives, hot melt adhesives, and humidity-cured adhesive compounds were obtained commercially and tested as received. The UV sample was tested immediately upon reception to prevent time-dependent degradation of the initiator. Humidity cured samples were tested in sequential order and appropriately resealed in between measurements.
All sample testing was performed on a TA Instruments™ Discovery™ HR 30 stress control rheometer. UV samples were tested on a rheometer equipped with a 365 nm LED UV accessory, 20 mm diameter disposable aluminum upper plates, and 20 mm diameter disposable acrylic plates, with an Upper Peltier Plate (UPP) used for active temperature control. Hot melt adhesives were tested with a combination of an Advanced Peltier Plate and the UPP using 40 mm diameter plates. Humidity-cured compounds were characterized using the humidity chamber available for the Discovery Hybrid Rheometer series with the corresponding relative humidity parallel plate kit, where 25 mm disposable plates were used. Methods for each case study are outlined in the corresponding sections.
Baseline PDMS Chirp vs Traditional Frequency Sweep
As a preliminary case study for the purposes of demonstrating the utility of fast frequency chirps, frequency sweeps were performed on PDMS using both traditional frequency sweeps as well as the newer fast frequency chirp method. PDMS is commonly used as a verification material for oscillatory tests to ensure the instrument is working reliably. Typically, a frequency sweep is performed with a strain within the linear viscoelastic region of the material (1-5% strain) with a frequency range from 100 to 0.1 rad/s and a point density of 5 points per decade, and default data acquisition parameters. Comparatively, in Figure 1, a fast frequency chirp method is outlined, where “single” is selected denoting a single frequency sweep, and a strain, frequency range (with logarithmic sweep selected), and point density are set. There are additional parameters including the acquisition mode, which allows for the selection of correlation, transient, or simultaneous data collection, and chirp shape modifiers for altering the characteristics of the continuous waveform.
There are several overall modes, including single, isothermal, temperature ramp, and temperature step. In general principle, the design of a chirp experiment can be as straightforward as a standard frequency sweep, where the strain and frequency range (and point density) are specified. Additional parameters are not always necessary to modify but can allow for more fine control of the chirp waveform and sample relaxation settings depending on the exact experimental needs.
In a traditional frequency sweep, the sample is either subjected to a controlled oscillatory deformation (or stress) at a list of given frequencies for a specified condition and sampling time, or several conditioning cycles and sampling cycles. Each frequency is tested discretely, where discontinuities are observed in between subsequent frequencies. A resulting plot of the transient data (waveforms) can be observed in Figure 2. Based on the frequency range, point density, and conditioning and sampling settings, the test took just under eight minutes to complete. The correlated oscillatory data can be found in Figure 4 with the appropriate label “traditional frequency sweep.” A fast frequency chirp experiment similarly sweeps through a range of frequencies with a controlled oscillatory deformation or imposed stress. The critical distinction between a traditional frequency sweep and fast frequency chirp is that the chirp ramps through the frequency range using a continuous waveform, where the waveform has been optimally windowed to minimize spectral leakage [10,11]. This allows for a more rapid measurement without a significant reduction in overall data quality after processing. A depiction of this can be observed in Figure 3, where a frequency sweep from 100 to 0.1 rad/s with a higher point density of 10 points per decade (relative to the traditional frequency sweep in Figure 2) was performed in just over one minute.
Figure 5A shows why the Winter-Chambon criterion is critically important for this sample. There are no modulus crossover points except for the lowest frequency shown (0.1 Hz, 0.628 rad/s). Crossover points occur where G’ and G” are equal, which is also observed when the phase angle is 45° (horizontal dashed line in Figure 5B). Frequencies at 0.5 Hz, or 3.14 rad/s, and above increase in modulus but never cross within this experiment so no effective gel point can be obtained from a crossover. Further, there are multiple crossover points for 0.1 Hz (0.628 rad/s). One crossover occurs near the gel point and another hundreds of seconds later. An unambiguous gel point is necessary to determine kinetics for optimizing component ratios and curing under different environmental conditions. The Winter-Chambon gel point is the only unambiguous gel point obtainable for these materials.
Epoxy B curing over time is shown in Figure 6 with frequencies distinguished by color and variable by line style. Epoxy B had some similarities to Epoxy A. The material was a weak and nearly Newtonian fluid with a phase angle close to 90° shortly after mixing. The material showed a dramatically increasing modulus and decreasing phase angle within a few hundred seconds after mixing.
No modulus crossover was observed within 6,000 s at any frequency. While the material showed a significant rise in modulus, the loss modulus remained dominant throughout the experiment. The Winter-Chambon gel point was observed much later for Epoxy B and there was a much less sudden transition to and through the gel point relative to Epoxy A. The phase angle converges very slowly over hundreds of seconds and appears to reach a plateau in phase angle vs. frequency (Figure 7) around 2279 seconds. The gel point occurs after the material has significantly stiffened. The gel point for Epoxy A is more in line with the “clamp time” of 1800 s specified by the manufacturer for Epoxy B, while the gel point for Epoxy A is close to the “set time” specified by the manufacturer.
A plot of the transformed (correlated) traditional frequency sweep and fast frequency chirp data is overlayed in Figure 4 for PDMS with appropriate labelling. Although the point density is higher and the overall test time was shorter for the fast frequency chirp, the data overlays nicely and demonstrates that the newer technique can produce more data faster, with no significant loss in quality. This baseline case demonstrates that throughput can be increased significantly, reducing test time from approximately eight minutes to one minute. In other scenarios, chirps allow for the measurement of time-dependent complex mechanical characteristics where samples may mechanically evolve, such as a polymer melt at a high temperature and/or oxygen containing environment, a hydrogel dehydrating at biologic test conditions, or a sample that cures with time. Lastly, the technique may also open new measurement space, where experiments that may have been limited by excess use of time can now be performed in realistic laboratory timescales. An example of this can be seen in the first case study of this application note, where frequency sweeps are performed on a UV cure adhesive after short pulses of irradiation. An experiment of this nature would have taken on the order of hours using a traditional frequency sweep; however, it can now be performed in tens of minutes, depending on the number of pulses and dosage desired.
Case Study #1 UV Pulse Curing (Single Chirp Mode)
In the first case study, a commercial UV cure adhesive was tested using the 365 nm LED fixture on an HR 30. A typical workflow using the UV LED (or light guide) accessory can be seen in a prior TA application note, RH118, where the sample is irradiated at different intensities (or gaps) until cure completion [12]. For this case study, a different approach was taken, where the sample is subjected to pulses of UV irradiation. The time-dependent complex mechanical properties of the adhesive were first measured prior to any curing using a fast frequency chirp. The sample was then subjected to a sequence of steps, in which the sample was partially cured using a short one second duration (pulse) of UV irradiation and the evolution of the sample (and associated shrinkage) captured using a fast-sampling time sweep. After the pulse and partial cure, the samples’ time-dependent characteristics were then measured using a fast frequency chirp. This process was then repeated for several pulses; here, six total pulses were considered.
The method used is outlined in Figure 5. A conditioning options step is set (with an axial force of 0 +/- 0.1 N) to maintain a null force, such that when the sample expands or contracts, the gap will be adjusted dynamically. There is then an alternating sequence, where the sample time-dependent behavior is characterized by using a fast frequency chirp, followed by a simultaneous fast sampling time sweep and UV pulsation to capture the curing (at a single frequency). This process is repeated several times (steps 3-5), and each chirp following a pulse characterizes the time-dependent characteristics of the adhesive at different states of cure. The benefit is that in a traditional oscillation time experiment, the evolution of the measured complex mechanical properties is only measured at a single frequency. By measuring the time (frequency) dependent characteristics, a more thorough understanding of the material can be gained. As the sample undergoes additional crosslinking, the longer-term structural relaxation associated with low frequencies is suppressed, which is captured by a frequency sweep.
In Figure 6, results from the fast-sampling time sweeps are presented for the six pulses considered, where the storage and loss modulus are plotted as a function of time. Although the moduli start to intersect at pulse 3 (into a gel-like state), the moduli still go on to increase in magnitude, and the sample starts to become elastically dominated. Overall, the sample goes from a viscousdominated modulus of tens of pascals, to an elastically-dominated modulus on the order of megapascals. Although the evolution of the moduli can be observed, including their eventual overlap and full solidification of the sample, the mechanical information is only determined at a single frequency. The time-dependent characteristics as determined by a frequency sweep can elucidate their longer-term mechanical response.
During each pulse, the sample also shrinks to some extent and results are plotted in Figure 7, where the normalized gap change percentage is measured as a function of time. The normalized gap change is calculated from the change in gap relative to the gap at the start of the specific step. In the first two pulses, the sample undergoes a negligible amount of shrinkage. In pulse 3, the shrinkage observed increases significantly and increases further in pulse 4; additional pulses start to have a diminishing effect.
The analysis observed in Figures 6 and 7 is not necessarily new and can be performed without the addition of fast frequency chirp measurements. The added novelty that comes from the addition of measurements using the fast frequency chirps can be observed in Figure 8, where storage modulus and loss modulus are plotted as a function of angular frequency for the virgin adhesive and following each UV pulse. The UV pulses do not have a sizable effect on the mechanical characteristics until around pulse 3, where the magnitude of both moduli increases, and the storage modulus and loss modulus start to overlay, forming a gel-like state. For pulse 2, the storage modulus increases over baseline, but the sample is still viscous-dominated over the timescales probed. In pulse 3, the sample has comparable moduli, and the extent of structural relaxation is now suppressed, where the overall decrease in the moduli overtime is not as significant. By pulse 5, the storage modulus reaches its approximate maximum and becomes relatively independent of time for the timescales probed here. Figure 9 features complex viscosity plotted as a function of time for the same dataset in Figure 8, and gives an indication of the increase in resistance to flow over time as the cure of the sample proceeds.
Overall, this is a considerably more detailed characterization and gives more insight into the nature of the evolved sample per UV dosage, than with single frequency time sweeps alone. If this had been performed using traditional frequency sweeps, the time of the frequency sweeps alone in the experiment would have been around one hour (seven frequency sweeps each eight minutes in duration) versus the overall 16-minute experiment performed using fast frequency chirps.
Case Study #2 Hot Melt Adhesives (Temperature Ramp Chirp Mode)
Hot melt adhesives are interesting to consider since a thorough shear characterization can include the complex mechanical properties measured as a function of temperature, as well as the properties as a function of rate (or frequency) at a given temperature. Here, fast frequency chirps are utilized to collect both sets of data simultaneously, where in an hour, a time temperature superposition (TTS) analysis can be performed in addition to the collection of thermal mechanical characteristics.
The first case study utilized the “single” mode as the fast frequency chirp mode, where only a single sweep is performed consistent with a frequency sweep experiment. In this case study, the “ramp” mode is selected, where the temperature is ramped linearly at some constant rate between an initial and final setpoint temperature, and chirps are continuously performed throughout the ramp. One can observe that for a given frequency range and point density (and chirp length multiplier), there is a display for the total length of the chirp.
The method used is shown in Figure 10. Auto strain adjustment is used in conjunction with axial force adjustment and gap temperature compensation calibration was performed prior. With careful consideration of the heating rate, the chirp length can be modified such that the chirps are made at some consistent temperature interval. Modification of the baseline and equilibration times can also be used to the same effect. For example, a heating rate of 3 °C/min results in a sample seeing a 1 °C spread for 20 seconds. By tuning the length of the chirp with the chirp length multiplier, one can tune the experiment such that one frequency sweep is performed for each degree C; if the chirp length was not modified, it could potentially result in an unwieldy amount of data. Here, the chirp was modified from an initial duration of six seconds to 20 seconds, by adjusting the length multiplier to a value of approximately three. Therefore, with a heating rate of 3 °C/min, a chirp is performed every degree of the temperature ramp.
The hot melt adhesive here was loaded and trimmed at a temperature of 150 °C and the sample was then cooled at a linear heating rate down to 0 °C. As the sample cools, fast frequency chirps were performed in a consecutive fashion, again resulting in a frequency sweep every degree C. A plot of the results is shown in Figure 11, where storage modulus, loss modulus, and complex viscosity are plotted as a function of angular frequency for every temperature. This form of overlay is typically used for TTS transformation, where frequency sweep data is shifted relative to a reference temperature dataset, resulting in many decades of extrapolated frequency for suitable polymeric materials. Higher temperature relative to the reference temperature shift to lower frequencies (or longer timescales), and lower temperatures relative to the reference temperature shift to higher frequencies (or short timescales). Depending on the application, material, and reference temperature, this can give insights into long-term performance of a material or alternatively give insights into relevant processing information.
Figure 12 features a TTS master curve with a reference temperature of 25 °C. At this reference temperature (near ambient), one can observe the structural relaxation of this adhesive in the linear viscoelastic state over time. To create this curve, the data shown in Figure 11 was shifted using the time temperature superposition (TTS) transformation function within TRIOS™ Software. As the sample goes from short timescales (high frequencies) to longer timescales (low frequencies), the material softens, eventually exhibiting a viscous dominated mechanical response. From this, the long-term linear viscoelastic mechanical characteristics of the adhesive can be understood and compared to other adhesives. Typically, if performing a TTS analysis on a polymeric material such as a hot melt adhesive, frequency sweeps are performed at several temperatures (some temperature range with 5-10 °C increments). If each frequency sweep takes 5-10 minutes, 15 frequency sweeps can take several hours to perform. Here, the testing took less than an hour and produced frequency sweeps at more temperatures, with a higher point density.
Additional thermal mechanical information is also gained from this same test. Employing the “rearrange frequency cycles into temperature sweeps” transformation in TRIOS Software, the frequency sweep datasets are transformed into several temperature ramp steps each with their own frequency. Using this transformation, the mechanical characteristics as a function of temperature can be obtained in addition to the time-dependent mechanical characteristics at each temperature simultaneously. This data can be observed in Figure 13, where the storage modulus, loss modulus, and complex viscosity are all plotted as a function of temperature for the various frequences. If looking at the storage modulus above 60 °C, the curves go from low frequency to high frequency in order of bottom to top. With these complementary datasets, the liquification temperature of the hot melt adhesive can be determined from the temperature ramp data; in this case, it is just above 45 °C from the crossover modulus at 1 rad/s.
Case Study #3 RH Cure Adhesive (Isothermal Chirp Mode)
The last case study considered is for the characterization of a moisture cure construction adhesive using the humidity chamber equipped on an HR 30. The isothermal fast frequency chirp mode is utilized, where the sample is held at constant temperature for some duration, and fast frequency chirps are performed continuously. Depending on the timescale of the cure and how rapid it progresses, there may be considerations for the overall chirp duration. In this case, the experiment was run for two full days, with the cure proceeding slowly, so a longer chirp length can be utilized to reduce the overall number of frequency sweeps.
A snippet of the method can be seen in Figure 15; consistent with the other methods seen above, a conditioning options segment is used. Additionally, a conditioning sample and conditioning humidity step are used to condition the humidity chamber to a desired temperature and humidity for the cure conditions. The last step here is the oscillation fast frequency chirp step with the appropriate parameters set.
Figure 16 features an overlay of the frequency sweeps performed throughout the duration of the two-day extended humidity cure, with storage modulus and loss modulus plotted as a function of angular frequency. The individual frequency sweeps can be plotted to observe changes in the structural relaxation profile at different times throughout the cure. The use of the “rearrange frequency cycles into temperature sweeps” transformation this time yields mechanical cure evolution profiles over time at several frequencies, shown in Figure 17. For relevant materials that feature a modulus crossover during the cure, where the storage modulus starts to exceed the loss modulus (not observed here, where the material started in an elastic dominate state), measuring the cure profiles at multiple frequencies can yield the frequency invariant gel time, where tan delta curves at multiple frequencies intersect at the true gel point, when plotted as a function of time [13].
Two sets of curing experiments were performed at 30 °C on the humidity cure samples: one set was featured in Figures 16 and 17, where the setpoint humidity was 5% relative humidity (RH), and another where the setpoint humidity was 85% RH. Data was transformed using the “rearrange frequency cycles into temperatures sweeps” for both data sets, and the curing profiles as a function of time at 10 rad/s were extracted and overlayed in Figure 18, where storage modulus, loss modulus, and tan delta are plotted as a function of time. It can be observed that the cure at 85% humidity is more rapid, and begins to plateau sooner, the solidification is apparent both from the time-dependent increase in the storage modulus, but also in the time-dependent decrease in tan delta. The humidity setpoints were chosen at extremes of 5% and 85% RH to get a sense of the range of time-dependent sample responses.
Lastly, the time-dependent complex mechanical characteristics are compared at the start of the curing experiment and also one day into the cure at both the 5% and 85% RH setpoints. This can be seen in Figure 19, where storage modulus, loss modulus, and complex viscosity are plotted as a function of angular frequency. At the start of the experiments, the samples have comparable moduli and complex viscosity, although the 85% RH sample did start a little higher, as the RH was first ramped to 85% RH from ambient at 2% RH per minute, meaning the sample had some short residence time at elevated humidity. Regardless, after one day of curing, for both samples the elastic modulus increased significantly, and the overall magnitude of structural relaxation is decreased, as the drop in the elastic modulus magnitude overtime decreases. Although the frequency sweep profiles were only compared at two different times across the two data sets, there are frequency sweeps generated every five minutes or so for the entirety of the experiment, so a more sophisticated analysis could be performed.
In this application note, fast frequency chirps were utilized in multiple modes (single, isothermal, and ramp) throughout three case studies on adhesive materials. UV adhesives were characterized by using pulsed cure conditions. The complementary time dependent and thermal-mechanical properties of hot melt adhesives were measured in a relatively short duration of time. Finally, the time-dependent complex mechanical properties of humidity-cured adhesive compounds were measured over extended times. Overall, the increased throughput and more thorough characterization of the samples was demonstrated, showing that fast frequency chirps can add a substantial amount of value to existing workflows, and can make traditionally lengthy measurements more viable for time constrained laboratories whether they are for quality or R&D purposes.
References
- Dinte, E., & Sylvester, B. (2018). Adhesives: Applications and Recent Advances. Applied Adhesive Bonding in Science and Technology. https://doi.org/10.5772/intechopen.71854
- Heinrich, L. A. (2019). Future opportunities for bio-based adhesives – advantages beyond renewability. Green Chemistry, 21(8), 1866–1888. https://doi.org/10.1039/c8gc03746a
- Urban, D., & Takamura, K. (2002). Polymer Dispersions and Their Industrial Applications. Wiley EBooks. https://doi.org/10.1002/3527600582
- Sun, S., Li, M., & Liu, A. (2013). A review on mechanical properties of pressure sensitive adhesives. International Journal of Adhesion and Adhesives, 41, 98–106. https://doi.org/10.1016/j.ijadhadh.2012.10.011
- A.J. Franck, “Hot Melt Adhesives,” TA Instruments, vol. AN001.
- “Pressure Sensitive Adhesives”, TA Instruments, vol. RH026
- Webster, I., & West, P. J. (2001). Adhesives for medical applications. In Polymeric Biomaterials, Revised and Expanded (pp. 717-752). CRC Press.
- Alam, M. O., & Bailey, C. (Eds.). (2011). Advanced adhesives in electronics: Materials, properties and applications. Elsevier.
- Dillard, D. A. (Ed.). (2023). Advances in structural adhesive bonding. Elsevier.
- Geri, M., Keshavarz, B., Divoux, T., Clasen, C., Curtis, D. J., & McKinley, G. H. (2018). Time-Resolved Mechanical Spectroscopy of Soft Materials via Optimally Windowed Chirps. Physical Review X, 8(4). https://doi.org/10.1103/physrevx.8.041042
- Hudson-Kershaw, R. E., Das, M., McKinley, G. H., & Curtis, D. J. (2024). σOWCh: Optimally Windowed Chirp rheometry using combined motor transducer/single head rheometers. Journal of Non-Newtonian Fluid Mechanics, 333, 105307. https://doi.org/10.1016/j.jnnfm.2024.105307
- K. Coasey, “Characterization of UV Curing resins for Photocuring 3D printing”, TA Instruments, vol. RH118
- Winter, H.H., Mours, M. (1997). Rheology of Polymers Near Liquid-Solid Transitions. In: Neutron Spin Echo Spectroscopy Viscoelasticity Rheology. Advances in Polymer Science, vol 134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68449-2_3
Acknowledgement
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This paper was written by Keith Coasey, Ph.D.
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