System, method and computer program product for generating viscoelastic master curves

Abstract

A method of determining mechanical properties of a sample using thermorheological data includes providing a sample in a dynamic mechanical analysis device; selecting a temperature for the sample; performing a high-bandwidth time / frequency / temperature sweep test comprising: applying a broadband mechanical impulse over a frequency range at the temperature, and collecting thermorheological data during application of the broadband mechanical impulse; and determining mechanical properties of the sample using the thermorheological data, and, optionally, generating a viscoelastic master curve.

Description

Attorney Docket No.5405.534.WO SYSTEM, METHOD AND COMPUTER PROGRAM PRODUCT FOR GENERATING VISCOELASTIC MASTER CURVES STATEMENT OF GOVERNMENT SUPPORT

[0001] This invention was made with Government support under Federal Grant No. 2040670 awarded by the National Science Foundation. The Federal Government has certain rights to this invention. RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Application Serial No. 63 / 669,378 filed July 10, 2024, the disclosure of which is hereby incorporated by reference in its entirety. TECHNICAL FIELD

[0003] The present inventive concept relates to the methods, systems, and computer program products for evaluating viscoelastic materials and generating viscoelastic master curves and / or shift factors. BACKGROUND

[0004] Realistic simulations of property and performance for polymer-based materials and composites are essential for current industries such as tire manufacturing, but also are poised to enable a revolution of application-oriented material design from aerospace structures to energy storage materials to implant customization. However, the realism of these simulations hinges on a library of the core time- and temperature-dependent polymer material properties. While the most common polymer materials properties can be found in collected works and databases, the vast majority of material data is sparsely scattered throughout the literature. Material data are often held in unstructured papers and manuscripts which may not be in machine-readable form, and it can be difficult and time-consuming to produce. For subfields, useful data may not even exist at all, or if it does exist, it rarely contains complete and reproducible descriptions of the experimental and computational methods used to generate, for example, master curves and / or shift factors.

[0005] Thus, there is an ongoing need for improved approaches to obtaining full-field viscoelastic properties of complex materials.Attorney Docket No.5405.534.WO SUMMARY

[0006] According to some embodiments of the present inventive concept, a method of determining mechanical properties of a sample using thermorheological data includes providing a sample in a dynamic mechanical analysis device; selecting a temperature for the sample; performing a high-bandwidth time / frequency / temperature sweep test comprising applying a broadband mechanical impulse over a frequency range at the temperature, and collecting thermorheological data during application of the broadband mechanical impulse; and determining mechanical properties of the sample using the thermorheological data, and, optionally, generating a viscoelastic master curve and / or shift factors.

[0007] According to some embodiments of the present inventive concept, a mechanical analyzer (DMA) system for determining mechanical properties of a sample using thermorheological data includes a dynamic mechanical analyzer device configured to receive a sample; and a controller configured to selecting a temperature for the sample, and to control the DMA device to perform a high-bandwidth time / frequency / temperature sweep test comprising: applying a broadband mechanical impulse over a frequency range at one temperature in the plurality of temperatures, and collecting thermorheological data during application of the broadband mechanical impulse; and configured to determine mechanical properties of the sample using the thermorheological data, and, optionally, to generate a viscoelastic master curve and / or shift factors.

[0008] In some embodiments according to the present inventive concept, a computer program product is configured for determining mechanical properties of a sample using thermorheological data in a dynamic mechanical analysis device. The computer program product includes a non- transient computer readable medium having computer readable program code embodied therein, the computer readable program code comprising: computer readable program code configured to select a temperature for the sample; computer readable program code configured to perform a high- bandwidth time / frequency / temperature sweep test in a dynamic mechanical analysis device, the high-bandwidth time / frequency / temperature sweep test comprising: applying a broadband mechanical impulse over a frequency range at the temperature, and collecting thermorheological data during application of the broadband mechanical impulse; and computer readable program code configured to determine mechanical properties of the sample using the thermorheological data, and, optionally, generating a viscoelastic master curve and / or shift factors.Attorney Docket No.5405.534.WO BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the inventive concept and, together with the description, serve to explain principles of the inventive concept.

[0010] FIG. 1A is a flowchart of operations according to some embodiments of the inventive concept.

[0011] FIG. 1B is a schematic diagram of systems, methods, and computer program products according to some embodiments of the inventive concept.

[0012] FIG. 2A is a graph of an example strain chirp according to some embodiments of the inventive concept.

[0013] FIG.2B is a graph of the strain response of FIG.2A.

[0014] FIG.2C is a graph of a complex Young’s modulus derived from the graphs of FIGS.2A- 2B.

[0015] FIG.3A illustrates a driving stress / strain frequency (prior art).

[0016] FIG. 3B is a graph of the resulting stress and strain frequencies from the sinusoidal frequency from the circuit of FIG.3A.

[0017] FIG. 3C is a graph of E’ and E’’ (Pa) as a function of frequency at 55º C applying the stress and strain frequencies of FIG.3A.

[0018] FIG.3D is a graph of the storage modulus as a function of frequency from FIG.3B

[0019] FIG.3E is a graph of the loss modulus as a function of frequency from FIG.3B

[0020] FIG. 4A illustrates a driving stress / strain frequency “chirp” according to some embodiments of the inventive concept.

[0021] FIG.4B is the stress and strain frequencies or chirp as applied by the circuit of FIG.4A.

[0022] FIG.4C is a graph of E’ and E’’ (Pa) as a function of frequency at 55º C using application of the chirp of FIG.4B.

[0023] FIG. 4D is a graph of the resulting storage modulus as a function of frequency from application of the chirp of FIG.4B.

[0024] FIG.4E is a graph of the loss modulus as a function of frequency from the application of the chirp of FIG.4B.

[0025] FIG. 5 is a graph of the Young’s modulus as a function of frequency for the storage modulus (E’) and loss modulus (E’’) according to some embodiments of the inventive concept.Attorney Docket No.5405.534.WO

[0026] FIG.6A is a graph of the Youngs modulus signal to noise ratio for the storage modulus as a function of frequency at different temperatures according to some embodiments of the inventive concept.

[0027] FIG.6B is a graph of the Young’s modulus signal to noise ratio for the loss modulus as a function of frequency at different temperatures according to some embodiments of the inventive concept.

[0028] FIG. 7 is a graph of the storage loss Young’s modulus (Pa) as a function of frequency according to some embodiments of the inventive concept.

[0029] FIG.8 is a graph of the Young’s modulus for the storage modulus (E’) and loss modulus (E’’), and corresponding Prony series, as a function of frequency according to some embodiments of the inventive concept.

[0030] FIGS. 9A-9B are graphs comparing master curves and shift factors produced from BOTTS and DFS-TTS according to some embodiments of the inventive concept. FIG. 9 A is a graph of the Young’s modulus as a function of frequency at 55º C and FIG.9B is a graph of the shift faction aT as a function of temperature.

[0031] FIG.10 is a graph of the Young’s modulus for the storage modulus (E’) and loss modulus (E’’), and corresponding Prony series, as a function of frequency according to some embodiments of the inventive concept. DETAILED DESCRIPTION

[0032] Embodiments according to the present inventive concept may be used to study and characterize viscoelastic materials, such as polymers or polymer composites, resins, gels, pastes, slurries, tissues, suspensions, colloids, or solutions, using a dynamic mechanical analyzer (DMA). Examples of dynamic mechanical analyzers include load frame, rheometer, viscometer, ultrasound, indenter, nanoindenter, atomic force microscopes, and scanning probe microscopes. Viscoelastic materials exhibit both elastic (solid-like) and viscous (liquid-like) behavior, and the response of a viscoelastic material depends on both time and temperature. It is noted that DMA refers to a dynamic mechanical analyzer or dynamic mechanical analysis, depending on context. DMA involves applying time-varying force to a material sample and measuring the resulting strain or stress. The oscillatory deformation allows for the determination of the material’s stiffness (storage modulus) and damping (loss modulus). DMA also involves varying the frequency of theAttorney Docket No.5405.534.WO applied force and / or temperature of the material sample to determine how a property of the material changes under different conditions.

[0033] DMA may be used to determine thermorheological data, including a) stress and strain; and b) shear, Young’s, and bulk modulus. Thermorheological data may be represented and / or collected in the time, frequency (Fourier), or “complex frequency” (Laplace) domain.

[0034] Accordingly, DMA may be used to determine various characteristics of the sample material. More specifically, the storage modulus (E’), which represent an elastic component of the material’s response to deformation, indicates the ability of the material to store energy. A higher storage modulus corresponds to a stiffer material. A loss modulus (E’’) represents a viscous component of the material, which indicates the energy dissipated as heat during deformation. A Tan Dela (tan δ) is the ratio of the loss modulus to the storage modulus (E’ / E’’), and is also referred to as a loss factor or damping factor. The tan δ quantifies how well a material dissipates energy as heat. DMA may also be used to determine the glass transition temperature (Tg), which is a temperature range where a material transitions from a glassy, rigid state to a rubbery, more flexible state. The glass transition temperature is a property used for understanding a behavior of a material under different conditions.

[0035] DMA may also utilize a “Prony series,” which is a mathematical model used to represent the time-dependent behavior of viscoelastic materials. A Prony series may be derived from DMA data. A Prony series is a mathematical representation of the time-dependent behavior, such as the relaxation modulus, to describe how stress relaxes over time under a constant strain placed on the material. The Prony series is a sum of exponential terms, each with its own coefficient and relaxation time. By fitting a Prony series to DMA data, a mathematical model may be created that represents the material’s viscoelastic properties. Therefore, DMA may provide experimental data, and the Prony series may provide a way to mathematically model that data for use in simulations or further analysis, such as simulations to predict the behavior of structures made from the material under dynamic loading conditions.

[0036] The traditional method to obtain time- and temperature-dependent mechanical properties of a viscoelastic material, such as a polymeric solid, is using a dynamic mechanical analyzer (DMA), which has two fundamental modes: temperature sweep at fixed frequency and frequency sweep at fixed temperature. The temperature-dependent properties are the fastest to obtain, but are valid only at the specific frequency of measurement, unless accompanied also by time-temperature shift factors, oftenAttorney Docket No.5405.534.WO represented by the symbols aTand bTfor horizontal and vertical shifts, respectively. The shift factors can be obtained via time-temperature superposition (TTSP), which is typically implemented in practice as frequency-temperature superposition using DMA frequency sweeps of the storage and loss moduli at an array of fixed temperatures spanning the glass transition. For thermorheologically simple materials, these curves at each temperature can be superposed, via shifting on the logarithmic frequency / time axis or logarithmic modulus axis, to obtain a “master curve” of the properties over a large frequency / time domain, spanning from rubbery to glassy behavior of the polymer compound. Such master curves may be used as the input for large scale design and optimization of new polymers and composites for applications with targeted design parameters.

[0037] Currently, there are several options to obtain time-optimal measurements of the linear viscoelastic properties of a material, all of which use a non-sinusoidal mechanical pulse to perturb a specimen, and then perform a Fourier transform of the response signal to observe the entire frequency response at once. Optimal Fourier Rheometry (OFR) is more broadly suitable for high bandwidth mechanical spectroscopy than Fourier Transform Mechanical Spectroscopy (FTMS or MultiWave (MW)) and I-Rheo because it uses a high-bandwidth mechanical impulse (“chirp”) with (a) a consistent maximum mechanical strain to avoid escaping the linear regime and (b) a 1 / fɑ(“pink”) power spectrum to maintain signal-to-noise ratio (SNR) at low frequencies. Optimally Windowed Chirps (OWCh) reduces error from both signal attenuation and spectral leakage due to “apparent” abrupt strain changes at the ends of a rectangular windowed chirp, the latter being particularly relevant in the context of TTSP as the periodic structure of the leakage artifact induces local minima during the shift factor optimization step.

[0038] As illustrated in FIGS. 1A-1B, methods, systems and computer program products of determining mechanical properties of a sample by generating a viscoelastic master curve using thermorheological data at different temperatures are provided. As shown in FIG.1A, a sample is provided in a dynamic mechanical analysis device (Block 10). One or a plurality of temperatures for the sample is selected (Block 12). A high-bandwidth time / frequency / temperature sweep test is performed (Block 14). The high-bandwidth time / frequency / temperature sweep test includes a) applying a broadband mechanical impulse over a frequency range at one temperature in the plurality of temperatures, and collecting thermorheological data during application of the broadband mechanical impulse; b) optionally, changing the temperature of the sample to another temperature in the plurality of temperatures; c) optionally, applying the broadband mechanical impulse over the frequency range after changing the temperature of the sample and collectingAttorney Docket No.5405.534.WO thermorheological data; and d) optionally, repeating steps b) and c) at the plurality of temperatures to collect additional thermorheological data. A viscoelastic master curve and / or shift factors is generated using the thermorheological data (Block 16). The viscoelastic master curve may be generated by applying a time-temperature superposition principle (TTSP) to the thermorheological data.

[0039] In some embodiments, a Prony series may be generated based on the thermorheological data, which may be used to further evaluate structures at least partially formed of the material of the sample.

[0040] In some embodiments, selecting the plurality of temperatures for the sample (Block 12) includes: estimating an uncertainty in thermorheological data for the sample at an initial plurality of temperatures; and selecting the plurality of temperatures or temperature array based on the uncertainty. Estimating an uncertainty in thermorheological data may include simulating an acquisition of thermorheological data at the initial plurality of temperatures. For example, if the uncertainty of the thermorheological data is relatively high, then the interval between temperatures in the array of temperatures may be reduced, i.e., additional temperature data may be collected to reduce the uncertainty. If the uncertainty of the thermorheological data is relatively low, then the temperatures in the array of temperatures may be decreased or spaced apart further.

[0041] The viscoelastic master curve and / or shift factors may be used to determine various mechanical properties of the material sample, such as to predict a storage modulus (E'), a loss modulus (E''), a loss factor (tan δ), or combinations thereof; to predict a storage modulus (E'), a loss modulus (E''), a loss factor (tan δ), or combinations thereof as a function of temperature; and / or to predict a glass transition temperature (Tg) of the sample. In some embodiments, a physical model of an object formed at least in part by material in the sample may be provided, and a simulation may be performed to generate a prediction of a mechanical performance of the object. The simulation to generate the prediction of the mechanical performance of the object may be based on the viscoelastic master curve, the Prony series, or combinations thereof.

[0042] FIG.1B illustrates an exemplary data processing system that may be included in devices operating in accordance with some embodiments of the present inventive concept, e.g., to carry out the operations illustrated in FIG.1A. As illustrated in FIG.1A, a data processing system 116, which can be used to carry out or direct operations includes a processor 100, a memory 136 and input / output circuits 146. The data processing system can be incorporated in a portableAttorney Docket No.5405.534.WO communication device and / or other components of a network, such as a server. The processor 100 communicates with the memory 136 via an address / data bus 148 and communicates with the input / output circuits 146 via an address / data bus 149. The input / output circuits 146 can be used to transfer information between the memory (memory and / or storage media) 136 and another component, such as a DMA Device 125 that is configured to perform dynamic mechanical analysis on a sample material. These components can be conventional components such as those used in many conventional data processing systems, which can be configured to operate as described herein.

[0043] In particular, the processor 100 can be a commercially available or custom microprocessor, microcontroller, digital signal processor or the like. The memory 136 can include any memory devices and / or storage media containing the software and data used to implement the functionality circuits or modules used in accordance with embodiments of the present inventive concept. The memory 136 can include, but is not limited to, the following types of devices: cache, ROM, PROM, EPROM, EEPROM, flash memory, SRAM, DRAM and magnetic disk. In some embodiments of the present inventive concept, the memory 136 can be a content addressable memory (CAM).

[0044] As further illustrated in FIG. 1B, the memory (and / or storage media) 136 can include several categories of software and data used in the data processing system: an operating system 152; application programs 154; input / output device circuits 146; and data 156. As will be appreciated by those of skill in the art, the operating system 152 can be any operating system suitable for use with a data processing system, such as IBM®, OS / 2®, AIX® or zOS® operating systems or Microsoft® Windows® operating systems Unix or LinuxTM. The input / output device circuits 146 typically include software routines accessed through the operating system 152 by the application program 154 to communicate with various devices. The application programs 154 are illustrative of the programs that implement the various features of the circuits and modules according to some embodiments of the present inventive concept. Finally, the data 156 represents the static and dynamic data used by the application programs 154, the operating system 152 the input / output device circuits 146 and other software programs that can reside in the memory 136.

[0045] The application programs 154 can include, e.g., a DMA controller 120. The application programs can be configured as a single application program or module or as additional applications configured to implement the operations described herein for controlling the DMA device 125Attorney Docket No.5405.534.WO and / or analyzing data acquired from the DMA device. The data 156 can include DMA acquisition data 124 and / or DMA control protocol data 126, for example, that can be used by DMA controller 120 control the DMA device 125 according to control protocol or to store and analyze data acquired by the DMA device 125. For example, the DMA control protocol data 126 may include frequency parameters, temperature parameters, and the like for controlling the data acquisition of the DMA device 125. Accordingly, the DMA controller 120 may be configured to operate the DMA device 125 and to collect and analyze data as described in FIG.1A.

[0046] While the present inventive concept is illustrated with reference to the DMA controller 120, the DMA acquisition data 124, and the DMA control protocol data 126 in FIG.1B, as will be appreciated by those of skill in the art, other configurations fall within the scope of the present inventive concept. For example, rather than being an application program 154, these circuits and modules can also be incorporated into the operating system 152, provided as part of the DMA device 125, or other such logical division of the data processing system. Accordingly, the functionality of the various components of FIG. 1B may be distributed across one or more data processing systems. Thus, the present inventive concept should not be construed as limited to the configurations illustrated in FIG.1B. In some embodiments, the system 116, including the DMA controller 120, DMA acquisition data 124, and the DMA control protocol data 126, may be provided in a DMA device 125 with an associated user interface for performing the operations described herein.

[0047] One aspect of the present disclosure provides a technique that can be referred to as Broadband-Optimized Time-Temperature Superposition (BOTTS). BOTTS may utilize the capabilities of existing rheological measurement instruments for the rapid collection of viscoelastic material properties from macroscale specimens. Among these, the OWCh technique provides a basis for time-optimal, noise-optimal, artifact-free complex modulus measurements, which the present disclosure uses to accelerate master curve and / or shift factor data acquisition in DMA for viscoelastic solid polymers. In some cases, the speed of data acquisition can be increased by a factor of five or more over prior techniques. Furthermore, these chirps collect data over a broad frequency range (e.g., 3 or more decades in frequency) which has been demonstrated to be of great importance for demonstrating thermorheological simplicity.

[0048] Given such an increase in data collection rate, and the robust and repeatable data analysis pipeline also demonstrated herein, BOTTS can enable the curation of vast quantities of high qualityAttorney Docket No.5405.534.WO thermorheological data and derived master curves, shift factors, WLF parameters, and relaxation spectra. This can decrease the cost of performing and curating large designs of experiments of advanced materials including composition, processing, and aging parameters. The increased availability of reliable high-bandwidth time / frequency / temperature property data for polymers and their composites can consequently dramatically accelerate and increase accuracy of design loops for new material applications.

[0049] Embodiments according to the present inventive concept will now be described with respect to the following non-limiting example.

[0050] Materials and Methods

[0051] Oxygen-tolerant thiol-ene resins with narrow loss tangent peaks were synthesized. Thiol crosslinker PETMP was mixed in stoichiometric ratio with allyl crosslinker TATATO or APE. The resin was stabilized with 0.1% MEHQ by mass, which was mixed on a 40 °C stirrer plate until dissolved. The stabilized resin was photosensitized by mixing 1% Benzoyl Peroxide by mass on a 40 °C stir plate, protecting from ambient light by wrapping the vial in foil, overnight or until fully dissolved. Resin was poured into a Sylgard 184 (Dow) silicone mold for 2x2 mm bar specimens and cured in air under 256 nm light for 30 minutes in an Asiga Flash curing oven and post-cured at 65 °C overnight in another oven to maximize photosensitizer conversion.

[0052] All dynamic mechanical analyses were performed on an RSA-G2 (TA Instruments, Newcastle, DE, U.S.A.) with forced convection oven using the 25 mm 3-point bend geometry. Autotension was used to adjust the gap to maintain a static “compression” force of 0.05 N. Strain sweeps were performed in the rubbery, glassy, and glass transition regimes of all materials to verify linear viscoelastic behavior. Prior to temperature sweeps, a temperature ramp is performed at - 5°C / min measuring cyclic response at 1 Hz with Autostrain across the glass transitions to reset specimens to a consistent thermal history and collect (or double check) approximately optimal strains for good signal-to-noise ratios at all temperatures of interest.

[0053] The padded inverse Gaussian windowed exponential chirp used in the present disclosure is defined by the equation:Attorney Docket No.5405.534.WO 0, ^^^^ < ^^^^ì ï^^^^−^^^^^^^^ 2 ^^^ −^^^^− ^^^^ � ^^^^�^^^^1^^^^ln(^^^^2⁄ ^^^^1 )^−^^^^ ^^^^^^^^ −^^^^ ≤ ^^^^ < + ^^^^

[0054] arbitrary wave, p is the time of the zero strain padding before and after the chirp, T is the total length of the windowed chirp steps (i.e.2p less than the total data collection time), r is the width parameter of the gaussian window function, ⍵1 is the lowest requested frequency in radians per second, and ⍵2 is the highest requested frequency in radians per second. The zero- strain padding period before and after the chirp may be used to detrend the data before Fourier analysis. Detrending is a common signal processing technique to suppress low frequency drift noise and ringing artifacts. An example is displayed in FIGS.2A-2C, which shows an example strain chirp and response in the time domain (FIG.2A), the corresponding strain Fourier transform magnitude of the strain chirp and stress response in the frequency domain (FIG.2B), and the derived complex Young’s modulus (FIG.2C).

[0055] These chirps are implemented in the TRIOS “Arbitrary wave” step, being careful to observe an 80-character limit on the length of the equation string.

[0056] The result of performing these chirps across several temperatures for an example polymer that softens around 60C is shown with an equivalent measurement by dynamic frequency sweep (DFS) for comparison in FIGS. 3A-3E (prior art DFS) and FIGS. 4A-4E (using a broadband mechanical impulse or broadband chirp, according to some embodiments of the current inventive concept).

[0057] FIG. 3A illustrates a driving stress / strain frequency according to prior art sinusoidal stress / strain frequency dynamic mechanical analysis. FIG. 3B is the resulting stress and strain frequencies. FIG.3C is a graph of E’ and E’’ (Pa) as a function of frequency at 55º C. FIG.3D is a graph of the resulting storage modulus as a function of frequency, and FIG.3E is a graph of the loss modulus as a function of frequency.

[0058] FIG. 4A illustrates a driving stress / strain frequency “chirp” according to some embodiments of the inventive concept. FIG.4B is the resulting stress and strain frequencies. FIG.Attorney Docket No.5405.534.WO 4C is a graph of E’ and E’’ (Pa) as a function of frequency at 55º C. FIG. 4D is a graph of the resulting loss modulus as a function of frequency, and FIG.4E is a graph of the storage modulus as a function of frequency. As can be seen in FIGS. 4A-4E, the stress / strain frequency chirp (referred to herein as BOTTS) collects significantly more thermorheological than the prior art sinusoidal stress / strain frequencies of FIGS.3A-3E.

[0059] Temperature stepping and soaking

[0060] To perform time-temperature superposition, isothermal frequency response data is collected at several temperatures. Common practice is to choose a constant temperature step between experiments that has provided good overlap for similar materials in the past. To increase or optimize the overall master curve collection rate, temperatures may be chosen considering(1) the bandwidth of the measurement (⍵2 / ⍵1above), (2) the temperature-frequency equivalence encoded in the aT shift factor plot (FIG. 5, inset), and (3) a redundancy buffer r to account for uncertainty in the shift factors and response data. Starting from an arbitrary reference temperature TR in the range of interest, the neighboring temperatures TR+1 and TR-1 should be aT(TR+1) / aT(TR) = (⍵2 / ⍵1) / r and aT(TR-1) / aT(TR) = r / (⍵2 / ⍵1) and so on until the temperature range of interest is spanned. Each of these numbered considerations requires additional information to select.

[0061] For bandwidth of the measurement (⍵2 / ⍵1above), the choices of ⍵2, ⍵1, and therefore⍵2 / ⍵1, can be limited by physical aspects of the DMA instrumentation. ⍵2is limited in theory by the Nyquist frequency determined by the sampling rate of the position and force transducers.Practically, ⍵2is also limited by thesensitivity of the instrument to high frequency force responsesand the ability of the instrument to effect high frequency displacements. These may be characterized by a high cutoff frequency that can be measured or specified by the manufacturer,⍵H. ⍵1 is limited by a more nebulous concept of drift, which appears as 1 / fɑ(“pink”) noise in thefrequency domain, and is a sum of vibration isolation, uncontrolled / uncompensated temperature shifts, radio frequency interference, and a variety of unknown contributions. This can be measured directly by the DMA as a cutoff frequency ⍵L. For instance, the assumption of isothermal data is ensured true in common practice by holding an instrument at a constant temperature setpoint for an arbitrary extended period before making a mechanical measurement. The “soak” period has been typically chosen based on values that have been successful for the instrument in the past. In this method, thermal drifts manifest in the detrended data as additional low frequency noise in theAttorney Docket No.5405.534.WO stress channel, increasing ⍵L. Inversely, the characteristic instrument thermal equilibration rate could be estimated and ⍵1chosen such that total soak time is negligible compared to the time spent collecting isothermal data. ⍵2 / ⍵1can be limited by ⍵H / ⍵Lbut there may be additional limits in the digital measurement and storage of the data. For example, a software may only be able to store 32767 evenly spaced stress / strain samples per experiment, leading to a Nyquist-limited bandwidth of 16383 or log10(16383) = 4.2 decades of frequency.

[0062] For the temperature-frequency equivalence encoded in the aTshift factor plot (FIG. 5, inset), aT is notably an output of time-temperature superposition, and so must be estimated to be of use as a method of selecting measurement temperatures optimally. Preliminary aT data could be estimated theoretically or with existing data from materials similar to the specimen under test, however the chirp method utilized for the other parts of this inventive concept could also estimate aT with short, narrow-bandwidth chirps during a necessary preliminary temperature ramp phase that is usually measured at a single frequency. Compared to a MultiWave temperature ramp, which has been commercially implemented before, the BOTTS ramp can easily be tuned to provide sufficient data for superposition and an estimate of aT.

[0063] For the redundancy buffer r to account for uncertainty in the shift factors and responsedata, r can be arbitrarily close to ⍵2 / ⍵1, providing a high level of redundancy ofinformation inadjacent isothermal experiments which leads to a greater certainty in theestimation of aT. However,this certainty comes at the cost of increasing the number of neededisothermal steps. On the otherhand, r has a natural lower limit of 1, such that the adjacent datasets do not overlap. In the subsequent section, it is argued this is not a hard limit when considering additional physical constraints. Between these limits, the choice of r trades off experiment time / resources for increased data and certainty of master curve estimates. Therefore, for any particular instrument configuration, some embodiments can increase a speed at which an experiment is conducted given a confidence requirement, or an increased or maximum possible confidence given an experiment time constraint.

[0064] Uncertainty estimation

[0065] The uncertainty in viscoelastic response at each frequency may be estimated according to an additive Gaussian white noise assumption. This may be conveniently estimated by first measuring the standard deviation of the padding regions of the stress and strain chirps or the mean or median value of the high-frequency region of the stress and strain power spectra and propagating that errorAttorney Docket No.5405.534.WO linearly through the calculation of complex modulus. A superior method for estimating the noise level is to measure the noise directly. There are multiple approaches viable to apply in this case.

[0066] One is to run the proposed viscoelastic measurement protocol from beginning to end with all the same settings except not driving the input chirp (or driving at a negligible amplitude). This provides direct background / noise data that can be transformed into weights for chi-squared optimization in the frequency domain, at the cost of having to essentially perform the experiment twice. However, many experiments will have similar expected noise profiles so under that assumption the measurement time can be amortized across all comparable experiments.

[0067] Another is to measure multiple chirps consecutively during isothermal steps of a viscoelastic measurement protocol. The chirps and responses can be averaged into a “mean chirp” which can be subtracted from the original data to produce a direct estimate of the noise level. This offers the opportunity to trade off bandwidth for total time by manipulating chirp parameters, as well as directly observe “special” noise contributions such as drift.

[0068] Superposing frequency responses

[0069] In common practice, the frequency response of a material at several temperatures may shifted “by eye” or by an algorithm embedded in commercial analysis software.

[0070] This practice may be problematic for reproducibility in principle, but the potential for large errors had historically been reduced due to the small number of points with approximately equal importance typically obtained. The dense, linearly-sampled, non-constant-variance data that is output in the present method obscures the visual quality of overlaps when shifting by eye and demands a full accounting of uncertainties while shifting by algorithm.

[0071] Nonlinear optimization of the reduced chi-squared goodness-of-fit statistic can perform this accounting while finding shift factors, given some model to fit to the shifted data. There are many potential models, including polynomials or splines, and even more complicated techniques like Gaussian process regression or artificial neural networks, but the disclosed approach uses a Prony series as the underlying model. A Prony series can fit any LVE material response, and LVE behavior is an assumption that has already been made and verified in the data collection stage. Prony fitting imposes a constraint that the superposition result is Kramers-Kronig consistent, i.e., it does not violate temporal causality. Furthermore, with this Prony model method, the data can be interpolated from each temperature to find an overall model that is consistent with the data, so it isAttorney Docket No.5405.534.WO not a hard constraint that the shifted frequency ranges overlap after shifting (r < 1 is permissible, another acceleration).

[0072] Prony series parameters (as opposed the TTS shift factors) can also be determined from any chi-squared optimization. Minimizing the reduced chi-squared statistic from a Prony series by adjusting shift-factors is sufficient to achieve a high-quality time-temperature superposition, because there are many Prony series expressions that adequately describe any given viscoelastic data, and the existence of multiple local optima is not excluded. Nevertheless, experience shows these are not problematic in practice. As an example, FIG. 5 shows a result of the optimization performed on the data from FIGS. 4A-4E. Complex modulus data from FIG. 4D is superposed through the Prony series reduced chi-squared minimization. The Prony series fit is displayed as black lines. The inset shows output data of the superposition, the vertical shift factors aT.

[0073] The Prony series reduced chi-squared minimization also works to perform TTS of common DFS data, if data uncertainty estimates are available (a step that is usually omitted).

[0074] FIG. 5 is a graph of the complex modulus data from FIGS. 4A-4E, represented as superposed through a Prony series reduced chi-squared minimization. The Prony series fit is displayed as a line, with the inset graph illustrating the output data of the superposition, the horizontal shift factors aT.

[0075] Optimizing the Prony and shift parameters

[0076] Without limitation of the above invention, several methods are described below for optimization of the Prony / shift parameterized chi-squared system. In all cases, regularized and constrained optimization provides robust, fast calculation of physically permissible parameters.

[0077] A nested iteration approach is possible where, given some candidate shift factors, an inner chi-squared optimization is performed on the Prony coefficients, such as the “Fast NLLS” nonnegative linear optimization algorithm or a regularized nonnegative optimization such as “sign- controlled Tikhonov regularization”. Then, the gradient of the chi-squared statistic is calculated with respect to the shift factors, and that information is used to iterate the shift factors toward the optimal value. Horizontal and vertical shifts are alternately iterated. This strategy is quite sensitive to the initial guess of shift factors due to some degenerate solutions of horizontal and vertical shifts and so is improved with restarts and regularization of the shift factors such as adding a weighted Kullback–Leibler divergence term for the shifts to the chi-squared loss or imposing a constraint toAttorney Docket No.5405.534.WO the permitted shifts (e.g. 1<r<10). The regularization weights can be optimized using cross validation or Morozov discrepancy.

[0078] A joint optimization approach is also possible by considering the simultaneous gradient of the Prony and shift parameters. However, the calculation is prohibitively slow due to interaction of the number of Prony coefficients typically required and the numerical gradient calculation. The joint optimization is enabled by selecting an automatically-differentiable representation for the regularized, constrained optimizations above. Examples include JAX, Torch, and Tensorflow.

[0079] A Bayesian Markov chain Monte Carlo approach to the optimization has proven extremely robust, although at the cost of further complication of the implementation in terms of software library and algorithm choices relative to the joint optimization scheme. In this mode, the regularizations and constraints of the parameters, including hyperparameters such as regularization weights or Morozov discrepancy factors, are made explicit by the selection of prior distributions for each parameter as well as the chi-squared distribution of the residuals. If the computational cost of the sampling scheme is too much for a particular use case, it is possible to use this approach to set the hyperparameters once for a representative experiment and then use the hyperparameters in joint optimization of an array of similar experiments, amortizing the computational cost across the entire experimental design while obtaining near-identical outputs.

[0080] Superposition of Broadband and Narrowband Modulus Data

[0081] The graphical superposition on a logarithmic plot of modulus data from different temperatures is essentially an assertion of the statement dependent complex modulus at temperature T and aT andfactors, respectively. If the statement holds, the material is considered TRS. E* can be generally described by a sum of Maxwell elements, sometimes called a Prony series,regime. Importantly, combining the shiftAttorney Docket No.5405.534.WO factors with this Prony series representation shows a factor of bTmore apparentstrain and a factor of aThigher apparent frequency at T compared to the reference temperature when subjected to the same actual sinusoidal strain. TRS materials can be thought of as having a one-to-one correspondence between a molecular-scale relaxation and a Maxwell element.

[0084] In the case of the DFS technique, the application of the above is straightforward. A constant temperature is held, a sinusoidal strain is driven at each frequency ε(ω), the initial unsteady state is discarded, and the lagged sinusoidal stress is recorded, containing the sum of the influence of each Maxwell element at that frequency. The complex modulus is calculated by measuring the phase lag, δ(ω), and stress magnitude, σ(ω), to further calculate |E*| =σ / ε and converting to its real and components,

[0085] ^^^^∗(^^^^)=|^^^^∗|^^^^^^^^^^^^(^^^^)+^^^^|^^^^∗|^^^^^^^^^^^^(^^^^)=^^^^′(^^^^)+^^^^^^^^′′(^^^^)

[0086] Where E′(ω) and E′′(ω) are the storage and loss moduli, respectively. At the next temperature, this is all repeated and, for TRS materials, all the elements experience shift factors at each temperature that are frequency independent. This renders the curves for E′(ω) and E′′(ω) superposable, and the superposition of these curves via the shift factor, aT(T), yields the master curve for the polymer at the chosen reference temperature.

[0087] In the case of broadband excitation as in BOTTS, there is an arbitrary strain function that obscures the connection of the stress function to the Prony series representation. The LVE properties above are assumed, so the property of frequency orthogonality is relied upon. Therefore, taking the Fourier transform of the stress and strain, a representation of all the component sines and cosines that compose the broadband impulse and response is generated. Then, as the waves form an orthogonal basis, each of the components is considered individually, applying the same logic as in DFS when interpreting the data and when superposing two curves. The difference here is that the response is digitally isolated at each frequency instead of through the choice of driving function.

[0088] To demonstrate the practical superposition of broadband frequency response data, the storage modulus E′ of PT resin obtained by Fourier transform of a windowed chirp and its responseAttorney Docket No.5405.534.WO at both 55 °C and 60 °C are displayed along with a shifted display of the 60 °C data shown in FIG. 7. The shifted modulus data overlap well over the entire two decades of frequency that the series have in common. This overlap is empirical evidence suggesting that BOTTS will work as a basis to form a master curve.

[0089] Master curves from BOTTS and DFS-TTS

[0090] The result of performing BOTTS on PT resin data from FIG. 5 and FIGS. 6A-6B is a master curve spanning 12 orders of magnitude in frequency with a single, relatively sharp, glass transition. In order to check that the master curves are Kramers–Kronig consistent, the BOTTS master curve is overlayed with a Prony series fit shown in FIG. 8, observing good agreement between the fit and the data, supporting the physical validity of BOTTS. The large number of data points obtained from transforming chirps means the uncertainty of the model fit is substantially smaller than the spread of the data, originating from lower SNR at high frequencies, and highly elastic (very low E′′) behavior at high temperatures.

[0091] To compare master curves and shift factors produced from BOTTS and DFS-TTS, PI viscoelastic response are collected from both techniques over the same range of frequencies and temperatures (see FIG.5) and subjected them to an automatic shift algorithm. As a baseline, shifts and a master curve are also generated from the same DFS data using the closed, commercial TRIOS TTS feature. The superposed storage moduli and shift factors from each are visualized together in FIGS.9A-9B.

[0092] BOTTS and DFS-TTS seem to have a similar range of validity, as the high and low frequency tails of the data in the glassy and rubbery regimes have increasing scatter between techniques with distance from the reference temperature Tref= 55 °C. (As with any superposition, the shift factors are unity at the reference temperature.) To shift the tail regions is an intrinsically ill-posed problem, as the storage moduli plateau and the loss moduli approach the noise threshold, limiting the detectable differences between curves. Therefore, for PT resin with the experimental parameters, shift factors in FIG.9A-9B may be relied upon from at least about 40 °C to 80 °C, or equivalently, moduli from 4 × 10−4to 8 × 104Hz at Tref.

[0093] PT resin is selected as a platform to develop BOTTS as it has a very narrow, reproducible, and stable glass transition due to its ideal network structure. As a demonstration of the broad applicability of BOTTS, the technique is applied to DI epoxy resin without first obtaining DFS- TTS data. The DI master curve, displayed in FIG.10, shows a broader glass transition indicativeAttorney Docket No.5405.534.WO of typical heterogeneous chemical structures in epoxy thermosets.

[0094] Beyond producing a reasonable master curve, it is noted that the data, from 100 °C to 180 °C in 5 °C increments, were collected in just under 100 minutes, including soak time. A comparable DFS-TTS experiment would take over 500 minutes. The speedup of BOTTS provides a unique additional advantage beyond the obvious time savings: the resin spends much less time at high temperatures, avoiding thermal side reactions and property drift common in amine-epoxy and other engineering thermosets.

[0095] Accordingly, BOTTS and the broadband mechanical impulses as described herein may provide a DMA technique that utilizes broadband chirps to take advantage of the data acquisition capabilities of DMA hardware to potentially accelerate the collection of frequency data for time– temperature superposition by, for example, 500% or more. Given such an increase in data collection rate, broadband mechanical impulses could enable the curation of vast quantities of high quality thermorheological data and derived master curves, shift factors, WLF parameters, and relaxation spectra. A higher instrumental bandwidth would increase the speed up to as much as 10×, and further gains could be realized in the choice of temperatures and soak times before measurement. This would decrease the cost of performing and curating data including composition, processing, and aging parameters and their uncertainties from large designs of experiments for a broad range of advanced materials. Broad uptake of this technique would lead to increased availability of reliable high-bandwidth time / frequency / temperature property data for polymers and their composites and could dramatically accelerate and increase the accuracy of design loops for new material applications. A data analysis pipeline is developed to incorporate the unique complex modulus data output from BOTTS. It should be understood by one of skill in the art that BOTTS strategy (including temperature steps, chirp duration, and other parameters) may be modified to reduce or minimize shift factor uncertainty given instrumental constraints and time allotment, or inversely to minimize experiment time while meeting a prescribed uncertainty of the shift factors, with direct comparison to similarly optimized MW and DFS methodologies. In some embodiments, partial or fully autonomous experimentation may be implemented.

[0096] The present inventive concepts are described herein with reference to the accompanying drawings and examples, in which embodiments are shown. Additional embodiments may take on many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, andAttorney Docket No.5405.534.WO will fully convey the scope of the inventive concepts to those skilled in the art.

[0097] Like numbers refer to like elements throughout. In the figures, the thickness of certain lines, layers, components, elements or features may be exaggerated for clarity.

[0098] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting thereof. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and / or “comprising,” when used in this specification, specify the presence of stated features, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof. As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items. As used herein, phrases such as “between X and Y” and “between about X and Y” should be interpreted to include X and Y. As used herein, phrases such as “between about X and Y” mean “between about X and about Y.” As used herein, phrases such as “from about X to Y” mean “from about X to about Y.” The term “about” should be understood to include variations of up to 20%.

[0099] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the specification and relevant art and should not be interpreted in an idealized or overly formal sense unless expressly so defined herein. Well-known functions or constructions may not be described in detail for brevity and / or clarity.

[0100] It will be understood that when an element is referred to as being “on,” “attached” to, “connected” to, “coupled” with, “contacting,” etc., another element, it may be directly on, attached to, connected to, coupled with or contacting the other element or intervening elements may also be present. In contrast, when an element is referred to as being, for example, “directly on,” “directly attached” to, “directly connected” to, “directly coupled” with or “directly contacting” another element, there are no intervening elements present. It will also be appreciated by those of skill in the art that references to a structure or feature that is disposed “adjacent” another feature may have portions that overlap or underlie the adjacent feature.

[0101] Spatially relative terms, such as “under,” “below,” “lower,” “over,” “upper” and the like,Attorney Docket No.5405.534.WO may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is inverted, elements described as “under” or “beneath” other elements or features would then be oriented “over” the other elements or features. Thus, the exemplary term “under” may encompass both an orientation of “over” and “under.” The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. Similarly, the terms “upwardly,” “downwardly,” “vertical,” “horizontal” and the like are used herein for the purpose of explanation only unless specifically indicated otherwise.

[0102] It will be understood that, although the terms “first,” “second,” etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. Thus, a “first” element discussed below could also be termed a “second” element without departing from the teachings of the present disclosure. The sequence of operations (or steps) is not limited to the order presented in the claims or figures unless specifically indicated otherwise.

[0103] Moreover, the present disclosure also contemplates that in some embodiments, any feature or combination of features set forth herein can be excluded or omitted. To illustrate, if the specification states that a complex comprises components A, B and C, it is specifically intended that any of A, B or C, or a combination thereof, can be omitted and disclaimed singularly or in any combination.

[0104] Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. For example, if a concentration range is stated as 1% to 50%, it is intended that values such as 2% to 40%, 10% to 30%, or 1% to 3%, etc., are expressly enumerated in this specification. These are only examples of what is specifically intended, and all possible combinations of numerical values between and including the lowest value and the highest value enumerated are to be considered to be expressly stated in this disclosure.

[0105] Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.

[0106] The foregoing is illustrative of the present inventive concept and is not to be construed as limiting thereof. Although a few example embodiments have been described, those skilled in theAttorney Docket No.5405.534.WO art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings of this inventive concept. Accordingly, all such modifications are intended to be included within the scope of this inventive concept as defined in the claims. Therefore, it is to be understood that the foregoing is illustrative of the present inventive concept and is not to be construed as limited to the specific embodiments disclosed, and that modifications to the disclosed embodiments, as well as other embodiments, are intended to be included within the scope of the appended claims.

Claims

Attorney Docket No.5405.534.WO WHAT IS CLAIMED IS:

1. A method of determining mechanical properties of a sample using thermorheological data, the method comprising: providing a sample in a dynamic mechanical analysis device; selecting a temperature for the sample; performing a high-bandwidth time / frequency / temperature sweep test comprising applying a broadband mechanical impulse over a frequency range at the temperature, and collecting thermorheological data during application of the broadband mechanical impulse; determining mechanical properties of the sample using the thermorheological data, and, optionally, generating a viscoelastic master curve and / or shift factors.

2. The method of claim 1, wherein the temperature is one of a plurality of temperatures and selecting a temperature comprises selecting the plurality of temperatures for the sample, and wherein performing a high-bandwidth time / frequency / temperature sweep test comprises: a) changing a temperature of the sample to another temperature in the plurality of temperatures; b) applying the broadband mechanical impulse over the frequency range after changing the temperature of the sample and collecting thermorheological data; and c) repeating steps a) and b) at the plurality of temperatures to collect additional thermorheological data; and and determining mechanical properties of the sample is based on the additional thermorheological data.

3. The method of any preceding claim, further comprising determining a Prony series based on the thermorheological data.

4. The method of any claims 2-3, wherein selecting the plurality of temperatures for the sample comprises: estimating an uncertainty in thermorheological data for the sample at an initial plurality of temperatures; andAttorney Docket No.5405.534.WO selecting the plurality of temperatures based on the uncertainty.

5. The method of claim 4, wherein selecting the plurality of temperatures for the sample comprises: selecting an optimal and / or constrained plurality of temperatures utilizing the uncertainty.

6. The method of claims 4-5, wherein estimating an uncertainty in thermorheological data comprises simulating an acquisition of thermorheological data at the initial plurality of temperatures.

7. The method of any preceding claim, further comprising using the viscoelastic master curve and / or shift factors to predict a storage modulus (E'), a loss modulus (E''), a loss factor (tan δ), or combinations thereof.

8. The method of any preceding claim, further comprising using the viscoelastic master curve and / or shift factors to predict a glass transition temperature (Tg) of the sample.

9. The method of any preceding claim, further comprising using the viscoelastic master curve and / or shift factors to predict a storage modulus (E'), a loss modulus (E''), a loss factor (tan δ), or combinations thereof as a function of temperature.

10. The method of any preceding claim, further comprising: providing a physical model of an object formed at least in part by material in the sample; and simulating a prediction of a mechanical performance of the object.

11. The method of claim 10, wherein simulating the prediction of the mechanical performance of the object is based on the viscoelastic master curve, the Prony series, or combinations thereof.Attorney Docket No.5405.534.WO 12. The method of any preceding claim, wherein the broadband mechanical impulse comprises an inverse Gaussian windowed exponential chirp.

13. A mechanical analyzer (DMA) system for determining mechanical properties of a sample using thermorheological data at different temperatures, the system comprising: a dynamic mechanical analyzer device configured to receive a sample; a controller configured to select a temperature for the sample, and to control the DMA device to perform a high-bandwidth time / frequency / temperature sweep test comprising: applying a broadband mechanical impulse over a frequency range at the temperature, and collecting thermorheological data during application of the broadband mechanical impulse; the controller configured to determine mechanical properties of the sample using the thermorheological data, and, optionally, to generate a viscoelastic master curve.

14. The system of claim 12, wherein the temperature is one of a plurality of temperatures and selecting a temperature comprises selecting the plurality of temperatures for the sample, and wherein the controller is configured to perform the high-bandwidth time / frequency / temperature sweep test by: a) changing a temperature of the sample to another temperature in the plurality of temperatures; b) applying the broadband mechanical impulse over the frequency range after changing the temperature of the sample and collecting thermorheological data; and c) repeating steps a) and b) at the plurality of temperatures to collect additional thermorheological data.

15. The system of any of claims 13-14, wherein the controller is configured to determine a Prony series based on the thermorheological data.

16. The system of any of claims 13-15, wherein the controller is configured to select the plurality of temperatures for the sample by:Attorney Docket No.5405.534.WO estimating an uncertainty in thermorheological data for the sample at an initial plurality of temperatures; and selecting the plurality of temperatures based on the uncertainty.

17. The system of claim 16, wherein estimating an uncertainty in thermorheological data comprises simulating an acquisition of thermorheological data at the initial plurality of temperatures.

18. The system of any of claims 13-17, wherein the controller is configured to use the viscoelastic master curve to predict a storage modulus (E'), a loss modulus (E''), a loss factor (tan δ), or combinations thereof.

19. The system of any of claims 13-18, wherein the controller is configured the viscoelastic master curve to predict a glass transition temperature (Tg) of the sample.

20. The system of any of claims 13-19, wherein the controller is configured to use the viscoelastic master curve to predict a storage modulus (E'), a loss modulus (E''), a loss factor (tan δ), or combinations thereof as a function of temperature.

21. The system of any of claims 13-20, wherein the controller is configured to provide a physical model of an object formed at least in part by material in the sample; and to simulate a prediction of a mechanical performance of the object.

22. The system of claim 21, wherein simulating the prediction of the mechanical performance of the object is based on the viscoelastic master curve, the Prony series, or combinations thereof.

23. The system of any of claims 13-22, wherein the broadband mechanical impulse comprises an inverse Gaussian windowed exponential chirp.Attorney Docket No.5405.534.WO 24. A computer program product for determining mechanical properties of a sample using thermorheological data in a dynamic mechanical analysis device, the computer program product comprising a non-transient computer readable medium having computer readable program code embodied therein, the computer readable program code comprising: computer readable program code configured to select a temperature for the sample; computer readable program code configured to perform a high-bandwidth time / frequency / temperature sweep test in a dynamic mechanical analysis device, the high- bandwidth time / frequency / temperature sweep test comprising: applying a broadband mechanical impulse over a frequency range at the temperature, and collecting thermorheological data during application of the broadband mechanical impulse; and computer readable program code configured to determine mechanical properties of the sample using the thermorheological data, and, optionally, generating a viscoelastic master curve.

Images