Sensing Water Absorption in Hygrothermally Aged Epoxies with Terahertz Time-Domain Spectroscopy

In the field of non-destructive testing, terahertz sensing has been used to analyze a wide range of materials where the most successful applications have involved materials that are semi-transparent to terahertz radiation. In this work, we demonstrate the sensitivity of terahertz time-domain spectroscopy to quantify water absorption in hygrothermally aged simple and commercial epoxy systems supported by conventional gravimetric analysis.


■ INTRODUCTION
Epoxies represent an interesting class of materials containing reactive monomers that can cross-link either themselves or with hardners such as amines as part of the curing process. Epoxy materials have found applications as encapsulations in the electronics industry, adhesives in structural bonding, anticorrosive protective coatings on metal structures, and in the creation of composites. 1 The terahertz range of the electromagnetic spectrum (loosely between 0.1 and 4 THz) can provide unique insights when investigating polymers, which are semi-transparent at these frequencies. Compared to other analytical methods such as neutron and X-ray diffraction, near-infrared (NIR), 2 and microwave spectroscopy, terahertz radiation offers an interesting opportunity for material analysis within the constraints of spatial resolution (at several hundred micrometers) and penetration depth (up to several millimeters). Terahertz radiation is also readily accessible via table-top instruments realizing terahertz time-domain spectroscopy (THz-TDS). In general, THz-TDS is an efficient technique for the coherent generation and detection of broadband terahertz radiation: a femtosecond pulsed near-infrared laser is focused onto a terahertz emitter (semiconductor photoconductive antenna or nonlinear crystal), where each optical pulse results in the excitation of sub-picosecond pulses with a bandwidth spanning from a few hundred GHz to a few THz. The emitted terahertz pulses in turn interact with the sample of interest, and the resulting terahertz electric fields are measured through a coherent detection scheme either by means of photoconduction or electro-optical detection. The advantage of this approach is that the amplitude and phase of a terahertz pulse can be resolved with an excellent signal-to-noise ratio, which can be used to extract the sample's complex refractive index, an intrinsic property of the material that includes both the refractive index and absorption coefficient at the terahertz spectral range.
The advent of THz-TDS has opened up many exciting applications. 3−9 Examples of where THz-TDS has been used in polymer science and testing include detecting morphology changes and monitoring glass transition temperature, 10 monitoring the polymer compounding process, 11 measuring moisture content and solvent diffusion dynamics, and evaluating adhesive bonds between non-absorbing materials. 12 For epoxies, in particular, THz-TDS has been used as part of standard characterization 13 and monitoring the degree of cure. 14,15 However, there is no report on investigating the water uptake of epoxies with THz-TDS. This is important because water exposure can cause a loss in physical properties such as swelling, hydrolysis, lowering of the glass transition temperature, cracking, and crazing. The extent of water uptake, however, depends on the chemistry of the network being formed, 16,17 the cure temperature, 18,19 and the presence of fillers. 20 In this investigation, we demonstrate the sensitivity of THz-TDS to quantify water absorption in hygrothermally aged epoxy systems, for both simple and commercial systems, supported by conventional gravimetric analysis.

■ MATERIALS AND METHODS
Materials and Ageing. A total of five epoxy systems were used for this study: two commercial systems with the names 8552 and RMT6, and three simple systems comprising the same epoxy (Epikote 828) and amine (Jeffamine T403) at three different stoichiometries (S060, S100, S180) where the number after the "S" refers to the proportion of reactive hydrogen sites as a percentage of the available epoxy ring sites. The process of making simple systems were: (1) Weighing out liquid epoxy monomer and amine (combined mass of 150 g using a balance with precision ±0.01 g). (2) Mixing: 120 s at 1000 rpm.
(3) Degassing under vacuum for 2−3 h. (4) Mold was filled and cured at room temperature for 3 days followed by a postcure at 70°C for 16 h. This process was slightly different for commercial systems. In particular, premixed resin and curative were weighted and mold was subsequently filled and cured at 180°C for 120 min (for both 8552 and RTM6). Each epoxy system was first manufactured into plaques and disc-shaped samples were cut out from the plaques by a water-jet cutting process (Mach 3B series, Hinckley, U.K.), measuring 13 mm in diameter with a nominal thickness of 2 mm. For each of the five epoxy specimens investigated, there were three repeats. To ensure unique identification of the samples, engravings were made onto the sample edges prior to ageing as this was found to be a robust method to encode sample IDs for express identification thereafter. Prior to any moisture exposure, all samples underwent a drying procedure, where the samples were placed in an oven at 70°C for 200 h, and on removal, they were packaged into air-tight containers with desiccant.
Terahertz Time-Domain Spectroscopy. The hygrothermal conditions provide means to the accelerated ageing. In particular, this was performed by immersing the samples, held in a plastic tube with perforated holes, in distilled water in a beaker at a temperature of 95°C, as shown in Figure 1a. At each time increment, the samples were (1) removed from the conditioning chamber and blotted dry using a lint-free towel; (2) measured in terms of mass using an analytical balance at ±0.1 mg (Fisher Scientific, Illkirch-Graffenstaden, France), thickness using a micrometer ±1 μm (Sealey Digital External Micrometer 0−25 mm; Rapid Electronics Limited, Colchester, U.K.) and THz-TDS; (3) returned to the conditioning chamber where the time between measurement and immersion was approximately 12 min. The duration of the ageing experiment was 80 h in total. The measurement of the samples at time, t = 0, corresponds to the dry epoxy discs prior to ageing. In the initial period, to track rapid changes of ageing, measurements were performed at 1 h intervals for the first 4 h of ageing followed by a 2 and a 3 h sampling intervals for the first day. Following an interval of approximately 10 h between the first and the second day, subsequent measurements on the second day were mostly performed at 5 h interval and followed by increasingly large time intervals until the end of the experiment. It is worth mentioning that the water level in the beaker, at any time, was kept at near constant level to ensure that the samples were kept fully submerged throughout the ageing time. This was achieved by refilling the beaker at set given time intervals during the ageing process.
We performed transmission terahertz spectroscopy using a commercial THz-TDS setup (Terapulse 4000, TeraView Ltd., Cambridge, U.K.) shown in Figure 1c. For the measurements, we selected the high-resolution scanning mode with 20 waveform averages, which took approximately 40 s per measurement. Given the sharp and distinct absorption features due to the rotational transitions of water molecules in the gas phase, all terahertz measurements were performed under a continuous purge with dry nitrogen in the sample chamber of the spectrometer. As a standard routine to all our measurements, a reference measurement was always acquired without the sample being present and taken immediately before the Analytical Chemistry pubs.acs.org/ac Article sample measurement to remove potential baseline drift effects. The acquired waveform of the terahertz electric field for both the sample and the reference were then converted to the frequency domain by fast Fourier transformation. By normalizing the sample spectra against the reference spectra, a complex-valued transmission function that contains both the amplitude and the phase of the transmission spectra that can be determined. The frequency-dependent refractive index and absorption coefficient of the samples can then be calculated from the measured phase and amplitude using eqs 1 and 2 where v is the frequency, t(v) is the complex ratio between the sample and reference measurement, φ(v) is the phase difference between the sample and reference, d is the sample thickness, and c is the speed of light in vacuum. 21 It should be noted that refractive index is extracted from the phase information only, first by unwrapping, a process of adding or subtracting multiples of 2π to the phase, followed by corrections where the unreliable low-frequency phase values are discarded and replaced with a low-frequency extrapolation down to DC frequencies phases based on the reliable phase measurements at higher frequencies. A detailed mathematical description of the steps can be found elsewhere. 22,23 These relations in turn can be converted to the complex relative permittivity ε(v) = ε′(v) − jε″(v), commonly used in dielectric measurements, with real and imaginary parts given by eqs 3 and 4, respectively ■ RESULTS AND DISCUSSION Figure 1b shows that the samples all underwent distinct irreversible color changes (yellowing) during the ageing process, with S180 being the most affected and S060 being the least. Yellowing in bulk is a well-known phenomenon in aliphatic amine cured epoxy systems and relates to various oxidation processes in which N−H 2 groups participate. 24 The observed color changes are most significant for the S180 specimens, which are at their greatest concentration of amines. The extracted frequency-dependent refractive indices and absorption coefficients of the samples at different time increments are shown in Figure 2. It should be noted that spectral oscillations observed at frequencies higher than 1.5 THz are due to noise, approaching the system's dynamic range. 21 As expected, the amorphous morphology of the epoxy materials results in featureless, monotonically increasing absorption spectra, with the refractive index spectra decreasing with increasing frequency. 13 Considering that the amine and epoxies are both polar molecules, it was expected that the cross-link density would be highest when epoxy and amine concentration was equal (S100). This hypothesis appears to be valid from Figure 3, where S100 does exhibit the highest mass. It is, however, not evident in the refractive index, a measure of a material's optical density, where specimen S060, with the lowest amine concentration, actually exhibited the highest refractive index. For the spectrometer used and the thickness  Diffusion of water into cured epoxies is generally thought to obey Fick's second law in one dimension, 25 which is described as where C is the concentration, t is the time, x is the position, and D is the diffusion coefficient. The diffusion coefficient in turn can be determined from the initial gradient of the sorption curve obtained by plotting the change in mass against the square root of time divided by the thickness, 26 as shown in Table 1. For comparison against gravimetric measurements, Figure 3 shows the refractive index and absorption coefficient at 1 THz as a function of water ageing time. Even though 1 THz is used to represent the spectra, in principle, other frequencies across the usable bandwidth could also be used, which either would shift the absorption coefficient curves vertically up or the refractive index curves down. The similarity of the curves, nevertheless, would remain approximately the same. Pearson correlation coefficients between the respective curves are shown in Table 2 and generally take values greater than 0.95, thus suggesting a strong linear correlation between the measured terahertz optical constants and the gravimetric measurement.
The dielectric properties of materials with different water content can be described using the methods of effective medium theory (EMTs). Such treatments make it possible to calculate macroscopic permittivity at terahertz frequencies as a function of water content. Here, we describe the mixture of water and epoxy resin using the Landau, Lifshitz, Looyenga (LLL) model, 27 which assumes a virtual sphere that includes particles of a given volumetric fraction and of arbitrary shapes. By successively adding an infinitesimal amount of particles, the effective permittivity is increased slightly and can be described by a Taylor approximation. As there is no particle shape dependency, the model can be applied to irregularly shaped particle mixtures and has been used successfully to quantify water content inside polymers and plant leaves. 28,29 It should be noted that while the LLL model was initially proposed for two-component mixtures, the model can be extended to three   Analytical Chemistry pubs.acs.org/ac Article components to account for additional contributions such as free water in a higher water absorbing polymers or the air pockets inside a plant leaf. The complex permittivity of aged epoxy εk(v) can be described as where ε̃B W (v) is the complex permittivity of bound water and ε̃D(v) is the complex permittivity of the dry epoxy. Both permittivities are weighted by their respective volumetric fractions f BW , k and 1 − f BW , k for a two-component mixture, where the sum of the volumetric fractions is 1. The volumetric fraction f BW ,k is determined by the following relation where m k is the mass of aged epoxy at time k, m 0 is the mass of dry epoxy before conditioning, ρ is the density of water taken as 1 g·cm −3 , and A is the sample area. Bound water here refers to the polar water molecules that bind to the polar functional groups of the epoxy macromolecules by means of intermolecular hydrogen bonds. The vibrations of the bound water molecules, as shown previously in polymers, such as polyamide and wood−plastic composites, 29 differ to that of the free water, which is characterized by double Debye relaxation processes. 30 The LLL model in eq 6 additionally requires an estimation of the bound water permittivity, which is approximated to be the average of the permittivities at time increments between 2 and 5 h. Even though the number of time increments can be extended, it would not result in significant improvement to fitting to the measurement. The method of determining the bound water permittivity by averaging out initial permittivity values is a similar approach to what was taken previously, where the average between the 2nd and the 10th day of measurements was used. 29 Noticeably, the number of data points needed here is significantly less due to the accelerated ageing applied as well as the different specimens studied. Contributions from the respective components are then weighed by the volumetric fraction determined from the gravimetric measurements to estimate the complex permittivity of aged epoxy.
Using eqs 1−4, the raw data were processed and Figure 4 shows the plots of the refractive index and absorption coefficients at 1 THz from the measurements as well as the results from the LLL model as a function of water uptake. The data are presented across the different epoxy systems for all samples, and generally the model is able to achieve a good fit to the data. Notable exceptions include samples S060 and S180, where the LLL model fails altogether, after 2 and 4% of water uptake, respectively. This means that the measured complex permittivity can no longer be considered a straightforward ideal mixture of dry and bound water epoxy, but that the dielectric responses of the constituent phases have changed, which is likely to be due to chemical changes in the epoxy material. The exact cause, however, is unclear given the complex nature of the chemical changes that take place during hygrothermal conditions as well as the different epoxy formulations used. At the same time, the observed changes are somewhat unsurprising because the stoichiometries used in these specimens were entirely artificial and extreme. In the case of S180, physical changes such as sample disintegrations and the associated weight loss were noted. In contrast, for S060, samples became noticeably softer. These physical changes could be due to various irreversible processes that occurred during the hygrothermal ageing process, such as hydrolysis, Analytical Chemistry pubs.acs.org/ac Article thermo-oxidation, and leaching, 24 and is the subject of future investigations. For the specimens where a good agreement between measurement and modeling were observed, such as the commercially relevant RTM6 and 8552, the results from our terahertz measurements suggest that there is a possibility to estimate water content inside an aged epoxy specimen without conventional gravimetric measurement. Instead, the water content can be estimated by performing a single terahertz point measurement on the sample and carrying out the aforementioned analysis thereafter using the permittivity and water uptake plots, such as in Figure 4, for calibrations. Considering the measurement error bars, the results also suggest that absorption coefficient is perhaps a more robust measure than refractive index, where measuring the sample thickness accurately becomes notably more difficult when the samples soften inherently as part of the ageing process. Compared to conventional gravimetric measurement and dielectric spectroscopy, the proposed measurement does not require physical contact to the sample and operates at a spatial resolution of several hundreds of micrometers, thus enabling water spatial distribution to be imaged.

■ CONCLUSIONS
In this study, we have demonstrated the sensitivity of THz-TDS to resolve water absorption during a hygrothermal ageing process, in a total of five different epoxy systems (two commercial and three simple with increasing amine concentration), benchmarked by conventional gravimetric analysis. Using EMT in the form of the LLL model, the bound water uptake can be quantified at sufficient fidelity across epoxy systems, where epoxy and amine concentration were equal. Without a loss of generality, the presented methodology can also be applied to other epoxy systems provided that they are semi-transparent to terahertz radiation. Our data shows that while measurement and analysis are understandably more complex, compared to conventional gravimetric analysis, THz-TDS is a highly interesting contactless, quantitative characterization technique with clear potential to complement existing characterization techniques and to open up new opportunities for future rapid and accelerated degradation testing.