2.1 Measuring techniques

In the epoxy bulk, chemistry is investigated by FTIR attenuated total reflection spectroscopy (ATR) as illustrated in Fig. 1a. The incident infrared light is totally reflected at the plane interface between the internal reflection element (IRE) and the sample.

A modest refractive index of the IRE (n_ZnSe = 2.43) and an incident angle of 60° (well above the critical angle of total reflection) are chosen for the s-polarised light in order to get a penetration depth of some microns. Hence, the spectra provide the bulk properties of the epoxy. Thin polymer films on metal substrates are evaluated by FTIR external reflection absorption spectroscopy (ERAS, Fig. 1b) with p-polarised light at 70° angle of incidence. Fig. 2a,b provides two spectra for illustration. In the case of ERAS, the light penetrates the polymer film and is reflected from the metal interface. The light undergoes partial reflection and refraction at the air interface (not shown in Fig. 1b). The multiple reflections and refractions produce an interference pattern that modulates the spectrum (see [28–30] for details). As a result, neither ATR spectra with ERA spectra nor ERA spectra from epoxy films of different thickness can be compared directly.

This problem of incomparability is solved in the following way (for the physics see, e.g., [28–31]). For the epoxy bulk, the optical function

Below 500 nm, $d_{\text{EP}}$ is estimated by variable angle spectroscopic ellipsometry (VASE, angles of incidence: 65°, 70°, 75°). For thicker films, part of the polymer layer is removed from the substrate. The resulting step between coated and free substrate areas is evaporated with a thin, still reflecting Al-layer (ca. 50 nm). The step height is evaluated by white light interferometry (WLI). Such $d_{\text{EP}}$-data derived by VASE and WLI are not always very precise due to inhomogeneities in ultra-thin films and to some non-uniformity of thick epoxy layers. Therefore, IR spectroscopy and spectra calculation [30] were combined as a non-destructive technique to confirm the results of VASE and WLI. The method is based on a profound comparison of several band intensities (preferably phenylene ring stretching vibrations) in measured spectra and in calculated ‘bulk-like’ spectra with varying $d_{\text{EP}}$.

Brillouin spectroscopy (BS) is an optical method and can be used to study the propagation of hypersonic modes (GHz-range) in amorphous viscoelastic liquids and in polymer glasses. It is not necessary to generate these modes by external influences because the thermal fluctuations themselves result in density fluctuations that can be described as propagating hypersonic modes. In addition to the longitudinal mode, acoustic shear modes also propagate in a liquid provided that the shear viscosity becomes a frequency-clamped transport quantity for the high frequencies involved in BS (a static shear modulus does not exist, of course). In the isotropic bulk, the mechanical behaviour is described by two elastic stiffness coefficients, the longitudinal stiffness $c_{\text{L}}=c_{11}$ and the shear stiffness $c_{\text{T}}=c_{44}$.

In the Brillouin experiment, some photons of the incident laser beam are scattered by the hypersonic modes in the transparent sample. The spectrum of the scattered light is analysed for a chosen scattering angle $\theta$. The hypersonic modes are interpreted as acoustic phonons that interact with the photons of the laser light illuminating the sample (cf. [32]). Fig. 3 illustrates a scattering geometry that is useful to study transparent films on a reflecting substrate [33].

As indicated in the insert of Fig. 3, momentum is conserved for the photons (${\stackrel{\rightharpoonup }{k}}_{\text{i}}$, ${\stackrel{\rightharpoonup }{k}}_{\text{s}}^{\text{L},\text{\hspace{0.17em}T}}$ wave vectors for incident and scattered photons) interacting with longitudinally (L) and transverse (T) polarised phonons (wave vectors ${\stackrel{\rightharpoonup }{q}}^{\text{L,T}}$ as selected by the angle $\theta$):

Energy conservation also holds for the scattering process

Fig. 4 depicts the schematic drawing for a Brillouin spectrum of an isotropic sample.

The frequencies $f_{\text{s}}^{\text{L,T}}={\omega }_{\text{s}}^{\text{L,T}}\text{/}2\text{π}$ are found at the maximum of the Brillouin lines L_S,AS and T_S,AS. $f^{\text{L,T}}\left(\stackrel{\rightharpoonup }{q}\right)={\Omega }^{\text{L,T}}\left(\stackrel{\rightharpoonup }{q}\right)\text{/}2\text{π}$ are the frequencies of the acoustic phonons that cause the light scattering according to eq. (4). The phase velocities $v_{\text{L,T}}\left(\stackrel{\rightharpoonup }{q}\right)$ of the acoustic phonon modes are calculated according to Eq. (5) from the phonon frequencies $f^{\text{L,T}}$ measured for the chosen $\overrightarrow{q}$

The elastic stiffness moduli are obtained by

So far it is assumed that all acoustic modes propagate in the plane wave limit and that ${\Gamma }_{\text{L,T}}\left(\stackrel{\rightharpoonup }{q}\right)<<f^{\text{L,T}}\left(\stackrel{\rightharpoonup }{q}\right)$. In thin films (thickness $d_{\text{film}}\le v_{\text{L,T\hspace{0.17em}}}\text{/}{f}^{\text{L,T}}$) with or without substrate, the concept of plane waves fails and the phonons propagate as guided waves. Usually this yields a complicated acoustic mode spectrum. It can be interpreted quantitatively only in simple cases, e.g., for a homogeneous film with exactly known boundary conditions. In other cases, a qualitative interpretation can be given at least. Thus, the glass transition of a film can be deduced from the temperature dependence of the mode diagram.

2.2 Materials and sample preparation

The epoxy system consists of the diglycidyl ether of bisphenol A (DGEBA, DOW Plastics D.E.R. 332) with two oxirane rings and diethylene triamine (DETA, DOW Plastics D.E.H.) with five reactive hydrogen atoms in two primary and one secondary amine groups:

The mass ratio is chosen as DGEBA: DETA = 100: 14. This corresponds to a mixing ratio of 1 mol DGEBA on 0.462 mol DETA and hence to 1.155 mol amine hydrogen on 1 mol oxirane rings. The components are stirred in a closed glass vessel in the molten state at 55 °C for 5 min and cooled down to room temperature within about 1 min. Then, the mixture is transferred into a glove box for film preparation in CO₂-reduced, dry air (dew point: –70 °C, residual CO₂ content: ≤ 200–300 ppm). Bulk samples as well as epoxy films with d_EP ≥ 3 μm are prepared by direct casting. Thin films with d_EP ≤ 2 μm are obtained by spin coating from the appropriately diluted solution in methyl ethyl ketone (MEK). This solvent is chosen because it inhibits the curing reactions during the film preparation. In general, ketones are known to form imines by condensation with primary and secondary amines:

As illustrated by the infrared spectra in Fig. 5, MEK reacts slowly with DETA. For an arbitrary mixing ratio chosen in this test, chemical equilibrium is reached within about 30 min.

The imine content can be increased by a growing MEK concentration or by removing water (as the co-product). Imine decomposes by removing MEK (e.g. in vacuum) or by addition of water. Reaction (8) is fully reversible. This is essential for the sample preparation from the diluted reactive epoxy system. MEK evaporates quickly from the spin coated layers. About 10 min after preparation, the IR bands of MEK disappeared from the thin film spectra (d_EP ≤ 200 nm) and imine is not found in these films (Fig. 9 for example). Hence, the majority of imine molecules decomposed very quickly due to the evaporation of MEK and to the amine-epoxy polyaddition. The thicker layers lose the solvent almost completely within 72 h (Fig. 8) and very little imine is present in the IR spectra. Therefore we conclude that MEK does not possess a significant influence on the amine conversion in the epoxy films at room temperature (see Sections 3.1 and 3.2 for further evidence).

The metal substrates are obtained by evaporation of ca. 100 nm of pure Al, Cu or Au onto Si (100) wafers. As shown by extensive surface analysis (XPS, Scanning Auger Microscopy, TOF-SIMS, AFM) [34,35], these native metal surfaces are extremely smooth (rms roughness < 1 nm) and the overall chemical state is reproducible within reasonable limits.

As a first curing step, the film specimens are stored in CO₂-reduced, dry air at room temperature (RT, ca. 23 °C) for 72 h. Only in case that curing was monitored by IR and by BS spectroscopy, a short contact with ambient atmosphere was necessary for sample transfer into the spectrometer. After 72 h, the gross reaction rate is very low but the oxirane consumption is well below 100%. These ‘RT-cured’ samples are ready for investigation. An additional ‘post-curing’ step at 120 °C in argon for 1 h provides complete oxirane consumption in the bulk. Post-cured epoxy films are also characterised.

All steps of the preparation regime must obey an exact timing and well-defined conditions concerning temperatures and ambient atmosphere.

3.1 Curing at room temperature

The chemical kinetics of room temperature curing is followed in situ by IR-ATR spectroscopy for the bulk and by IR-ERAS for epoxy films on the Al substrate (Fig. 2 as an example for the spectra). Neither the amine bands nor the hydroxyl bands are suited for a quantitative analysis because they overlap strongly with each other (NH and OH stretching region) or with other bands (e.g., NH₂ deformation at ca. 1597 cm⁻¹) in the mid IR range. As a quantitative measure, the spectroscopic degree of epoxy consumption $U_{\text{EP}}^{\text{IR}}$ can be calculated from the normalised band intensity I_915, norm (peak height) of the oxirane stretching vibration at 915 cm⁻¹:

The phenylene ring stretching vibration at 1510 cm⁻¹ serves as internal standard. In eq. (9), the band intensities also depend on the respective extinction coefficients. Therefore, $U_{\text{EP}}^{\text{IR}}$ is not a priori identical with the chemical consumption. Fig. 6 depicts $U_{\text{EP}}^{\text{IR}}\left(t_{\text{cure}}\right)$ and the corresponding spectroscopic reaction rate ${\dot{U}}_{\text{EP}}^{\text{IR}}\left(t_{\text{cure}}\right)$ for a couple of layers on Al. Additionally, the reference curves (marked as ‘bulk-like’) are presented for each epoxy thickness. These reference curves are obtained from the ‘bulk-like’ ERA spectra that are calculated for the given $d_{\text{EP}}$ from the optical function ${\widehat{\text{n}}}_{\text{EP}}\left(\tilde{\nu },t_{\text{cure}}\right)$ of the epoxy bulk and other parameters of the thin film sample as described in Section 2.1.

The ‘bulk-like’ curves are very similar in both plots. The small differences are due to the influence of $d_{\text{EP}}$ on the IR-ERA spectra (interference of the IR light) which is very weak in the range of 100–200 nm. In the initial stage of curing, the slight s-shape in $U_{\text{E}\text{P}}^{\text{I}\text{R}}\left(t_{\text{c}\text{u}\text{r}\text{e}}\right)$ and the corresponding maximum in the rate ${\dot{U}}_{\text{EP}}^{\text{IR}}\left(t_{\text{cure}}\right)$ for the ‘bulk-like’ curves confirm a weak auto-acceleration of the chemical reactions. Such an effect has been reported in the literature. It is attributed to the auto-catalytic influence of the hydroxyl and tertiary amine groups in the forming epoxy polymer – cf. eqs. (1, 2). $U_{\text{EP}}^{\text{IR}}\left(t_{\text{cure}}\right)$ reaches 73% as the final value for RT-curing in the ‘bulk-like’ curves.

The real thin layers are different. The auto-catalytic effect is not observed in the initial reaction stage and hence the initial gross reaction rates are slower than in the bulk. After 48 h, the remaining reaction rates are small but significantly higher than in the bulk. The most striking difference appears for the final values of $U_{\text{EP}}^{\text{IR}}\left(t_{\text{cure}}\right)$ in the real samples. It reaches only 38% and 36% in the 200-nm and the 100-nm layers, respectively, instead of the 73% that should be obtained in the case that the chemical reactions would have proceeded as in the bulk. A lack of amine groups owing to the formation of imine with MEK is not the reason for the low oxirane conversion because no imine band is found in the IR spectra of such thin films (Fig. 9). Hence, the chemical kinetics of oxirane conversion requires more time with decreasing epoxy thickness.

Curing-induced changes of the mechanical properties are depicted by the phonon frequencies $f_i\left(t_{\text{cure}}\right)$ as measured by BS. These samples were in contact with air inside the thermostat of the spectrometer at 298 K. Some of our results indicate that the measuring atmosphere (contents of water and CO₂) influences the curing to some extent. Therefore, the BS results on curing should be related only in a qualitative manner with the IR spectroscopic data given above. Fig. 7 provides the curves for the bulk and for 200 nm epoxy on Al as an example. In the bulk, the phonons propagate as plane waves but in thin films they form guided waves with complexly shaped wave fronts. Therefore, only the development of $f_i$ with $t_{\text{cure}}$ may be compared.

All functions $f_i\left(t_{\text{cure}}\right)$ grow as it is expected for the ongoing network formation in the bulk and in the film as well. For the longitudinal bulk phonon, $f_{\text{L}}^{\text{bulk}}\left(t_{\text{cure}}\right)$ goes up steeply within the first 6 h. As for the spectroscopic epoxy consumption in Fig. 6, the curve possesses a weak s-shape at this stage. It levels after ca. 9 h. In the layer, only one broad guided wave phonon at f₁ is observed in the initial stage of curing. That phonon possesses an average longitudinal polarisation. f₁ rises strongly for at least 12 h. Then, it does not level but continues to increase weakly until the end of the measurement (48 h). Hence, progress of chemical reactions is much slower than in the bulk and it does not cease within two days. The transverse bulk phonon at $f_{\text{T}}^{\text{bulk}}$ belongs to the shear wave. Therefore, the increase of $f_{\text{T}}^{\text{bulk}}$ monitors the solidification in the bulk which almost levels after about 9 h. In the thin film, it takes about 22 h before three more phonons are observed in addition to $f_1$ in the Brillouin spectrum. The strongest one at $f_2$ is shown in Fig. 7. The average polarisation of the $f_2$-phonon resembles very much a transverse wave. Therefore, its appearance indicates that there is a liquid-solid transition in the thin epoxy films but it is much delayed in comparison to the bulk.

In conclusion, room temperature curing is hampered in thin epoxy films. The BS provides first hints on network structures with a polymer dynamics that is different from the bulk.

3.2 Properties of the RT-cured films

As discussed in Section 3.1, the curing reactions have virtually stopped in the epoxy samples after 72 h. For the bulk network, it is well established that this stop results from the vitrification which is caused by the curing itself. Gravimetric measurements show that small bulk samples (< 10 mg) lose just about 1% of their mass during RT-curing due to evaporation of DETA [36]. Even with this loss of hardener, an excess of 1.072 mol amine hydrogen on 1 mol oxirane rings remains. One could suspect for the thin films, however, that more DETA might evaporate due to the higher surface-volume-ratio and less amine hydrogen would be available than in the bulk samples. As a precaution, the epoxy mixture is pre-cured at room temperature for 1 h prior to the preparation of the films considered now. During that pre-curing step, about 18% of the oxirane groups are consumed. Assuming a reactivity ratio of 2.5:1 for primary and secondary amine hydrogen, it is estimated by a simple Monte-Carlo simulation that ca. 60% of the DETA molecules formed oligomers at this stage of reaction. The tests with other reactivity ratios show that the percentage of oligomerised DETA does not change dramatically – a ratio of 1:1 results in about 80%. Experiments prove that oligomers do not evaporate at moderate temperatures. Additional arguments against the evaporation hypothesis will be given below for our samples.

We start with an analysis of the IR-ERA spectra in order to compare the chemical state of the films (20 nm ≤ d_EP ≤ 2 μm) on the three metal substrates. As mentioned in Sect. 2.1, reference to the bulk is made by using ‘bulk-like’ ERA spectra that are calculated for the given experimental conditions with the measured optical function of the RT-cured epoxy bulk. Apart from a small excess of residual oxirane, the chemical state of thick epoxy layers on all metals corresponds very well to the bulk – see Fig. 8 for example. In particular, no specific ether band is observed (asymmetric stretching at ca. 1140 cm⁻¹) where the intensity should be higher if the metal surfaces would have stimulated the reaction of oxirane with hydroxyl groups (cf. eq. (2)).

Thin films like 110 nm epoxy on Al (Fig. 9), contain some more residual oxirane groups than the bulk. Hence, the curing reached a lower level. Again, no ether band is observed at 1140 cm⁻¹. This indicates that the oxirane-hydroxyl reaction does not take place during RT-curing. Instead, in the region between 1150 and 1060 cm⁻¹ where lattice vibrations of the tertiary amines are involved, the spectral intensity is somewhat lower for the 110-nm sample than for the corresponding ‘bulk-like’ spectrum. In accordance with the reduced oxirane consumption in the real thin film, this is explained by a lower content of tertiary amine groups that have weak bands in this frequency range.

Fig. 10 summarises the data for the IR-spectroscopic degree of oxirane consumption in the epoxy films on the three metals after 72 h cure at room temperature.

Although the residual oxirane content in the bulk is constant after the RT-curing from the chemical point of view, the three ‘bulk-like’ curves for the spectroscopic final consumption $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}$ depend on $d_{\text{EP}}$ in Fig. 10. This illustrates how the interference pattern modifies the IR-ERA spectra of thin films.

In the real layers on the three metal substrates, the $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}$-data fall more and more behind the expected bulk value with decreasing $d_{\text{EP}}$. This behaviour proves once more that a MEK-amine condensation (cf. reaction in eq. (8)) does not explain the reduced oxirane consumption in thin spin coating films. The content of residual imine tends to grow with $d_{\text{EP}}$ and hence $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}$ should go down for the thicker layers but it approaches the oxirane consumption in the solvent-free bulk. In the second place, the curves for $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}\left(d_{\text{EP}}\right)$ seem to support the DETA evaporation hypothesis: The thinner the film the stronger the effects caused by evaporation of DETA. Hence, the oxirane consumption would go down with $d_{\text{EP}}$ as well. Things are not that simple, however. In the thin films made from pre-cured epoxy, the level of oxirane consumption after RT-curing is higher (e.g., $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}\text{(}100\text{nm}\text{)}$ = 59% and $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}\mathrm{(200 }\text{ nm}\text{)\hspace{0.17em}}$ = 61% on Al, see Fig. 10) than in the thin films prepared from the freshly mixed epoxy (36% and 38%, respectively, cf. Sect. 3.1, Fig. 6). Hence, some material may have evaporated during the measurement of reaction kinetics in films made of freshly prepared epoxy. Moreover, we have strong evidence that water vapour and CO₂ in environmental air have an essential impact on the evaporation mechanism of DETA and therefore on the final degree of cure. But for the epoxy films made of pre-cured material, the following experiment proved that evaporation is negligible in dry atmosphere. Such a film ($d_{\text{EP}}$ ≈ 100 μm) was prepared by the Doctor's blade technique in argon atmosphere on a Cu substrate. Another Cu substrate was placed 1.5 mm above this sample forming a sealed compartment. The temperature was kept constant at 25 °C for the curing sample while the upper Cu substrate was cooled by a Peltier element. After about 2 h of curing, the upper Cu substrate is transferred into the IR spectrometer without contact to ambient air and an ERA spectrum is taken. Within the limits of spectroscopic sensitivity, no adsorption products were detected on the Cu mirror. Since DETA undergoes chemisorption on copper (see below) this result proves that amine does not evaporate significantly out of films made of pre-cured material under the given conditions.

Additionally, it can be seen in Fig. 10 from the data for the thinnest films that the $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}$ depend on the kind of metal surface. $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}\left(\approx 20\text{nm}\right)$ reaches only ca. 55% on Au and Al while it is about 58% at the Cu substrate. With increasing thickness, $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}\left(d_{\text{EP}}\right)$ rises stronger on Au than on Al. On Cu, the situation differs in another aspect: $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}$ is no longer a monotonous function but has a minimum in the 100-nm layers. Near to the copper oxide, the oxirane consumption rises again. Such a minimum cannot be explained by DETA evaporation but it can result from a catalytic effect of the copper substrate on network formation.

Summing up, the observed $U_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}$-data are influenced by the metal substrates that impede the curing reactions. It is surprising that this reduced oxirane consumption does not confine to the vicinity of the substrate but it extends some micrometers into the epoxy. That can hardly be explained by DETA adhesion to the metal surfaces because the surface area would not accommodate so many molecules, even for a closely packed monolayer. On the other hand, each phase boundary modifies the thermodynamic potential and this could provoke special processes of structure formation of an interphase on the local scale. We presume that the components of the epoxy system undergo segregation or even some kind of phase separation while the thin films are in the liquid state. These processes are stimulated by the metal substrates, probably in conjunction with a latent incompatibility of the components in the reacting system. We showed in previous studies [37,38] that the DGEBA-DETA system can develop inhomogeneities in the bulk.

Otherwise, shape and structure of the thin film spectra on Au or on Al are similar to the ‘bulk-like’ spectra (Fig. 9). The three little peaks on the broad OH stretching band in the ‘bulk-like’ spectra represent NH stretching modes. Their intensity is overrated by the spectra simulation. It should be noted, however, that Roche et al. [39] report on Al complexes formed by amine compounds in the epoxy on native Al substrates. On Cu (Fig. 11), massive deviations from the bulk arise in the OH and NH stretching region (3600–3100 cm⁻¹). The bands possess quite a different shape and position. For the phenylene ring stretching doublet (1610 and 1580 cm⁻¹), the intensity increased considerably but the phenylene band at 1510 cm⁻¹ does not change. Additionally, a new band appears at about 1390 cm⁻¹.

Hence, the chemical state in the epoxy must have been considerably modified by the copper surface during the RT-curing. Fig. 12 gives evidence that DETA forms a complex with the Cu substrate.

As a consequence of this interaction, amine band intensities altered considerably, in particular within the spectral regions of 3000 – 3400 cm⁻¹ (NH stretching vibrations) and 1600 cm⁻¹ (NH₂ deformation). As shown in Fig. 11, these specific spectral features are also present in ultra-thin epoxy films on Cu. Recently, Cu²⁺ ions have been detected by XPS and TOF-SIMS in such films and in real adhesive joints epoxy-copper [35]. Hence, a Cu-DETA complexation takes place in the epoxy interphase on copper. DETA literally dissolves the copper hydroxide on the Cu substrate. This process explains why the OH stretching intensity (3600–3200 cm⁻¹) is significantly reduced (Fig. 11). It is important to note that these effects are observed on copper only. In our case, their intensity is moderate because the uncoated Cu substrates were stored in dry air (cf. also the band shape at 1600 cm⁻¹ in Fig. 19). They increase considerably on Cu substrates that were stored under environmental conditions (i.e. humid air).

As discussed above, the incomplete chemical conversion of oxirane groups could be related to some heterogeneity in the epoxy films. The lateral variation of mechanical film properties is obtained by a sequence of locally measured Brillouin spectra. Resolution is determined by the diameter of the laser beam (ca. 10 μm). As an example, Fig. 13 depicts a selection of results for the longitudinal phonon in thick films that are beyond the guided wave limit. The propagation of these plane sound waves does not depend on $d_{EP}$ but it is only a function of the elastic properties of the epoxy network. Hence the local frequency values depict the variations of the elastic stiffness and density.

The high-frequency elastic stiffness coefficient $c_{11}$ on the right ordinate in Fig. 13 is calculated by

With the measured variations of $\delta {\rho }_{\text{EP}}/{\rho }_{\text{EP}}\approx \mathrm{0.4\%}$ and $\delta f_{\text{L}}/f_{\text{L}}\approx \mathrm{0.3···1.5}\%$, the influence of $f_{\text{L}}$ dominates the local variation of $c_{11}$ in general. Hence, the measured frequency variations are mainly caused by the local elastic properties of the epoxy films that vary on the sub-mm scale. This result supports the view that the epoxy films are inhomogeneous.

Table 1 summarises the average values $\overline{c_{11}}$ for each layer along the lateral traces given in Fig. 13.

For the 3.2 μm-layers, the $\overline{c_{11}}$-data correspond to the mean bulk value $\langle c_{11}^{\text{bulk}}\rangle$ = 9.1 ± 0.3 GPa. We note that the relatively big experimental error of $\langle c_{11}^{\text{bulk}}\rangle$ is due to the averaging over an ensemble of bulk samples that were prepared at differing room temperatures within a period of more than one year. The error of $\overline{c_{11}}$ is significantly smaller because it refers to lateral variations of $c_{11}$ on a given sample. Therefore, it is significant that $\overline{c_{11}}$ tends to increase with decreasing epoxy thickness in the considered $d_{\text{EP}}$-range for each metal. This seems to be surprising in view of the inverse trend found for the oxirane consumption. However, the mechanical properties of polymer films are influenced by the interfaces to the substrate and to the atmosphere. Both effects are not present in the bulk. The epoxy adheres to the rigid metal substrate which causes a stiffening effect on the polymer in a relevant gradient layer. The free surface could have the opposite effect. In these Brillouin measurements, the scattering volume extends over the whole thickness of the films. Hence, the decreasing function $\overline{c_{11}}\left(d_{\text{EP}}\right)$ indicates that the adhesive interphase causes on average a dominant stiffening even for the 0.65-μm films.

Fig. 14 provides the lateral frequency variations for three guided sound waves observed in a RT-cured 200-nm epoxy film on Al. Hence, $c_{11}$ cannot be easily determined. All phonons show a simultaneous pattern of frequency variation. The $f_i$ vary locally by ± 150 MHz at maximum ($\delta f_i/f_i\approx \mathrm{1.5,}\mathrm{1.9,}2.8\%$) around their mean values. This is in the same range as for the plane waves in the thick films. Therefore, the slight local variations of $d_{\text{EP}}$ (as observed by SFM) do not dominate the $f_i$-variations. The thin epoxy film possesses a significant lateral inhomogeneity in terms of high-frequency elastic properties on the sub-mm scale.

The Brillouin frequencies $f_i$ reveal a remarkable dependence of the glass transition temperature on $d_{\text{EP}}$ for the RT-cured films. For these measurements, the position of the scattering volume is chosen randomly. The laser beam is defocussed to 50-μm diameter. The specimen is cooled down to low temperature (e.g., 110 K). Then, after stepwise heating, the spectra are recorded isothermally at subsequent temperatures. The $f_i$ are depicted as a function of temperature – see Fig. 15 for an example.

Coming from low temperature, the curves $f_i\left(T\right)$ show a simultaneous kink that marks the static glass transition temperature $T_{\text{G}}^{\text{static}}$ in the polymer film [32]. Above 300 K, all frequencies start growing. That corresponds to a rising mechanical modulus due to the re-activated curing reactions. This curing finished at about 325 K. The temperature range is so small because of the long acquisition time at each isothermal step. The upward curvature in $f_i\left(T\right)$ between 360–420 K indicates the termination of the structural glass relaxation process.

Table 2 summarises the static glass transition temperatures $T_{\text{G}}^{\text{static}}$ on Au, Al and Cu as measured at randomly chosen spots on the samples.

On all metals, the data reveal a pronounced decline of $T_{\text{G}}^{\text{static}}$ with $d_{\text{EP}}$ although the positions for the scattering volume were not allocated to a particular feature in the laterally varying stiffness. Most samples even do not vitrify during RT-curing. These epoxy layers remain in the viscoelastic state at room temperature although the chemical reactions have almost stopped. This result is in contrast to the bulk where the curing rate slows down by many orders of magnitude due to vitrification. Therefore, a new mechanism must prevent the reaction partners from reacting in the epoxy films at some stage of RT-curing. A homogeneous chemical immobilisation of amine or epoxy groups can be excluded because the T_G-depression is also present on the inert gold substrates. However, the partial demixing effect discussed above can provide an alternative explanation. Demixing would lead to a heterogeneous structure that separates the reaction partners. They have to diffuse through the phase boundaries before they react. The flux of diffusing molecules is directly related to the area of the phase boundaries. In the bulk, the reactant molecules diffuse from one phase through the whole area of the phase boundary, that can by approximated as a sphere with the surface $\pi D^2$, into the surrounding phases. In the epoxy bulk, the diffusion is effective during RT-curing until $T_G$ reached 326 K. Now, the heterogeneities deduced from the laterally resolved Brillouin data possess lateral dimensions on the sub-mm scale. We presume that this scale corresponds to the characteristic size D of the supposed phases. As a consequence, the area of the phase boundary is cut by the interfaces air–film and film–substrate if $d_{\text{EP}}$ becomes smaller than the phase size D. This is the case for the epoxy films. The remaining diffusive flux is restricted to the curved surface $\pi \text{D}{d}_{\text{EP}}$ of the remaining spherical layer. The effective rate of chemical reactions is small, therefore, and $T_{\text{G}}^{\text{static}}$ is lower for the thinner films just after the RT-curing.

Fig. 16 provides the results of μ-BS measurements for the depth profile in 1 mm epoxy layers on Al, Cu and Au after RT-cure. On the upper side of the layer, a thin glass plate completes the adhesive joint thus preventing evaporation of DETA. As above, the bulk density ρ_EP = 1.17 g cm⁻³ is used for an estimation of $c_{11}$.

Inside the three epoxy layers, the plateau values $c_{11}^{\text{plateau}}$ are almost the same ($c_{11}^{\text{plateau}}$(Au) = 9.84 GPa, $c_{11}^{\text{plateau}}$(Al) = 9.75 GPa, $c_{11}^{\text{plateau}}$(Cu) = 9.66 GPa). The values appear to be slightly higher than the mean bulk value $\langle c_{11}^{\text{bulk}}\rangle$ = (9.1 ± 0.3) GPa, but this could simply result from variations of room temperature during preparation. Furthermore, the statistical ensemble might have been not big enough for the determination of a true $\langle c_{11}^{\text{bulk}}\rangle$.

At the metal side, specific maxima in $c_{11}$ indicate a surprisingly broad interphase with mechanical properties modified due to the presence of the metal substrate. In the interphases on the native oxides of Al and Cu, the maximum in $c_{11}$ reaches about 107% of the corresponding $c_{11}^{\text{plateau}}$. At these two metal interfaces we have $c_{11}\approx 1.05\cdot c_{11}^{\text{plateau}}$. The interphase appears to be slightly narrower on Al (ca. 230 μm, measured at the foot of the $c_{11}$-peak) than on Cu (ca. 300 μm). On Au, the interphase extends only to some 190 μm into the epoxy and the stiffness maximum (at $z_{\text{EP}}$ ≈ 930 μm) is closer to the interface than on Al or Cu (at ca. 880 μm). Another interphase with a drop in $c_{11}$ is found at the glass side of the samples. Actually, it would be expected to be the same in all specimens but this is not the case. We suppose that appearance and profile of this interphase are also sensitive to the state of the glass surface which was not controlled explicitly in these experiments.

The data points that are closest to the metal surfaces, represent the elastic properties averaged over a $\text{Δ}{z}_{\text{EP}}$-region of 5-μm. Tentatively, they can be compared with the data given in Table 1 for the films with $d_{\text{EP}}$ ≈ 3.2 μm. In the 1-mm adhesive joints, the $c_{11}$-data at the metals are by ca. 0.8–1.3 GPa higher than in the 3.2-μm films. This is an indication that the thin films might be not representative for the mechanical properties of the interphase in the thick adhesive joints.

It is not straightforward to understand why $c_{11}$ goes through a maximum far from the metal and why the interphases are so broad. The maximum implies that the polymer structure formed under the influence of at least two competing processes. They can not relate directly to the mechanisms of fundamental adhesion because of the broadness of the interphase. However, an increase of stiffness $c_{11}$ would be caused by an increased epoxy consumption which would result in a denser network. As the consequence, the observed maximum in $c_{11}$ corresponds to a maximum network density. This picture fits qualitatively to the view that segregation or even phase separation are triggered by the metal surfaces. It seems that the lateral heterogeneity, observed on the thin epoxy films, now extends considerably into the epoxy in the adhesive joint. A plausible explanation for the maximum itself will be given in the next section.

3.3 Properties of the post-cured films

Post-curing (120 °C, 1 h) increases the oxirane consumption to 100% in bulk, but it remains incomplete in the epoxy layers on the metals. The ERA spectra do not show the formation of any ether species. Hence the reaction between oxirane rings and hydroxyl groups (cf. eq. (2)) did not take place. This conclusion is further supported by the spectroscopic changes in the OH / NH stretching region - see the spectra in Fig. 17 for the 50 nm films.

As expected for the oxirane–amine reaction, post-curing results in a rise of intensity for the OH band on each metal. For the epoxy layer on Cu, we note in passing that the post-curing process ‘corrected’ the ‘deformed’ shape of the OH / NH band. Therefore, the particular Cu-induced chemical reactions in the epoxy at room temperature must have been reversed during post-curing.

Fig. 18 summarises the $U_{\text{postcured}\text{EP}}^{\text{IR}}\left(d_{\text{EP}}\right)$-data for Al, Cu and Au.

The thick layers approach the full oxirane consumption as it is characteristic for the bulk (note that the accuracy of $U_{\text{postcured}\text{EP}}^{\text{IR}}\left(d_{\text{EP}}\right)$ is not that good around 100% because the IR band intensities go to zero). Even in the thinnest films, the oxirane consumption increases to more than 75%. These high values are another point against the assumption that a considerable amount of DETA could have evaporated out of the epoxy films. For a final answer, post-cured films on Au have been stored in argon at 40 °C for 100 d [40]. The residual oxirane groups reacted fully in the thin epoxy films within about 50 days. Again, no new band developed in the ether region. Keeping in mind that the oxirane ring does not react with the Au surface, we conclude from these findings that the oxirane groups reacted only with amine hydrogen in the epoxy films under the given conditions. As a consequence, the necessary amount of DETA must have been available in the thin layers.

Generally, the residual oxirane contents increase with decreasing epoxy thickness in the post-cured samples (Fig. 18). The absolute values of $U_{\text{postcured}\text{EP}}^{\text{IR}}\left(d_{\text{EP}}\right)$ scatter somewhat from sample to sample. It is obvious that the metals influence the post-curing specifically. In the range of 100–600 nm, most oxirane is consumed on Cu, followed by Al and Au.

In addition to the specific oxirane consumption, new IR bands are observed at ca. 1660 cm⁻¹ and 1738 cm⁻¹ in the post-cured epoxy layers on all three metals. Fig. 19 compares the situation prior and after post-curing for 50 nm films as an example.

On Al and Au, the band at 1738 cm⁻¹ is very weak in the RT-cured films. It grows slightly as a result of post-curing, mainly for the thinner films. For Cu, the situation is different again. The well separated band at 1738 cm⁻¹ is already present after RT-curing and the intensity increases significantly due to post-curing. Fig. 20 summarises $I_{\text{RT}-\text{cured}\text{EP}}^{\text{IR}}\left(d_{\text{EP}}\right)$ and $I_{\text{post}-\text{cured}\text{EP}}^{\text{IR}}\left(d_{\text{EP}}\right)$ for the band at 1738 cm⁻¹.

The band at 1660 cm⁻¹ is well developed in the RT-cured films on Cu while it is hardly observed on Al and Au (Fig. 19). Post-curing results in some rise of band intensity in the epoxy on Al as well as on Au and even more pronounced on Cu. Band intensity is largest for the thinnest films, which do not contain any residual MEK after room temperature curing. All these features show that now the band at 1660 cm⁻¹ does not depict the imine that would result from the condensation reaction of MEK and DETA according to eq. (8). It is concluded from these metal-specific differences that the bands at 1660 cm⁻¹ and 1738 cm⁻¹ indicate two different functional groups or chemical products because the band intensities do not develop simultaneously.

These data confirm the specific influence of the metals on the curing chemistry. Its long range over some hundred nanometres supports again the view that some kind of segregation or phase separation must be present also in the post-cured epoxy films. That results in interphases with specific chemical structures.

Fig. 21 provides the μ-BS results for 1-mm epoxy on Cu after post-curing as an example for the effect of post-curing on the mechanical properties in the adhesive joints.

Generally, the post-curing produces the expected increase in network stiffness. It is most interesting, however, that the $c_{11}$-profile changed completely. The plateau level of $c_{11}$ inside the epoxy increased to the value for the original maximum at the Cu side. Post-curing replaced this old maximum by a new one. It is very small and it is located almost on the metal interface. At the glass side, the minimum converted into a maximum but we will not consider that further.

Post-curing at 120 °C means at first that the epoxy network reaches the viscoelastic state where the internal stresses relax quickly. Such stresses developed at room temperature as the result of adhesive bonding between epoxy and metal surface on one hand and shrinkage due to polymerisation on the other hand. That introduces lateral shear stress which tends to reduce $c_{11}$ [32]. At least in part, this stress would explain the decrease of $c_{11}$ between the maximum and the metal interface. Secondly, the chemical reactions continue at 120 °C and increase the network density but without substantial shrinkage. It is known for the bulk that this post-curing results in full epoxy consumption and in a network structure which is not per se homogeneous. For the adhesive joint, the high plateau value ($c_{\mathrm{11,}\text{post}-\text{cured}}^{\text{plateau}}$(Cu) ≈ 10.6 GPa) represents the stiffness for the post-cured bulk. It is equal to the former maximum found in the RT-cured joint. This coincidence suggests that this former maximum should reflect a region with fully cured network. The clear $c_{11}$-decrease, found for the RT-cured samples between their $c_{11}$-maximum and the metal, almost vanished during the post-curing. This should be caused by the stress relaxation mentioned above. In the post-cured epoxy, the little new maximum near to the metal could indicate that there is a new interphase (< 100 μm broad) with increased effective stiffness due to the internal stresses that arise during cooling from 120 °C to room temperature.