3.1. Rheological Analysis of the Stencil Printing and Electronic Components’ Placement
The printing parameters and stencil designs used at the industrial plant for the stencil printing and component placements are portrayed in
Figure 1. Note here that the shear and extension histories related with the semi-manual dispensing of material on the stencil before another cycle of prints were not considered, as they are difficult to quantify. Nonetheless, a rest time of
tr = 2.5 s after dispensing was observed before starting stencil printing. Equally, the extensional rates associated with the separation of the stencil from the PCB were not considered. Two stencils with thickness
T of 0.05 and 0.08 mm were used. The squeegee was submitted to a force F = 75 N and traveled at a velocity
vp ranging from 25 to 50 mm.s
−1, whereas the separation velocity vs. varied between 1 and 5 mm.s
−1. The shear rates
involved during printing were obtained through the relation
, whereas the shear rates
involved during separation were obtained through the relation
, where
X is the half-length, half-width or radius of the apertures. Given the footprints of the stencil design and the velocities, the ranges of shear rates applied on the solder paste or ECA were as follows: 312 s
−1 <
< 1000 s
−1 and 0.16 s
−1 <
< 16 s
−1.
A pick-and-place machine allowed the placement of electronic components on the printed solder paste and ECA deposits with a controlled force ranging from 2 to 15 N. Assuming for simplicity that this force was applied on the areas of the deposits and that the squeezing of components involved more shear than biaxial extension, shear stresses σp ranging from 50 kPa to 62.5 MPa were applied during a time tp.
Three characteristic times of the SMT still needed to be defined as they condition the structural and rheological recovery of the printed materials under different conditions. The first was the time lapse tl1 between stencil printing and PCB separation. The second was the time tl2 needed to transfer the printed PCB from the printer to the pick-and-place machine. This time is usually of the order of a minute or more, as the quality of the printing is often controlled before placing the electronic components. The third was the duration tl3 of the conveying of the PCB from the pick-and-place machine to the reflow soldering oven. During tl3, the solder paste or ECA was loaded with the weight of the electronic component, which corresponded to a maximum stress of 206 Pa. However, the rotational rheometer used in the present study did not allow for measuring the flow or displacement of the sample under a compressive load of the order of 200 Pa. This was in contrast with the sample viscoelastic recovery during tl1 or tl2, which can be measured as detailed below.
3.2. Design of the Rheological Protocol
Rheological testing of ECA should mimic the shear rates and stresses applied during SMT and quantified above. In addition to the determination of the yield stress and flow behavior, the rheological characterization should also ideally give access to the recovery time of the material after flow cessation and to its characteristic response time upon imposition of flow or stress. The values of the SMT rheological parameters computed from the analysis presented above are gathered in
Table 2. Note that the magnitudes of the shear rates and stresses displayed in
Table 2 for the printing are in harmony with the values computed from the modelling of shear rates and stresses taking place within 1 mm close to the tip of the squeegee [
9,
12,
17]. The rheological protocol is presented in
Figure 2 together with the rheological response of the commercial solder paste, whose rheology is to be benchmarked.
The protocol started with the application of a step shear rate
= 0.5 s
−1 during 120 s (see
Figure 2a), followed by a small amplitude oscillatory shear (SAOS) test where both strain amplitude and frequency were maintained at 0.5% and 1 Hz, respectively, and a data point was measured each 7 s during 5 min (see
Figure 2b). The storage modulus
and the loss modulus
were computed from the ratio of the measured oscillatory shear stress amplitude
σ0 over the applied 0.5% SAOS strain
γ0, taking into account the phase shift
δ between the oscillatory shear stress response and the imposed SAOS strain. The purpose of applying a step shear rate is to rejuvenate the paste and erase all mechanical and structural history associated with the sample loading. The value of
= 0.5 s
−1 was chosen as this shear rate is small enough to avoid any fracture or shear instabilities, as established in preliminary trials, while the shear-induced rejuvenation enhances the experimental reproducibility in the rheological characterization of colloidal suspensions [
16,
18]. The duration (120 s) of the step shear rate was much larger than the estimate of the rest time
tr after dispensing. However, such long shearing time was needed to ensure the reading of a steady-state shear viscosity, which indicates the establishment of a constant and reproducible shear-induced structure before subsequent rheological testing. Data in
Figure 2b indicate that the structural build-up of the paste following the rejuvenation reached an apparent equilibrium within the 5 min of testing, which thus allowed the start of the rheological characterization of the samples.
A SAOS frequency sweep was thus performed from 100 Hz down to 0.1 Hz to record the mechanical spectra of the samples (see
Figure 2c), where
G’ and
G’’ was computed as above for each applied frequency. Qualitatively similar spectra were measured for all samples and were reminiscent of solid-like viscoelastic materials. The value
G0.1 of the storage modulus measured at 0.1 Hz can be used to quantitatively compare the elasticities of samples. Then a ramp in shear stress from 100 Pa to 2500 Pa was performed, with 20 stress values per decade. Each stress was applied during 10 s, whereas a shear viscosity was computed from the average of the shear rate data measured during the last second of applied stress. This test allows for the experimental determination of the dynamic yield stress
σy (also called shearing strength), which shows up as a stress plateau in the low shear rate regime (see
Figure 2d), while minimizing the occurrence of shear localization [
19]. The test also returns a shear viscosity
ηx for a range of measured shear rates
x, which match those encountered during SMT. 10 seconds stress loading was chosen, as the equipment can apply a steady controlled stress within a much shorter time, whereas a sufficient angular deflection or rotation can be detected by the optical encoder of the stress rheometer at smaller stresses. However, measurements within times as short as tens of milliseconds could not be performed to mimic the characteristic times of the stencil printing. Finally, the test performed in
Figure 2b was reproduced to measure the recovery of the sample after flow cessation in the stress ramp (see inset to
Figure 2d). The kinetics of such recovery,
tr, can be compared with the characteristic times
tl1 and
tl2.
To summarize this section, the protocol presented in
Figure 2 was adopted to rejuvenate samples and, thus, improved experimental reproducibility, while it opened the route to the determination of various viscoelastic properties under rheological conditions matching the rheology of SMT. These properties, namely,
G0.1,
σy,
ηx, and
tr, are known to be key rheological functions characterizing yield stress materials used in printing application [
19].
3.3. Rheological Results and Analysis
Figure 3 presents the mechanical spectra of the materials listed in
Table 1. The curves were vertically shifted by a factor
a to clarify the plot and offer a qualitative comparison of the spectra without overlapping of data points. These were all reminiscent of viscoelastic solids where the storage modulus
G’ was larger than the loss modulus
G’’ at lower frequencies, but both depended on the frequency.
The commercial solder paste showed a crossover between G’ and G’’ at a lower frequency fc than the crossover frequencies measured with all ECA. This indicated a solid behavior, which extended from long times up to relaxation times of 1 s (fc = 1 Hz for the commercial paste), in contrast to the ECA, which behaved as solids on a wider spectrum of relaxation processes, up to relaxation times of the order of 0.05 s. Note that no crossover was measured for the ECA that had the largest content in carbon conductive fillers, which suggested that this material was solid-like up to a characteristic relaxation time of the order of 10 milliseconds.
Values of
G0.1 are listed in
Table 3, whereas
Figure 4 shows its dependence with the total content of carbon nanoparticles. Errors reported for
G0.1 were computed from tests performed at 800 and 300 microns. They represented less than 10% of the value of the shear modulus, which is the accepted error range for rotational rheometry [
20].
The solid character in ECA builts on the elastic network of percolated SWCNT existing at SWCNT content as low as 0.2 wt.%. This is illustrated in the inset to
Figure 4, which shows the viscoelastic solid-like mechanical spectra of SWCNT suspended in epoxy. In addition,
fc in G2SW02 and G5SW02 were related to the SWCNT content, as their values were nearly similar to the crossover frequency showing up in the mechanical spectrum of the 0.2 wt.% SWCNT suspended in epoxy (see inset to
Figure 4). Essentially, the structural information conveyed by the mechanical spectra displayed in
Figure 3 and
Figure 4 was that the elastic network structure related to the SWCNT content. The elasticity of the hybrid network of GNP and SWCNT was not proportional to the total content of conductive carbon fillers (see
Figure 4). This result, together with the SWCNT network structure inferred from the mechanical spectra, suggested that the GNP reinforced the SWCNT network.
Coming back to the rheological benchmarking of ECA with the commercial solder paste, only the ECA formulated with the smallest amount of carbon nanoparticles showed a smaller
G0.1. This does not mean that this formulation was not stencil printable, as the literature does not detail the relationship between the paste elastic shear modulus and its printability [
4,
5,
13,
19]. However, as much as the SMT process was concerned, and assuming that all samples did not yield under the weight of electronic components, the lower
G0.1 of sample G2SW02 implied that the printed ECA deposit will deform more than the benchmark deposit during the conveying of the PCB from the pick-and-place machine to the reflow soldering oven.
The flow properties measured through the ramp in shear stresses are depicted in
Figure 5.
The flow curves exhibit a stress plateau at smaller shear rates before a monotonic increase in stress with larger shear rates. This behavior indicated a solid-to-liquid transition, which is characteristic of yield stress fluids. Sample G5SW02 showed a peculiar behavior, which can be described in three flow regimes. At large stresses, the flow curves measured with different sample thicknesses coincided and showed an onset for plateauing at smaller stress before exhibiting a kink. The kink showed up when a critical shear rate
was reached (see the vertical arrow in
Figure 5). At stresses below the kink, a second yield stress behavior was characterized, which strongly depended on the sample thickness. This thickness dependence and the three flow regimes are the hallmark of slip at the shearing wall–sample interface, which has been reported for various types of highly filled suspensions [
21]. The yield stress
σy of sample G5SW02 can, however, be computed by fitting the slip-free regime (for shear rates in excess of
) to the Herschel–Bulkley equation, which reads:
where
K is the flow consistency and
n the shear thinning exponent. Fits of Equation (1) to the high-stress regime of G5SW02 data are presented in
Figure 5, together with the fits to other flow curves. The computed yield stresses
σy are reported in
Table 3 with the error bars resulting from the quality of the fit. Note that the latter are as big as the standard error computed from the two tests performed at different sample thicknesses, which validated the bulk flow of material in the high-stress regime.
Sample G5SW05 showed a thickness-dependent, non-linear rheology, which again suggested that slip occurred below and above yielding. This was expected, as slip velocity was found to depend linearly on the suspension shear modulus [
22]. Thus, the more elastic ECA formulated with more SWCNT slipped more than sample G5SW02. However, a slipping yield stress was computed from the fit of Equation (1) to the data measured with a sample thickness of 800 microns.
Whereas shear rates as large as 1000 s
−1 could be measured with the ECA formulated with the lower content in carbon nanoparticles, shear fracture did impede the proper rheological characterization of the remaining samples at shear rates in excess of 400 s
−1 (see
Figure 5). Therefore, the fits of Equation (1) to the data displayed in
Figure 5 were used to compute the shear viscosities
at shear rates
x relevant to the SMT process. The computed
ηx are listed in
Table 3 with the corresponding errors estimated as for
σy. Overall, data in
Table 3 confirmed the rheological message conveyed by
Figure 5: The ECA formulated with 2 wt.% GNP and 0.5 wt.% SWCNT showed the flow behavior that best matched the commercial solder paste rheology at lower shear rates. The yield stresses reported in
Table 3 are smaller than the stresses involved during the placement of electronic components. This implies the flow of all materials listed in
Table 3 during this step of the SMT process. ECA made of more than 5 wt.% carbon nanofillers exhibited high shear viscosities, which matched the high shear viscosity of the commercial solder paste. As such, ECA with more than 5 wt.% carbon could also be good candidates for SMT, in particular if one considers that wall slip will compensate the large viscosity measured at shear rates corresponding to the stencil–PCB separation. A dedicated study of slip effects at gaps relevant for this part of the process could help clarify the applicability of G5SW02 and G5SW05 to the SMT.
We are now left with the quantification of the recovery of the materials after flow cessation.
Figure 6 presents the results from the recovery experiments performed after the pre-shear of 0.5 s
−1 and after the largest stress imposed during the ramp in stress.
The time evolution of the storage modulus
G’ is only reported in
Figure 6 as all samples showed
G’ >
G’’ already for the first data point collected at 10 s after flow cessation. This indicates that all ECA recovered a solid-like behavior within 10 s, which matched the time scale of the commercial solder paste. Results from tests carried out at different sample thicknesses are also reported in
Figure 6a to show the satisfactory reproducibility of the recovery data. This confirms that the first step of the rheological protocol was efficient in erasing any flow history induced by the loading of samples in the rheometer. The recovery of the samples was fitted with an exponential growth function, and the resulting relaxation times
tr are reported in
Table 3. Note here that the errors reported for
tr measured at lower shear rates were computed from the statistical analysis of the duplicated tests reported in
Figure 6a. These errors were of the same magnitude as the fitting errors (compared with those reported for
tr computed at larger shear rates), which again underlines the satisfactory reproducibility of relaxation data after imposing a small shear rate of 0.5 s
−1. Overall, all ECA showed a recovery time at lower shear rates, which matched
tr measured for the commercial solder paste. The relaxation times measured at larger shear rates were significantly larger. This was expected because, in highly filled colloidal suspensions, the recovery is known to strongly depend on the flow-induced structure achieved prior to flow cessation [
16], as it connects to the thixotropic restructuring time [
19]. The longer restructuring relates to the larger structural break-up achieved under flow. The values reported for
tr in the last column of
Table 3 for the ECA were of the same magnitude as for the commercial paste, whereas the latter was submitted to smaller shear rates during the ramping of stresses (see
Figure 5). Therefore, all formulated ECA should comply with the structural recovery necessary after stencil printing and before the placement of electronic components. Note also that all times reported in
Table 3 are faster than the processing times
tl1 and
tl2, which confirms the ECAs’ compliance with the process in terms of structural recovery.
Table 3 summarizes the rheological analysis performed here. Sample G2SW02 showed the worst rheological benchmarking with the commercial solder. Sample G5SW05, though showing a significantly larger elastic modulus, showed flow properties (yield stress and shear thinning) that were closely matching the flow behavior of the commercial paste. However, the underlying slip phenomena need to be further assessed before concluding on the ability of G5SW05 to be processed with the present SMT. The two remaining ECA exhibited a rheology that either nicely matched the commercial paste rheology (G2SW05) or was adequate to the rheology of the SMT process.
3.4. Electrical and Thermal Characterizations
Electrical characterization was performed for all hybrid formulations and additionally for two composites without GNP but with the same composition of SWCNT, 0.2 and 0.5 wt.%. Electrical resistivity and electrical conductivity results are presented in
Table 4. The electrical conductivity of the composites with both SWCNT concentrations presented an increase in the electrical conductivity upon addition of GNP. While the composites with 0.2 wt.% SWCNT showed a marginal increase in electrical conductivity that increased with GNP composition, the composite with 0.5 wt.% SWCNT presented a larger increase of the electrical conductivity when GNP was added, however, remaining almost invariant with GNP amount.
Figure 7 presents the DSC curves of the composite G2SW05 obtained at the heating rates of 10 °C.min
−1 (to measure the cure enthalpy) and 60 °C.min
−1 (designed to reproduce the thermal profile of the reflow oven). Both curves showed an exothermic peak that occurred around 150 °C for the scan at 10 °C.min
−1, and 190 °C for the scan at 60 °C.min
−1. The second scan at 10 °C.min
−1, carried out on the sample that was first heated at 60 °C.min
−1, showed that the composite was fully cured under the conditions of the first heating step. This curve depicted the glass transition (≈100 °C) of the ECA cured at a heating rate of 60 °C.min
−1.
Table 5 and
Table 6 present the results of the thermal characterization of all the ECA prepared and the neat epoxy resin. The results obtained for the cure analysis are shown in
Table 5, reporting the thermal characteristics of the cure measured on the DSC scans performed at 10 °C.min
−1. The curves obtained were similar for all the composites.
Table 5 shows that the peak temperature and the enthalpy of the cure reaction were not significantly changed by the presence of the carbon nanomaterials while the onset temperature was slightly shifted upwards by approximately 6%.
The results obtained for the scans at 60 °C.min
−1, presented in
Table 6, also depicted a similar peak temperature for the composites and neat resin and an upshift of the composites’ onset temperature. Isothermal tests at 150 °C presented a cure peak at 2.1 min for the neat resin and 2.3 to 2.4 min for the ECA.