Time-resolved study of variable frequency microwave processing of silver nanoparticles printed onto plastic substrates

An ink (Suntronic U5714, SunChemical) containing 40 wt% of AgNPs with the particle diameter ranging from 20 to 50 nm was used for preparing 1 cm × 1 cm square patterns (figure 1). The exact composition of the ink is considered proprietary by the manufacturer, nevertheless based on available data it is believed that the AgNPs were encapsulated with a polymer and dispersed in a mix of polar solvents composed of ethanol, ethylene glycol, and glycerol. Printing was performed in a drop-on-demand inkjet printer (DMP-2800, Fujifilm Dimatix). Depending on the experiment, the ink was deposited onto one of two different types of transparent PET substrates. The first one was a glossy thermostabilized, a 125 μm thick PET (Lumirror^® 60.28, Toray). The second one was a 140 μm thick PET, with an ink-receptive mesoporous coating (Novele IJ-220, Novacentrix). This ink-receptive layer quickly absorbs the solvents and an initial electrical conductivity of printed patterns can be achieved without any drying process. Although the electrical conductivity of these prepared patterns was very low, by omitting the drying step, total processing time can be significantly reduced. Nevertheless, in order to improve the conductivity of the printed samples, a sintering was still required.

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All the experiments were carried out in a microwave multimode cavity (Microcure 2100, Lambda Technologies). The cavity was connected via rectangular C-band waveguide to a variable frequency generator. The generator was set to operate at a central frequency of 6.425 GHz with a sweeping bandwidth of 1.15 GHz. The sweep time was set to 1.25 s, and the applied power was tuned from 10 to 500 W for specific items. The microwave processing of the printed patterns was in situ monitored with the use of CCD camera (TM-4200GE, JAI) and specifically developed pyrometer. The camera and the pyrometer were located outside the cavity and were pointed at the sample through a microwave choke that was carefully designed in order to avoid the microwave leakage outside the cavity. Illustration of the experimental setup is presented in figure 2.

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2.3.1. Principles of the radiometric temperature measurement

The principle of operation of the radiometer-pyrometer sensors has already been extensively described in details in the past [16, 17]. In short, typical pyrometers are equipped in a narrow band photodiode (PD) embedded with an amplifier circuit. These PDs generate photocurrent (I) proportional to the intensity of thermal radiation emitted by an investigated object in the narrow spectral band corresponding to its spectral response with maximal sensitivity wavelength according to the modified Planck's formula (equation (1)).

$$\begin{eqnarray}&&I=\epsilon \cdot K\cdot \displaystyle \frac{C1}{{\lambda }^{5}}\cdot {\rm{\exp }}\left(-\displaystyle \frac{C2}{T\lambda }\right)=\epsilon \cdot B\cdot {\rm{\exp }}\left(-\displaystyle \frac{A}{T}\right),\end{eqnarray} \tag{ 1 }$$

where $A=\tfrac{C2}{\lambda }$, $B=K\cdot \tfrac{C1}{{\lambda }^{5}}$,

• I—photocurrent (nA) (registered by the photodiode),
• C1 and C2—radiation constants in the Planck's law ($\mu {\rm{m}}\,{\rm{K}}$),
• K—factor defined by the specific electronic circuit and the optical scheme,
• —emissivity of an object,
• λ—maximal sensitivity wavelength of a specific photodiode ($\mu {\rm{m}}$),
• T—temperature (K).

After an appropriate transformation, the equation (1) can be solved with regard to temperature as follows:

$$\begin{eqnarray}&&T=\displaystyle \frac{A}{{\rm{ln}}(B)+{\rm{ln}}(\epsilon )-{\rm{ln}}(I)}.\end{eqnarray} \tag{ 2 }$$

Although the above equation converts simply and accurately the measured photocurrent to temperature, it assumes that the emissivity value is known. In practice, the emissivity varies with the temperature and with the sample surface properties, e.g. roughness changes during the sintering. Owing to the emissivity variations the two-color pyrometers are frequently used. In contrast to the monochromatic sensors, the two-color pyrometers are equipped in two photodiodes that permit to measure the temperature independent of the emissivity changes. The ratio of the photocurrents generated by the two PDs at wavelengths ${\lambda }_{1}$ and ${\lambda }_{2}$ is converted to the temperature according to equation (3). Reliable temperature measurements with the use of bichromatic pyrometers state that the emissivity variations have to be the same for both wavelengths, i.e. the ratio between the emissivities variations has to be constant across the entire temperature measuring period according to equation (3).

$$\begin{eqnarray}T & = & \displaystyle \frac{\tfrac{C2}{{\rm{\Lambda }}}}{5\cdot {\rm{ln}}\left(\tfrac{{\lambda }_{1}}{{\lambda }_{2}}\right)+{\rm{ln}}\left(\tfrac{{K}_{2}}{{K}_{1}}\right)+{\rm{ln}}\left(\tfrac{{\epsilon }_{2}}{{\epsilon }_{1}}\right)-{\rm{ln}}\left(\tfrac{{I}_{2}}{{I}_{1}}\right)}\\ & = & \displaystyle \frac{{A}_{0}}{{\rm{ln}}({B}_{0})+{\rm{ln}}\left(\tfrac{{\epsilon }_{2}}{{\epsilon }_{1}}\right)-{\rm{ln}}\left(\tfrac{{I}_{2}}{{I}_{1}}\right)},\end{eqnarray} \tag{ 3 }$$

where $\tfrac{1}{{\rm{\Lambda }}}=\tfrac{1}{{\lambda }_{2}}-\tfrac{1}{{\lambda }_{1}}$, (${\lambda }_{1}$ and ${\lambda }_{2}$ correspond to specific wavelengths of different photodiodes in the pyrometer),

${A}_{0}=\tfrac{C2}{{\rm{\Lambda }}}$,

${B}_{0}=\tfrac{{B}_{2}}{{B}_{1}}$, (B₁ and B₂ are B in the equation (1) with corresponding factors related to channels '1' and '2' of the pyrometer).

2.3.2. Description of the bichromatic pyrometer developed

The optical schematic of the pyrometer was designed in such a way that the thermal radiation emitted by the investigated sample was registered at a circular spot that has 1 cm in diameter. The temperature was calculated on the basis of the thermal radiation energy measured on that spot. Illustration and an optical schematic of the pyrometer are shown in figure 3. The thermal radiation from the sample is focused by a sapphire lens (diameter D = 25.4 mm, focal length F = 50.8 mm, Edmund Optics) on a silicon beam splitter (400 μm thick silicon plane mirror set at an angle of 45°). The beam splitter divides the radiation coming from the object with a ratio of about 1:1.5. After the signal division, two photodiodes (PD42Su, ${\lambda }_{1}$ = 4.15 ± 0.2 μm and PD34Su, ${\lambda }_{2}$ = 3.25 ± 0.15 μm, IoffeLED, Ltd.) were used to collect the thermal radiation. The greater part of the registered radiation is directed to the PD42Su photodiode that produced about 1.5–2 times greater electrical noise. Thus, the accuracy signal-to-noise ratio (SNR) for both PDs is almost the same.

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The selection of the PDs follows from the fact that for the radiometric-pyrometric measurements the largest responsivity to the temperature changes can be achieved with the wavelength-temperature product (λT) close to about 1500 (μm K). This relation applied to low-temperature pyrometry (below 400 °C) defines optimal wavelengths to be in the middle infrared (mid-IR) spectral range (λ = 2–5 μm). Note that the selection of the PDs wavelengths ${\lambda }_{1}$ and ${\lambda }_{2}$ should be chosen far apart in order to minimize the error in the temperature measurements that is related to the variation of emissivities (${\epsilon }_{1}$ and ${\epsilon }_{2}$ in equation (3)). However, the detectivity (D*) and the SNR must be also maximized for better accuracy. Finally, the desorption of gaseous species like hydrocarbons during the heating has to be taken into account. They may alter the measured signal because of a partial light absorption. The specific parameters of the selected immersion lens PDs, as well as an example of measuring error, has already been described by Sotnikova et al [17].

To ensure thermal stability of the PDs, each of them was mounted on a thermoelectric cooling module. The temperature was stabilized at 20 ± 2 °C. The photocurrents from PDs were amplified with a transfer coefficient $\kappa =5\times {10}^{5}\,({\rm{V}}\,{{\rm{A}}}^{-{\rm{1}}})$ and transferred to a two-channel 12 bit analog-digital converter (ADC) operating at a fixed frequency of 30 KHz (sampling rate of about 30 kS s⁻¹), which provides high-speed data acquisition, suitable for monitoring of fast microwave heating processes. Digital data corresponding to both channels of the pyrometer were real-time transferred with an Ethernet cable to the PC for further calculations. The housing of the pyrometer was equipped with a laser pointer in order to facilitate positioning of the sample with the area scanned by the pyrometer. During the temperature measurements, a geometrical center of the printed pattern (1 cm × 1 cm) was superposed with the center of the pyrometer's measuring spot.

2.3.3. Calibration of the pyrometer

The both channels of the two-color pyrometer were calibrated with a black body (BB) (BB703, OMEGA). The temperature of the heat source was increased with a constant rate of 1 °C min⁻¹. The measured values of photocurrents and the temperature of the BB calibrator were registered simultaneously. The calibration curves presented in figure 4 match the BB model (fitted based on the equation (1) with = 0.95) from about 70 °C. It defines the lower limit for the temperature measurements. The highest temperature that can be measured by our pyrometer was about 350 °C. At that temperature, the thermal radiation of the heat source ( = 0.95) causes saturation of signal measured by the PD sensitive at λ = 3.25 μm. This signal saturation is related to the resolution of the ADC (12 bit). An extension of the upper-temperature limit would be possible if higher resolution ADC is implemented. The developed two-color pyrometer was intended to be used for real-time temperature monitoring of samples printed on various plastic substrates that are usually heat-sensitive and thus the operating temperature range was sufficient.

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The ability of polar solvents to heat under microwaves is characterized by the loss tangent (tan δ) defined by equation (4). For efficient microwave heating, a moderate value for ${\varepsilon }^{{\prime} }$ should be combined with the high value of ${\varepsilon }^{{\prime\prime} }$.

$$\begin{eqnarray}&&{\rm{\tan }}\,\delta =\displaystyle \frac{{\varepsilon }^{{\prime\prime} }}{{\varepsilon }^{{\prime} }},\end{eqnarray} \tag{ 4 }$$

where ${\varepsilon }^{{\prime} }$—real permittivity characterizing the penetration of microwaves into the material, ${\varepsilon }^{{\prime\prime} }$—loss factor indicating the material's ability to store the energy.

A vector network analyzer equipped with a dielectric probe kit (85070E, Agilent) was used to measure ${\varepsilon }^{{\prime} }$ and ${\varepsilon }^{{\prime\prime} }$ of the materials investigated. Silver ink as well as a blend of solvents (mainly ethylene glycol, ethanol, and glycerol) with the same chemical composition as the ink but without the AgNPs, were analyzed under various temperatures and frequencies.

During the measurements, test-tubes were filled with about 1 ml of each of these materials, so that the volume was enough to immerse the test probe. The loss tangent of distilled water was additionally measured and demonstrated as a reference to the analyzed materials.

The frequency-dependent loss tangent (tan δ) analysis at 25 °C, 80 °C, and 125 °C, is presented in figure 5. The results exhibit no significant differences between the ink and the blend of solvents. At room temperature, both mixtures reach maximum tan δ values at a frequency (f_max) of about 2.45 GHz. The increase in the temperature causes a shift in f_max toward higher frequencies. This phenomenon has been already reported by Lou et al [18, 19] and was ascribed to decrease in solvent viscosity at higher temperatures.

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The similar changes of the loss tangent for the both analyzed mixtures indicates a negligible impact of AgNPs on the microwave absorption and thus the microwave heating. The values of the tan δ are mainly related to the dielectric properties of the polar solvents mixture. Within the operating frequency range of the microwave generator (5.85–7 GHz), the loss tangent at three different temperatures exhibits a relatively high value of about 0.8 and confirms the ability of the ink to high microwave absorption.

Microwave heating of a printed silver square pattern on the glossy PET substrate is demonstrated in figure 6. The progress in solvent evaporation was in situ monitored by using the CCD camera. Although the applied power was relatively high (300 W), about 100 s were needed to observe the onset of solvent evaporation (figure 6(B)). This is because the volume of the inkjet-printed ink layer was very small, and thus the heating efficiency was limited. The total dissipated power per unit volume of a sample related to the heating can be described by the equation (5):

$$\begin{eqnarray}&&P=\displaystyle \frac{1}{2}\sigma | E{| }^{2}+\pi f{\varepsilon }_{0}{\varepsilon }_{r}^{{\prime\prime} }| E{| }^{2}+\pi f{\mu }_{0}{\mu }_{r}^{{\prime\prime} }| H{| }^{2},\end{eqnarray} \tag{ 5 }$$

where P is the power dissipation (W cm⁻³), σ is electrical conductivity (S m⁻¹), E and H are amplitudes of the electric field (V m⁻¹) and magnetic field (H m⁻¹), respectively, f is frequency, ${\varepsilon }_{0}$, ${\varepsilon }_{r}^{{\prime\prime} }$, ${\mu }_{0}$, ${\mu }_{r}^{{\prime\prime} }$ are permittivity of vacuum, relative dielectric loss, permeability of vacuum, relative magnetic loss, respectively. According to this equation, for thin film samples characterized by low electrical conductivity, heat can be efficiently generated if sufficient power is employed. Because the ink is relatively poor electrical conductor interactions with the magnetic field are negligible and thus the last term of the equation can be omitted at the initial stage of heating. It becomes significant once the solvent is evaporated.

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At the beginning of the MW irradiation, we noticed that the solvent evaporation process takes place preferentially at the thinner edges. While the evaporation starts on the sides, the nanoparticles previously separated in the ink are spontaneously brought into contact. Locally, a newly formed layer of AgNPs appears. This layer is electrically conductive and thus began to dissipate the microwave energy more efficiently than the liquid solvents. The energy absorbed by the conducting layer increases as the conductivity augments, causing a subsequent rise in the temperature [20]. The solvents evaporate progressively, until a point (conductivity) is reached where the trend reverses and the microwave field energy is mainly reflected [20, 21]. An illustration of silver nanoparticles at diverse stages of the microwave processing is demonstrated in figure 7. We observed that when the silver layer on the edges forms a closed loop around the central part of the sample (remaining still liquid), a sudden acceleration in the evaporation takes place (figure 6(C)). The closed metal loop is subject to excessive heat generation, few milliseconds after being formed. This effect is probably caused by Joule heating related to the induced eddy currents that occur in conductors under an alternating magnetic field. This spatial non-uniformity of electromagnetic field distribution within the sample (between the metallic edges and the still liquid areas) is liable to cause excessive temperature gradients with localized hot spots. Therefore, the generated thermal stress leads to significant deformation, cracks and even local melting spots in the sample (figures 6(D)–(F)).

Consequently, the direct microwave sintering of silver nanoparticles from colloid ink becomes challenging. In practice, a feedback control system has to be developed where the forward power level can be automatically dropped down as the sample's temperature suddenly surges. Nevertheless, the non-uniform spatial heating makes it difficult to measure the overall temperature accurately. Another possibility for the microwave curing process is to use a so-called susceptor that may dissipate the microwave field energy. Although the susceptors are typically made of materials that absorb the microwave energy very efficiently, like silicon-based materials, usually, they cause excessive heat generation. For this reason, susceptors are not suitable for use in the proximity of the heat-sensitive plastic substrates. The damages and large sample's deformation seem to be inevitable in the present configuration of the microwave heating system. Alternatively, the printed patterns can be dried prior to the sintering process or an ink-receptive substrate that quickly absorbs the solvents can be used.

To overcome the problem related to the sudden and non-uniform overheating of the silver ink and the resultant deformations, a PET substrate with an ink-receptive mesoporous coating was used. The exact composition and relevant information on the PET coating material are kept confidential by the manufacturer. However, based on the data available, its composition is believed to contain some acidic or anionic coating that facilitates the detachment of the organic layer surrounding the nanoparticles. Moreover, Kang et al [12] analyzed this porous layer using SEM which reveals pore size of about 22 nm. Thanks to the porosity, the solvents were absorbed almost immediately resulting in a low-conductivity metallic thin film without any thermal treatment. The dry thin metallic film had relatively high resistivity of about 4000 $\mu {\rm{\Omega }}$ cm and its processing was still required in order to improve the electrical conductivity.

Now we thoroughly detail how the microwave irradiation parameters relate to the thermal response of the metal films and impact their final conductivity. During the processing, the samples were in situ monitored by using the experimental setup described in figure 2. Figure 8 demonstrates a set of data registered during each experiment of the microwave heating. For a given applied power, a thermal response of the printed pattern was registered as an evolution of photocurrents at the two wavelengths of the photodiodes. The temperature was real-time and automatically calculated using equation (3) with a relative emissivity ratio set to 1.

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First, in order to check for reproducibility of the thermal response of the samples under the microwave exposure, the processing time was varied at two fixed power levels (200 and 300 W). The resulting thermal profiles are shown in figure 9. We noticed almost identical trajectory of the collected results what indicates on high repeatability of the microwave heating process. Next, the samples were investigated at five different power levels ranging from 100 to 500 W (figure 10). At the very beginning of the microwave irradiation and for all samples, we observed very fast heating rates (over 100 °C s⁻¹) up to certain temperature levels depending on the power selected. The as-printed layer made of silver nanoparticles exhibits low electrical conductivity which leads to strong microwaves absorption. This results in a significantly increased Joule heating by the concomitant of loss current by free charge carrier in the material under E field and eddy current induced by the alternating H field (see equation (5)). Ma et al [15] suggested that the strong microwave absorption by copper powder compact is attributed to the ohmic heating by the skin effect as the size of microparticles is much smaller than the skin depth. In the present study, the skin depth was in the micro-scale which is far greater than the mean diameter of AgNPs.

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Micro-focusing effect by E and H field occurring in small particles can also be responsible for the considerable heating rate at the initial stage [22]. This effect describes the intensification of the externally applied field in the neck region between two touching particles, resulting in a large absorbed energy at the interface between these particles.

As the temperature increases rapidly, the film undergoes microstructural evolution since sintering process promotes inter-particle neck growth and lead to improvement in the electrical conductivity upon a certain limit. At this step, the induced E field magnitude decreases in the film resulting in a reduction of the absorbed power density from the electric field. On the other hand, the eddy current density related to ohmic heating, expressed as $J=\sigma \cdot E$ (where E is the electric field induced H field and σ is the electrical conductivity), is enhanced with increasing the electrical conductivity. Thus, the ohmic loss by eddy current became dominant heating mechanism. The heating rate is slowed down at this second stage of heating as the electric field is reflected by the film. With the improvement in electrical conductivity of the silver film its thermal conductivity increases. It leads to thermal losses of the generated heat to the surrounding environment. Therefore, for the applied power below certain level (in this work about 300 W) heat generation is compensated by thermal energy losses and in spite of continuous irradiation the temperature slowly decreases.

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Final resistivities of the patterns were measured using van der Pauw method [23], the results are shown in figure 11. We observed that the most significant improvement in the electrical conductivity occurs at the very beginning of the irradiation. This is in accordance with the fast heating rates that occur at the first stage of the microwave processing. The resistivity decreases significantly with applied power and then tends to stabilize regardless the irradiation time. Analysis of film microstructures by SEM reveals no significant differences between the samples heated at various power as no evident grain growth was observed (figure 11). The improvement in the electrical conductivity is mainly due to inter-particles neck growth during the initial short microwave heating periods, which is probably assisted by the micro-focusing effect as discussed above.

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The stabilization of resistivity is in accordance with the establishment of film microstructures. This confirms that the second heating stage observed for powers above 200 W does not imply significant film modification. The lowest measured resistivity of 30 $\mu {\rm{\Omega }}$ cm was obtained at 500 W in less than 5 s, which is 18 times higher than that of the bulk resistivity of silver. Increasing the irradiation time at 500 W improves the electrical conductivity of samples, however their thermomechanical deformations have been visually observed.