# Investigating the Reliability and Dynamic Response of Fully 3D-Printed Thermistors
## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**PC Substrate**} \\ \hline
**Property** & Specific gravity & Melt mass-flow rate & Glass transition & Heat deflection \\
**Unit** & g/cm\({}^{3}\) & g/min & \({}^{\circ}\)C & \({}^{\circ}\)C \\
**Value** & 1.18–1.20 & 2.30–2.60 & 107.70 & 104.50 \(\pm\) 0.70 \\ \hline  & \multicolumn{4}{c}{**Ag electrode**} \\ \hline
**Property** & Viscosity & Sheet resistance & Specific gravity & Solid content \\
**Unit** & Pa.s & m\(\Omega\)/sq & g/cm\({}^{3}\) & \% \\
**Value** & 7.00–10.00 & 25.00–85.00 & 1.996 & 55.69–57.69 \\ \hline  & \multicolumn{4}{c}{**PEDOT:PSS layer**} \\ \hline
**Property** & Viscosity & Resistance & Concentration & Appearance \\
**Unit** & Pa.s & \(\Omega\)/sq & \% & Color \\
**Value** & \(\geq\)50.00 & \(\leq\)130.00 & 5.00 wt & Dark to very dark \\  & & & blue and black \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Technical details of PC, Ag, and PEDOT:PSS materials. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Unit** & **PC Substrate** & **Ag Electrode** & **PEDOT:PSS Layer** \\ \hline
**Thickness** & [\(\mu\)m] & 500 & 50 & 50 \\
**Layer thickness** & [mm] & 0.05 & 0.05 & 0.05 \\
**Nozzle diameter** & [mm] & 0.4 & 0.2 & 0.2 \\
**Dispensing width** & [mm] & 0.04 & 0.15 & 0.15 \\
**Print speed** & [mm/s] & 20 & 30 & 25 \\
**Nozzle temperature** & [\({}^{\circ}\)C] & 275 & - & - \\
**Curing temperature** & [\({}^{\circ}\)C] & - & 100 (for 2 h) & 80 (for 1 h) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Manufacturing parameters of thermistor layers. the measurement capability of the manufactured thermistors [39]. Therefore, data collected during both the heating and cooling phases were employed to determine the \(\beta\) values using Equation (1):  
\[\beta=\frac{\ln\left(\frac{\mathrm{R_{1}}}{\mathrm{R_{0}}}\right)}{\left(\frac{ \mathrm{1}}{\mathrm{T_{1}}}-\frac{\mathrm{1}}{\mathrm{T_{0}}}\right)}, \tag{1}\]  
where  
R\({}_{1}\): the resistance at the peak temperature,  
R\({}_{0}\): the resistance at the base temperature,  
T\({}_{1}\): the peak temperature (K),  
T\({}_{0}\): the base temperature (K). To reflect the variation in \(\beta\) values across consecutive temperature points and provide insight into the stability of the thermistor's performance over the measured temperature range, the calculated \(\beta\) values were used to evaluate the consistency of the thermistor's response to temperature changes. For this, the percentage error between the \(\beta\) value measured at a given temperature and the \(\beta\) value measured at the previous temperature was calculated using Equation (2):  
\[\%\mathrm{Error}=\frac{\left|\beta_{\mathrm{i}}-\beta_{\mathrm{i-1}}\right|} {\beta_{\mathrm{i-1}}}\times 100\%, \tag{2}\]  
where \(\beta_{\mathrm{i}}\) is the \(\beta\) value calculated at the current temperature step, and \(\beta_{\mathrm{i-1}}\) is the \(\beta\) value calculated at the previous temperature step. Dynamic response measurements were performed in triplicate using a Model DI-145 data acquisition kit (DATAQ(r) Instruments Inc., Akron, OH, USA) to capture the instantaneous resistance changes in the thermistors in response to temperature fluctuations. For this purpose, an electrical circuit, as illustrated in Figure 2, was created. The voltage across the thermistors, reflecting resistance variations with temperature, was recorded using the DATAQ hardware manager software. The recorded data were then exported to an Excel spreadsheet, where resistance changes were calculated based on Ohm's Law. As the PEDOT:PSS sensing layer directly contacts both the PC substrate and Ag contact electrode pair, its mechanical reliability was evaluated by dispensing a square PEDOT:PSS (20 mm \(\times\) 20 mm, 50 \(\upmu\)m thick) film on the PC substrate and on a square Ag film (25 mm \(\times\) 25 mm, 50 \(\upmu\)m thick) that was deposited onto a different PC substrate. A  
Figure 2: **(a)** Schematic of the dynamic performance measurement circuit and (**b**) the experimental test setup.