*3.3. In Situ Rheological Characterization of WO3 Gelation Process*

A detailed insight into the progress of the rheological properties of WO3 sols during gelation process was obtained with in situ oscillatory test in the linear viscoelastic range at deformation so small that no destruction of the structure could occur. For inkjet printing we used material deposit system—Dimatix Materials Printer DMP2800 [20]. It enables temperature modulation of printer vacuum plates (up to 60 ◦C) and cartridge temperature (up to 70 ◦C), which should be tailored for each material or ink. For inkjet printing of the sol-gel WO3 ink the most optimal temperature of printer plates was 35 ◦C, which warmed ink in cartridge up to 26 ◦C. Moreover, to predict stability of inkjet process we studied temperature dependence of the WO3 sol-gel characteristics. In situ oscillatory test in the linear viscoelastic range was used for 5 different temperatures: 20 ◦C, 30 ◦C, 40 ◦C, 50 ◦C and 60 ◦C, respectively. The progress of viscoelastic properties, i.e., elastic G and viscous modulus G, during gelation process of WO3 sol was similar, especially for the temperatures from 30 ◦C to 60 ◦C (Figure 7a). Initial sols exhibited "liquid-like" behavior with low consistency and only viscous contribution G detected. As the gelation process started the loss modulus G commenced to increase continuously, while the storage modulus G suddenly appeared after a certain time and rose sharply until it intersected and exceeded the loss modulus G. The time at which the both moduli reached the same value indicated the sol to gel transition point, which is often referred to as a "gel-point" [34]. From this point onward, the elastic behavior G dominated and the behavior of the sample became "solid-like". Both moduli leveled off as the reaction came to completion; moreover, at the end of gelation the viscous modulus was too low to be detected. As a result, the formed gel became brittle without any viscous effects. The gels, formed at 30 ◦C to 60 ◦C exhibited similar values of G and G at the end of sol-gel process, while the gel, formed at 20 ◦C exhibited softer gel structure with lower values of G and G; moreover, the values of G were not negligible. We can conclude that the gelation time depended strongly on the temperature, to which the sol was exposed. Higher temperature leaded to faster gelation process, i.e., for the sol, which was exposed to 60 ◦C (Figure 7a), the gel formed after ~0.55 h, while the transition from sol to gel at 20 ◦C was observed not earlier as after

~10 h (Figure 7b). The final values of G were for the gels, formed at temperatures from 30 ◦to 60 ◦C in the range of 3000 Pa, while G was negligible. On the other hand, the gel, formed at 20 ◦C exhibited the G below 1000 Pa, while the G was in the range of 100 Pa.

**Figure 7.** Dependence of dynamic moduli G and G on time of the WO3 gelation process at different temperatures: (**a**) 30 ◦C, 40 ◦C, 50 ◦C and (**b**) 20 ◦C. The tests were performed in linear viscoelastic range. Solid symbols represent viscous modulus G", hollow symbols represent elastic modulus G'.

To evaluate different parameters, important for the sol-gel process, the experimental asymmetric dependences of phase shift angle δ on the time of gelation could be the best fitted with five-parameter logistic function [35]:

$$\delta = \delta\_1 - \frac{\left(\delta\_1 - \delta\_2\right)}{\left(1 + \left(\frac{t}{t\_\mathcal{I}}\right)^{-W}\right)^s} \tag{2}$$

where *δ*<sup>1</sup> and *δ*<sup>2</sup> are the highest (initial) and the lowest (the end) values of phase shift angle, respectively, *tg* is the time of sol-gel transition, while *s* jointly with *W* controls the rate of approach to the *δ*<sup>2</sup> asymptote. The values of the five parameters, obtained by fitting the experimental data are presented in Table 1, while the experimental data of phase shift angle *δ* and calculated values obtained with the above equation are presented in Figure 8. The results show excellent agreement of the experimental data with the predicted values for all five temperatures, used in the presented study. The five-parameter logistic model enabled the exact determination of the time at which sol to gel transition occurs (*tg*) together with precise viscoelastic properties of formed gels (*δmin*). Moreover, the model can be used for accurate prediction of total rate and time of sol-gel process (*W*, *s*).


**Table 1.** The parameters of the five-parameter logistic model (Equation (1)) for the gelation process at different temperatures.

Gelation times (*tg*), determined from the Equation (1) are organized as a dependence of the temperature (Table 1), to which the initial sol was exposed. The dependence (Figure 9) is very good fitted with the exponential function, which shows that the time of gelation exponentially decreased with increasing temperature of the gelation process.

**Figure 8.** Changing of phase angle d with time of gelation process at different temperatures. Dependence of dynamic moduli G and G on time of the WO3 gelation at different temperatures.

**Figure 9.** Dependence of gelation time on temperature of the gelation process of the WO3 ink.
