*3.4. Ex-Situ Rheological Characterization of WO3 Gelation Process*

In addition to the in-situ rheological characterization the ex-situ rheological tests were performed for the sol, exposed to the room temperature for several days. Moreover, we followed the sol stability, prepared with different solvents (ethanol, isopropanol and a mixture of isopropanol and 2-propoxy ethanol) stored in a 100 mL glass bottle in the refrigerator. Our observation was that sol-gel transition occurs in 22 days, when using the mixture of isopropanol and 2-propoxy ethanol, 6 months, when using isopropanol and 10 months when using ethanol. It should be noted here that the transition from sol to gel in the bulk of the beaker (sample volume ~100 mL) occurred much later compared to the transition, which occurred in the sensor system of the rheometer and inkjet cartridge content, where the whole volume of the sample was considerably lower (cca 1.6 mL). The stability of the sols could be significantly prolonged by keeping the inks at lower temperature, for example when kept in freezer (below −15 ◦C) the sols remain stable over 1 year.

In the ex-situ characterization various rheological tests were performed under destructive and non-destructive shear conditions. First, the flow behavior was followed with flow tests under destructive shear conditions (Figure 10). One day after the sol preparation, the sol (Figure 10, initial) exhibited Newtonian flow behavior with constant viscosity of 0.0054 Pa.s (at T = 23 ◦C). 14 days after the preparation the sol maintained the Newtonian character, while the value of the viscosity slightly increased to 0.0065 Pa.s (at T = 23 ◦C). Higher increase of the viscosity and the first deviation from Newtonian flow behavior was observed on the 21st day after the preparation. The next day (22nd day) the viscosity again slightly increased with similar flow behavior, while 24th day after the preparation the flow behavior of the solution significantly changed to pronounced shear thinning flow behavior, where the viscosity decreased for almost three decades as the shear rate increased from 0.1 to 1000 s−1. A constant decreasing of the viscosity curve from the low to the high shear rates indicates that these solutions showed some structure stability at rest [34], while hysteresis loop during the decreasing of the shear rate towards initial value (0.1 s<sup>−</sup>1) indicates time-dependent flow properties during structure recovery.

**Figure 10.** Flow curves (the dependence of viscosity on shear rate) for WO3 sols at T = 23 ◦C.

The rheological properties of WO3 sols were, at different times during the gelation process, followed also with non-destructive oscillation tests in the range of linear viscoelastic response (Figure 11). At the beginning, immediately after the preparation, the sol exhibited Newtonian flow behavior as only viscous contribution G was present, which linearly increased with the frequency of oscillation. As it was observed during flow tests, at 21st day some changes were observed also with frequency tests. Newtonian character of the sol changes to viscoelastic liquid as the dynamic storage modulus G occurred with lower values compared to the loss modulus G; moreover, the moduli exhibited similar, linear dependences with frequency of oscillation. The next day (22nd day) the values of the moduli increased and their dependences on the frequency changed. The G equaled G, and both moduli depended on the frequency of oscillation by the order of 0.45. Such behavior is characteristic for weak gels, which resemble the strong gels in their mechanical behavior, particularly at low frequencies, but as the deformation increases, their networks undergo a progressive breakdown into smaller clusters. As a consequence, the system can flow with flow properties typical of a disperse system [36]. Gel was formed after 26 days, when the sample exhibited "solid-like" behavior with much higher values of storage modulus G compared to the loss modulus G; moreover, the moduli were frequency independent, i.e., G ~G~ω0. Such behavior is characteristic for strong gels [37], which are usually, due to lack of viscous contribution, also very hard and brittle. Under the conditions of small deformation, strong gels manifest the typical behavior of viscoelastic solids and, above a critical deformation value, they rupture rather than flow [37]. At other temperatures examined, the sol to gel transition was similar to the one, explained in Figure 11; except that the time of gelation process was shorter.

**Figure 11.** Dependence of dynamic moduli G and G on the frequency of oscillation in the range of linear viscoelastic response of the WO3 ink. Solid symbols represent viscous modulus G, hollow symbols represent elastic modulus G .

For chemical, i.e., covalently cross-linked gels formed in our study, linear viscoelastic behavior has been extensively investigated in the vicinity of the sol-gel transition point. Winter and Chambon [38,39] showed that at critical gel point dynamic moduli follow a simple power law: G (ω) ≈ G (ω)~ωn, where *n* depends on the particular gelation mechanism. In our work, the transition from sol to gel was observed for the sol at 23 ◦C (Figure 11), where after 22 days the G and G depended on the frequency by the order of 0.5 (G ~G~ω0.5).

At the end of gelation process the initial Newtonian structure of the sol changed to solid-like gel at all temperatures examined. The formed gels were examined with oscillatory tests in linear viscoelastic range to evaluate the influence of the temperature on the structure of formed gels. For the sake of clarity only gels, formed at temperatures 60 ◦C, 40 ◦C and 20 ◦C, respectively, are presented in Figure 12. The results indicate that all formed gels exhibited similar dependences of G and G on the frequency of oscillation. The differences in the structure can be observed regarding consistency of the gels. Higher temperature of the gelation process led to faster gelation process and higher consistency of formed gel. Thus, the gel, formed at the highest temperature exhibited the highest consistency with the most "solid-like" structure, while the gel, formed at 20 ◦C, exhibited softer gel structure with lower consistency.

**Figure 12.** Dependence of dynamic moduli G and G on the frequency of oscillation in the range of linear viscoelastic response for gels, formed at 60 ◦C, 40 ◦C and 20 ◦C, respectively. Solid symbols represent viscous modulus G", hollow symbols represent elastic modulus G'.

#### **4. Conclusions**

The IR analysis of the WO3 sols showed the difference of the cross-linking of the peroxopolytungstic acid (P-PTA) clusters for the sols based on different alcohols. The most pronounced cross-linking of the tungsten polyhedral is found for the ethanol, followed by the 2-propanol based sol. In the WO3 sol based on 2-propoxy ethanol the cross-linking of the P-PTA is hindered which is demonstrated by the strong presence of terminalW=O bonds and the peroxo groups in the IR spectra of the corresponding sol. The drying of the 2-propoxy ethanol based WO3 sol at room temperature was not complete as is the case for ethanol and 2-propanol. The slower evaporation could have slowed down the gelation process, but the rheological studies show that the gelation was even faster in case of the WO3 sol prepared by 2-propoxy-ethanol. The reason for the faster gelation can be attributed to a different way of cross-linking of the tungsten polyhedra through corners and edges when different alcohols are used. The IR spectra analysis of the gels shows that the WO3 gel based on 2-propoxy ethanol has the solvent kept in the gel structure, the structure of the P-PTA clusters is to some extent preserved and the cross-linking of the tungsten polyhedra is not complete which results in a weaker and softer WO3 gel compared to the gels formed from the ethanol and 2-propanol tungsten sols.

The IR analysis of the 2-propoxy ethanol WO3 gels performed after the gelation of the WO3 sol in a rheometer at 20 ◦C, 30 ◦C, 40 ◦C, 50 ◦C and 60 ◦C showed no significant difference on the chemical structure of the WO3 gel which is well in accordance with the rheological studies confirming similar progress of viscoelastic properties, i.e., elastic G and viscous modulus G, during gelation process of WO3 sol. Initial sols exhibit "liquid-like" behavior with low consistency and only viscous contribution G while during gelation process the elastic modulus G suddenly appeared after a certain time and rise sharply until it intersected and exceeded the loss modulus G. The gelation time decreases exponentially with the temperature, the gelation of the sol exposed to 60 ◦C was completed in 0.55 h, while the transition from sol to gel at 20 ◦C was observed not earlier as after ~10 h. To evaluate the parameters, important for the sol-gel process, the experimental asymmetric dependences of phase shift angle *δ* on the time of gelation were fitted with five-parameter logistic function [35]. The results show excellent agreement of the experimental data with the predicted values for all five temperatures which enabled the exact determination of the time at which sol to gel transition occurred (*tg*), the precise viscoelastic properties of formed gels (*δmin*) and the accurate prediction of total rate and time of sol-gel process (W, s).

The ex-situ rheological characterization of WO3 sols prepared with different alcohols was performed to study the stability of the sol during ageing at RT. The results show that the fastest gelation for the 2-propoxy ethanol-based sol (22 days), while the 2-propanol and ethanol remain stable up to 6 and 10 months, respectively. The fresh sol (1 day after preparation) exhibited Newtonian flow behavior with constant viscosity of 0.0054 Pa.s, after 14 days the sol maintained the Newtonian character, while the viscosity slightly increased to 0.0065 Pa.s. The first deviation from Newtonian flow behavior was observed on the 21st day after the preparation. On the 22nd day the G equaled G, and both moduli depend on the frequency of oscillation by the order of 0.45 which is characteristic for weak gels. Gel was formed after 26 days, when the sample exhibited "solid-like" behavior with much higher values of storage modulus G compared to the loss modulus G; moreover, the moduli were frequency independent, i.e., G ~G~ω0. Such behavior is characteristic for strong gels [37], which are usually, due to lack of viscous contribution, also very hard and brittle.

In overall the results of this study confirmed that in-depth rheological characterization linked with the IR spectroscopy of the sol-gel inks could provide the information on the stability of the sol and a better insight on how the temperature influences the gelation time. It provides the information on the temperature and the time window at which the continuous inkjet printing of the sol-gel inks could be performed without clogging. The WO3 ink was stable in a beaker and have Newtonian flow behavior at room temperature over 3 weeks, while the gelation time decreases exponentially with the temperature down to 0.55 h at 60 ◦C.

**Author Contributions:** Conceptualization, U.O.K. and L.S.P.; methodology, T.V. and M.K.G.; formal analysis, U.O.K., L.S.P., T.V., R.C.K. and M.K.G.; investigation, U.O.K., L.S.P., T.V., R.C.K. and M.K.G.; writing—original draft preparation, U.O.K. and L.S.P.; writing—review and editing, U.O.K., L.S.P., T.V., R.C.K. and M.K.G.; supervision, L.S.P.; project administration, L.S.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors acknowledge the financial support from the Slovenian Research Agency (research core funding No. P2-0264, P2-0244 and P2-0393).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**

