A Novel Route for the Easy Production of Thermochromic VO2 Nanoparticles

Abstract In this work, a simple, fast and dry method for the fabrication of a thermochromic product with a high load of VO2(M1) consisting of the controlled heat treatment of pure vanadium nanoparticles in air is presented. After a complete design of experiments, it is concluded that the most direct way to attain the maximum transformation of V into VO2(M1) consists of one cycle with a fast heating ramp of 42 °C s−1, followed by keeping 700 °C for 530–600 seconds, and a subsequent cooling at 0.05 °C s−1. Careful examination of these results lead to a second optimum, even more suitable for industrial production (quicker and less energy‐intensive because of its lower temperatures and shorter times), consisting of subjecting V to two consecutive cycles of temperatures and times (625 °C for 5 minutes) with similar preheating (42 °C s−1) but a much faster postcooling (∼ 8 °C s−1). These green reactions only use the power for heating a tube open to atmosphere and a vanadium precursor; without assistance of reactive gases or catalysts, and no special vacuum or pressure requirements. The best products present similar thermochromic properties but higher thermal stability than commercial VO2 particles. These methods can be combined with VO2 doping.


SECTION B. DESING OF EXPERIMENTS AND REFINEMENT FOR ONE-CYCLE OXIDATIONS
The Response Surface Methodology (RMS) was applied to determine the best conditions for obtaining the maximum transformation of V into VO2 (given as the peak area of the DSC curves for the heating transformation of the products). RMS was performed employing the Statgraphics Centurion XVIII software. In order to plan and conduct the experiments, a strategy of experimentation based on several phases was followed.

The first phase of the experiment
In the early stages of the research and mainly based on both the literature and technical conditions we had just identified four potential significant factors. Due the fact we were able to address all factors a specific DOE screening technique was not necessary. In the first RMS phase, a central composite design (CCD) model with four factors and three levels consisting of 30 randomized runs with six replicas at the central points was used to optimize the process variables (maximum "temperature" of reaction (A), residence "time" at this temperature (B), "heating" rate (C) and "cooling" rate (D)). Table S1 (A1-A30) shows the independent factors and levels to design the response surface matrix, and also the experimental values of the response variable (Y: DSC area, or the latent heat of phase change on heating). In order to reduce the prediction uncertainty, we have removed the four least not significant terms from the initial model, namely, the quadratic terms AA, BB, CC and the interaction term BD, having p-values 0.4765, 0.2129, 0.5661 and 0.7347, respectively. Table S6 shows the ANOVA table of the final fitted model and the polynomial regression equation. Figure S1 shows the response surface depending on time (B) and temperature (A), and the standardized effect given by the Pareto diagram. The final model has a R 2 of 95.4679%. The estimate of the residual standard deviation is 0.529554. The Durbin-Watson test (p-value = 0.8143) shows no autocorrelation in the residuals at a significant level 0.05. Finally, the lack-of-fit test of goodness (p-value =0.4019) also shows the model fits well the data at the 95% confidence level. (Table S6) indicates that the response variable depends on the linear terms of the processing variables temperature (A), time (B) and cooling (D), the interaction terms AD and AB, and the quadratic term DD (p-value < 0.05). It also shows a slight dependency on the interaction term BC. In order to interpret the surface response, we compute in Table S7 the partial derivatives of the polynomial regression equation. First, it is clear that there is not a stationary point in the experimental range. Second, just observing the sign of the partial derivatives in the experimental region, the response variable increases when time increases and cooling decreases. Therefore, the optimal solution is achieved at time=300s and cooling=0.2 o C/s. Third, conditioning to those values the response variable always increases when temperature increases and then taking temperature=625 o C, we finally obtain that the response variable also increases when heating increases. In conclusion, the optimal solution is achieved at a vertex of the experimental region at A=625 o C, B=300s, C=42 o C/s, and D=0.2 o C/s. The optimal response value is 11.5696 J/g. Due to the fact that the global optimum seems to be out of the experimental region, some additional data are required. We next provide some remarks which will help us to move our process variables.   Remark 1. Figure S2 shows a direct extrapolation of the response surface out of the experimental region. Although in the experimental region the response variable always increases when time and temperature increase, the negative sign of the interaction term AB suggests that for a certain threshold the effect of time on the response variable is opposite depending on the value of temperature and vice versa. Just fixing heating = 42 o C/s and cooling = 0.2 o C/s a straightforward computation shows the response surface has a theoretical saddle point at temperature =763.56 o C and time = 526.79s out of the experimental region. A saddle point is neither a maximum nor a minimum for the surface response. The existence of that saddle point suggests the response will start decrease when temperature and time exceed a theoretical threshold. Additionally, it should be explored the effect on the response when time decreases and temperature increases and vice versa.

Conclusion of the first phase. The analysis of variance
Remark 2. Although in the experimental region the response variable always decreases when cooling decreases, having a higher cooling value opens up a new path of investigation. Just observing the partial derivatives given in Table S7, a higher value of cooling has a negative impact in the partial derivative of the temperature. This fact suggests that fixing a large value of cooling we could expect the response variable increases when temperature decreases. Figure S2. Extrapolation of the response surface out of the experimental region of phase 1.

The second phase of the experiment
In order to explore the different research paths, we split the second phase in several steps.
Step 1. In light of Remark 2, the effect of having a large value of cooling was first explored. Due to the available technical conditions, D=2.42 o C/s was fixed. By also fixing C=42 o C/s, we theoretically expect the response variable increases when time increases and temperature decreases. Table S2 shows nine new runs (B1-B9) consisting in decreasing the temperature and increasing the time. It is apparent that these data do not reflect the hypothesis assumption. Therefore, we decided to close this research path.
Step 2. Here, a theoretical saddle point is looked for, by increasing simultaneously time and temperature. It was noticed in the first phase the response variable in the experimental region increases when cooling decreases, having the cooling the second major standardized effect. Therefore. we decide to fix the cooling process variable to the minimum feasible technical value. i.e., to 0.05 o C/s. Using a similar argument, the heating process variable was also fixed to the maximum feasible technical value. i.e., to 42 o C/s. Now taking in account Remark 1, nine new runs were carried out to study the effect on the response variable of simultaneously increasing time and temperature (B10-B18 of Table S2). It was first empirically observed that the response has larger values compared to those in the first phase. Second, the response keeps increasing when time and temperature increase. Finally,. we also empirically observe how the response begins to decrease at A=775 o C and B=600s which reinforces the existence of a saddle point. All those runs help us to move our process towards a local growth direction. Note that runs B19-B24 were performed with the purpose of validation.
Step 3. Here, the process is moved to confirm the existence of a theoretical saddle point. By fixing heating = 42 o C/s and cooling =0.05 o C/s, a full factorial design (FFD) model with two factors and three levels consisting of 12 randomized runs with three replicas at the central point was used to optimize the process variables (temperature (A) and time (B)). Table S3 (samples C1-C11) shows the independent factors and levels to design the response surface matrix and also the experimental values of the response variable (Y). One of the replica at the central point was taken from B17 in the previous step. As the error (residuals) seems to be larger in this phase, we decide to use the logarithmic transformation of the response. Table S8 shows the ANOVA table of the final fitted model and the polynomial regression equation. Figure S3 shows the response surface depending on time and temperature (complementary to Figure 2(e)), and the standardized effect given by the Pareto diagram. The final model has a R 2 of 88.22%. The estimate of the residual standard deviation -in logarithmic scale-is 0.103547. The Durbin-Watson test (p-value = 0.2543) shows no autocorrelation in the residuals at a significant level 0.05. Finally, the lack-of-fit test of goodness (p-value =0.2380) also shows the model fits well the data at the 95% confidence level. (Table S8) indicates that the response variable depends on the linear terms of temperature (A) and time (B). It also shows a slight dependency on the interaction term AB and the quadratic term BB. The mathematical optimal solution is achieved inside the experimental region at A=700 o C and B=529.083s. The optimal response value is Y = exp(2.94123) = 18.94 J/g. The polynomial regression equation obtained at this stage reinforces the result pointed out in Remark 1. It can be observed how the response starts to decrease when temperature and time exceeds a theoretical threshold. It is also apparent that there exists a region where the response variable does not vary significantly. It is worth noticing that the residual standard deviation provides a larger uncertainty compared to that obtained in the first phase of the experiment, =exp(0.103547)=1.11 J/g. To conclude, in Table S9 a validation of this surface is provided by comparing the adjusted and observed value for two observations close to the experimental region (B19,B20), two other observations more distant of this experimental region (B21,B22) and, finally, two other ones inside the experimental region (B23, B24).   The third phase of the experiment Based on the extrapolation given in Figure S3 it is natural to explore the effect of the pairs high temperature and short time and vice versa. For such a purpose we carried out new eight runs given in Table S4 (samples D1-D8). Note that those experimental values were considered by starting from a hypothetical center and the technical extreme values. Data reflect that the response is far from the optimum value when temperature decreases and time increases and it takes values close to the optimum one when temperature increases and time noticeably decreases.

Conclusion of the second phase. The analysis of variance
By considering all experimental values obtained through the different phases having heating = 42 o C/s and cooling = 0.05 o C/s, i.e., collecting data from samples B10-B24, C1-C11 and D1-D8, we compute a R 2 of 61.03%. We first empirically observe that variability increases when temperature increases and time decreases. We second note that the optimal values obtained in the second phase could also be reached as a combination of high temperatures, 830-900°C, and time values less than 250 seconds. In fact, the sample D4 (900°C and 30 s) provided 18.05 J/g. Nevertheless, we think a new experiment should be designed to study in depth the effect of the response variable when temperature and time noticeably increases and decreases, respectively. On the other hand, higher process temperatures to reach similar yields Iess less attractive for a possible transfer of the synthesis method to industry.

Final conclusion
By starting at temperature= 475°C and time = 1s the response variable increases when temperature and time increase simultaneously. However, there exists a theoretical point where this effect is the opposite. i.e., the response starts to decrease when time and temperature increases. Additionally, for low temperatures the response variable increases when time increase but it seems those response values are far from the ones obtained by increasing simultaneously time and temperature. On the other hand, for high temperatures the response variable increases when time decreases obtaining response values close to the optimum. In this way, the following paragraph was stated in the article, concerning the supplementary sections A and B: The influence of key process parameters was verified by an exhaustive design of experiments (DOE). Tables S1, S2, S3 and S4 (Section A of the Supporting Information file) show the data associated to the 73 performed experiments resulting of programming (StatGraphics Centurion XVIII) first a randomized central composite design (CCD) model with four factors and three levels, and three further refinements for the search of the optima. We will denote by "A" the first group consisting of 30 randomized runs while improvements were named as series "B", "C" and "D".  Figure S1 to S3).

SECTION C. X-RAY DIFFRACTION: IMPLICATED PHASES AND RIETVELD QUANTIFICATIONS
The XRD diffractograms recorded throughout the series A, B and C (single cycle) revealed the unwanted formation of different vanadium oxides. In this sense, it is essential to find out which oxidation conditions promote the upwelling or decreasing of such oxides in order to limit their generation and thus achieving a purer VO2 final product. Figure S4(a)-(d) display the progression of the characteristic XRD peaks of many of the resulting oxides in accordance with the oxidation conditions. A preliminary overview of these graphics lead to discern between oxides generated at severe conditions of temperature and reaction times (V2O5, V6O13 and V2O3) and other oxides whose development occurs at moderate temperatures and reaction times (VO, V16O3 and VOx).
With regard to the oxides formed at severe conditions, V2O5 ( Figure S4(a)) and V2O3 (Figire S4(c)) species stand out, which start to emerge from 700 o C and 775 o C respectively, becoming more extensive as reaction time increases. The arising of these two species always leads to a decrease in the generated VO2, which suggests that the dioxide can act as one of the reagents for the formation of the trioxide and the pentoxide. Hence, limiting the formation of these two oxides becomes a key issue in the search for high VO2 yields. In this way, it should be also highlighted the formation V6O13 at temperatures above 625 o C ( Figure S4(b)). However, it seems that its generation is stopped at about 700 o C, probably due to the preferential development of V2O5 and V2O3. Figure S4(d) shows the progression of VO, V16O3 and VOx, the latter being considered as a mixture of metastable and intermediate vanadium oxides. As can be observed, the signals of all these oxides become weaker for greater temperatures and times, which may imply that they are first oxides to be formed, even earlier than the VO2 itself. As a point of interest, it is worth mentioning the progressive evolution of VO into V0.775O at higher temperatures (above 625 o C) and reactions times (beyond 300 seconds), leading to a more oxygen enriched specie (O/V ratio = 1.29). In this light, it is thought that VO, V16O3 and VOx could act as seeds for the formation of VO2 when the temperature is kept below 625 o C since, as mentioned above, higher temperatures would promote the development of V2O5, V2O3 and V6O13 species with the subsequent VO2 consumption.

Fig S4.
Details of XRD spectra for many vanadium thermally treated specimens illustrating the various phases appearing at the different analyzed oxidation stages.
As can be seen in Table S11, XRD quantifications disclosed the presence of minority amounts of the VO2(M2) polymorph, which also presents thermochromic properties, especially in samples belonging to the serie A of experiments. Note that, throughout this work, all the references made to the thermochromic VO2 phase have been only referred to the VO2 M1 phase, always neglecting the M2 polymorph. Nonetheless, it is also worth mentioning that the sum of M1 and M2 phases gives rise to similar linear relationships between the DSC value, and the percentage of these two thermochromic VO2 phases (R 2 =0.95). Likewise, metastable and intermediate vanadium oxides (VOx) were found in samples of the A series as well. In this way, due to the limited information available in crystallographic databases for such species, they were finally indexed as "impurities" in the Highscore Plus software. Finally, it is also worth mentioning that, although they were quantified by the Rietveld method as well, the samples E2 and E6 were not included in the studies referred in Figure 4 of the article.

SECTION D. TRANSMISSION ELECTRON MICROSCOPY STUDIES OF OPTIMAL SPECIMENS
High-resolution TEM (HRTEM) and selected area electron diffraction (SAED) were performed for freestanding isolated or aggregates of nanoparticles in C11 and E17, in order to ratify the presence of monoclinic VO2 proved by XRD as the majoritarian phase of their complete mass. Many reflections at SAED patterns could be indexed for M1-VO2 (not shown here), along with lattice distances in HRTEM micrographs. Figure S5 shows a collection of irregular shape particles detached from aggregates of sample C11 after ultrasonication, and HRTEM images of two different particles, with insets showing atomic columns of monoclinic VO2 (M1) and of a V6O13 single crystals, both oriented in the [001] zone axis, with families of planes and their parameters and angles highlighted. Figure S6 shows three HRTEM images of three different regions within the same agglomeration of particles from sample E17, which exhibit lattice resolution proper from the thermochromic VO2 (M1) phase or orthorhombic V2O5 as demonstrated by the indexed families of planes and angles. Figure S5. TEM studies of sample C11.