Computational and Experimental Study of Thermodynamics of the

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Computational and Experimental Study of Thermodynamics of the Reaction of Titania and Water at High Temperatures Quynhgiao N. Nguyen, Charles W Bauschlicher, Dwight L Myers, Nathan S. Jacobson, and Elizabeth J. Opila J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b08614 • Publication Date (Web): 13 Nov 2017 Downloaded from http://pubs.acs.org on November 18, 2017

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The Journal of Physical Chemistry

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Computational and Experimental Study of Thermodynamics of the Reaction of Titania and Water at High Temperatures Q. N. Nguyen†, C. W. Bauschlicher, Jr. ‡, D. L. Myers†,§, N. S. Jacobson†,*, and E. J. Opila†,§§ †

NASA Glenn Research Center Cleveland, OH 44135

‡

NASA Ames Research Center Moffett Field, CA 94035

-------------------------------------------------------------------------------------------------------------------Corresponding Author *E-mail: [email protected] Present Addresses § Summer Faculty Fellow at NASA Glenn, Permanent address East Central University Ada, OK 74820 §§ University of Virginia, Charlottesville, VA 22904

ACS Paragon Plus Environment


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2 ABSTRACT Gaseous titanium hydroxide and oxyhydroxide species were studied with quantum chemical methods. The results are used in conjunction with an experimental transpiration study of titanium dioxide (TiO2) in water vapor-containing environments at elevated temperatures to provide a thermodynamic description of the Ti(OH)4(g) and TiO(OH)2(g) species. The geometry and harmonic vibrational frequencies of these species were computed using the coupled-cluster singles and doubles method with a perturbative correction for connected triple substitutions [CCSD(T)]. For the OH bending and rotation, the B3LYP density functional theory was used to compute corrections to the harmonic approximations. These results were combined to determine the enthalpy of formation. Experimentally, the transpiration method was used with water contents from 0-76 mole % in oxygen or argon carrier gases for 20-250 hour exposure times at 1473-1673 K. Results indicate that oxygen is not a key contributor to volatilization and the primary reaction for volatilization in this temperature range is: TiO2(s) + H2O(g) = TiO(OH)2(g). Data were analyzed with both the second and third law methods using the thermal functions derived from the theoretical calculations. The third law enthalpy of formation at 298.15K for TiO(OH)2(g) at 298 K was –838.9 ± 6.5 kJ/mol which compares favorably to the theoretical calculation of –838 ± 25 kJ/mol. We recommend the experimentally derived third law enthalpy of formation at 298.15K for TiO(OH)2, the computed entropy of 320.67 J/mol-K, and the computed heat capacity [149.192+(–0.02539)T+(8.28697E-6)T2+(–15614.05)/T+(–5.2182E11)/T2] J/mol-K, where T is the temperature in K.


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3 1. INTRODUCTION Many common oxides react with water vapor at high temperatures to form hydroxide and oxyhydroxide species 1, 2. Precise thermodynamic data are available for some of these species such as the Group I and Group II hydroxides 3, 4, Si(OH)4(g) 5-7 and CrO2(OH)2(g) 8. However, data are unavailable for many important hydroxides and oxyhydroxides. In particular questions remain about transition metal hydroxides and oxyhydroxides. Titania-forming and titania-containing materials are of great interest for applications in high temperature environments due to their temperature capabilities, light weight, good strength-toweight ratio and corrosion resistance. Examples include Ti(Pt)Ni nitinol, Ti-Al alloys, TiB2, TiN, TiC, and refractory coatings containing TiO2. Since high temperature combustion environments contain water vapor, the interaction of water vapor and titania is important. In addition, such processes are important in geological phenomena. However we could find no thermodynamic data for titanium hydroxides or oxyhydroxides. Further, the exact stoichiometry of the titanium hydroxide or oxyhydroxide species is not known. There is laboratory evidence that TiO2 does indeed react with water vapor. Several groups have conducted matrix isolation experiments and obtained infrared spectra of species condensed on an Ar matrix. Most of the studies examine the interaction of Ti metal atoms with H2O. Kauffman et al.9 see evidence for HxTi(OH)2 and Ti(OH)x. Zhou et al. 10 suggest H2Ti(OH)2. Wang and Andrews11 see evidence of Ti(OH)2 and Ti(OH)4. Shao et al. 12 examined TiO2 interactions with H2O and report on the structure and vibrational frequencies of OTi(OH)2. At high temperatures, Ueno and colleagues reported evidence of attack of rutile in a 30 mass percent H2O/Air environment at 1773 K 13 in the form of weight loss and etch pits. A geological study discusses the reaction of TiO2 with hot water, which is attributed to the formation of



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4 Ti(OH)4(g) 14. Golden and Opila report the recession of single crystal TiO2 in high velocity steam15 attributed to gaseous hydroxide formation, although the identity of the vapor species is unknown. Thus questions remain on the identity of the principal vapor species and the thermodynamic functions for these species. On the basis of previous work on Cr hydroxides and oxyhydroxides and the prevalent +4 oxidation state of Ti, the most likely species are Ti(OH)4(g) or TiO(OH)2(g). In this paper we first present a computational study of these two species which yields their structures and thermodynamics. Then we present an experimental transpiration study to determine the principal species and thermodynamics via the second and third law methods. 2. COMPUTATIONAL STUDIES 2.1 Methods We use the B3LYP hybrid16, 17 functional and the coupled cluster singles and doubles approach18, including the effect of connected triples determined using perturbation theory19, CCSD(T) to study the species of interest. For open-shell calculations the partially spin restricted RCCSD(T) approach20 is used. Some calculations using other functionals and Møller-Plesset second order perturbation were performed and noted below as appropriate. The CCSD(T) calculations use the cc-pVnZ sets20 for H, the aug-cc-pVnZ sets21, 22 for O and the core-valence cc-pwCVnZ-DK sets23 for Ti, where n takes the values, T, Q, and 5. The Ti basis sets allow the inclusion of Ti 3s and 3p correlation and the inclusion of scalar relativistic effects using the Douglas-Kroll approach. We denote these basis sets as TZ, QZ, and 5Z. The CCSD(T) calculations are extrapolated to the complete basis set limit (CBS) using the X−3 approach of Helgaker et al. 24. Unless otherwise noted, the O 1s and Ti 1s, 2s, and 2p electrons are not correlated. The B3LYP calculations are performed using augmented correlation consistent triple


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5 zeta (aug-cc-pVTZ) sets21–23, which we denote as TZ’. All of the DFT calculations were performed using Gaussian 0925, while MOLPRO26 was used to perform the CCSD(T) calculations. The interactive molecular graphics tool Jmol27 was used for the visualization of the molecular structures and the vibrational modes. The OH groups have a low rotational barrier and therefore need to be treated as hindered rotors for the calculation of thermodynamic properties8. The hindered rotor option25 in Gaussian 09 is used to compute this effect using the Pitzer-Gwinn29 option. The OH bending potential is very anharmonic and we account for this by solving for the vibrational levels of the bending potential and computing the thermodynamic properties using these computed levels. 2.2 Results We compute the heat of formation of a target molecule by computing a reaction energy for a case where the heats of formation of the reactants are known. The reactions we study in this work are: Ti + O2 → TiO2

(1)

TiO2 + H2O → TiO(OH)2

(2)

Ti + O2 + H2O → TiO(OH)2

(3)

Ti + O2 + 2H2O → Ti(OH)4

(4)

TiO2 + 2H2O → Ti(OH)4

(5)

TiO(OH)2 + H2O → Ti(OH)4

(6)

For reactions (1) to (5) the heats of formation of the starting materials from both the JANAF3 and Gurvich et al.4 tables are summarized in Table 1. Note that the values all species are in the gas



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6 phase and the values for Ti(g) and H2O(g) are the same, whereas the values for TiO2(g) differ. Reaction (6) is used to obtain the relative energies of our two target molecules. Table 1. Reference compound heats of formation in kJ/mol ∆fH(0 K) (JANAF)3 ∆fH(298 K) (JANAF)3 Ti(g) 470.92 ± 16.7 473.63 ± 16.7 TiO2(g) –303.28 ± 12.6 –305.43 ± 12.6 H2O(g) –238.921 ± 0.042 –241.826 ± 0.042 O2(g) 0 0

∆fH(0 K) (Gurvich et al.)4 471 ± 2 -320 ± 20 -238.923 ± 0.040 0

∆fH(298 K) (Gurvich et al.)4 474 ± 2 -323 ± 20 -241.826 ± 0.040 0

For the molecules studied in this work it is possible to optimize all of the geometries and compute the vibrational frequencies using the CCSD(T)/TZ approach. However, this is very time consuming and finding a less expensive alternative is desirable. Therefore the first step was to optimize the geometries of TiO2 and TiO(OH)2 at the CCSD(T)/TZ level. Using the TZ basis set and correlating the same electrons, the geometries were optimized at the MP2 level. For TiO2 the O-Ti-O angle at the MP2 level is 6 degrees smaller than at the CCSD(T) level. The geometries computed at the B3LYP/TZ’ level are in better agreement with CCSD(T)/TZ than are the MP2/TZ. The B3LYP/TZ’ O-Ti-O angle differs by less than 0.1 degrees from the CCSD(T)/TZ. For TiO(OH)2 the O-Ti-O(H) angle at the B3LYP/TZ’ is in better agreement with the CCSD(T)/TZ than is the MP2 result, but for this molecule the MP2 only differs by 1.3 degrees from the CCSD(T) value. We should note that we also optimized the geometries using the M06/TZ’ and BPW91/TZ’ approaches. These two functionals yield a non-planar structure for TiO(OH)2, where the Ti atom is above the plane of the three O atoms. This is in contrast with the CCSD(T)/TZ and B3LYP/TZ’ approaches, which yield a planar structure. On this basis, we conclude that the B3LYP/TZ’ is best alternative to the CCSD(T). We should note that the zero-point energy contribution to reaction (2) at the CCSD(T) and B3LYP approaches are in good agreement, 6.2 vs 6.4 kJ. However, to be fair, the values only vary from 5.9 (MP2) to 6.5 kJ (BPW91) when all of the methods tests are considered. In addition to the geometry tests,


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7 we also tested the effect of inner shell correlation for reaction (2). The O 1s and Ti 2s and 2p electrons were correlated in addition to the valence electrons. The O and Ti basis sets were made more flexible to describe this inner shell correlation. The oxygen basis set was switched to the aug-cc-pCVTZ set and the Ti TZ basis was more flexibly contracted and tight polarization functions added. The heat of reaction was increased by 0.2 kJ when inner shell correlation was added. Considering the very small effect and the significant increase in computational cost, only the valence electrons are correlated in the reported calculations. Our calculated structures are shown in Figure 1. The calculated vibrational frequencies are given in Table 2. Table 2. Computed CCSD(T)/TZ Harmonic Frequencies, in cm–1 O2 3∑1574.0 H2O 1A1 1648.0 3810.4 3920.8 TiO2 1A1 330.2 955.3 989.8 TiO(OH)2 1A1 70.6 187.7 219.4 461.2 465.8 480.2 521.4 683.1 794.4 1029.8 3890.6 3891.0 Ti(OH)4 1A 92.9 140.2 153.0 181.6 209.8 219.6 234.3 252.4 295.5 419.3 423.21 454.4 457.6 708.3 765.1 783.6 786.7 3878.0 3878.0 3881.0 3884.6

We first study the heat for formation of TiO2(g) at 0 K using reaction (1). The results are summarized in Table 3. Our best value for the reaction energy is determined as follows, the CBS(QZ,5Z) limit value is corrected for inclusion of zero-point energy and for the Ti spin orbit effect (computed as the difference between the weighted average of the J levels and the lowest Ti 3

F2 level). It is very difficult to rigorously assign error bars to our calculations. The three largest sources

of error are expected to be: the basis set incompleteness, higher levels of correlation not included



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8 in the CCSD(T), and anharmonic contributions to the zero-point energy. In principle the extrapolation complete basis limit should remove any basis set incompleteness error, however, the difference between the CBS(TZ,QZ) and CBS(QZ,5Z) values is 2.8 kJ, suggesting that some uncertainty remains. All of the species considered in this work are well described by a single reference and therefore the neglect of higher excitations is expected to be smaller than the basis set incompleteness. For water, the anharmonic contribution to the zero-point energy is 5% of the harmonic value. Assuming that the anharmonic contribution to the reaction energy is similar to that for water, yields a maximum anharmonic correction to the reaction energies of 0.5 kJ, which is significantly smaller than the basis set incomplete error. On this basis, we estimate the uncertainty in our best values as twice the difference between the 5Z and CBS(QZ,5Z) values or ±10 kJ. Combining our best estimate with the heats of formation for Ti and O2 yields the heat of formation given in Table 3. We deduce the uncertainty by combining our uncertainty for the reaction energy with that for the Ti atom. Our value is in good agreement with that recommended by the JANAF tables3 (∆fH°(0) = -303.28 ± 12.6 kJ/mol), but does not rule out the Gurvich et al. value4 (∆fH°(0) = -320 ± 20 kJ/mol) value. Table 3. Summary of Calculation of the Enthalpy of Formation for Listed Molecules in kJ/mol Reaction energy (kJ/mol) without zero-point energy in rows 1-5; Best adds ZPE and Ti spin orbit to CBS(QZ,5Z) Rxn(1) Rxn(2) Rxn(3) Rxn(4) Rxn(5) Rxn(6) TZ –753.4 –310.3 –1063.6 –1252.4 –499.1 –188.8 QZ –762.8 –309.7 –1072.4 –1261.3 –498.5 –188.9 5Z –767.5 –308.7 –1076.3 –1264.7 –497.2 –188.4 CBS(TZ, QZ) –769.7 –309.2 –1078.9 –1267.8 –498.1 –188.9 CBS(QZ, 5Z) –772.5 –307.8 –1080.3 –1268.3 –495.8 –188.1 ZPE 4.2 6.2 10.4 10.6 6.4 0.1 Ti spin orbit 2.8 0.0 2.8 2.8 0.0 0.0 Best –765.5 –301.5 –1067.0 –1254.9 –489.4 –187.9 Enthalpy of Formation (kJ/mol) TiO2(g) TiO(OH)2(g) TiO(OH)2(g) Ti(OH)4(g) Ti(OH)4(g) ∆fH(0 K) –294.6 ± 27 –843.7 ± 21 –835.0 ± 25 –1261.9 ± 25 –1270.6 ± 21 ∆fH(298 K) –295.6 ± 27 –847.5 ± 21 –838.7 ± 25 –1274.2 ± 25 –1283.0 ± 21


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9 The heat of formation of TiO(OH)2 is computed using reactions (2) and (3). The difference between the 5Z and the CBS(QZ,5Z) and between the two CBS values is smaller for reaction (2), as expected from its smaller exothermicity. Using twice difference between the 5Z and CBS values gives uncertainties of ±4 and ±8 kJ for reactions (2) and (3) respectively. Adding these uncertainties to those for TiO2 and Ti yields our final uncertainties of ±21 and ±25 kJ/mole. The two values differ by the difference between our computed ∆fH for TiO2 and that recommended by JANAF 3. The preferred values of the enthalpy of formation of TiO(OH)2(g) and Ti(OH)4(g) are from reactions (3) and (4), which do not require the TiO2(g) enthalpy of formation. This avoids the small disagreement between the JANAF3 and Gurvich et al.4 tables. The heat of formation of Ti(OH)4 was determined using reactions (4) and (5). The heats of formation from these two reaction differ by the expected 8.7 kJ, the difference between our computed heat of formation of TiO2 and that recommended by JANAF3. If the Gurvich et al.4 v al u e is used, the ∆H value would be an additional 16.7 kJ lower. Reaction (6) shows that the reaction of TiO(OH)2 with H2O to form Ti(OH)4 is exothermic by 187.9 kJ. We note that this reaction is actually a two-step process, where a TiO(OH)2.H2O complex forms. At the CCSD(T)/TZ level, this complex is 124 kJ below the reactants. There is a barrier of 69 kJ between this complex and the transition state. However the transition state is 55 kJ below the reactants, so in spite of the barrier, we suspect that the reaction will occur easily. Up to this point we have computed all thermodynamic properties at 0 K. It is known from CrO2(OH)2 that OH rotation has a low barrier8 and must be treated using a hindered rotor approximation. In Figure 2, we show the OH rotational barrier for TiO(OH)2 and Ti(OH)4. We first note that the CCSD(T)/TZ and B3LYP/TZ’ barriers are very similar, therefore the larger Ti(OH)4 is only studied at the B3LYP/TZ’ level. The numerical values are given in the



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10 Supplemental Information—Table 1. Using the computed barriers and the Pitzer-Gwinn approach, the OH hindered rotation contributions to ∆S, ∆H, and Cp are accounted for. In addition to the OH rotation, we have found that the Ti-O-H bending potential is very flat. In Figure 3 we show the B3LYP/TZ’ bending potential for one OH in Ti(OH)4. Using this potential, it is possible to solve for the vibrational levels, which are also shown in the figure. The double well shape results in level spacing’s that are significantly different from that expected for a harmonic oscillator. Using the computed levels it is possible to compute the ∆S, ∆H, and Cp contributions, and we use these values instead of the harmonic ones. The details of each contribution to the entropy, enthalpy, heat capacity and Gibbs free energy are given in Supplemental Information—Table 2. The key thermochemical information is summarized in Table 4 for the two gaseous species TiO(OH)2(g) and Ti(OH)4(g). This is typically the data required by the common computational thermodynamics databanks (e.g. FactSage30) and from these data all relevant thermodynamic functions can be derived. As discussed, we have selected the data from reactions (3) and (4) to derive the enthalpies of formation of TiO(OH)2(g) and Ti(OH)4(g). These reactions do not involve TiO2(g) as a reactant, only using the elements and H2O, which have more reliable data. Figure 4 is a plot from the computed data of the vapor pressure of TiO(OH)2(g) and Ti(OH)4(g) over TiO2 + 50% H2O/Ar at 1 bar total pressure. Note the TiO(OH)2(g) dominates. Table 4. Enthalpy of Formation, Entropy, and Heat Capacity for TiO(OH)2(g) and Ti(OH)4(g) TiO(OH)2 Ti(OH)4 ∆fHo(0) –835.0 ± 25 kJ/mol –1270.6 ± 21 kJ/mol ∆fHo(298) –838.7 ± 25 kJ/mol –1274.2 ± 21 kJ/mol So(298) 320.67 J/mol-K 373.7 J/mol-K Cp (298-1600K) 149.192+(–0.02539)*T+ 169.25+(–7.1896E-3)*T+ (8.28697E-6)*T2+(–15614.05)/T+ (7.5164E-6)*T2+(–10818.0308)/T+ (–5.2182E-11)/T2 J/mol-K (–4.8145E-11)/T2 J/mol-K

3. EXPERIMENTAL PROCEDURE A generalized reaction for TiO2(s) with oxygen and water vapor is:


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11 TiO2(s) + xO2(g) + yH2O(g) = TiO(2+2x+y)H(2y) (g)

(7)

Thus P(TiO(2+2x+y)H(2y)) varies with [P(O2)]x and [P(H2O)]y. In our laboratories and others, the transpiration method has been found to be particularly useful for the study of this type of reaction at elevated temperatures5, 6, 31, 32. The transpiration method as reviewed by Merton and Bell33, involves flowing reactant gases over a condensed sample at a suitable rate in order for solid-gas equilibrium to be established. The product gas flows downstream and is condensed in a cooler portion of the gas train, collected and analyzed to quantitatively determine the amount of sample transported. By independently varying the reactant gas partial pressures and determining the dependence of volatile product formation on reactant gas concentration, the identity of volatile species can be determined. The partial pressure of the volatile species, TiO(2+2x+y)H(2y) (g), can then be determined over a range of temperatures, which allows the extraction of an enthalpy and entropy of reaction. 3.1 TiO2 Pellets Acros Organics, 99.999% pure titanium oxide, predominately rutile, powder was cold-pressed in a ¼” O.D. stainless steel die to a pressure of 141 kg/cm2 (2000 psig). These pellets were dried overnight in a 100 °C drying oven and were sintered in air at 1200 °C for 24 hours. The TiO2 pellets were weighed and the density was calculated to be 3.75 g/cc, corresponding to 88% of the theoretical density. After the transpiration runs were complete, the reaction chamber was opened and the pellets were examined with x-ray diffraction and scanning electron microscopy. No significant changes in composition were noted. Typical surface morphologies of the pellets before and after exposure are shown in Figure 5. The grains were still rutile, as confirmed by x-ray diffraction, but significant grain growth occurred.



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12 3.2 Transpiration System The transpiration system is shown schematically in Figure 6. The cell is made out of platinum-20% rhodium, (Pt/20Rh), and laser welded with the sintered TiO2 pellets packed inside. A type R thermocouple is inserted through the bottom of the cell to monitor the reaction temperature. A carrier gas composed of argon and/or oxygen flowed through the reaction cell and was controlled and monitored with a calibrated electronic flowmeter (Tylan FC-260). The transpiration system used a furnace with molydisilicide heating elements (Applied Test Systems, Inc.) and a 99.8% pure alumina furnace tube. Deionized water was introduced through the bottom of the transpiration gas train into the carrier gas via a peristaltic pump. The liquid water flow rate ranged from 0.5 to 9.3 ml/hr and was calibrated before and after each test to verify the flow consistency. A quartz wool plug, located at the junction of the water inlet with the gas train, was used to ensure that liquid to vapor disbursement occurred. The gases (Ar, O2, and water vapor) were introduced through the bottom of the transpiration gas train and then flowed into the transpiration cell. The flow rates of the gases (argon/oxygen) ranged from 60 to 275 cc/min. Whenever the furnace was above room temperature, the blanket Ar gas that flows on the exterior of the transpiration cell was flowing at rates of 90 cc/min or higher. The gas lines and water line were heated with heating tape (260 °C) prior to introduction into the furnace. This prevented condensation and provided some pre-heating of the gas. The gas stream traveled up through the sealed reaction chamber, located in the hot zone of the furnace, and then exited through a series of three fused quartz (99.995% purity) condensation (collection) tubes, as shown in red on Figure 6. From our previous studies on the Cr-O-H system8, it was found to be critical to analyze all the deposits in the entire gas train after the reaction chamber. The series of three fused quartz


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13 condensation tubes was held together by polyfluoroethylene fittings. The first condensation tube (#1), as mentioned above was located in the hot zone at the exit of the transpiration cell in the center of the furnace. This condensation tube was the location of the primary condensate. The end that sat in the hot zone of the furnace had an internal beveled edge that fit snuggly over the transpiration cell exit, thus allowing for a tight seal and maintaining pressure as the gases exited. This straight condensation tube was replaced after each experiment due to the devitrification and resultant damage that occurs during cooling from the high temperature exposures. An image of this tube is shown in the inset in Figure 6. The second fused quartz condensation tube (#2) was a bent one located at the top of the furnace tube. This second fused quartz condensation tube was wrapped with heating tape to ensure the water vapor did not condense prior to reaching the third condensation tube (#3). The third tube was at room temperature, thus allowing the water vapor to condense, collect in a buret, and be measured. Both the second and third fused quartz condensation tubes were reused after the Ti-deposits had been extracted by an analytical method explained in the next section. All the fused quartz tubes and polyfluoroethylene fittings were kept in a clean drying oven held at 100 °C to eliminate any moisture when not in use for an experiment. The experiments were conducted at ambient pressure. The transpiration cell pressure was recorded with a capacitance manometer (Leybold Inficon) that varied between 0.96-1.00 atm (730-763 Torr) during the two years of testing. This capacitance manometer was verified by a separate barometric standard (NASA Glenn Aircraft Hanger Barometer). To verify that there were no leaks in the system, the pressure was checked for each experiment by closing the exhaust and watching the back pressure increase as measured by the capacitance manometer. 3.3 Chemical Analyses



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14 The amount of Ti condensate in the three fused quartz condensation tubes along with the polyfluoroethylene fittings and water that was collected through the exhaust was quantitatively analyzed using inductively coupled plasma atomic emission spectroscopy (ICP-AES) (Varian Vista-Pro, Axial configuration). Although the fittings and exhaust waters contained no visible deposits, they were all analyzed. The fittings were digested in a 5% (by volume) hydrochloric acid (HCl) + 2% hydrofluoric (HF) solution for 2-3 hours. This solution and the exhaust water were diluted to a known volume and ICP-AES was used to measure the Ti concentration. The absence of deposit in the exhaust water was also verified in the first several runs by a filtration step resulting in no weight change on Whitman grade #44 filter paper (nominal particle retention size > 3 µm, filtration speed: slow). The inside of the main straight fused quartz condensation tube #1 (which includes the hot zone) contained a film on the internal walls in the form of a brown to black deposit. This main condensation tube acquired the most Ti-deposit relative to the other tubes, although some deposit was also formed in the internal walls of tube #2. The fused quartz tubes were soaked in an aqua regia solution (3 part HCl + 1 part nitric acid (HNO3)) for 2 hours followed by a rinse with concentrated HF. The entire solution was analyzed with ICP-AES. All runs that contained oxygen, where PtO2(g) formation from the transpiration cell is possible, went through a second series of analyses in which an acidic flux (fusion) step through the use of potassium hydrogen sulfate and potassium pyrosulfate was used in order to extract the Ti-condensate. This mixture was heated over a Bunsen burner until it liquefied, thus converting any remaining deposited TiO2(s) into a soluble solution that can be analyzed in the ICP-AES. Some runs had a black deposit that did not fully dissolve in the solution. The first several runs’ black deposits were filtered and dried after the acidic flux (fusion) extraction and


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15 characterized by WDXRF to confirm the absence of Ti. The WDXRF analyses suggested primarily PtO. The typical weight of these black deposits was estimated to be 10-20 mg. Since the WDXRD sensitivity to Ti is typically about 0.1% 34, it is possible that up to 20 µg still remained in this deposit. Several additional methods were tried to dissolve the black deposits. These include successive aqua regia and concentrated HF exposures; a flux of sodium carbonate and sodium tetraborate; and a flux of boric acid and sodium fluoride. The black deposit was not significantly attacked. The resultant solution from the acid dissolution contained only 1 µg Ti. The potential for trace concentrations of Ti in the black deposit must be considered a possible source of error. The second and third quartz condensation tubes along with all the polyfluorethylene fittings were reused since they were not exposed to high temperatures. The third tube and fittings went through a series of acid soaks, which involved an overnight soak in 50% solution of HCl followed by a deionized water rinse, drying and were stored in a clean drying oven (100 °C) prior to reuse. It is also important to note that the ICP-AES procedure is very sensitive for measuring cations and can detect to several micrograms, as found in previous studies6, 8. The amount of Ti in the condensate ranged between 9 and 262 µg. 3.4 Calculations with Experimental Data to Identify the Species and Extract Thermodynamic Data The identity of the volatile species was determined by using the measured data to calculate the coefficients x and y in reaction (7). The same calculation methods were used in previous studies [6, 8]. The vapor pressure of the volatile Ti-O-H species, PTi-O-H, is given by equation (8). =


(8)


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16 Here is the molar rate of transport of Ti from the reaction cell, R is the ideal gas constant, Tcell is the measured temperature inside the cell, and is the total volumetric flow rate through the reaction cell. The molar flow rate of Ti is simply the rate at which Ti is deposited downstream. =

(9)

Here mTi is the mass of Ti collected at the end of an experiment, MTi is the atomic weight of Ti, and t is duration of an experiment. The total flow rate through the cell is simply the sum of all the flow rates through the cell.

= + + +

(10)

Here Ptot is the total pressure. The last quantity in Equation (4), , is the same as and is much smaller than the others. It can thus be neglected. Note also that these flow rates are all at 298.15 K. Initially a series of experiments was conducted to identify the product of the reaction of TiO2 and O2/H2O. This was done by systematically varying and . Once the molecule was identified, vapor pressures were determined. Second and third law methods were then used to derive thermodynamic parameters35, 36. The second law method gives a heat of reaction, ∆ !$"# , at the average temperature of measurement, Tav, using the van’t Hoff equation. %('( )* ) , %( )

=−

∆. "#

(11)

Here Kp is the equilibrium constant for reaction (1) with known x and y and R is the gas constant. In order to obtain a heat of reaction at 298.15 K, the following expression is used. T o ∆ r H To = ∆ r H 298 +

∫ ∆C

p dT

298


(12)

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17 Here ∆/0 is the change in heat capacity of the reaction and uses the heat capacity of the product in Table 4. The Gibbs energy function is given by equation (13). $ 123456.89 = (:$ − !456.89 )/

Computational and Experimental Study of Thermodynamics of the

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