Synthesis and Characterization of Nano-Aerogels

8.2. Experimental

The TiO₂ and ZrO₂ aerogel particles (denoted as a-TiO₂ and a-ZrO₂, respectively) were synthesized using the methods previously described (Chapters 5 and 6). A-TiO₂-A and a-TiO₂–B aerogel were synthesized using 1.10 M titanium(IV) isopropoxide and 1.10 M titanium(IV) butoxide polycondensated with 4.95 M and 6.05 M acetic acid, respectively, at 40 C and 6000 psig of scCO₂. A-ZrO₂ was synthesized using 1.13 M zirconium butoxide reacting with 2.52 M acetic acid at 40 C and 6000 psig of scCO₂. Since aerogels are well-known to adsorb significant quantities of water or organic solvents that also interact with CO₂, special attention was made to dry the aerogels. ScCO₂ drying and vacuum drying at 120 C and 0.8 pa was conducted until the IR spectrum showed no traces of water peaks at 3000-3600 cm^-1. Samples of the dried aerogels were calcined at 500 C to obtain oxides.

The dried aerogels, with and without calcination, were studied using ATR-FTIR spectroscopy (ReactIR 4000, ASI Applied System Inc.). The experimental setup was described in detail in Chapter 3. Since the ATR-FTIR can only detect materials a few microns from the mirror, the absorbance peaks of powder is low. In order to obtain significant peaks, the aerogel powder was pressed against the diamond mirror by using the agitation shaft with a rubber disk in between (Figure 8.3). The spectra of the pure aerogels were collected before addition of CO₂. Then, the temperature and pressure were kept at 40 C and 4000 psig for 30 minutes after addition of CO₂. Because of the strong absorbance of bulk CO₂, which prevents clear observation of CO₂ interacting with the aerogel, FTIR spectra were collected 1 minute after venting of CO₂ from the autoclave when adsorbed CO₂ was still present. FTIR spectra were collected from 600 to 4000 cm^-1 with a resolution of 2 cm^-1. The subtraction and curve fitting of the IR spectra were obtained using ACD UVIR Processor version 7.0 software (ACD Inc. Toronto, Ontario). The curve fitting was processed by assuming a Gaussian peak profile, and the limit of the half-peak width was set as 80 cm^-1 for a better curve fit.

Figure 8.75. Schematic drawing of ATR-FTIR analysis. The aerogel powder was pressed against the diamond mirror to obtain higher absorbance peaks.

8.3. Results and Discussion

8.3.1. FTIR Spectroscopy and LA-LB interaction

Figure 8.4 shows the spectra of both the pure and CO₂-impregnated aerogels of a-TiO₂-A, a-TiO₂-B and a-ZrO₂. In the spectra, the peaks in the region of 1400-1600 cm^-1 are attributed to M-acetate bidentate,^229 those at 1325-1346 cm^-1 to hydrocarbon groups,^306 that at 1118 cm^-1 to M-O-C, those at 1025-1026 cm^-1 to bridging OR groups,^228 and those lower than 900 cm^-1 to oxo bonds. In the spectra of CO₂-impregnated a-TiO₂-A, a-TiO₂-B and a-ZrO₂, besides the peaks from the pure aerogels in the region of 680 –1680 cm^-1, there are new peaks at 668, 654, 649 and 648 cm^-1. The very sharp peak at 668 cm^-1 is due to free CO₂, while the relatively wide peaks in the 642-654 cm^-1 region are the overlapping results of ν₂ bending vibration of the impregnated CO₂ and vibration of the oxo bonds.^289



Figure 8.76. The ATR-FTIR spectra of (a) a-TiO₂-A, (b) a-TiO₂-B and (c) a-ZrO₂ before addition of CO₂ (black) and at one minute after venting of CO₂ (red).

In order to examine the vibration wavenumbers of the impregnated CO₂, subtraction of the corresponding aerogel spectrum is necessary. Figure 8.5 presents the spectra of CO₂ impregnated in the aerogels after the subtraction and the curve-fitting results. The peaks in the region of 630–665 cm^-1 were attributed to CO₂ ν₂ vibration splitting. Understanding the complex peaks requires a careful consideration of the electronic structures of metal-acetate and the nature of CO₂ ν₂ vibration.

Figure 8.77. The IR spectra and the curve-fitting results of CO₂ interacting with (a) a-TiO₂-A, the residual sum of squares: 3.86E-3; (b) a-TiO₂-B, the residual sum of squares: 4.01E-4; and (c) a-ZrO₂, the residual sum of squares: 1.81E-3. Note: the black curves = experimental spectra; the pink curve = the fitting curve; blue curves = the individual Gaussian function curves; and the red curve = the residual curve.

In the bridging acetate bidentate, the atoms of the bridging carbon, oxygen and metal are sitting almost in one plane, as shown in Figure 8.2a. The π electrons are delocalized around the two bridging oxygen atoms and the α-carbon atom, which are sp² hybridized. Previous studies by others showed that the chemical bond between transition metals and the oxygen of the bridging carboxylate is due to the overlap of the d orbital of the former, and the p orbital of the latter.^307-311 Besides the p orbital and one σ bond (O-C), each of the two oxygen atoms still has two lone pairs, as shown in Figure 8.6. When a CO₂ molecule approaches the lone pairs, the partial positive carbon can associate with the sp² oxygen as either in plane or out-of-plane due to the LA-LB interaction, where the plane is defined as the lone pairs of the oxygen. The π bond of the bridging acetate is also an electron donor and has potential to interact with the partially positive carbon atom of CO₂.

When we consider the molecular structure of CO₂, there are two IR active bending modes. In the case of free CO₂, the two bending vibrations absorb at the same frequency due to the symmetry of the CO₂ molecule (Figure 8.7). In the case of LB-associated CO₂, it is expected that the degeneracy would disappear, and two absorption peaks (in-plane and out-of-plane) will appear for each LA-LB association mode. From our IR experimental results, there are two distinct peaks (at 663 and 657 cm^-1 before curve-fitting, and at 663 and 655 cm^-1 after curve-fitting) from a-TiO₂-A associated CO₂ (Figure 8.5). This result is in a good agreement with the literature that CO₂ bending peaks shifted to 662 and 654 cm^-1 resulting from the carbonyl group of PMMA.^289 This suggests that the split of CO₂ ν₂ vibration is mainly due to the lone pairs of the oxygen atom. In the case of a-TiO₂-B and a-ZrO₂ associated CO₂, however, there is a wider combined peak. Four individual peaks were produced after curve-fitting, indicating more than one association mode exists, either due to the lone pairs or from the π bond. There is noticeable difference between the IR spectra of CO₂ impregnated into a-TiO₂-A and a-TiO₂–B (Figure 8.5). This difference cannot be easily explained, because the detailed structures around the bridging acetate remain unknown. However, we may exclude the effect of the alkoxide groups in a-TiO₂-A and -B, which are isopropoxide and n-butoxide, respectively, because of their small amounts in the aerogels, as shown by the IR spectra (Figure 8.4).



Figure 8.78. Schematic of possible association modes of LA-LB interaction between CO₂ and metal bridging acetate. (a) d-p orbital overlap between metal (M) and acetate, and CO₂ associates with the π bond either in a vertical or a parallel mode; (b) the partial positive carbon CO₂ associates with the lone pairs of oxygen either in T-shape or bended T-shape.


Figure 8.79. The bending and stretching vibrations of a free CO₂ molecule. The two bending vibrations absorb at the same frequency of IR beam due to the symmetry of the CO₂ molecule.

Figure 8.8 shows the IR spectra of CO₂ impregnated into a-TiO₂-A, a-TiO₂-B and a-ZrO₂ in the ν₃ stretching mode region. These spectra show a high peak at 2337 cm^-1 and an asymmetric wide peak around 2358 cm^-1. The peak at 2337 cm^-1 is assigned to the free CO₂, while the small right shoulder of the peak at 2337 cm^-1 can be assigned to the (ν₂ + ν₃) - ν₃ band.^289 The peak at 2358 cm^-1 is due to the interaction between CO₂ and the aerogels that caused the CO₂ ν₃ stretching mode split. When we compare Figure 8.8a and d, the free CO₂ peak at 2337 cm^-1 decreased faster than the peak at 2358 cm^-1, suggesting that the free CO₂ weakly interacts with the aerogel_.

Figure 8.80. IR spectra of CO₂ impregnated into (a) a-TiO₂-A, (b) a-TiO₂-B and (c) a-ZrO₂ in the ν₃ stretching mode region, at one minute after venting of CO₂; (d) CO₂ impregnated into a-TiO₂-A at five minutes after venting of CO₂.

It is necessary to point out that the above discussion of the LA-LB interaction was based on the structure of the metal bridging acetate obtained from single crystal analysis. Although the IR spectra in Figure 8.4 indicates that the acetate bidentate structure remains in the aerogels, the detailed structure of the chemical environment around the acetate in the aerogels is unknown. From the IR experimental results, we cannot determine the exact LA-LB association mode; however, the splitting of the CO₂ ν₂ peak strongly supports that CO₂ acts as an electron accepter.

From an electronic structure point of view, the above discussion has described the LA-LB interaction between a CO₂ molecule and an aerogel with a complex metal-bridging acetate. In addition, a semi-quantitative study on the interaction can be carried out by calculation of the solubility parameters (δ) of the colloidal particles and comparison with that of the CO₂-based reaction solvent.

8.3.2. Solubility Parameter Study

Estimation of  of CO₂. The solubility parameters of CO₂ can be calculated either from the density by using Giddings Equation^304 or from the models developed from an empirical equation of state (EOS).^{300, 303} According to Giddings et al.,^312

(8.43)

where, is the critical pressure in atmospheres, is the reduced density of CO₂, = 2.66 is the reduced density of liquid CO₂ at its normal boiling point,^304 and is the density of CO₂ in mol/L. Giddings’ equation correctly predicts that a higher density of CO₂ results in a higher solubility parameter; however, it was found to be poor for quantitative predictions.^300 By using the EOS of Huang et al, Williams et al recently calculated the solubility parameters of CO₂ under a variety of temperatures and pressures, and the calculated results were close to Allada’s.^300 In Table 8.1, the solubility parameters of CO₂ obtained from Allada’s method are listed, under the typical conditions at which the direct sol-gel synthesis in scCO₂ was carried out in this thesis.

Table 8.7. Solubility parameters of scCO₂ under selected temperatures and pressures. ^{300, 303}

Temperature (°C)	40	40	60	60	60
Pressure (psia)	4000	6000	4000	5000	6000
Solubility parameters, (cal/cm^3)^1/2	6.99	7.46	6.23	6.65	6.83

Estimating  of Alkoxides. The solubility parameters of solvents and small molecules can be calculated from the cohesive energy density or the molar energy of vaporization:^313

(8.44)

where, is the energy change upon isothermal vaporization of the saturated liquid to the ideal gas state at infinite dilution in cal/mol, is the molar volume of the liquid in cm³/mol, is the enthalpy change during vaporization in cal/mol, is the gas law constant in cal/(mol·K), and the temperature in K.

Using Equation 8.3 and the thermodynamic data from Bradley in Table 8.1,^{314, 315} the solubility parameters of titanium alkoxides at 298 K were calculated as presented in Table 8.2.

Table 8.8. The thermodynamic properties and the average solubility parameters of the alkoxides.

Molecule	Hf^0 ^* (liquid) Kcal/mol	Hf^0 ^* (gas) Kcal/mol	HV^0^* Kcal/mol	^0(liquid) cm^3/mol	 (cal/cm^3)^1/2
Ti(OPr^i)4	-377^**	-360^**	17	296^***	7.44
Ti(OBu^n)4	-399^**	-377^**	22	340^***	7.93
Note: ^* Hf^0, HV^0 and ^0 denote the standard formation enthalpy, the enthalpy change of vaporization and the molar volume of the liquid, respectively. ^**Ref. ^314 ^***The molar volume was calculated from the density at 293 K. The liquid volume change was neglected for temperature changes from 293 to 298 K.

Estimating  of Ti-acetate complexes and macromolecules. Fedors’ group contribution method has been widely used to estimate the solubility parameters of a variety of materials.^316-318 This method is especially attractive when vaporization energies of the interested materials are available, as in the case of metal alkoxides. According to Fedors, the solubility parameters of small molecules and macromolecules can be calculated by using Equations 8.4 and 8.5, respectively.^{305, 319}
(8.45)

where, Δe_i is the energy of vaporization in cal/mol, and Δυ_i the mole volume in cm³/mol. In the case of macromolecules,^305

(8.46)

where Δe_ir is the energy of vaporization of the repeating unit in cal/mol, and Δυ_ir is the mole volume of the repeating unit in cm³/mol. The related atomic and group contributions to the energy of vaporization and mole volume at 298 K are listed in Table 8.3.^305 The detailed calculations of Ti atom’s group contributions are described in Appendix 11.

Table 8.9. The related atomic and group contributions to the energy of vaporization and mole volume at 25 °C.^305

Atom or group	Δei (cal/mol)	Δυi (cm^3/mol)
CH3	1125	33.5
CH2	1180	16.1
CH	820	-1.0
COO	4300	18.0
O	800	3.8
Ti ^*	500 ^**	7.2^**
Note: ^* Calculated in this work. ^** The values were the average calculated from the thermodynamics data of TIP and TBO in Table 8.2 using Equation 8.3 and 8.4.

The titania colloidal particles were derived from the condensation of the hexamer complexes,^{105, 320} such as Ti₆O₆(OPrⁱ)₆(OAc)₆ (2) and Ti₆O₄(OBuⁿ)₈(OAc)₈ (1). Since the condensation takes place on the OR groups,^105 the repeating unit of the macromolecules of a-TiO₂-1 and a-TiO₂-2 can be estimated to be -(Ti₆O₁₂(OAc)₆)-, and -(Ti₆O₁₂(OAc)₈)-, respectively. In the case of the SiO₂ and ZrO₂ colloidal particles, there is no building-block information available (i.e. crystal structure data). Based on the values in Table 8.3, the solubility parameters of the macromolecules with repeating units of -(Ti₆O₁₂(OAc)₆)-, and -(Ti₆O₁₂(OAc)₈)- can be calculated as shown in Table 8.4 (The detailed calculation is described in Appendix 11).

Table 8.10. Solubility parameters of the macromolecules calculated using the group contribution method.

Repeating Unit	Δeir (cal/mol)	Δυir (cm^3/mol)	δ (cal^0.5cm^-1.5)
-(Ti6O12(OAc)6)-	45.2 ×1000	397.8	10.7
-(Ti6O12(OAc)8)-	56.0 ×1000	500.8	10.6
-(Ti6O12)-^*	12.6 ×1000	88.8	11.9
Note: ^* The imaginary repeating unit for comparison of with and without acetate.

According to the results from Table 8.4, the solubility parameters of the macromolecules with acetate group are approximately 10.7 cal^0.5cm^-1.5. For comparison purpose, the solubility parameters of the corresponding macromolecules without bridging acetate were also calculated, which are approximately 11.9 cal^0.5cm^-1.5. The results show that the bridging acetate results in a lower solubility parameter which is closer to that of CO₂, e.g., at 40 °C and 6000 psig when the solubility parameter is 7.46 cal^0.5cm^-1.5, and a favorable stabilization of the colloidal particles can be expected.

From the above study, we can see that the solubility parameter of the colloidal particles with Ti-acetate groups is still larger than that of CO₂ under the utilized synthesis conditions. It can be expected that addition of a cosolvent may improve the solubility of the macromolecules in CO₂. In fact, during the synthesis of the aerogel particles, extra acetic acid was added (Chapters 4-6), and in the case of ZrO₂, extra alcohol was added (Chapter 6). In addition, the ester and alcohol were generated as by-products during the process. The polar organic species generally exhibit higher solubility parameters. For example, acetic acid, isopropanol and isopropyl acetate have solubility parameters of 9.83, 11.55 and 8.51 cal^0.5cm^-1.5, respectively.^321 It can be anticipated that the existence of these species in CO₂ will increase the solubility parameter. Using Equation 8.6, the solubility parameter of the mixed solvent can be calculated:^{321, 322}

(8.47)

where, is the solubility parameter of the mixed solvent, and and are the volume fraction and the solubility parameter of solvent i, respectively. For example, in a typical synthesis of titania nanomaterials, the volume fractions of acetic acid and CO₂ are about 0.27 and 0.73, respectively.^320 The calculated solubility parameter of the mixture of acetic acid and CO₂ at 40 °C and 6000 psi is 8.10 cal^0.5cm^-1.5, with an increase of 8.6% from 7.46 cal^0.5cm^-1.5 of pure CO₂. Even though the acetic acid is consumed during the reactions, the resulting ester, water and alcohol will compensate for the consumed acetic acid in regards to .