**Probing Water and CO2 Interactions at the Surface of Collapsed Titania Nanotubes Using IR Spectroscopy**

#### **Kaustava Bhattacharyya, Weiqiang Wu, Eric Weitz, Baiju K. Vijayan and Kimberly A. Gray**

**Abstract:** Collapsed titania nanotubes (cTiNT) were synthesized by the calcination of titania nanotubes (TiNT) at 650 °C, which leads to a collapse of their tubular morphology, a substantial reduction in surface area, and a partial transformation of anatase to the rutile phase. There are no significant changes in the position of the XPS responses for Ti and O on oxidation or reduction of the cTiNTs, but the responses are more symmetric than those observed for TiNTs, indicating fewer surface defects and no change in the oxidation state of titanium on oxidative and/or reductive pretreatment. The interaction of H2O and CO2 with the cTiNT surface was studied. The region corresponding to OH stretching absorptions extends below 3000 cmí1 , and thus is broader than is typically observed for absorptions of the OH stretches of water. The exchange of protons for deuterons on exposure to D2O leads to a depletion of this extended absorption and the appearance of new absorptions, which are compatible with deuterium exchange. We discuss the source of this extended low frequency OH stretching region and conclude that it is likely due to the hydrogen-bonded OH stretches. Interaction of the reduced cTiNTs with CO2 leads to a similar but smaller set of adsorbed carbonates and bicarbonates as reported for reduced TiNTs before collapse. Implications of these observations and the presence of proton sources leading to hydrogen bonding are discussed relative to potential chemical and photochemical activity of the TiNTs. These results point to the critical influence of defect structure on CO2 photoconversion.

Reprinted from *Molecules.* Cite as: Bhattacharyya, K.; Wu, W.; Weitz, E.; Vijayan, B.K.; Gray, K.A. Probing Water and CO2 Interactions at the Surface of Collapsed Titania Nanotubes Using IR Spectroscopy. *Molecules* **2015**, *20*, 15469-15487.

#### **1. Introduction**

Nano-scale TiO2 materials have attracted scientific interest due to their unusual physico-chemical properties such as high specific surface area, ion-exchangeability, and photocatalytic activity. Interest in nano-scale titania materials has extended to one-dimensional structures including nanotubes, nanorods, and nanowires, which can now be synthesized by relatively standard methods [1–6].

In the late 1990s, Kasuga *et al.* reported the first hydrothermal synthesis of a nano-tubular structure of titania [1,2]. Researchers subsequently showed that these structures consist of hydrated dititanate (H2Ti2O5), trititanate (H2Ti3O7) [3–5], and H2Ti4O9·*x*H2O stoichiometries [6], as well as their Na salts. These structures can be thermally treated to improve phase crystallinity, although there is still no clear consensus on the specific conditions under which thermal treatment leads to the transformation of titania/titanates in titania nanotubes (TiNTs) to TiO2 (B), rutile, or brookite. Nevertheless, it is clear that the morphology of the TiNTs starts to undergo a change around 550 °C. Poudel *et al.* [7] observed a change from nanotubes to nanowire morphology at an annealing temperature of 650 °C. Tsai and Teng [8], Yoshida *et al.* [9], and Vijayan *et al.* [10] all reported a drop in surface area and pore volume with increasing temperature*.* The surface area of the TiNTs steadily decreases as a function of temperature for as long as the nanotube morphology is retained and then decreases sharply upon further elevation of the temperature, which results in the loss of the tubular morphology [11]. Vijayan *et al.* characterized these morphological changes to TiNTs over a range of calcination temperatures from 200 to 800 °C and, using EPR, they detailed how these changes altered charge trapping behavior and photocatalytic reactivity [10].

There is an enormous body of literature on the photocatalytic reactivity, particularly oxidation reactions, of titania and doped titania materials of various morphologies. Comparatively less is known about the details of the photocatalytic reduction of CO2 by titania materials, especially the molecular level mechanism(s) for this complex process. Our prior study of the adsorption of CO2 on the surface of TiNTs and platinized TiNTs focused on changes in adsorptive chemistry that took place when the TiNTs were subjected to reductive and/or oxidative pretreatments. We found that differences in the surface species formed, which included carbonates and bicarbonates, could be correlated with the Lewis acidity and basicity of the Ti and O on the TiNT surface [12].

Calcination temperature affects the chemistry taking place on TiNTs. Vijayan *et al.* [10] reported maximum CO2 conversion for TiNT calcined at 400 °C and dramatically decreasing CO2 photo-reduction with increasing calcination temperature, particularly above 600 °C. The collapse of the tubular nanostructure is accompanied by a diminished number of under-coordinated Ti sites and marked changes in charge trapping as characterized by EPR. Differences in the respective reactivity of TiNT and collapsed TiNT (cTiNT) with CO2 may be explained by differences in CO2 binding at the catalyst surface [10,12]. Water has been found to be a critical participant in the reduction of CO2. The presence of water has been shown to facilitate CO2 photoreductive chemistry. This is not surprising since water can provide the protons needed to go from CO2 to hydrocarbons and the coordination of water can potentially lower the barrier for reactions to desired hydrocarbon products such as formic acid and methanol.

The objective of the research reported herein is to spectroscopically probe the interactions of water and CO2 at the cTiNT surface with the ultimate goal of identifying the surface characteristics of photocatalytic materials capable of driving CO2 conversion. Specifically, we report the effect of higher temperature annealing on the phase, structure, and morphological distortion, which leads to changes in the chemical interactions of CO2 with cTiNT. We also address an issue in the literature with regard to the assignment of low frequency absorptions in the OH stretching region of the infrared. These absorptions are assigned to OH stretches that form on exposure of the nanotubes to water. We speculate that hydrogen bonding between H-containing moieties within the structure of the nanotubes may be the sources of these low frequency OH absorptions.

#### **2. Results**

#### *2.1. X-ray Diffraction Data*

The interpretation of the X-ray diffraction data (Figure 1) for the titania nanotubes that have been heated to 350 °C has been discussed previously in detail [12]. These data confirm that the TiNTs are essentially pure anatase. Thermal annealing at 650 °C leads to formation of a rutile phase along with the characteristic anatase phase. As seen in Figure 1, after annealing at 650 °C, a series of diffraction peaks appear which are consistent with anatase TiO2 (JCPDS 75-1537): (101), 25.7°; (200), 47.9°; (105), 53.7°; (211), 55.0°; (213), 61.9°; (204), 62.8°; (116), 68.3°; (220), 69.7°; and (301), 75.2°. An additional diffraction peak characteristic of the rutile phase is seen at 27.3° (110) (JCPDS-77-0443, 77-0444). This new peak indicates that there is a partial transformation between anatase and rutile as a result of heating to 650 °C. Though anatase is metastable in the bulk, it has been reported that the anatase phase is more stable as nano-scale TiO2 than as bulk TiO2 [13–17]. A prior report for TiNT prepared by anodization of Ti foil indicated that above 550–600 °C, rutile is the dominant phase (>50%) [18,19]. In contrast, Albu *et al.* found that double-walled anodized TiNTs were extraordinarily stable, retained their structural integrity even when annealed to temperatures higher than 600 °C, and showed only traces of rutile [20]. Similarly, we determine a rutile composition of only ~5.5%. The smaller amount of rutile formed is probably due to the enhanced stability of anatase in nano-scale titania materials, but the transformation could also be kinetically limited, possibly as a result of the hydrothermal synthesis process. However, the peak at a 2ș value of 13.3° is completely absent in the XRD pattern, indicating the loss of the titania nanotubular morphology for samples calcined at 650 °C.

**Figure 1.** XRD profiles of (**a**) TiNT; (**b**) TiNT-O2; (**c**) TiNT-O2-H2; (**d**) cTiNT-; (**e**) cTiNT-O2; (**f**) cTiNT-O2-H2. Note that traces **a**–**c** have been included here for completeness and are reproduced from Figure 2 in reference [12]. Reprinted with permission from: Kaustava Bhattacharyya, Alon Danon, Baiju K. Vijayan, Kimberley A. Gray, Peter C. Stair, and Eric Weitz, *The Journal of Physical Chemistry C* **117** (2013), 12661–12678, Copyright 2013, American Chemical Society.

**Figure 2.**  Note that panels (**b**,**d**) are included here for completeness and are from Figure 1 in Reference [12]. Reprinted with permission from: Kaustava Bhattacharyya, Alon Danon, Baiju K. Vijayan, Kimberley A. Gray, Peter C. Stair, and Eric Weitz, *The Journal of Physical Chemistry* C **117** (2013), 12661–12678, Copyright 2013, American Chemical Society.

#### *2.2. Transmission Electron Microscopy*

The interpretation of the electron microscopy data for the titania nanotubes heated to 350 °C has been discussed in detail previously [12]. Briefly, the data in Figures 2–4 compare HRTEM images of the TiNTs calcined at 350 °C and 650 °C. The conclusion from the HRTEM data is that the nanotubular morphology of the TiNTs is intact for the TiNTs calcined at 350 °C and after pretreatment under an oxygen atmosphere, and subsequently under H2. However, when these TiNT are calcined at 650 °C, the tubular morphology is lost and the tubes transform into a variety of other nanoscale shapes, although nanorods are the predominant shape.

**Figure 3.**  BET Surface Area*

Measurement involving a determination of the BET surface area and pore size distribution of TiNTs has been previously reported [10,12]. Briefly, the as-prepared TiNTs have a surface area of ~235 m2 /g, which is almost 20 times that of the TiO2 anatase powder from which the tubes were prepared. Upon calcination at 350 °C the surface area decreases to ~200 m2 /gm. When these TiNTs are subject to either oxidative and/or reductive pretreatments at 350 °C the surface area decreases further, into the ~180–195 m2 /gm range, which is still comparable to that before pretreatment. Upon calcinations of the TiNTs at 650 °C the surface area decreases substantially to ~90 m2 /g. The surface areas do not change significantly for the cTiNT samples as a result of oxidization and subsequent reduction. Thus, as the temperature increases toward 650 °C, the collapse of the nanotubes leads to formation of coarser grain particles and as the crystallite size grows, so does the inter-particle pore size.

**Figure 4.**  Note that panel 2.3d is from Figure 1 in reference [12]. It has been included here for completeness and is reprinted with permission from: Kaustava Bhattacharyya, Alon Danon, Baiju K. Vijayan, Kimberley A. Gray, Peter C. Stair, and Eric Weitz, *The Journal of Physical Chemistry* C **117** (2013), 12661–12678, Copyright 2013, American Chemical Society.

#### *2.4. XPS*

The top panel in Figure 5 shows the XPS Ti 2p spectra of the cTiNT subjected to oxidative and reductive pretreatments. All of the cTiNT samples have Ti 2p3/2 and Ti 2p1/2 peaks at 458.6 and 464.3 eV, respectively, in their Ti XPS spectra. These peak positions are typical of anatase TiO2 nano-powder samples [21,22]. There is no observed change in these peaks as a function of oxidation or reduction. The lack of change in these peaks on oxidation and/or reduction is in marked contrast to what is observed for TiNT samples, where upon reduction there is formation of the Ti3+ and splitting of the Ti4+ peak [12].

The O 1s XPS spectra shown in the bottom panel in Figure 5 for the samples calcined at 650 °C (cTiNT) exhibits analogous behavior. Each sample shows an O 1s XPS peak at 531.66 eV, which is typical of bulk anatase TiO2 samples. These O 1s peaks are symmetric and possess a smaller FWHM than the TiNT samples calcined at 350 °C, which is indicative of fewer O defects and fewer OH groups. Thus, we can infer based on the XPS data [21,23] that the electronic environment of surface Ti and O atoms in the nanotubular morphology is more sensitive to oxidation and/or reduction than their counterparts in the nanotubes that have collapsed as a result of annealing. Overall, there is no observable shift in either the Ti or the O XPS peaks upon oxidation of the cTiNT, and upon reduction there is neither formation of Ti3+ for this sample nor is there any splitting of the Ti4+ peak, as was observed for the corresponding TiNTs that were annealed at 350 °C [12].

**Figure 5.** The XPS spectra for (**top panel**) Ti 2p and (**bottom panel**) O 1s for the cTiNTs which have been subjected to different pre-treatments: (**bottom trace**) cTiNT; (**middle trace**) cTiNT-O2; (**top trace**) cTiNT-O2-H2.

#### *2.5. FT-IR Spectroscopy*

Figure 6 shows a spectrum of the cTiNTs after they have been collapsed by calcining to 650 °C and then cooled to room temperature. There is an absorption that stretches from ~3700 cmí1 down to ~2700 cmí1 . The absorption appears to consist of at least two overlapped peaks as a result of the increase in intensity near 3000 cmí1 . There are no observable absorptions due to Ti-OH stretches, which are expected near 3700 cmí1 [24]. The insert shows the cTiNT-O2 after exposure to water vapor at room temperature and subsequent to evacuation of the water vapor.

**Figure 6.** *In situ* FT-IR spectra of the c-TiNT. The collapsed NTs were prepared by calcination at 650 °C in a furnace and were allowed to cool to room temperature and introduced into the IR cell and an IR spectrum was recorded (**a**). Spectrum **b** was recorded after these cTiNTs were exposed to vacuum for 2 h at 350 °C. Spectrum **c** was recorded after the same cTiNTs were heated in O2 for 3 h at 350 °C to produce cTiNT-O2. Spectrum **d** was recorded after the oxygen was evacuated from the cell subsequent to obtaining spectrum **c** and the oxidized cTiNTs were heated in H2 for 3 h at 350 °C to produce cTiNT-O2-H2. The inset shows a cTiNT-O2 sample that has been exposed to 10 Torr of water vapor for 15 min at room temperature. The background for all spectra was the cell with the tungsten wire grid in place but no sample on the grid.

To probe the source of these absorptions we exposed the sample to D2O. Figure 7 shows that exposure to 10 Torr of gas-phase D2O produces a broad absorption between ~2700 and ~1950 cmí1 . A "negative absorption" is also seen between ~3500 and ~2700 cmí1 . We note that the spectra shown are referenced to background spectra of the cTiNTs. Thus, depletion of a species that is present and absorbs in the background spectrum will appear as a "negative absorption" in the sample spectrum. The upper trace also has absorptions due to OD stretching modes of D2O in the ~2900 to ~2500 cmí1 range, which show the rotational structure characteristic of gas-phase absorptions, as do the absorptions below 1600 cmí1 , which are due to the bending mode of D2O. The lower trace demonstrates that evacuation removes the gas-phase D2O. Evacuation also leads to a decrease in intensity of the 1950 to 2700 cmí1 absorption, with a larger decrease in intensity at higher frequencies, where weakly bound D2O would be expected to absorb. There is also a sharp peak at 2350 cmí1 that is superimposed on the broad absorption. This is where gas-phase CO2 absorbs [25], and this absorption is likely due to a small change in the CO2 content of the purged housing that takes place over the timescale of the experiment.

**Figure 7.** The upper spectrum is the *in situ* FT-IR spectra of the cTiNT-O2-H2 after exposure to D2O vapor for 10 min at room temperature. The lower spectrum is of the same sample after exposure to vacuum at room temperature. The background for these spectra is the c-TiNT-O2-H2s.

Figure 8 shows the spectrum obtained on exposure of the reduced cTiNTs to 20 Torr of CO2. The very intense absorption centered at 2350 cmí1 is due to the asymmetric stretch of CO2 and the absorptions near ~3610 and ~3715 cmí1 are due to combination bands of CO2 [25]. Carbonates and bicarbonates have characteristic absorptions below ~1700 cmí1 [26]. As shown in the insert, exposure to CO2 also leads to a small "negative" absorption in the OH stretching region. The nature of these absorptions along with the absorption at ~1718 cmí1 is discussed in more detail below.

**Figure 8.** The upper trace is an *in situ* FT-IR spectrum of the cTiNT-O2-H2 exposed to 20 Torr of CO2 for 30 min at room temperature. The lower trace is the same sample after exposure to vacuum at room temperature. The background for these spectra is the c-TiNT-O2-H2. The insert is a blow-up of the 4000 to ~2400 cmí1 region.

#### **3. Discussion**

#### *3.1. Structure of the NTs*

It is clear from the XRD results that as the TiNTs are annealed to 650 °C, the anatase TiNTs are partially transformed to the rutile phase. The TEM results show that the tubular morphology is completely lost upon calcining at 650 °C. In contrast to XPS data showing significant changes in the electronic environment around the Ti and O sites on oxidation and/or reduction of the TiNTs heated to 350 °C [12], the XPS spectra shown in Figure 5 reveal that there are no significant changes in the electronic environment around the Ti and O surface sites on oxidation and/or reduction of the cTiNT. All of the XPS spectra for the cTiNTs exhibit Ti 2p3/2 and Ti 2p1/2 peaks at 458.6 and 464.3 eV, respectively. They also have very similar O 1s XPS spectra, which are not affected by further oxidation or reduction. Each spectrum shows an O 1s XPS peak at 531.6 eV that is typical of bulk anatase TiO2 samples. These O1s peaks [27] are symmetric and possess a smaller FWHM than seen for the TiNT samples that were calcined at 350 °C [12]. The narrowing and the symmetry of this peak are likely the result of either fewer surface –OH groups, O defect sites, non-stoichiometric O sites, or some combination of the three [23,27]. One of the more interesting observations with the TiNT samples is that reduction subsequent to oxidation leads to the appearance of a XPS peak that is characteristic of Ti3+ [12]. No Ti3+ signals are seen for any treatment of the cTiNT samples that we have studied.

#### *3.2. Interactions of H2O and D2O with c-TiNT*

Titania nanotubes are formed from the dehydration of titanates, such as H2Ti2O5, that is driven by calcination at elevated temperatures. Figure 6 shows the IR spectrum of cTiNT (calcined at 650 °C in an oven, allowed to cool to room temperature, and then transferred to our IR cell). Traces are shown for the cTiNTs after being transferred into the cell, after 2 h under vacuum at room temperature, after oxidation by heating in oxygen at 350 °C for 3 h, and after reduction in hydrogen at 350 °C for 3 h (subsequent to oxygen pretreatment and evacuation of oxygen). The high energy portion of the four spectra are dominated by a broad absorption starting near ~2700 cmí1 with a feature with maximum amplitude near 2950 cmí1 and another broad feature that peaks in the 3300 to 3400 cmí1 region.

There have been many studies of water adsorption on metal oxides and on titania in particular. Suda and Morimoto report three features above 3000 cmí1 on rutile titania powder [28]. One is a sharp absorption near 3660 cmí1 , which is split into a doublet at elevated temperature. This feature is assigned to surface OH groups, and the two components of the peak are attributed to monodentate and bidentate OH binding. The remainder of the absorption above 3000 cmí1 is assigned to surface-bound water. They assign the feature at 3520 cmí1 to hydrogen-bonded OH groups and the broad feature at ~3400 cmí1 to molecular water. The interaction of water with a thin titania film was studied by Nakamura *et al.*, and a broad absorption due to physisorbed water is reported centered at 3500 cmí1 [29]. This water can be removed by evacuation at room temperature. More strongly absorbed water is reported to be centered at 3270 cmí1 . This assignment parallels those for other metal

oxides where physisorbed water is reported at higher frequencies than more strongly adsorbed water and both absorb above 3000 cmí1 [24]. Ti-OH absorptions, if present, are typically reported around 3700 cmí1 [24]. Interestingly, a spectrum reported by Tsuchiya *et al.* [30] for anodic titania NTs shows a broad absorption centered at 3450 cmí1 that extends below 3000 cmí1 . Chen *et al.* [5] also present a spectrum of titania NTs that shows a broad absorption from just above 2500 cmí1 to ~ 3400 cmí1

The spectra reported by Tsuchiya *et al.* [30] and Chen *et al.* [5] are qualitatively similar in extent and shape to the water absorption shown in Figure 6. There is no absorption characteristic of OH groups in Figure 6 (or in the two references cited above). This is consistent with the removal of OH groups from the surface when the TiNTs are heated to 650 °C. Presumably this can occur as a result of a reaction to form water. This water then either desorbs into the gas phase or adsorbs on the cTiNTs. Water can also adsorb on the cTiNTs as they cool in air. Gas-phase water has its asymmetric stretching vibration centered at 3756 cmí1 , its symmetric vibration centered at 3651 cmí1 , and its bending mode centered at 1595 cmí1 [25]. The manifold of small peaks between 3900 and 3500 cmí1 and between 1400 and 1900 cmí1 in Figure 6 are due to absorptions of gas-phase water. These absorptions are likely due to small changes in water content in the purged spectrometer housing taking place over the timescale of hours. Inspection of Figure 6 clearly demonstrates that adsorbed water absorbs at a lower frequency than gas-phase water. The observation that there is little change in the shape of the higher energy portion of the water absorption upon evacuation at an elevated temperature (350 °C) is consistent with the dominant water species that is present being strongly adsorbed water, which absorbs at a lower frequency than weakly bound water [24]. We now turn to the lower frequency portion of the absorption in this region.

Absorptions at lower frequencies than seen for adsorbed water on anatase powder or thin films were noted in the literature [5,30] and in a prior study of TiNTs in our group [31]. In that study, TiNTs decorated with Pt nanoparticles were exposed to supra-bandgap light [31]. Pt nanoparticles can act as a "sink" for photo-generated electrons, extending the lifetime of photo-generated holes. The longer hole lifetime leads to greater oxidation of water. On illumination of the platinized TiNTs, the intensity in the region near 3000 cmí1 decreases below the baseline. Again, we note that a "negative absorption" is characteristic of a depletion of a species that is present in the background spectrum. This depletion on illumination of the platinized TiNTs is preferentially in the low frequency region of the water absorption and suggests that this lower frequency region is dominated by a different type of water than water absorbing at higher frequencies. Since the holes are primarily expected to be generated within the Pt-TiNTs, the water that they react with leading to preferential depletion of the low frequency region of the absorption near 3000 cmí1 was referred to as "structural water". This term is meant to indicate water within the structure of the TiNT, where it may be more proximate to the location of hole generation than surface water. The depletion of structural water is accompanied by an increase in the absorption at higher frequencies as more surface-bound water is produced as a result of H and OH thus generated with other OH groups [31]. Thus, our findings are consistent with previous work and suggest that there are two different OH stretching regions.

We note that the shape of the spectrum in the water region in Figure 6 is also consistent with two absorption regions: one that dominates the high frequency region and the other that dominates the low frequency region. The lower frequency band has a maximum near 2900 cmí1 and a relatively sharp drop-off near 3000 cmí1 . The partitioning of amplitude between these two bands is affected by the treatment and history of the cTiNTs. Though we have not studied this effect in detail, as discussed below, there are reports in the literature that protons are incorporated in the TiNT structure. This is expected based on the exchange of Na+ with protons during the TiNT synthesis. This could result in a change in the effective pH of the interior of the TiNTs and lead to a change in the hydrophilicity of the interior, making it a more favorable environment for "structural water". On collapse, some of this water and/or protons could be trapped in the interior of the cTiNTs.

The data in Figure 7 show the spectrum of the collapsed oxidized cTiNTs after exposure to gas-phase D2O. New absorptions as a result of interaction with D2O are seen in the 1950–2700 cmí1 region and loss of absorption is seen in the 2700–3500 cmí1 region. It is difficult to provide an exact delineation of the extent of either region because of uncertainties in the baseline. However, a "negative absorption" is seen between ~3550 and ~2700 cmí1 . These spectra are referenced against a background spectrum of the cTiNT-O2-H2s. A negative absorption indicates that a species that was present in the background is no longer present in the displayed spectrum. New absorptions are seen between ~2700 and ~1950 cmí1 . A new absorption with rotational structure is seen between ~2500 and ~2900 cmí1 . The asymmetric stretching mode of gas-phase D2O is centered at 2789 cmí1 and the symmetric stretch is centered at 2666 cmí1 . A Q branch is apparent at 2789 cmí1 . Thus, the new absorption with rotational structure centered at ~2789 cmí1 is due to stretching modes of gas-phase D2O. The ratio of the frequencies of the vibrational modes of gas-phase D2O and their protonated counterparts is calculated from their spectra to be between ~0.73 and 0.74 [25]. A value of ~0.73 would be predicted from the ideal harmonic oscillator model for an OH stretch. There is a wider spread in these ratios for water absorptions in solid hydrates [32]. The ratio of the frequencies of the high and low energy edges of the loss in absorbance (negative absorption) and the new absorption is ~0.76 and ~0.72. Given the uncertainties as to where the two regions begin and end, and potential perturbations due to the difference in the environment in these experiments and the gas phase, we conclude that these frequency ratios are consistent with deuterated water exchanging with protonated water. The fact that the entire absorption band above 2700 cmí1 is depleted on interaction with D2O is strong evidence that this absorption is due to moieties whose protons are readily exchanged by exposure to D2O and, thus, this observation is consistent with absorptions being due to OH stretching modes.

The question remains, though, why do we see absorptions from OH stretching modes at a significantly lower frequency than the OH stretches in water adsorbed on the surface of titania powders? We do not have a definitive answer, but there is considerable evidence in the literature that interactions in the solid state can lead to shifts in OH stretching frequencies. The OH and OD stretching frequencies for solid hydrates can be significantly red-shifted [32]. Hydrogen bonding can lead to the appearance of an absorption that is at a lower frequency than a typical OH absorption. The length of the hydrogen bond has been correlated with its absorption frequency, and has been reported to be as low as 2000 cmí1 [33]. The exact structure of TiNTs is still unresolved, and may be influenced by the synthesis procedure and subsequent treatments. The cTiNTs have been subjected to much less detailed study. However, evidence has been presented in the literature to show that TiNTs can contain water and protons [34,35]. This opens up the possibility for hydrogen bonding within the structure of TiNTs. The structure of the cTiNTs is different than those of the multi-walled TiNTs; however, the similarity between what we observe and what is observed in prior studies [5,30] suggests similar factors leading to a lower frequency band in the region of the spectrum in which OH absorptions appear. This hydrogen bonding would involve water and/or protons. It is possible that the cTiNTs trap water and/or protons within their structure on collapse of the TiNTs. It is also likely that the cTiNTs adsorb atmospheric water as they cool after being collapsed in an oven.

#### *3.3. Interactions of CO2 with cTiNT*

Figure 8 shows the spectrum taken after exposure of the cTiNT-O2-H2 to CO2. The new absorptions in the 1700 to 1200 cmí1 region are characteristic of carbonates and bicarbonates [12,26,31]. Though the exact nature of the observed carbonate or bicarbonate species is not of major significance in the current study, for completeness we provide the assignments we have deduced for the observed absorptions with the caveat that some of these assignments are still a subject of discussion [12,26,31].

We note that many of the absorption features are lost on evacuation, which is consistent with weakly bound species. The peak frequencies of the remaining absorptions may then shift slightly due to overlap with other absorptions that disappeared on evacuation. Evacuation results in bidentate carbonate absorptions at 1563, 1358, and 1307 cmí1 , a bicarbonate at 1404 cmí1 , and a monodentate carbonate at 1266 cmí1 . The absorption at 1718 cmí1 is too high in energy to be due to a carbonate or bicarbonate. It is in a region in which carbonyl stretching absorptions can appear [36]. The carbonyl stretch of gas-phase formic acid absorbs at 1740 cmí1 [25] and an absorption due to formic acid has been assigned previously for an uncollapsed platinized TiNT at ~1725 cmí1 [31]. Thus, we assign the 1718 cmí1 absorption to the carbonyl stretch of formic acid. The observation of formic acid is interesting since there are reports of dissociative adsorption of formic acid to formate for anatase titania, particularly for the (101) plane [37]. A search of the literature does not provide a definitive explanation for our observation of formic acid. However, we note that formate and formic acid are expected to be in equilibrium. The observation of formate on exposure to formic acid suggests that in those systems, the equilibrium is heavily shifted toward formate. Since titania provides an acidic surface [12] and our infrared studies provide evidence for the presence of protons and/or water, we hypothesize that in our system, the presence of proton sources is sufficient to shift the equilibrium for the nanotubes towards formic acid. Other factors could also contribute to our observation of formic acid. One suggested pathway for formic acid formation involving isolated hydroxyls [38] would not be expected to be significant in our system due to the absence of isolated OH moieties. It is also possible that the efficient sites for dissociation of formic acid in the presence of water, such as the (101) plane [37,39], have been annealed as a result of high temperature calcination of the samples under study.

Clearly there is less adsorption due to carbonates and bicarbonates than seen with the uncollapsed TiNTs. A decrease in absorbance would be expected due to a decrease in surface area of the cTiNTs *versus* the uncollapsed TiNTs. There is also a difference in the pattern of the absorptions seen relative to that for the reduced TiNTs. However, what is perhaps most surprising is the degree of similarity in the absorptions between the similarly treated collapsed and uncollapsed reduced TiNTs, though there are more species absorbing for the reduced uncollapsed TiNTs. The observation of formic acid suggests that these cTiNT-O2-H2s are capable of inducing C-H bond formation. We note that similarly prepared cTiNTs have been shown to be photochemically active for carbon dioxide reduction, albeit at much lower yields [10]. How, then, do we rationalzie this qualitative similarity in adsorption behavior but disparity in photoreduction of CO2? As shown by XPS results, defects on cTiNTs are substantially less than on the TiNTs. Defects such as oxygen vacancies and associated Ti3+ sites promote significant surface carboxylate formation due to CO2 adsorption, which is, in turn, postulated to be a critical intermediate in the photoconversion of CO2 [12].

Figure 8 shows a blow-up of the 1800–4000 cmí1 region which exhibits a weak "negative absorption" between ~2500 and ~3500 cmí1 . Bicarbonate formation must involve the interaction of CO2 with an H-containing moiety. The negative absorption due to the depletion of moieties present in the background spectrum is consistent with the formation of bicarbonates and indicates a depletion of surface adsorbed water. The lower frequency OH stretch region is due to OH stretches of H-containing moieties within the cTiNTs. It is also possible that CO2 and water compete for the same surface sites and this competition leads to the depletion of OH bond-containing moieties that absorb between ~2500 and 3500 cmí1 .

#### **4. Experimental Section**

#### *4.1. Synthesis of TiNT, cTiNT, and in Situ Pretreatments*

Titania nanotubes were prepared by a modified hydrothermal method that has been previously reported [1,2,40]. In a typical experiment, 2 g of anatase titania powder (purity 99%, Sigma Aldrich Chemicals, St. Louis, MO, USA) were stirred with 50 mL of 10 M NaOH solution (purity 97%, BDH Chemicals, Radnor, PA, USA) in a closed 125 mL Teflon cup. The Teflon cup is sealed inside a stainless steel outer vessel and placed in an oven for 48 h at 120 °C. The resulting precipitate was washed with 1 M HCl (purity 38%, EMD Chemicals, Billerica, MA, USA) followed by several washings with deionized water to attain a pH between 6 and 7. The TiNT powder thus formed was dried overnight in an oven held at 110 °C. Some of the TiNT samples were then calcined at a temperature of 650 °C to probe the effect of temperature on the morphology of these materials. The TiNTs were initially heated *in situ* under an O2 atmosphere at 350 °C [O2 ~2 Torr] to clean the surface, and were then allowed to cool to room temperature under vacuum. The TiNTs that are only heated to 350 °C are labeled by the pretreatment (*i.e.*, -TiNT-O2 for oxidized TiNTs) while those heated to 650 °C are labeled as cTiNT and the pretreatment (*i.e.*, -cTiNT-O2). After oxidative pretreatment, some of the TiNTs were treated in a H2 atmosphere at 350 °C [H2 ~2 Torr] for 3 h and then allowed to cool to room temperature under vacuum. The TiNTs heated to 350 °C that were reduced are referred to as TiNT-O2-H2 while those heated to 650 °C and then reduced after oxidation are referred to as cTiNT-O2-H2.

#### *4.2. Characterization of the TiNTs*

The morphology of titania nanomaterials was probed by transmission electron microscopy (TEM, STEM JEOL-2100F, Peabody, MA, USA), with an accelerating voltage of 200 kV. To establish crystallinity and phase purity, the powder X-ray diffraction (XRD) patterns of the TiNT and the cTiNT were recorded on a Rigaku Domex diffractometer (The Woodlands, TX, USA) using Cu KĮ radiation, a continuous scan, and a scintillation-type detector for 2ș from 5° to 90°. X-ray photoelectron spectra (XPS) were obtained with an Omicron (Houston, TX, USA) ESCA-2000-125 based spectrometer using an Al KĮ radiation source (1486.6 eV, 30 mA × 8 kV). These spectra provided data on the oxidation states of the ions in the TiNT samples. The C 1s response at 284.6 eV was used as an internal reference for the absolute binding energy.

#### *4.3. In Situ FT-IR Spectroscopy*

*In situ* FT-IR spectra were recorded with a Nicolet (Madison, WI, USA) 6700 FTIR spectrometer equipped with both a mercury cadmium telluride (MCT) and a DTGS (Deuterated Triglycine Sulfate) detector. Each spectrum was obtained by averaging 64 scans at a resolution of 4 cmí1 . The custom fabricated infrared cell, which was designed to study highly scattering powder samples in a transmission mode, has been described previously [31]. Briefly, it consists of a stainless steel cube with two CaF2 windows positioned on opposite sides of the cube. For this study, samples were pressed onto a highly transmissive tungsten wire grid held between two nickel jaws. The grid, which is resistively heated to a temperature measured by a Chromel-Alumel thermocouple attached to its center, provides a support for highly scattering samples so that very thin samples can be studied in transmission mode. The vacuum system was pumped using a Turbo pump backed by a mechanical forepump to achieve a base pressure of 1 × 10í5 Torr. The infrared beam was directed out of the spectrometer, allowed to pass through the cell windows and the sample on the wire grid, and was detected with the MCT detector. The cell and detector were contained in an enclosure that was purged with boiled off nitrogen before acquisition of spectra. Unless otherwise stated, background spectra are of the samples cooled to ambient temperature, under vacuum, after pretreatment. A Baratron capacitance manometer was used to monitor the pressure of CO2. D2O, used in some of the IR experiments, was specified as 99% atomic purity.

#### **5. Conclusions**

This research probes the interaction of water on the cTiNTs and we propose an explanation for the unusual low frequency OH stretching region. On exposure to water the OH stretching region of c-TiNT-O2, illustrated in Figure 6, is broader than that reported for titania powder and what is typical for other metal oxides [41,42], extending below 3000 cmí1 . Interaction with D2O demonstrates that the OH region contains exchangeable protons, and absorptions due to the deuterated analogs of the species are observed with absorptions between ~2700 and ~1950 cmí1 . Taking into account that variations in the baseline of the spectra produce uncertainty in the extent of these absorptions, the shifts in the absorptions on deuteration are consistent with expectations based on typical frequency ratios for OH *vs.* OD stretches. Based on these observations and data in the literature, we suggest that the unusually low frequency OH stretching modes are best explained by hydrogen bonding involving H-containing moieties within the structure of the TiNTs. It is recognized that the addition of water can increase the efficiency of photoinduced reduction reactions taking place on titania [43], and proton sources are needed for the formation of hydrocarbon products. We note that the present results suggest that proton sources can be sequestered on and within the structure of the TiNTs and c-TiNTs

Exposure of the c-TiNT-O2-H2 to CO2 leads to the formation of new species on the c-TiNTs, which are identified as carbonates and bicarbonates, as well as formic acid. Though there are differences in the number and nature of the carbon-containing species observed on the surface of the c-TiNT-O2-H2 *versus* the TiNT-O2-H2, many moieties are observed on both types of TiNTs. The large decrease in surface area that occurs on the collapse of the TiNTs to c-TiNTs would be expected to contribute to a smaller amount of surface carbonates and bicarbonates. However, the fact that many of the surface moieties are the same for the c-TiNT-O2-H2 and the TiNT-O2-H2 suggests that many of the sites of interaction on TiNT-O2-H2 remain on c-TiNT-O2-H2, but despite adsorption, CO2 photoreduction is low on the cTiNTs. We suggest that adsorption mediated by specific defects (O-vacancy and Ti3+), which are largely absent on cTiNT, is required for the significant photoreduction of CO2. An implication of these findings, then, is that a material's defect structure is crucial for CO2 photoconversion.

#### **Acknowledgments**

This work was supported by the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy (Award No. DE-FG02-03- ER15457). The XPS work was performed in the Keck-II facility of NUANCE Center at Northwestern University. NUANCE Center is supported by NSF-NSEC, NSF-MRSEC, Keck Foundation, the State of Illinois, and Northwestern University.

#### **Author Contributions**

K. Bhattacharyya, W. Wu, and B. K. Vijayan synthesized the materials and conducted the experimental work. The research and manuscript preparation were supervised by E. Weitz and K.A. Gray.

#### **Conflicts of Interest**

The authors declare no conflict of interest.

#### **References**

1. Kasuga, T.; Hiramatsu, M.; Hoson, A.; Sekino, T.; Niihara, K. Titania Nanotubes Prepared by Chemical Processing. *Adv. Mater.* **1999**, *11*, 1307–1311.

*Sample Availability:* The methods by which material samples were synthesized are available from the authors.

Chapter 2: UV and Visible-Light Sensitive Photocatalysts: Efficiency Effects of Nature, Composition, Preparation, Structure and Texture


Johnson, S., M. Zinkler and S. Priebe. 2001. Psychiatrische Gesundheitsversorgung in GroBbritannien. In: Aktion Psychisch Kranke. (eds.) *25 Jahre Psychiatrieenquette.* Band 1+2. Bonn: Psychiatrieverlag.

Johnson, S., M. Zinkler and S. Priebe. 2001a. Mental health service provision **in**  England. *Acta Psychiatrica Scandinavica.* 104 (suppl. 410): 47-55.

Katschnig, **H.,** E. Etzersdorfer and M. Muzik. 1993. *.,Nicht nur eine minderwertige Gesundheit": Eine Untersuchung iiber die Einstellung der osterreichischen Bevolkerung zu psychisch Kranken und zur Psychiatrie.*  Research report. Wien.

Katschnig, H., W. Bois!, G. Eichberger, E. Etzersdorfer, P. Fischer, R. Fliedl, A. Marksteiner, E. Tatzer, J. Wancata and J. Windhaber. 1996. *Der Niederosterreichische Psychiatrieplan 1995.* St. Polten: Landesregierung Niederosterreich.

Katschnig, H. 1998.  *Wiener Klinische Wochenschrift* 110: 207-211.

Katschnig, H., E. Ladinser, M. Scherer, G. Sonneck and J. Wancata. 2001. *6sterreichischer Psychiatriebericht 2001.* Wien: BMSG.

Katschnig, H., P. Denk and B. Weibold. 2003. *Evaluation des Niederosterreichischen Psychiatrieplans 1995.* Wien: Universitatsklinik fiir Psychiatrie.

Katschnig, H., P. Denk and M. Scherer. 2004. *Osterreichischer Psychiatriebericht 2004.* Wien: BMGF.

Kaufmann, F-X. 2003. *Sozialpolitisches Denken.* Frankfurt/Main: Suhrkamp.

Kavanagh, S. 1996. Northern Ireland Care in the Community. *PSSRU Bulletin* IO: 30-32.

Keat, R., N. Whitely and N. Abercrombie. 1994. *The authority of the consumer.*  London: Routledge.

Kessler, RC., KA. McGonagle, S. Zhao, CB. Nelson, M. Hughes, S. Eshleman, HU. Wittchen and DS. Kendler. 1994. Lifetime and 12 month prevalence of DSM-III-R psychiatric disorders in the United States. *Archives of General Psychiatry* 51: 8-19.

Kieffer, CH. 1984. Citizen Empowerment: A Developmental Perspective. In: JC. Rappaport and R. Hess. (eds.) *Studies in Empowerment. Steps Towards Understanding and Action.* New York: Haworth Press.

Klatzer, E. 2002 Engendering Budgets. Ein wichtiger Beitrag zur Demokratisierung der Wirtschaftspolitik und ein zentrales Instrument einer umfassenden Gender-Mainstreaming-Politik. *Kurswechsel* 1: 78-90.

Knapp, M. (ed.) 1995. *The Economic Evaluation of Mental Health Care.*  Aldershot: Ashgate.

Knapp, M., D. Novick, L. Genkeer, C. Curran and D. McDaid. 2003. Financing health care in Europe: Context for the Schizophrenia Outpatient Health Outcomes Study. *Acta Psychiatrica Scandinavica* (Suppl. 416): 30-40.

Krautgartner, M., J. Berner and J. Wancata. 2001. Die Belastung der osterreichischen Bevolkerung durch Demenzerkrankungen zwischen den Jahren 2000 und 2050. *Gemeindenahe Psychiatrie* 22: 33-49.

Kruckenberg, P. 2000. Der Mensch im Mittelpunkt: Von einem institutions- zu einem personenzentrierten psychiatrischen Hilfesystem. *Sozialpsychiatrische lnformationen* 3: 17-21.

Kruger U. and H. Kunze. 2004. Passgenaue Hilfe. In der Psychiatrie gibt es bereits gute Erfahrungen mit personlichen Budgets. *Blatter der Woh/fahrtspflege*  4: 140-142.

Kunze, H. 2001. Diskussion zum Beitrag von Ulrich Frick. *Psychiatrische Praxis*  28 (Sonderheft): 63-65.

Kvale, S. 1996. *lnterViews. An Introduction to Qualitative Research Interviewing.*  London: Sage.

Laing and Buisson. 2003. *Thriving private hospital market.* Press release. Online available under http://www.laingbuisson.co. uk (April 2003)

Lakoff, G. and M. Johnson. 1980. *Metaphors we live by.* Chicago: University Press.

Landesregierung Oberosterreich. 2002. *Psychiatrieweiterentwicklungsplan.* Linz: Landesregierung.

Landesregierung Oberosterreich. 2002a *Diskussionsentwurf far ein Landesgesetz zur Chancengleicheit far Menschen mit Beeintriichtigungen (Oo. Chancengleichheitsgesetz* - *Oo. ChG).* Linz: Landesregierung.

Landesregierung Oberosterreich. 2003. *Projekt KL-QS (Kunde-Leistung-Qualitiit-Steuerung). Kurzbeschreibung und Zwischenbericht.* Linz: Landesregierung.

Landesregierung Salzburg. 2002. *Leistungen far psychisch kranke Menschen. Bedarft- und Entwicklungsplan.* Salzburg: Landesregierung.

Landesregierung Steiermark. 2001. *Die extramurale Psychiatrie in der Steiermark.* Graz: Landesregierung.

Launois, R., M. Toumi and J. Reboul-Marty. 1998. Cost of illness: An inextricable maze or an aid in decision making? The case of schizophrenia. *Encephale* 24: 83-99.

Leibenkuft, E. 2000. Women with bipolar illness: An update. *Bulletin of the Menninger Clinic* 64: 5-17.

Lercher, JR. 1998. *Leistungsorientierte Krankenanstaltenfinanzierung.* Innsbruck: Master Thesis.

Lerner, Ch. 1999. *The Language of Central Banking. Terminological Aspects and Discourse Analysis with Special Focus on the Federal Reserve System and the European System of Central Banks.* Wien: Doctoral Thesis.

Lesky, E. 1978. *Die Wiener Medizinische Schule im 19. Jahrhundert.* Graz-Koln: Bohlau.

Lewis, L. 2003. *User involvement discourse in mental health policy: A critical feminist approach.* Conference paper: BSA annual conference.

Lewis, L. 2004. User involvement within Scottish Mental Health Policy: Locating Power and Inequality. To be published in *'Scottish Affairs'.*

Lien, L. 2003. Financial and organisational reforms in the health sector: implications for the financing and management of mental health care services. *Health Policy* 63: 73-80.

Lueger, M. 2001. *Auf den Spuren der sozialen Welt. Methodologi,e und Organisierung interpretativer Sozialforschung.* Frankfurt: Peter Lang.

MacKenzie, D. 1981. *Statistics in Britain 1865-1930. The Social Construction of Scientific Knowledge.* Edinburgh: University Press.

Mannion, R. and N. Small. 1999. Postmodern Health Economics. *Health Care Analysis* 7: 255-272.

Markert, A. and S. Wieseler. 2001. Sozialberichterstattung und Sozialplanung. In: H-U. Otto and H. Thiersch. (eds.) *Handbuch Sozialarbeit, Sozialpiidagogik.* 2nd ed. Neuwied; Kriftel: Luchterhand.

Mautner, G. 2000. *Der britische Europa-Diskurs. Methodenreflexion und Fallstudien zur Berichterstattung in der Tagespresse.* Wien: Passagen Verlag.

Mayer, G. 1982. *Individuelle Bediirfnisse und Gesundheitspolitik.* Augsburg: Maro.

Meise, U., F. Hafner and H. Hinterhuber. (eds.) 1991. *Die Versorgung psychisch Kranker in dsterreich. Eine Standortbestimmung.* Wien: Springer.

Meise, U., W. Rossler, V. Gunther and H. Hinterhuber. 1993. *Biirgernahe Psychiatrie: Leitlinien far die Reform der psychiatrischen Versorgung in Tirol.* Innsbruck: VIP- Verlag.

Meise, U. und H. Hinterhuber. 1998.  *Neuropsychiatrie* 12: 177-186.

Mental Health Foundation. 1995. *Annual Report.* London: Mental Health Foundation.

Meyer, M. 2001. Between theory, method and politics: positioning of the approaches to CDA. In: R. Wodak and M. Meyer. (eds.) *Methods of critical discourse analysis.* London: Sage.

MHEEN. 2004. *Mental Health Economics European Network.* Online available under http://www.mentalhealth-econ.org (July 2004)

MHEEN.2004a. *Mental Health Economics. Final Report.* Brussels: Mental Health Europe. Online available under http://europa.eu.int/comm/health/ph projects/2002/promotion/promotion 2002 0 7 en.htm (May 2005)

Michalitsch, G. 2000. Jenseits des homo oeconomicus? Geschlechtergrenzen der neoklassischen Okonomie. In: B. Krondorfer. (ed.) *Frauen und Okonomie. Oder: Geld essen Kritik auf* Wien: Pro Media.

Ministry of Health Welfare and Sport (VWS) and T. Institute. 2000. *Major challenges to Dutch Mental Health Care* (Fact sheet mental health care (GGZ) No 1, August. Utrecht: Trimbos Institute.

Mory, C., J. Jungbauer and MC. Angermeyer. 2002. Finanzielle Belastungen von Eltem und Partnem schizophrener Patienten im Vergleich. *Psychiatrische Praxis*  29: 175-180.

Morchen, G., V. Pieters, A. Weicert, C. Niederle, E. Fiihndrich and W. Voigtlander. 2002. Armut und soziale Unterversorgung bei stationiir behandelten psychisch Kranken. *Psychiatrische Praxis* 29: 295-300.

Mossialos, E. and SMS. Thomson. 2002. Voluntary health insurance in the European Union. In: E. Mossialos, A. Dixon, J. Figueras and J. Kutzin. (eds.) *Funding health care: options for Europe.* Buckingham: Open University Press.

Mueser, KT., SM. Glynn, PW. Corrigan and W. Barber. 1996. A Survey of Preferred Terms for Users of Mental Health Services. *Psychiatric Services.* 47: 760-761.

Murray, C. and A. Lopez. 1996. The Global Burden of Disease in 1990: final results and their sensitivity to alternative epidemiological perspectives, discount rates, age-weights and disability-weights. In: C. Murray and A. Lopez. (eds.) *The global Burden of Disease: A Comprehensive Assessment of Mortality and Disability from diseases, Injuries and Risk Factors in 1990 and projected to 2020.*  Havard: School of Public Health.

Nam, H-J. 2003. *A/ten- und Pflegeheime in Osterreich: Tragerstruktur, Angebotsstruktur und Beschaftigung.* Wien: Working paper.

Nam, H-J. 2003a. *Soziale Sicherungssysteme bei Pflegebedurftigkeit alter Menschen: Europaische Wohlfahrtsstaaten als Vorbild fur Sudkorea?* Wien: Doctoral Thesis.

Nelson, G., J. Lord und J. Ochocka. 2001. Empowerment and Mental Health in Community: Narratives of Psychiatric Consumer/Survivors. *Journal of Community and applied Social Psychology* 11: 125-142.

Netten, A. and J. Beecham. (eds). 1993. *Costing Community Care.* Aldershot: Ashgate.

Novy, A. 2002. *Entwicklung gestalten. Gesellschaftsveranderung in der Einen Welt.* Frankfurt/Main: Brandes & Apsel/Siidwind.

Novy, A. and E. Hammer. 2002. *Reflections on History and Content of Social Innovation in Austria.* Unpublished project report 2002.

OECD. 2002. *OECD Health Care Data.* CD-Rom. Paris: OECD.

OECD. 2004. *OECD Health Care Data.* Paris: OECD.  Wien: BMSG.

OBIG. 1997. *Struktureller Bedarf der psychiatrischen Versorgung in Osterreich.*  Wien: OBIG.

OBIG. 2000. *Karntner Psychiatrieplan.* Klagenfurt: Landesregierung.

OBIG. 2002.   Wien: OBIG.

OBIG. 2004. *Psychotherapie auf Krankenschein. Beschreibung und Evaluierung der bisherigen Umsetzung.* Wien: OBIG.

Osterle, A. 2001. *Equity Choices and Long-Term Care Policies in Europe. Allocating resources and burdens in Austria, Italy, the Netherlands and the United Kingdom.* Aldershot: Ashgate.

Office of Fair Trading. 1996. *Health insurance.* London: Office of fair Trading.

Ortmann, F. (ed.) 1976. *Sozialplanung far wen? Gesellschaftsstruktur, Planung und Partizipation.* Darmstadt: Luchterhand.

Palmer, S. and DJ. Torgerson. 1999. Definitions of efficiency. *British Medical Journal* 318: 1136.

Patel, A. and M. Knapp. 1998. Costs of mental illness in England. *Mental Health Research Review* 5: 4-10.

Patel, V., R. Araya, M. de Lima, A. Ludemir and C. Todd. 1999. Women, poverty and common mental disorders in four restructuring societies. *Social Science & Medicine* 49: 1461-1471.

Pelizzari, A. 2001. *Die Okonomisierung des Politischen.* Konstanz: UVK Verlagsgesellschaft.

Pelizzari, A. 2003. *Entpolitisierung des Verwaltungswissens: Okonomisierungstendenzen am Beispiel des Zuricher Spitalswesens.* Unpublished conference paper.

Pereira, J., AC. Campos, F. Ramos, J. Simoes and V. Reis. 1999. Health care reform and cost containment in Portugal. In: E. Mossialos and J. Le Grand. (eds.) *Health Care and Cost Containment in the European Union.* London: Ashgate.

Pfeil, W. 2001. *Vergleich der Sozialhilfesysteme der osterreichischen Bundesliinder.* Wien: BMSG.

Piccinelli, M. and FG. Homen. 1997. *Gender Differences in the Epidemiology of Effective Disorders and Schizophrenia.* Geneva: WHO.

Pijl, YJ., H. Kluiter and D. Wiersma. 2000. Change in Dutch mental health care: an evaluation. *Social Psychiatry and Psychiatric Epidemiology.* 35: 402-407.

Pilgrim, D. and A. Rogers. 1994. *A Sociology of Mental Health and Illness.*  Buckingham: Open University Press.

Polland, E. and H. Liebeck. 1994. *The Oxford Paperback Dictionary.* Oxford: University Press.

Porter, T. 1996. *Trust in numbers. The invention of objectivity.* Princeton: University Press.

Priebe, S. 2003. Zukunft psychiatrischer Versorgung - Triiume und Alptriiume. *Psychiatrische Praxis* 30 (Sonderheft): 48-53.

Prior, L. 1993. *The Social Organization of Mental Illness.* London: Sage.

Piiringer, U., M. Truschnig and P. Konstantinuik. 2000. *Bedarfsgerechte psychosoziale Versorgung der Steiermark.* Graz: Landesregierung Steiermark.

Ramos, F., J. Sennfelt, MJ. Amaral and P. Valente. 1996. Economia da saude e saude mental: Os custos da depressao. *Revista Portuguesa de Saitde Pitblica* 14: 53-68.

Rainer, M., S. Jungwirth, Ch. Kruger-Rainer, A. Croy, G. Gatterer and M. Haushofer. 2002. Pflegende Angehorige von Demenzerkrankten: Belastungsfaktoren und deren Auswirkungen. *Psychiatrische Praxis* 29: 142-147.

Rechnungshof. 1998. *Wahrnehmungsbericht des Rechnungshofes. Konvergenzkriterien. Psychiatrische Versorgung.* Wien: Rechnungshof.

Reichert, R. 2003. *Ein besseres Selbst werden.* Vortragsmanuskript Armutskonferenz. Salzburg. 20.3.03.

Resch, R. 2001. *Sozialrecht.* 2nd ed. Wien: Manz.

Rice, D., S. Kelman and LS. Miller. 1992. The Economic Burden of Mental Illness. *Hospital and Community Psychiatrie* 43: 1227-1232.

Rice, N. and PC. Smith. 2002. Strategic resource allocation and funding decisions. In: E. Mossialos, A. Dixon, J. Figueras and J. Kutzin. (eds.) *Funding health care: options for Europe.* Buckingham: Open University Press.

Robinson, R. and A. Dixon. 1999. *Health Care Systems in Transition. UK.*  Copenhagen: European Observatory on Health Care Systems (EOHCS). Online available under http://www.observatory.dk (July 2004)

Rossler, W. 1992. Sozialpsychiatrische Dienste in der Bundesrepublik Deutschland - ein Oberblick. *Gesundheitswesen* 54: 19-24.

Rossler, W., H-J. Salize, U. Biechele and A. Riecher-Rossler. 1994. Stand und Entwicklung der psychiatrischen Versorgung. *Nervenarzt* 65: 427-437.

Rossler, W. 1998. Bedarfsindikatoren einer regionalisierten psychiatrischen Versorgungsplanung. In: L. Balk. (ed.) *Grundlagen der Bedarfsplanung in der psychiatrischen Versorgung.* Bocholt: Eicanos.

Rossler, W. 2001.  *Psychiatrische Praxis* 28 (Sonderheft): 29-31.

Rose, N. 1999. *Powers of Freedom. Reframing Political Thought.* Cambridge: University Press.

Rose, N. 2000. Tod des Sozialen? Eine Neubestimmung der Grenzen des Regierens. In: U. Brockling, S. Krasmann and T. Lemke. (eds.) *Governmentalitiit der Gegenwart.* Frankfurt/Main: Suhrkamp.

Rothbard, AB. and E. Kuno. 2000. The success of deinstitutionalization. Empirical findings from case studies on state hospital closures. *International Journal of Law and Psychiatry* 23: 329-344.

Rothschild, KW. 2003. The absence of power in contemporary economic theory. *Journal of Socio-Economics* 31: 433-442.

Rowe, R. and M. Shepherd. 2002. Public Participation in the New NHS: No Closer to Citizen Control? *Social Policy & Administration* 36: 275-290.

Riimmele, M. 2005. *Kranke Geschiifle mit unserer Gesundheit. Symptome, Diagnosen und Nebenwirkungen.* St.Polten: NP Bucherverlag.

Russel, LB. 1989. *Medicare's New Hospital Payment System: Is It Working?*  Washington: Brookings Institution.

Sainsbury Centre for Mental Health. 2003. *Money for Mental Health. A Review of Public Spending on Mental Health Care.* London: SCMH. Summary online available under

http://www.scmh.org.uk/8025694D00337EFl/vWeb/fsCPIR4PDJ8T (July 2004)

Salize, H-J. 2001. Die Kosten der Schizophrenie - was wissen wir (nicht)? *Psychiatrische Praxis* 28 (Sonderheft): 21-28.

Salize, H-J., W. Rossler and I. Reinhard. 2001. Kostenermittlung in einem fragmentierten psychiatrischen Versorgungssystem. *Gesundheitswesen* 58 (Sonderheft): 10-17.

Salize, H-J. 2004. *Expert interview.* Unpublished correspondence.

Saraceno, B. and C. Barbui. 1997. Poverty and Mental illness. *Canadian Journal of Psychiatry* 42: 285-290.

Sayce, L. 2000. *From Psychiatric Patients to Citizens. Overcoming Discrimination and Social Exclusion.* London: Macmillan.

Schmidl, F. and S. Rudas. 1999. Die Entwicklung organisierter psychiatrischer Hilfen in Wien. In: B. Keintzl. (ed.) *Grunde der Seele.* Wien: Picus Verlag.

Schmidt, MG. 1995. *Demokratietheorien.* 3rd ed. Opladen: Leske+ Budrich.

Schneider, U. and B. Trukeschitz. 2003. *Was leisten Leistungsvertriige? Erste Ergebnisse einer Befragung unter NPO Praktikerlnnen.* Wien: Working paper.

Schnurr, S. 2001. Partizipation. In: H-U. Otto and H. Thiersch. (eds.) *Handbuch Sozialarbeit/Sozialpiidagogik.* 2nd ed. Neuwied; Krieftel: Luchterhand.

Schroder, C. 2004. Die Selbstbestimmung fordem.  *Blotter der Wohlfahrtspflege* 4: 143-144.

Schiilein, J. 1987. *Theorie der Institution.* Opladen: Westdeutscher Verlag.

Schiilein, JA. 1994. Homo oeconomicus und soziologische Theorie. In: JA. Schiilein and G. Bohmann. (eds.) *Okonomie und Gesellschaft.* Wien: Springer Verlag.

Schiilein, JA. and S. Reitze. 2002. *Wissenschaftstheorie far Einsteiger.* Wien: Universitiitsverlag.

Schulenburg, v. d. JM. 2000. Die Entwicklung der Gesundheitsokonomie und ihre methodischen Ansiitze. In: 0. Schoffski und JM. v. d. Schulenburg. (eds.) *Gesundheitsokonomische Evaluationen.* 2nd ed. Berlin: Springer.

Scottish Development Centre for Mental Health Care. 2001. *Route Map to User and Carer Participation. Part I: Introduction and Guide to Using the Route Map.*  Edinburgh: Socttish Development Centre for Mental Health. Online available under

http://www.sdcrnh.org. uk/publi cations.htm (September 2003)

Scull, A. 1979. *Museums of madness. The social organization of insanity in the I 9th century England.* London: Allen Lane.

Scull, A. 1985. Humanitarism or Control? Some Observations on the Historiography of Anglo-American Psychiatry. In: S. Cohen and A. Scull. (eds.) *Social Control and the State.* Oxford: Blackwell.

Sheldrick, BM. 2003. Judical Review and the Allocation of Health Care Resources in Canada and the United Kingdom. *Journal of Comparative Policy Analysis: Research and Practice* 5: 149-166.

Shelton, G. 1998. Zu den jiingsten Psychiatriereformen in England. *Sozialpsychiatrische Informationen* 3: 19-22.

Simpson, CJ. 1998. Contracting in mental health. *British Journal of Psychiatry*  172: 4-6.

Smith, SR. and M. Lipsky. 1993. Services and Clients under Contracting. In: Smith SR. und M. Lipsky. (eds.) *Nonprofits for Hire. The Welfare State in the Age of Contracting.* Cambridge/London: Havard University Press.

Smutny, G. 2002. Haushaltswesen der Lander. In: G. Steger. (ed.) *Ojfentliche Hausha/te in Osterreich.* Wien: Verlag Osterreich.

Sozialministerium. 2002. *Richtlinien far die Forderung von sozialpsychiatrischen Diensten.* Berlin: Sozialministerium.

Speicher, J. 2004. *Wechselwirkung zwischen Vergiitungssystem und Patientenversorgung. Rheinland-pfalzische Erfahrungen mit dem Personlichen Budget.*  Vortragsmanuskript. Konferenz ,Untemehmen Psychiatrie'. 15.-16.6.04.

Statistische Nachrichten. 2000. Sozial(hilfe)leistungen der Bundesliinder 1998. *Statistische Nachrichten* 6: 433-439.

Statistische Nachrichten. 2004. Sozial(hilfe)leistungen der Bundesliinder 2002. *Statistische Nachrichten* 8: 762-769.

Statistisches Bundesamt. 2002. *Gesundheitsausgaben nach Ausgabentriigern.*  Online available under http://www.destatis.de (July 2004)

Stepan, A. and M. Sommersguter-Reichmann. 2001. *Analyse des neuen leistungsorientierten Krankenanstalten-Finanzierungssystems in Osterreich.* **Wien:**  Working paper.

Stevens, A., J. Raftery and RA. Mendelsohn. 2001. Commissioners' information requirements on mental health needs and commissioning for mental health services. In: G. Thornicroft. (ed.) *Measuring Mental Health Needs.* 2nd ed. London: The Royal College of Psychiatrists.

Stoppard, J. 2000. *Understanding Depression: Feminist Social Constructionist Approaches.* London: Routledge.

Strouhal, E. 1989. The case of W. A critical journey to the border between psychiatry and justice. In: R. Wodak. (ed.) *Language, power and ideology.*  Amsterdam: John Benjamin.

Szasz, TS. 1974. *The Myth of Mental Illness: Foundations of a Theory of Personal Conduct.* New York: Harper & Row.

Tarricone, R., S. Gerzele, R. Montanelli, L. Fattura, M. Percudani and G. Racagni. 2000. Direct and indirect costs of schizophrenia in community psychiatric services in Italy. The GISIES Study. Interdisciplinary Study Group on the Economic Impact of Schizophrenia. *Health Policy* 51: 1-18.

Theurl, E. 1996. Notwendige BegleitmaBnahmen einer Neuordnung der Krankenhausfinanzierung in Osterreich. *OKZ* 1 lA: 26-35.

Thornicroft, G. (ed.) 2001. *Measuring mental health needs.* London: Institute of Psychiatry.

Torfing, J. 1999. *New Theories of Discourse. Laclau, Mouffe and Ziiek.* Oxford: Blackwell.

Ungerson, C. 1995. Gender, cash and informal care. *Journal of Social Policy* 24: 31-52.

Verband der privaten Krankenversicherung. 2002. *PKV Zahlenbericht 2001/2002.*  Koln: Verband der privaten Krankenversicherung. Online available under http://www.pkv.de/ downloads/Zb02.pdf (July 2004)

Von Cranach, M. 2000. Housing for psychiatric patients inside and outside of hospitals. *Psychiatrische Praxis* 27 (Sonderheft): 59-63.

Wancata, J., B. Kaup and M. Krautgartner. 2001. Die Entwicklung der Demenzerkrankungen in Osterreich in den Jahren 1951 bis 2050. *Wiener Klinische Wochenschrift* 113: 172-180.

Warner, R. 1994. *Recovery from Schizophrenia. Psychiatry and Political Economy.* New York: Routledge.

Weber, B. 2001. Offentlich/Privat - neue Grenzziehungen im Ubergang zum Postfordismus. *Kurswechsel* 4: 24-37

Weber, M. 1980. *Wirtschaft und Gesellschaft. Grundlagen einer verstehenden Soziologie.* Tiibingen: Mohr.

Weintraub, R. 2002. *How Economics became a Mathematical Science.* Duke: University Press.

Weiss, G. and R. Wodak. 2003. Introduction: Theory, Interdisciplinarity and Critical Discourse Analysis. In: G. Weiss and R. Wodak. (eds.) *Critical Discourse Analysis. Theory and lnterdisciplinarity.* Hampshire/New York: Palgrave Macmillan.

WeiB, U. 1995. Macht. In: D. Nohlen. (ed.) *Politische Theorien.* Miinchen: Beck.

Wendt, C. 2003. *Krankenversicherung oder Gesundheitsversorgung. Gesundheitssysteme im Vergleich.* Wiesbaden: Westdeutscher Verlag. WHO. 2000. *World Health Report.* Geneva: WHO.

WHO. 2001. *The Mental Health Report.* Geneva: WHO.

WHO. 2001a. *Atlas. Mental Health Resources in the World.* Geneva: WHO. Online available under http://www.who.int/mental health/evidence/atlas/ (June 2004)

Williams, R. and DP. Doessel. 2001. *Economics of Mental Health Care. Industry, Government and Community Issues.* Aldershot: Ashgate.

Wilson, J. 2000. Mental health services in New Zealand. *International Journal of Law and Psychiatry* 23: 215-228.

Wirtschaftsblatt. 2003. *Spitalskonzern KRAGES sol/ ab 2004 von privatem Betreiber gefahrt werden.* 16.5.2003.

Wittmund, B., HU. Wilms and MC. Angermeyer. 2002. Depressive Disorders in Spouses of Mentally Ill Patients. *Social Psychiatry and Psychiatric Epidemiology*  37: 177-182.

Wittmund, B. and R. Killian. 2002.  *Psychiatrische Praxis* 29: 171- 172.

Wodak, R.1989. (ed.) *Language, Power and Ideology.* Amsterdam: John Benjamin.

Wodak, R. 2001. What is CDA about - a summary of its history, important concepts and its developments. In: R. Wodak and M. Meyer. (eds.) *Methods of critical discourse analysis.* London: Sage.

Wolff, S. 2000. Dokumenten- und Aktenanalyse. In: U. Flick, E. Kardorff and I. Steinke. (eds.) *Qualitative Forschung: Ein Handbuch.* Hamburg: Rowohlt.

Zechmeister, I. and A. 6sterle. 2001. *Finanzierungsstrukturen der psychiatrischen Versorgung in Niederosterreich.* Wien: Unpublished report.

Zechmeister, I. 2002. *Bedarfsplanung far die psychiatrische Versorgung im auj3erstationaren Bereich: Eine Reflexion uber Bedarfszahlen als adaquate Planungsrichtlinie zur quantitativen Dimensionierung des auj3erstationaren Versorgungsbedarfs.* Unpublished report commissioned by Grillich, Scheucher & Dressel GmbH.

Zechmeister, I., A. 6sterle, P. Denk and H. Katschnig. 2002. Incentives in financing mental health care in Austria. *Journal of Mental Health Policy and Economics* 5: 121-129.

Zechmeister, I. 2004. Frauen und Psychiatrie: Eine polit-i:ikonomische Perspektive. *,Neuropsychiatrie* ' 17: 106-112.

Zechmeister, I., J. Meichenitsch and J. Hagleitner. 2004. *Analyse und Empfehlungen zur zukiinftigen Finanzierbarkeit des Gesundheitswesens.* Wien: Gruner Klub im Nationalrat.

Zechmeister, I. and A. 6sterle. 2004. *Herausforderungen und mogliche Neuansiitze far die Finanzierung einer gemeindenahen psychiatrischen Versorgung. Endbericht zum Jubiliiumsfondsprojekt (Nr. 9710).* Wien: Unpublished research report.

Zechmeister, I. and A. Osterle. 2004a. *Mental Health Care Financing in Europe in the Light of Health Policy Trends: Distributional Issues in the UK, Germany and Austria.* Conference paper presented at the II ESPAnet Conference, Oxford September 9th-I 1th 2004.

#### **Forschungsergebnlsse der Wirtschaftsunlversitiit Wien**

Herausgeber: Wirtschaftsuniversitat Wien vertreten durch l'l.o. Univ. Prof. Dr. Barbara Sporn

www.peterlang.de


**Acknowledgements**

This research has been partially supported by the Spanish CDTI research project CEN‐ IT-2008-1019, the CICYT TIN2011-27767-C02-01 project and the regional projects with refer‐ ence PAI06-0093-8836 and PII2C09-0185-1030. I would like to especially thank to Yolanda Cotillas Aranda y Erica González Gutierrez for their collaboration on this project.


**Abstract**

Exosomes are a subgroup of extracellular vesicles that are released by all types of cells, including tumor cells, and mediate intercellular communication via the transport of various intracellular components, including microRNAs, messenger RNAs, and proteins. Radiation produces reactive oxygen species and induces DNA doublestrand break in cancer cells and normal cells.  Irradiated cells generate communication signals and cause biological changes in neighboring or distant non-irradiated cells. This review outlines the role of exosomes in radiation therapy. In the tumor microenvironment, exosomes are considered to regulate cell survival, migration, and resistance to therapy by interacting with vascular endothelial cells and various types of immune cells. Nowadays, radiation therapy is typically combined with immunotherapy. Regulation of the activity of exosomes may overcome the problem of resistance to immunotherapy. Furthermore, exosomes can attenuate resistance to chemotherapy by transporting certain types of microRNA. The current evidence suggests that exosomes may be useful in the diagnosis and treatment of cancer in the future.

**Keywords:** exosomes, cancer, microRNAs, liquid biopsy, radiation therapy


*2.2. Precoding*

We consider the *n*th MIMO-NOMA cluster that contains *m* users, the channel matrix **H***n* ∈ C*m*×*N* could be defined [24]:

$$\mathbf{H}\_{\rm tr} = \begin{bmatrix} \mathbf{h}\_{n,1}, \mathbf{h}\_{n,2}, \cdots, \mathbf{h}\_{n,m} \end{bmatrix} \tag{7}$$

By taking the Singular Value Decomposition (SVD) of the channel matrix **H***n* we obtain:

$$\mathbf{H}\_n^T = \mathbf{U}\_n \sum\_n \mathbf{V}\_n^H \tag{8}$$

Each beam is utilized by a MIMO-NOMA cluster so that the channel corresponding to the nth beam is: **~**

$$\mathbf{h}\_n = \mathbf{H}\_n \mathbf{u}\_n^\* \tag{9}$$

where **u**∗*n* is the first column of **u***n*.The equivalent channel matrix can be expressed as follows:

$$\tilde{\mathbf{H}} = [\tilde{\mathbf{h}}\_1, \tilde{\mathbf{h}}\_2, \cdots, \tilde{\mathbf{h}}\_G] = [\mathbf{H}\_1 \mathbf{u}\_1^\*, \mathbf{H}\_2 \mathbf{u}\_2^\* \cdots, \mathbf{H}\_G \mathbf{u}\_G^\*] \tag{10}$$

Then, the precoding matrix can be written as:

$$
\tilde{\mathbf{W}} = [\tilde{\mathbf{w}}\_1, \tilde{\mathbf{w}}\_2, \dots, \tilde{\mathbf{w}}\_G] = \tilde{\mathbf{H}} (\tilde{\mathbf{H}}^H \tilde{\mathbf{H}})^{-1} \tag{11}
$$

After normalization of the precoding matrix, the precoding vector of the nth beam is:

$$\mathbf{w}\_{n} = \frac{\tilde{\mathbf{w}}\_{n}}{\left\| \tilde{\mathbf{w}}\_{n} \right\|\_{2}} \tag{12}$$

#### *2.3. Power Allocation*

In the NOMA system, the channel gain di fference between users can be converted to a multiplexing gain by superposition coding. Therefore, power allocation has an important impact on system performance [25]. We proposed a dynamic power allocation method for the MIMO-NOMA system. Firstly, the transmission power is allocated according to the number of beams, which is proportional to the number of users served by the beam. Each beam is used by all users of the cluster and each MIMO-NOMA cluster contains users with near-similar channel di fferences. Therefore, the power allocation of users in the cluster is very important. We allocate power to users within the cluster for maximizing the cluster communication rate. The proposed power allocation method is described as:

$$P\_{\mathcal{S}} = P \times \frac{\left| \mathcal{S}\_{\mathcal{S}} \right|}{|\mathcal{S}\_1| + |\mathcal{S}\_2| + \dots + |\mathcal{S}\_G|} \tag{13}$$

The first step is to allocate the transmit power between beams. *Pg* is the transmitted power in the *g*th beam, *g* = 1, 2 ··· *G*. *P* denotes the total transmitted power. After obtaining the transmit power of each beam, *Sg* is a set of the users served by the *g*th beam. The second step is to perform power allocation on the user cluster served by the beams. We assume that the interference between users is small within the same user cluster, and the problem can be defined as:

$$\max\_{p\_{\mathcal{S}^1}, p\_{\mathcal{S}^2} - p\_{\mathcal{S}, \mathcal{S}\_{\mathcal{S}}}} \mathbf{C}\_{\mathcal{S}} = \sum\_{n=1}^{|S\_{\mathcal{S}}|} \log\_2(1 + \frac{\left| \mathbf{h}\_{\mathcal{S}, n} \right|^2 p\_{\mathcal{S}, n}}{\sigma})$$

$$\text{s.t. } \mathbf{C}\_1 : \sum\_{n=1}^{S\_n} p\_{\mathcal{S}, n} = P\_{\mathcal{S}} \tag{14}$$

where **h***g*,*n* is the channel of the *n*th user in the *g*th beam (*g* = 1, 2, ··· *G*, *n* = 1, 2, ···*Sg*). *pg*,*n* denotes the transmitted power for the *n*th user in the *g*th beam. σ denotes noise power spectral density. To solve the convex optimization problem (14), we define the Lagrange function as:

$$L(\lambda, p\_{\mathcal{S},1}, p\_{\mathcal{S},2} \cdots p\_{\mathcal{S},S\_{\mathcal{S}}}) = \sum\_{n=1}^{|\mathcal{S}\_{\mathcal{S}}|} \log\_2(1 + \frac{|\mathbf{h}\_{\mathcal{S},n}|^2 p\_{\mathcal{S},n}}{\sigma}) + \lambda (\sum\_{n=1}^{|\mathcal{S}\_{\mathcal{S}}|} p\_{\mathcal{S},n} - P\_{\mathcal{S}}) \tag{15}$$

where λ ≥ 0,

> By calculating the derivative (15):

$$\frac{\partial L}{\partial p\_{\mathcal{S},\mathcal{U}}} = \frac{\mathbf{h}\_{\mathcal{S},\mathcal{U}}}{(1 + p\_{\mathcal{S},\mathcal{U}} \mathbf{h}\_{\mathcal{S},\mathcal{U}})In2} - \lambda = 0 \tag{16}$$

we have:

0

$$p\_{\mathcal{S},n} = \frac{1}{\overline{\lambda}} - \frac{1}{|\mathbf{h}\_{\mathcal{S},n}|}\tag{17}$$

where λ = λ*In*2, // /**h***g*,*n* // / is the channel gain of the *n*th user in the *g*th beam. By substituting (17) into the constraint C1 in (14) we have:

$$\sum\_{n=1}^{S\_n} \frac{1}{\overline{\lambda}} - \frac{1}{\left| \mathbf{h}\_{\mathcal{S},n} \right|} = P\_{\mathcal{S}} \tag{18}$$

 λ can be written as:

0

$$\overline{\lambda} = \frac{|S\_{\mathcal{S}}|}{P\_{\mathcal{S}} + \sum\_{n=1}^{|S\_{\mathcal{S}}|} \frac{1}{|\mathbf{h}\_{\mathcal{S}^n}|}} \tag{19}$$

Substituting (19) into (17), we have

$$p\_{\mathcal{S},n} = \frac{P\_{\mathcal{S}} + \sum\_{n=1}^{|\mathcal{S}\_{\mathcal{S}}|} \frac{1}{|\mathbf{h}\_{\mathcal{S},n}|}}{|\mathbf{S}\_{\mathcal{S}}|} - \frac{1}{|\mathbf{h}\_{\mathcal{S},n}|} = \frac{P\_{\mathcal{S}}}{|\mathbf{S}\_{\mathcal{S}}|} + \frac{\sum\_{n=1}^{|\mathcal{S}\_{\mathcal{S}}|} \frac{1}{|\mathbf{h}\_{\mathcal{S}}|}}{|\mathbf{S}\_{\mathcal{S}}|} - \frac{1}{|\mathbf{h}\_{\mathcal{S},n}|}\tag{20}$$

where *Pg* is the transmitted power in the *g*th beam, ///*Sg*/// represents the number of users served by the *g*th beam, and ///**h***g*,*n*/// is the channel gain of the *n*th user in the *g*th beam. From (20) we obtain the transmitted power of the *n*th user in the *g*th beam and find that when the number of users in the group is larger, the power allocated to user would be reduced.

#### **3. Energy Harvesting Maximizing**

To maximize the harvested energy while meeting the minimum communication rate, we propose the addition of a power splitter for each user at the receiver to help implement SWIPT. This method is called SWIPT with power split [26], as shown in Figure 4. The signal received by each user is divided into two parts. One part is forwarded to the information decoder for information decoding, and the other part is subjected to Energy Harvesting (EH). The received signal to EH at the *m*th user in the *n*th beam can be can be formulated [27]:

$$
\Delta y\_{n,m}^{EH} = \sqrt{1 - \beta\_{n,m}} y\_{n,m} \tag{21}
$$

**Figure 4.** Simultaneous Wireless Information and Power Transfer (SWIPT) split receiver Power Split (PS) mode.

The harvested energy at the *m*th user in the *n*th beam is

$$P\_{n,m}^{EH} = \left. \eta (1 - \beta\_{n,m}) \left( \left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} + \sigma\_v^{-2} \right) \tag{22}$$

where η is the energy conversion efficiency, β*n*,*m* is the power splitting factor at the *m*th user in the nth beam, 0 ≤ β*n*,*m* ≤ 1.

Meanwhile, the signal used to carry out the information decoding is expressed as

$$y\_{n,m}^{ID} = \sqrt{\beta\_{n,m}} y\_{n,m} + u\_{n,m} \tag{23}$$

Substituting (1) into (23), we have

$$\begin{split} \mathbf{y}\_{n,\mathbf{m}}^{ID} &= \sqrt{\beta\_{\mathbf{n},\mathbf{m}}} \Big( \mathbf{h}\_{\mathbf{n},\mathbf{m}}^{H} \mathbf{w}\_{\mathbf{n}} \sqrt{\mathbf{p}\_{\mathbf{m},\mathbf{n}}} \mathbf{s}\_{\mathbf{m},\mathbf{n}} + \mathbf{h}\_{\mathbf{n},\mathbf{m}}^{H} \mathbf{w}\_{\mathbf{n}} \sum\_{j=1}^{\mathbf{m}-1} \sqrt{\mathbf{p}\_{i,\mathbf{n}}} \mathbf{s}\_{i,\mathbf{n}} \\ &+ \mathbf{h}\_{\mathbf{n},\mathbf{m}}^{H} \mathbf{w}\_{\mathbf{n}} \sum\_{i=m+1}^{|\mathcal{S}\_{i}|} \sqrt{p\_{i,\mathbf{n}}} \mathbf{s}\_{i,\mathbf{n}} + \mathbf{h}\_{\mathbf{n},\mathbf{m}}^{H} \sum\_{i \neq n}^{|\mathcal{S}\_{i}|} \sum\_{j=1}^{|\mathcal{S}\_{i}|} \mathbf{w}\_{j} \sqrt{p\_{i,j}} \mathbf{s}\_{i,j} + \boldsymbol{\nu}\_{n,\mathbf{m}} \bigg) + \boldsymbol{u}\_{n,\mathbf{n}} \end{split} \tag{24}$$

where *un*,*m* is the noise the distribution CN(0, σ*u*2). By applying NOMA in each beam, intra-beam superposition coding of the transmitter and the receiver is realized. The *m*th user in the *n*th beam can eliminate the interference of the *i*th user (for all *i* > *m*) in the *n*th beam by performing SIC, and the remaining received signal of the *m*th user in the *n*th beam to information decoding can be rewritten as

$$\mathbf{y}\_{n,m}^{ID} = \sqrt{\beta\_{n,m}} \Big| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \sqrt{p\_{n,m}} s\_{n,m} + \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \sum\_{j=1}^{m-1} \sqrt{p\_{i,n}} s\_{i,n} + \mathbf{h}\_{n,m}^{H} \sum\_{i \neq n}^{G} \sum\_{j=1}^{|\mathcal{S}\_{i}|} \mathbf{w}\_{j} \sqrt{p\_{i,j}} s\_{i,j} + \boldsymbol{\upsilon}\_{n,m} \bigg) + \boldsymbol{\mu}\_{n,m} \tag{25}$$

Then, according to (25), the SINR at the *m*th user in the *n*th beam can be written as

$$\gamma\_{n,m} = \frac{\left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m}}{\xi\_{n,m}} \tag{26}$$

where,

$$\boldsymbol{\xi}\_{n,m} = \left\| \mathbf{h}\_{n,m}^H \mathbf{W}\_n \right\|\_2^2 \sum\_{j=1}^{m-1} p\_{n,j} + \sum\_{i \neq n}^G \left\| \mathbf{h}\_{n,m}^H \mathbf{W}\_i \right\|\_2^2 \sum\_{j=1}^{|S\_j|} p\_{i,j} + \sigma\_v^2 + \frac{\sigma\_u^2}{\beta\_{n,m}} \tag{27}$$

The achievable rate of the *m*th user in the *n*th beam can be written as

$$R\_{n,m} = \log\_2(1 + \gamma\_{n,m})\tag{28}$$

We have grouped users, designed a precoding matrix, and allocated power to users in Sections 2 and 3. According to (22), we know we need to find the power splitting coefficient of each user for making the harvested energy at the receiver is maximized. We formulate the problem as

$$\begin{array}{l}\underset{\{\beta\_{n,m}\}}{\max}P^{EH}\\\text{s.t. C}\_{1}:\,\mathcal{R}\_{m,n}\geq\mathcal{R}\_{\text{min}}\\\text{C}\_{2}:\,0\leq\beta\_{n,m}\leq1\end{array} \tag{29}$$

Substituting (22), (28), into (29), we have

$$\begin{aligned} \max\_{\{\boldsymbol{\beta}\_{n,m}\}} & \sum\_{i=1}^{G} \sum\_{j=1}^{|S\_j|} \eta (1 - \beta\_{n,m}) \left( \left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} + \sigma\_v^2 \right) \\ \text{s.t.} & \,\mathbf{C}\_1: \log\_2(1 + \chi\_{n,m}) \ge R\_{\min} \\ & \mathbf{C}\_2: 0 \le \beta\_{n,m} \le 1 \end{aligned} \tag{30}$$

where *PEH* is the total harvested energy. *R*min denotes the minimum achievable rate of the user.

To maximize the total harvested energy, the energy harvested by each user is maximal, the problem is converted to maximize the energy harvested by each user:

$$\begin{aligned} \max\_{\{\beta\_{n,m}\}} P\_{n,m} &= \eta (1 - \beta\_{n,m}) \left( \left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} + \sigma\_\upsilon^2 \right) \\ \text{s.t.} &\,\mathbf{C}\_1: \log\_2(1 + \gamma\_{n,m}) \ge R\_{\min} \\ &\mathbf{C}\_2: 0 \le \beta\_{n,m} \le 1 \end{aligned} \tag{31}$$

Substituting (26), (27) into (31), we have

$$\begin{split} \max\_{\{\boldsymbol{\beta}\_{n,m}\}} P\_{n,m} &= \eta (1 - \beta\_{n,m}) \left( \left\| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \right\|\_{2}^{2} p\_{n,m} + \sigma\_{v} \boldsymbol{\varepsilon} \right) \\ \text{s.t. } \mathbb{C}\_{1}: \log\_{2} \left( 1 + \frac{\left\| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \right\|\_{2}^{2} p\_{n,m}}{\left\| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \right\|\_{2}^{2m-1} p\_{n,j} + \sum\_{j=n}^{G} \left\| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{i} \right\|\_{2}^{2} \sum\_{j=1}^{[S\_{i}]} p\_{i,j} + \sigma\_{v}^{2} + \frac{\sigma\_{u}^{2}}{\rho\_{n,m}}} \right) \geq R\_{\text{min}} \\ \text{C}\_{2}: 0 \leq \beta\_{n,m} \leq 1 \end{split} \tag{32}$$

By simplifying C1 in (32),

$$1 + \frac{\left\|\mathbf{h}\_{n,m}^H \mathbf{w}\_n\right\|\_2^2 p\_{n,m}}{\omega\_{n,m} + \frac{\sigma\_n^2}{\beta\_{n,m}}} \ge 2^{R\_{\text{min}}} \tag{33}$$

where,

$$\boldsymbol{\omega}\_{n,\rm m} = \left\| \mathbf{h}\_{n,\rm m}^{\rm H} \mathbf{W}\_n \right\|\_2^2 \sum\_{j=1}^{m-1} p\_{n,j} + \sum\_{i \neq \rm n} \left\| \mathbf{h}\_{n,\rm m}^{\rm H} \mathbf{W}\_i \right\|\_2^2 \sum\_{j=1}^{|S\_i|} p\_{i,j} + \sigma\_v^2 \tag{34}$$

By simplifying (33),

$$\beta\_{n,m} \ge \frac{\sigma\_u^2 (2^{R\_{\min}} - 1)}{\left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{u,m} - \alpha\_{n,m} (2^{R\_{\min}} - 1)}\tag{35}$$

Then, the constraint C1 in (32) can be rewritten as

$$\begin{aligned} \max\_{\{\beta\_{n,m}\}} P\_{n,m} &= \eta (1 - \beta\_{n,m}) \left( \left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} + \sigma\_\upsilon^2 \right) \\ \text{s.t. } \mathbf{C}\_1: \beta\_{n,m} &\ge \frac{\sigma\_u^2 (2^{R\_{\min}} - 1)}{\left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} - \omega\_{n,m} (2^{R\_{\min}} - 1)} \\ \mathbf{C}\_2: 0 &\le \beta\_{n,m} \le 1 \end{aligned} \tag{36}$$

According to (36), we know that when β*n*,*m* is the minimum that meets constraint C1, 1 − β*n*,*m* is the maximum. Then we obtain the maximum *Pn*,*m*. Accordingly, we get the optimal power splitting coefficient at the *m*th user in the *n*th beam:

$$\beta\_{n,m} = \frac{\sigma\_{\rm u}^{2} (2^{K\_{\rm min}} - 1)}{\left\| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{\rm n} \right\|\_{2}^{2} p\_{n,m} - \omega\_{n,m} (2^{R\_{\rm min}} - 1)} \tag{37}$$

Substituting (37) into (22), The maximal harvested energy at the *m*th user in the *n*th beam is

$$P\_{n,m\_{\rm max}} = \eta \left( 1 - \frac{\sigma\_u^2 (2^{R\_{\rm min}} - 1)}{\left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} - \omega\_{n,m} (2^{R\_{\rm min}} - 1)} \right) \left( \left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} + \sigma\_v^2 \right) \tag{38}$$

#### **4. Simulation Results**

We consider a typical downlink mmWave massive MIMO-NOMA system, the spectral efficiency is defined as the reachability rate in equation (6), and the energy efficiency is defined as the ratio of reachability to total power consumption [28],

$$EE = \frac{R\_{sum}}{P + N\_{RF}P\_{RF} + P\_{BB}} \tag{39}$$

where *P* is the total transmitted power,*PRF* is the power consumed by each RF chain, *PBB* is the baseband power consumption, *NRF* is the number of the RF chain, *Rsum* is from (6).Simulation parameters are shown in Table 1.

**Table 1.** Simulation parameters.

In the simulation, we first consider three kinds of mmWave massive MIMO systems and compare them by using two different user grouping methods proposed in Section 2.1:

The power allocation method proposed in this paper is applied to the MIMO-NOMA system and we compare the performance with the system using traditional average power allocation method that it allocated equal power to all users. Finally, the SWIPT technology is integrated into the system to compare the power harvested by the MIMO-NOMA and MIMO-OMA.

Figure 5 shows the spectral efficiency against Signal to Noise Ratio(SNR)of the considered five schemes mentioned above, where the number of users *K* is set to 32 and the number of antennas is set to 256. From the figure, we can see that the proposed MIMO-NOMA scheme has a higher spectral efficiency than the MIMO-OMA scheme. It is intuitive that the fully digital MIMO can achieve the best spectrum efficiency, as shown in Figure 5. However, the number of RF chains required in the full digital MIMO scheme is equal to the number of antennas (*NRF* = *N*), and the number of RF chains required in MIMO-NOMA is 8. The full digital MIMO scheme needs higher hardware costs and overhead. Through the simulation diagram, we can obtain that the UC\_CG algorithm gives higher spectral efficiency than the UC\_FAG algorithm. Given the users that are matched according to the correlation between all channels of the user and the cluster-head user in UC\_CG algorithm, in the UC\_FAG algorithm, the users are matched according to the correlation between the part of the channel of the user and the cluster-head user. In comparison with the UC\_FAG algorithm, the interference between users in the group is smaller in the UC\_CG algorithm.

*Electronics* **2020**, *9*, 32 correlation between all channels of the user and the cluster-head user in UC\_CG algorithm, in the UC\_FAG algorithm, the users are matched according to the correlation between the part of the channel of the user and the cluster-head user. In comparison with the UC\_FAG algorithm, the interference between users in the group is smaller in the UC\_CG algorithm.

**Figure 5.** Spectral efficiency of the considered five schemes system against SNR **Figure 5.** Spectral efficiency of the considered five schemes system against SNR

Figure 6 shows the energy efficiency of the five schemes considered under different SNR, where the number of users is set to 32, the number of antennas is set to 256. From Figure 6, we know that the MIMO-NOMA scheme has a higher energy efficiency than MIMO-OMA and fully digital MIMO, where the number of RF chains of the fully digital MIMO is equal to the number of base station antennas, which results in very high energy consumption. In contrast, in the MIMO-NOMA scheme, the number of RF chains is much smaller than the number of antennas. Therefore, the energy consumption of the RF chain can be significantly reduced when compared with the fully digital MIMO scheme. Figure 6 shows the energy efficiency of the five schemes considered under different SNR, where the number of users is set to 32, the number of antennas is set to 256. From Figure 6, we know that the MIMO-NOMA scheme has a higher energy efficiency than MIMO-OMA and fully digital MIMO, where the number of RF chains of the fully digital MIMO is equal to the number of base station antennas, which results in very high energy consumption. In contrast, in the MIMO-NOMA scheme, the number of RF chains is much smaller than the number of antennas. Therefore, the energy consumption of the RF chain can be significantly reduced when compared with the fully digital MIMO scheme. *Electronics* **2019**, *8*, x FOR PEER REVIEW 13 of 16

According to Figure 5, the communication rates of UC\_CG with MIMO-NOMA is higher than UC\_FAG with MIMO-NOMA. When the total power consumption of the system is the same, UC\_CG

A comparison of the performance of energy efficiency with the number of users is shown in Figure 7 in which the SNR is set to 10dB. We can see that, as the number of users increases, the energy efficiency is gradually reduced. Even with a very large number of users, the proposed MIMO-NOMA scheme is more energy efficient than MIMO-OMA and the fully digital MIMO scheme. **Figure 6.** Energy efficiency against SNR

**Figure 7.** Energy efficiency against the number of users K. **Figure 7.** Energy efficiency against the number of users K.

The next experiment considers the spectral efficiency of the SNR under two different power allocation algorithms. From Figure 8, we obtain that the power allocation algorithm proposed in this paper has higher spectrally efficient than the traditional average power allocation algorithm. We understand that the power allocation algorithm proposed is better than the traditional average allocation algorithm. The next experiment considers the spectral efficiency of the SNR under two different power allocation algorithms. From Figure 8, we obtain that the power allocation algorithm proposed in this paper has higher spectrally efficient than the traditional average power allocation algorithm. We understand that the power allocation algorithm proposed is better than the traditional average allocation algorithm.

Figure 9 shows the energy harvesting performance against SNR. To enable the user to maximize harvested power and meet the communication requirement, in Section 3, we proposed a method that finds the power splitting optimization. From Figure 9, we can see that, when signal power is low, the received signal performs information decoding. The receiver can start harvesting energy when the signal becomes larger. In comparison with the MIMO-OMA scheme, MIMO-NOMA can harvest more energy. Therefore, the proposed MIMO-NOMA scheme with SWPIT is superior to MIMO-OMA scheme, which can realize the recycling of energy.

Figure 9 shows the energy harvesting performance against SNR. To enable the user to maximize harvested power and meet the communication requirement, in Section 3, we proposed a method that finds the power splitting optimization. From Figure 9, we can see that, when signal power is low, the received signal performs information decoding. The receiver can start harvesting energy when the signal becomes larger. In comparison with the MIMO-OMA scheme, MIMO-NOMA can harvest more energy. Therefore, the proposed MIMO-NOMA scheme with SWPIT is superior to MIMO-OMA scheme, which can realize the recycling of energy.

**Figure 9.** Energy harvesting against SNR. In this paper, we designed two different user grouping methods for MIMO-NOMA system: the UC\_CG algorithm and the UC\_FAG algorithm. From the simulation, we can see that the UC\_CG algorithm is better than the UC\_FAG algorithm, which improves spectral efficiency. We proposed a new power allocation method. The simulation results show that the algorithm is superior to the traditional average power allocation algorithm. Finally, we apply the SWIPT for MIMO-NOMA system. Under the premise of satisfying the minimum communication rate of each user, we proposed the method based on maximizing the harvested energy to find the optimal power splitting factor for each user. This method allows the system to harvest more energy and meets the user's minimum communication rate, thereby achieving the recycling of energy and green communication.

**Author Contributions:** Conceptualization, S.L.; Methodology, Z.W.; Supervision, L.J. and J.D.; Writing—review & editing, S.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by National Nature Science Funding of China (NSFC): 61401407, 61601414 and the Fundamental Research Funds for the Central Universities.

**Conflicts of Interest:** The authors declare no conflict of interest.


*3.2. Tool Wear in Conventional Drilling UNS A97075*

During conventional drilling of the aluminium alloy UNS A97075, the interaction between the workpiece and the tool caused a large helical chip (Figure 8), which makes machining difficult [2]. The zinc (Zn) contained in the UNS A97075 alloy provides a high degree of plasticity, making breakage difficult due to its ductility [3].

**Figure 8.** Chip evacuation during dry drilling of alloy UNS A97075.

The secondary adhesion of the aluminium alloy on the tool was the main wear mechanism detected. This was favoured by the absence of refrigeration and lubrication, as happened in this case. Thus, in the first stage, the aluminium matrix was melted down and welded onto the tool surface, forming a pure Al layer and giving rise to the primary BUL (Figure 9a). This circumstance provided the conditions for the mechanical adhesion of the alloy, mainly in the areas of the edge, resulting in a built-up edge (BUE) that grew to a critical size at which it began to extrude, giving rise to a secondary BUL that was deposited as a second layer over the primary BUL [4–6,17].

The location of the BUE is usually over boundary edge zones, but the BUL, during the drilling, may extend to areas outside the rake face, such as the chip evacuation channel, seriously hampering the quality of the process (Figure 9b).

**Figure 9.** Wear by bonding mechanisms (BUL–BUE) on the tool after conventional drilling of the aluminium alloy UNS A97075: (**a**) Main cutting edge; (**b**) evacuation channel.

The raised friction in the piece–tool–chip interactions during cutting resulted in an elevation of the process temperature, increasing the affinity between the tool material and the aluminium, and intensifying the plasticity of the alloy, which facilitated this type of wear [7–9]. This process caused higher adhesion of the aluminium over the rake face, as in the regrowth of the cutting edges (Figure 10).

**Figure 10.** Increased bond wear with the number of holes.

The analysis of the cutting edges showed irregularities. These were produced by the dynamic phenomenon of primary adhesion, which, with the detachment of the BUE and its new generation, slowly removes material from the tool (Figure 11a). At the same time, this action can cause abrasive wear on the tool surface or affect the quality of the surface generated on the workpiece itself (Figure 11b).

**Figure 11.** (**a**) Primary adhesion mechanism; (**b**) geometric irregularities observed in the cutting edges.

#### *3.3. Tool Wear in Conventional Stack Drilling CFRP/UNS A97075*

When drilling stacks of CFRP/UNS A97075, the drill bit comes into contact with two materials at the same time and acts on them with similar parameters.

Observation of the tools showed how adhesion was the main type of wear in the conventional drilling of this stack. During machining, the rake face was subjected to increased pressure and temperature [18,19], hence helping in the formation of an adhesive layer in the contact zone between the tool and the workpiece [14,20]. Adhesion wear was caused by the mechanical removal of the tool material when the adhesive junctions were broken. The effects of the abrasion wear mechanism were attenuated by the adhered material (Figure 12).

**Figure 12.** Wear located on the tool after conventional drilling of the CFRP/UNS A97075 stack: (**a**) Flute (BUL); (**b**) cutting lip (BUE y BUL); (**c**) tool tip; (**d**) joining of primary and secondary cutting edges (BUL).

It was seen how the adhered material was composed of both aluminium alloy and carbon fibre particles. This caused a geometric change in the tool, affecting the final quality of the hole [20–22] but also its mechanical characteristics, since the incorporation of the Al–CFRP mixture was abrasive to the material that had to be machined (Figure 13).

This blend of aluminium and CF seemed to facilitate chip adhesion along the tool during dry drilling of CFRP/ UNS A97075, as shown in Figure 14.

One method to decrease wear during the drilling process is to reduce the temperature. This can be done by the use of lower cutting speeds and higher feed rates and the use of advanced techniques (vibration-assisted drilling, strategies with minimum quantity lubricant (MQL) and cryogenic machining, for instance).

**Figure 13.** (**a**) Composition analysis of the BUE and release side after dry drilling of the stack CFRP/UNS A97075; (**b**) details of the BUE with carbon nanotube adhered to aluminium.

**Figure 14.** Chip removal during stacking drilling CFRP/UNS A97075 using conventional technology.