Theory of Hybrid Solar Hydrogen Generation

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Thermally assisted solar electrolysis consists of (i) light harvesting, (ii) spectral resolution of thermal (sub-bandgap) and electronic (super-bandgap) radiation, the latter of which (iiia) drives photovoltaic or photoelectrochemical charge transfer V(i^2O), while the former (iiib) elevates water to temperature T, and pressure, p;

finally (iv) V(i^O) driven electrolysis of H2O(T,p). A schematic representation for this solar thermal water electrolysis (photothermal electrochemical water splitting) is presented in Figure 2, and rather than a field of concentrators, systems may use individual solar concentrators. This hybrid process provides a pathway for efficient solar energy utilization. Electrochemical water splitting, generating H2 and O2 at separate electrodes, largely circumvents the gas recombination limitations of direct solar thermochemical hydrogen formation and the multiple-step Carnot losses of indirect thermochemical processes.

Photodriven charge transfer through a semiconductor junction does not utilize photons which have energy below the semiconductor bandgap. Hence a silicon photovoltaic device does not utilize radiation below its bandgap of ~1.1 eV, while an AlGaAs/GaAs multiple bandgap photovoltaic device does not utilize radiation of energy less than the 1.43-eV bandgap of GaAs. As will be shown, this unutilized, available long wavelength insolation represents a significant fraction of the solar spectrum. This long wavelength insolation can be filtered and used to heat water prior to electrolysis. The thermodynamics of heated water dissociation are more favorable than that room temperature. This is expressed by a free-energy chemical shift and a decrease in the requisite water electrolysis potential, which can considerably enhance solar water splitting efficiencies.

The spontaneity of the H2 generating water splitting reaction is given by the free energy of formation, AG°f, of water and with the Faraday constant, F, the potential for water electrolysis:

where AG0H O (25 °C, 1 bar, H2Oliq) = -237.1 kJ mol-1, and

AG 0

Reaction 15 is endothermic and the electrolyzed water will undergo self-cooling unless external heat is supplied. The enthalpy balance and its related thermoneutral potential, £tneut, are given by:

where AHf" (25 °C, 1 bar, H2Oliq) = -285.8 kJ mol-1, and f, H 2Oliq

The water electrolysis rest potential is determined from extrapolation to ideal conditions. Variations of the concentration, c, and pressure, p, from ideality are respectively expressed by the activity (or fugacity for a gas), as a = yc (or yp for a gas), with the ideal state defined at 1 atmosphere for a pure liquid (or solid), and extrapolated from p = 0 or for a gas or infinite dilution for a dissolved species. The formal potential, measured under real conditions of c and p can deviate significantly from the (ideal thermodynamic) rest potential, as for example the activity of water, aw, at, or near, ambient conditions generally ranges from approximately 1 for dilute solutions to less than 0.1 for concentrated alkaline and acidic electrolytes.91-93 The potential for the dissociation of water decreases from 1.229 V at 25 °C in the liquid phase to 1.167 V at 100 °C in the gas phase. Above the boiling the point, pressure is used to express the variation of water activity. The variation of the electrochemical potential for water in the liquid and gas phases are given by:

g H2Ogas 2F y H2O PH2O

The critical point of water is 374 °C and 221 bar. Below the boiling point, E°h2o is similar for 1 bar and high water pressure, but diverges sharply above these conditions. Values of EVo include at pHiO = 1 bar: 1.229 V (25 °C), 1.167 V (100 °C), 1.116 V (300 °C), 1.034 V (600 °C), 0.919 V (1000 °C), 0.771 V (1500 °C), and at PH2O = 500 bar: 1.224 V (25 °C), 1.163 V (100 °C); 1.007 V (300 °C); 0.809 V

(600 °C); 0.580 V (1000 °C). Due to overpotential losses, Z, the necessary applied electrolysis potential is:

VH2OT - E0i2O(T) + Zanode + Zcathode - (1 + Z)eH2O(T) (22)

The water electrolysis potential energy conversion efficiency occurring at temperature, T, is nechem(T) - E°h2o(T)/Vh2o(T). Solar water splitting processes utilize ambient temperature water as a reactant. An interesting case occurs if heat is introduced to the system; that is when electrolysis occurs at an elevated temperature, T, using water heated from 25 °C. The ratio of the standard potential of water at 25° C and T, is r = E°h2o(25 oC) / E°h2o(T). As shown in Fig. 6, E°h2o(7) diminishes with increasing temperature, as calculated using contemporary thermodynamic values summarized in Table 4.94,95 In this case, an effective water splitting energy conversion efficiency of n'echem > 1 can occur, to convert 25 °C water to H2 by electrolysis at T:

nechem - r -nechemW ) - r • —--— --—-—--(23)

For low overpotential electrolysis, Vh2o(T > 25 °C) can be less than E°h2o (25 °C), resulting in n'echem > 1 from Eq. 23. Whether formed with pn or Schottky type junctions, the constraints on photovoltaic (solid state) driven electrolysis are identical to those for photoelectrochemical water splitting, although the latter poses additional challenges of semiconductor/electrolyte interfacial instability, area limitations, catalyst restrictions, and electrolyte light blockage. The overall solar energy conversion efficiency of water splitting is constrained by the product of the available solar energy electronic conversion efficiency, nphot, with the water electrolysis energy conversion efficiency.5 For solar photothermal water electrolysis, a portion of the solar spectrum will be used to drive charge transfer, and an unused, separate portion of the insolation will be used as a thermal source to raise ambient water to a temperature T:

Solar Power Water Electrolysis

Fig. 6. Thermodynamic and electrochemical values for water dissociation to H2 and O2 as a function of temperature.3 The curves without squares are calculated at one bar, for liquid water through 100 °C and for steam at higher temperatures. The high pressure utilized in this additional curve (pH2O = 500 bar; pH2 = pO2 = 1 bar) is of general interest as (i) the electrolysis potential is diminished compared to that of water at 1 bar, (ii) the density of the high pressure fluid is similar to that the liquid and (iii) may be generated in a confined space by heating or electrolyzing liquid water.

Fig. 6. Thermodynamic and electrochemical values for water dissociation to H2 and O2 as a function of temperature.3 The curves without squares are calculated at one bar, for liquid water through 100 °C and for steam at higher temperatures. The high pressure utilized in this additional curve (pH2O = 500 bar; pH2 = pO2 = 1 bar) is of general interest as (i) the electrolysis potential is diminished compared to that of water at 1 bar, (ii) the density of the high pressure fluid is similar to that the liquid and (iii) may be generated in a confined space by heating or electrolyzing liquid water.

' m nsolar - "Hphot ' r '"Hechem - "Hphot

1.229

Conditions of ^solar > nphot can be shown to place specific restrictions on the photoabsorber. When Vh2o < Etneut, heat must flow to compensate for the self-cooling which occurs at the electrolysis rate. That is, for an enthalpy balanced system any additional required heat must flow in a flux equivalent to ¿heat = ¿H2O, and at an average power Pheat, such that:

Table 4. Thermodynamic free energy and enthalpy of water formation for (a) all constituents at 1 bar, and (b) 500 bar water and 1 bar H2 and O2.

Table 4. Thermodynamic free energy and enthalpy of water formation for (a) all constituents at 1 bar, and (b) 500 bar water and 1 bar H2 and O2.

T(K)

P of H2O

= 1 bar

P of H2O =

500 bar

Ph2o

H2O

AG°r

AH°f

Ph2O

H2O

AG°r

AH°f

(bar)

state

kJ/mol

kJ/mol

(bar)

state

kJ/mol

kJ/mol

298

1

liquid

237.1

285.8

500

liquid

236.2

285.0

300

1

liquid

236.8

285.8

500

liquid

235.9

285.0

373

1

liquid

225.2

280.2

373

1

gas

225.2

239.5

400

1

gas

223.9

243.0

500

liquid

220.1

282.0

500

1

gas

219.1

243.8

500

liquid

204.9

278.8

600

1

gas

214.0

244.8

500

liquid

190.5

274.9

647

critical point P = 221

bar

700

1

gas

208.8

245.7

500

super critical

176.9

268.3

800

1

gas

203.5

246.5

500

super critical

164.6

258.1

900

1

gas

198.1

247.2

500

super critical

153.2

254.6

1000

1

gas

192.6

247.9

500

super critical

142.0

253.2

1100

1

gas

187.0

248.4

500

super critical

130.9

252.5

1200

1

gas

181.4

248.9

500

super critical

119.9

252.1

1300

1

gas

175.7

249.4

500

super critical

108.8

252.0

1400

1

gas

170.1

249.9

500

super critical

97.8

251.9

1500

1

gas

164.4

250.2

500

super critical

86.8

251.9

1600

1

gas

158.6

250.5

500

super critical

75.8

251.9

1700

1

gas

152.9

250.8

500

super critical

64.8

252.0

1800

1

gas

147.1

251.1

500

super critical

53.8

252.0

2300

gas

118.0

252.1

2800

gas

88.9

252.8

3300

gas

59.6

253.5

3800

gas

30.3

254.2

4310

0.0

255.1

A photoelectrolysis system can contain multiple photo-harvesting units and electrolysis units, where the ratio of electrolysis to photovoltaic units is defined as R. Efficient water splitting occurs with the system configured to match the water electrolysis and photopower maximum power point. This is illustrated in Fig. 1 representing the photosensitizers as power supplies driving electrolysis with a photo-driven charge from a photon flux to generate a current density (electrons per unit area) to provide the two stoichiometric electrons per split water molecule. For example, due to a low photopotential, a photodriven charge from three serial arranged Si energy gap devices may be required to dissociate a single room temperature water molecule, as described in the lower right portion of the figure. Alternately, as in a multiple bandgap device such as AlGaAs/GaAs, the high potential of a single photo-driven charge may be sufficient to dissocate two room temperature water molecules, as described in the upper right portion of the figure. In the figure, consider, four different photoelectrolysis systems, each functioning at the same efficiency for solar conversion of electronic power, ^pi«, and the same efficiency for solar conversion of thermal power,nheat. Whereas the photoconverter in the first system generates the requisite water electrolysis potential, that in the second system generates twice that potential (albeit at one half the photocurrent), while the photoconverter in the third and fourth units generate respectively only half or a third this potential (albeit at twofold or threefold the photocurrent to retain the same efficiency). The harvested photon power for electronic energy per unit insolation area will be the same in each of the four cases. Furthermore, the number of harvested photons for thermal energy, and the total thermal power available to heat water, will be the same of the four cases. For example in Case II, although twice the number of electrolysis units are utilized, each operates at only half the hydrolysis current compared to Cases I, III and IV, splitting the same equivalents of water.

For solar driven charge transfer, this maximum power is described by the product of the insolation power, Psun, with nphot, which is then applied to electrolysis, nphotPsun = Pechem = ¿h2oVh2o. Rearranging for ¿H20 , and substitution into Eq. 25, yields for heat balanced solar electrolysis at conditions of T and p, initiating with 25 °C, 1 bar water:

nphot ^sun

As also elaborated in Chapter 2, Fig. 7 presents the available insolation power, PÀmax (mW cm 2) of the integrated solar spectrum up to a minimum electronic excitation frequency, Vmin (eV), determined by integrating the solar spectral irradiance, S(mWcm-2nm-1), as a function of a maximum insolation wavelength, Xmax (nm). This P^max is calculated for the conventional terrestial insolation spectrum either above the atmosphere, AM0, or through a 1.5 atmosphere pathway, AMI.5. Relative to the total power, Psun, of either the AM0 or AM1.5 insolation, the fraction of this power available through the insolation edge is designated Prel = P^max / Psun. In solar energy balanced electrolysis, excess heat is available primarily as photons without sufficient energy for electronic excitation. The fraction these sub-bandgap photons in insolation is aheat = 1 - Prel , and comprises an incident power of aheatPrel.

Figure 8 presents the variation of the minimum electronic excitation frequency, Vmin with aheat, determined from Prel using the values of P^max summarized in Fig. 7. A semiconductor sensitizer is constrained not to utilize incident energy below the bandgap. As seen in Figure 8 by the intersection of the solid line with Vmin, over one third of insolation power occurs at Vmin < 1.43 eV (867 nm), equivalent to the IR not absorbed by GaAs or wider bandgap materials. The calculations include both the AM0 and AM1.5 spectra. In the relevant visible and IR range from 0.5 to 3.1 eV (±0.03 eV) for both the AM0 and AM1.insolation spectra, Vmin(aheat) in the figure are well represented (R2 >0.999) by polynomial fits.

When captured at a thermal efficiency of nheat, the sub-bandgap insolation power is nheataheatPsun. other available system heating sources include absorbed superbandgap photons which do not effectuate charge separation, Precomb, and noninsolation sources, Pamb, such as heat available from the ambient environment heat

Hydrogen Spectrum
Fig. 7. The solar irradiance (mW cm 2 nm ') in the figure inset, and the total insolation power (mW cm-2) in the main figure of the solar spectrum;3 see also Chapter 2.

sink, and Precov, such as heat recovered from process cycling or subsequent H2 fuel utilization. The power equivalent for losses, such as the low power consumed in delivering the heated water to electrolysis, Ppump, can also be incorporated.

In Figs. 9 to12, determinations of the solar water splitting energy conversion are summarized, calculated using the E°H2o(T,p) data in Fig. 8, and for various solar water splitting system's minimum allowed bandgap, Eg-min(T,p) for a wide temperature range. Figures 9 and 10, or 8 and 11, are respectively modeled based on AM1.5, or AM0, insolation. Figures 9 and 11 are calculated, at various temperatures for pH2O = 1 bar; while Figures 10 and 12 repeat these calculations for pmo = 500 bar. The nsoiar-max value is significantly greater for higher pressure photoelectrolysis (pmo = 500 bar). However as seen comparing the minimum bandgap in these figures (or in Figures 11 and 12 in the analogous AM0 models), at these higher pressures, this higher rate of efficiency increase with temperature is offset by lower accessible temperatures (for a given bandgap). Larger Z in Vh2o will diminish nsolar, but will extend the usable small bandgap range. Together, Figs. 9-12 show the constraints on nsolar from various values of nphot.

Photoelectrolysis Hydrogen

Fig. 8. aheat, the fraction of solar energy available below the minimum sensitizer insolation frequency used to drive charge transfer, Vmin.3 The aheat is determined as 1- Prel, with Prel = P^max/Psun, and using values of P^max summarized in Fig. 7. The available incident power below Vmin will be aheatPsun. The bandgaps of various semiconductors are superimposed as vertical lines in the figure.

Fig. 8. aheat, the fraction of solar energy available below the minimum sensitizer insolation frequency used to drive charge transfer, Vmin.3 The aheat is determined as 1- Prel, with Prel = P^max/Psun, and using values of P^max summarized in Fig. 7. The available incident power below Vmin will be aheatPsun. The bandgaps of various semiconductors are superimposed as vertical lines in the figure.

The high end of contemporary experimental high solar conversion efficiencies ranges from 100% nphot = 19.8% for multicrystalline single junction photovoltaics to 27.6% and 32.6% for single junction and multiple junction photovoltaics.97 The efficiency of solar thermal conversion tends to be higher than solar electrical conversion, nphot, particularly in the case of the restricted spectral range absorption used here with values of n«« = 0.5, 0.7 or 1. While a small bandgap, Eg < 1.23 eV, is insufficient for water cleavage at 25 °C, its inclusion in Figs. 9-12 is of relevance in two cases,

1. where high temperature decreases Vh2o(T) below Eg, and

2. where this Eg is part of a multiple bandgap sensitization contributing a portion of a larger overall photopotential.

Generation Bandgap

Fig. 9. Energy conversion efficiency of solar driven water splitting to generate H2 as a function of temperature for AM1.5 insolation, with the system minimum bandgap determined at pmo = 1 bar.3 The maximum photoelectrolysis efficiency is shown for various indicated values of nphot.

Fig. 9. Energy conversion efficiency of solar driven water splitting to generate H2 as a function of temperature for AM1.5 insolation, with the system minimum bandgap determined at pmo = 1 bar.3 The maximum photoelectrolysis efficiency is shown for various indicated values of nphot.

Photoelectrolysis Hydrogen

Fig. 10. The energy conversion efficiency of solar driven water splitting to generate H2 as a function of temperature at AM1.5 insolation, with the system minimum bandgap determined at PH20 = 500 bar.3 The maximum photoelectrolysis efficiency is shown for various indicated values of nphot.

Fig. 10. The energy conversion efficiency of solar driven water splitting to generate H2 as a function of temperature at AM1.5 insolation, with the system minimum bandgap determined at PH20 = 500 bar.3 The maximum photoelectrolysis efficiency is shown for various indicated values of nphot.

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