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  <front>
    <journal-meta><journal-id journal-id-type="publisher">ESD</journal-id><journal-title-group>
    <journal-title>Earth System Dynamics</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ESD</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Earth Syst. Dynam.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">2190-4987</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/esd-10-1-2019</article-id><title-group><article-title>ESD Ideas: Photoelectrochemical carbon <?xmltex \hack{\break}?> removal as negative emission technology</article-title><alt-title>Photoelectrochemical carbon sinks</alt-title>
      </title-group><?xmltex \runningtitle{Photoelectrochemical carbon sinks}?><?xmltex \runningauthor{M.~M.~May and K.~Rehfeld}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>May</surname><given-names>Matthias M.</given-names></name>
          <email>matthias.may@physik.hu-berlin.de</email>
        <ext-link>https://orcid.org/0000-0002-1252-806X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3 aff4">
          <name><surname>Rehfeld</surname><given-names>Kira</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-9442-5362</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW, Cambridge, UK</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Institute for Solar Fuels, Helmholtz-Zentrum Berlin für Materialien <?xmltex \hack{\break}?> und Energie, Hahn-Meitner-Platz 1, 14109 Berlin, Germany</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>British Antarctic Survey, High Cross, Madingley Road, CB3 0ET, Cambridge, UK</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Institute of Environmental Physics, Ruprecht-Karls-Universität Heidelberg, <?xmltex \hack{\break}?> Im Neuenheimer Feld 229, 69120 Heidelberg, Germany</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Matthias M. May (matthias.may@physik.hu-berlin.de)</corresp></author-notes><pub-date><day>4</day><month>January</month><year>2019</year></pub-date>
      
      <volume>10</volume>
      <issue>1</issue>
      <fpage>1</fpage><lpage>7</lpage>
      <history>
        <date date-type="received"><day>18</day><month>July</month><year>2018</year></date>
           <date date-type="rev-request"><day>31</day><month>August</month><year>2018</year></date>
           <date date-type="rev-recd"><day>4</day><month>December</month><year>2018</year></date>
           <date date-type="accepted"><day>17</day><month>December</month><year>2018</year></date>
      </history>
      <permissions>
        
        
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://esd.copernicus.org/articles/10/1/2019/esd-10-1-2019.html">This article is available from https://esd.copernicus.org/articles/10/1/2019/esd-10-1-2019.html</self-uri><self-uri xlink:href="https://esd.copernicus.org/articles/10/1/2019/esd-10-1-2019.pdf">The full text article is available as a PDF file from https://esd.copernicus.org/articles/10/1/2019/esd-10-1-2019.pdf</self-uri>
      <abstract>
    <p id="d1e115">The pace of the transition to a low-carbon economy – especially in the fuels
sector – is not high enough to achieve the 2 <inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C target limit for
global warming by only cutting emissions. Most political roadmaps to tackle
global warming implicitly rely on the timely availability of mature negative
emission technologies, which actively invest energy to remove <inline-formula><mml:math id="M2" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> from the
atmosphere and store it permanently. The models used as a basis for
decarbonization policies typically assume an implementation of such
large-scale negative emission technologies starting around the year 2030,
ramped up to cause net negative emissions in the second half of the century
and balancing earlier <inline-formula><mml:math id="M3" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> release. On average, a contribution of
<inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> Gt <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is expected by 2050
<xref ref-type="bibr" rid="bib1.bibx2" id="paren.1"/>. A viable approach for
negative emissions should (i) rely on a scalable and sustainable
source of energy (solar), (ii) result in a safely storable product,
(iii) be highly efficient in terms of water and energy use, to
reduce the required land area and competition with water and food demands of
a growing world population, and (iv) feature large-scale feasibility and affordability.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

      <p id="d1e188">Processes for the extraction of <inline-formula><mml:math id="M7" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> from the atmosphere are
energy-intensive. This energy has to be supplied by low- or zero-carbon
sources. At present, primarily direct air capture (followed by geologic
injection) and biomass production are explored and there is an active
discussion on costs and scalability of the various technologies (see
<xref ref-type="bibr" rid="bib1.bibx18" id="altparen.2"/>, and
references cited therein). Renewably driven direct air capture is believed to
be expensive and has not yet demonstrated scalability. Therefore, the
currently most feasible option appears to be the use of natural
photosynthesis to generate biomass through afforestation or ocean
fertilization <xref ref-type="bibr" rid="bib1.bibx18" id="paren.3"/>. Grown
plants are then permanently stored, building a new stock of fossil fuels.
Alternatively, the plant material can be combusted with carbon capture and
storage to act as a low-carbon fuel. However, the efficiency of natural
photosynthesis drops at high light conditions and because a significant
fraction of the energy is used for the metabolism
<xref ref-type="bibr" rid="bib1.bibx15" id="paren.4"/>, the storage of solar energy in
biomass is limited to 2 %–3 % efficiency. Therefore large areas of agricultural
land would be required for the achievement of the negative emission goals:
the removal of 1 Gt <inline-formula><mml:math id="M8" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> can demand more than 1 million square kilometres, the
combined area of Germany and France
<xref ref-type="bibr" rid="bib1.bibx18" id="paren.5"/>. There is
an ongoing discussion of whether scaling biomass production to the required
10 Gt <inline-formula><mml:math id="M10" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is at all compatible with planetary constraints
<xref ref-type="bibr" rid="bib1.bibx9" id="paren.6"/>.</p>
      <p id="d1e264">We suggest to employ photoelectrochemical <inline-formula><mml:math id="M12" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reduction, also called
<italic>artificial photosynthesis</italic>, to this end. As in its natural
counterpart occurring in plants, photons in the artificial photosynthesis
process excite charge carriers, which then reduce (and oxidize) reactants in
a liquid electrolyte to solar fuels. The photon energy is only briefly
converted to<?pagebreak page2?> electron energy and then stored in molecular bonds. Light is
absorbed in synthetic materials such as semiconductors or dyes and the
chemical conversion typically takes place at (co)catalysts at the interface
between electrolyte and light absorber. We primarily focus on tightly
integrated photoelectrochemical systems, where the absorber is immersed into
the electrolyte. While this approach imposes restrictions on the light
absorber design, the tight integration also promises cost benefits
<xref ref-type="bibr" rid="bib1.bibx10" id="paren.7"/>.</p>
      <p id="d1e284">Artificial photosynthesis already delivers 5-fold higher efficiencies than
natural photosynthesis, as 13 % for <inline-formula><mml:math id="M13" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reduction and 19 % for solar water
splitting have recently been demonstrated
<xref ref-type="bibr" rid="bib1.bibx17 bib1.bibx5" id="paren.8"/>, more than
half of the theoretical limits. Using solar fuels, either hydrogen or
carbon-based from <inline-formula><mml:math id="M14" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reduction, would cut greenhouse gas emissions.
However, while the combustion product of hydrogen is water, using renewably
generated carbon-based fuels releases the captured greenhouse gas back into
the atmosphere. Recapturing the <inline-formula><mml:math id="M15" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> from the atmosphere would be
energy-intensive and hereby lower the overall carbon reduction efficiency,
which is why solar-energy-driven water splitting may be the preferable fuel,
eliminating carbon completely from the energy system
<xref ref-type="bibr" rid="bib1.bibx16" id="paren.9"/>.
Photoelectrochemical <inline-formula><mml:math id="M16" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reduction could, therefore, be better placed to
generate carbon-rich products that can safely and permanently store carbon
extracted from the atmosphere. The electrochemical reactions have to be
chosen to generate products that can be stored safely below-ground over
thousands of years. Liquids or solids appear preferable, as gaseous products
could leak back to the atmosphere, depending on the trapping mechanism
<xref ref-type="bibr" rid="bib1.bibx6" id="paren.10"/>. The handling of a solid product in an
efficient flow-cell reactor is not practical. Although a large variety of
products is in principle feasible, the production of carbon-rich liquids,
such as alcohols or (fatty) acids, appears most promising. These could be
stored in underground reservoirs such as depleted oil fields, be sequestered
in the form of organic minerals, and used as precursors for organic
construction materials.</p>
      <p id="d1e341">Any competitive artificial approach should provide a significantly higher
turnover than natural photosynthesis. To assess the technologies, their
efficiency for carbon removal has to be estimated and compared. The typically
used solar-to-fuel efficiency <xref ref-type="bibr" rid="bib1.bibx14" id="paren.11"/> is not
suitable, as it only describes the relative fraction of incident solar
radiation that is converted to chemical energy. Instead, negative emission
technologies based on solar energy are better assessed by the
<italic>solar-to-carbon</italic> (STC) efficiency, which we define as the ratio of
converted <inline-formula><mml:math id="M17" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> molecules to the incoming photon flux (Appendix A).</p>
      <p id="d1e362">Our calculations in the following were performed under the – highly
idealized – assumption that the overpotential is dominated by the oxygen
evolution reaction for a very good catalyst, which can be justified for water
splitting. <inline-formula><mml:math id="M18" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reduction with the currently available catalysts, on the
other hand, is associated with significantly higher overpotentials. The
direct impact of catalysis performance on achievable efficiencies can be seen
in Fig. <xref ref-type="fig" rid="Ch1.F1"/>a and b, where obtainable STC efficiencies and
resulting module areas are plotted as a function of Tafel slope and exchange
current density.</p>
      <p id="d1e378">Artificial solar energy conversion does – unlike natural photosynthesis – not
suffer from an efficiency decrease due to high light conditions, as
beneficial effects of light concentration on the solar cell and higher
temperatures on catalysis can overcompensate the detrimental effect of
temperature on the absorber. Hence, near-equatorial regions with high solar
irradiation are viable target areas for its deployment. Under the assumption
of 3500 kWh m<inline-formula><mml:math id="M19" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> available per year for a two-axis tracker in the Sahara
desert region <xref ref-type="bibr" rid="bib1.bibx1" id="paren.12"/>, we can estimate
the required module area for the 2050 negative emission target of
10 Gt <inline-formula><mml:math id="M20" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M21" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. At a maximum STC efficiency of ca. 19 % (for formic acid, see
Appendix A), this would be approximately 13 500 km<inline-formula><mml:math id="M22" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>. Under the assumption
that for a mature technology the overall system efficiency is half of the
theoretical efficiency, this translates to an areal requirement of about
27 000 km<inline-formula><mml:math id="M23" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="Ch1.F1"/>c). The typical space factor for
tracking photovoltaics of 0.2 <xref ref-type="bibr" rid="bib1.bibx3" id="paren.13"/> finally leads
to a land footprint of ca. 135 000 km<inline-formula><mml:math id="M24" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>. Other desert areas such as the
Gobi desert, or the Thar Desert in north-western India, would also be
interesting regions. In areas such as central Europe, a lower irradiance
translates to larger footprints (Fig. <xref ref-type="fig" rid="Ch1.F1"/>d). The scale of such
an effort, if one tried to realize it in a single project, would be
considerable. However, it could be realized alongside with biomass approaches
in other world regions, as it does not rely on agriculturally usable land.
With the 2 <inline-formula><mml:math id="M25" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C target, there is a truly global incentive to realize such
an undertaking. Especially if spread over several projects, the economic
added value would be created in the regions that suffer most under global warming.</p>
      <p id="d1e463">Carbon removal by artificial photosynthesis is water-efficient, compared to
its natural counterpart, as water is only used as chemical precursor and not
evaporated from the closed system. Considering formic acid a product to be
stored, and the target of 10 Gt <inline-formula><mml:math id="M26" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M27" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> to be removed, the water demand
is about 4.1 Gt yr<inline-formula><mml:math id="M28" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. This would be a substantial amount in dry regions.
Desalination of seawater would be possible, albeit energetically
inconvenient. However, the direct use of seawater was already demonstrated
for electrochemical hydrogen production <xref ref-type="bibr" rid="bib1.bibx7" id="paren.14"/> and might therefore also
be possible for <inline-formula><mml:math id="M29" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reduction. Another challenge is that high-efficiency
carbon sinks concentrated in large-scale facilities could, in principle,
suffer from mass transport limitations of dilute <inline-formula><mml:math id="M30" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in the atmosphere.
This could be alleviated by selecting sites with high atmospheric convection
rates, by spacing facilities sufficiently widely apart, or to combine them
with solar updraft towers for electricity generation.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><caption><p id="d1e529">Theoretical efficiency limits and module area for the
<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> Gt <inline-formula><mml:math id="M32" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M33" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> scenario. <bold>(a)</bold> STC efficiency
limit of a dual-junction absorber for formic acid (without system loss) as a
function of exchange current density and Tafel slope. <bold>(b)</bold> Resulting
module area at Sahara irradiance and 50 % system loss. <bold>(c)</bold> STC
efficiency and module area required under Sahara irradiance for a selection
of products at 50 % system loss. Error bars indicate 40 % and 60 %
loss, respectively. <bold>(d)</bold> Module area for formic acid production over
the yearly irradiance at 50 % (solid line), as well as 40 % and 60 %
(dashed lines) system loss. Vertical lines mark typical irradiances
accessible to a two-axis tracker.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://esd.copernicus.org/articles/10/1/2019/esd-10-1-2019-f01.png"/>

    </fig>

      <p id="d1e584">Requirements for the safe storage will vary significantly with the choice of
the sink product. Formic acid would<?pagebreak page3?> certainly be problematic due to its
corrosiveness, also in the case of spilling events. Acetic acid and the
alcohols are inflammable at high concentrations and would have to be diluted
with water, increasing the water and volume footprint. For oxalate, the sink
product with the highest STC efficiency, mineral trapping by reaction with a
suitable calcium source, such as calcium chloride, to the stable mineral
whewellite could be anticipated. The 10 Gt <inline-formula><mml:math id="M34" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> goal would result in
roughly 17 Gt of the mineral. As a solid product, this – or other organic
minerals – would not require underground injection and hence at this stage
appears to be the most attractive option, with similar requirements as
biomass storage. However, post-processing will increase the energy footprint
and hereby also the costs.</p>
      <p id="d1e599">In principle, electrochemical reduction of <inline-formula><mml:math id="M35" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> would also be possible using
photovoltaics or wind power to first generate electricity, and then drive
electrolysis and the chemical conversion. This introduces the intermediate
step of converting solar to electrical energy. For the scales required, it
appears that the potential of solar energy will, unlike wind, not be a
limiting factor <xref ref-type="bibr" rid="bib1.bibx11" id="paren.15"/>.
Hybrid approaches, where inorganic solar cells are combined with bacteria,
are also possible <xref ref-type="bibr" rid="bib1.bibx12" id="paren.16"/>, but efficiencies are
currently low and it is unclear how the drop in production rate under high
illumination conditions can be overcome.</p>
      <p id="d1e619">Artificial photosynthesis in the form of <inline-formula><mml:math id="M36" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reduction represents
consequently an interesting technological option for negative emissions due
to its high efficiency. This would greatly reduce land use for the
anticipated 2050 negative emission target compared to so far considered – mainly
biomass-based – technologies. The installation of the required
minimum module area of about 30 000 km<inline-formula><mml:math id="M37" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> would, however, still be an
enormous undertaking. While we estimate the costs for photoelectrochemical
<inline-formula><mml:math id="M38" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> conversion to the sink product to roughly EUR 65 per tonne (see
Appendix B), we emphasize that the development stage of highly efficient
photoelectrochemical <inline-formula><mml:math id="M39" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> conversion does not yet allow a robust estimate of
the costs, rendering this value rather speculative. Furthermore, some of the
anticipated sink products have an economic value as energy carriers and
therefore require the creation of incentives to actually sequester and not
combust the product. Physical feasibility and technological challenges can,
however, already be anticipated.
The greatest challenges to overcome with regards to<?pagebreak page4?> the application are, for now, to develop and implement systems that are
stable under operating conditions, as well as the derivation of
earth-abundant, efficient catalysts <xref ref-type="bibr" rid="bib1.bibx17 bib1.bibx5" id="paren.17"/>.</p><?xmltex \hack{\newpage}?>

      
      </body>
    <back><notes notes-type="codeavailability">

      <p id="d1e671">The Python source code to reproduce the calculations is
available at <ext-link xlink:href="https://doi.org/10.5281/zenodo.1489158" ext-link-type="DOI">10.5281/zenodo.1489158</ext-link> <xref ref-type="bibr" rid="bib1.bibx13" id="paren.18"/>.</p>
  </notes><?xmltex \hack{\clearpage}?><app-group>

<?pagebreak page5?><app id="App1.Ch1.S1">
  <title>Solar-to-carbon efficiency measure</title>
      <p id="d1e689">Given a PEC device and a target sink product, we define the STC efficiency by
the ratio of carbon atoms, which are chemically fixed, over the total
incoming photon flux, <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>j</mml:mi><mml:mi mathvariant="normal">ph</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, given by the integrated solar spectrum. The
electronic current corresponding to this total photon flux would be the
photocurrent that could be extracted from an ideal absorber with an
infinitesimally small bandgap, where each photon contributes to one electron
in the photocurrent. The STC efficiency limit for an ideal
photoelectrochemical solar cell can then be calculated as follows: the Gibbs
free energy difference per electron, <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:math></inline-formula>, constitutes the
electrochemical load of the cell. It limits, together with the terrestrial
solar spectrum, <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the electronic current density, <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>j</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Tandem
solar cells are required for high efficiencies in photoelectrochemical energy
conversion as they provide high currents and sufficient voltage to drive the
reaction. The current density of an ideal tandem absorber under air mass
1.5 global illumination with very good catalysts can be calculated in the
detailed-balance-scheme <xref ref-type="bibr" rid="bib1.bibx14" id="paren.19"/>. Under the
assumption of unity absorption above the bandgap, the top cell absorbs
photons <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> in the range between the far UV
(<inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>→</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> nm) and the wavelength <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> corresponding to its bandgap;
the bottom cell experiences the photon flux filtered by the top cell and
therefore absorbs between the respective bandgaps of top and bottom cell. The
smaller of the two values then gives the maximum photocurrent at zero load.
The operational photocurrent is then obtained by intersecting the overall
current-voltage curve of the solar cell with the curve of its load, given by
the Gibb's free energy of the redox couple and the catalyst characteristics
described by exchange current density and Tafel slope (see Asset). The
selected product then defines the electron efficiency, <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, i.e. the
inverse of how many electrons are consumed for the formation of one product
molecule from <inline-formula><mml:math id="M48" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and water. With the faradaic efficiency <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">F</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,
describing the efficiency of the conversion from current to desired product,
the STC can be formulated as

              <disp-formula id="App1.Ch1.E1" content-type="numbered"><mml:math id="M50" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="normal">STC</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">F</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">min</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mfenced open="[" close="]"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:mi>n</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>)</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow><mml:mrow><mml:munderover><mml:mo movablelimits="false">∫</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mi mathvariant="normal">∞</mml:mi></mml:munderover><mml:mi>n</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>)</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">F</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:msub><mml:mi>j</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>j</mml:mi><mml:mi mathvariant="normal">ph</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e928"><?xmltex \hack{\newpage}?>For formic acid (HCOOH, <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.4</mml:mn></mml:mrow></mml:math></inline-formula> eV, <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula>), these idealized
assumptions result in a maximum electronic photocurrent density of
<inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>j</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>≃</mml:mo><mml:mn mathvariant="normal">26</mml:mn></mml:mrow></mml:math></inline-formula> mA cm<inline-formula><mml:math id="M54" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. For unity faradaic efficiency, we obtain a product current
density equivalent of <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">η</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:msub><mml:mi>j</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">13</mml:mn></mml:mrow></mml:math></inline-formula> mA cm<inline-formula><mml:math id="M56" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. It follows that ideally
ca. 19 % of the incoming solar photons transform a <inline-formula><mml:math id="M57" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> molecule to the
liquid – and hence storable – product. The STC efficiency would therefore
be 19 %. Taking into account photoconversion, faradaic, and system losses,
values of 10 % STC or more appear feasible as 85 % of the material-specific and
ca. <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> of the overall theoretical efficiency limit were already demonstrated on
a lab scale for the similar process of
photoelectrochemical water splitting <xref ref-type="bibr" rid="bib1.bibx5" id="paren.20"/>. This is high compared to the
currently achieved energetic efficiencies for natural photosynthesis of
2 %–3 %, which translate to roughly 1.5 %–2 % STC efficiency.</p>
      <p id="d1e1047">STC efficiencies are a function of the reaction path, similar to <inline-formula><mml:math id="M59" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
reduction for fuel generation, where the obtainable efficiency depends on the
Gibbs free energy <xref ref-type="bibr" rid="bib1.bibx14" id="paren.21"/>. The distribution of
energy over the chemical bonds varies for different products, yet for <inline-formula><mml:math id="M60" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
removal, we are primarily interested in the number of converted <inline-formula><mml:math id="M61" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
molecules. Therefore, the STC efficiencies can deviate significantly for
products that have a similar energetic efficiency (Fig. <xref ref-type="fig" rid="Ch1.F1"/>c).
Feasible products are associated with distinct storage requirements as well as
different catalysts. Though the electronic photocurrent could be higher for
acetic acid compared to formic acid due to a reduced electrochemical load,
four electrons are required for the conversion of one <inline-formula><mml:math id="M62" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> molecule, which in the
end almost halves the efficiency. The theoretical efficiency limit, as shown
in Fig. <xref ref-type="fig" rid="Ch1.F1"/>c, largely varies based on the number of
electrons consumed per <inline-formula><mml:math id="M63" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> molecule, which is one for oxalate, two for
formic acid, four for acetic acid and formaldehyde, and six for methanol,
ethanol, and 1-propanol. Therefore, using the carbon conversion rate as the
benchmark for solar-driven negative emissions will result in a different
choice of product compared to solar fuels, where energetic considerations dominate.</p><?xmltex \hack{\newpage}?>
</app>

<?pagebreak page6?><app id="App1.Ch1.S2">
  <title>Cost estimate</title>
      <p id="d1e1120">To roughly estimate the costs of negative emissions by photoelectrochemical
<inline-formula><mml:math id="M64" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reduction, we assume the module costs to be twice the module costs
<xref ref-type="bibr" rid="bib1.bibx4" id="paren.22"/> of current crystalline silicon
photovoltaics. With a depreciation period of 20 years, and running costs of
10 % of the investment sum, this would translate to EUR 55.60 per tonne of
<inline-formula><mml:math id="M65" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Additional costs can arise from the diffusion limitation due to the
high conversion rate, which might necessitate technically creating
convection by means of mechanical fans. The energy costs of capturing
atmospheric <inline-formula><mml:math id="M66" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> are estimated to be about 30–88 kJ mol<inline-formula><mml:math id="M67" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
<xref ref-type="bibr" rid="bib1.bibx8" id="paren.23"/>. With an average of 50 kJ mol<inline-formula><mml:math id="M68" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
and a current photovoltaic electricity price of EUR 30 per megawatt hour, this adds
another EUR 9.50 per tonne, finally totalling EUR 65 per tonne. Transport costs to the
storage location will vary with the chosen product and the vicinity between
production and storage facility. If we assume, as a very rough estimate,
similar transport costs of formic acid as for crude oil over a distance of
2000 km <xref ref-type="bibr" rid="bib1.bibx19" id="paren.24"/>, this would result
in additional EUR 24 per tonne of <inline-formula><mml:math id="M69" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. The overall volume to be transported
would be of the same order of magnitude as the present-day oil production.
The costs for storage will vary with the sink product, the product volume,
and the required post-processing. Some of the products could, in principle,
be used as “plastic-based” construction materials, creating an economic value
and hence reduce the overall costs. Considering the required scale, however,
the market volume for such construction materials will probably not be significant.</p><?xmltex \hack{\clearpage}?>
</app>
  </app-group><notes notes-type="authorcontribution">

      <?pagebreak page7?><p id="d1e1206">MM and KR conceived of the presented idea. MM developed the
model and performed the calculations. KR and MM discussed the results and wrote the manuscript.</p>
  </notes><notes notes-type="competinginterests">

      <p id="d1e1212">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e1218">We thank the fellowship programme of the German National Academy of Sciences
Leopoldina, grant LPDS 2015-09 (Matthias M. May) and the German Research
Foundation (code RE3994-1/1 and RE3994-3/1, for Kira Rehfeld) for funding.
Gregor Schwerhoff, Carl Poelking, and Klaus Pfeilsticker are acknowledged for
comments on the manuscript. The authors thank the referee Bruce Parkinson for
the idea to use oxalate as a sink product. <?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
Edited by: Ning Zeng <?xmltex \hack{\newline}?>
Reviewed by: Bruce Parkinson and one anonymous referee</p></ack><ref-list>
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