REPORTS
the critical point, the density shows a strong var-
iation, whereas the pressure, the integral of the
density over m at constant T, is naturally less sen-
sitive to the superfluid transition.
In conclusion, we have performed thermody-
namic measurements of the unitary Fermi gas
across the superfluid phase transition at the level
of uncertainty of a few percent, without any fits
or input from theory, enabling validation of the-
ories for strongly interacting matter. Similar un-
biased methods can be applied to other systems,
for example, two-dimensional Bose and Fermi
gases or fermions in optical lattices.
12. S. Nascimbène, N. Navon, K. J. Jiang, F. Chevy,
32. J. Carlson, S.-Y. Chang, V. R. Pandharipande,
C. Salomon, Nature 463, 1057 (2010).
K. E. Schmidt, Phys. Rev. Lett. 91, 050401 (2003).
33. G. E. Astrakharchik, J. Boronat, J. Casulleras,
A. S. Giorgini, Phys. Rev. Lett. 93, 200404 (2004).
34. K. Van Houcke et al., Feynman diagrams versus
Fermi-gas Feynman quantum emulator, preprint
abs/1110.3747.
13. Materials and methods are available as supporting
material on Science Online.
14. Y. Shin, M. W. Zwierlein, C. H. Schunck, A. Schirotzek,
W. Ketterle, Phys. Rev. Lett. 97, 030401 (2006).
15. G. B. Partridge et al., Phys. Rev. Lett. 97, 190407
2006).
(
35. S. Nascimbène, Thermodynamics of ultracold Fermi
16. C.-H. Cheng, S.-K. Yip, Phys. Rev. B 75, 014526 (2007).
17. T.-L. Ho, Phys. Rev. Lett. 92, 090402 (2004).
18. X.-J. Liu, H. Hu, P. D. Drummond, Phys. Rev. Lett. 102,
160401 (2009).
gases, thesis, Ecole Normale Supérieure, Paris (2010).
36. A. Bulgac, J. E. Drut, P. Magierski, Phys. Rev. Lett. 96,
90404 (2006).
0
19. D. Rakshit, K. M. Daily, D. Blume, Thermodynamics of
two-component Fermi gas with large scattering length:
Fourth- and higher-order virial coefficients, preprint
arXiv:1106.5958; available at http://arxiv.org/abs/
Acknowledgments: We thank B. Svistunov, N. Prokof'ev,
and F. Werner for fruitful discussions; Z. Hadzibabic for
a critical reading of the manuscript; the authors of
(
11, 12, 23, 26, 27, 36) for kindly providing us with their
1106.5958.
data; and André Schirotzek for help during the early
stages of the experiment. M.J.H.K. acknowledges financial
support from NSERC. This work was supported by the NSF,
Air Force Office of Scientific Research (AFOSR) - Multidisciplinary
Research Program of the University Research Initiative
References and Notes
20. J. R. Ensher, D. S. Jin, M. R. Matthews, C. E. Wieman,
E. A. Cornell, Phys. Rev. Lett. 77, 4984 (1996).
21. L. Luo, J. Thomas, J. Low Temp. Phys. 154, 1 (2009).
22. L. Pollet, N. V. Prokof’ev, B. V. Svistunov, Phys. Rev. Lett.
104, 245705 (2010).
1
2
3
4
5
6
7
. M. Tinkham, Introduction to Superconductivity (Dover,
Mineola, New York, ed. 2, 2004).
. D. Vollhardt, P. Wölfle, The Superfluid Phases of Helium 3
(Taylor & Francis, London, 1990).
(
MURI), Army Research Office (ARO) - MURI, Office of Naval
. J. A. Lipa, J. A. Nissen, D. A. Stricker, D. R. Swanson,
T. C. P. Chui, Phys. Rev. B 68, 174518 (2003).
. M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek,
C. H. Schunck, W. Ketterle, Nature 435, 1047 (2005).
. W. Ketterle, M. Zwierlein, Riv. Nuovo Cim. 31, 247
23. R. Haussmann, W. Rantner, S. Cerrito, W. Zwerger,
Research, Defense Advanced Research Projects Agency (DARPA)
Young Faculty Award, a grant from the ARO with funding
from the DARPA Optical Lattice Emulator program, an
AFOSR Presidential Early Career Award in Science and
Engineering, the David and Lucile Packard Foundation,
and the Alfred P. Sloan Foundation.
Phys. Rev. A 75, 023610 (2007).
24. C. A. Regal, M. Greiner, D. S. Jin, Phys. Rev. Lett. 92,
040403 (2004).
25. M. W. Zwierlein et al., Phys. Rev. Lett. 92, 120403
(2004).
26. O. Goulko, M. Wingate, Phys. Rev. A 82, 053621 (2010).
27. E. Burovski, N. Prokof’ev, B. Svistunov, M. Troyer,
Phys. Rev. Lett. 96, 160402 (2006).
28. J. P. Gaebler et al., Nat. Phys. 6, 569 (2010).
29. Y. Castin, F. Werner, The BCS-BEC Crossover and the
Unitary Fermi Gas, W. Zwerger, ed. (Springer-Verlag,
Berlin, 2012), chap. 5.
30. M. M. Forbes, S. Gandolfi, A. Gezerlis, Phys. Rev. Lett.
106, 235303 (2011).
(
2008).
. S. Giorgini, L. P. Pitaevskii, S. Stringari, Rev. Mod. Phys.
0, 1215 (2008).
. I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80,
85 (2008).
8
Supporting Online Material
www.sciencemag.org/cgi/content/full/science.1214987/DC1
Materials and Methods
Figs. S1 to S4
References (37–45)
8
8
9
. J. Kinast et al., Science 307, 1296 (2005).
. J. T. Stewart, J. P. Gaebler, C. A. Regal, D. S. Jin,
Phys. Rev. Lett. 97, 220406 (2006).
10. L. Luo, B. Clancy, J. Joseph, J. Kinast, J. E. Thomas,
Phys. Rev. Lett. 98, 080402 (2007).
7 October 2011; accepted 3 January 2012
Published online 12 January 2012;
10.1126/science.1214987
11. M. Horikoshi, S. Nakajima, M. Ueda, T. Mukaiyama,
Science 327, 442 (2010).
31. P. Arnold, J. E. Drut, D. T. Son, Phys. Rev. A 75, 043605
(2007).
erization of the terminal alkenes to internal isomers.
Undesired isomerization often necessitates sub-
sequent purification steps that are both energy
and cost intensive. Furthermore, decomposition
of the catalyst to colloidal platinum contributes to
unwanted side reactions and also causes dis-
coloration of the final products.
Iron Catalysts for Selective
Anti-Markovnikov Alkene
Hydrosilylation Using Tertiary Silanes
It has been estimated that the worldwide sil-
icone industry consumed ~180,000 troy ounces
1
1
2
2
Aaron M. Tondreau, Crisita Carmen Hojilla Atienza, Keith J. Weller, Susan A. Nye,
3
4
1
Kenrick M. Lewis, Johannes G. P. Delis, Paul J. Chirik *
(
5.6 metric tons) of platinum in 2007 and most is not
recovered (13). The high cost, coupled with the in-
Alkene hydrosilylation, the addition of a silicon hydride (Si-H) across a carbon-carbon double bond, creasing demands on precious metals due to fuel-cell
is one of the largest-scale industrial applications of homogeneous catalysis and is used in the
commercial production of numerous consumer goods. For decades, precious metals, principally
and other emerging technologies, has increased the
volatility of the platinum market (14). The combi-
compounds of platinum and rhodium, have been used as catalysts for this reaction class. Despite nation of chemical, economic, and political chal-
their widespread application, limitations such as high and volatile catalyst costs and competing
lenges inspires the exploration of inexpensive and
side reactions have persisted. Here, we report that well-characterized molecular iron coordination Earth-abundant catalysts using iron, manganese,
compounds promote the selective anti-Markovnikov addition of sterically hindered, tertiary silanes and cobalt (15). At the core of this challenge is sup-
to alkenes under mild conditions. These Earth-abundant base-metal catalysts, coordinated by
optimized bis(imino)pyridine ligands, show promise for industrial application.
pressing tendencies of first-row transition metals
toward one-electron redox processes in favor of the
two-electron chemistry associated with the heavier
etal-catalyzed olefin hydrosilylation, which For more than three decades, precious metal com- metals that probably make up the fundamental
forms alkylsilanes by cleaving a silicon- pounds with Pt, Pd, Ru, and Rh have been used steps in a catalytic cycle for alkene hydrosilylation.
M
hydrogen bond and adding the frag- almost exclusively as catalysts. Platinum com-
1
ments across a carbon-carbon double bond (1, 2), pounds such as Karstedt’s and Speier’s cata-
finds widespread application in the commercial lysts, Pt {[(CH =CH)SiMe O} (Me, methyl) and
manufacture of silicone-based surfactants, fluids, PtCl O/ PrOH( Pr, isopropyl), respective-
molding products, release coatings, and pressure- ly, are the most widely used industrial catalysts
Department of Chemistry, Princeton University, Princeton, NJ
2
0
8544, USA. Momentive Performance Materials, 260 Hudson
2
2
2
]
2
3
3
i
i
River Road, Waterford, NY 12188, USA. Momentive Perform-
H
2
6 2
·6H
ance Materials, 769 Old Saw Mill River Road, Tarrytown, NY
1
4
0591, USA. Momentive Performance Materials bv, Plasticslaan
sensitive adhesives (3, 4). Consequently, hydro- (1, 10–12), though they suffer from chemical lim- 1, 4612PX Bergen op Zoom, Netherlands.
silylation has emerged as one of the largest-scale itations such as intolerance to amino-substituted *To whom correspondence should be addressed. E-mail:
applications of homogeneous catalysis (5–9). olefins and a tendency to catalyze competing isom- pchirik@princeton.edu
www.sciencemag.org SCIENCE VOL 335 3 FEBRUARY 2012
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