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Fullerenes: their role in interstellar extinction and

diffuse microwave emission in our Galaxy.

Susana Iglesias Groth

Instituto de Astrofísica de Canarias.

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Fullerenes: the third alothropic form of carbon(graphite+diamond+fullerenes)

1985 The discovery of C60 Experimentsby Kroto and Smalley aimed to reproduce thechemistry of the atmospheres of red giant stars(H.W.Kroto et al.,Nature 318,1985)

• General characteristics C60

- 60 carbon atoms

Hollow - atoms follow simmetry of a truncated icosahedral

molecule distributed in pentagons (12) and hexagons (20)

- Approximated radius of the sphere 3.55 Å

•Electronic structure:-Each of the 60 atomic orbitals 2pz (π molecular states)

• Orbitals 2s, 2px y 2py distributed in a plane tangential to the molecular surface --> σ orbitalsTheir combination produces 3 hybrid orbitals sp2

C60

π

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Fullerene families-Fullerenes with a number of atoms 20 (m2 + n2 + nm) icosahedrum

simmetry groups I ó Ih. Higher stability m=n (60 n2) (C60 ,C240 ,C540 ,C960 , C1500 , C2160 , C2940 , C3840 , C4860 ...)

-Buckyonions, multishell fullerenesHigher stability than individual fullerenesMany shells with separations 3.4-3.5 Å

Discovery: Ugarte (Nature, 359, 1992) electronic

bombardment on carbon soot . -annealing of carbon soot and nanodiamonds( T approx. 2000 K ) ( Kuznetsov et al., 1994;

Tomita et al., 1999 and 2001)

-carbon ions in metallic substrates (Cabioc´h 1995; 1997)

C60@C240@C540@C960@C1500

Real pictureElectronic microscopy

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Fullerenes in Meteorites and Earth

Mass spectrum measured in the AllendeMeteorite (carbonaceous chondrite)

0.1 ppm

Detected in sedimentary layers of the cretaceous-Tertiary (KTB) boundary

¿Formation mechanism ?Red giant stars and outflows of carbon stars

Becker et al1994,1999Met. Allende.

S. Vries et al. 1993, Geochim. Cosmochim. Acta 57, 933 (1993); L. Beckeret al., Nature 372, 507 (1994); L. Becker and T.E.Bunch, Meteorities & Planetary Science 32, (1997) 5-10 ppb, + C60HX

Met. Munchinson L. Becker et al., Proc.Natl.Acad Sci. USA 97, 2979 507 (2000)

Met. Lake Tagisch (Canadá) S. Pizzarello et al., Science 293 (2000).

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Goal of this study:

Calculate the photoabsorption spectrum

of fullerenes and buckyonions and

compare with the main features of

interstellar extinction

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Photoabsorption spectrum of icosahedric fullerenes: a semiempirical model

-Theoretical approach based:Hückel, Pariser-Parr-Pople (PPP)

-Strong electronic correlation -> screening effects arerelevant (Random Phase Approximation)

2 Prominent spectral features of C60 bands at 6 and 23 eV

Berkowitz

Kamke

Spectra obtained in gaseous phase

Molecular monoelectronic Hamiltonian:an effective monoelectronic model-Born-Openheimer approximation

-Use of valence electrons

-Separability−π/σ The effective electronic hamiltonian is built as sum of monoelectronic contributions

-The spatial part of the spin-orbital is built as a lineal combination of atomic orbitals

-The molecular wave function for the fundamental state of the He0 is built as a Slater determinant from

monoelectronic spin-orbitals.

-The excited state functions are monoelectronic transitions between the fundamental and excited state.

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Monoelectronic hamiltonians in the formalism of tight-binding as a function of its N orbitals and in the notation of second quantization

Hopping between orbitals 2pz β Repulsion integrals γss=γ ,γst=χ/rstThe eigenvalue equation is solved in the formalism HF-SCF

Adopted as matrix elements effective values that reproduce the energy levels

and wave functions selfconsistently calculated following the PPP

•Hamiltonian associated to electrons σ

•Hamiltonian associated to electrons π

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Icosahedric fullerenes: isotrophic polarizability tensorUnscreened polarizabilities

Cartesian components of the dipolar moment operator

Screened polarizabilityInteraction effects

(canje y correlación)RPA

ζ=1/R3e

•Photoabsorption cross sections

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Results for single fullerenes

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Photoabsorption cross sections calculated for five icosahedric fullerenes.

Width : Γω=0.001 eV y Γω =0.06 ωPhotoabsorption cross section of C60 and experimental spectra Berkowitz and Kamke

0.001

0.06ω

Γω=0.3eV (ω<8eV) Γω=0.3+0.2(ω−8) (eV) (ω>8eV)

S. Iglesias-Groth, Ruiz, Bretón, Gómez Llorente, Journal of Chemical Physics 116, 1648 (2002)Thesis, S. Iglesias-Groth, Univ. La Laguna (2003)

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Results obtained for buckyonions

(multishell fullerenes)

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Theoretical model

Polarizabilities and photoabsorption spectra of buckyonions-Assumption: each shell contributes independently to the global monoelectronic structure

-The effects of inter and intrashell electronic interactions (screening) RPA use of classical electrostatic model

Distribution of dipolar charge (l=1) on each sphere + boundary conditions

Induced dipolar moment Coupled polarizability

It is only required knowledge of the effective monoelectronicstructure for each fullerene shell

S. Iglesias-Groth, A. Ruiz, J. Bretón and J.M.Gómez Llorente, J.Chem. Phys., 118, 7103, 2003

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C60@C240@C540@C960@C1500

C60@C240@C540

C240@C540

C60@C540

C60@C240@C540@C960

Photoabsorption spectraof buckyonions

PhD Thesis, S. Iglesias-Groth (2003)

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Fullerenes and buckyonions

in the

interstellar medium

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-The extinction of radiation λi can be approximated(N surface density of particles)

Fullerenes and buckyonions in the interstellar medium.

absabs

The reddening factor in the diffuse interstellar medium isRV =3.1

Band 2175Å5.7eV4.6µ−1

Extinction curves from Fitzpatrick 1999

Range of peak position 2193 y 2157 Å range of widths : 0.96-1.55 eV

-Suggested explanations:

Graphite : peak 4.68-4.8 µ -1;

PAHs : in general produce bands

at lower energies than graphite;

Multishell spherical layers:

electrostatic approach (promising)

2.-The diffuse interstellar bands-More than 400 bands known between 4000 y 10000 Å see e.g. Herbig (An. Rev. Astron. Astroph. 1995)

9577 and 9632 Å bands associated to C60+

(Foing and Ehrenfreund Nature, 369, 1994)

1.-UV Bump

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Fullerenes and buckyonions:carriers of interstellar absorption?Our theoretical spectra and the 2175 Å band

Comparison between cross sections of buckyonions and extinction curves

C180@C720C60@C240@C540 Curve

Fitzpatrick Rv=3.1

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Best fit for a grain size distribution

consistingof a power law

dn/dR ∝ R-3.5 ±1.0

monoshells+ buckyonions60 3840

Estimation of porcentage of carbon locked in fullerenes and buckyonions in the ISM

0.2-0.08 fullerenes per million Hydrogen atoms (ppm)

-Interstellar Carbon in fullerenes and buckyonions

n(C ) /n(H) = 90-110 x 10-6 (25%)

Iglesias-Groth, 608:L37, ApJ Letter 2004

Buckyonions spectra3840

Consistency with carbon budget for ISM.

2175Å

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Theoretical spectra and DIBs

Monoshell fullerenes

Buckyonions with acomplete number of shells

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Comparison of predicted transitions with the wavelengths ofthe 30 stronger DIBs

+ Single fullerenesBuckyonions complete shells

--- stronger observed DIBs

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Another prediction:Fullerene based molecules should

rotate at high speed in theinterstellar medium....

If they had a dipole moment, then

we may expect electric dipoleradiation

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Rotational damping mechanisms:ω

Collisional drag

Plasma drag

Infrared emision

Electric dipole damping

Excitación by the plasma

Infrared emission

Photoelectric emission

Εlectric dipole emission of fullerene based molecules

Η

Dipole moment C-H =0.3 Debye

Dipole moment of fullerane with N H atomsµ=0.3(N)0.5

25% Hidrogenation

CNM25% Hydrogenation

(1 - 7 Debyes)

HC60

Processing affects to the rotation molecules in ISM

Rotation excitation mechanisms:

(Drain & Lazarian, 1998)

υ (GHz)rotationangular velocity

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forIndividual molecules

The emissivity as a function of frequency

Asuming the law R-3.5

30% Hydrogenation

(GHz)υ

Εmissivity (Jy sr-1/H)

forthe mixture propoused to explain UV bump

Peak at 15-30 GHz

The values obtained are closeto the measurements of

anomalous diffuse galactic emission

obtained by the COBE and Tenerife CMB experiments

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Conclusions:• The cross sections obtained for single fullerenes and buckyonions reproduce the

behaviour of the interstellar medium UV extinction curve. The prominent band obtained between 5 and 6 eV in the theoretical cross sections can explain the position and widths observed for the 2175 Å bump. They also reproduce the rise in the extinction curve at higher energies.

• We infer ISM densities of 0.2 and 0.08 ppm for single fullerenos and buckyonionsrespectively (very similar to the densities of fullerenes observed in meteorites 0.1 ppm). We show that these results are consistent with estimates for the carbon budget in the ISM. Fullerenes and buckyonions are possibly the most abundant form of carbon in the ISM.

• Our computations also show that fullerenes and buckyonions present weaker transitions in the optical and near infrared with their number decreasing towards longer wavelengths. These transitions may be responsible for some of the known but unexplained diffuse interstellar bands.

• Finally, hydrogenated forms of fullerenes may produce electric dipole radiation and contribute to the so far unexplained anomalous microwave emission detected by Cosmic Microwave Background experiments like COBE and Tenerife.