a S c i T e c h n o l j o u r n a lResearch Article

Torrens and Castellano, J Nanomater Mol Nanotechnol 2013, S1http://dx.doi.org/10.4172/2324-8777.S1-001

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Journal of Nanomaterials & Molecular Nanotechnology

Elementary Polarizability of Sc/Fullerene/Graphene Aggregates and Di/Graphene–Cation InteractionsFrancisco Torrens1* and Gloria Castellano2

1Institut Universitari de Ciència Molecular, Universitat de València, Edifici d’Instituts de Paterna, P. O. Box 22085, E-46071 València, Spain2Facultad de Veterinaria y Ciencias Experimentales, Universidad Católica de Valencia San Vicente Mártir, Guillem de Castro-94, E-46001 València, Spain

AbstractInteracting induced-dipoles polarization in code POLAR allows molecular polarizability, which is tested with Scn/Cn [fullerene/graphene (GR)]/Scn@Cm clusters. Polarizability sees clusters of unlike sizes, parting isomers. Bulk limit is estimated from Clausius–Mossotti relation. Clusters are more polarizable than the bulk. Theory yielded this for small Sin/Gen/GanAsm; however, experiment, reversely for larger Sin/GanAsm/GenTem. Smaller clusters need not act like middle: surface dangling bonds cause small-clusters polarizability that resembles metallic. Code AMYR models GR(2)–Mz+. A 24-atom plane models GR. Mz+ is placed on GR top (T)/bridge (B)/hollow (H). GR–Mz+ stability decays: H>E>T. From H to T, stability drops 75%, 16%, 14%, 35%, 19% and 31% for Li+/Na+/K+/M+ mean/Ca2+/average. In GR2–Mz+ from H to B to T, stability decays 4%/1%. Drops are smaller than GR–Mz+. Dispersion differs less than GR–Mz+. GR is more aware than GR2 to Mz+, M+/2+ swap and site.

KeywordsInteracting induced-dipole polarization model; Applequist method; Polarizability; Clausius–Mossotti relationship; Inclusion compound; Isomer separation

*Corresponding author: Francisco Torrens, Institut Universitari de Ciència Molecular, Universitat de València, Edifici d’Instituts de Paterna, P. O. Box 22085, E-46071 València, Spain, Tel: +34 963 544 431; Fax: +34 963 543 274; E-mail: francsico.torrens@uv.es

Received: June 16, 2013 Accepted: July 29, 2013 Published: August 09, 2013

excitation energy [13]. Crystallized C60-fullerite was predicted a direct band-gap semiconductor like GaAs [14-16]. T e polarizability of Li

n

(2 ≤ n ≤ 22) was measured [17]. Ab initio computations were reported with special basis sets for Li4 [18]. A density functional theory (DFT) study of the polarizability of Cn (n  ≤  8) was presented [19]. Te polarizability of LinHm was calculated using DFT [20]. A DFT method was used to compute Sin (10 ≤ n ≤ 20) polarizability [21]. Te polarizability of Sin (9 ≤ n ≤ 28) was calculated using a DFT cluster method [22,23]. Experimental polarizability of As4 was deduced from refractivity measurements in As(v) [24].

Te notion that atoms could be trapped in fullerene cages [25] was supported by mass spectral evidence that La–fullerene complexes were produced by laser vaporization of La-impregnated graphite [26,27]. Techniques to produce metallofullerenes in bulk were developed, allowing detailed spectroscopic characterization of a metallofullerene and leading to experimental studies of endohedral fullerenes [28,29]. By analogy with alkali-doped fullerenes in which electrons are donated to the fullerene cage by interstitial metal atoms, solid-metallofulerenes conductivity will depend on internal dopant [30]; some may be superconductors [31]. Endohedral fullerenes containing small polar molecules could be assembled into useful ferroelectric materials [32,33]. Production of fullerenes containing internal species complements the work on fullerene chemistry involving reagents outside the carbon cage [34]. Mono-metallofullerenes M@Cn [35], di-metal M2@Cn [36] and tri-metal species, e.g., Sc3@Cn, were characterized [37]. A few noble gas elements were trapped inside the fullerene cage, which made the observation of unusual physical and chemical properties of isolated atoms encircled by a π-electron cloud possible [38,39]. Spectroscopic evidence exists that charge is transferred from metal atoms to fullerene, in agreement with low ionization potential of metals and high electron affinity of fullerenes [40]. Internal atoms form clusters with weak metal–metal bonds; clusters donate electrons to the cage in agreement with experimental periodic properties [41]. Nanographene, two-dimensional (2D) membrane one-atom thick, emerged as material. Being only one-atom thick and composed of C-atoms arranged in a hexagonal honeycomb lattice structure, its interest exploded exponentially since it was isolated and characterized [42]. Cgraphene is building block for C-nanomaterials with different dimensionalities: if it is wrapped up into a ball, a 0D fullerene is obtained, when rolled, a 1D C-nanotube (CNT) and if stacked, a 3D graphite [43-48]. Cgraphene atoms exhibit sp2 hybridization which, together with atomic thickness, makes it unique: extremely high electron/hole mobilities even at room temperature (RT), high thermal conductivity at RT, 2.3% of light absorbance over a wide range of visible, mechanical strength and impermeability to gases. Cgraphene and CNTs show strong third-order nonlinerity. Te electronic properties of semiconductor monolayers are better than the bulk material, spawning efforts to create functionalized monolayers of other bonded crystal structures. Higher carrier mobility is achieved via ultra-thin topologies but terminating monolayers with ligands for specific applications, ultra-thin materials are made far more sensitive than the bulk for sensor uses. Cgraphene-like layered materials were produced (e.g., WS2, MoS2, BC2N, BC3, BN).

In earlier publications Sc, Cfullerene [49], Sc-hexagonal close

IntroductionTe role of size in modifying materials properties was not exploited

until recently [1-4]. A technique allows clusters to be deposited on an inert substrate and probed with photons [5]. Another procedure is to produce a cluster beam [6]. Based on interatomic potentials Si13 structure is special [7]: the predicted ground state is a close-packed icosahedron but ab initio studies yielded a capped antiprism [8]. Electronic structure theory was not capable of handling exchange and correlation contributions [9]. Nanocrystalline powders were used to synthesize materials with physical processing: sintering [10,11]. Rutile processing reduced sintering temperatures without sacrificing mechanical properties [12]. Quantum confinement engineered the

Citation: Torrens F, Castellano G (2013) Elementary Polarizability of Sc/Fullerene/Graphene Aggregates and Di/Graphene–Cation Interactions. J Nanomater Mol Nanotechnol S1:001.

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Graphene: Emerging Trends, Prospects and Challenges

packing (HCP), Cgraphene [50-52], Si, Ge and GaAs [53,54] clusters were calculated with program PAPID and previous version of algorithm POLAR [55]. In the present report, the scores obtained for polarizability are variable according to the computational program used. Te size of clusters appears to be very important as it influences the atomic topography and polarizability. Digraphene–cation association energy is less stable than the graphene–cation interaction. Te next section introduces the computational method. Next, the calculation results are presented and discussed. Te last section summarizes our conclusions.

Polarization Model of Interacting Induced Dipoles for Molecular Polarizabilities

Program POLAR was written for theoretical simulation of molecular electrostatic properties and polarizability [56-60]. Atomic net charges and polarizabilities are calculated from σ/π-terms. Describing partial charge method developed for Mulliken scale [61], Huheey mentioned that most elements double their electronegativities as partial charge approaches +1 whereas electronegativities disappear as partial charge moves toward –1 [62], which is expressed in Pauling units [63]:

eq A A AX X X= + ∆ (1)

where Xeq is the electronegativity equalized via Sanderson’s principle, XA, initial, pre-bonded electronegativity of atom A and ∆A, σ-partial charge on A [64]. Charge conservation leads to:

eqA

atoms A

N qX

Xν+

=∑

(2)

where N=Σν equals the total number of atoms in the species formula and q is the σ-molecular charge. Te σ-partial charge ∆A on atom A is generalized as:

,eq b AA

bonds A

X XX

−∆ = ∑

(3)

and the electronegativity equalized for bonds results:

,

2

1 1eq b

A B

qmX

X X

+=

+

(4)

where m is number of bonds in molecule. Diagonal form of σ-tensor atomic polarizabilities has two distinct components: α|| and α⊥, parallel and perpendicular, respectively, to bond axis [65]. Bonding polarizabilities were implemented in SIBFA program database [66]. Te σ-net charges and polarizabilities were calculated by electronegativity equalization principle applied bond by bond. Te π-atomic net charges and polarizabilities were calculated with Hückel Molecular Orbital theory. Molecule is brought into its principal inertial co-ordinate system. Te π-conjugation vanishes for perpendicular structures. Hückel 𝛽-parameter is evaluated in first approximation between pz orbitals twisted from co-planarity by an angle 𝜃: 𝛽=𝛽 ocos𝜃, where 𝛽

o is taken from benzene [67-

77]. Electronic coupling Vab

of binuclear mixed valence MII–L–M

III

complex [(NH3)

5Ru-bipyridyl-Ru(NH

3)

5]

5+ was evaluated [78]. When

pyridine ring rotates around ligand axis Vab(𝜃) for π–π was fitted by

function cos1.15𝜃. Function- 𝛽 is assumed universal and has form: 𝛽=𝛽

ocos1.15𝜃. A way to understand substances optical effects is based on atom-dipole interaction model. Atoms in molecule are regarded as isotropic and interact via dipole moments induced by an external field. In a diatomic molecule A–B whose atoms present isotropic polarizabilities αA and αB, additive model allows isotropic molecular polarizability αmol=αA + αB, which diagonal form is:

A B

mol A B

A B

0 00 00 0

α αα α α

α α

+ = + +

(5)

In interacting induced-dipole polarization model, AB molecular polarizability is placed in a simple and explicit form: diagonal form of anisotropic αmol presents two distinct components α|| and α⊥, parallel and perpendicular to bond axis. Silberstein’s equations are [79-81]:

3A B A B

|| 6A B

41 4

rr

α α α αα

α α+ +

=−

(6)3

A B A B6

A B

21

rr

α α α αα

α α⊥

+ −=

− (7)

mol

||

0 00 00 0

αα

α

⊥

⊥

=

α (8)

Te mean polarizability α and anisotropy 𝛿 are defined:

( )|| 2 3α α α⊥= + (9)

( )||δ α α α⊥= − (10)

Molecular-polarizabilities calculation was performed by interacting induced-dipoles polarization model, which calculates tensor effective anisotropic point polarizabilities by Applequist method for poliatomic molecules [82,83]. One considers molecule as being made up of N atoms (i, j, k,…), each of which acts as a point particle located at the nucleus and responds to an electric field by only dipole-moment induction, which is a linear function of local field. If a field Cartesian component because of permanent multipole moments is Ei

a, induced moment 𝜇ia in atom i is:

( )

Ni i i ij ja a ab b

j i

E Tµ α µ≠

= +

∑

(11)

where αi is the polarizability of atom i and Tijab, the symmetrical

field gradient tensor Tijab=(1/e)∇i

aEjb, where e is the charge of the

proton and subscripts a, b, c,…, the Cartesian components x, y, z. Linear Equations (11) for the induced-dipole moments are expressed in compact matrix equation, if one introduces the 3N×3N matrices T and α with elements Tij

ab and αiab𝛿ij (𝛿ij being the Kronecker 𝛿),

respectively. Te diagonal elements Tjjab are defined as zero. Te E

and 𝛍 are 3N×1 column vectors with elements Eia and μ i

a. Equation (11) is written in matrix form:

( ) I E T I E Tµ α µ α α µ= + = + (12)

where I is the 3N×3N-dimensional unit matrix. Matrix equation can be solved for induced dipoles:

( ) 1

I T E AEµ α α−

= − = (13)

Citation: Torrens F, Castellano G (2013) Elementary Polarizability of Sc/Fullerene/Graphene Aggregates and Di/Graphene–Cation Interactions. J Nanomater Mol Nanotechnol S1:001.

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Graphene: Emerging Trends, Prospects and Challenges

where the symmetrical many-body polarizability matrix A was introduced:

( ) 1

A I Tα α−

= − (14)

Te compact matrix equation 𝛍=AE is equivalent to the N matrix equations:

1

N iji j

j

A Eµ=

= ∑ (15)

Let the molecule be in a uniform applied field so that Ej=E for all j. Ten this equation becomes:

,

1

N ij eff ii

j

A E Eµ α=

= =

∑ (16)

Coefficient of E is effective polarizability of unit i, αeff,i. Total moment induced in molecule 𝛍mol is:

,

1 1 1 1

N N N ij N eff imol i

i i j i

A E Eµ µ α= = = =

= = =

∑ ∑∑ ∑

(17)

from which it is seen that the molecular polarizability tensor αmol is:

,

1 1 1

mol N N ij N eff i

i j i

Aα α= = =

= =∑∑ ∑

(18)

Hermitian matrix α must be symmetric if all elements are real [84,85]. Te significance of an infinite polarizability is that molecule is in a resonance state and absorbs energy from applied field [86-89]. Improvements were implemented. (1) A damping function was used in calculating symmetrical field gradient tensor to prevent polarizability from going to infinity [90,91]. (2) Interaction between atoms bonded or with a distance ranged in [rinf, rsup] was neglected. (3) Atomic polarizability tensors αi=αi

σ  +  αiπ were used instead of

scalar polarizability αi. A version of program POLAR was applied

to molecular mechanics (MM2) [92] and empirical conformational energy program for peptides (ECEPP2) [93]. Version of MM2 (MMID) [94,95] was extended to co-ordination complexes of transition metals (MMXID) [96-99]. New version of ECEPP2 is ECEPPID [100,101].

Calculation Results and DiscussionIn the elementary dipole–dipole polarizabilities <α> for Scn

clusters (Figure 1) the atom–atom contact distances were held at 2.945Å. For all the clusters our program POLAR underestimates polarizability when compared with our version of reference algorithm PAPID. In particular for Sc1, POLAR and PAPID results are underestimated with respect to the numerical restricted Hartree-Fock (RHF) value calculated by Stiehler and Hinze (22.317Å3) [102]. A reference polarizability bulk limit was estimated from the Clausius–Mossotti relationship:

( )( )

3 14 2

vεα

π ε−

=+

(19)

where v is an elementary volume per atom in the crystalline state and 𝜀, the bulk permittivity. Value of vSc=15.0Å3, αSc=3.581Å3, vC=5.3Å3 and αC=1.265Å3 per atom. Te polarizability trend for POLAR and PAPID Scn clusters vs. size is different from what one might have expected. On changing number of atoms, clusters show peaks indicative of particularly polarizable structures. All POLAR and PAPID Sc

n clusters are more polarizable than what one might have

inferred from the bulk. Previous theoretical work with DFT within one-electron approximation yielded equal trend for Si

n, Ge

n and

GanAs

m small clusters [103]; however, preceding experimental work

yielded the opposite trend for Sin, Ga

nAs

m and Ge

nTe

m larger clusters

[104]. Difference origin is problematic: smaller clusters do not need to behave like those of intermediate size. Error bars in experiments are quite large. High polarizability of Sc

n clusters is attributed to dangling

bonds at the cluster surface. Most atoms within small clusters reside on surface. Semiconductor clusters resemble metallic ones and tend to present higher co-ordination numbers than in the crystalline state. Structures are thought more closely related to high-pressure metallic phases than to diamond; e.g., alkali-clusters polarizabilities exceed bulk limit and tend to decay with increasing cluster size [105,106].

Elementary dipole–dipole polarizability for fullerenes and one-shell nanographene models (Figure 2) shows that for all clusters, POLAR overestimates polarizability when compared with PAPID. For C1, POLAR lies between PAPID and numerical RHF (1.783Å3)/DFT value calculated by Fuentealba (1.882Å3). For C60, POLAR is closer to experiment measured by Antoine et al. [107] (1.28 ± 0.13 Å3) and ab initio computation by Norman et al. [108] (1.430Å3) than PAPID. C6-cyclic POLAR is closer to DFT (1.445Å3) than PAPID. Changing number of atoms, clusters also show figures indicative of particularly polarizable structures. All fullerenes calculated with

Figure 1: Average polarizability per atom of Scn clusters vs. cluster size. Dotted lines correspond to bulk polarizability.

Figure 2: Average atom–atom polarizability per atom of fullerene models vs. cluster size.

Citation: Torrens F, Castellano G (2013) Elementary Polarizability of Sc/Fullerene/Graphene Aggregates and Di/Graphene–Cation Interactions. J Nanomater Mol Nanotechnol S1:001.

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Graphene: Emerging Trends, Prospects and Challenges

POLAR are more polarizable than bulk; however, most PAPID results are less polarizable than the bulk.

Te one-shell nanographene models (Figure 3) also show numbers indicative of particularly polarizable structures. All the graphenes calculated with POLAR are more polarizable than the bulk; notwithstanding, most PAPID results are less polarizable than the bulk. Results of POLAR for greater clusters diverge from while PAPID results converge to the bulk.

Te elementary dipole–dipole polarizabilities for endohedral Sc@C82, Sc@C60, Sc2@C82 and Sc3@C82 metallofullerenes (Figure 4) shows the elementary volume per atom in the crystalline state calculated as weight average for Sc and C atoms. For all the Scn@Cm POLAR overestimates polarizability when compared with PAPID. When comparing Cm cages with corresponding Scn@Cm POLAR polarizability increases 154% from C60 to Sc@C60, 28% from C82 to Sc@C82, 8% from C82 to Sc2@C82, 19% from C82 to Sc3@C82, 18% (average) from C82 to Scn@C82 and 52% (average) from Cm to Scn@Cm. On the other hand PAPID polarizability augments 32% from C60 to Sc@C60, 13% from C82 to Sc@C82, 105% from C82 to Sc2@C82, 131% from C82 to Sc3@C82, 83% (average) from C82 to Scn@C82 and 70% (average) from Cm to Scn@Cm. Polarizability increment of POLAR for Sc@C60 is overestimated when compared with PAPID, and POLAR increases for Scn@C82 are in general underestimated with respect to PAPID. POLAR Scn@Cm are more polarizable than the bulk. With PAPID, both Sc@Cn are less polarizable than the bulk while Sc2/3@C82 are more polarizable than the bulk. Results of POLAR and PAPID for greater clusters diverge from the bulk.

All versions of POLAR are providing so many discrepancies because it was originally written for classical molecules (CH4, NH3, H2O, etc.) where polarizability inter-atomic coupling is small instead of clusters, which present greater off-diagonal inter-atomic coupling in the many-body polarizability matrix A (Equation 14). Table 1 illustrates the elementary dipole–dipole polarizabilities for Sc, fullerene, graphene and Scm@Cn models.

Computer program AMYR for the calculation of molecular associations uses Fraga’s pairwise atom–atom potential. Te interaction energy is evaluated via 1/R expansion. A pairwise dispersion energy term is included in the potential and corrected

by a damping function. Systems are nanographene–mono/divalent cation Mz+ (Mz+=Li+, Na+, K+ and Ca2+). A 24-atom planar shell models graphene. Bridge C–C distance is 1.415Å. Tree structures are distinguished with cation placed on a graphene top (T, atom, Figure 5), bridge (B, bond) and hollow (H, centre of ring).

Nanographene–cation stability (–Etotal, Figure 6) decays as H  >  B  >  T. On going from H to B stability drops 40%, 13%, 11%, 21%, 15% and 20% for Li+, Na+, K+, M+ mean, Ca2+ and Mz+ average, respectively; from H to T stability decreases 75%, 16%, 14%, 35%, 19% and 31%. Dispersion rises association energy by 63%, 21%, 56%, 47%, 118% and 65%. Dispersion allows greater discrimination among structures. Graphene–cation association is calculated more stable for divalent Ca2+ (Z=20) than monovalent cations, especially K+ (Z=19), by dispersion.

For digraphene–cation intercalation compounds, digraphene is modelled by a pair of 24-atom planar nanographene shells above, stacked at a separation of 6.800Å. Tree sandwich structures are distinguished with cation placed between pairs of graphene T, B and H. Again stability (Figure 7) decays as H>B>T. On going from H to B, stability drops 4% for Li+, Na+, K+, M+ mean, Ca2+ and Mz+ average, which results less than graphene–cation. For digraphene–cation when going from H to T, stability decreases 5%, 5%, 6%, 5%, 5% and 5%, respectively, which results less than graphene–cation. For digraphene–cation B–H and T–H relative decays are smaller than for graphene–cation. Dispersion results 22%, 15%, 44%, 27%, 89% and 43%. One more time it permits greater discrimination; however, its relative contributions are smaller than for graphene–cation. Graphene–cation is computed more stable for divalent Ca2+ than M+, especially by dispersion.

Figure 3: Average atom–atom polarizability per atom of one-shell graphene models vs. cluster size.

Figure 4: Average atom–atom polarizability per atom of the endohedral Scn@Cm fullerenes.

Figure 5: Graphene–cation structures with different sites: top (T), bridge (B) and hollow (H).

Citation: Torrens F, Castellano G (2013) Elementary Polarizability of Sc/Fullerene/Graphene Aggregates and Di/Graphene–Cation Interactions. J Nanomater Mol Nanotechnol S1:001.

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doi:http://dx.doi.org/10.4172/2324-8777.S1-001

Graphene: Emerging Trends, Prospects and Challenges

Figure 6: Graphene–cation association energy for different cations and binding sites.

Figure 7: Digraphene–cation association energy for different cations and binding sites.

Scn Fullerene Graphene

An <α> (Å3)a <α> Ref.b <α> (Å3)a <α> Ref.b <α> (Å3)a <α> Ref.b

A1 16.893 16.893 1.763 1.322 1.763 1.322

A2 4.524 13.744 - - 2.187 1.160

A3 6.885 11.557 - - 2.017 1.153

A4 7.288 10.041 - - 2.545 1.130

A5 7.546 9.690 - - 2.303 1.097

A6 8.306 10.330 - - 1.834 1.024

A7 7.596 9.321 - - - -

A10 - - - - 2.009 1.067

A12 8.383 8.724 5.825 0.722 - -

A13 - - - - 3.186 1.074

A16 - - - - 2.180 1.091

A17 7.819 25.278 - - - -

A19 - - - - 3.491 1.109

A22 - - - - 3.539 1.116

A24 - - - - 2.280 1.117

A42 - - - - 2.538 1.185

A54 - - - - 3.633 1.212

A60 - - 1.546 0.904 - -

A70 - - 1.579 0.920 - -

A74 23.143 23.471 - - - -

A82 - - 3.349 0.911 - -

A84 - - - - 4.040 1.273

A96 - - - - 4.313 1.293

Sc@C60 - - 3.933 1.193 - -

Sc@C82 - - 4.303 1.026 - -

Sc2@C82 - - 3.613 1.866 - -

Sc3@C82 - - 3.976 2.101 - -

Table 1: Elementary dipole–dipole polarizabilities for Sc, fullerene, graphene and Scm@Cn models.

a Average dipole–dipole polarizability (Å3). b Reference: calculations carried out with the PAPID program.

Citation: Torrens F, Castellano G (2013) Elementary Polarizability of Sc/Fullerene/Graphene Aggregates and Di/Graphene–Cation Interactions. J Nanomater Mol Nanotechnol S1:001.

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doi:http://dx.doi.org/10.4172/2324-8777.S1-001

Graphene: Emerging Trends, Prospects and Challenges

Te comparison of elementary di/graphene–cation association energy (Figure 8) shows that, in general, nanographene–cation results more stable than digraphene–cation association. Graphene is more sensitive to cation than digraphene. It is more delicate to substitution of divalent Ca2+ for a monovalent cation than digraphene. It is more susceptible to binding site than digraphene.

ConclusionsFrom the present results and discussion the following conclusions

can be drawn.

1. Clusters show numbers indicative of particularly polarizable structures. Polarizability is important for clusters identification and isomers separation. Polarizability results are of the same order of magnitude as PAPID. Results clearly indicate that because of differences between POLAR and PAPID it may become necessary to recalibrate POLAR. Quality ab initio calculations might be suitable as primary standards for such a calibration. Work is in progress on POLAR recalibration.

2. Te polarizability trend for the clusters vs. size is different from what one might have expected. Te Scn clusters (POLAR/PAPID), fullerenes, graphenes and metallofullerenes (POLAR) are more polarizable than what is inferred from the bulk. Te higher polarizability of smaller clusters is attributed to arise from dangling bonds at cluster surface. Results for greater Scn and Scn@Cm clusters (POLAR/PAPID) diverge from the bulk while for graphene clusters (POLAR) diverge from and PAPID converges to the bulk. Recommended elementary polarizability values are 17–22Å3 (Sc

n),

1.8–1.9Å3 (small fullerene), 1.3–1.9Å3 (small graphene) and 1.3Å3 (large C

n).

3. Polarizability calculated with POLAR increases 52% from Cm to endohedral Scn@Cm, which results underestimated when compared with PAPID outcomes that give a rise of 70%.

4. Program AMYR for molecular-associations calculation uses Fraga’s atom–atom potential. Systems are di/graphene–Mz+. A 24-atom planar cluster models nanographene. Structures distinguished

Mz+ placed on graphene top/bridge/hollow. Stability decays: hollow>bridge>top. From hollow to top, stability drops 75%, 16%, 14%, 35%, 19% and 31% for Li+, Na+, K+, M+ mean, Ca2+ and Mz+ average. For digraphene–Mz+ from hollow to bridge, stability decays 4%. From hollow to top, it drops 5%. Relative decays are smaller than graphene. Dispersion results 22%, 15%, 44%, 27%, 89% and 43%; it raises discrimination among structures but this is smaller than graphene. Graphene–Mz+ is more stable and sensitive than digraphene to Mz+, substitution of M+ by M2+ and site. Versatile properties of graphene-based nanomaterials makes them desirable nanoplatform for future research.Acknowledgments

The authors want to dedicate this manuscript to Dr. Luis Serrano-Andrés, who was greatly interested in this research and would have loved to see its conclusion. F. T. thanks support from the Spanish Ministerio de Ciencia e Innovación (Project No. BFU2010–19118).

e/digraphene–cation association energies.

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Figure 8: Comparison of elementary graphene/digraphene–cation association energies.

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Author Affiliations Top

1Institut Universitari de Ciència Molecular, Universitat de València, Edifici d’Instituts de Paterna, P. O. Box 22085, E-46071 València, Spain2Facultad de Veterinaria y Ciencias Experimentales, Universidad Católica de Valencia San Vicente Mártir, Guillem de Castro-94, E-46001 València, Spain

This article was originally published in a special issue, Graphene: Emerging Trends, Prospects and Challenges handled by Editor, Dr. Farid Menaa, Fluorotronics, Inc., USA