We studied the edge states and their roles in conductivity and magnetism of graphene nanoribbions and flakes. we studied the Aharonov-Bohm effect in graphene nanodisks and rings. We described the quantum oscillations of the magnetization of graphene flakes. we have examined the snake-like states of transport electrons in the configurations of graphene ribbons with a domain wall in the centre.

In this thesis, a series of computational studies based on density functional theory (DFT) and density functional tight-binding (DFTB) is presented to deeply understand experimental results on the synthesis of endohedral fullerenes and graphene/iron hybrids at atomic level. In the first part, a simple and efficient model is proposed to evaluate the strain experienced by clusters encapsulated in endohedral metallofullerenes (EMFs). Calculations for the sole cluster, either in the neutral or the charged state, cannot be used for this goal. However, when the effect of the carbon cage is mimicked by small organic π-systems (such as pentalene and sumanene), the cluster has sufficient freedom to adopt the optimal configuration, and therefore the energetic characteristics of the EMF-induced distortion of the cluster can be evaluated. Both nitride and sulfide clusters were found to be rather flexible. Hence, they can be encapsulated in carbon cages of different size and shape. For carbide M2C2 cluster the situation is more complex. The optimized cluster can adopt either butterfly or linear shapes, and these configurations have substantially different metal-metal distance. Whereas for Sc2C2 both structures are isoenergetic, linear form of the Y2C2 cluster is substantially less stable than the butterfly-shaped configuration. These results show that phenomenon of the “nanoscale fullerene compression” once proposed by Zhang et al. (J. AM. CHEM. SOC. (2012),134(20)) should be “nanoscale fullerene stretching”. Finally, the results also reveal that both Ti2S and Ti2C2 cluster are strained in corresponding EMF molecules, but the origin of the strain is opposite: C78-D3h(5) cage imposes too long Ti···Ti distance for the sulfide cluster and too short distance for the carbide cluster. In the second part of the thesis, possible fullerene geometries and electronic structures have been explored theoretically for the species detected in mass spectra of the Sc-EMF extract synthesized using CH4 as a reactive gas. Two most promising candidates, namely Sc4C@C80-Ih(7) and Sc4C3@C80-Ih(7), have been identified and further studied at the DFT level. For Sc4C@C80, the tetrahedral Sc4 cluster with the central μ4-C atom was found to be 10 kJ/mol more stable than the square cluster. For Sc4C3@C80, the calculation showed that the most stable is the Sc4C3 cluster in which the triangular C3 moiety is η3- and η2-coordinated to Sc atoms. Whereas Sc4C@C80 has rather small HOMO-LUMO gap and low ionization potential, the HOMO-LUMO gap of Sc4C3@C80 is substantially higher and exceeds that of Sc4C2@C80. In the third part, computational studies of structures and reactivity are described for a new type of EMFs with a heptagon that has been produced in the arc-discharge synthesis. DFT computations predict that LaSc2N@Cs(hept)-C80 is more stable than LaSc2N@D5h-C80, so the former should be synthesized in much higher yield than observed. This disagreement may be ascribed to the kinetic factors rather than thermodynamic stability. Because of prospective applications of this EMFs by introducing functional groups, the influence of the heptagon on the chemical properties have been further evaluated. Thermodynamically and kinetically preferred reaction sites are studied computationally for Prato and Bingel-Hirsch cycloaddition reactions. In both types of reactions the heptagon is not affected, and chemical reactivity is determined by the adjacent pentalene units. Thermodynamically controlled Prato addition is predicted to proceed regioselectively across the pentagon/pentagon edges, whereas the most reactive sites in kinetically-controlled Bingel-Hirsch reaction are the carbon atoms next to the pentagon/pentagon edge. Fourth, although various EMFs have been successfully synthesized and characterized, the formation mechanism is still not known in details, and hence control of the synthesis products is rather poor. Therefore, EMF self-assembly process in Sc/carbon vapor in the presence and absence of cooling gas (helium) and reactive gas (NH3 and CH4) is systematically investigated using quantum chemical molecular dynamics (QM/MD) simulations based on the DFTB potentials. The cooling gas effect is that the presence of He atoms accelerates formation of pentagons and hexagons and reduces the size of formed carbon cages in comparison to the analogous He-free simulations. As a result, the Sc/C/He system yields a large number of successful trajectories (i.e. leading to the Sc-EMFs) with more realistic cage-size distribution than the Sc/C system. Encapsulation of Sc atoms within the carbon cage was found to proceed via two parallel mechanisms. The main mechanism involves nucleation of the several hexagons and pentagons with Sc atoms already at the early stages of the carbon vapor condensation. In such proto-cages, both Sc–C σ-bonds and coordination bonds between Sc atoms and the π-system of the carbon network are present. Sc atoms are thus rather labile and can move along the carbon network, but the overall bonding is sufficiently strong to prevent dissociation even at high temperatures. Further growth of the carbon cage results in encapsulation of one or two Sc atoms within the forming fullerene. Another encapsulation mechanism is observed in rare cases. In this process, the closed cage is formed with Sc being a part of the carbon network, i.e. being bonded by three or four Sc–C σ-bonds. However, such intermediates are found to be unstable, and transform into the endohedral fullerenes within few picoseconds of annealing. In perfect agreement with experimental studies, extension of the simulation to Fe and Ti showed that Fe-EMFs are not formed at all, whereas Ti is prone to form Ti-EMFs with small cage sizes, including Ti@C28-Td and Ti@C30-C2v(3). The role of “reactive gas” in the EMF synthesis is revealed in dedicated simulations of the fullerene formation in the presence of several molecules of CH4 or NH3. When concentration of reactive gas is high, carbon vapor tends to form graphene flakes or other carbon species terminated by hydrogen atoms, whereas the yield of empty fullerenes is very low. Conversely, with additional metal atoms (Sc) and the same number of NH3 molecules, the yield of fullerenes constantly increase from 5 to 65% which is ascribed to the catalytic activity of metal atoms in the nucleation of carbon cages already at early stage. Moreover, due to the presence of hydrogen atoms from the reactive gas, the carbon cage formation requires much longer time, which provides sufficient reaction time to encapsulate 3 or 4 Sc atoms within one cage. It explains preferential formation of clusterfullerenes in experiments with reactive gas. At the same time, monometallofullerenes and dimetallofullerenes are the main products in absence of reactive gas. We also provide possible growth mechanisms of carbide and cyano-clusterfullerenes in details to elucidate how the intracluster goes into the cage. A possible growth mechanism of nitride clusterfullerenes has been proposed based on DFT results. In the last part, a free-standing crystalline single-atom thick layer of Fe has been studied theoretically. By investigating the energy difference, ΔE, between a suspended Fe monolayer and a nanoparticle using the equivalent number of Fe atoms, one can estimate that the largest stable membrane should be ca. 12 atoms wide or 3 × 3 nm2 which is in excellent agreement with the experimental observation. Otherwise, the possibility of C, O, N atoms embedded into the Fe membrane can been fully excluded by DFTB and DFT simulations, which agrees with electron energy loss spectroscopy (EELS) measurement. A significantly enhanced magnetic moment for single atom thick Fe membranes (3.08 μB) is predicted by DFT as compared to the bulk BCC Fe (2.1 μB), which originates from the 2D nature of the Fe membrane since the dz2 orbital is out-of-plane while the dxy orbital is in-plane.

In this thesis, a series of computational studies based on density functional theory (DFT) and density functional tight-binding (DFTB) is presented to deeply understand experimental results on the synthesis of endohedral fullerenes and graphene/iron hybrids at atomic level. In the first part, a simple and efficient model is proposed to evaluate the strain experienced by clusters encapsulated in endohedral metallofullerenes (EMFs). Calculations for the sole cluster, either in the neutral or the charged state, cannot be used for this goal. However, when the effect of the carbon cage is mimicked by small organic π-systems (such as pentalene and sumanene), the cluster has sufficient freedom to adopt the optimal configuration, and therefore the energetic characteristics of the EMF-induced distortion of the cluster can be evaluated. Both nitride and sulfide clusters were found to be rather flexible. Hence, they can be encapsulated in carbon cages of different size and shape. For carbide M2C2 cluster the situation is more complex. The optimized cluster can adopt either butterfly or linear shapes, and these configurations have substantially different metal-metal distance. Whereas for Sc2C2 both structures are isoenergetic, linear form of the Y2C2 cluster is substantially less stable than the butterfly-shaped configuration. These results show that phenomenon of the “nanoscale fullerene compression” once proposed by Zhang et al. (J. AM. CHEM. SOC. (2012),134(20)) should be “nanoscale fullerene stretching”. Finally, the results also reveal that both Ti2S and Ti2C2 cluster are strained in corresponding EMF molecules, but the origin of the strain is opposite: C78-D3h(5) cage imposes too long Ti···Ti distance for the sulfide cluster and too short distance for the carbide cluster. In the second part of the thesis, possible fullerene geometries and electronic structures have been explored theoretically for the species detected in mass spectra of the Sc-EMF extract synthesized using CH4 as a reactive gas. Two most promising candidates, namely Sc4C@C80-Ih(7) and Sc4C3@C80-Ih(7), have been identified and further studied at the DFT level. For Sc4C@C80, the tetrahedral Sc4 cluster with the central μ4-C atom was found to be 10 kJ/mol more stable than the square cluster. For Sc4C3@C80, the calculation showed that the most stable is the Sc4C3 cluster in which the triangular C3 moiety is η3- and η2-coordinated to Sc atoms. Whereas Sc4C@C80 has rather small HOMO-LUMO gap and low ionization potential, the HOMO-LUMO gap of Sc4C3@C80 is substantially higher and exceeds that of Sc4C2@C80. In the third part, computational studies of structures and reactivity are described for a new type of EMFs with a heptagon that has been produced in the arc-discharge synthesis. DFT computations predict that LaSc2N@Cs(hept)-C80 is more stable than LaSc2N@D5h-C80, so the former should be synthesized in much higher yield than observed. This disagreement may be ascribed to the kinetic factors rather than thermodynamic stability. Because of prospective applications of this EMFs by introducing functional groups, the influence of the heptagon on the chemical properties have been further evaluated. Thermodynamically and kinetically preferred reaction sites are studied computationally for Prato and Bingel-Hirsch cycloaddition reactions. In both types of reactions the heptagon is not affected, and chemical reactivity is determined by the adjacent pentalene units. Thermodynamically controlled Prato addition is predicted to proceed regioselectively across the pentagon/pentagon edges, whereas the most reactive sites in kinetically-controlled Bingel-Hirsch reaction are the carbon atoms next to the pentagon/pentagon edge. Fourth, although various EMFs have been successfully synthesized and characterized, the formation mechanism is still not known in details, and hence control of the synthesis products is rather poor. Therefore, EMF self-assembly process in Sc/carbon vapor in the presence and absence of cooling gas (helium) and reactive gas (NH3 and CH4) is systematically investigated using quantum chemical molecular dynamics (QM/MD) simulations based on the DFTB potentials. The cooling gas effect is that the presence of He atoms accelerates formation of pentagons and hexagons and reduces the size of formed carbon cages in comparison to the analogous He-free simulations. As a result, the Sc/C/He system yields a large number of successful trajectories (i.e. leading to the Sc-EMFs) with more realistic cage-size distribution than the Sc/C system. Encapsulation of Sc atoms within the carbon cage was found to proceed via two parallel mechanisms. The main mechanism involves nucleation of the several hexagons and pentagons with Sc atoms already at the early stages of the carbon vapor condensation. In such proto-cages, both Sc–C σ-bonds and coordination bonds between Sc atoms and the π-system of the carbon network are present. Sc atoms are thus rather labile and can move along the carbon network, but the overall bonding is sufficiently strong to prevent dissociation even at high temperatures. Further growth of the carbon cage results in encapsulation of one or two Sc atoms within the forming fullerene. Another encapsulation mechanism is observed in rare cases. In this process, the closed cage is formed with Sc being a part of the carbon network, i.e. being bonded by three or four Sc–C σ-bonds. However, such intermediates are found to be unstable, and transform into the endohedral fullerenes within few picoseconds of annealing. In perfect agreement with experimental studies, extension of the simulation to Fe and Ti showed that Fe-EMFs are not formed at all, whereas Ti is prone to form Ti-EMFs with small cage sizes, including Ti@C28-Td and Ti@C30-C2v(3). The role of “reactive gas” in the EMF synthesis is revealed in dedicated simulations of the fullerene formation in the presence of several molecules of CH4 or NH3. When concentration of reactive gas is high, carbon vapor tends to form graphene flakes or other carbon species terminated by hydrogen atoms, whereas the yield of empty fullerenes is very low. Conversely, with additional metal atoms (Sc) and the same number of NH3 molecules, the yield of fullerenes constantly increase from 5 to 65% which is ascribed to the catalytic activity of metal atoms in the nucleation of carbon cages already at early stage. Moreover, due to the presence of hydrogen atoms from the reactive gas, the carbon cage formation requires much longer time, which provides sufficient reaction time to encapsulate 3 or 4 Sc atoms within one cage. It explains preferential formation of clusterfullerenes in experiments with reactive gas. At the same time, monometallofullerenes and dimetallofullerenes are the main products in absence of reactive gas. We also provide possible growth mechanisms of carbide and cyano-clusterfullerenes in details to elucidate how the intracluster goes into the cage. A possible growth mechanism of nitride clusterfullerenes has been proposed based on DFT results. In the last part, a free-standing crystalline single-atom thick layer of Fe has been studied theoretically. By investigating the energy difference, ΔE, between a suspended Fe monolayer and a nanoparticle using the equivalent number of Fe atoms, one can estimate that the largest stable membrane should be ca. 12 atoms wide or 3 × 3 nm2 which is in excellent agreement with the experimental observation. Otherwise, the possibility of C, O, N atoms embedded into the Fe membrane can been fully excluded by DFTB and DFT simulations, which agrees with electron energy loss spectroscopy (EELS) measurement. A significantly enhanced magnetic moment for single atom thick Fe membranes (3.08 μB) is predicted by DFT as compared to the bulk BCC Fe (2.1 μB), which originates from the 2D nature of the Fe membrane since the dz2 orbital is out-of-plane while the dxy orbital is in-plane.

In dieser Arbeit werden verschiedene Aspekte des Designs und der Funktionsweise von in Flüssigkeit betriebenen Graphen-basierten Sensoren untersucht, wodurch neue Einblicke in grundlegende Prozesse an der Graphen-Flüssigkeits-Grenzfläche gewonnen werden. Zunächst wird die Wirkung redoxaktiver Moleküle in der Elektrolytlösung in elektrochemisch gesteuerten Graphen-FETs untersucht. Während des Betriebs kann ein heterogener Elektronentransfer stattfinden, der zu Faradayschen Strömen am Graphenkanal führt. Diese führen zu Verschiebungen der Transferkurve von Graphen, da die Graphen-Flüssigkeits-Grenzfläche eine nur teilweise polarisierbare Elektrode darstellt. Dies wird als „Faradayscher Effekt“ bezeichnet. Er unterscheidet sich grundlegend von typischen Transduktionsmechanismen. Parameter, die den Faradayschen Effekts beeinflussen, werden detailliert untersucht. So sind die Verschiebungen z.B. abhängig von der Graphenkanalfläche. Der zweite Abschnitt konzentriert sich auf die Kante von Graphen, die einen nanoskopischen eindimensionalen Defekt des zweidimensionalen Materials darstellt. In dieser Arbeit wird ein neuer Graphen-FET vorgestellt, der auf der Steuerung von Graphen nur über die elektrochemische Doppelschicht an der Kante basiert. Um dies zu erreichen, wird der basale Teil des Graphens durch eine Passivierung vollständig von der Elektrolytlösung abgeschirmt. Des Weiteren wird gezeigt, dass die Kante des Graphens durch elektrochemische Modifizierung kovalent funktionalisiert werden kann, wodurch die Ladungsdichte an der Graphenkanten-Flüssigkeits-Grenzfläche effektiv verändert wird. Dabei bleiben die vorteilhaften Eigenschaften der Devices erhalten. Schließlich wird ein neuartiger Ansatz zu Untersuchungen an der Graphenkante in Form von mit hexagonalem Bornitrid-verkapseltem Graphen-Elektroden verfolgt. Die elektroanalytische Detektion von Ferrocenmethanol und Dopamin an der Graphenkante mittels zyklischer Voltammetrie wird an diesen Elektroden gezeigt. / Several aspects of the design and function of sensors based on graphene operated in liquid have been investigated in this thesis, providing new insight into fundamental processes at the graphene-liquid-interface. First, the effect of the presence of redox active molecules in the analyte solution of electrochemically gated graphene FETs is explored. During operation, heterogeneous electron transfer may occur at relevant potentials leading to Faradaic currents at the graphene channel. These lead to doping-like shifts of the transfer curve of graphene, as the graphene-liquid-interface represents a partially polarizable electrode. Due to the origin of the shifts, this observation is termed “Faradaic effect”. It is fundamentally different from typically discussed transduction mechanisms. Parameters influencing the direction and magnitude of the Faradaic effect are discussed in detail, e.g. the shifts are the stronger, the larger the area of the graphene channel. The second part focuses on the edge of graphene, which represents a nanoscopic one-dimensional defect of the two-dimensional material. Here, a new type of graphene FET is introduced based on electrochemical gating of graphene exclusively via the electrical double layer at its edge. To achieve edge-gating, the basal part of graphene is passivated by a photoresist and shielded entirely from interaction with the solution. It is demonstrated that the edge of graphene can be functionalized covalently via electrografting. This changes the charge density at the graphene edge-liquid-interface effectively, while maintaining the favorable transfer characteristics of the devices. Finally, a novel approach towards graphene edge devices was pursued in the form of hexagonal boron nitride encapsulated graphene. The electrochemical detection of ferrocene methanol and dopamine was demonstrated in standard and fastscan cyclic voltammetry at the edge of graphene in these devices.

Diese Arbeit präsentiert eine einfache eine einfache, auf Photolithographie basierende Methode zur Darstellung einer isolierten Graphenkante (oder GrEdge) einer Monolage als Nanoelektrode auf einem isolierenden Substrat vorgestellt. Trotz ihrer Millimeter-Länge verhält sich die nur einen Nanometer breite GrEdge-Elektrode wie ein Nanodraht mit einem hohen Seitenverhältnis von 1000000 zu 1. Des Weiteren wird der Einsatz von elektrochemischer Modifikation (ECM) demonstriert, um die GrEdge selektiv mit Metall-Nanopartikeln und organischen Schichten nicht-kovalente oder kovalente zu funktionalisieren, wodurch die Chemie der Kante verändert werden kann. Durch die Anbringung von Metall-Nanopartikeln kann zusätzlich oberflächenverstärkte Raman-Spektroskopie (SERS) genutzt werden, um die chemische Beschaffenheit sowohl der unberührten als auch der funktionalisierten GrEdge zu charakterisieren. Die GrEdge weist sehr hohe Mass-entransportraten auf, was charakteristisch für Nanoelektroden ist. Dementsprechend wird die voltammetrische Antwort von der Kinetik des heterogenen Elektrontransfers (HET) diktiert. An der GrEdge-Elektrode werden hohe HET-Raten beobachtet: mindestens 14 cm/s für Außensphäre sonde Ferrocenmethanol (FcMeOH) mit einem quasi-Nernst'schen Verhalten und 0,06 cm/s oder höher für innere Sphäre sonde Ferricyanide ([Fe(CN)6]3-) mit einer kinetisch kontrollierten Reaktion. Nach der selektiven Modifikation der Kante mit Goldnanopartikeln erweist sich der HET als reversibel, mit einer massentransportbegrenztes Nernst‘sches Verhalten aufweisen für beide Redoxmoleküle. Darüber hinaus ermöglicht die schnelle HET-Kinetik die Detektion der reduzierten Form von Nicotinamid-Adenin-Dinukleotid (NADH) und Flavin-Adenin-Dinukleotid (FAD) mit niedrigen Ansatzpotentialen und hinunter bis zu niedrigen mikromolaren Konzentrationen. Entsprechend verbessert die vorliegende Arbeit das Verständnis der Kante von Graphen und deren Chemie. / This thesis presents a simple photolithography-based method to realize the isolated monolayer graphene edge (or GrEdge) nanoelectrode on an insulating substrate. The millimeter-long and a nanometer-wide GrEdge is found to behave like a nanowire with a high aspect ratio of 1000000-to-1. Further, the use of electrochemical modification (ECM) is demonstrated to selectively functionalize the GrEdge with metal nanoparticles and organic moieties in a non-covalent/ covalent manner to tune the chemistry of the edge. The attachment of metal nanoparticles was used to exploit surface-enhanced Raman scattering (SERS) to characterize the chemistry of both the pristine and the functionalized GrEdge. The GrEdge electrodes were found to exhibit very high mass transport rates, characteristic of nanoelectrodes. Accordingly, the voltammetric response is found to be dictated by the kinetics of heterogeneous electron transfer (HET), attributed to the nanoscale geometry and a unique diffusional profile at such electrodes. At the GrEdge electrode, high HET rates are observed: at least 14 cm/s for outer-sphere probe, ferrocenemethanol (FcMeOH) with a quasi-Nernstian behavior; and 0.06 cm/s or higher for inner-sphere probe, ferricyanide ([Fe(CN)6]3-) with a kinetically controlled response. Upon selective modification of the edge with gold nanoparticles, the HET is found to be reversible, with a mass-transport-limited Nernstian response for both probes. Furthermore, the fast HET kinetics enables the sensing of the reduced form of nicotinamide adenine dinucleotide (NADH) and flavin adenine dinucleotide (FAD) with low onset potentials and down to low micromolar concentrations. Hence, this thesis improves the understanding of the edges of graphene and their chemistry. It also realizes isolated GrEdge as a new class of nanoelectrode which forms an important basis within the fields of fundamental electrochemistry and analytical sciences.