Régis Y N Gengler
email: r.gengler@rug.nl

Konstantinos Spyrou

Petra Rudolf
email: p.rudolf@rug.nl

A roadmap to high quality chemically prepared graphene

Keywords: graphene, graphene oxide, reduced graphene oxide, functionalized graphene, exfoliated graphene

Graphene was discovered half a decade ago and proved the existence of a two-dimensional system which becomes stable as a result of 3D corrugation. It appeared very quickly that this exceptional material had truly outstanding electronic, mechanical, thermal and optical properties. Consequently a broad range of application appeared, as the graphene science speedily moved forward. Since then, a lot of effort has been devoted not only to the study of graphene but also to its fabrication. Here we review the chemical approaches to graphene production, their advantages as well as their downsides. Our aim is to draw a roadmap of today's most reliable path to high quality graphene via chemical preparation.

In the past few years much interest has focused on graphene, a flat monolayer of carbon atoms tightly packed into a two-dimensional (2D) honeycomb lattice. K.S. Novoselov and A.K.Geim's discovery that micromechanical cleavage of bulk graphite allows to isolate graphene, [START_REF] Novoselov | Electric Field Effect in Atomically Thin Carbon Films[END_REF] has triggered a tremendous amount of scientific interest for this new material, at first mainly for its electronic properties. Graphene was immediately seen as the successor of the current silicon-based technology since the 2D honeycomb carbon structure features semi-metallic behaviour and high carrier motilities, which are ideal for a potential implementation as computing element. Therefore, graphene sheets, if processable, could be used in classical computer, even though examples of use as qubit elements or for spintronics potentially extend its use further then to purely classical transistor-based microprocessors. Alongside with this main research stream, pure graphene was found to exhibit outstanding mechanical (2) thermal (3) and optical properties (4), while graphene derivatives like graphene oxide or other types of functionalized graphene display remarkable catalytic, mechanical, sensing and electronic properties.

Although graphene has so far been explored mainly in fundamental research, creating or depositing high quality graphene for application purposes has been one of the main challenges. Without realizing the future impact of his research, Brodie was the first to produce exfoliated graphite (through oxidation). [START_REF] Brodie | On the Atomic Weight of Graphite[END_REF] The final product was not graphene but graphene oxide (noticed by Brodie because of the increased mass of the reaction product).( 5) More then a century later, a drastically different method, micromechanical cleavage,(1) used to produce isolated graphene sheets, revealed graphene to the physics world . Since then chemists and physicists have used a plethora of (more or less successful) methods, among which chemical vapour deposition (CVD) is one of the most promising [START_REF] Kim | Large-scale pattern growth of graphene films for stretchable transparent electrodes[END_REF] in terms of coverage and layer quality. In fact, while micromechanical cleavage has been very successful in producing samples for fundamental studies, its extremely low yield and lack of control in placement of the sheets, gives it no future in application. Other methods based on the use of SiC as a substrate and as a precursor have excellent potential in the pursuit of the best quality synthetic graphene [START_REF] Van Bommel | LEED and Auger electron observations of the SiC(0001) surface[END_REF] [START_REF] Forbeaux | Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure[END_REF] [START_REF] Berger | Ultrathin Epitaxial Graphite: 2D Electron Gas Properties and a Route toward Graphene-based Nanoelectronics[END_REF] [START_REF] Seyller | Schottky barrier between 6H-SiC and graphite: Implications for metal/SiC contact formation[END_REF] [START_REF] Emtsev | Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide[END_REF]. An alternative road is chemically prepared graphene, which we review in this contribution, focussing on properties and quality as a function of the production method (electronic properties, transparency, ambipolar behaviour, sheet size and related features such as defect/ impurity level and coverage on various substrates).

Chemical preparation processes of graphene sheets use graphite as starting material and delaminate it by various means, namely by chemical functionalization, oxidation, or by intercalation. To give a good representation of today's scientific landscape concerning chemical methods for graphene production we divided the subject in two subcategories, the preponderant graphene oxide (GO) production as a first one and all the other methods (intercalation with N-Methylpyrrolidone (NMP), functionalized surfactants, perfluorinated aromatic molecules, etc) as a second one.

Graphene from Graphene Oxide

The first reports on the production of GO date from 1840 by Schafhaeutl (12) and 1859 with Brodie [START_REF] Brodie | On the Atomic Weight of Graphite[END_REF].

In the latter GO was prepared by treating natural graphite (Ceylon) with an oxidation mixture consisting of potassium chlorate and fuming nitric acid, for reaction times of 3-4 days with the solution kept at a temperature of 60 o C, until no further change was observed. Interestingly, the author, B.C. Brodie, proposed also an alternative method, where the heating was replaced by exposing the oxidation mixture flasks to the sunlight and described it as advantageous because faster. Staudenmaier [START_REF] Staudenmaier | Verfahren zur Darstellung der Graphitsäure[END_REF] proposed a variation to Brodie's method, where the graphite is oxidized in concentrated sulphuric and nitric acids with potassium chlorate. 99 years after Brodie's first experiments, Hummers and Offeman [START_REF] Hummers | Preparation of Graphitic Oxide[END_REF] presented a method where the oxidation of graphite to graphitic oxide is accomplished by treating graphite with water-free mixture of concentrated sulphuric acid, sodium nitrate and potassium permanganate. This process requires less than two hours for completion and rather low temperatures (below 45 o C). In the pursuit of high quality graphene these three methods have been extensively used over past few years. Based on the results obtained with a variety of modern analysis techniques such as NMR [START_REF] Cai | Synthesis and Solid-State NMR Structural Characterization of 13C-Labeled Graphite Oxide[END_REF], XPS [START_REF] Becerril | Evaluation of Solution-Processed Reduced Graphene Oxide Films as Transparent Conductors[END_REF] [START_REF] Mattevi | Evolution of Electrical, Chemical, and Structural Properties of Transparent and Conducting Chemically Derived Graphene Thin Films[END_REF] [START_REF] Yang | Chemical analysis of graphene oxide films after heat and chemical treatments by X-ray photoelectron and Micro-Raman spectroscopy[END_REF], TEM [START_REF] Mkhoyan | Atomic and Electronic Structure of Graphene-Oxide[END_REF] and Raman [START_REF] Gomez-Navarro | Electronic Transport Properties of Individual Chemically Reduced Graphene Oxide Sheets[END_REF] [START_REF] Kudin | Raman Spectra of Graphite Oxide and Functionalized Graphene Sheets[END_REF], the most recent model of GO's structure is the one depicted in schematically in Figure 1, where hydroxyl and epoxide groups grafted randomly (for older structural models of GO and details of derivation of this model see ref. [START_REF] Dreyer | The chemistry of graphene oxide[END_REF]) to the carbon mesh alter the sp 2 -bonded carbon network of pure graphene sheets [START_REF] Park | Chemical methods for the production of graphenes[END_REF]. Owing to the presence of such hydrophilic polar groups the GO presents swelling and intercalation properties very similar to clay. [START_REF] Karaborni | The Swelling of Clays: Molecular Simulations of the Hydration of Montmorillonite[END_REF] In the next four sections, we shall review some of the characteristics of this new material.

Ambipolar behaviour -the quest for high field effect mobility

While an incredibly high number of publications on graphene have appeared in the last 3-4 years, very few actually testify to the truly amazing properties of this material. In particular, most of the recent publications concerning the development of new synthesis methods for graphene, comprising exfoliation, reduction, deposition, etc, omit giving evidence for ambipolar behaviour by recording the Dirac curve, as the conductivity, resistivity or drain-source current vs gate voltage measured in a Field Effect Transistor [FET] device configuration is called. Transmission electron microscopy or atomic force microscopy, often used to demonstrate the graphene character of newly produced material, are very local probes and do not inform on the overall graphene quality. If one wants to compare chemically produced material with high quality graphene created by micromechanical cleavage, the Dirac curve is the best non local probe. Both graphene and graphite display a good conductivity; therefore measuring a high flake conductivity without gate voltage dependence does not prove a bipolar behaviour. To the best of our knowledge the measurements reported by Gómez-Navarro et al. [START_REF] Gomez-Navarro | Electronic Transport Properties of Individual Chemically Reduced Graphene Oxide Sheets[END_REF] were the first to actually show the ambipolar character of the deposited chemically prepared material, i.e. reduced graphene oxide. The room-temperature field-effect mobilities of 2-200 cm 2 /Vs for holes and 0.5-30 cm 2 /Vs for electrons reported for these reduced GO samples are approximately 2 orders of magnitude lower than those of mechanically cleaved graphene (1) and definitely lower then the 200,000 cm 2 V -1 s -1 field effect mobility of free-standing graphene [START_REF] Bolotin | Ultrahigh electron mobility in suspended graphene[END_REF] because of the defective nature of the reduced layers (see section below). The reader should be aware that field effect mobility values depend on channel length and electrode material, therefore the cited numbers (here and below) always refer to the devices employed in the cited works. As we will discuss further on, extracting mobility values from incomplete Dirac curves, like the ones recorded by Gómez-Navarro et al., [START_REF] Gomez-Navarro | Electronic Transport Properties of Individual Chemically Reduced Graphene Oxide Sheets[END_REF] where the metallic regime is not reached, is a non trivial task and gives only approximate values. The data, shown in Figure 2, collected at various temperatures under a low pressure of helium exhibit maximal resistance close to zero gate voltage because of this inert atmosphere. Prolonged exposure to ambient air (>24 h) resulted in a pronounced shift of the maximum toward positive gate voltages, which could be reversed by placing the sample in vacuum. This observed shift was attributed to doping by oxygen and/or water absorption, similarly to what was observed in the past with for carbon nanotubes [START_REF] Martel | Ambipolar Electrical Transport in Semiconducting Single-Wall Carbon Nanotubes[END_REF] and for micromechanically cleaved graphene (1) Similarly Jung et al. [START_REF] Jung | Tunable Electrical Conductivity of Individual Graphene Oxide Sheets Reduced at "Low" Temperatures[END_REF] [START_REF] Jung | Effect of Water Vapor on Electrical Properties of Individual Reduced Graphene Oxide Sheets[END_REF] demonstrated the high sensitivity of the GO to water vapour by recording Dirac curves at various stages of exposure. As shown in figure 2b), when sweeping the gate voltage there is a large hysteresis effect for the maximum of the Dirac curve of the sample exposed to air. In analogy with water adsorbed on carbon nanotubes [START_REF] Kim | Hysteresis Caused by Water Molecules in Carbon Nanotube Field-Effect Transistors[END_REF] this effect has been attributed [START_REF] Jung | Effect of Water Vapor on Electrical Properties of Individual Reduced Graphene Oxide Sheets[END_REF] as presumably due to charge trapping resulting from water (and various microsolvated contaminants) adsorbed both on the graphene oxide sheet and the underlying substrate. Additional treatment in vacuum causes this hysteresis to disappear [START_REF] Jung | Tunable Electrical Conductivity of Individual Graphene Oxide Sheets Reduced at "Low" Temperatures[END_REF] and drastically alters the electrical properties: the FWHM of the Dirac curve, which is directly connected to the mobility (1), becomes smaller, while the maximum decreases and moves to negative gate voltage, revealing a slight p-doping (see fig 2b). Similar observations have been reported for differently functionalized GO films (17) (32) [START_REF] Gengler | Large-Yield Preparation of High-Electronic-Quality Graphene by a Langmuir-Schaefer Approach[END_REF].

Particularly interesting are results on GO layers deposited using a Langmuir Schaefer method and measured at various stages of treatment, starting from a chemical reduction followed by annealing and exposure of the hot sample to ethylene (in UHV) (see fig. 2c) [START_REF] Gengler | Large-Yield Preparation of High-Electronic-Quality Graphene by a Langmuir-Schaefer Approach[END_REF], where it was shown that this last step triggers not only a further reconstruction of the graphene oxide to graphene but also protects the reduced GO sheets from the environment. In fact, subsequent exposure to air barely affected the electronic properties.

In the quest for best quality chemically prepared graphene, a very recent study by Kaiser et al. (31) where the GO flakes were chemically reduced in a hydrogen plasma shows the Dirac curve with the smallest FWHM ever observed for reduced GO (fig 2 b) and with a maximum at zero gate voltage (measurement performed at 220K). Even this best Dirac curve does not display a clear transition to the pure metallic regime where one should observe a flattening of the curve at high positive or negative gate voltage value since the resistance becomes independent of the applied gate voltage. The best criterion for the quality of reduced GO is the charge carrier mobility µ, given by the formula µ=(neR) -1 , where n is the carrier density, e is the electron charge and R is the sheet resistivity. However, one has to keep in mind that this formula is valid only in the metallic regime where the carrier density can be considered uniform and the presence of electron hole puddles does not play a role [START_REF] Martin | Observation of electron-hole puddles in graphene using a scanning single-electron transistor[END_REF] using it in the vicinity of the Dirac neutrality point can be misleading. Due to the very broad resistivity curves that are measured in graphene prepared by reducing GO (see Fig. 1), the applied gate voltages prove not to be enough to reach the metallic regime. To extract the carrier mobility, one can assume that the resistivity versus gate voltage curve resembles the typical resistivity behaviour of micromechanically cleaved graphene in the metallic regime as well, but with a scaling factor for both the gate voltage and the resistivity. As shown in figure 2 c) [START_REF] Gengler | Large-Yield Preparation of High-Electronic-Quality Graphene by a Langmuir-Schaefer Approach[END_REF] the comparison with the measurements on mechanically exfoliated graphene samples and using this scaling yields a carrier mobility for the studied reduced GO in the range of 4 cm 2 V -1 s -1 in the metallic regime, i.e. a factor of 500 lower than in mechanically exfoliated graphene. For this and from the data presented in Figure 2 for other reduced GO, it seems quite clear that the transport properties of reduced GO are limited by structural defects or imperfections. A structural model that captures the essential features of transport through an individual GO sheet at different stages of reduction by thermal annealing was proposed by Mattevi et al [START_REF] Mattevi | Evolution of Electrical, Chemical, and Structural Properties of Transparent and Conducting Chemically Derived Graphene Thin Films[END_REF] and is presented by a series of sketches in figure 3. First (figure 3a) sp 2 clusters are isolated by areas functionalized with oxygen atoms.

As the material is progressively reduced, hopping and tunneling among the clusters increase (Fig. 3b).

Further reduction by removal of oxygen leads to greater connectivity among the original graphitic domains by formation of new smaller sp 2 clusters, but also to an increase in structural defects via evolution of CO and/or CO 2 species (especially from epoxy groups), indicated as pentagons in Figure 3c andd in anhydrous hydrazine prior to deposition were also studied (named HG-A and HG-B in the figure 3 right panel). The devices made with the latter were annealed in N 2 /H 2 (90/10) atmosphere at 150 °C for 1 h prior to measurements and exhibit an even better conductivity. However, one also notes that the 'V' shape of the ambipolar graphene transfer characteristics becomes less pronounced as the reduction time progresses. In micromechanically cleaved graphene, this dip in conductivity is well understood and the minimum corresponds to a conductivity ~4e 2 /h at the charge neutrality point, Vg = V Dirac , where e and h are the electric charge and Planck constant, respectively a way to quantify the depression of the conductivity dip in reduced GO is to establish the so-called on/off ratio, which is the ratio between the current in the 'supposedly metallic' regime and the current at the neutrality point. In the data plotted in the right panel of figure 3 a change in on/off ratio from 10 3 to 2 is observed. A similar behaviour was observed for a three layer GO flake studied by Mattevi et al [START_REF] Mattevi | Evolution of Electrical, Chemical, and Structural Properties of Transparent and Conducting Chemically Derived Graphene Thin Films[END_REF] as shown in the left panel of figure 3: as the flake was heated in vacuum to induce reduction thermally, the conductivity went from 10 -5 to 10 S.cm -1 but again the 'V' shape of the ambipolar graphene transfer characteristics was more pronounced for GO reduced at 150 o C compared to films reduced at 450 o C and the on/off ratio of the film annealed at 150 o C is 10 and decreased to ~2 with further reduction. GO reduced by exposure to hydrazine monohydrate vapour at 80 o C also exhibited the 'V' shape, comparable to devices made with the film annealed at 250 o C. These results demonstrate that while higher temperature or longer exposure time to a reducing agent clearly lead to an increased conductivity of the reduced GO sheets, a mild reduction (well tuned timing of exposure to the reducing agent or annealing to around 150-200 o C) seems advantageous in order to preserve the 'V' shape of the ambipolar graphene transfer characteristics (i.e. a high on/off ratio). Alternatively, improvement can be achieved with the use of ethylene and temperature ranging from 500-600 o C (30). However, from all these measurements by various research groups it seems quite clear that the intrinsic properties of graphene are never completely recovered.

To close this section dedicated to electronic properties of graphene another proof of the versatility and quality of the chemical approach was given by impressive results of X. Li et al [START_REF] Li | Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors[END_REF] who deposited graphene nanoribbons with a width of ~10 nm from a stabilized solution using non covalent polymer functionalization and integrated them in field effect transistors to test their low dimensional (quasi 1D) properties. In detail, these nanoribbons were synthesized from commercial expandable graphite (a graphite intercalated with sulphuric acid and nitric acid and hence very similar to the oxidized graphite even if not named so) through exfoliation by brief (60s) heating to 1000°C in a mixture of 3% hydrogen in argon. The resulting exfoliated graphite was dispersed in a 1,2-dichloroethane solution of poly(mphenylenevinylene-co-2,5-dioctoxy-p-phenylenevinylene) (PmPV) by sonication to form a homogeneous suspension. AFM images of the nanoribbons indicate a height of 1 -1.8 nm which results from not perfect exfoliation yielding a few layers graphite and from the non-covalent functionalization with the polymer. In figure 5 we present the transfer characteristics (Dirac curves) of these nanoribbons (right panel) together with those recorded for devices fabricated with mechanically cleaved graphene which was lithographically patterned into a ribbon structure [START_REF] Han | Energy Band-Gap Engineering of Graphene Nanoribbons[END_REF]. The left part of Figure 5 shows electrical measurements of mechanically cleaved etched graphene [START_REF] Han | Energy Band-Gap Engineering of Graphene Nanoribbons[END_REF] resulting in a quasi onedimensional structure with narrow width and atomically smooth edges, which exhibits the opening of a band gap. For such structure, lateral confinement of charge carriers manifests itself (36) at room temperature with the typical V-shaped conductance vs gate voltage, but showing a minimum conductance of the order of 4e 2 /h(W/L). But, unlike large graphene sheets, nanoribbons with width W<100 nm show a decrease in minimum conductance of more than one order of magnitude at low temperatures. For example, for the nanoribbon with W~24+4 nm [Fig. 5 (d) left panel], a large ''gap'' region appears for 25<Vg < 45 V, where the conductance is below detection limits. This strong temperature dependence differs strongly from to that of the large micromechanically cleaved graphene samples where the minimum conductance changes less than 30% in the temperature range 30 mK-300 K [START_REF] Tan | Temperature dependent electron transport in graphene[END_REF]. The suppression of the usual V shape curve characteristics of the graphene and its replacement by a clear on/off behaviour around the neutrality point is generated by the opening of the bandgap. Similar transfer characteristics were also observed for the chemically produced graphene nanoribbons (figure 5 right panel) for which Li et al. [START_REF] Li | Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors[END_REF] observed that the room-temperature on-off current switching (I on /I off ) induced by the gate voltage increased exponentially with decreasing nanoribbon width. All their measurements gave evidence for p-type unipolar graphene nanoribbon FETs (it is not explained why the behaviour is unipolar) and electrostatic simulations of the gate capacitances gave an estimated hole mobility in the 10 nm wide ribbons of ~100 to 200 cm 2 /V s.

Structural integrity of chemically prepared graphene

As shown in the previous section, reduced graphene oxide (RGO) shows the typical ambipolar behaviour expected for graphene but strongly influenced by the presence of defects/impurities. The structural integrity of the RGO can be investigated by several methods as described hereafter. Low energy electron diffraction and selected area electron diffraction (SAED) have been the methods of choice to reveal local and global high crystallinity of reduced GO and exfoliated samples (see last section for the latter) because the cross section for interaction with electrons is 10 5 higher than with Xrays, electrons can be focussed on very small spots and these techniques do not require access to large scale facilities like synchrotron or neutron sources. Scanning tunneling microscopy (STM) and high resolution transmission electron microscopy (HR-TEM) are probably today's most powerful tools to investigate, locally, the structural integrity of a given material. Therefore, we review hereafter some of the most relevant studies realized on GO and reduced GO. Figure 6 (a) shows the STM image of a GO sheet deposited onto HOPG after dispersion in water with the help of soft sonication [START_REF] Gomez-Navarro | Electronic Transport Properties of Individual Chemically Reduced Graphene Oxide Sheets[END_REF], The hexagonal lattice of graphene is clearly preserved in some parts of the sheet while the regions marked by green contours presumably contain functional groups from the oxidation process and appear disordered. The degree of oxidation/defect level of this type of sheets was calculated from a range of measurements and agrees with spectroscopic data [START_REF] Gomez-Navarro | Electronic Transport Properties of Individual Chemically Reduced Graphene Oxide Sheets[END_REF]. The STM image in figure 6 Surface functionalization of GO can be a means to introduce desired chemical groups for control of the surface properties and for integration into devices. In this context it is not only important to understand the functionalization process itself but also to identify how the introduced groups influence the graphene properties. As a representative example [START_REF] Chua | Deoxidation of graphene oxide nanosheets to extended graphenites by ``unzipping'' elimination[END_REF], STM images GO nanosheets functionalizedwith octadecylamine are displayed in figure 8; the line profile across the sheet edge extracted from these images is also shown. The authors argue that by adding the van der Waals radius of graphene to twice that of octadecylamine since the molecules are grafted on both of sides of the nanosheet, one obtains a total van der Waals radius of 1.0-1.2 nm, in agreement with the observed STM image. Note that-this value also agrees with atomic force microscopy (AFM) data (30) of octadecylamine-functionalized GO.

The series of STM imagines on figure 8 displays the thickness and morphology evolution as a function of the temperature. No changes in morphology/coverage of grafted groups are observed for annealing at to 373 K, while annealing beyond this temperature results in a progressive diminution of the bright features on top of graphene, identified as the grafted groups as well as a decrease in the average thickness. This trend is observed up to a temperature of 973 K where very few bright features remain.

One can conclude from these observations that the octadecylamine functionalities progressively detach from the graphene sheet.

Going large scale

While in the previous section we mainly focused on the properties and quality of the graphene flakes prepared by various methods, in this section we review which approaches can be considered best in terms of "large-scale" production. To this end we compared various preparation methods on the basis of different microscopies or optical images of the produced material. In this comparison we consider first the chemically exfoliated flakes and then how controllably surfaces can be covered with single graphene sheets. Figure 11 shows one of the first AFM images of isolated exfoliated single layer GO, namely a 10µm

2 sheet deposited from a colloidal suspension to a mica substrate and measured to be ~1nm thick. [START_REF] Stankovich | Stable aqueous dispersions of graphitic nanoplatelets via the reduction of exfoliated graphite oxide in the presence of poly(sodium 4-styrenesulfonate)[END_REF] In the bottom right panel of figure 11, one can see the size distribution of the first chemically derivatized graphite oxide exfoliated in organic solvents (also deposited on mica). [START_REF] Stankovich | Synthesis and exfoliation of isocyanate-treated graphene oxide nanoplatelets[END_REF] These two examples of single layers of pure and chemically functionalized GO are among the first where complete exfoliation was achieved and have therefore been chosen to illustrate the starting point of a rapid evolution. In these pioneering results neither the coverage nor the number of deposited layers was controlled (see figure 11 top and bottom left). Few years later, still using the same Hummers and Offeman's method to produce the starting GO, new deposition procedures were developed to achieve larger flake size, high controllability of the packing and last but not least single layer deposition. With increasing surface pressure, the packing increases from image (b), where the inter-flake distance is 1-2 µm to less then 1 µm with some contact between the flakes in image (c), to finally the most dense case in image (d), where the GO flakes are so compressed that they start to overlap at the borders. GO flakes reaching mm sizes for use as thin film electrodes when reduced, were reported by Su et al. [START_REF] Su | Electrical and Spectroscopic Characterizations of Ultra-Large Reduced Graphene Oxide Monolayers[END_REF]. Copyright 2008 American Chemical Society.

A last example of deposition we review here is one where selectivity is achieved through surface modification, namely a study by Wei et al.(50) of GO transferred from a colloidal dispersion to a patterned substrate. As summarized by the figure 13, the authors show that a charged molecular template created using microcontact printing can direct the attachment of a single graphene oxide layer.

The method is based on a few simple steps: first the desired template is printed using microcontact printing; the molecule chosen by the authors was 11-amino-1-undecanethiol. Then the gold substrate printed with the pattern of self-assembled molecules is immersed in a GO solution. The authors show that this later step is critical: time, pH and GO concentration influence drastically the quality of the deposition. Once this attachment is achieved, the adsorbed layer can be processed further -for example with a reduction treatment of GO to obtain graphene. Figure 13 The roadmap to high quality -going oxide?

The scientific landscape has been flooded in the few last years by a huge amount of reports on new methods in terms of production, deposition, reduction or exfoliation of graphene, supposedly one better then the other. In this last chapter we draw up a condensed summary of the most relevant examples and point out what we believe to be the best currently available ways to prepare graphene. Scheme 2, our roadmap to high quality graphene, displays CVD, mechanical cleavage, Si carbide and other methods defined previously but we shall focus our attention on the methods using chemically derived graphene.

Graphite is on top of this scheme and represents today's reality: all or a huge majority of the chemical approaches are top down; in opposition to bottom up approaches so commonly used in material science.

Bottom up approaches for graphene-like 2D polymers are not the scope of this review but we refer the

Scheme 2

The roadmap to high quality graphene.

Anyone getting started in graphene production can choose from many different routes leading to the goal but requiring/involving a series of procedures that will result in the same end material, though of various quality. Starting from graphite, one has two options, going through oxidation or avoiding it. The easiness and relative high yield of the graphite oxide approach lead a lot of research group to follow that path. The starting point is in this first case the oxidation of graphite (any type) by means of potassium chlorate and fuming nitric acid treatment(s) as described by Brodie in 1859 [START_REF] Brodie | On the Atomic Weight of Graphite[END_REF] or, as proposed by Staudenmaier (13), by use of sulfuric and nitric acid combined with potassium chlorate or still, as suggested by Hummers and Offeman ( 14), using concentrated sulphuric acid, sodium nitrate and potassium permanganate as explained in the first section of this review. This last method is the most commonly used for the synthesis of graphite oxide and accepted as the most efficient. To the best of our knowledge, Shen et al. [START_REF] Shen | Fast and Facile Preparation of Graphene Oxide and Reduced Graphene Oxide Nanoplatelets[END_REF] is the only report of a recent alternative method where benzoyl peroxide is reacted with graphite at moderate temperature and under sonication to produce exfoliated graphene oxide sheets. Depending on the application or fundamental study graphene/graphene oxide is destined for, a number of processing steps is then needed in order to achieve the desired properties, i.e. in many cases to recover a decent conductivity-while still keeping transparency. Other studies report on the creation of composite material, which either consists in stacked pure GO, GO mixed with a polymer alone or combined with other layered material like clay.(54)(55) Some of these composite materials do not require any reduction treatment and use graphene oxide as it is, the GO paper discovered by Ruoff et al. ( 56)(57) being a famous example of such composite film. On the other hand, the overwhelming majority of the literature of the past few years concentrates on the reconversion of GO to graphene and its deposition for various purposes. Scheme 2 lists the most relevant reduction methods. To the best of our knowledge, the flash photoreduction discovered by Cote et al, [START_REF] Cote | Flash Reduction and Patterning of Graphite Oxide and Its Polymer Composite[END_REF] is the fastest reduction process ever (10 -4 s) and involves in terms of equipment only a conventional flash of a digital camera. The reduction occurs because the very large photon flux induces a thermal deoxygenation. Unfortunately, little evidence supports the graphene-like behaviour of the product. Nevertheless we believe this approach to be promising. Today's most efficient procedure for the reduction of GO seems to be the H plasma reduction method proposed by Kern et al [START_REF] Kaiser | Electrical Conduction Mechanism in Chemically Derived Graphene Monolayers[END_REF], even though it requires more time (5-10s) and more equipment is needed. This statement is supported by the outstanding Dirac curve displayed in figure 1b. [START_REF] Kaiser | Electrical Conduction Mechanism in Chemically Derived Graphene Monolayers[END_REF]. The optimized conditions were found to be 5-10s of exposure to a plasma operating at ). The most suitable temperature for annealing is still undefined: some groups report on the damage of the ambipolar characteristic after annealing above ~200 o C (17), others report on an improved ambipolar behaviour for temperatures up to 500-600 o C (accompanied by ethylene exposure) [START_REF] Gengler | Large-Yield Preparation of High-Electronic-Quality Graphene by a Langmuir-Schaefer Approach[END_REF]. Two additional methods leading to reduced graphene oxide are listed in the lower part of the scheme 2. Firstly, solvothermal reduction (including hydrothermal reduction) which proceeds in a solvent (water when hydrothermal) while applying mild annealing. The trick is to keep single layers suspended in the solution after reduction. Zhou et al [START_REF] Zhou | Hydrothermal Dehydration for the "Green" Reduction of Exfoliated Graphene Oxide to Graphene and Demonstration of Tunable Optical Limiting Properties[END_REF] showed such an example of hydrothermal reduction and proved using Raman spectroscopy, X-ray photoelectron spectroscopy

Alternative routes

While so far we concentrated on the ambipolar behaviour, structural properties and the coverage analysis concerning reduced graphene oxide, this section is dedicated to the chemical preparation of graphene without oxidation (listed in the right part of our roadmap to graphene [scheme 2]). A very effective method for the exfoliation of graphite with the help of organic solvents such as N-Methylpyrrolidone (NMP), N,N-Dimethylacetamide (DMA), g-butyrolactone (GBL) and 1,3-dimethyl-2-imidazolidinone (DMEU) was proposed by Hernandez et al.(77). This exfoliation takes place because the energy required to exfoliate graphene matches the solvent-graphene interaction energy and extra energy provided through sonication activates the process. It works for solvents which have the an interaction energy with graphene that is equal with graphene-graphene interaction energy (1) (78) [START_REF] Novoselov | Twodimensional atomic crystals[END_REF], resulting in a minimal energy cost to overcome the Van Der Waals forces between the graphene sheets.

High quality graphene is produced in this way but the very low concentration of single layer graphene in the suspension (0.01 mg ml -1 ) ( 77) is a drawback. Some of the best TEM images using the solvent exfoliation route are displayed in figure 14 where one can distinguish monolayer graphene with sizes in the range of 0.5-1 µm. Among the proposed solvents NMP seems to yield the best results since one can clearly see graphene single layers in the corresponding TEM images. Selected area electron diffraction of the exfoliated material is in figure 15, and shows a hexagonal pattern illustrative of the hexagonal carbon honeycomb arrangement of graphite. The existence of monolayer and bilayer graphene arrangements is as well demonstrated by {2110} spots appearing more intense relative to the {1100}.

An alternative route, still NMP based but avoiding the sonication step to afford bigger flakes, was proposed by Vallés et al. [START_REF] Vallés | Solutions of Negatively Charged Graphene Sheets and Ribbons[END_REF]. Inspired by carbon nanotube processing technology (81), they showed that the exposure of graphite to an ternary potassium salt K(THF) x C 24 (THF) tetrahydrofurane, x ) 1-

3) in NMP leads to stable exfoliation of graphite. As depicted in scheme 3, an alkali metal graphite intercalation compound is formed, which thanks to its charge, helps the exfoliation of graphite in NMP and leads to a stable suspension of negatively charge graphene in NMP mixed with the alkaline salt. for the exfoliation of graphite with the help of solvents with a surface energy that matches the graphenegraphene interaction energy (1) (78) [START_REF] Novoselov | Twodimensional atomic crystals[END_REF]. Some of the solvents of this approach belong to a peculiar ignored in this histogram) from which one deduces that ~43% of flakes have less then 5 layers and about ~3% of the flakes were monolayer graphene. While this value is considerably smaller than that observed for graphene/solvent dispersions, working in aqueous systems has its own advantages. In general, the majority of these few-layer flakes had lateral dimensions of ~1 µm. Though these results do not compete with the top quality of the reduced graphene oxide, we believe that today's research is at the beginning and much more can be expected from such an approach. Characterization of the electrical properties would be of great help to learn more about the true quality of the prepared material and it is obvious that efforts are still needed to conserve larger flake sizes in this kind of approach.

Conclusion

We reviewed the chemical approaches to graphene production, their advantages as well as their downsides. Doing so, we have drawn a roadmap of today's most reliable path to high quality graphene via chemical preparation, hopefully helping researcher to find their path among this huge diversity of approaches. This roadmap also reveals the weak points of today's knowledge regarding chemically prepared graphene and points out directions for further research effort. For additional reading, we refer the reader to a review focused on graphene oxide by Compton and Nguyen (93), a general overview by Allen et al. [START_REF] Allen | Honeycomb Carbon: A Review of Graphene[END_REF] and one on chemistry and functionalization of graphene by Loh et al. [START_REF] Loh | The chemistry of graphene[END_REF].

Figure 1 .

 1 Figure 1. Schematic representation of the structure of Graphene Oxide sheets (GO); grafted hydroxyl and epoxide groups disrupt the sp 2 -bonded carbon mesh of pure graphene. Scheme taken from S. Park

Figure 2 .

 2 Figure 2. Resistance as a function of back gate voltage of various graphene oxide and reduced graphene

  . Thus, transport in the initial stages of reduction occurs via tunneling or hopping among the sp 2 clusters. In the following section we shall review what is known about the nature of defects studied by Scanning Tunneling Microscopy (STM) and High-Resolution Transmission Electron Microscopy (HR-TEM) but before we would like to focus on how the electronic properties change as a function of the reduction treatment.

Figure 3 .

 3 Figure 3. Structural model of graphene oxide at different stages of reduction by thermal annealing taken

Figure 4 .

 4 Figure 4.: Conductivity (left panel graph reprinted with permission from C. Mattevi et al. (17)

Figure 5

 5 Figure 5 left panel (a)-(c) Conductance as a function of gate voltage measured at different

  (b) shows similar features for different GO, called functionalized graphene in the original report, prepared trough rapid heating of GO in solution (21) and subsequent deposition on HOPG and is also clearly distinguishable from pristine graphene (shown in the insert of fig 6 (b). Even though figure 6(b) does not reveal large regions with a honeycomb lattice as seen in fig. 6 (a), a Fourier transform of the image (see insert fig 6b) shows a clear hexagonal structure, signature of a graphitic backbone. The observed separation of pristine graphene and disordered regions in these GO sheets agrees with the theoretical prediction that these functional groups should arrange in islands and rows (38). GO shown in figure 6 appears quite rough with a peak to peak distance of about 1nm, most likely due to the presence of random -O and -OH or defects. However, a model for the possible bonding sites of -O and -OH on a graphene layer (39) reproduced in figure 7 (right panel), shows a possible arrangement where top and bottom -O and -OH groups are attached to the graphene sheet in a periodic fashion.

Figure 6 .

 6 Figure 6. (a) Scanning tunneling microscopy image of a graphene oxide monolayer on HOPG. Oxidized

Figure 7 .

 7 Figure 7. (left panel) Scanning tunneling microscopy image Reprinted from D. Pandey et al (40) with

Figure 8 .(

 8 Figure 8. (left) Scanning tunneling microscopy image from L. Chua et al. (41) of Octadecylamine

Figure 9 .

 9 Figure 9. Transmission electron micrograph of water soluble functionalized GO, Reprinted with

Figure 9 Figure 10 .

 910 Figure 10. Transmission electron micrographs of benzoyl peroxide oxidized Graphene Oxide. Scale bar

Figure 11 .

 11 Figure 11. (top) Non-contact mode AFM image of isolated exfoliated single layer graphene oxide; from

Figure 12 .( 47 )

 1247 Figure 12. (Top) SEM images of the monolayers of highly covered sample. Scale bars represent 100

Figure 13 .

 13 Figure 13. (Left) A scheme of the templating process that shows the formation of the amino-terminated

  documents the success of this method, since in the AFM image on the left (labelled c) selective adsorption can be clearly distinguished. The images on the right of figure 13 show instead the influence of the dipping time on the coverage of the patterned surface, in fact, a dipping time of 5s (fig 13 a) produces a coverage of ~50% while immersion for 17h (fig 13d) covered the patterned surface up to ~90%. A similar templated deposition was reported by Li et al. (51) and in principle one can envision other methods for producing the template such as dip pen lithography.[START_REF] Wang | Controlling the shape, orientation, and linkage of carbon nanotube features with nano affinity templates[END_REF]

~10 - 4 sEda

 4 reader to Junji Sakamoto et al.(53) Cote et al. 30W at 0.8mbar for 5 to 10 s Kern et al Ruoff;100 o C for 24h of KNO 3 0 to -1V Hernandez et al Nat Nano 2008 Bourlinos et al. Small 2009 Lotya et al. JACS 2009 Sakamoto et al. Angew. Chem. 2009

0. 8

 8 mbar of H and 30W of power. Ranking next in terms of proven efficiency come purely thermal treatments or heat treatments in vacuum or controlled atmosphere preceded by Hydrazine or NaBH 4 reduction process (for further reading, we recommend recent theoretical works (59) (60) which present possible models for the hydrazine induced deoxygenation ). Once more, the reduction effectiveness is clearly proven by the Dirac curves of devices prepared by various groups ((61) (62) (17) (31) (27) (30) (63) (64) (65) see as well fig 1

  Fig 14h displays histogram of the number of layers per sheet for the exfoliation of graphite in NMP which is peaked between 1 and 4 layers.

Figure 14 .

 14 Figure 14. Electron microscopy of graphite and graphene. (a), SEM image of sieved, pristine graphite

Figure 15 .

 15 Figure 15. Evidence of monolayer graphene from TEM. (a, b), High-resolution TEM images of

Scheme 3

 3 Scheme 3 Representation of the potassium salt K(THF) x C 24 (THF ) tetrahydrofurane, x ) 1-3) driven exfoliation of graphite in NMP. Scheme reprinted with permission from C.Vallés et al. (80). Copyright

Figure 16 .

 16 Figure 16. Ambient STM image of a filed-down graphite deposit drop casted from solution on a HOPG

Figure 17 .

 17 Figure 17. Tapping mode AFM image of a deposit performed by dip-coating of a graphene solution

  class of perfluorinated aromatic molecules[START_REF] Züchner | The Pentafluoropyridine Cation[END_REF] [START_REF] Langer | Electron capture by pentafluoronitrobenzene and pentafluorobenzonitrile[END_REF] and include hexafluorobenzene (C 6 F 6 ), octafluorotoluene (C 6 F 5 CF 3 ), pentafluorobenzonitrile (C 6 F 5 CN), and pentafluoropyridine (C 5 F 5 N).Aside from the aromatic compounds Boulinos et al. also found that some non-aromatic solvents tested successfully for dispersing graphite, namely ethyl acetate, vinyl acetate, methyl chloroacetate, 2methoxyethyl ether, acetylacetone, and N,N,N0,N0-tetramethylmethylenediamine, which all exhibited remarkable colloidal stabilities and concentrations of 0.2-0.3 mg ml -1 . Examples of the dispersions and TEM images are presented inFig 18. Uniform dark dispersions testify to the absence of aggregation, while single to 2-3 layer thick graphene with flake size is in the order of few micrometers were observed by TEM.

Figure 18 .

 18 Figure 18. (Top) Colloidal dispersions obtained after liquid-phase exfoliation of graphite using the

Figure 19 .

 19 Figure 19. High-resolution TEM images of surfactant exfoliated graphene flakes. (a) A HRTEM image

Figure 20 .

 20 Figure 20. Histograms of the number of layers per flake for dispersions from original sieved graphite

  (XPS) and AFM that the material was substantially reduced but still single or bilayer. Other examples of solvothermal reduction procedures can be found in the literature (67) (68); Wang et al[START_REF] Wang | Solvothermal Reduction of Chemically Exfoliated Graphene Sheets[END_REF] reported We finish our review of GO deoxygenation by two examples of catalytic reduction. The first, reported by Williams et al.[START_REF] Williams | TiO2-Graphene Nanocomposites. UV-Assisted Photocatalytic Reduction of Graphene Oxide[END_REF], describes how graphene oxide suspended in ethanol undergoes reduction as it accepts electrons from UV-irradiated TiO 2 suspensions. The second[START_REF] Li | One-step synthesis of graphene/SnO2 nanocomposites and its application in electrochemical supercapacitors[END_REF] involves the use of SnCl 2 in HCL and Urea, the reaction that creates SnO 2 nanoparticules. The reduced nature of the end product was established by XPS in the SnO 2 case and qualitatively proven by a colour change in the TiO 2 suspensions. The effect of such a nanoparticule overlayer on the electrical properties is unfortunately not documented.

	Dirac curves of a solvothermally reduced material, whereas Fan et al (70) prepared a graphene
	suspension through deoxygenation by simply heating an exfoliated-GO suspension under strongly
	alkaline conditions at moderate temperatures (50-90 o C). Based on these results hydro/solvothermal
	reduction can be considered as a good candidate for reduced GO production if the single layer character
	can be preserved, for example by depositing the layer beforehand.
	An alternative approach reported by Liu et al (71), Ganganahalli et al.(72), Zhou et al. (73) and Wang
	et al. (74) (most probably without knowing of each other's work) is the reduction of graphene oxide
	using electrochemistry. While voltametry seem to prove an irreversible transformation of the oxidized
	material, preventing the single layers from aggregating is once more a central issue. Ganganahalli et
	al.(72) is the only group actually showing that their electrochemical reduced GO consists of single
	layers. Though electrochemical methods seem promising, a lot of effort is still needed to develop
	procedures for a more complete reduction while conserving monolayer characteristics if one actually
	wants to produce graphene and not very thin graphite!


F Sigeneger

K Rackow

D Uhrlandt

J Ehlbeck

G Lieder

Barium transport in the hot spot region of fluorescent lamps

Keywords: numbers: 51.50.+v, 52.80.Hc, 52.80.-s, 52.65.-y, 52.70.Kz

The transport of barium atoms and ions in the vicinity of the hot spot in fluorescent lamps operating at 25 kHz is investigated by a combined experimental and theoretical approach. By laserinduced fluorescence, the particle densities of barium atoms and ions were measured timeresolved at different distances from the spot center. In addition, the time-dependent cathode fall voltage was measured using an improved band method. The model combines a kinetic part for the electrons with a fluid part for the barium atoms and ions. Both parts are spatially resolved in spherically symmetric geometry. The space-dependent electron Boltzmann equation yields the electron density and the ionization rate coefficient of barium as functions of the cathode fall voltage. These results are used to solve the time-dependent particle balance equations of barium atoms and ions which include the ionization of barium as gain and loss terms, respectively. Good agreement between the measured and calculated particle densities of barium atoms is obtained. A sensitive dependence of the ionization frequency and of the barium particle densities on the cathode fall voltage was found.

Introduction

Fluorescent lamps play an important role for the energy saving in the light generation. The thermionic electrodes of these lamps are very crucial for an effective lamp operation. These electrodes are double or triple coiled and covered with emitter material which lowers the work function. The emitter material is typically composed of mixtures of alkaline earth oxides with barium as the commonly most important component. As a consequence, currents of several hundred mA can be delivered by the electrode which works normally in spot mode with temperatures between 1000 and 1500 K in the spot.

Unfortunately, the emitter material, mainly barium, is transported from the electrode into the plasma volume and finally to the lamp wall or to other surfaces surrounding the electrode. The dominant loss process is the evaporation of barium because of the high temperature at the spot. Sputtering of barium due to the ion bombardment requires cathode fall voltages larger than the threshold energy which is rarely reached during the normal lamp operation.

The loss of emitter material limits the lifetime of fluorescent lamps if these lamps are started with preheated coils and thus the tungsten sputtering as occurring in instant-start lamps is avoided. Therefore, the determination of this loss, especially of barium, is of main interest for the estimation of the lifetime of a lamp. Consequently, a detailed knowledge of the plasma in the cathode region is required.

Several investigations of the cathode region of fluorescent lamps have already been reported in the literature [1][START_REF] Hilbig | Proc. 5th Int. Symp. on the Science and Technology of Light Sources[END_REF][START_REF] Hadrath | [END_REF]. The dynamics of the plasma-electrode coupling in an argon-mercury discharge was experimentally and theoretically investigated in [4]. The model consists of a time-dependent, one-dimensional self-consistent description of the negative glow suplemented by a 0d sheath model at the cathode side and a 0d model for the positive column. The transition from the localized spot to the negative glow covering the full tube is approximately taken into account by the corresponding ratio of surface and cross sectional areas.

A two-dimensional model of a helium-xenon dc discharge have been presented in [5]. The model spacially resolves the sheath in front of the spot and describes the transition of the discharge from the spot through the negative glow towards the anode.

The current paper describes an somewhat alternative approach which is more concentrated on the barium transport. For this purpose, experimental and theoretical investigations at a fluorescent model lamp driven at 25 kHz have been performed. The densities of Ba atoms and ions at different distances from the spot center have been measured time-resolved by laser induced fluorescence (LIF). Furthermore, the time-dependent cathode fall voltage was approximately determined using an improved band method. A model is applied to deduce the net flux of barium from the cathode surface. The model comprises the solution of the time-dependent particle balance equations of Ba and Ba + which include the Ba ionization as gain and loss terms, respectively. The ionization rate coefficient of Ba and the electron density are determined by solving the space-dependent electron Boltzmann equation using the measured cathode fall voltage and the discharge current as input. As a result, the time-dependent particle flux of barium atoms and ions is obtained by the model.

The paper is organized as follows. The experimantal investigations are reported in section 2. In section 3 the model including the kinetic and the fluid part are described and the results are presented in section 4. To generate a lamp current comparable to commercial ballasts, a current controlled power supply working at 25 kHz is used. The lamp voltage and current are measured by a high voltage differential probe and a high frequency current probe, respectively.

Experiments

Model lamp

LIF-measurements

The density of barium atoms and ions in ground state is measured by laser induced fluorescence in a short distance from the spot. This distance is varied in steps of 0.5 mm in axial direction of the tube. The laser radiation at 350.1 nm excites the barium atom from the ground state 6s 2 1 S 0 to the upper level 5d6p 1 P 1 . This level decays spontaneously via different channels as indicated in Fig. 2. The detected fluorescent radiation at 582.6 nm from the transition to the 6s5d 1 D 2 level is used to determine the population density of the ground state. In case of barium ions the excitation from ground state 6s 2 S 1/2 to 6p 2 P 3/2 (455.4 nm) and the spontaneous transition to the 5d 2 D 5/2 level is used. The atomic data were taken from [6].

The setup of the LIF measurement is shown in Fig. 3. For the generation of the laser beam, a Nd:YAG pumped dye laser operating at 10 Hz is used. In case of barium atoms, the dye laser is pumped at 532 nm. It provides radiation at 700.2 nm which is frequency doubled by a KDP crystal to the desired 350.1 nm. In case of barium ions, the dye laser is pumped at 355 nm and provides the desired 455.4 nm directly. The output beam is expanded by a Galilean telescope. For defining the beam diameter, the beam is directed through a 1 mm aperture which covers only a small region of the original beam. A spatial filter is used to restore the resulting degraded beam profile to a nearly Gaussian shape. It consist of two lenses (f = 100 mm each) in a distance of 200 mm with a 20 µm pinhole located at the common focal point. The resulting beam is directed perpendicular to the glass surface through the lamp directly in front of the coil as illustrated in Fig. 1. Its intensity is measured by a photodiode. The lamp is movable in three dimensions by stepping motors which allows to adjust the distance from the hot spot to the beam. The position of the coil is determined by moving it through the laser beam and observing the shadowing. As the beam has a diameter of 1 mm, the minimal distance from coil to beam is approximately 0.5 mm. The fluorescent radiation at 582.6 nm is observed perpendicular to the beam. The region of interest is imaged (1:3) to the entrance slit of a 0.5 m monochromator (Acton Research SpectraPRO-500I) with a 1800 grooves-per-millimeter grating. To attenuate the scattered laser light, a long pass filter is placed in front of the entrance slit. The fluorescent radiation is measured using a photomultiplier and averaged over an observation volume of about 0.7x0.7x1.0 mm 3 . In general, the fluorescent signal is averaged over 600 laser pulses. The Rayleigh calibration technique was applied to determine absolute barium atom densities. This commonly used method is described in text books. Hadrath [7] applied this method to measure absolute tungsten atom densities. Because of the strong dependence of the Rayleigh scattering intensity on the wavelength, this calibration method could not successfully be applied for the barium ion measurements.

Cathode fall measurements

For determination of the cathode fall voltage, the so-called band technique is used [8,9]. As shown schematically in Fig. 4, a copper band is wounded around the outside of the glass tube in the electrode region and the voltage between band and electrode is measured. This voltage represents the capacitively coupled wall potential and includes the cathode fall, the voltage drop in the plasma from axis to wall and the wall sheath. To deduce the cathode fall voltage from this measurement some considerations are required. Garner has investigated [8] the relation between the various voltage drops inside the discharge and the voltage measured at the band for conditions which are similar to those considered here. It was shown that the band voltage can be used as a measure for the cathode fall voltage if an appropriate correction factor is taken into account. The measuring circuit consists of the band capacity with respect to the inner wall and a resistor and capacity inside the probe. This circuit represents a high pass filter with a characteristic frequency response which has to be considered for the used frequency. At 25 kHz a correction factor of 1.2 is applied to the measured voltage in correspondence to comparisons with internal probe measurements [8]. The high pass characteristic also eliminates the DC part of the potential. Therefore, we assume a cathode fall equal to zero at the beginning of the cathode phase (lamp voltage is equal to zero) by adding a DC voltage. Figure 5 shows the measured band voltage for two different lamp currents as well as the used scaled and shifted voltage. 3. Barium transport model

Electron kinetics

The main impact of the plasma on the barium transport is the ionization of barium atoms. Therefore, the ionization frequency ν io Ba must be determined in dependence on the cathode fall voltage U CF . For this purpose, the space-dependent electron Boltzmann equation

v • ∇ r f - e 0 m E • ∇ v f = C el + k,l C ex k,l + k C io k (1)
is solved which includes the electric field E and the action of elastic, exciting and ionizing collisions of the electrons with the gas atoms in the related collision integrals

C el , C ex k,l and C io k .
Here, e 0 and m denote the electron charge and mass. The threshold energies of the inelastic processes which have been included are listed in Table 1. The excitation cross section for argon were taken from Ref. [10] and the ionization cross section for argon as well as all cross sections for krypton from Ref. [START_REF] Hayashi | Plasma Material Science Handbook Appendix[END_REF]. The cross section set for mercury is the same as that used in Ref. [START_REF] Sigeneger | [END_REF]. For barium, the ionization cross section was taken from Ref. [13]. Visual observations of the spot as shown in Fig. 1b suggest that the plasma is largely spherically symmetric within the near vicinity of the spot. Therefore, a one-dimensional spherically symmetric approach [14] is chosen to solve eqn. (1). Taking into account the radially directed electric field E = E r e r , the electron velocity distribution function f (v, r) can be expanded with respect to the ratio v r /v ≡ v r /|v| in Legendre polynomials. In the lowest approximation order, the two-term approximation, the velocity distribution is represented by

Ar Kr Hg Ba U in [eV] level U in [eV] level U in [eV] level U in [
f (u, v r v , r) = 1 2π m 2 3 2 f 0 (u, r) + f r (u, r) v r v (2)
where f 0 (u, r) and f r (u, r) are the isotropic and anisotropic parts of the velocity distribution function and u = mv 2 /2 denotes the electron kinetic energy. As detailed in [14], the electron Boltzmann equation is transformed using (2) into a partial differential equation with shifted energy arguments which is solved as an initial boundary value problem from higher to lower energies. The spatial solution region spans from the approximated radius of the spot r c up to the radius r a of an assumed outer virtual spherical anode.

Because the cathode fall region in front of a thermionic cathode is very thin the spatial profile of the electric field within this region is not resolved in the kinetic treatment. Instead, the action of the cathode fall voltage U CF is taken into account in the boundary condition. The Gaussian-like function fr

(u) = c u exp[-( u -e 0 U CF ∆u ) 2 ] ( 3
)
is prescribed to the anisotropic distribution part f r (u, r c ) at the cathode position r c . This function models the influx of electrons into the plasma which have been released from the cathode due to thermionic emission and accelerated in the cathode fall up to the energy e 0 U CF with an energetic half-width of ∆u. The factor c is used to normalize the solution f (u, r) in the whole solution region. It is determined as detailed below. In the plasma volume a very low electric field strength E 0 is assumed.

From the solution of the Boltzmann equation the electron density n e and the ionization rate coefficient k io Ba are calculated according to

n (0) e (r) = ∞ 0 u 1/2 f (u, r)du, (4)
k io Ba (r) = 1 n (0) e (r) 2 m e ∞ 0 uQ io Ba (u)f 0 (u)du (5)
Similarly, the rate coefficients k io Ar , k io Kr and k io Hg for the ionization of argon, krypton and mercury atoms are calculated. To get the normalization factor c, additionally the current through the shell i e (r) = 4πe 0 r 2 φ r (r) is calculated where the particle flux φ r depends on the anisotropic distribution part according to

φ r (r) = 1 3 2 m ∞ 0 f r (u, r)udu. (6)
The electron particle balance equation reads 1

r 2 d dr (r 2 φ(r)) = S e (r) = n (0) e (r) α N α (r)k io α (r), (7)
At larger distances from the spot the source S e becomes very small and the current i e through the shell is nearly independent of r. At these positions, the contribution of the ion current can be neglected. Therefore, the relation i e (r a ) = i

L is used to determine the factor c in (3) and to the results on a fixed discharge current i (0) L . The collision integrals in (1) include the particle densities of the various gas atoms in the discharge. Due to the large temperature of the cathode in the spot also the increased gas temperature and the resultant decrease of the gas density must be taken into account. This effect is approximately included by solving the simplified heat balance equation ∆T = 0 in spherical symmetry which yields the result T = c 1 r + c 2 . The temperature T S at the spot and T ∞ far away from the spot are used to determine the coefficients c 1 and c 2 .

Some results derived from the solution of the electron Boltzmann equation are shown in Figs. 67. These results have been obtained for a discharge in a mixture of α Ar =90% argon and α Kr =10% krypton at a pressure p of 210 Pa. The Hg vapor pressure is determined according to ln p HG (T HG ) = 30.804 -0.8254 ln T HG -7564/T HG with p HG in mTorr [15]. A cold spot temperature of T HG = 300K was used. The spot radius r c and the field in the negative glow E 0 are assumed to be 0.5 mm and 0.2 V/cm, respectively. A radius r a =2 cm was taken for the spherical virtual anode. The energetic half-width of the influx profile (3) was assumed to be 0.2 eV.

In Fig. 6 the isotropic part of the electron velocity distribution function is shown as function of the kinetic energy u and the radius r for a cathode fall voltage U CF of 10 and 20 V. The group of primary electrons has a mean energy which is related to the cathode fall voltage. Further groups of electrons are generated due to inelastic collisions with the gas atoms. The energy gaps between the groups correspond to the various threshold energies listed in Table 1. As shown, a very complex distribution function is generated due to the superimposed action of inelastic collisions. Similar electron distribution functions, but with somewhat less pronounced structures have been observed by Monte Carlo simulations [16] and by probe measurements [17] in the cathode region of glow discharges. Furthermore, the ionization cross section of barium Q io Ba is included in Fig. 6. The integral over both quantities shown in Fig. 6 according to (5) yields the ionization rate coefficient k io Ba as function of the radius r and the cathode fall voltage U CF . The result is shown in Fig. 7 together with the electron density. Due to the complex structure of the distribution function a non-monotonous dependence of both quantities on U CF was obtained. Especially, a pronounced minimum around U CF = 15 V can be observed in the ionization rate coefficient which is important for the modelling of the barium transport.

Ba transport model

The transport of the barium atoms and ions is investigated by solving the particle balance equations

∂ ∂t n a + ∇ • Γ a = -ν io Ba (r)n a (9)
∂ ∂t n i + ∇ • Γ i = ν io Ba (r)n a (10)
which include the time-and space-dependent densities n a and n i of barium atoms and ions. The atom flux Γ a = -D Ba ∇n a and the ion flux -11.

Γ i = µ i n i E -D Ba
-10.

-9.

-8.

-7.

-6. coefficient D Ba , the mobility µ i and the electric field strength E. Similar to the kinetic equation, the balance equations ( 9)-( 10) are solved in one dimension assuming spherical symmetry. The standard diffusion coefficients D Ba,Ar 0 and D Ba,Kr 0 of barium ground state atoms in argon and krypton were experimentally determined in [18]. The diffusion coefficient D Ba 0 of barium atoms in the gas mixture of argon and krypton was calculated using Blank's law

D Ba 0 = α Ar D Ba,Ar 0 + α Kr D Ba,Kr 0 -1
which results in D Ba 0 = 0.113 cm 2 /s. This standard diffusion coefficient is related to the standard temperature T 0 = 273 K and pressure p 0 =760 Torr or the related density N 0 = 2.687 • 10 19 cm -3 . The actual diffusion coefficient D Ba (r) for barium near the spot is determined by the relation [18]

D Ba (r) = D Ba 0 p 0 p T (r) T 0 3/2
where the dependence of the gas temperature T on the distance r from the spot center is taken into account. For the mobility µ i of barium ions a field dependent standard mobility µ i,0 (|E|) has been taken from [19]. The space-dependent temperature is considered by the relation

µ i (r) = µ 0 (| E|)N 0 /N (r) with N (r) = p/(k B T (r)).
The impact of the plasma on the barium transport is mainly caused by the ionization of barium atoms with the ionization frequency ν io Ba . This time-and space-dependent quantity is deduced in the cathode phase according to

ν io Ba (t, r) = k io Ba (U CF (t), r)n e (t, r) (11)
by using the measured temporal evolution of the cathode fall voltage U CF (t). The time-and spacedependent electron density is determined by the relation n e (t, r) = n

(0) e (U CF (t), r)i L (t)/i (0)
L using the measured discharge current i L (t) and the electron density n (0) e (U CF , r) which is calculated in the electron kinetic treatment and normalized on the fixed discharge current i (0) L . In the anode phase the barium ionization frequency is assumed to be negligible. This approach corresponds to the quasi-stationary solution of the electron Boltzmann equation and neglects the delayed response of the electron density as observed e.g. by Garner [4]. Nevertheless, the ionization frequency ν io Ba is rapidly droped down during the transition from the cathode to the anode phase due to the diminishing cathode fall voltage.

Appropriate boundary conditions have to be chosen at the spot (r = r c ) and the virtual anode (r = r a ). At the spot a constant flux Γ c a is prescribed to the flux of barium atoms. This corresponds to the assumption of a time independent temperature profile of the electrode surface in the spot. The determination of the barium atom flux generally requires a detailed description of the Ba diffusion in the emitter and the evaporation process. To avoid possible errors due to the insufficience of existing models and limited knowledge of corresponding data, the value of Γ c a is used as a scaling factor. Including the measured densities of Ba atoms in absolute units, the whole solution is scaled to reproduce on average the measured atom densities. This procedure allows finally to determine the value of the evaporation flux independent of the treatment of the evaporation process itself.

For the barium ions the boundary condition

Γ i •n = 1 -R 1 + R µ i E S •nn i + v th i n i /2 (12)
was used [20] where n denotes the outward directed normal vector, R ≈ 0.1 the reflection coefficient and v th i = 8k B T πm i the ion thermal velocity. The surface electric field E S at the cathode surface was approximated using a sheath model [4] according to

E 2 S (t) = 2 k B T 0 e e 0 λ D (t) 2 1 + 2η sh (t) + e -η sh (t) -2 (13)
with the Debye length λ D (t) = ε 0 k B T 0 e /(n e (t, 0)e 2 0 ) and η sh (t) = e 0 U CF (t)/(k B T 0 e ). The electron temperature T 0 e at the plasma/sheath boundary was approximated by a value of one eV. To determine the drift flux of the barium ions the electric field E in the plasma volume is required. This field could be determined by a self-consistent model including all ions and the Poisson equation. However, such a model is not the subject of the current investigation. Therefore, the constant value E = E 0 e r in accordance with the kinetic part is used. The influence of this parameter on the ion density and flux is discussed below.

The radius r a of the virtual anode was chosen much larger than the region around the spot where remarkable barium densities can be detected. Therefore, simple boundary conditions n a (r a ) = 0 and n i (r a ) = 0 are used there because the desired results near the spot are not sensitive to these conditions.

Results

Using the corresponding time-dependent electrode fall voltage from the measurements, electron kinetic and transport equations are solved to determine the Ba atom and ion densities. The solution is scaled to meet the atom densities measured by calibrated LIF on average. The time-dependent calculated courses of the Ba atom densities at different distances from the spot are compared in Fig. 8 with corresponding results which have been obtained from the LIF measurements for a discharge current of i L = 320 and 500 mA, respectively. The measured LIF results represent densities averaged over the finite cuboid observation volume of about 0.7x0.7x1.0 mm 3 . The deviation of the local atom density from the spatially averaged one was checked using the calculated radial density profile for i L = 500 mA as shown in Fig. 8. If using the period averaged profile, the local density at r = 1 mm is about 2% larger than the spatially averaged one and about 14% lower if using the steepest profile in the cathode phase (t = 30µs). Good agreement of the calculated time-dependent atom densities with the measured results was obtained for both discharge currents at different distances from the spot center. The figures illustrate the decrease of the atom densities in the cathode phase caused by the Ba ionization. During the anode phase the atom density again increases due to the diffusion of atoms from the cathode. The decrease of the atom density is more pronounced at 500 mA than at 320 mA because of the larger electron density and corresponding increased ionization rate. The ion density is shown in Fig. 9 for both discharge currents. As to be seen, the decrease of the atom density in the cathode phase coincides with an increase of the ion density which is available in arbitrary units only. As shown in Fig. 9, the measured modulation of the ion density agrees well with the model result. The radial profiles as shown in the right diagrams of Fig. 9 have a local maximum due to the absorption of ions at the cathode. The ion density at the cathode is strongly decreased in the cathode phase because of the increased electric field. The particle fluxes of atoms and ions are shown in Fig. 10. The time-independent atom fluxes Γ c a at the electrode represent the boundary values which have been used for the discharge currents i L = 320 and 500 mA, respectively. The modulation of the atom flux at different distances from the electrode roughly corresponds to that of the atom density. However, the ion flux shows a more complicated behavior with positive and negative branches. The backward flux towards the electrode strongly increases during the cathode phase due to the larger density gradient as shown in Fig. 9 which is caused by the enhanced ionization and the larger electric field in the sheath E S .

The ion flux includes the drift flux which depends on the assumed field strength E 0 . The influence of this parameter on the ion density and flux has been analysed by solving the fluid equations also for E 0 = -0.4 and +0.2 V/cm. The influence is small in the region between the electrode surface (r = 0.5mm) and the position where the ion density is maximal (r ≈ 1mm) because the ion diffusion flux is dominant in this region due to the large density gradient.

The combination of Ba atom and ion fluxes at the electrode surface allows to determine the net flux of Ba out of the electrode according to

Γ net (t) = Γ a (t, r c ) -(1 -R)Γ i (t, r c ) (14)
This quantity corresponds to the loss of Ba material which lastly limits the lifetime of the lamp. It is additionally included in the left diagrams of Fig. 10. Due to the increased back flux of ions in the cathode phase the net flux is strongly decreased during this phase. The temporal evolution of the electron density n e is shown in Fig. 11. The maximal values in the cathode phase are about 2•10 12 cm -3 and 3.5•10 12 cm -3 , respecticely, for both cases. Similar results were obtained in Ref. [4], however with a temporal delay. Due to the quasi-stationary approach of the current model, the electron density is present here in the cathode phase only. However, the main purpose of this investigation is to describe the barium transport in the close vicinity of the spot. In this context, the ionization frequency [START_REF] Hayashi | Plasma Material Science Handbook Appendix[END_REF] is the key quantity which peaks with n e and k io Ba in the cathode phase. The impact of the cathode fall voltage is illustrated in Fig. 12. So far a calibration factor of C CF = 1.2 has been used to relate the measured voltage from the band method to the cathode fall voltage. In Fig. 12 the Ba atom densities are shown which have been obtained by varying C CF . In both cases the increase of the cathode fall voltage leads to a weaker drop of the Ba density during the cathode phase. This unexpected behavior is caused by the non-monotonous dependence of the Ba ionization rate coefficient on the cathode fall voltage as shown in Fig. 7. The cathode fall voltage varies between 10 and 12 V during the main time span (t = 2 • • • 15 µs ) of the cathode phase (cf. Fig. 5) and reaches about 14.5 V in the peak at about t = 23µs. Around this cathode fall voltage the ionization rate coefficient decreases with increasing voltage. At the higher discharge current i L = 500 mA the results obtained for C CF = 1.0 and 1.2 nearly agree because the ionization rate coefficient only weakly changes around the averaged cathode fall voltage of about U CF =10.5 V.

Conclusion

The temporal and spatial behaviour of Ba atom and ion densities originating from the spot evaporation at the coiled electrode of a commercial fluorescence lamp in ac operation at 25 kHz has been studied. The determination of Ba evaporation flux and total Ba loss over the whole period of the ac operation became possible due to the combination of absolute calibrated LIF measurements, estimations of the cathode fall and the coupling with an electron kinetic and a Ba atom and ion transport model. The distinct impact of the diffusion and of the ionization by plasma electrons in the cathode phase has been revealed. The diffusion is influenced by the gas temperature profile around the spot too. In the frame of the model the non-equilibrium and nonlocal behavior of the electron component in the spot region is reflected in the nonlinear dependence of the ionization frequency on the electrode fall voltage. Despite of this, the fall voltage magnitude is of lower importance for the estimation of the Ba evaporation flux. The good agreement of the temporal and spatial course of the densities obtained by the model and the LIF measurements reveals the accuracy of the measurements and confirms the assumptions made in the modeling.

Because the study omitted a detailed description of the evaporation itself, it further on enables a comparison with results of electrode and evaporation models as well as their validation together with measurements of the electrode temperature distribution. The latter will be subject of future investigations.

AFigure 1 .

 1 Figure 1. Sketch of the cathode region in the fluorescent lamp (a) and typical observation of the spot at the lower end of the coil (b).

Figure 2 .

 2 Figure 2. Radiation transitions used for the LIF measurements of barium atom and ions. The dotted lines symbolize radiative transitions to other levels which are not used for the measurements.

Figure 3 .

 3 Figure 3. Setup for the LIF measurement.

Figure 4 .

 4 Figure 4. Electrical setup for lamp operation and cathode fall measurement.

Figure 5 .

 5 Figure 5. Measured band voltage and corrected voltage used as cathode fall. (top) Lamp voltage and lamp current. (bottom)

α

  = {Ar, Kr, Hg, Ba} and yields in integrated form the relation i e (r) = i e (r c ) + 4πe 0 r rc S e (r)r 2 dr.

Figure 6 .

 6 Figure 6. Isotropic electron velocity distribution part f 0 and ionization cross section of Ba Q io Ba .

∇n i are determined by the diffusion

Figure 7 .

 7 Figure 7. Electron density and Ba ionization rate coefficient as functions of U CF . The electron density was normalized on a discharge current of 500 mA.

Figure 8 .

 8 Figure 8. Ba atom densities for i L = 320 (top) and 500 mA (bottom) as function of time and the radial coordinate. The calculated results (curves) are compared with the measured ones (symbols).

10

 10

Figure 9 .

 9 Figure 9. Ba ion densities for i L = 320 (top) and 500 mA (bottom). The measured ion density (circles) for 320 mA and distance 1 mm is shown in arbitrary units.

Figure 10 .Figure 11 .

 1011 Figure 10. Ba atom (left) and ion (right) fluxes for 320 (top) and 500 mA (bottom). The dashed curves in the right figures represent negative fluxes. The straight solid lines represent the chosen atom flux Γ c a at the spot.

Figure 12 .

 12 Figure 12. Ba atom density for different values of the calibration factor C CF for 320 (top) and 500 mA (bottom).

Table 1 .

 1 Collision cross sections used for solving the electron Boltzmann equation. Ar

	eV] level

* , Kr * and Hg * denote lumped levels of higher excited states.

Acknowledgments

This work was supported by Osram Munich.