松尾 吉晃

<jats:title>Abstract</jats:title><jats:p>In this review, fundamental aspects of the electrochemical intercalation of anions into graphite have been first summarized, and then described the electrochemical preparation of covalent‐type GICs and application of graphite as the cathode of dual‐ion battery. Electrochemical overoxidation of anion GICs provides graphite oxide and covalent‐fluorine GICs, which are key functional materials for various applications including energy storage devices. The reaction conditions to obtain fully oxidized graphite has been mentioned. Concerning the application of graphite for the cathode of dual‐ion battery, it stably delivers about 110 mA h g<jats:sup>−1</jats:sup> of reversible capacity in usual organic electrolyte solutions. The combination of anion and solvent as well as the concentration of the anions in the electrolyte solutions greatly affect the performance of graphite cathode such as oxidation potential, rate capability, cycling properties, etc. The interfacial phenomenon is also important, and fundamental studies of charge transfer resistance, anion diffusion coefficient, and surface film formation behavior have also been summarized. The use of smaller anions, such as AlCl<jats:sub>4</jats:sub><jats:sup>−</jats:sup>, Br<jats:sup>−</jats:sup> can increase the capacity of graphite cathode. Several efforts on the structural modification of graphite and development of electrolyte solutions in which graphite cathode delivers higher capacity were also described.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The effects of soft X-ray irradiation and atomic hydrogen annealing (AHA) on the reduction of graphene oxide (GO) to obtain graphene were investigated. To clarify the interaction between soft X-rays and GO, soft X-rays of 300 eV and 550 eV were used for C 1s and O 1s inner-shell electron excitation, respectively at the NewSUBARU synchrotron radiation facility. Low-temperature reduction of the GO film was achieved by using soft X-ray at temperatures below 150 °C at 300 eV, and 60 °C at 550 eV. O-related peaks in X-ray photoelectron spectroscopy, such as the C–O–C peak, were smaller at 550 eV than those at 300 eV. This result indicates that excitation of the core–shell electrons of O enhances the reduction of GO. Soft X-rays preferentially break C–C and C–O bonds at 300 and 550 eV, respectively.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Graphene-like graphite (GLG) is a promising anode material for sodium-ion batteries, and is believed to have unique kinetic properties compared to hard carbon due to its different intercalation mechanism. In this study, electrochemical impedance spectroscopy was used to investigate the kinetic properties of sodium-ion intercalation in GLG. Our results indicate that the activation energies for interfacial sodium-ion transfer in GLGs were nearly identical to those reported for graphite, regardless of the heat treatment temperature applied to the GLGs. Furthermore, these activation energies were lower than those observed for hard carbon, suggesting better sodium-ion intercalation kinetics. In addition, the diffusion coefficient of sodium ions in the GLG was similar to that of graphite, with the highest value observed for GLG800, the GLG heat-treated at the highest temperature of 800°C. This may indicate that the diffusion coefficient increases with the presence of nanopores in the graphene layer of GLG. It has also been reported that GLG800 is superior in terms of reversible capacity and working potential compared to GLGs synthesized at other temperatures. Consequently, the results clearly demonstrate that GLG800 has the best electrochemical properties in terms of both thermodynamics and kinetics among the GLGs investigated in this study.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>It has been reported that lithium-rich cathode materials of LIB emit singlet oxygen during charging, which chemically oxidizes electrolyte solutions, and the decomposition products form surface film on the material. However, the detailed conditions and mechanism of the surface film formation and its effect on the electrochemical reaction at the electrode/electrolyte interface have not been clarified in detail. In this study, using 0.5LiCoO2 • 0.5Li2MnO3 thin-film electrodes as the model electrodes of the lithium-rich cathode materials, the surface film formation behavior was investigated. After a constant current-constant voltage (CCCV) measurement to 4.8 V, passivation of the electrodes did not occur. On the other hand, the electrode after cyclic voltammetry (CV) up to 4.8 V showed complete passivation. The results of spectroscopic analyses revealed that decomposition products of the solvent formed thick surface film on the electrode after CV. From the results, it was concluded that the passivation surface film was formed by the simultaneous decomposition of the solvent via electrochemical oxidation at high potentials and chemical oxidation by singlet oxygen. Furthermore, the electrode with the surface film showed better cycleability than that without the surface film, indicating that it contributes to the suppression of side reactions at the electrode/electrolyte interface.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The reduction of graphene oxide (GO) through atomic hydrogen annealing (AHA) and soft X-ray irradiation is investigated using microwell substrates with μm-sized holes with and without Ni underlayers. The GO film is reduced through AHA at 170 °C and soft X-ray irradiation at 150 °C. In contrast, some GO films are not only reduced but also amorphized through soft X-ray irradiation. The effect of the Ni underlayer on GO reduction differs between AHA and soft X-ray irradiation. In AHA, the difference in GO reduction between SiO<jats:sub>2</jats:sub> and Ni underlayer was originated from the atomic hydrogen density on sample surface. On the other hand, in soft X-ray irradiation, the difference in GO reduction between SiO<jats:sub>2</jats:sub> and the Ni underlayer originates from the excited electrons generated by soft X-ray irradiation. Reduction without damage is more likely to occur in the suspended GO than in the supported GO.</jats:p>

Dual carbon batteries have recently attracted significant attention because of their ecofriendliness and reliability. In this study, graphene-like graphite (GLG) was prepared by thermal reduction of graphite oxide to be used as a cathode material, and the electrochemical PF₆⁻ anion-intercalation reaction into GLG was investigated. Decreasing the heat-treatment temperature of GLGs from 900 °C to 600 °C resulted in increasing the reversible capacities and interlayer distances of GLG samples. Among them, GLG synthesized at 700 °C (GLG700) showed the largest discharge capacity of 137 mAh g⁻¹, which was much larger than that of graphite (52 mAh g⁻¹). Variations in the X-ray diffraction patterns and Raman spectra of GLG700 indicated that the stage number reached 1 at 4.8 V (vs Li⁺/Li) while that of graphite was 2 at the same potential. This indicates that GLG could store PF₆⁻ anion in every interlayer, which is probably one of the main causes of the larger capacity. The charge–discharge cycling test of GLG700 showed that the capacity gradually increased during cycling, and the coulombic efficiency was approximately 97% at every cycle after the 5th cycle. These results clearly demonstrate that GLG can be used as a cathode material with a large capacity for dual carbon batteries.

We demonstrate the effect of sheet conductivity and infiltration using the example of two graphite types, showing that, in general, the graphite type is very important. Amorphous and pyrolytic graphite were applied to carbon electrodes in fully printable carbon-based multiporous-layered-electrode perovskite solar cells (MPLE-PSCs): . The power conversion efficiency (PCE) using amorphous graphite-based carbon (AGC) electrode was only 5.97% due to the low short-circuit photocurrent density (J(sc)) value, which was due to the low incident photon-to-current efficiency (IPCE) in the short wavelength region caused by the poor perovskite filling into the porous TiO2-ZrO2 layers. Conversely, using pyrolytic graphite-based carbon (PGC) electrode, J(sc), open-circuit photovoltage (V-oc), fill factors (FF), and PCE values of 21.09 mA cm(-2), 0.952 V, 0.670, and 13.45%, respectively, were achieved in the champion device. PGC had poorer wettability and a small specific surface area as compared with AGC, but it had better permeability of the perovskite precursor solution into the porous TiO2/ZrO2 layers, and therefore a denser filling and crystallization of the perovskite within the porous TiO2/ZrO2 layers than AGC. It is confirmed that the permeability of the precursor solution depends on the morphology and structure of the graphite employed in the carbon electrode.

Graphene-like graphite prepared by heating graphite oxide under vacuum at 800 degrees C was fluorinated by elemental fluorine in the presence of HF at room temperature. The interlayer spacing of the resulting material was 0.639 nm and it showed CxF type characteristics. The fluorine content of it (x = 1.7) was higher than that obtained from natural graphite (x = 2.3). The discharge capacity of it as a cathode of lithium primary battery reached 940 mAhg(-1) at a low current density, which was 50% larger than the theoretical capacity based on the 100% discharge of fluorine. (C) The Author(s) 2020. Published by ECSJ.

More than 25 weight percent of lithium ions were accommodated in silsesquioxane-pillared carbon with very small interlayer expansion. It delivered reversible capacity of 1023mAh/g with a relatively high first columbic efficiency of 67% and good cycling property as an anode of an all-solid-state lithium ion battery.

One of the challenging targets in materials synthesis is a direct conversion of molecular based crystalline substances into crystalline ordered carbonaceous frameworks (OCFs). Though we have discovered the first example of the direct conversion with Ni-cyclic porphyrin dimer bridged by diacetylene moieties, such dimer requires a multi-step synthesis procedure with low yield and the resulting OCFs are not highly porous. Herein, we report the direct conversion of Ni-porphyrin monomer with ethynyl groups into OCF with developed microporosity. Upon heat-treatment, Ni-porphyrin monomer is thermally polymerized via ethynyl groups and the resulting polymer is successively converted into OCF at 873 K. Thus, ordered microporous material with conductive carbonaceous framework is obtained. The porphyrin Ni-N-4 coordination structure is well retained after the carbonization and the microporous OCF exhibits specific electrocatalysis for CO2 conversion into CO with high selectivity.

Fluorine-intercalated graphite, CxF with x = 2.8, was tested for the cathode active material of an all-solid-fluoride-ion shuttle battery. The addition of copper fluoride facilitated the discharge reaction of CxF. It was discharged up to 0.4 V vs. Pb and the resulting carbon was charged up to 1.6 V, regenerating C-F bonding. A highest capacity of 230 mAh g−1 was delivered when 80 wt% (67 mol%) of CuF2 was added and utilization of CxF reached 98%.

<p>Deoxofluorination of graphite oxide with sulfur tetrafluoride forms graphite oxyfluoride in the presence of hydrogen fluoride. Hydroxy and carbonyl groups are selectively fluorinated by this method.</p>

Inexpensive and sensitive graphite electrodes were fabricated by applying flame annealing to pencil-graphite rods (PGRs) as electrodes for water electrolysis cells. The resin (polymer, binder) on the surface of PGR was removed by flame annealing to make it porous, and the graphite electrodes with high activity and low cost were obtained. By flame annealing the PGR, although the PGR electrode became active upon water electrolysis, the PGR electrode became instable for long-time operation. The effects of flame annealing on PGR for water electrolysis were analyzed by SEM, FT-IR spectroscopy, Raman spectroscopy, NEXAFS, and electrochemical impedance spectroscopy (EIS).

Graphene like graphite (GLG) samples containing various amounts of oxygen are prepared from the thermal reduction of graphite oxide (GO) and are used as anodes of lithium ion battery. The oxygen/carbon (O/C) ratios in GLG varied from 0 to 0.08, depending on the thermal reduction temperature, oxygen gas pressure during heat treatment and degree of oxidation of the starting GO. The cell voltage during discharge almost linearly increases below 1 V independent of the oxygen contents in them. The discharge capacity of GLG above 1 V increases with the increase in the oxygen content with a slope of lithium/oxygen ratio of 3 at lower O/C ratios. Then the slope becomes smaller and the discharge capacity reaches 673 mAhg−1 for GLG with O/C = 0.08. When GLG is treated with hydrogen gas, considerable amounts of oxygen atoms are substituted by hydrogen ones. The discharge capacity of the resulting GLG samples is larger than that expected form their oxygen contents and coulombic efficiency is slightly improved up to 59%. Introduction of oxygen atoms within carbon layers results in the large increase in the interlayer spacing during charging, which leads to accommodation of large amounts of lithium ions.

Photoinduced macroscopic deformation behavior of crosslinked liquid-crystalline polymer is induced in crosslinked N-benzylideneaniline polymer films. The film is prepared by in situ polymer reaction using polymethacrylate-containing phenylaldehyde side chains and o-tolidine crosslinker. The film exhibits macroscopic bending upon exposure to UV light and then immediately reverts to the initial shape when the light is turned off. The bending behavior is strongly affected by the fabrication conditions the changes in the macroscopic shape and photomechanical properties in response to UV light for the film prepared from a mixture solution are small, while those for the film prepared by top coating the crosslinker solution onto the prepolymer substrate are large.

Here we propose the use of a carbon material called graphene-like-graphite (GLG) as anode material of lithium ion batteries that delivers a high capacity of 608 mAh/g and provides superior rate capability. The morphology and crystal structure of GLG are quite similar to those of graphite, which is currently used as the anode material of lithium ion batteries. Therefore, it is expected to be used in the same manner of conventional graphite materials to fabricate the cells. Based on the data obtained from various spectroscopic techniques, we propose a structural GLG model in which nanopores and pairs of C-O-C units are introduced within the carbon layers stacked with three-dimensional regularity. Three types of highly ionic lithium ions are found in fully charged GLG and stored between its layers. The oxygen atoms introduced within the carbon layers seem to play an important role in accommodating a large amount of lithium ions in GLG. Moreover, the large increase in the interlayer spacing observed for fully charged GLG is ascribed to the migration of oxygen atoms within the carbon layer introduced in the state of C-O-C to the interlayer space maintaining one of the C-O bonds.

We evaluated graphene oxides (GOs) synthesized by different methods in terms of magnetism and chemical structure. GO samples were synthesized by Brodie and Hummers methods, which are labeled as BGO and HGO, respectively. The temperature dependence of magnetic susceptibility indicates an order of magnitude larger localized spin concentration of HGO (N-s = 2 x 10(19)) than that of BGO (N-s = 2 x 10(18)). The FT-IR spectra for GO exhibits peaks for hydroxyl, carboxyl, epoxy and carbonyl groups in spite of absence of any peak for graphite. Interestingly, the peak around 1224 cm(-1) attributed to C-OH stretching for HGO is larger than that for BGO, while the peak around 1050 cm(-1) for C-O-C stretching is larger for BGO. The difference of functional groups between HGO and BGO explains the larger spin magnetism for HGO. In the case of introduction of epoxy group, oxygen atom bonds to adjacent carbon atoms, remaining symmetry regarding A, B sub-lattices of graphene lattice. On the other hand, attaching hydroxyl group occurs randomly on carbon atoms of graphene and breaks symmetry of A, B-sublattices, resulting in the emergence of the localized states and the spin magnetism. (C) 2017 Elsevier Ltd. All rights reserved.

Despite recent advances in the carbonization of organic crystalline solids like metal-organic frameworks or supramolecular frameworks, it has been challenging to convert crystalline organic solids into ordered carbonaceous frameworks. Herein, we report a route to attaining such ordered frameworks via the carbonization of an organic crystal of a Ni-containing cyclic porphyrin dimer (Ni-2-CPDPy). This dimer comprises two Ni-porphyrins linked by two butadiyne (diacetylene) moieties through phenyl groups. The Ni-2-CPDPy crystal is thermally converted into a crystalline covalent-organic framework at 581 K and is further converted into ordered carbonaceous frameworks equipped with electrical conductivity by subsequent carbonization at 873-1073 K. In addition, the porphyrin's Ni-N-4 unit is also well retained and embedded in the final framework. The resulting ordered carbonaceous frameworks exhibit an intermediate structure, between organic-based frameworks and carbon materials, with advantageous electrocatalysis. This principle enables the chemical molecular-level structural design of three-dimensional carbonaceous frameworks.

Pillared carbon thin films were prepared from the thermal reduction of graphite oxide silylated with octyltrichlorosilane and then dimethyldichlorosilane. The interlayer spacing of the resulting pillared carbon thin film was 1.29 nm, and it contained hydrophobic Si-CH3 groups, excluding Si-OH ones. The resistance of it increased during the exposure to acetone vapor, while it was unchanged when it was exposed to the water vapor. Moreover, in the presence of water vapor, the resistance changed in a similar manner.

Electrochemical oxidation of graphite was performed at high current densities in 47% HF aqueous solution. Cyclic voltammetry indicated that covalent C-F bonding formed above 2.4 V vs Pb/PbF2. The sample obtained at higher current densities than 200 mA cm(-2) was stage 1 type material with an interlayer spacing of 0.55 nm and it contained a considerable amount of oxygen, together with the covalently bonded fluorine. The discharge profile of this sample as a cathode of lithium primary battery was similar to that of C2.5F prepared under F-2 gas atmosphere and the capacity reached 550 mAh g(-1). This strongly indicated that not only fluorine but also oxygen in this sample was utilized. (C) 2016 Published by Elsevier B.V.

1-aminpyrene was reacted with graphite oxide (GO) in the presence of 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide hydrochloric salt as a catalyst. As the reaction time and the concentration of 1-aminopyrene increased, the amount of attached 1-aminopyrene increased and reached 6.9 mmol/100 g GO. At the same time, the interlayer spacing of the GO increased to 1.26 nm. Based on various spectroscopic measurements, it has been proved that two reactions mainly occurred: (a) an acid-base reaction between hydroxyl groups on the basal plane of the GO and protonated amine, and (b) the formation of amide bonding between 1-aminopyrene and carboxylic groups on the edge of GO. In the course of these reactions, partial reduction of GO layers also occurred. The 1-aminopyrene molecules in (a) are almost completely removed and those in (b) are partially removed by treating with HCl, which was accompanied by further reduction of the GO.

A three-dimensional (3D) fine network structure of thin carbon microflakes inside a loosely entangled carbon-fiber matrix was formed by applying an ice-template method to a graphite oxide (GO) dispersion in the matrix and thermal reduction of the GO. Vanadium-ion redox reactions were investigated in the network of reduced GO (RGO) for potential application as electrodes in vanadium redox flow batteries (VRFB). The development of the fineness, the degree of graphitization, the structural disorder, and the surface composition were characterized. The interaction between the carbon surface species and the vanadium ions was implied by the X-ray absorption fine structure (XAFS). The structure of the 3D RGO network was clearly correlated to the activity for the VRFB positive electrode reactions, and the development of the fine network structure effectively enhanced the reactions due to increased exposure of the edge planes and sufficient dispersion of the active sites.

The structure of carbon obtained from the thermal reduction of graphite oxide at 900 degrees C after electrochemical storage sodium ions was investigated. X-ray diffraction measurement of the carbon sample after charged to various potentials indicated that sodium ions are stored between the layers of carbon below 0.3V vs. Na/Na+ though the interlayer spacing of it was similar to that of graphite. The lower LUMO energy as revealed from the broad pi* peak in the region of CK observed in soft X-ray absorption measurement was responsible for the intercalation of a large amount of sodium ions into the present carbon material. (C) The Electrochemical Society of Japan, All rights reserved.

Carbons with various interlayer spacings of 0.422-0.334 nm were prepared from the pyrolysis of graphite oxide at various temperatures. Raman measurement indicated that these carbons contain many defects even when the interlayer spacing was almost comparable to that of graphite. The charge and discharge potentials monotonically changed when they were used for the negative electrode of sodiumion battery, which was rather similar to that observed for soft carbons. The maximum reversible capacity reached 252 mAh g(-1) for the carbon prepared at 300 degrees C and it showed relatively good cycling stability. The X-ray diffraction pattern of it after charged to 0 V indicated that sodium ions are inserted between the carbon layers, forming a stage 1 intercalation compound. The capacity slightly decreased as the increase in the temperature for pyrolysis and more steeply decreased above 900 degrees C, however, the carbon obtained at 1000 degrees C still delivered a capacity of 95 mAh g(-1). (C) 2014 Elsevier B.V. All rights reserved.

Silylated graphite oxide thin films were reduced by UV light irradiation using a super high pressure Hg lamp at 95 degrees C. The reduction of silylated graphite oxide was completed within 24 h and a new pillared carbon with an interlayer spacing of 0.81 nm was obtained. Pillared carbons with larger interlayer spacings of about 1.13 nm were also obtained from graphite oxide silylated with octyltrichlorosilane and then with 3-aminopropyltriethoxysilane for 1.5-6 h, when they were reduced by UV light irradiation and heating at 200 degrees C under vacuum. Selective electrical response during exposure to gaseous vinylene carbonate, acetonitrile, ozone and hydrogen molecules has been achieved by changing the pillar density in the resulting pillared carbon films. (C) 2014 Elsevier Ltd. All rights reserved.

The preparation and application of new intercalation compounds of graphite oxide are reviewed. Graphite oxide was silylated with different silylating reagents such as alkyltrichlorosilane and 3-aminopropylethoxysilanes. After they were bidentately or monodentately attached to layers of graphite oxide, Si-OH groups which are available for further functionalization were introduced. When highly silylated graphite oxide was heated under vacuum, microporous or mesoporous pillared carbons in which adjacent carbon layers are connected with siloxane or silsesquioxane pillars were obtained. Organic molecules were size-selectively intercalated into the pillared carbon obtained from graphite oxide silyated 3 times with methyltrichlorosilane. The excess hydrogen adsorption of pillared carbons at ambient temperature reached 0.6 wt% at 20 MPa. Pillared carbon thin films were prepared and they showed a selective electrical resistance change response to electron donating and smaller organic molecules.

Graphene layers with silica pillars which widen. the interlayer distance and functionalize the space as micropores have been prepared as one of the new porous carbon materials. In this study, the silica-pillared graphene with Fe-N units as a catalytic active site for cathodic oxygen reduction was formed as a new type of carbonaceous noble-metal-free oxygen reduction catalysts with the ordered pore structure. The formation of the pillared carbon was performed by introducing silylating reagents as the pillar source and also as the nitrogen source of the units in the graphite oxide interlayer spaces, introducing the Fe ions, and heat treatment in vacuum at 500 degrees C. The X-ray diffraction (XRD) patterns showed the ordered layered structure. The X-ray absorption fine structure (XAFS) of the Fe-K edge showed that the unit was a square planar Fe-N-4 moiety. The catalytic activity for the O-2 reduction was demonstrated by measurements using rotating disk electrodes with the pillared carbon fixed on the surface and immersed in an oxygen-saturated acidic solution. The activity was enhanced by the combination of the nitrogen containing compound to the silylating reagent and using the nitrogen-rich silylating reagent. (C) 2013 Elsevier Ltd. All rights reserved.

Silylated magadiite containing perfluorooctyl groups was prepared and rhodamine and, pyrene dyes were covalently attached to the layers of them. The interlayer spacing of silylaetd, magadiite containing perfluorooctyl groups was larger than that those containing octyl or even, octadecyl groups. However, the content of rhodamine dyes in it was much smaller when compared to, those in silylated magadiite without fluorine. The decrease of the fluorescence from rhodamine dyes in, silylated magadiite became smaller when they were surrounded by thick and rigid perfluorooctyl, groups, which was ascribed to the suppression of twisting motion of diethylamino groups in them. (C) 2013 Elsevier B.V. All rights reserved.

Microporous pillared layered titanates with large surface areas were prepared through the pyrolysis of silylated layered titanate under various atmospheres. The sample containing some organic residues showed visible-light photocatalytic activity toward methanol decomposition.

A novel pillared magadiite with soft micropores were prepared from the pyrolysis of magadiite silylated with octyltrichlorosilane and then with 3-aminopropyltriethoxysilane. The interlayer spacing of the pillared magadiite samples changed from 1.80 to 2.74 nm, depending on the water contents added during the second step silylation. At the same time, the BET surface area increased and the pore size decreased. Polar organic molecules were included between the layers of pillared magadiites, accompanying the interlayer expansion. The inclusion behaviors of organic molecules with different molecular widths indicated that the distance between the adjacent pillars for the entrance of organic molecules decreased with the increase in the content of 3-aminopropyltriethoxysilane in the precursors of pillared magadiites. (C) 2012 Elsevier Inc. All rights reserved.

Microporous pillared carbons were prepared from graphite oxide silylated by a two-step method. Graphite oxide was first silylated with octyltrichlorosilane and then, with 3-aminopropyltriethoxysilane at 110 degrees C. The addition of excess silylating reagents in the second step reaction led to the decrease in the interlayer spacings of the resulting silylated graphite oxides. Pillared carbon with interlayer spacing of 1.58 nm was formed when the silylated graphite oxides with the layer spacing of 2.63 nm were heated at 500 degrees C under vacuum. The BET surface area of the pillared carbon reached a relatively large value of 756 m(2)/g and alpha(s) analysis indicated that the pore width was 0.74 nm. (C) 2011 Elsevier Ltd. All rights reserved.

Thin films of graphite oxide silylated with octyltrichlorosilane were first prepared and they were further silylated with 3-aminopropyltriethoxysilane. Pillared carbon thin films with an interlayer spacing of 1.7 nm were prepared from the pyrolysis of the resulting thin films. Larger propylene carbonate molecules were not intercalated into them. They showed selective electrical response to electron donating and smaller organic molecules. The increase in the electrical resistance upon exposure to organic molecule seems to be larger for those with larger donor numbers. (C) 2012 Elsevier Ltd. All rights reserved.