Lithium ion storage between graphenes
© Chan and Hill; licensee Springer. 2011
Received: 26 October 2010
Accepted: 9 March 2011
Published: 9 March 2011
In this article, we investigate the storage of lithium ions between two parallel graphene sheets using the continuous approximation and the 6-12 Lennard-Jones potential. The continuous approximation assumes that the carbon atoms can be replaced by a uniform distribution across the surface of the graphene sheets so that the total interaction potential can be approximated by performing surface integrations. The number of ion layers determines the major storage characteristics of the battery, and our results show three distinct ionic configurations, namely single, double, and triple ion forming layers between graphenes. The number densities of lithium ions between the two graphenes are estimated from existing semi-empirical molecular orbital calculations, and the graphene sheets giving rise to the triple ion layers admit the largest storage capacity at all temperatures, followed by a marginal decrease of storage capacity for the case of double ion layers. These two configurations exceed the maximum theoretical storage capacity of graphite. Further, on taking into account the charge-discharge property, the double ion layers are the most preferable choice for enhanced lithium storage. Although the single ion layer provides the least charge storage, it turns out to be the most stable configuration at all temperatures. One application of the present study is for the design of future high energy density alkali batteries using graphene sheets as anodes for which an analytical formulation might greatly facilitate rapid computational results.
The development of an efficient lithium ion battery, which has the highest energy density and the quickest recharge time, relies on a complicated optimization of novel materials for the anode, the cathode, and the electrolyte. Graphite is currently the most common material used for the anodes of commercial batteries because of its capability for reversible lithium intercalation in the layered crystals, which represents the maximum theoretical lithium storage capacity, around 372 mAh/g . A single layer of graphite, referred to as graphene, has been synthesized using the mechanical exfoliation of graphite by Novoselov et al. , and quite recently the 2010 Nobel Prize for Physics was awarded to A. Geim and K. Novoselov for this discovery. The extreme mechanical and chemical properties of graphene have already been exploited for possible energy storage and microelectronics [3, 4]. Numerous experiments have been performed to confirm the utilization of graphene nanosheets and nanoribbons to enhance lithium storage capacity and to improve recharge cyclic performance [5–7]. Semi-empirical molecular orbital calculations have been used to investigate lithium ion storage states between two graphene sheets , as well as some heteroatom-substituted carbon materials . Density functional theory has also been used to investigate the structure, bonding, and magnetic properties of metal atoms embedded between graphenes . Other hybrid carbon structures containing graphenes such as silicon-graphene , TiO-graphene , and Sn-graphene  have been shown experimentally to possess very high ion storage capacities.
In this article, we adopt the continuous approach employed by Cox et al. [14, 15] and the 6-12 Lennard-Jones potential and we assume that the carbon atoms can be uniformly distributed across the surface of nano-structures, so that the total potential energy between various non-bonded molecules can be determined analytically by performing surface integrations. The total potential energy can be used to investigate the relative motion of certain nano-structures, such as the oscillatory motion of a fullerene or an ultra-small nanotube inside a single-walled carbon nanotube . In addition, the same methodology has successfully been used to study the encapsulation of drug molecules inside single-walled nanotubes as the 'magic bullet' concept [16, 17] and the encapsulation of methane molecules and hydrogen atoms inside metal-organic frameworks for gas storage .
In the next section, we present the continuous approach in the context of the current investigation. Numerical results and discussions are given in "Numerical results and discussion" section and a general conclusion is provided in the final section.
where V denotes the cavity volume between the two graphenes. Equation (5) can be readily evaluated using a numerical integration technique such as Simpson's Rule.
Numerical results and discussion
Number density (graphene)
Number density (single layer)
Number density (double layer)
Number density (triple layer)
The resulting lithium storage for r = 2.8 Å roughly corresponds to that predicted for C54H18 in Suzuki et al. . We comment that the larger the graphene sheets, the more lithium ions can be stored and which becomes beyond the computational capacity of the method of Suzuki et al. . This study might offer a far more realistic engineering estimation procedure for battery design using graphene nanosheets as anodes. The merit of the continuous approximation is that we may predict the lithium storage capacity for graphene sheets of any size, which could be computationally challenging using molecular orbital calculations. We also comment from Figure 7 that the increase in layer numbers involves higher lithium ion storage. For the double and triple ion layers, the calculated storage capacities are both higher than the maximum theoretical storage capacity for conventional graphitic carbon materials, i.e., 372 mAh/g , which is approximately equivalent to the case of a single ion layer, i.e., D = 5 Å . Although the triple layers store more lithium ions than the double layers, the more sophisticated calculations performed by Suzuki et al.  show that the double ion layers configuration is the most preferable candidate for higher lithium storage. Their calculations take into account the charge-discharge property to prevent the formation of hysteresis resulting from a decrease in positive charges of lithium ions with an increase in ion layers.
In this article, we adopt the continuous approximation and basic statistical mechanics to investigate suitable storage configurations for different battery designs using graphene sheets as the anode. Although we extract some accurate parameters from the molecular orbital calculations, our theoretical methodology yields very rapidly the numerical results for graphene sheets of various sizes under different surrounding temperatures and external effects. While the double layer configuration predicts a larger storage capacity than that of graphite, the single layer configuration turns out to be the most suitable candidate for the safest and stablest ion battery operating at extreme temperatures.
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