Graphite flake self-retraction response based on potential seeking
© Ng et al; licensee Springer. 2012
Received: 8 November 2011
Accepted: 9 March 2012
Published: 9 March 2012
The high elastic modulus and interlayer strengths of graphite flakes make them a durable solid superlubricant. Apart from this, they have configurable electrical properties, exhibit quantum Hall effects, and possess a myriad of useful photonic properties. The self-retraction behavior of graphite flakes can have significant impact on the creation of ordered stacks for various applications because any accidental or intentional displacement of the top flake over the stacks below may result in a misalignment of the carbon-carbon atomic arrangement which, in turn, can have influence over the electrical and photonic properties. It has also been revealed that there was a tendency of the displaced microflake to fail at times to return to its original starting position and orientation. Here, we elucidate this behavior by considering the influence of the interlayer potential forces based on minimal potential energy seeking. The maps of the parameters interrogated here provide the ability for precautions to be undertaken. They also potentially permit the creation of an array of microflake stacks in which the metastable states permit different information to be encoded by virtue of the differentiated photonic or electrical characteristics readable from each array site.
The many favorable mechanical, electrical, thermal, and biocompatible properties of graphite render it as an important material. Much work has been expended to investigate the superlubricity [1, 2] between graphite layers where the high elastic moduli and interlayer strengths make it a durable solid lubricant. It also has configurable electrical properties [3–5], exhibits quantum Hall effects , and possesses a myriad of useful photonic properties [7–10]. Digressing to the mechanical property aspect of a closely related structure, the ability of nested shells in individual multi-walled carbon nanotubes (MWCNTs) to slide has been known for some time [11, 12]. These MWCNTs have comparable superlubricity as graphite, in which the interwall shear strength against sliding ranges from 0.08 to 0.3 MPa. An interesting behavior of these extracted inner shells is in their ability to self-retract into the outer shells when the extracting force is removed . This has been attributed to the action of van der Waals (vdW) interaction forces [11, 12]. Such a feature has led to the conception of MWCNT-based actuator bearings  as well as nanoelectromechanical oscillators which offer the possibility of operating at frequencies in the gigahertz range [14, 15]. More recently, a similar self-retraction capability was demonstrated on two graphite microflakes  of equal sizes. Although not mentioned previously, such a behavior can have significant impact in the creation of ordered graphene stacks for various applications. This is because any inadvertent or intentional displacement of the top flake over the stacks below may result in a misalignment of the carbon-carbon atomic arrangement which, in turn, can have influence over the electrical and photonic properties. It has also been revealed that there was a tendency of the displaced microflake to fail at times to return to its original starting position and orientation  unlike the MWCNT. Here, we attempt to elucidate this behavior by considering the influence of the interlayer potential forces.
Results and discussion
In the plot of distributions of AC using φ = 0° in Figure 4, we find that there is an ability for the top flake center to self-retract to a high degree back to its original position center (e.g. <a). There is a somewhat reducing ability to do this when × and y are increased. This is logical as there is a greater opportunity for the flake to encounter more local minima during retraction even though the overall potential difference is higher with greater displacement. Nevertheless, one finds an easier capability to self -retract fully when displaced in the y as opposed to the × direction. This demeanor is rather preserved despite the angle φ changing, as seen in the other plots with values ranging from 15° to 90° at intervals of 15°. Overall, however, one finds that there are a myriad of states with which the top flake is able to stop at, depending on the displacing positions and orientations. The plot of distributions of α with φ in Figure 5 essentially tells of the quadrant the flake returns to. There were cases wherein if AC was small, the flake may move into other quadrants. Nevertheless, we did not find unexpected cases in which the flake could move to another quadrant when AC was large.
We highlight certain caveats to the results provided here. The position and orientation tracing approach here assumes that there is no defect in either of the interacting flakes. The ability for graphite layers to be deform has been studied , and it is possible that such defects may strongly affect the self-retraction behavior . This will be more evident for micron-scale flakes where the creation of entire interacting regions with perfect lattices is understandably more difficult. Such lattices should, however, be more achievable if the dimensions of the flakes are smaller. It is also important to note that the model here assumes that the force to move the top flake does not comprise an axial component that deforms the lattice. In previous demonstrations of self-retraction behavior, a mechanical probe that depressed and pulled the top flake laterally was utilized [16, 24] in which such an effect cannot be ruled out. The measure of moving the flake with minimal axial deformation will most likely be accomplished using either optical , magnetic , electrical quadruple ions , or vibration  that have recently been reported with graphene sheets. The vibration of graphene nanostrips, it appears, offers the possibility of creating bending resonators with high sensitivity to environmental change . It is conceivable, based on the findings here, for metastable misaligned states to appear with each cycle of actuation, to the extent of leaving a wrinkling effect on the sheets . It is also noteworthy that long strips can result in gravity causing the structure to flop downwards. Remedy, however, is available by adopting a dangling arrangement, which has been demonstrated workable in applications associated with wetting monitoring [30, 31].
In summary, we have investigated the self-retraction of a graphite flake over another flake of the same size. This was done using a registry dependent interlayer interaction potential previously reported that is sensitive enough to account for the registry of the honeycomb structures and its layers. Under the assumption that the mass of the flake is small, the retraction process can be depicted as a series of quasi-static steps that seek the lowest potential. The results show that while there is an overall impetus to retract to the original position and orientation to restore to the lowest potential, there is a possibility for the return trajectory to encounter local potential minima that prevents the top flake from restoring fully. Essentially, this means that the graphite flake is able to assume meta-stable states.
Such a behavior can have significant impact in the creation of ordered graphene stacks for various applications. The maps of the parameters that we interrogated here provide the ability for precautions to be undertaken. For instance, any movement in the y direction keeping × and φ constrained will generally result in total retraction. Alternatively, it might be desirable to attain the meta-stable positions and orientations in order to obtain a different photonic or electrical behavior from an aligned stack. The maps then provide a road map to accomplish this. Such a behavior allows one to contemplate the creation of an array of microflake stacks in which the metastable states permit different information to be encoded by virtue of the differentiated photonic or electrical characteristics readable from each array site. Using the maps, these metastable states may be altered to or 'erased' using the retraction behavior to the original stable state. This portends the possibility of high density data recording and retrieval at the nanometer scale. The understanding of the metastable states may also shed light into the wrinkling behavior of graphene sheets, particularly if strips of them are to be used as resonators.
Parts of this work were made possible by the support from Australian Research Council Discovery project grant DP0878454. Preliminary discussions with A. Neild are noted.
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