Abstract:
Methods for the formation of nanotube from thin films are provided. The methods involve the adsorption of atoms to the surface of the films. The adsorbed atoms introduce surface stress, inducing a curvature in the films. The curvature is sufficient to bring atoms at the edges into sufficiently close proximity to form covalent bonds. Other methods include the step of desorbing the atoms from the surface of the film. The films may comprise a variety of nanomaterials, including graphene sheets and semiconductor thin films.

Description:
FIELD OF THE INVENTION 
       [0001]    This invention pertains generally to the formation of nanotubes from thin films, such as graphene sheets and silicon films, using atomic adsorption. 
       BACKGROUND OF THE INVENTION 
       [0002]    Recent efforts have been devoted to developing technically and economically viable methods for synthesizing carbon nanotubes, which exhibit a wealth of fascinating electrical, optical, and mechanical properties and have a broad range of applications. Currently, there are three major methods for forming carbon nanotubes, including arc discharge, laser ablation, and chemical vapor deposition. Each of the existing methods of carbon nanotube formation is based on bottom-up, self-assembled growth processes that are stochastic in nature. 
         [0003]    These stochastic synthetic processes inherently lack control over carbon nanotube size and chirality. Therefore, post-synthesis separation, purification, and sorting of carbon nanotubes are often required, resulting in additional technical difficulties and higher production costs. Although recent progress with chemical vapor deposition methods has led to the production of well-aligned and ordered carbon nanotubes with better control over tube diameter and chirality, synthesizing mass quantities of carbon nanotubes with uniform size and chirality remains a great challenge. A deterministic synthetic approach to carbon nanotube formation, in which the size and chirality of the carbon nanotubes may be predefined, has not yet been accomplished. 
         [0004]    Further objects, features, and advantages of the invention will be apparent from the following detailed description when taken in conjunction with the accompanying drawings. 
       SUMMARY OF THE INVENTION 
       [0005]    The present invention provides methods for forming nanotubes from thin films using atomic adsorption to induce bending of the films. When the film comprises a single graphene sheet (i.e., a “graphene nanoribbon”), the methods may be used to form single-walled carbon nanotubes (SWNTs). Because graphene nanoribbons can be patterned onto substrates with predefined widths and directions, the size and chirality of the resulting SWNTs may be controlled. Thus, the methods of the present invention eliminate the need for any post-synthesis steps, allow mass production of nanotubes of uniform size and chirality and offer easy integration of the nanotubes into nanodevices on a substrate. 
         [0006]    One embodiment of the invention provides a method for forming the nanotubes. In the method, a thin film is patterned onto a substrate. Atoms, such as hydrogen (H) and fluorine (F) atoms, are adsorbed to the surface of the film, inducing surface stress that bends the film downward, away from the adsorbed atoms. The radius of curvature of the nanotubes may be controlled through the selection of appropriate adsorbants and surface coverages. When the free ends of the film meet each other or the free ends of another thin film, chemical bond (such as covalent bond) linkages are formed between the edges and a nanotube is formed. The adsorbed atoms may then be desorbed from the surface of the resulting nanotube. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]      FIG. 1  shows the formation of SWNTs using first-principles molecular dynamics (“MD”) simulations. A 1.7 nm wide graphene nanoribbon is patterned onto a graphite substrate (a(1)). H atoms are adsorbed to a surface coverage of 50% (a(2)). The adsorbed atoms cause the nanoribbon to bend into a SWNT (a(3)-(5)).  FIG. 1   b  (1)-(5) show the formation of a SWNT from a 2.0 nm wide graphene nanoribbon and adsorption of F atoms to a surface coverage of 45%. 
           [0008]      FIG. 2  shows the formation of SWNTs using classical MD simulations. A 1.6-nm-wide (3.5, 3.5) graphene nanoribbon is patterned onto a graphite substrate and H atoms are adsorbed to a surface coverage of 50% (a(1)). The adsorbed atoms cause the nanoribbon to bend into a (4, 4) armchair SWNT (a(2)-(3)). The adsorbed atoms are desorbed at high temperature (a(4)-(6)).  FIG. 2   c  shows a sideview of the resulting armchair SWNT.  FIG. 2   b  (1)-(6) show the formation of a (14, 0) zigzag SWNT from a 3.3-nm-wide (13, 0) graphene nanoribbon and adsorption of H atoms to a surface coverage of 45%.  FIG. 2   d  is a sideview of the resulting zigzag SWNT. 
           [0009]      FIG. 3  shows the formation of SWNTs from two layers of graphene nanoribbons using classical MD simulations. Two 1.6-nm-wide and 1.1-nm-wide graphene nanoribbons are patterned onto a graphite substrate and H atoms are adsorbed to the top layer graphene nanoribbon to a surface coverage of 50% (a(1)). The adsorbed atoms cause the nanoribbons to bend until the carbon atoms at the edges of the two graphene sheets covalently bond together into a SWNT (a(2)). Atoms are desorbed at high temperature (a(3)).  FIG. 3   b  (1)-(3) show the formation of a larger SWNT from two 3.1-nm-wide and 2.6-nm-wide graphene nanoribbons and adsorption of H atoms to a surface coverage of 50%. 
           [0010]      FIG. 4  includes schematics of H adsorption on graphene nanoribbons (a, b, and d), and theoretical calculations relating to the adsorption of H atoms on graphene nanoribbons (c, e). 
           [0011]      FIG. 5  depicts the bending of a graphene nanoribbon where the nanoribbon width W is much greater than the circumference 2πR of the SWNT. 
       
    
    
     DETAILED DESCRIPTION 
       [0012]    The present invention provides methods for forming nanotubes from thin films. The films are desirably a single atom thick, as in the case of graphene nanoribbons, or only a few (e.g., 2-10) atomic layers thick, as in the case of semiconductor, metal, or other material films. The methods involve the adsorption of atoms onto the surface of the films. The adsorbed atoms introduce a surface stress, inducing a curvature in the films. As a result of this curvature, edges of the thin films are brought into contact with each other, or with edges of other thin films. Covalent bonds form between the edges, resulting in nanotube formation. 
         [0013]    In one embodiment of the present invention, the method for forming a nanotube comprises three steps. In a first step, a thin film is patterned onto a substrate. Various substrate materials may be used, including graphite. The film may comprise a variety of different shapes having different dimensions. The width of the thin films will depend on the desired diameter of the nanotubes. In some embodiments, the width is in the range of 1 to 20 nm. In other embodiments, the width is in the range of 1 to 10 nm. In yet other embodiments, the width is in the range of 1 to 2 nm. The length of the films, while not critical to the method, is generally many times greater than the width of the nanoribbon. 
         [0014]    The films may be defined using semiconductor processing techniques, such as lithography, patterning and etching. This is advantageous because it provides an inexpensive parallel process capable of making many identical, or different, sized films in a single run. In the case of graphite, stacks of many layers of graphene may be defined in the substrate. In this embodiment, each graphene layer in the stack provides a separate thin film. 
         [0015]    After the thin film has been formed, atoms are adsorbed to its surface. Atoms or combinations of atoms may be adsorbed onto the films. Many different atoms may be used for this purpose. The only requirement is that the selected atoms introduce a surface stress on the thin film that induces a curvature in the film when they are absorbed onto the film. As a result, film edges are brought together, where they undergo covalent or other chemical bonding to form nanotubes. In some embodiments, the adsorbed atoms are selected from the group consisting of H atoms, F atoms, and combinations thereof. The adsorption step can provide different surface coverages of adsorbed atoms. Because the degree of surface coverage will affect the radius of curvature, the degree of surface coverage will depend on the desired diameter of the nanotubes. In some embodiments, the surface coverage is in the range of about 40% to 60%. The adsorption step may be accomplished at room temperature. 
         [0016]    Once the nanotube has formed, the adsorbed atoms are desorbed from the surface of the film. Desorption may be accomplished at a high temperature. For example, the desorption of H atoms from a graphene sheet may be carried out at 600 K or higher. 
         [0017]    In one variation of the method, the nanotubes are formed from a single thin film, whereby the adsorbent-induced curvature causes opposing edges of the film to meet and form covalent or other chemical bonds. Examples 1 and 2, below, illustrate this variation of the method. 
         [0018]    In another variation of the method, a nanotube is formed from a plurality (e.g., two) of layered thin films. In such methods, atoms are adsorbed onto the surface of one or more of the films, causing the edges of the films to contact and form covalent and other chemical bonds, resulting in the formation of a closed tube. In some such embodiments, the widths of the two nanoribbons are substantially the same, while in other embodiments the widths are different. Example 3, below, illustrates this variation of the present methods. 
         [0019]    Without wishing to be bound to a particular theory, it is hypothesized that the driving force for the formation of nanotubes from films according to the present invention is the stress induced by the adsorption of atoms on the surface of the films. For a given atomic surface coverage, the thinner the film, the larger the bending curvature, and the smaller the radius of the bending curvature. 
         [0020]    As noted above, the magnitude of the bending curvature can be controlled by adjusting the coverage of adsorbed atoms to tune the magnitude of the surface-adsorption-induced stress. This is illustrated for the case of a graphene nanoribbon in  FIG. 4 . As illustrated in  FIG. 4   a , first-principle MD calculations show that the preferred H adsorption site on a graphene nanoribbon is on top of a carbon atom. As depicted in  FIG. 4   b , H adsorption leads to a transition of the bonding configuration of the underlying carbon atom from sp 2  to sp 3 . As a result, the carbon atom is pulled up by about 0.3 Å, while its three neighboring carbon atoms are pushed out and down, inducing a tensile stress in the graphene nanoribbon. Calculations also show that the induced stress and bending curvature increases linearly with H coverage, as shown in  FIG. 4   c . A maximum H coverage of 50% corresponds to the experimentally determined upper limit of H adsorption on graphite surfaces. Zecho, T., Guttler, A., Sha, X. W., Jackson, B. &amp; Kuppers, J., Adsorption of hydrogen and deuterium atoms on the (0001) graphite surface,  J. Chem. Phys.  117, 8486-8492 (2002). 
         [0021]    For carbon nanotube formation from graphene nanoribbons, the appropriate surface coverage will determine the width of the patterned nanoribbon. To form a perfectly closed tube, the nanoribbon width, W, should approximate 2πR, where R is the radius of bending curvature as defined by the surface coverage of adsorbed atoms. As shown in  FIG. 5 , if W is much larger than 2πR, two open nanotubes will form at the opposite edges of the nanoribbon. Alternatively, if W is much smaller than 2πR, the nanoribbon will bend, but the opposite edges will not meet to form a completely closed tube. 
         [0022]    Another important consideration for carbon nanotube formation is that the patterned graphene nanoribbon is not a free-standing film, but is weakly bonded to the underlying substrate through van der Waals attractive forces. The surface stress induced by atomic adsorption should be large enough to overcome this attraction in order for the graphene nanoribbon to detach from the underlying substrate during the bending process. For example, a particular surface coverage of H atoms induces a surface stress, σ, resulting in a bending moment of M=σt/2, where t is the “effective” film thickness, including the adsorbent layer ( FIG. 4   d ). This moment, M, can be viewed as an upward force F at the midpoint of the nanoribbon, F=2σt/W, where W is the nanoribbon width. In order to detach the nanoribbon from the underlying substrate, F should be greater than or equal to F vdW , the van der Waals force of attraction. Therefore, for a given surface stress σ (i.e., H coverage), the maximum width of the graphene nanoribbon is desirably W m =2σt/F vdW . 
         [0023]    Because 2πR≦W m , the existence of a maximum nanoribbon width sets an upper limit on the radius R of the formed nanotube. In principle, because R ∝ 1/σ, as shown in  FIG. 4   e , it is possible to decrease atomic surface coverage, which decreases the induced surface stress σ, in order to achieve a larger R. However,  FIG. 4   e  also shows that W m  ∝ σ. Therefore, the maximum radius R is determined by the crossing point of the curves in  FIG. 4   e . For H adsorption, the crossing point is at a surface stress of about 380 meV/Å 2 , corresponding to a maximum nanotube radius R of about 0.7 nm. However, these radial limitations may be overcome by forming carbon nanotubes from layered graphene nanoribbons, as described in Example 3. 
         [0024]    The formation of carbon nanotubes from graphene nanoribbons using atomic adsorption is further illustrated by the following non-limiting examples. 
       EXAMPLES 
       [0025]    Methods: Unless otherwise specified, the following methods were used in the examples below. 
       First-Principles MD Simulations 
       [0026]    First-principles MD simulations were performed using the pseudopotential plane-wave method within the local density approximation as implemented in the VASP code. Kresse, G. &amp; Haiher, J., Ab initio molecular dynamics for liquid metals,  Phys. Rev. B  47, 558-561 (1993). Single Γ k-point for Brillouin zone sampling and plane wave cutoffs of 21.3 Ryd (H-C system) and 31.2 Ryd (F-C system) were used. The super cell dimension was 27.016×4.2532×23 Å 3  with a vacuum layer of ˜15 Å. As shown in  FIG. 1 , the system contained a maximum of about 90 atoms. The graphite layer underneath the graphene nanoribbon was fixed at the bulk position. The equation of atomic motions was integrated using the Verlet algorithm with a time step of 0.5 fs. Total simulation times of up to 3 ps were used. 
       Classical MD Simulations 
       [0027]    Classical MD simulations were performed using a modified form of the bond-order potential developed by Brenner et al. Brenner, D. W., et al., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons,  J. Phys. - Cond. Matt.  14, 783-802 (2002). Because the original Brenner potential predicted an H adsorption energy of about 2.6 eV, a new bond-order term was introduced for the C—H bond to give an H adsorption energy of about 0.9 eV on graphite, as predicted by the first-principles calculations. In addition, Lennard-Jones potential parameters were developed to give a ˜42 meV/atom interlayer cohesive energy for graphite, in accordance with experiments. Girifalco, L. A. &amp; Lad, R. A., Energy of cohesion, compressibility, and the potential energy functions of the graphite system,  J. Chem. Phys.  25, 693-697 (1956). As shown in  FIGS. 2 and 3 , the system contained about 1200 atoms. Two graphite layers were placed underneath the graphene nanoribbon, with the bottom layer fixed at the bulk position. Given that the tube length is usually much greater than the tube diameter, the periodic boundary condition along the tube axis represents an infinite long tube for the purposes of these calculations. However, simulations using a finite tube length and free ends gave the same results. The equation of atomic motions was integrated using the Verlet algorithm with a time step of 0.2 fs. Total simulation times of up to 2 ns were used. 
       Example 1 
     Simulation of SWNTs using First-Principles MD Simulations 
       [0028]    Single-walled carbon nanotubes were simulated using first-principles MD simulations. In the simulations, a 1.7-nm-wide graphene nanoribbon was patterned onto a graphite substrate ( FIG. 1   a  (1)). Next, H atoms were randomly adsorbed onto the surface of the graphene nanoribbon to a coverage of 50% ( FIG. 1   a  (2)). As shown in  FIG. 1   a  (3), the adsorption of H atoms introduced a surface stress which caused the opposite edges of the graphene nanoribbon to fold downward.  FIG. 1   a  (4) shows the graphene nanoribbon detaching from the underlying graphite substrate.  FIG. 1   a  (5) shows the opposite edges of the graphene nanoribbon bonded together to form an SWNT. Similarly,  FIG. 1   b  (1)-(5) illustrate the simulation of an SWNT using a 2.0 nm wide graphene nanoribbon and adsorption of F atoms to a surface coverage of 45%. 
       Example 2 
     Simulation of SWNTs using Classical MD Simulations 
       [0029]    Classical MD simulations were used to simulate armchair and zigzag SWNTs.  FIG. 2   a  shows snapshots of the formation of a 0.5-nm-diameter (4, 4) armchair SWNT. In the simulations, a 1.6-nm-wide, (3.5, 3.5) graphene nanoribbon was patterned onto a graphite substrate comprised of two graphite layers. Next, H atoms were adsorbed to the surface of the graphene nanoribbon at room temperature to a coverage of 50% ( FIG. 2   a  (1)). Tube formation is shown in  FIG. 2   a  (2)-(3). Finally, the SWNT was heated to 1800 K to desorb the surface H atoms ( FIG. 2   a  (4)-(6)). A sideview of the armchair SWNT is shown in  FIG. 2(   c ). Similarly,  FIG. 2   b  (1)-(6) illustrate the formation of a 0.9-nm-diameter (14, 0) zigzag SWNT, using a 3.3-nm-wide, (13, 0) graphene nanoribbon and adsorption of H atoms to 45% surface coverage.  FIG. 2(   d ) shows a sideview of the zigzag SWNT. 
       Example 3 
     Simulation of SWNTs from Two Layers of Graphene Nanoribbons 
       [0030]    Single-walled carbon nanotubes were simulated from two layers of graphene nanoribbons using classical MD simulations. As shown in  FIG. 3   a  (1), a 1.6-nm-wide top layer graphene nanoribbon and a 1.1-nm-wide bottom layer graphene nanoribbon were patterned onto a graphite substrate. H atoms introduced at room temperature to 50% coverage adsorb onto the top layer graphene nanoribbon, causing it to bend downward. During tube formation, the two layers of graphene nanoribbons become “stitched” together to form a single 1.0 nm diameter SWNT ( FIG. 3   a  (2)). Finally, the SWNT was heated to 1800 K to desorb the surface H atoms ( FIG. 3   a  (3)). Similarly,  FIG. 3   b  illustrates the formation of a 2.2-nm-diameter SWNT using a 3.1-nm-wide, top-layer graphene nanoribbon and a 2.6-nm-wide, bottom-layer graphene nanoribbon and adsorption of H atoms to 50% coverage. 
         [0031]    For the purposes of this disclosure, and unless otherwise specified, “a” or “an” means “one or more.” All patents, applications, references, and publications cited herein are incorporated by reference in their entirety to the same extent as if they were individually incorporated by reference. 
         [0032]    As will be understood by one skilled in the art, for any and all purposes, particularly in terms of providing a written description, all ranges disclosed herein also encompass any and all possible subranges and combinations of subranges thereof. Any listed range can be easily recognized as sufficiently describing and enabling the same range being broken down into at least equal halves, thirds, quarters, fifths, tenths, etc. As a non-limiting example, each range discussed herein can be readily broken down into a lower third, middle third and upper third, etc. As will also be understood by one skilled in the art, all language such as “up to,” “at least,” “greater than,” “less than,” and the like includes the number recited and refers to ranges which can be subsequently broken down into subranges as discussed above. Finally, as will be understood by one skilled in the art, a range includes each individual member. 
         [0033]    It is understood that the invention is not confined to the particular embodiments set forth herein as illustrative, but embraces all such forms thereof as come within the scope of the following claims.