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The formation of low-dimensional chiral inorganic nanotubes by filling single-walled carbon nanotubes
Chemical Physics Letters 397 (2004) 340–343 www.elsevier.com/locate/cplett
The formation of low-dimensional chiral inorganic nanotubes by filling single-walled carbon nanotubes Mark Wilson
*
Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK Received 7 April 2004; in final form 9 August 2004 Available online 25 September 2004
Abstract Two classes of ionic inorganic nanotube (IINT) are predicted to form within carbon nanotubes via the use of ion-based computer simulation models. These structures can be rationalised (and labelled) in terms of folding infinite two-dimensional sheets of hexagons and squares, respectively. Many of the formed IINTs appear twisted (and hence are stereochemically active) and is shown to be a result of the strong electrostatic interactions which control these structures. Such filling offers the opportunity of producing IINTs in a highly controlled (morphological and stereochemical) fashion. Furthermore, the electronic properties of these tubes should be tunable. 2004 Elsevier B.V. All rights reserved.
The growth of low-dimensional crystallites within carbon nanotubes has been the focus of significant high resolution transmission electron microscopy (HRTEM) experimental study over the past decade (see [1,2] for reviews). Theoretical work (based on the use of potential models), supported by more recent experiments [3], has uncovered the possible existence of a range of inorganic nanotubular structures [4–7]. The use of relatively simple potential models has allowed for effective phase diagrams, as a function of the carbon nanotube pore diameter, to be mapped. These phase diagrams indicate the existence of a rich variety of low-dimensional (predominantly chiral) crystals whose structures may be unique to the tubular confining environment and which have not yet been observed experimentally. Analogous nanotubular structures have been observed or predicted for a range of materials (GaN, GaSe, B/C composites, MoS2, WS2, NiCl2) [8–11] although experimental growth requires the use of extreme conditions with a corresponding loss of product control. *
Fax: + 44 20 7679 7463. E-mail address: [email protected].
0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.08.036
At the simplest level, simulation models may be used to interpret existing HRTEM experimental data (responsive mode). This is, in itself, extremely useful since the interpretation of the internal structures becomes highly problematic once their structure becomes removed from easily recognisable bulk fragments. The application of potential models, operative in a predictive mode, opens the door to an understanding of the factors controlling, and the mechanisms of formation of, these nanostructures. Such an understanding may lead to the ability to grow structures in a controlled fashion using the carbon nanotube as a template, leading to the ability to exploit and control potentially interesting electronic properties, potential stereochemical control (passing of chiral information between the outer and inner nanotubes), and potential uses as low friction materials [12–14] and nanoropes [15,16]. In this Letter, we demonstrate how the stability of two classes of ionic inorganic nanotube (IINT) can be rationalised by using simple (and physically related) atomistic ionic models and considering the underlying bulk structures. The morphology of the structures formed inside the carbon nanotubes can be expressed
M. Wilson / Chemical Physics Letters 397 (2004) 340–343
in a nomenclature analogous to that used to describe the carbon nanotubes themselves [17]. In addition we will show how the mechanism of formation of these crystals, which form directly by filling the carbon nanotubes from the bulk ionic liquid, can be understood. The simulation potentials employed are simple ionbased models using full formal ion charges and a pairwise additive description of the short-range interactions, augmented with a description of the (many-body) ion polarization (see [18] for details). The carbon nanotubes are considered as fixed with the ion–carbon interactions accounted for using standard Lennard–Jones potentials. Two models are considered in the present work. In the first (hereafter referred to as model I) the potential parameters are chosen so as to reproduce a range of properties of KI. This system is chosen for two reasons. Firstly, the filling of carbon nanotubes by liquid KI has been extensively studied by HRTEM [19,20]. Secondly, this model acts as an archetypal system which crystallises into a rocksalt (B1, six-coordinate [octahedral] ions) structure. The potential parameters for the second model (model II) are chosen, by contrast, so as to predict a wurtzite (B4, four-coordinate [tetrahedral] ions) crystal structure and so this model is a useful paradigm for a range of important semiconducting materials. Two basic simulation methodologies are employed. In the first, the direct filling of the carbon nanotubes is observed using molecular dynamics in which empty nanotubes, which vary in both diameter and morphology, are immersed in the bulk liquids (see [4,5] for details). Secondly, energy minimisations, employing a steepest descent method, are performed on a range of possible internal crystal structures which are set up directly. The advantage of combining these methodologies is that any structures which form inside the tubes as a result of the direct filling simulations can then be incorporated into the energy minimisations (which allow for the construction of an effective phase diagram for the internal crystal structures as a function of the carbon nanotube pore radii). As a result, the requirement to use only structures imagined as being significant is effectively removed. Fig. 1a,b shows molecular graphics snapshots of the IINT structures formed inside two carbon nanotubes (of morphology (11,11) and (16,0), diameters 14.94 and ˚ , respectively) generated for models I and II. 12.55 A In both cases the internal structures formed are clearly crystalline in nature and are indicative of the existence of two basic classes of IINT. In the case of model I (which predicts the six-coordinate rocksalt as the bulk ground-state structure) the crystals formed can be considered as constructed from a tesselation of 2 · 2 square-nets, each of which consist of two anion–cation pairs. For model II (for which the four-coordinate tetrahedral wurtzite is predicted to be the ground-state crystal structure) the structures formed are based on
341
(16,0)
(11,11)
(a)
(b)
Major axis
Fig. 1. (a) Molecular graphics snapshots of the two ionic inorganic nanotube (IINT) structures formed from models I (lower panel) and II (upper panel), respectively. The yellow (smallest) circles represent the carbon nanotube templates (of morphologies (16,0) and (11,11), respectively) and are cut off in order to highlight the internal IINT structures. The red and magenta circles represent the cations and anions in the two IINTs which are of morphology (3,2)sq (lower) and (3,2)hex (upper), respectively. In both cases a linked chain of tesselating polyhedra (hexagons in the upper panel and squares in the lower) are highlighted in order to show the twisting of the formed IINTs which makes them stereochemically active. Each IINT shown is the mean structure calculated by averaging over 100 configurations (3 ps of molecular dynamics) in a fully filled carbon nanotube. (b) Molecular graphics snapshots of the mean (3,2)hex and (3,2)sq structures with the templating carbon nanotubes removed for clarity. The left figures show how the view perpendicular to the nanotube major axis with the righthand figures showing the view along the major axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
tesselating hexagons which consist of three anion–cation pairs. As a result, the nearest-neighbour anion–cation coordination numbers are four and three for the structures based on the tesselating squares and hexagons, respectively. The hexagon-based nanostructures can be considered as constructed by folding a graphene-like sheet (but in which the two atoms in the unit cell have different chemical identities) in the analogue of the relationship between the pure carbon nanotubes and a single
342
M. Wilson / Chemical Physics Letters 397 (2004) 340–343
ofpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the formed IINT), L = jChj, is given by a0 n2 þ m2 þ nm, whilst, for thepnanotubes formed ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi from the square-net sheets, L ¼ a0 n2 þ m2 , the difference simple reflecting the areas of the two-dimensional unit cells. The above analysis of the direct filling simulations indicates the stability of two classes of ionic inorganic nanotube, based on the folding of hexagonal and square-planar sheets, respectively. It is useful, therefore, to consider the experimental HRTEM data in this context. The mixed halide system AgCl/AgBr has been shown to form a crystallite inside a carbon nanotube ˚ ) whose structure was rationalised in (diameter 14.0 A terms of extracting a section from the bulk (wurtzite) crystal structure [21]. In the context of the present work, the same structure can equally be rationalised as a (3,0)hex nanotube formed by folding a hexagonal plane constructed from the mixed halide (as in Fig. 2a). For the 2 · 2 square net-based crystallites, liquid KI has been shown to fill a carbon nanotube of diameter ˚ to form a structure which is again rationalised 13.6 A in term of the underlying (rocksalt) bulk crystal structure. In this case the structure formed can be considered
graphene sheet. Fig. 2a shows such a graphene-like hexagonal plane, along with the unit cell vectors {a1,a2}, highlighting the chiral vector Ch (”na1 + ma2) and associated translational vector, T, which determine the direction along which the sheet is folded and the direction of the resulting nanotube major axis. The chiral vector highlighted is that required to form the (3,2)hex IINT formed inside the (16,0) C-SWNT (and shown in Fig. 1b). The hex notation indicates that the nanotube is formed by folding the sheet of hexagons as shown. An analogous analysis can be constructed in order to rationalise the square net-based structures formed by model I. Fig. 2b shows a plane of square-nets (equivalent to considering a single {1 1 0} plane from a rocksalt structure) constructed from a simple two ion unit cell (highlighted) using the orthogonal cell vectors {a1,a2} shown. As an example, the figure highlights the chiral vector, and associated translational vector, required to give the (3,2)sq IINT formed inside the (11,11) C-SWNT and highlighted in Fig. 1a. The sq notation indicates that the tube is formed by folding a plane of tesselating 2 · 2 square-nets. The length of the chiral vector formed from the hexagonal sheets (and hence the circumference
T
(3,2)
Ch a2
(a)
a1
a0 T
(3,2)
a2
Ch
a1 (b)
a0
Fig. 2. The construction of the observed IINTs from corresponding planar structures for: (a) the hexagon, and (b) the square-based crystallites. The red and blue circles represent the two ionic species. Ch is the chiral vector along which both structures must be folded in order to form the (3,2)hex and (3,2)sq IINTs, respectively (as shown in the figure and as shown formed directly from the simulated liquid in Fig. 1). The T-vectors (for which Ch Æ T = 0) become the IINT major axes. The planar structures have their respective two-ion unit cells highlighted along with the associated cell vectors {a1,a2} and unit cell length a0.
M. Wilson / Chemical Physics Letters 397 (2004) 340–343
as constructed from successive layers of bi-molecular squares which link to form an infinite crystallite (termed a 2 · 2 crystal as the crystal is 2 ions in width) [19,20]. Such a structure can be rationalised in terms of folding the square plane sheet (Fig. 2b), giving a (2,2)sq IINT. The formation mechanism of these nanotubular structures can be readily understood in terms of the dominant ionic interatomic forces present in both models employed. In a narrow pore, such as that offered by the template carbon nanotube, the strong coulombic ion–ion forces (which are both attractive and repulsive) effectively reduce the number of readily accessible configurations whilst the relative ion radii control the thermodynamic stability of the three- and four-coordinate (hexagonal and square-based) sheets. For example, for the (2,2)sq IINT, a single ion place on the inner wall of the carbon nanotube will effectively govern the location of the other ions in the tube (as illustrated in Fig. 3a). The formation of the twisted structures, such as the (3,2)sq IINT shown in Fig. 1, can be explained using the same rationale with the twisting of the forming IINT resulting from the necessity to avoid nearest-neighbour like-like ion–ion interactions (as shown in Fig. 3b). Analogous arguments predict the stability of the hexagon-based structures. The diameter of the formed IINTs are, therefore, controlled by the diameter of the confining carbon nanotube. However, multiple filling simulations employing distinct liquid starting configurations, demonstrate that more than one IINT morphology (with similar diameters) may form within a given carbon nanotube, indicative of a significant element of kinetic control over the IINT growth morphology.
+ –
+
– + y
y x
z
+ – + + –
+ y
y x
z
Fig. 3. Schematic representation of the role of the electrostatic forces in determining the IINT structures formed inside a given carbon nanotube. The left to centre panels show how a single cation effectively determines the locations of the other ions in the xy-plane (perpendicular to the major axis of the carbon template). The nanotube diameter effectively controls the number of ions that can fit in this xy crosssection. The lower panel shows how the twisting of the IINTs may arise in order to overcome potential repulsive like-ion interactions in the xy-plane.
343
A potentially significant aspect of both classes of inorganic nanotube is that they may form chiral nanotubes in an analogue of those formed by pure carbon tubes. Indeed, both the (3,2)sq and (3,2)hex nanotubes shown in Figs. 1 and 2 are specific enantiomers of that morphology. As a result, it may be possible to control the stereochemistry of the growing IINTs with respect to that of the confining carbon nanotube. Such control may be significant since the electronic properties of these materials may vary as a function of both the diameter and morphology. Indeed, the present calculations can act as a useful feed into higher level (and hence much more computationally demanding) calculations. Recent experiments support the theoretical observation that the morphology of the crystallites formed inside the nanotubes may be relatively complex and unique to the low-dimensional confining environment [3]. The extraction of these structures from the experimental HRTEM images does, however, become problematic owing to this inherent complexity. The simple models presented here may greatly aid the interpretation of these data.
References [1] J. Sloan, A.I. Kirkland, J.L. Hutchison, M.L.H. Green, Chem. Commun. (2002) 1319. [2] J. Sloan, A.I. Kirkland, J.L. Hutchison, M.L.H. Green, C.R. Physique 4 (2003) 1063. [3] P. Eilidh, J. Sloan, A.I. Kirkland, R.R. Meyer, S. Friedrichs, J.L. Hutchison, M.L.H. Green, Nature Mater. 2 (2003) 788. [4] M. Wilson, P.A. Madden, J. Am. Chem. Soc. 123 (2001) 2101. [5] M. Wilson, J. Chem. Phys. 116 (2002) 3027. [6] M. Wilson, Chem. Phys. Lett. 366 (2002) 504. [7] M. Wilson, Nano Lett. 4 (2004) 299. [8] R. Tenne, Colloids Surf. A 208 (2002) 83. [9] M.L. Cohen, Mater. Sci. Eng. C 15 (2001) 1. [10] S.M. Lee, Y.H. Lee, Y.G. Hwang, J. Elsner, D. Porezag, T. Frauenheim, Phys. Rev. B 60 (1999) 7788. [11] M. Coˆte´, M.L. Cohen, D.J. Chadi, Phys. Rev. B 58 (1998) R4277. [12] S. Prasad, J. Zabinski, Nature 387 (1997) 761. [13] L. Rapoport, Yu. Bilik, Y. Feldman, M. Homyonfer, S.R. Cohen, R. Tenne, Nature 387 (1997) 791. [14] L. Rapoport, N. Fleischer, R. Tenne, Adv. Mater. 15 (2003) 651. [15] M. Remsˇkar, Z. Sˇkraba, R. Sanjine´s, F. Le´vy, Appl. Phys. Lett. 74 (1999) 3633. [16] M. Remsˇkar, Z. Sˇkraba, M. Regula, C. Ballif, R. Sanjine´s, F. Le´vy, Adv. Mater. 10 (1998) 246. [17] R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, London, UK, 1998. [18] P.A. Madden, M. Wilson, Chem. Soc. Rev. 25 (1996) 339. [19] J. Sloan, M.C. Novotny, S.R. Bailey, G. Brown, C. Xu, V.C. Williams, S. Friedrichs, E. Flahaut, R.L. Callendar, A.P.E. York, K.S. Coleman, M.L.H. Green, R.E. Dunin-Borkowski, J.L. Hutchison, Chem. Phys. Lett. 329 (2000) 61. [20] R.R. Meyer, J. Sloan, R.E. Dunin-Borkowski, A.I. Kirkland, M.C. Novotny, S.R. Bailey, J.L. Hutchison, M.L.H. Green, Science 289 (2000) 1324. [21] J. Sloan, M. Terrones, S. Nufer, S. Friedrichs, S.R. Bailey, H.-G. Woo, M. Ru¨hle, J.L. Hutchison, M.L.H. Green, J. Am. Chem. Soc. 124 (2002) 2116.
The formation of low-dimensional chiral inorganic nanotubes by filling single-walled carbon nanotubes Mark Wilson
*
Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK Received 7 April 2004; in final form 9 August 2004 Available online 25 September 2004
Abstract Two classes of ionic inorganic nanotube (IINT) are predicted to form within carbon nanotubes via the use of ion-based computer simulation models. These structures can be rationalised (and labelled) in terms of folding infinite two-dimensional sheets of hexagons and squares, respectively. Many of the formed IINTs appear twisted (and hence are stereochemically active) and is shown to be a result of the strong electrostatic interactions which control these structures. Such filling offers the opportunity of producing IINTs in a highly controlled (morphological and stereochemical) fashion. Furthermore, the electronic properties of these tubes should be tunable. 2004 Elsevier B.V. All rights reserved.
The growth of low-dimensional crystallites within carbon nanotubes has been the focus of significant high resolution transmission electron microscopy (HRTEM) experimental study over the past decade (see [1,2] for reviews). Theoretical work (based on the use of potential models), supported by more recent experiments [3], has uncovered the possible existence of a range of inorganic nanotubular structures [4–7]. The use of relatively simple potential models has allowed for effective phase diagrams, as a function of the carbon nanotube pore diameter, to be mapped. These phase diagrams indicate the existence of a rich variety of low-dimensional (predominantly chiral) crystals whose structures may be unique to the tubular confining environment and which have not yet been observed experimentally. Analogous nanotubular structures have been observed or predicted for a range of materials (GaN, GaSe, B/C composites, MoS2, WS2, NiCl2) [8–11] although experimental growth requires the use of extreme conditions with a corresponding loss of product control. *
Fax: + 44 20 7679 7463. E-mail address: [email protected].
0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.08.036
At the simplest level, simulation models may be used to interpret existing HRTEM experimental data (responsive mode). This is, in itself, extremely useful since the interpretation of the internal structures becomes highly problematic once their structure becomes removed from easily recognisable bulk fragments. The application of potential models, operative in a predictive mode, opens the door to an understanding of the factors controlling, and the mechanisms of formation of, these nanostructures. Such an understanding may lead to the ability to grow structures in a controlled fashion using the carbon nanotube as a template, leading to the ability to exploit and control potentially interesting electronic properties, potential stereochemical control (passing of chiral information between the outer and inner nanotubes), and potential uses as low friction materials [12–14] and nanoropes [15,16]. In this Letter, we demonstrate how the stability of two classes of ionic inorganic nanotube (IINT) can be rationalised by using simple (and physically related) atomistic ionic models and considering the underlying bulk structures. The morphology of the structures formed inside the carbon nanotubes can be expressed
M. Wilson / Chemical Physics Letters 397 (2004) 340–343
in a nomenclature analogous to that used to describe the carbon nanotubes themselves [17]. In addition we will show how the mechanism of formation of these crystals, which form directly by filling the carbon nanotubes from the bulk ionic liquid, can be understood. The simulation potentials employed are simple ionbased models using full formal ion charges and a pairwise additive description of the short-range interactions, augmented with a description of the (many-body) ion polarization (see [18] for details). The carbon nanotubes are considered as fixed with the ion–carbon interactions accounted for using standard Lennard–Jones potentials. Two models are considered in the present work. In the first (hereafter referred to as model I) the potential parameters are chosen so as to reproduce a range of properties of KI. This system is chosen for two reasons. Firstly, the filling of carbon nanotubes by liquid KI has been extensively studied by HRTEM [19,20]. Secondly, this model acts as an archetypal system which crystallises into a rocksalt (B1, six-coordinate [octahedral] ions) structure. The potential parameters for the second model (model II) are chosen, by contrast, so as to predict a wurtzite (B4, four-coordinate [tetrahedral] ions) crystal structure and so this model is a useful paradigm for a range of important semiconducting materials. Two basic simulation methodologies are employed. In the first, the direct filling of the carbon nanotubes is observed using molecular dynamics in which empty nanotubes, which vary in both diameter and morphology, are immersed in the bulk liquids (see [4,5] for details). Secondly, energy minimisations, employing a steepest descent method, are performed on a range of possible internal crystal structures which are set up directly. The advantage of combining these methodologies is that any structures which form inside the tubes as a result of the direct filling simulations can then be incorporated into the energy minimisations (which allow for the construction of an effective phase diagram for the internal crystal structures as a function of the carbon nanotube pore radii). As a result, the requirement to use only structures imagined as being significant is effectively removed. Fig. 1a,b shows molecular graphics snapshots of the IINT structures formed inside two carbon nanotubes (of morphology (11,11) and (16,0), diameters 14.94 and ˚ , respectively) generated for models I and II. 12.55 A In both cases the internal structures formed are clearly crystalline in nature and are indicative of the existence of two basic classes of IINT. In the case of model I (which predicts the six-coordinate rocksalt as the bulk ground-state structure) the crystals formed can be considered as constructed from a tesselation of 2 · 2 square-nets, each of which consist of two anion–cation pairs. For model II (for which the four-coordinate tetrahedral wurtzite is predicted to be the ground-state crystal structure) the structures formed are based on
341
(16,0)
(11,11)
(a)
(b)
Major axis
Fig. 1. (a) Molecular graphics snapshots of the two ionic inorganic nanotube (IINT) structures formed from models I (lower panel) and II (upper panel), respectively. The yellow (smallest) circles represent the carbon nanotube templates (of morphologies (16,0) and (11,11), respectively) and are cut off in order to highlight the internal IINT structures. The red and magenta circles represent the cations and anions in the two IINTs which are of morphology (3,2)sq (lower) and (3,2)hex (upper), respectively. In both cases a linked chain of tesselating polyhedra (hexagons in the upper panel and squares in the lower) are highlighted in order to show the twisting of the formed IINTs which makes them stereochemically active. Each IINT shown is the mean structure calculated by averaging over 100 configurations (3 ps of molecular dynamics) in a fully filled carbon nanotube. (b) Molecular graphics snapshots of the mean (3,2)hex and (3,2)sq structures with the templating carbon nanotubes removed for clarity. The left figures show how the view perpendicular to the nanotube major axis with the righthand figures showing the view along the major axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
tesselating hexagons which consist of three anion–cation pairs. As a result, the nearest-neighbour anion–cation coordination numbers are four and three for the structures based on the tesselating squares and hexagons, respectively. The hexagon-based nanostructures can be considered as constructed by folding a graphene-like sheet (but in which the two atoms in the unit cell have different chemical identities) in the analogue of the relationship between the pure carbon nanotubes and a single
342
M. Wilson / Chemical Physics Letters 397 (2004) 340–343
ofpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the formed IINT), L = jChj, is given by a0 n2 þ m2 þ nm, whilst, for thepnanotubes formed ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi from the square-net sheets, L ¼ a0 n2 þ m2 , the difference simple reflecting the areas of the two-dimensional unit cells. The above analysis of the direct filling simulations indicates the stability of two classes of ionic inorganic nanotube, based on the folding of hexagonal and square-planar sheets, respectively. It is useful, therefore, to consider the experimental HRTEM data in this context. The mixed halide system AgCl/AgBr has been shown to form a crystallite inside a carbon nanotube ˚ ) whose structure was rationalised in (diameter 14.0 A terms of extracting a section from the bulk (wurtzite) crystal structure [21]. In the context of the present work, the same structure can equally be rationalised as a (3,0)hex nanotube formed by folding a hexagonal plane constructed from the mixed halide (as in Fig. 2a). For the 2 · 2 square net-based crystallites, liquid KI has been shown to fill a carbon nanotube of diameter ˚ to form a structure which is again rationalised 13.6 A in term of the underlying (rocksalt) bulk crystal structure. In this case the structure formed can be considered
graphene sheet. Fig. 2a shows such a graphene-like hexagonal plane, along with the unit cell vectors {a1,a2}, highlighting the chiral vector Ch (”na1 + ma2) and associated translational vector, T, which determine the direction along which the sheet is folded and the direction of the resulting nanotube major axis. The chiral vector highlighted is that required to form the (3,2)hex IINT formed inside the (16,0) C-SWNT (and shown in Fig. 1b). The hex notation indicates that the nanotube is formed by folding the sheet of hexagons as shown. An analogous analysis can be constructed in order to rationalise the square net-based structures formed by model I. Fig. 2b shows a plane of square-nets (equivalent to considering a single {1 1 0} plane from a rocksalt structure) constructed from a simple two ion unit cell (highlighted) using the orthogonal cell vectors {a1,a2} shown. As an example, the figure highlights the chiral vector, and associated translational vector, required to give the (3,2)sq IINT formed inside the (11,11) C-SWNT and highlighted in Fig. 1a. The sq notation indicates that the tube is formed by folding a plane of tesselating 2 · 2 square-nets. The length of the chiral vector formed from the hexagonal sheets (and hence the circumference
T
(3,2)
Ch a2
(a)
a1
a0 T
(3,2)
a2
Ch
a1 (b)
a0
Fig. 2. The construction of the observed IINTs from corresponding planar structures for: (a) the hexagon, and (b) the square-based crystallites. The red and blue circles represent the two ionic species. Ch is the chiral vector along which both structures must be folded in order to form the (3,2)hex and (3,2)sq IINTs, respectively (as shown in the figure and as shown formed directly from the simulated liquid in Fig. 1). The T-vectors (for which Ch Æ T = 0) become the IINT major axes. The planar structures have their respective two-ion unit cells highlighted along with the associated cell vectors {a1,a2} and unit cell length a0.
M. Wilson / Chemical Physics Letters 397 (2004) 340–343
as constructed from successive layers of bi-molecular squares which link to form an infinite crystallite (termed a 2 · 2 crystal as the crystal is 2 ions in width) [19,20]. Such a structure can be rationalised in terms of folding the square plane sheet (Fig. 2b), giving a (2,2)sq IINT. The formation mechanism of these nanotubular structures can be readily understood in terms of the dominant ionic interatomic forces present in both models employed. In a narrow pore, such as that offered by the template carbon nanotube, the strong coulombic ion–ion forces (which are both attractive and repulsive) effectively reduce the number of readily accessible configurations whilst the relative ion radii control the thermodynamic stability of the three- and four-coordinate (hexagonal and square-based) sheets. For example, for the (2,2)sq IINT, a single ion place on the inner wall of the carbon nanotube will effectively govern the location of the other ions in the tube (as illustrated in Fig. 3a). The formation of the twisted structures, such as the (3,2)sq IINT shown in Fig. 1, can be explained using the same rationale with the twisting of the forming IINT resulting from the necessity to avoid nearest-neighbour like-like ion–ion interactions (as shown in Fig. 3b). Analogous arguments predict the stability of the hexagon-based structures. The diameter of the formed IINTs are, therefore, controlled by the diameter of the confining carbon nanotube. However, multiple filling simulations employing distinct liquid starting configurations, demonstrate that more than one IINT morphology (with similar diameters) may form within a given carbon nanotube, indicative of a significant element of kinetic control over the IINT growth morphology.
+ –
+
– + y
y x
z
+ – + + –
+ y
y x
z
Fig. 3. Schematic representation of the role of the electrostatic forces in determining the IINT structures formed inside a given carbon nanotube. The left to centre panels show how a single cation effectively determines the locations of the other ions in the xy-plane (perpendicular to the major axis of the carbon template). The nanotube diameter effectively controls the number of ions that can fit in this xy crosssection. The lower panel shows how the twisting of the IINTs may arise in order to overcome potential repulsive like-ion interactions in the xy-plane.
343
A potentially significant aspect of both classes of inorganic nanotube is that they may form chiral nanotubes in an analogue of those formed by pure carbon tubes. Indeed, both the (3,2)sq and (3,2)hex nanotubes shown in Figs. 1 and 2 are specific enantiomers of that morphology. As a result, it may be possible to control the stereochemistry of the growing IINTs with respect to that of the confining carbon nanotube. Such control may be significant since the electronic properties of these materials may vary as a function of both the diameter and morphology. Indeed, the present calculations can act as a useful feed into higher level (and hence much more computationally demanding) calculations. Recent experiments support the theoretical observation that the morphology of the crystallites formed inside the nanotubes may be relatively complex and unique to the low-dimensional confining environment [3]. The extraction of these structures from the experimental HRTEM images does, however, become problematic owing to this inherent complexity. The simple models presented here may greatly aid the interpretation of these data.
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