Mechanism of Nanostructure Growth

The key to developing and exploiting new nanostructured materials lies in an increased understanding of how synthesis conditions affect the properties of nanostructured materials in order to tailor materials to specific needs. A knowledge of the mechanism of nanostructure formation is of particular importance.

Nanotubes

Since the discovery of the wet chemical method of transformation of raw titania to nanotubular titanates, many attempts have been made to describe this mechanism and to rationalise these transformations. Current ideas concerning the mechanism for the formation of nanotubular titanates are reviewed below. Originally, Kasuga et al.22 considered that nanotubular morphology occurred during post hydrothermal acid washing. Some researchers still support this suggestion,26 but it was clearly demonstrated, by washing samples with ethanol or acetone,27,28 that nanotubular sodium titanates are formed during alkaline hydrothermal processing.

Unfortunately, it has not proved possible to adapt the concept of the catalytic growth of hollow fibres on the metal nanoparticles of catalysts, where the diameter of fibres corresponds to the diameter of the particles involved in the preparation of carbon nanotubes. Indeed, during the alkaline hydrothermal synthesis of titanate nanotubes, there is no possible candidate to play the role of a size-determining nanoparticle. Unlike carbon nanotubes, which are often produced by the catalytic pyrolysis of hydrocarbons, titania nanotubes produced via the alkaline hydrothermal method have never been observed in a single layer form. All reports of TiO2 nanotubes describe these samples as nanotubular structures with multilayered walls.

Although the detailed sequence of events is still under discussion, it is clear that, during transformation of TiO2 (anatase, rutile or amorphous) under alkaline conditions, the observed intermediate single-layer and multilayered titanate nanosheets play a key role in the formation of tubular morphology.29,30 These nanosheets can scroll or fold into a nanotubular morphology. The driving force for curving these nanotubes has been considered by several groups.

Zhang et al.31 considered that single surface layers experienced an asymmetrical chemical environment, due to the imbalance of H1 or Na1 ion concentrations on the two different sides of a nanosheet, giving rise to an excess surface energy, resulting in bending. The system could be presented as a plane with two springs on each side parallel to this plane (crystallographic axes c and b; Figure 2.5). When both sides have a symmetrical chemical environment, both spring constants have similar values. As a result, all tensions are compensated and the plane is straight. When the trititanate nanosheet has an asymmetric

Figure 2.5 The driving force for bending titanate nanosheets under alkaline hydrothermal conditions. An asymmetrical chemical environment results in a difference in surface tension on each side of the nanosheet; k1 and k2 are the spring constants for each side.

proton distribution, then each side has a different free surface energy value (spring constant) and, in order to compensate for the imbalance in the surface tensions, the plane bends towards the surface with the higher spring constant value. During the bending process, a strain energy arises which prevents work against bending. In a simple approach, the excess of energy of the layer (Elayer) can be expressed as the difference between two terms:

where r is the radius of curvature of the curved nanosheet, a and b are the proportionality constants responsible for the elasticity of the nanosheet and the imbalance in surface tension, respectively. The detailed analysis of the structural changes of nanosheets and ab initio DFT calculations of the total energy of a curved fragment of trititanate nanosheets as a function of curvature radius,32 demonstrates that the optimal radius of nanotubes is ca. 4nm and the number of layers in the final titanate nanotube is four. However, these results contradict the recently observed dependence of the average nanotube diameter on conditions of synthesis e.g. temperature or the ratio of TiO2 to NaOH.26,33

Another reason for the bending of multilayered nanosheets,29 is that mechanical tensions arise during the process of dissolution-crystallisation in nanosheets.34 In a layered chemical compound, the interaction energy between atoms in neighbouring layers is usually less than that between atoms in the same layer. The growth of nanosheets predominately occurs at the edges of the individual layers, rather than in the initiation of a new layer. During spontaneous crystallisation and the rapid growth of layers, it is possible that the width of the different layers varies as shown in Figure 2.6a. It is likely that the imbalance in the layer width (Ax) creates a tendency of layers to move within the multi-walled nanosheet in order to decrease the excess surface energy (see Figure 2.5b). This can result in the bending of multilayered nanosheets, as seen in Figure 2.6c. It was demonstrated by simplified considerations that, during the simultaneous shift of layers and the bending of a nanosheet, the gain in surface energy can be sufficient to compensate for the mechanical tensions arising in the material during curving and wrapping into nanotubes. This statement can be described by the inequality:

where the left side corresponds to the mechanical energy of the bent nanosheet, and the right side corresponds to the excess surface area associated with an imbalanced layer, Ay is the curving deformation of the layer, k is the spring constant, s is the excess surface energy per unit area at the solution-particle interface and L is the length of the imbalanced layer in the nanosheet. A detailed analysis29 of the inequality (2.2) showed that a change in surface

Figure 2.6 The driving forces for bending multilayered titanate nanosheets under alkaline hydrothermal conditions due to an imbalance in layer widths, Ax, resulting in shifting of layers and bending of nanosheets.

energy for one nanosheet is approximately 500 x 10 18 J, whereas the change in elastic energy is approximately 1 x 10-18 J. Thus, the gain in surface energy is sufficient to compensate for the mechanical tensions arising in the material during curving and wrapping into nanotubes.

In the absence of factors which stabilise the bent form of nanosheets, the reverse process of transformation of bent nanosheets back to the planar form should occur. While it is difficult to find the stabilisation factors for a curved single-layer nanosheet, (and unless an asymmetrical environment is maintained) the curved form of multilayered nanosheets could be stabilised by periodic potentials in the crystal lattice.

In order to visualise such stabilization, let us consider a model of nanosheets consisting of only two layers with n and n + m elements in each layers as seen in Figure 2.7. Each element (shown as a ball) represents the motifs of the crystalline titanates, which could be TiO6 octahedra. a and b are the distances between layers and elements within one layer, respectively, which can be associated with the lattice parameters of titanates (see Chapter 3).

Assuming that during bending of multilayered nanosheets the distances between layers and between motifs within one layer are constant, one can describe such bending as a gradual decrease of the radius of curvature of the nanosheets from infinity (flat nanosheet) to a certain value r. The coordinates of the ball can be expressed as:

y2j t^, ■ ij ' j = 0, n + m - 1 (r + a)* sin(r-*a)

where xlj and y1t are the coordinates of i balls in the first layer and x2j and y2j are the coordinates of j balls in the second layer. In layered compounds, the interaction energy between layers is usually much weaker than the interaction energy between atoms in the layer. It is possible to describe such weak interaction as Van der Waals type using Lennard-Jones potentials. The interaction energy between all balls in Figure 2.7 can then be expressed as:

J(x\, — x2j )2+(y1i — y2j f) U(x1, — x2j )2+(yh — y2j)

a a where e is the coefficient characterising the strength of the interactions. Figure 2.8 shows the total interaction energy, W, between two layers in the nanosheets as a function of the radius of curvature of the nanosheet. The value of W was calculated by inserting Equations (2.3) and (2.4) into Equation (2.5), followed by summing over all i and j balls. The parameters a and b were selected to be as close as possible to the lattice parameters of layered titanates.

Figure 2.7 A model for bending of an imbalanced two-layer nanosheet with n and n + m elements in each layer; a and b are lattice parameters, r is the radius of curvature and f1 and f2 are arc angles of the first and second layers, respectively.

Figure 2.7 A model for bending of an imbalanced two-layer nanosheet with n and n + m elements in each layer; a and b are lattice parameters, r is the radius of curvature and f1 and f2 are arc angles of the first and second layers, respectively.

Figure 2.8 Interaction energy between the elements in two nanosheet layers (with n and n+m elements in each layer) as a function of the radius of curvature of the nanosheet. The interaction energy between two elements from different layers is described by the Lennard-Jones potential.

The results of the calculations show that the bending of two imbalanced layers in the nanosheet results in a decrease of the total energy. This corresponds to the decrease of r from infinity towards a smaller curvature radius (see Figure 2.8). When the radius of curvature becomes too small, the additional bending will result in a sharp rise in energy, pushing the system into an energetically unfavourable state. It is important to note that at the point of minimum energy, the arc angles for the first and second layers are approximately equal to each other, meaning that the edge balls are situated in radial lines.

The radius of minimum interaction energy depends on the parameters n and m. These parameters can be associated with the kinetic rate of nanosheet crystallization, which can be controlled by the conditions of nanotube growth. This is in agreement with the experimental observation that the kinetic rate of curving of nanotubes might control the diameter of the resultant nanotubes.29

In contrast to the asymmetrical chemical environment, the mechanism of multilayer nanosheets bending cannot be applied to single-layer nanosheets, which remain unfolded in aqueous solution according to experimental obser-vations.29,35 The bending of multilayer nanosheets36 may, however, result in the formation of several different types of nanotubes, depending on the method of loop closing (see Figure 2.9). The ideal sealing of matching layers ends in scrolled multilayer nanosheets would result in the formation of a seamless cross-section structure composed of concentric rings (as shown in Figure 2.9b for chrysotile nanotubes).37 The sealing of non-matching layers results in the possibility of a nanosheet forming ''snail'' type scrolls, which can also be

Figure 2.9 Three methods of loop closing resulting in a) "onion," b) "concentric" and c) "snail" type nanotubes. (Images are reproduced with kind permission as follows: a) from ref. 29 b) from ref. 39 and the bent multilayer nanosheet in the top left corner from ref. 36).

Figure 2.9 Three methods of loop closing resulting in a) "onion," b) "concentric" and c) "snail" type nanotubes. (Images are reproduced with kind permission as follows: a) from ref. 29 b) from ref. 39 and the bent multilayer nanosheet in the top left corner from ref. 36).

formed by the helical scrolling of a single-layer nanosheet (as seen in Figure 2.9c). Sometimes, the sealing of nanosheet ends cannot be completed due to steric restraints, resulting in the formation of "onion"-type structures in which the continuous seam is seen along the length of the nanotube.

It is believed that the existence of nanosheets is crucial to the subsequent formation of nanotubes. It is remarkable that, starting from colloidal single-layered isolated trititanate nanosheets, titanate nanotubes can be readily produced in alkaline conditions at room temperatures.30 In contrast, starting from bulk-layered sodium trititanate (Na2Ti3O7) in hydrothermal alkaline conditions, the formation of nanotubes is not observed.38 However, after several days of hydrothermal treatment (without further additions of NaOH) at temperatures in the range 140-170 °C the resultant titanate nanotubes are characterised by very wide diameter (several tens of nanometres).39 Such results suggest that not only is the presence of layered titanates in the reaction mixture important, but so too is their morphology.

Nanofibres

Under alkaline hydrothermal conditions, nanosheets can also be converted to nanofibres instead of scrolling into nanotubes. This usually occurs at temperatures above 170 °C or when KOH is used in place of NaOH. In both cases, the concentration of dissolved Ti(iv) was found to be similar to, but higher than, that in the case of nanotube synthesis.58,62 An increase in the local concentration of Ti(iv) may result in a faster rate of nanosheet growth, with less effect on the rate of nanosheet scrolling. In this case, if the rate of crystallisation is large enough, the thickness of nanosheets can exceed a particular value where they become too rigid to bend before curving can occur. This will result in the formation of nanofibres rather than nanotubes.

Energetically, nanofibres are thermodynamically more stable than nano-tubes since the latter have an increased surface area and higher stresses within the crystal lattice. It has been reported that long-term alkaline hydrothermal treatment of TiO240 or over intensification of the synthesis conditions by the use of a revolving autoclave,51 the addition of nanotube seeds41 or microwave radiation42 may result in favourable conditions for the formation of nanotubes, but nanofibres may be formed instead. This suggests that kinetic factors can exert a strong control over the route of nanosheet transformation.

It is interesting to note that the axis of nanotubes (direction [010]) does not always coincide with the axis of nanofibres (direction [001]). This provides an insight into the mechanism of titanate nanotube growth. The fact that nano-fibres prefer to crystallise along the crystallographic axis c43 suggests that the rate of dissolution-crystallisation along this axis is maximised. Under certain conditions, an imbalance in nanosheet width is expected along the c axis. Thus, a bending of nanosheets will occur around axis b. When the curved nanosheet closes the loop (a nanoloop38 or rather short tubes), the direction of fastest growth disappears. There will be only two directions for nanotube growth: the radial direction (along crystallographic axis a) and the axial direction (along crystallographic axis b). Kukovecz et al.38 propose that the nanoloops provide seeds for the further growth of nanotubes along the preferred direction of growth of axis b. If the nanosheet rolls up into conical shaped tubes, then further growth will result in the formation of closed-end nanotubes. At higher temperatures, bending of nanosheets does not occur readily and the resulting nanofibres are long in the crystallographic direction c.

Overall, the process of transformation of raw TiO2 to nanotubular titanate can be considered to take place in several stages: (1) the slow dissolution of raw TiO2, accompanied by the epitaxial growth of layered nanosheets of sodium trititanates; (2) the exfoliation of nanosheets; (3) the crystallisation of dissolved titanates on nanosheets, resulting in mechanical tensions which induce the curving and wrapping of nanosheets to nanotubes; (4) the growth of nanotubes along the length; and (5) the exchange of sodium ions by protons during washing and the separation of nanotubes. The sequence of events during titanate nanofibre growth is similar except for the absence of the curving step.

2.2.3 Methods to Control the Morphology of Nanostructures

Since the introduction of the alkaline hydrothermal synthesis of titanate nanotubes,22 many efforts have been made to adapt this technique to more suitable technological processes allowing an easy and low-cost scale up of production. Potential routes for the preparation of titanate nanotubes are shown in Figure 2.10. The original method (route 1 in Figure 2.10) includes the use of TiO2 raw material in aqueous NaOH (10moldm~3) at temperatures in the range of 110 to 150 °C for 24 hours. The form of the TiO2 reactant can include anatase, rutile, amorphous TiO2, or even Ti metal. The choice of initial raw material may affect the morphology of the resultant nanotubes, but no systematic data on this subject is available. The hydrothermal method traditionally requires the use of an autoclave with chemically resistant vessels (usually lined with PTFE), in order to withstand such a concentrated and hot alkaline environment. The advantages of this method, however, are that it involves a single-stage process and relatively low hydrothermal temperatures are required to achieve an essentially complete conversion of initial raw materials into titanate nanotubes. Most of the recent modifications of this process have been targeted at an improved control of the morphology of nanotubes (including the length, diameter and size of agglomerates), a reduction in the synthesis temperature and process intensification.

Figure 2.10 Prospective routes to the synthesis of titanate nanotubes and nanofibres.

Effective ways to control the length of nanotubes include: the ultrasonic treatment of initial raw TiO244 or an improvement in the fluid flow and mass transport during alkaline hydrothermal treatment,38 which probably improves the dynamics of nanotube growth in the axial direction due to the availability of the dissolved titanium(IV) species. The average diameter of nanotubes can be controlled, to some extent, by the synthesis temperature.29 A degree of control over the shape of the nanotubular agglomerates can be achieved by using either hydrogen peroxide45 or raw TiO2 with a controlled initial particle size distribution.44

There are several approaches to process intensification of nanotubular tita-nate growth, including: microwave heating46 49 or ultrasonication50 of the reaction mixture during synthesis; improved mixing by use of a revolving autoclave;51 or the hot press fabrication method.52 All of these approaches allow the synthesis time to be reduced from 24 hours down to just a few hours.

The need to use pressurised reactors for the preparation of nanotubes greatly increases the manufacturing cost and complicates the health and safety requirements. Attempts to avoid autoclave operations, by a reduction of the synthesis temperature below the boiling temperature of the alkaline solution (ca. 106 °C), usually result in the formation of multilayered, lepidocrocite-type nanostructures (nanosheets) instead of nanotubes.53,54 There are several reports of titanate nanotubes obtained under reflux conditions.55 In such cases, local overheating of the reaction mixture is possible or a particular form of raw TiO2 (characterised by a higher rate of dissolution in alkaline solvents) tends to be used.

One of the prospective low-temperature routes to titanate nanotubes is via titanate nanosheets, which can be produced by exfoliation of lepidocrocite-type caesium titanate (route 2 in Figure 2.10). The method is based on the phenomenon of the spontaneous formation of titanate nanotubes, at room temperature, with the addition of NaOH to a colloidal solution of titanate nanosheets.56 The method includes: the calcination stage of TiO2 with Cs2CO3; followed by ion-exchange of Cs1 to H1; and then exfoliation of titanate nanosheets in the presence of tetrabutylammonium hydroxide (TBAOH) at room temperature.57 This route does not require the use of autoclaves and most of the stages can be undertaken under ambient conditions. However, the limitations of this method are an increased overall process time and the multi-stage nature of the process.

One approach adopted to reduce the temperature during the synthesis of titanate nanotubes, involves the search for a solvent, or mixture of the solvents, in which the concentration of dissolved Ti(IV) is similar at low temperatures, to that in pure NaOH at 110-150 °C. This has resulted in a lower temperature route to the synthesis of nanotubes using a mixture of NaOH with KOH58 (route 3 in Figure 2.10), allowing a substantial conversion to be achieved at approximately 100 °C, under reflux conditions and atmospheric pressure. Further improvements to this route might include an optimisation of the ratio between NaOH and KOH to further lower the temperature, and the use of additives to achieve a high conversion of TiO2 to titanate nanotubes within several hours under simple reflux conditions.

The formation of titanate nanofibres usually occurs during the hydrothermal treatment of TiO2 raw materials with NaOH solution (10moldm~3) at temperatures higher than 170 °C (route 4 in Figure 2.10).29,59 The use of KOH (10moldm~3) solution as a solvent also results in the formation of nano-fibres,60,62 while a mixture of nanotubes and nanofibres tend to be formed at lower temperatures61,62 (route 5 in Figure 2.10).

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