ISSN 10637834, Physics of the Solid State, 2011, Vol. 53, No. 11, pp. 2375–2384. © Pleiades Publishing, Ltd., 2011. Original Russian Text © I.Yu. Gotlib, A.K. IvanovSchitz, I.V. Murin, A.V. Petrov, R.M. Zakalyukin, 2011, published in Fizika Tverdogo Tela, 2011, Vol. 53, No. 11, pp. 2256– 2264.
ATOMIC CLUSTERS
Molecular Dynamics Simulation of Silver Bromide Nanostructures in SingleWalled Carbon Nanotubes I. Yu. Gotliba, *, A. K. IvanovSchitzb, I. V. Murina, A. V. Petrova, and R. M. Zakalyukinb a
St. Petersburg State University, Universitetskaya nab. 7–9, St. Petersburg, 199034 Russia * email:
[email protected] b Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskii pr. 59, Moscow, 119333 Russia Received April 11, 2011
Abstract—Nanostructures formed upon filling singlewalled carbon nanotubes of different diameters (rang ing from 11.5 to 17.6 Å) with silver bromide have been investigated using the molecular dynamics method. The results of molecular dynamics computer simulation have demonstrated that, in such tubes, AgBr nano tubes in the form of rolledup twodimensional crystalline networks (including structures both with a trigonal coordination and with a tetragonal coordination of ions) can be produced as well as fragments of the NaCl type structure, which is typical of bulk AgBr crystals. In the initial stage of their filling, the carbon nanotubes in the silver bromide melt are deformed, on average, to a greater extent than those in a similar system with AgI. After taking out from the melt, the degree of deformation of the nanotubes decreases and, in the majority of cases, AgBr nanotubular structures based on a hexagonal network are formed inside them. DOI: 10.1134/S1063783411110126
1. INTRODUCTION In recent years, considerable scientific interest has been expressed by researchers in nanocrystalline structures formed by clusters of inorganic compounds that contain from several tens to several thousands of atoms and which either reside in vacuum, or are placed in cavities of crystalline or glassy host matrices, or are located in nanotubes [1, 2]. In particular, a number of studies have been devoted to inorganic nanostructures formed in carbon nanotubes [3, 4]. The structure and different (electrical, optical, etc.) properties of the systems including onedimensional (1D) nanocrystals of ionic inorganic compounds inside carbon nanotubes depend on the nature of a fill ing compound (in the simplest approximation, on the stoichiometric ratio of ions and their radii) and on the geometry of the nanotube. For a singlewalled nano tube (SWNT), they depend on the diameter and the rollingup vector (chirality) [3, 5].
the contribution introduced by the electronic struc ture varying with time to the energy and the force (ab initio molecular dynamics). By properly choosing an appropriate, and, at the same time, rather simple approximation for calculating the desired energy, the molecular dynamics method provides a means for reli ably reproducing the relevant properties of systems with a considerably larger number of atoms as com pared to that available for the direct quantum mechanical calculation [6]. The classical molecular dynamics simulation has been used for investigating the formation of nanocrystalline inorganic ionic struc tures in carbon SWNTs and the properties of the newly formed nanocomposite systems. These investigations have been performed using both the “conventional” model potentials and the potentials constructed in such a way as to reproduce the properties of bulk phases of the real materials (KI, SrCl2, LaCl3, PbI2) [7–11].
Computer simulation, primarily, using the molecu lar dynamics method is an important supplementary tool to the existing techniques (highresolution trans mission electron microscopy, Raman scattering spec troscopy, etc.) used for experimentally studying nano structures of the aforementioned type. This method makes it possible to calculate both the energy and structure of the systems under investigation and their dynamic (in particular, transport) characteristics. The molecular dynamics simulation can be purely classical or can include a quantummechanical calculation of
Nanostructures of silver halides in carbon SWNTs are of considerable interest owing to both the physical properties of the Ag(Cl,Br,I) nanophases by them selves (in particular, the possibility of controlling the structure and electrical conductivity of the materials depending on the geometry of nanotubes and the com position of mixed halides) and their ability to be reduced with the formation of metallic silver under exposure to light or electrons. In the experimental works dealing with pure or mixed silver halides in car bon nanotubes, the structural characteristics of
2375
2376
GOTLIB et al.
nanocrystals first of all have been investigated using electron microscopy, energydispersive Xray spec troscopy (EDX), and electron energy loss spectros copy (EELS) [12, 13]. A similar investigation of nano structures of the AgCl, AgBr, and AgI halides in car bon SWNTs (AgCl@SWNTs, AgBr@SWNTs, and AgI@SWNTs, respectively) has been performed recently by Eliseev et al. [14], who, in addition, have used optical absorption spectroscopy and Raman scat tering spectroscopy for studying the electronic struc ture of these composite systems and have demon strated that the silver halides exhibit electronacceptor properties with respect to the carbon nanotube. Silver iodide in carbon SWNTs was simulated using the molecular dynamics method, for the first time, by Baldoni et al. [15], and, more recently, by the authors of the present paper in their previous works [16, 17]. We considered the dependence of the morphology of the formed nanostructures of silver iodide AgI and the mobility of ions in these structures on the diameter of the nanotubes [17]; the model structures of AgI@SWNTs were compared with the structures obtained by Wootton and Harrowell [18] for individual nanoclusters of silver iodide by minimizing their energy (and using a rather simple approximation of the potential). Based on the results obtained in these works, we can draw the conclusion (in the framework of the approximate model used) that the AgI nano clusters containing several hundred atoms, both in vacuum and in carbon SWNTs, have a tendency toward the formation of nanotubular structures based, first of all, predominantly, on a hexagonal network with a trigonal coordination of ions. At the same time, there is evidence for the formation of AgI nanotubes based on a square network as well (with a tetragonal coordination of ions). The structures of AgI@SWNTs are characterized by a lower mobility of ions as com pared to that in the bulk phase of silver iodide; this is especially true in regard to thin nanotubes. The tem perature interval, where the superionic state is observed (with a noticeable mobility of silver ions and the absence of an appreciable migration of iodine ions), for the AgI@SWNT system is narrower than that for the bulk phase αAgI. In this work, the molecular dynamics simulation has been applied to the AgBr@SWNT system. As is known, the ionic radius of bromine is smaller than that of iodine (the “effective ionic radii” according to Shannon [19] are equal to 1.96 and 2.20 Å, respec tively), and the degree of covalency of the Ag–Br bond is lower than that of the Ag–I bond. These features are responsible for the differences in the experimentally observed structural and transport characteristics of AgBr and AgI. In particular, at a normal pressure, sil ver bromide does not form a superionic phase similar to the αAgI modification (which is thermodynami cally stable in the temperature range from 420 K to the melting temperature equal to 828 K) and the thermo dynamically stable solid phase of AgBr has a NaCl
structure, whereas silver iodide at low temperatures forms crystals with a wurtzitetype structure (the sta ble β modification) or a sphaleritetype structure (the metastable γ modification). At high pressures (several thousands or several tens of thousands of atmo spheres), it has been possible to obtain other polymor phic modifications (in particular, a modification with a NaCl structure for AgI and a modification with a cinnabar structure for AgBr) [20]. The aforemen tioned difference in the ionic sizes is also associated with the anomalously high ionic conductivity observed in the βAgI–AgBr binary system with specific com positions [21]. The purpose of this work was to perform the molec ular dynamics simulation of the processes of the for mation of AgBr nanostructures inside carbon SWNTs with different thicknesses, determination of their structural characteristics, and comparison with the results of the simulation of the AgI@SWNT system. 2. DESCRIPTION OF THE MODEL In earlier works [22–29], the molecular statics or molecular dynamics simulation of the AgBr or AgBr containing systems was performed using different approximate model potentials proposed by those authors. The simplest approximation, which, at the same time, makes it possible to obtain the results being in satisfactory agreement with the experiment, can be taken as the model Parrinello–Rahman–Vashishta potential [30] q i q j H ij P ij W ij U ij = + – – . r ij r nij r 4 r 6 ij
ij
(1)
ij
Here, rij is the distance between the ith and jth ions; qi and qj are the effective electrostatic charges of the ith and jth ions, respectively; Hij and nij are the parameters describing the dispersion repulsion; Wij is the van der 2 2 Waals attraction; and Pij = 1 (α i q j + α j q i ) is the 2 polarization interaction, where αi and αj are the polar izabilities of the ith and jth ions, respectively. For silver bromide, we performed the molecular dynamics sim ulation using three different sets of values of the parameters Hij, nij, Wij, and Pij (see [24, 26, 29], respectively), which were chosen so as to reproduce the properties of the AgBr or AgBrcontaining binary systems at temperatures close to the melting tempera ture. In the present work, we used the values reported by Matsunaga [26, 27], who performed the molecular dynamics investigation of the properties of the superi onic phase and the melt of the mixed AgBrxI1 – x sys tem; it should be noted that, in these works, Matsu naga described interactions with the participation of iodine ions by the same parameters (taken from [31]) as we used in our previous studies [16, 17]. The values of the parameters for the Ag–Ag, Ag–Br, and Br–Br
PHYSICS OF THE SOLID STATE
Vol. 53
No. 11
2011
MOLECULAR DYNAMICS SIMULATION
interactions are presented in Table 1. In this model, all values of Wij for the ions are taken to be equal to zero; i.e., the shorter range effects of the van der Waals attraction are considered to be negligible as compared to the contribution from the polarization interactions. The interaction of the silver and bromine ions with carbon atoms was described by the LennardJones potential 6
The energy of the system of carbon atoms forming a nanotube was calculated using the Tersoff potential [33] U ij = f C ( r ij ) [ f R ( r ij ) + b ij f A ( r ij ) ],
(3)
f R ( r ij ) = A ij exp ( – λ ij r ij ),
(4)
f A ( r ij ) = – B ij exp ( – μ ij r ij ),
n i n i 1/2n i
b ij = χ ij ( 1 + β i ζ ij )
ζ ij =
,
R ij < r ij < S ij
∑ f (r C
(5)
ik )ω ik g ( θ ijk ),
k ≠ i, j
χ ii = 1,
ω ii = 1,
g ( θ ijk ) = 1 +
2 ci 2 di
χ ij = χ ji ,
ω ij = ω ji ,
(6)
2 ci
– 2 , 2 d i + ( h i – cos θ ijk )
λi + λj λ ij = , 2 1/2
μi + μj μ ij = , 2 1/2
A ij = ( A i A j ) ,
B ij = ( B i B j ) ,
1/2
S ij = ( S i S j ) .
R ij = ( R i R j ) ,
(7)
1/2
Here, rij is the distance between the ith and jth ions and θijk is the angle between the i–j and i–k bonds. The parameters used for carbon are as follows: AC = 1393.6 eV, BC = 346.7 eV, λC = 3.4879 Å–1, μC = 2.2119 Å–1, βC = 1.5724 × 10–7, nC = 0.72751, cC = 3.8049 × 104, dC = 4.3484, hC = –0.57058, RC = 1.8 Å, and SC = 2.1 Å. The molecular dynamics simulation was carried out with the DL_POLY program package [34]. PHYSICS OF THE SOLID STATE
i
j
nij
Ag
Ag
11
Ag
Br
9
Br
Br
7
Hij, eV Å
n ij
0.162348 547.583 2299.52
Pij, eV Å4
Wij, eV Å6
0.0
0.0
9.5059
0.0
19.0121
0.0
(2)
with the following parameters: εAgC = 0.0335 eV, σAgC = 2.926 Å [15–17]; and εBrC = 0.0057684 eV, σBrC = 3.47 Å [32].
⎧ 1, r ij ≤ R ij ⎪ ⎪1 1 π ( r ij – R ij ) f C ( r ij ) = ⎨ + cos , S ij – R ij ⎪2 2 ⎪ 0, r ≥ S , ij ij ⎩
Table 1. Parameter of model potential (1) for AgBr
Note: qAg = +0.5815|e| and qI = –0.5815|e|.
σ σ U ij = 4ε ij ⎛ ⎛ ij⎞ – ⎛ ij⎞ ⎞ , ⎝ ⎝ r ij ⎠ ⎝ r ij ⎠ ⎠ 12
2377
Vol. 53
No. 11
3. THE SIMULATION PROCEDURE AND DISCUSSION OF THE RESULTS The general algorithm used for simulating the AgBr@SWNT system was similar to that applied to the AgI@SWNT system in our previous works [16, 17]. In the preliminary stage, we simulated pure silver bro mide. In a molecular dynamics cubic computational cell, we placed 4000 silver ions and 4000 bromine ions (10 × 10 × 10 = 1000 unit cells of the rock salt struc ture, each containing four AgBr formula units). In the initial configuration, the ions were located at sites of the ideal NaCltype lattice. We used the standard cubic periodic boundary conditions. The electrostatic contribution to the energy was calculated using the Ewald summation method. By using the Nosé– Hoover algorithms of thermostating and barostating, the system was brought to equilibrium at a zero pres sure and a temperature of 1200 K, which corre sponded to the liquid state of AgBr (the experimental melting point was 705 K). The length of the generated phase trajectory was equal to 250 ps, and the time interval was 10–3 ps. Then, in the configuration corresponding to the equilibrium melt, we cut out a cavity (the silver and bromine ions were removed so that the electroneutral ity condition of the model system was satisfied) in the central part of the molecular dynamics computational cell in such a way that this cavity could contain a car bon SWNT with a required diameter d (the values of d were varied from 11.52 Å for the “ideal” nanotube with the rollingup vector (9, 8) to 17.63 Å for the (13, 13) “ideal” nanotube) and a length of 40 Å. The system with a nanotube in the cavity was thermostated and barostated at a temperature of 500 K and a zero pres sure for 300 ps. In the process, the nanotube was filled with ions simultaneously with cooling and solidifying the melt. Then, the system was additionally held for 400 ps at a temperature of 400 K and a zero pressure. This resulted in the formation of an AgBr nanostruc ture inside the SWNT. Thereafter, the filled SWNT could be “extracted” from the melt by means of the removal of all ions outside the nanotube, provided that the electroneutrality condition of the system was satis fied (the number of cations must be equal to the num ber of anions). The AgBr nanostructures formed inside the nano tubes have the form of either nanotubes, or nanocrys 2011
2378
GOTLIB et al. (a)
(b)
(a)
(b)
Fig. 2. Structures of the AgBr@SWNTs in the (13, 13) model carbon nanotube with a length of 40 Å: (a) view of the nanotube located in the silver bromide melt and (b) view of the nanotube withdrawn from the melt after the evolution outside the melt for 20 ps. The notation of ions is the same as in Fig. 1.
Fig. 1. Typical structures of AgBr@SWNTs obtained upon filling of the model (“unfrozen”) nanotubes with a length of 40 Å. The inside view in the direction of the nanotube axis and the side view. (a) The (9, 8) carbon nanotube con taining the “flattened” AgBr (3, 3)sq nanotube and (b) the (11, 11) carbon nanotube containing the AgBr (5, 3)hex nanotube with an additional AgBr filament in the central part. Largesized spheres show the bromine ions, and the smallsized spheres represent the silver ions.
tals with the NaCltype structure, or a combination of fragments of both these types. It is worth noting that the carbon SWNTs in a number of cases are deformed, thus, most frequently, taking on the shape of a “rounded rectangle” in the cross section, which also affects the geometry of the AgBr nanostructures in these nanotubes. For silver bromide in strongly deformed SWNTs, the calculations have demon strated a tendency toward the formation of fragments of the crystal with the rock salt structure, which have the form of a parallelepiped with an m × n cross section of the cubic lattice elements, i.e., octants of the unit cell; at m = 1, this parallelepiped can also be consid ered as an ultimately flattened AgBr nanotube based on a square network with the rollingup vector (n + 1, n + 1) – (n + 1, n + 1)sq in the Wilson notation [9]. In order to evaluate how the deformation of the carbon nanotube to be filled affects on the result of the filling, we carried out a similar computer simulation
experiment. In this experiment, we simulated a con ventional “rigid” nanotube placed in the AgBr melt, so that all carbon atoms in this nanotube were fixed (“frozen”) in the positions of the ideal SWNT with the corresponding rollingup vector. Then (as was done for silver iodide in [16, 17]), the configuration of silver and bromine ions was “extracted” from the nanotubes thus filled (provided that the electroneutrality condi tion was satisfied), and five “replicas” of this configu ration were placed in a 200Ålong carbon SWNT with the same rollingup vector (n, m). These nano tubes with AgBr were further simulated outside the melt in a confining spherical–cylindrical field, which can be considered as an approximate description of the behavior of the nanotube when it is not isolated but is clamped in a bundle; thereafter, they were balanced for 120 ps at a temperature of 820 K and then were cooled to 400 K. At a temperature of 400 K, phase tra jectories with a length of no less than 400 ps were gen erated. Moreover, the model nanotubes with a length of 40 Å, which were filled in the melt and extracted from it, were also held outside the melt at a tempera ture of 400 K for 400 ps. The time of filling of the “unfrozen” model carbon SWNTs varies from ~100 ps for the thinnest nanotubes to 250–300 ps for the thickest nanotubes under con sideration. The “frozen” model carbon SWNTs, in which there occurs the formation of singlewalled AgBr nanotubes, are filled in the course of the com puter simulation experiment for no longer than 100 ps; the filling time of the “frozen” nanotubes with a larger diameter can be substantially longer, i.e., up to 300 ps. The geometric characteristics of the AgBr nano structures formed in the model carbon nanotubes under investigation are presented in Table 2. Examples of these structures are given in Figs. 1 and 2. Figure 3a
PHYSICS OF THE SOLID STATE
Vol. 53
No. 11
2011
MOLECULAR DYNAMICS SIMULATION
2379
Table 2. Geometry of the AgBr nanostructures formed in the “unfrozen” and “frozen” carbon SWNTs with different roll ingup vectors (n, m) (n, m)
d, Å
In the “unfrozen” nanotube in the melt
In the “frozen” nanotube in the melt
1
2
3
4
(9, 8)
11.52 The “flattened” (3, 3)sq nanotube, The (3, 3)sq nanotube i.e., a distorted fragment of the NaCltype lattice with a 1 × 2 cross section of the lattice element
In the nanotube 40 Å In the nanotube 200 Å long after holding long outside the melt outside the melt after “annealing” 5
6
The (3, 3)sq nanotube The (3, 2)hex nanotube or the (3, 2)hex nano tube (depending on the initial configura tion) The (3, 2)hex nano The (3, 2)hex nanotube tube
(10, 7) 11.57 The “flattened” (3, 3)sq nanotube, The same i.e., a distorted fragment of the NaCltype lattice with a 1 × 2 cross section of the lattice element (9, 9) 12.19 The deformed (4, 3)sq nanotube The (4, 3)sq nanotube The (3, 3)hex nano tube The same The same (10, 8) 12.21 The deformed (4, 4)sq nanotube (10, 9) 12.87 The same The (4, 4)sq nanotube The (4, 4)sq nanotube (11, 8) 12.92 The (4, 4)sq nanotube The same The same (10, 10) 13.54 The (5, 4)sq nanotube containing The (5, 4)sq nanotube The (4, 3)hex nano one additional AgBr filament containing one addi tube containing one tional AgBr filament additional AgBr fila ment (11, 9) 13.56 The deformed (4, 3)hex nanotube The same The (5, 1)hex nano (“flattened” at one end and con tube containing one taining an additional AgBr fila additional AgBr fila ment at the other end) ment
(12, 8) 13.63 The “flattened” (4, 4)sq nanotube, The same i.e., a distorted fragment of the NaCltype lattice with a 1 × 3 cross section of the lattice element
The (4, 3)hex nano tube containing one additional AgBr fila ment
(11, 11) 14.90 The (5, 3)hex nanotube containing The (4, 4)hex nano one additional AgBr filament tube containing one additional AgBr fila ment (12, 12) 16.27 The (6, 3)hex nanotube containing The (6, 6)sq nano two (discontinuous) additional tube containing AgBr filaments three (discontinu ous) additional AgBr filaments
The (4, 4)hex nano tube containing one additional AgBr fila ment The (7, 1)hex nano tube containing three (discontinuous) addi tional AgBr filaments
The (3, 2)hex nanotube The same The (3, 3)hex nanotube The same The (5, 1)hex nanotube containing one addi tional AgBr filament A combination of frag ments of the nano tubes (4, 3)hex + (5, 1)hex containing one additional AgBr filament A combination of frag ments of the nanotubes (6, 0)hex + (5, 1)hex containing one addi tional AgBr filament The (6, 1)hex nanotube containing one addi tional AgBr filament
A combination of frag ments of the nanotubes (6, 3)hex + (7, 1)hex + (8, 0)hex containing three (discontinuous) additional AgBr fila ments (13, 13) 17.63 The nanotube is strongly and non The (8, 1)hex nano The (8, 1)hex nano The (8, 1)hex nanotube uniformly “flattened”; at one end, tube containing four tube or the (7, 3)hex containing four (discon nanotube containing tinuous) additional there is a distorted fragment of the (discontinuous) NaCltype lattice with a 1 × 6 cross additional AgBr fila four (discontinuous) AgBr filaments section of the lattice element; and, ments additional AgBr fila at the other end, there is a fragment ments of the NaCltype lattice with a 2 × 2 cross section of the lattice element with two fragments of the nanotubes based on the square network
Note: The nanotubes are presented in the Wilson notation [7, 9] used for AgI in [16, 17] (in [16], some structures were designated erro neously; in [17] and in this work, these mistakes were corrected). PHYSICS OF THE SOLID STATE
Vol. 53
No. 11
2011
2380
GOTLIB et al.
SWNTs with the same rollingup vector [17]. More over, the carbon SWNTs filled by the silver bromide melt with the simultaneous crystallization are deformed to a considerably higher extent than those in the corresponding system with AgI. The nonrigidity of the carbon skeleton affects the result of the nano tube filling in such a way that the spread in the values of N/L increases for the carbon nanotubes with close diameters; the maximum distortion of the nanotube shape is observed for the widest nanotubes, in which this leads to a noticeable decrease in the values of N/L as compared to the “frozen” carbon SWNTs. The dependences N/L(d) for both AgBr and AgI are char acterized by an upward shift due to the appearance of additional filaments of silver and halogen ions in the central region of the nanotube. The ratio of the quan tity N/L for AgBr@SWNTs in the model “frozen” nanotube to the corresponding quantity for AgI@SWNTs proves to be maximum (>50%) in the case of the carbon nanotubes (10, 10), (11, 9), and (12, 8) (with a diameter of 13.5–13.6 Å), where silver bro mide forms a nanotube with additional ions in the central region and silver iodide forms a singlewalled nanotube, and in the case of the (12, 12) carbon nan otube (with an “idea” diameter of 16.27 Å), where AgBr forms a nanotube with three (even though dis continuous) additional filaments of ions in the central region of the nanotube and AgI forms a nanotube with one additional filament. For the same values of d in the computer experiment, we observed increased values for the density of silver bromide inside the “frozen” carbon nanotubes (Fig. 3b); for the “unfrozen” car bon SWNTs, the effect of increase in the density of the AgBr structure is less pronounced owing to the appearance of new filaments of ions in the central region of the nanotube.
(a) 3.0
N/L, Å−1
2.5 2.0 1.5
1 2 3
1.0 0.5 0
12
14
16
18 (b)
ρ, g/cm3
7.0
6.5
ρexp
6.0
5.5
12
14
16
18
d, Å Fig. 3. Dependences of (a) the average number of AgBr formula units per unit length N/L of the carbon SWNT and (b) the density ρ of AgBr inside the nanotube on the nanotube diameter for the (1) “unfrozen” and (2) “fro zen” nanotubes. (3) Data taken from [17] for N/L in the case of AgI@SWNTs (presented for comparison); ρexp is the experimental value of the density of crystalline AgBr at a temperature of 400 K.
shows the dependences of the average number of AgBr formula units (and, for comparison, the average number of AgI formula units) per unit length N/L of the filled carbon SWNT on the nanotube “ideal” diameter d for the “frozen” and “unfrozen” nano tubes. Figure 3b shows the dependences of the density ρ of AgBr inside the nanotube on the nanotube diam eter d also for the “frozen” and “unfrozen” nanotubes. The density ρ is calculated from the ratio of the aver age number of AgBr formula units inside the nanotube N to the internal free volume Vf . In turn, the internal free volume is estimated as the volume of the part of the internal space of the carbon SWNT which is sepa rated from the nanotube walls by a distance of no less than 1.7 Å. A comparison of the data obtained from the molec ular dynamics computer experiment on the filling of carbon nanotubes of AgI [16, 17] and AgBr has dem onstrated that the values of N/L for AgBr are substan tially higher than those for AgI in the model carbon
The above results are in agreement with the exper imental data on the density of the bulk crystalline phases of AgBr and AgI: at room temperature and atmospheric pressure, the molar density of AgBr (with the NaCl structure) is 43% higher than that of AgI (with a looser structure of wurtzite), whereas at a pres sure of 0.5 GPa, when the stable phases of AgBr and AgI each have the NaCl structure, the molar density of AgBr is 18% higher than that of AgI [35]. The calcu lated densities ρ for AgBr@SWNTs in both the “fro zen” and “unfrozen” nanotubes nonmonotonically change in an increase in the nanotube diameter d and deviate from the experimental value of the density of the bulk AgBr phase at a temperature of 400 K, i.e., ρexp ≈ 6.39 g/cm3, by no more than 10%. The deformation of carbon nanotubes placed in a cavity inside the melt predominantly occurs before their filling with ions and at the first stage of the nano tube filling, when an empty space still remains inside the nanotube; for 30–50 ps, clearly visible flattened regions are formed on the surface of the nanotube with initial shape close to a regular cylinder. In the case
PHYSICS OF THE SOLID STATE
Vol. 53
No. 11
2011
MOLECULAR DYNAMICS SIMULATION
At the same time, the qualitative differences between the AgI and AgBr structures formed in carbon SWNTs are less significant than those for the bulk phases. Under these conditions, silver iodide is able to form nanotubes based on a square network with a tet ragonal coordination of ions [16, 17], whereas in our computer experiment, we obtained the AgBr@SWNT structure in the 40Ålong carbon nanotubes (11, 9), (11, 11), and (12, 12) in the solidifying melt, in which AgBr near the inner surface of the filled carbon SWNT forms a nanotube based on a hexagonal network (with a trigonal coordination of ions). However, upon “annealing,” in the 200Ålong isolated nanotubes, all the AgBr@SWNT structures considered in our work are rearranged with the transition to a hexagonal net work. A similar evolution was observed in the majority of 40Ålong nanotubes during their holding at a tem perature of 400 K outside the melt, except for the (10, 9) and (11, 8) carbon SWNTs, as well as the (9, 8) car bon nanotube with one of the two initial configura tions. It should be noted that, in the (9, 8) carbon nan otube with a length of 200 Å, many hexagons in the (3, PHYSICS OF THE SOLID STATE
Vol. 53
No. 11
0.08 ρAg, Å−3
(a)
(n, m) (9, 8) (10, 8) (10, 10) (11, 11) (12, 12) (13, 13)
0.10
0.06 0.04 0.02 0 0.10
1
2
3
4
5
6
7 (b)
0.08 ρBr, Å−3
when the filling of the carbon SWNTs with a silver halide is simulated not at a temperature of 400 K but at 1000 K, i.e., without solidification of the melt, the degree of deformation of the nanotubes is substantially lower than that in the former case and is close to the degree of deformation of the AgI and AgBr nanotubes. When the 40Ålong model nanotubes, which were deformed in the melt, are then held outside the melt, the shapes of both the outer carbon skeleton and the inorganic nanocluster inside the nanotube rapidly (for 5–10 ps) become “rounded” (Fig. 2). Therefore, we can draw the conclusion that the basic factor, which is responsible for the deformation of the carbon nano tubes, is most likely the formation of fragments of a flat surface of the inorganic phase near the outer surface of the nanotube, so that the interaction with these frag ments leads to a distortion of the geometry of the SWNT itself. The difference in the degrees of defor mation of the model carbon SWNTs in the solidifying melts of AgBr and AgI is consistent with the fact that, as was demonstrated in the computer experiment, sil ver bromide in nanostructures inside the nanotubes also tends to crystallize into fragments whose shape, even if locally, is close to parallelepipeds cut from the structure of the bulk NaCltype phase and which have a relatively flat surface. The distortion of the nanotube shape upon interaction with the outer (solidifying) melt was investigated, both experimental and theoret ically, using the example of the behavior of different metals near the surface of carbon nanotubes by Cha et al. [36], who showed that the degree of deformation substantially decreases upon transition from the melt that does not wet the surface of the nanotube to the melt wetting it (the latter melt is thus more ready to form a curved contact surface that retains its shape upon solidification, and, consequently, the shape of the nanotube is also retained).
2381
0.06 0.04 0.02 0
1
2
3
4 r, Å
5
6
7
Fig. 4. Density profiles for the (a) silver ions and (b) bro mine ions as a function of the distance r from the nanotube axis in the carbon SWNTs with a length of 200 Å ((n, m) is the rollingup vector) at a temperature of 400 K.
2)hex structure of AgBr are also noticeably distorted; i.e., they are “compressed” so that one of the long diagonals is shorter than the other two diagonals. This can be considered as a “reminiscence” of the tetrago nal structure. In the latter case, the rearrangement of the structure of silver bromide in the nanotube pre dominantly occurred during the first approximately 10 picoseconds; i.e., it lasted for approximately the same time as the relaxation of the carbon skeleton. There fore, there are grounds to assume that the character of the interaction of the carbon nanotube with the envi ronment affects not only the geometry of the nanotube itself but also the morphology of the nanostructures formed in it. Moreover, in the absence of the deform ing effect exerted by the surrounding inorganic phase, the nanotubular structures of AgBr in carbon SWNTs and, especially, the structures based on a hexagonal network are stabilized as compared to the small frag ments of the bulk crystal with flat surfaces. Figure 4 presents the radial profiles of the average density for silver ions ρAg(r) and bromine ions ρBr(r) in some carbon SWNTs with a length of 200 Å. Figure 5 shows the radial distribution functions gAgBr(r) for the Ag–Br correlations. A comparison of the density pro 2011
2382
GOTLIB et al.
files with the results obtained in [16, 17] for AgI has demonstrated that, on the whole, the specific features in the distributions of ions in AgBr@SWNTs and AgI@SWNTs are similar to each other, with the only correction that, in the case of AgBr, the ions in the central part of the nanotube (which, as a rule, are aligned into an additional filament consisting of anions and cations) are observed in noticeable amounts already in the (10, 10) carbon SWNT (d = 13.54 Å), whereas in the case of AgI, they are observed only in the (11, 11) carbon SWNT (d = 14.90 Å).
tively), whereas in AgBr@SWNTs, the positions of the maxima in the density profiles ρAg(r) and ρBr(r) almost completely coincide with each other, which is in agreement with the difference in the effective radii of the I–1 and Br–1 ions. In the nanotubes with one additional filament of ions in the central part ((11, 11) for AgI@SWNTs, (10, 10) and (11, 11) for AgBr@SWNTs), the distribution of anions in the central region is characterized by a sharp peak at small values of r, whereas the distribu tion of the “central” cations in AgBr@SWNTs is con siderably more uniform than that in AgI@SWNTs. In the (12, 12) and (13, 13) carbon nanotubes with AgBr, where there arise additional filaments of ions, the den sity profile ρBr(r) is characterized by two welldefined maxima (1.8–1.9 and 5.1–5.2 Å in the (12, 12) SWNTs, and 2.15–2.25 and 5.75–5.85 Å in the (13, 13) SWNTs; here, the second values correspond to the “nearsurface” nanotube), whereas the density profile ρAg(r), apart from the “nearsurface” maximum, clearly demonstrates a considerably increased density of cations at small values of r and a weakly pronounced maximum at 2.5–3.0 Å. For the radial distribution functions gAgBr(r) in the nanotubes, the first maximum is slightly shifted toward smaller values of r as compared to the bulk phase of silver bromide (2.40–2.45 Å in AgBr@SWNTs, 2.60–2.65 Å in the model bulk crys tal); i.e., a compression of the structure in the nano tube takes place (which is confirmed by the experi mental data [14]). For larger values of r, the behavior of the function gAgBr(r) in AgBr@SWNTs strongly dif fers from its behavior in the bulk phase, which is not surprising for this difference between the structures. For the AgBr nanotubes based on a hexagonal net work, the radial distribution function gAgBr(r) has a maximum at 4.8–4.9 Å, which corresponds to the long diagonal of the hexagon of the network, as is the case observed for AgI@SWNTs [17], where the presence of such maximum distinguished the structures based on a hexagonal network from the “tetragonal” structures. The exception is provided by AgBr in the (9, 8) carbon SWNT, for which the function gAgBr(r) due to the dis tortion of hexagons exhibits two maxima: the first maximum at 3.9 Å and the second (considerably higher) maximum at 5.3–5.4 Å, which correspond to the smaller and two larger long diagonals of the hexa gon, respectively.
As in AgI@SWNTs, the density profiles ρAg(r) and ρBr(r) in the peripheral region of the nanotube exhibit a welldefined maximum corresponding to the “near surface” (or, in thin nanotubes, singlewalled) nano tube of AgBr. It should be noted that, in AgI@SWNTs, the density of cations has a maximum at the values of r which, as a rule, are ~0.25 Å higher than the density of anions (for example, in the (10, 10) carbon nano tube, these values are equal to 3.75 and 3.50 Å, respec
4. CONCLUSIONS In the course of the molecular dynamics computer simulation, we have reproduced nanostructures of sil ver bromide in carbon SWNTs, which can exist in the form of both the nanotubes based on a square or hex agonal network (in this case, additional AgBr fila ments can be formed in the central part of the carbon nanotubes whose diameter exceeds 13.5 Å) and frag
12 (n, m) (9, 8) (10, 8) (10, 10) (11, 11) (12, 12) (13, 13) Bulk AgBr
10
gAgBr(r)
8
6
4
2
0
1
2
3
4
5 6 r, Å
7
8
9
10
Fig. 5. Radial distribution functions gAgBr(r) for the Ag–Br correlations in the carbon SWNTs with a length of 200 Å ((n, m) is the rollingup vector) at a temperature of 400 K. Shown also is the radial distribution function gAgBr(r) cal culated for the bulk crystal of AgBr.
PHYSICS OF THE SOLID STATE
Vol. 53
No. 11
2011
MOLECULAR DYNAMICS SIMULATION
ments of the bulk NaCltype structure; moreover, intermediate transition morphologies can also be formed. The formation of structural fragments of the bulk cubic crystal, as a rule, is associated with a signif icant deformation of the carbon nanotube in the melt. In the nanotubes isolated from the outer melt, silver bromide transforms into nanotubular structures; in the majority of cases, it transforms into those based on a hexagonal network. The results of the molecular dynamics computer simulation are in agreement with the experimental data [14], which confirm that the possibility exists of forming hexagonal nanocrystalline structures of silver bromide inside the carbon nanotubes. At the same time, as was noted in [17], the highresolution scan ning electron microscopy data count in favor of the assumption that, in carbon SWNTs with the diameter ranging from 13 to 14 Å, nanostructures of AgBr and AgI are formed in the form of fragments of the bulk wurtzitetype structure, whereas the molecular dynamics simulation carried out both in carbon nano tubes and in vacuum (for silver iodide [18]), as a rule, has reproduced “classical” nanotubular structures based on a hexagonal network. Further experimental investigations performed in combination with the computer simulation based on the use of refined model potentials, probably, would be advisable for a more accurate determination of the structure of silver halide nanoclusters. The similarity of the nanotubular structures of sil ver bromide and silver iodide suggests that, in the AgBr nanotubes at specific temperatures, the silver ions can exhibit a high mobility in the “internal” channel, which is similar to that observed in the computer sim ulation experiment performed for AgI@SWNTs [17], in contrast to the nonconducting bulk phase with the NaCl structure. Therefore, the AgBr@SWNT systems and, especially, the AgI–AgBr solid solutions in nano tubes (Ag(I,Br)@SWNTs) require further investiga tion as possible superionic nanophases. ACKNOWLEDGMENTS This study was supported by the Russian Founda tion for Basic Research (project nos. 080301039 and 110300875) and St. Petersburg State University (NIR 12.37.135.2011 “Nanostructuring of Materials for Solid State Ionics as the Basis for the Development of Solid Electrolytes of a New Generation”). REFERENCES 1. The Chemistry of Nanomaterials: Synthesis, Properties, and Applications, Ed. by C. N. R. Rao, A. Müller, and A. K. Cheetham (Wiley, Weinheim, 2004). PHYSICS OF THE SOLID STATE
Vol. 53
No. 11
2383
2. R. Tenne, M. Remškar, A. Enyashin, and G. Seifert, in Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties, and Applications, Ed. by A. Jorio, G. Dresselhaus, and M. S. Dresselhaus (Springer, Ber lin, 2008), p. 631. 3. A. A. Eliseev, M. V. Kharlamova, M. V. Chernysheva, A. V. Lukashin, Yu. D. Tret’yakov, A. S. Kumskov, and N. A. Kiselev, Usp. Khim. 78, 901 (2009). 4. H. Chu, L. Wei, R. Cui, J. Wang, and Y. Li, Coord. Chem. Rev. 254, 1117 (2010). 5. J. Sloan, A. I. Kirkland, J. L. Hutchison, and M. L. H. Green, Chem. Commun. 13, 1319 (2002). 6. A. Nakano, M. E. Bachlechner, R. K. Kalia, F. Li dorikis, P. Vashishta, G. Z. Voyiadjis, T. J. Campbell, S. Ogata, and F. Shimojo, Comput. Sci. Eng. 3, 56 (2001). 7. M. Wilson, Nano Lett. 4, 299 (2004). 8. M. Wilson and S. Friedrichs, Acta Crystallogr., Sect. A: Found. Crystallogr. 62, 287 (2006). 9. M. Wilson, Faraday Discuss. 134, 283 (2007). 10. C. L. Bishop and M. Wilson, J. Phys.: Condens. Matter. 21, 115301 (2009). 11. A. N. Enyashin, R. Kreizman, and G. Seifert, J. Phys. Chem. C 113, 13664 (2009). 12. J. Sloan, D. M. Wright, HeeGweon Woo, S. Bailey, G. Brown, A. P. E. York, K. S. Coleman, J. L. Hutchi son, and M. L. H. Green, Chem. Commun. 8, 699 (1999). 13. J. Sloan, M. Terrones, S. Nufer, S. Friedrichs, S. R. Bailey, HeeGweon Woo, M. Rühle, J. L. Hutch ison, and M. L. H. Green, J. Am. Chem. Soc. 124, 2116 (2002). 14. A. A. Eliseev, L. V. Yashina, M. M. Brzhezinskaya, M. V. Chernysheva, M. V. Kharlamova, N. I. Verbitsky, A. V. Lukashin, N. A. Kiselev, A. S. Kumskov, R. M. Zakalyukin, J. L. Hutchison, B. Freitag, and A. S. Vinogradov, Carbon 48 (8), 2708 (2010). 15. M. Baldoni, S. Leoni, A. Sgamellotti, G. Seifert, and F. Mercuri, Small 3, 1730 (2007). 16. I. Yu. Gotlib, A. K. IvanovShitz, I. V. Murin, A. V. Pet rov, and R. M. Zakalyukin, Inorg. Mater. 46 (12), 1375 (2010). 17. I. Yu. Gotlib, A. K. IvanovSchitz, I. V. Murin, A. V. Pet rov, and R. M. Zakalyukin, Solid State Ionics (2010) (in press). 18. A. Wootton and P. Harrowell, J. Phys. Chem. B 108, 8412 (2004). 19. R. D. Shannon, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 32, 751 (1976). 20. R. N. Schock and J. C. Jamieson, J. Phys. Chem. Solids 30, 1527 (1969). 21. K. Shahi and J. B. Wagner, Jr., J. Phys. Chem. Solids 43, 1713 (1982). 22. P. W. Jacobs, J. Corish, and B. A. Devlin, Photogr. Sci. Eng. 26, 50 (1982). 23. D. C. Gupta and R. K. Singh, Phys. Rev. B: Condens. Matter 43, 11185 (1991). 2011
2384
GOTLIB et al.
24. C , . Tasseven, J. Trullás, O. Alcaraz, M. Silbert, and A. Giro, J. Chem. Phys. 106, 7286 (1997). 25. A. K. IvanovSchitz, G. N. Mazo, E. S. Povolotskaya, and S. N. Savvin, Solid State Ionics 173, 103 (2004). 26. S. Matsunaga, Solid State Ionics 176, 1929 (2005). 27. S. Matsunaga, J. NonCryst. Solids 353, 3459 (2007). 28. S. Matsunaga, Prog. Theor. Phys. Suppl. 178, 113 (2009). 29. S. Matsunaga, J. Phys.: Conf. Ser. 144, 012011 (2009). 30. M. Parrinello, A. Rahman, and P. Vashishta, Phys. Rev. Lett. 50, 1073 (1983). 31. F. Shimojo and M. Kobayashi, J. Phys. Soc. Jpn. 60, 3725 (1991).
32. C. Yang, X. Zhu, X. Lu, and X. Feng, J. Mol. Struct. (THEOCHEM) 896, 6 (2009). 33. J. Tersoff, Phys. Rev. B: Condens. Matter 39, 5566 (1989). 34. W. Smith, The DL_POLY: Molecular Simulation Package; http://www.cse.clrc.ac.uk/msi/software/DL_POLY/. 35. S. N. Vaidya and G. C. Kennedy, J. Phys. Chem. Solids 32, 951 (1971). 36. J. J. Cha, M. Weyland, J.F. Briere, I. P. Daykov, T. A. Arias, and D. A. Muller, Nano Lett. 7, 3770 (2007).
Translated by O. BorovikRomanova
PHYSICS OF THE SOLID STATE
Vol. 53
No. 11
2011
