Odd–Even Effects in the Dynamics of Liquid Crystalline Thin Films on

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Odd−Even Effects in the Dynamics of Liquid Crystalline Thin Films on the Surface of Single Walled Carbon and Silicon Carbide Nanotubes: Computer Simulation Study Krzysztof Górny,* Przemysław Raczyński, Zbigniew Dendzik, and Zygmunt Gburski Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland ABSTRACT: Translational and reorientational dynamics of monolayer films of ncyanobiphenyl (with n = 5−8) series of mesogens on the surface of single walled carbon nanotubes and heterogeneous silicon carbide nanotubes has been studied using molecular dynamics computer simulation. Activation characteristic of diffusion of the mesogens on the surface of the heterogeneous nanotube is selective with respect to the number of carbon atoms in the aliphatic tail of the mesogen, opposite to the case of the mesogens on the surface of the homogeneous carbon nanotube, which reveals nonselective activation. The orientational order parameter ⟨P2⟩ and thermal activation energy of dipolar relaxation of the studied systems also exhibit a characteristic odd−even pattern with respect to the length of the hydrocarbon chain of the mesogen molecule.

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INTRODUCTION Molecular systems encapsulated in carbon nanotubes1 or physisorbed on their surface2 have been studied for both scientific reasons and intersting potential applications.3,4 Besides homogeneous carbon nanotubes (CNTs), also a variety of heterogeneous nanotubes have been studied in this context. Molecular systems based on silicon carbide nanotubes (SiCNTs) have been studied because of interesting potential applications, such as desalination of water5 or removal of cholesterol molecules from a protein surface,6 to name but a few. Liquid crystals (LCs) are a phase of matter that combines the mobility of an isotropic liquid with the long-range orientational order, which is normally associated with crystalline solids, and have been used for applications that rely on their anisotropic electrooptical properties. The first cyanobiphenyl, 5CB, was synthesized in 1972 as an outcome of research aiming at finding a mesogen with the specific intention of using them in liquid crystal displays. The series of n-cyanobiphenyls (nCB; 4-n-alkyl4′-cyanobiphenyl) consists of important liquid crystals, with their liquid crystalline phases at the temperatures near room temperature, which have intensively been studied through experiment and with use of computer simulation methods.7 Because the ordering of molecules is known to be essentially influenced by interfaces and dopants,8 anchoring of the liquid crystals and other functional organic molecules at a variety of interfaces has been studied for fundamental scientific reasons but also because the molecular organization of liquid crystals at their interfaces is essential for designing and optimizing a variety of devices ranging from displays to organic field effect transistors and implementing new promising concepts in nanoand biotechnology.9 © 2015 American Chemical Society

Anchoring of liquid crystals at their interfaces with such substrates as graphene,10 carbon nanotubes,11 or polymer nanofibers12 proved to essentially affect their orientational order and their electrooptic and dielectric properties. In a series of publications, Zannoni and co-workers have investigated orientation and ordering of mesogen films at their interfaces with a variety of substrates, such as crystalline silicon,13 cristobalite and glassy silica,14 and fullerene planar structure15 as well as studying the impact of the cylindrical geometric confinement.16,17 Alignment of carbon nanotubes, which can be viewed as highly anisotropic rigid particles, is crucial for properties of nanotube based materials. Carbon nanotubes dispersed in liquid crystalline medium may form spontaneously ordered aggregates.18−21 Reorientational dynamics of polar molecular systems in confined geometries is often studied in terms of dipolar relaxation.1,2,22 Broadband dielectric relaxation spectroscopy provides the link between the methods which probe the properties of the individual molecules and techniques characterizing the bulk properties of the sample.23 Relaxation spectra are sensitive to intermolecular interactions and provide information on cooperative processes, revealing features mutual to different types of condensed matter systems.24,25

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SIMULATION DETAILS The models of 5CB, 6CB, 7CB, and 8CB liquid crystals molecules have been adopted from the CHARMM-type united atom potential developed by Tiberio and co-workers,7 and have Received: June 22, 2015 Revised: July 29, 2015 Published: July 30, 2015 19266

DOI: 10.1021/acs.jpcc.5b05961 J. Phys. Chem. C 2015, 119, 19266−19271

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The Journal of Physical Chemistry C been fitted against experimental data and proved to well describe the isotropic−nematic phase transition temperatures and the appropriate values of the order parameter assigned to these phases. The homogeneous carbon nanotube as well as the silicon carbide nanonube have been modeled using all atoms potentials described elswhere.1,5,6 Interactions between the mesogens have been described taking into account electrostatics and van der Waals forces modeled with Lennard-Jones 12−6 potential with Lorentz−Berthelot mixing rules and cutoff of 20 Å. Interactions between SiCNTs or CNTs and mesogens have been described with a model that accouts for van der Waals interactions modeled with Lennard-Jones 12−6 potential. Periodic boundary conditions were applied and long-range interactions were calculated using particle mesh Ewald (PME)26 summation technique with grid spacing of 1.5 Å. Equations of motion were integrated using the Brunger− Brooks−Karplus (BBK) scheme,27 implemented in NAMD 2.9,28 with the time step of integration of 1 fs. The simulation was performed in NVT ensemble, for temperatures 270, 290, 310, 330, and 350 K. Temperature was controlled using the Langevin thermostat with damping coefficient γ = 5.0 ps−1. In order to generate the initial configurations of mesogen monolayers physisorbed on the surface of each nanotube, we performed a series of preliminary NPT simulations of nanotubes immersed in bulk liquid crystals. Subsequently, we imposed cylindrical geometrical constraints to remove mesogens which do not belong to the immediate vicinity of the surface of the nanotube. Then we performed auxiliary NVT simulations to test whether the mesogen molecules form a uniformly distributed and continuous monolayer, repeating the whole procedure if necessary. Depending on the specific mesogen and the nanotube, the simulation cell contained monolayers that consisted of different numbers of molecules. For the system based on the homogeneous CNT, the simulation cell of 100 × 100 × 57 Å3 contained a single (10,10) carbon nanotube (with diameter of approximately 13 Å) covered with the monolayer of 40 mesogens in the case of 5CB, 38 mesogens in the case of 6CB, 36 mesogens in the case of 7CB, and up to 34 mesogens in the case of 8CB. In the case of the heterogeneous SiCNT, the simulation cell of 100 × 100 × 74 Å3 contained a single (10,10) silicon carbide nanotube (with diameter approximately 16 Å) covered with the monolayer of 59 mesogens in the case of 5CB, 56 mesogens in the case of of 6CB, 53 mesogens in the case of 7CB, and up to 50 mesogens in the case of 8CB. A snapshot of the monolayer of 6CB mesogens on the surface of the silicon carbide nanotube is shown in Figure 1. The initial states have been then used to perform the simulations of the mesogen monolayers on the surface of the nanotubes. The simulated system was thermalized for 5 ns before each trajectory production. The trajectories were produced over 20 000 000 time steps (20 ns).

Figure 1. 6CB mesogens on the SiCNT surface: a snapshot of the simulated system.

from the long-time limit of the mean square displacement defined as ⟨Δr 2(t )⟩ =

1 N

N

∑ |ri(t ) − ri(0)|2 i=1

(2)

which represents a canonical average over all intervals of the MD trajectory corresponding to a time t; N is the total number of mesogens, and ri is the position vector of the ith mesogen, determined from two frames separated by an interval t. Figure 2 shows the thermal activation plot of diffusion of liquid crystal molecules on the surface of carbon and silicon carbide nanotubes determined from calculated trajectories. We observed that silicon carbide nanotube affects the diffusion of nCB molecules in a selective way. Activation energy of nCB molecules increases with the number of carbon atoms (n) in the aliphatic tail of the molecule, from approximately EA = 13.5

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RESULTS AND DISCUSSION We have studied dynamical properties of 5CB, 6CB, 7CB, and 8CB liquid crystal molecules on the surface of single walled carbon and silicon carbide nanotubes. First, we studied the diffusion characteristics of the studied liquid crystal layers. To do so, we calculated the diffusion coefficients, D, using the Einstein relation ⟨Δr 2(t )⟩ = 6Dt

Figure 2. Thermal activation characteristic of diffusion coefficient of 5CB (□), 6CB (○), 7CB (△), and 8CB (▽) molecules on the surface of the carbon nanotube and on the surface of the silicon carbide nanotube (analogous solid symbols), plotted versus the number of carbon atoms (n) in the aliphatic tail of the nCB molecule. The inset shows activation energies.

(1) 19267

DOI: 10.1021/acs.jpcc.5b05961 J. Phys. Chem. C 2015, 119, 19266−19271

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The Journal of Physical Chemistry C kJ/mol for 5CB, up to EA = 16.5 kJ/mol for 8CB mesogen molecule. On the other hand, the nCB series on the carbon nanotube interface does not exhibit the selective diffusion pattern. In the latter case, the activation energy of diffusion is approximately EA = 11 kJ/mol and does not depend on the number of carbon atoms in the aliphatic tail of the nCB molecule. Considerably higher values of activation energy in the case of the silicon carbide nanotube interface, as compared to the homogeneous carbon nanotube, suggest that in this case the diffusion mechanism is based on hopping between the potential minima imposed by the structure of the surface of the silicon carbide nanotube. This feature does not exist in the case of nCB on the surface of the carbon nanotube.

N

Q=

∑i = 1 [3û i(t ) ⊗ û i(t ) − I] 2N

(5)

where û(t) is an arbitrary selected molecular axis, I is the identity matrix; the sum runs over all the molecules forming a single layer on the surface of the nanotube, and the time averaging is calculated over all recorded time steps in the MD trajectories. The principal axis of inertia has been selected for û(t). For the systems with spherical and cylindrical geometries modifications of the order parameter were proposed,16,17 which corresponds to an arbitrary direction which accounts for the specific geometry confinements. In the case of both, CNT and SiCNT based nCB layers, the mesogens anchoring were planar and aligned along the nanotube axis in the whole range of temperatures. Figure 4

Figure 3. Lindemann index of 5CB (□), 6CB (○), 7CB (△), and 8CB (▽) molecules on the surface of the carbon nanotube and on the surface of the silicon carbide nanotube (analogous solid symbols), plotted versus the number of carbon atoms (n) in the aliphatic tail of the nCB molecule.

Figure 3 shows the temperature dependence of the Lindemann index, a measure of thermally driven disorder, defined as δi =

δ=

1 N−1 1 N

N

∑ j = 1, j ≠ i

⟨rij 2⟩ − ⟨rij⟩2 ⟨rij⟩

(3)

N

∑ δi i=1

(4)

calculated for all studied systems, where rij = |rij| is the distance between the ith and jth mesogen and N is the total number of mesogens. It does not exhibit discontinuities, which might suggest changes in the diffusion mechanism of a given system in the whole range of temperatures studied and indicates greater mobility of the liquid crystal molecules on the surface of the cabon nanotube, compared to the systems based on its silicon carbide counterpart. Orientational order of the system is usually characterized in terms of the order parameter ⟨P2⟩, expressing ordering of the liquid crystal molecules with respect to local director n(z). The values of ⟨P2⟩ and n can be calculated from the largest eigenvalue and corresponding eigenvector of the ordering matrix Q defined as14

Figure 4. Director components of 5CB mesogens on the surface of SiCNT at temperature T = 350 K.

shows the director components of the 5CB mesogens on the surface of the silicon carbide nanotube at the temperature T = 350 K, in Cartesian coordinates in which the z axis is oriented along the axis of the nanotube, which shows that the averaged director of the sample is parallel to the axis of the nanotube (only very slight precession of the director around the geometrical axis of the nanotube can be discerned). As a consequence, calculating the order parameter with respect to the geometrical axis of the nanotube would lead to only a very small decrease of the value of the order parameter, compared to the value obtained using the normally used definition of the 19268

DOI: 10.1021/acs.jpcc.5b05961 J. Phys. Chem. C 2015, 119, 19266−19271

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The Journal of Physical Chemistry C order parameter (eq 5). Because of the preceding, we decided to plot the order parameter corresponding to the instantaneous director of the mesogen system rather than that corresponding to the fixed axis aligned along the axis of the nanotube. Figure 5 presents the temperature dependence of ⟨P2⟩ for a series of nCB liquid crystal molecules on the surface of a single

Figure 5. Temperature dependence of ⟨P2⟩ for 5CB (□), 6CB (○), 7CB (△), and 8CB (▽) molecules on the surface of the carbon nanotube and on the surface of the silicon carbide nanotube (analogous solid symbols), plotted versus the number of carbon atoms (n) in the aliphatic tail of the nCB molecule.

walled carbon nanotube and its silicon carbide counterpart. For all studied systems, ⟨P2⟩ decreases with increasing temperature from 0.8 to 0.65. The liquid crystal molecules on the surface of the silicon carbide nanotube generally exhibit a higher degree of order than the molecules on the surface of the carbon nanotube. To gain deeper insight into the degree of order of different molecules of the nCB series, we replotted the values of the ⟨P2⟩ order parameter against the number of carbon atoms (n) in the aliphatic tail of a given nCB series molecule. Figure 6 shows ⟨P2⟩ versus n. For all temperatures studied, the odd− even effect occursthe degree of order which can be assigned to the layers composed of nCB molecules with an odd value of n are higher than that which can be assigned to their even counterparts. This feature agrees well with the experimentally and computationally observed odd−even pattern of nematic− isotropic transition temperatures.7 The odd−even effect is more pronounced for the mesogens on the surface of the silicon carbide nanotube than in the case of the systems based on the carbon nanotube (Figure 6). This can be attributed to the difference in the diffusion mechanism in the case of the mesogens on the surfaces of the SiCNT and CNT (Figure 2). In the system based on SiCNT, the adsorption energy landscape is more corrugated, compared to the case of CNT based systems, leading to the mechanism of diffusion which is based on hopping. Dipolar relaxation characteristic was studied in terms of normalized total dipole moment autocorrelation function (TDCF) Φ(t ) =

M(0) M(t ) M(0) M(0)

Figure 6. Values of ⟨P2⟩ order parameter for 5CB (□), 6CB (○), 7CB (△), and 8CB (▽) molecules on the surface of the carbon nanotube and on the surface of the silicon carbide nanotube (analogous solid symbols), plotted versus the number of carbon atoms (n) in the aliphatic tail of the nCB molecule, at the temperatures T = 270 K, T = 310 K, and T = 350 K. N

M(t ) =

∑ μi

(7)

i=1

using the procedure described in our previous works.1,29 The dipole moment of each mesogen was recalculated for each trajectory frame, with respect to the charge distribution and position of atoms in the molecule. TDCF was then plotted, − ln(− ln(Φ(t))) against ln(t), and fitted with Kohlrausch− Williams−Watts (KWW) decay function Φ(t ) = −(t /τKWW )β

(8)

where τKWW is a measure of the characteristic relaxation time and 0 < β < 1 is interpreted as a measure of distribution of the relaxation time or cooperativity of the relaxation process. The mean relaxation time, τ, has been calculated using the following relation 0

τ=

∫∞ Φ(t ) dt =

τKWW ⎛ 1 ⎞ Γ⎜ ⎟ β ⎝β⎠

(9)

where Γ denotes the gamma Euler function. The calculated values of the mean relaxation time were then plotted on the activation plot ln(τ) against 1/T. Figure 7 shows the dipolar relaxation thermal activation energies, EA′ , determined from the

(6)

where M is the total dipole moment of the system, defined as a sum of dipole moments μi of mesogens 19269

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The Journal of Physical Chemistry C

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REFERENCES

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Figure 7. Thermal activation energies of dipolar relaxation of 5CB (□), 6CB (○), 7CB (△), and 8CB (▽) molecules on the surface of the carbon nanotube and on the surface of the silicon carbide nanotube (analogous solid symbols), plotted versus the number of carbon atoms (n) in the aliphatic tail of the nCB molecule.

activation plot for simulated mesogen monolayers, for different values of the length of the aliphatic tail of nCB molecules. The odd−even effect which occurs in the activation energy of the dipolar relaxation of the studied mesogen monolayers exhibits a different characteristic than in the analogous dependence of ⟨P2⟩. The activation energies of dipolar relaxation of mesogen systems composed of nCB molecules with an odd value of n are lower than that with even values of n. This can be attributed to the fact that, in the case of strongly ordered systems, the influence of thermal disorder on the reorientation is lower.

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CONCLUSIONS We studied translational and reorientational dynamics of monolayers of n-cyanobiphenyl molecules with n ranging from 5 to 8, on the surface of single walled carbon and silicon carbide nanotubes. Contrary to the homogeneous carbon nanotube, the silicon carbide nanotube affects the diffusion of nCB mesogens in a selective waythe activation energy of diffusion increases with the increase of the number of carbon atoms in the nCB aliphatic tail. In the case of the mesogen monolayers on the surface of the silicon carbide nanotube, as well as in the case of the systems based on the homogeneous carbon nanotubes, ordering of the mesogens considerably depends on n and the characteristic odd−even effect occurs. The monolayers composed of the mesogens with an odd value of n exhibit a higher degree of order than the mesogens with even values of n. Dipolar relaxation exhibits a different characteristic of dependency of thermal activation energy on the value of n. Mesogens with an odd value of n exhibit lower activation energies than their counterparts with even values of n.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 19270

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