Author’s Accepted Manuscript

Measurement of magnetic anisotropy ofmultiwalled carbon nanotubes in nematic host

Cristina Ciˆrtoaje, Emil Petrescu

PII: S1386-9477(16)30260-0DOI: http://dx.doi.org/10.1016/j.physe.2016.06.011Reference: PHYSE12486

To appear in: Physica E: Low-dimensional Systems and Nanostructures

Received date: 19 April 2016Revised date: 7 June 2016Accepted date: 13 June 2016

Cite this article as: Cristina Ciˆrtoaje and Emil Petrescu, Measurement ofmagnetic anisotropy of multiwalled carbon nanotubes in nematic host, Physica E:Low-dimensional Systems and Nanostructures,http://dx.doi.org/10.1016/j.physe.2016.06.011

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Measurement of magnetic anisotropy of

multiwalled carbon nanotubes in nematic host

Cristina Cırtoaje

University Politehnica of Bucharest, Department of Physics, Splaiul Independentei313, 060042, Bucharest, Romania

Emil Petrescu

University Politehnica of Bucharest, Department of Physics, Splaiul Independentei313, 060042, Bucharest, Romania, telephone: +40 021 4103603, e-mail:

emilpd@yahoo.com, Corresponding author

PACS numbers: 61.30.Gd, 42.70.Df, 81.07.De

Abstract

The magnetic anisotropy of multiwalled carbon nanotubes (MWCNT-s) is measuredusing their dispersion in nematic liquid crystal (NLC). Due to their ability to alignthemselves with inserted nano-particles, NLC are very useful for the study of thephysical properties of MWCNT as well as for other micro or nano-particles. Thusan organized system is obtained from the beginning and the influence of initialrandom orientation is considerably reduced. The average magnetic anisotropy ofMWCNT dispersed in NLC was calculated from the system relaxation on time andthe obtained value (6.61×10−5) was in good agreement with other reported values.

Key words: Freedericksz transition, nanotubes, magnetic anisotropy.

1 INTRODUCTION

Discovered by Iijima [1] in 1991, carbon nanotubes (CNT-s) are widely usedin various fields such as engineering, science, environmental protection ormedicine due to their unique properties. Many studies revealed their impor-tance in electro-optical devices [2], [3], in waste water cleaning from a widevariety of pollutants [4], [5] or in some medical devices as they proved to haveantibacterial properties [6], [7]. All these results encouraged the scientists notonly to develop new chemical synthesis methods but also to improve theirproperties by functionalization or other chemical or physical procedures [10].

Preprint submitted to Physica E 14 June 2016

Since the physical properties of micro- or nano-particles are different from thebulk properties of the same substance the researchers must find new methodsto organize these particles in relatively stable systems that can be easily andefficiently studied. A proper organization can be reached by inserting them inNLC [4,5]. There have been developed many devices based on NLC with in-serted dyes, micro-particles or nano-particles. These mixtures can be used forthe study of particle’s physical properties as well as in engineering to improveexisting devices or to develop new ones [10–19]. The liquid crystals, mainlyused in LCD’s, combine the properties of crystalline structure of solid statewith those of liquid phase, leading to an organized movement of inserted toCNT. Theoretical and experimental studies performed on CNT-NLC mixturesfrom the orientation, elastic, optic or magnetic properties point of view [20],[21] helped us to develop a new procedure for the measurement of MWCNTmagnetic anisotropy. This method can also be applied for any other rod – likenano- or micro-particles by taking advantage of nematic molecules orienta-tional abilities.

Since CNT were discovered, their magnetic properties were studied in manytheoretical or experimental ways [22–25] but they all have to face the incon-venience of clustering and disordered orientation that must be compensatedby the magnetic field. Previous results [22–25] showed that carbon nanotubesare diamagnetic both on parallel and perpendicular orientation to their axisbut the magnetic susceptibility χ⊥ is larger than χ‖ resulting a paramagneticoverall behavior and a reorientation of carbon nanotubes parallel to the ap-plied field. This makes them easy to be used in thermotropic liquid crystalsas they also to have positive anisotropy.

2 Theoretical background

When a nematic liquid crystal (NLC) is subjected to an external field higherthan critical Freedericksz transition threshold, a reorientation of molecular di-rector is induced leading to a birefringence variation. Thus when the LC issubjected to a laser beam a succession of maxima and minima of the trans-mitted light through the sample appears. The order number N of intensityminima can be expressed as a function of the maximum deviation angle θm[26]:

N =dΔn

2λ

(θ2m − θ4m

4

)

where d is the cell thickness and λ is laser wavelength.

The maximum deviation angle can be calculated (for nematic LC) using elasticcontinuum theory of liquid crystals. This theory is based on the evaluation ofthe system’s free energy density considering all the the interactions between

2

n�

�

u�

�

0n�

Fig. 1. Molecular orientation of the nematic molecule on the nanotubes’s surface.

the system’s components: LC molecule – MWCNT, LC molecule–external fieldand MWCNT–external field.

Assuming a parallel orientation of carbon nanotubes to nematic molecules[5,27] and an interaction process based on Burylov’s model [28] we can evaluatethe LC molecule – MWCNT interaction energy density:

f =wc

2R

(1− 3cos2α

)(�u�n0)

2 = w(�u�n0)2 (1)

which can be written in a simplified form:

f = w(�u�n0)2

where:w =

wc

2R

(1− 3cos2α

),

α is the anchoring angle of nematic molecule on the MWCNT, w is the an-choring energy, �u is the molecular orientation of the MWCNT, �n0 is the un-perturbed nematic director, c is the volumetric concentration of nanotubesand R is the MWCNT radius (Fig. 1).

When an external field is applied perpendicular to the undisturbed nematicdirector (Fig. 2a) both the LC molecules and carbon nanaotubes tend toalign themselves parallel to the field direction due to their positive magneticanisotropy. A detailed descrition of this reorientational process made in asimilar system is given in [29]. The system’s free energy density is the sum ofthe density energies describing all the interactions mentioned above

f = fNLC + fMLC + fMWCNT + fint + fγ (2)

- fNLC – the elastic term, characterizing elastic deformation of the NLC

- fMCL – the influence of the applied magnetic field on the NLC reorientation

- fMWCNT – the magnetic field action on MWCNT

3

n0 n0

2

d�

2

d

2

d�

2

d

B�

u�

u�

n�

n�

a) b)

Fig. 2. 2 MWCNT and nematic molecule orientation inside the cell: a) the magneticfield is switched on; b) the magnetic field is switched off.

- fint – the NLC–MWCNT interaction term

- fγ – the rotational viscosity term

Each of these energy densities can be written in mathematical terms as itfollows:

fNLC =1

2

[K1cos

2θ +K3sin2θ] (∂θ

∂z

)2

(3)

where K1 and K3 are splay and bend elastic constants,

fMCL = −1

2μ−10 χaB

2sin2θ (4)

where χa is NLC’s magnetic anisotropy,

fMWCNT = −1

2μ−10 χaNcB

2sin2β (5)

where χaN is MWCNT’s magnetic anisotropy,

fint = wcos2 (θ − β) (6)

where θ is NLC’s deviation angle and β is MWCNT’s deviation angle in mag-netic field (Fig. 2a), and

fγ = −1

2γ

(∂θ

∂t

)(7)

where γ is the rotational viscosity coefficient.

4

The total free energy is:

FT =∫ d/2

−d/2f (z) dz (8)

By applying Euler–Lagrange equations to the function described in Eq. 8,using small angles approximation, we obtain:

β =2wθ

2w − μ−10 cχaNB2

(9)

and

[K1

(θ2 − 1

)−K3θ

2] ∂2θ

∂z2+

(θ − 2θ3

3

)(K1 −K3)

(∂θ

∂z

)2

−

Aθ +D2θ3

3= −γ

∂θ

∂z(10)

where by A and D we denoted:

A = 2w

( −μ−10 cχaNB

2

2w − μ−10 cχaNB2

)+ μ−1

0 χaB2

and

D = 2w

(μ−10 cχaNB

2

2w − μ−10 cχaNB2

)3

+ μ−10 χaB

2

The deviation angle θ doesn’t have a constant value on the whole cell thicknessdue to the anchoring effects of NLC molecules on the glass plates. Thus thedeviation angle reaches its maximum value θmin the center of the cell and itcan be written as:

θ = θm cosπz

d(11)

By replacing θ in Eq. 10, multiplying it with cos πzd

and integrating over theall thickness (from z = −d

2to z = d

2) we obtain:

p1θm − p2θ3m = γ

∂θm∂t

(12)

where

p1 = A−K1π2

d2(13)

5

and

p2 =K3 −K1

2

π2

d2+

D

2(14)

From Eq. 12 we obtain the time dependence of θm:

θ2m (t) =θ2m (0)

p2p1θ2m (0) +

[1− p2

p1θ2m (0)

]exp

(− t

τA

) (15)

with the relaxation time τA

τA =γ

2[2wE + μ−1

0 χaB2 −K1π2

d2

] (16)

where

E =−μ−1

0 cχaNB2

2w − μ−10 cχaNB2

(17)

When the magnetic field is switched off, a relaxation process from the previ-ously disturbed state (when the field was on) will occur with the relaxationtime τB (Fig. 2b). This time can be evaluated using the same procedure asbefore with the difference that the free energy density does no longer containthe magnetic field term:

f = fn + fint + fγ (18)

τB =γ

2[K1

π2

d2− F

] (19)

where

F = 2w

( −2w

2w − μ−10 cχaNB2

)(20)

From Eq. 15 and Eq. 20 we obtain a simple system where the unknown pa-rameters are the interaction energy and magnetic anisotropy of MWCNT:

χaN = − Eμ0

2fB2

⎛⎝1±

√1 +

4E

F

⎞⎠ (21)

6

magnetic poles

Fig. 3. Experimental set-up for the measurements of MWCNT’s magneticanisotropy.

In this equation we shall only consider the positive value as it has been proventhat the carbon nanotubes has positive magnetic anisotropy [23–25]

3 EXPERIMENTAL SET-UP AND RESULTS

Planar aligned cells were prepared using 180 μm myler as spacers. The glassplates of the cell were previously coated with a layer of polyvinyl alcoholsolution and baked in the oven at 120 ◦C for 60 minutes, then rubbed with asmooth cloth.

The cells were filled with a mixture of nematic MCL 6601 and 0,5 % volumetricfraction of MWCNT. Static measurements were performed in order to findthe Freedericksz transition threshold for magnetic field, leading to the valueof 0.0650 T.

Dynamic measurements of relaxation times when the field was switched onand off were made for several fields higher than the critical threshold.

Experimental setup is presented in Fig. 3. The sample is placed between thepoles of an electromagnet and subjected to the action of a 632.8 nm laser beam.In order to apply the laser beam parallel to the magnetic field direction, thereare some small holes performed in the poles which do not have a significantinfluence on the magnetic field. A couple of crossed polarizers are used: one ofthem for a better polarization of the incident beam and the second one as ananalyzer for the emergent fascicle. A photodiode is used to record this fascicleand send it to the acquisition system. When the magnetic field is switchedon, a light intensity versus time plot is obtained (Fig. 4a) with a successionof maxima and minima as given in Eq. 1. The order number of minima wasplotted as a function of time (Fig.4b) then a theoretical fit was performedusing Eq. 15 and a dependence of the relaxation time τA a on interactionenergy and magnetic anisotropy was found.

7

a) b)

Fig. 4. Experimental results when a magnetic field B = 0.1959 T was applied: a)intensity versus time plot; b) fitting curve of minima order versus time.

a) b)

Fig. 5. Experimental results when a magnetic field B = 0.1959 T was switched off:a) intensity versus time plot; b) fitting curve of minima order versus time.

A similar procedure was followed when the magnetic field was switched offand another intensity versus time distribution was obtained (Fig. 5a). In thiscase, the order number intensity minima versus time plot looks different (Fig.5b). The fitting function was obtained in B = 0 assumption given in Eq. 18.The relaxation time τB resulted from fitting parameters also depends on theinteraction energy and magnetic anisotropy.

Using Eq. 21 we obtain the magnetic anisotropy of MWCNT given in Table1, with an average value of 6.61× 10−5.

8

Table 1

B (T) 1/τA (s−1) 1/τB (s−1) χCN

0.1605 0.0091 0.0163 5.71× 10−5

0.1676 0.0118 0.0196 6.27× 10−5

0.1746 0.0164 0.0201 6.68× 10−5

0.1817 0.0214 0.0193 6.87× 10−5

0.1888 0.0324 0.0128 6.75× 10−5

0.1959 0.0342 0.0135 6.81× 10−5

0.2030 0.0357 0.0135 6.76× 10−5

0.2101 0.0382 0.0152 7.04× 10−5

The results are in good agreement with the ones reported in other papers [22–25] on SWCNT’s. One can notice that the magnetic anisotropy of MWCNT ishigher than those of SWCNT. This can be explained by the fact, alreadyproved that magnetic susceptibility perpendicular to the nanotube axis islarger than the one parallel to it. Since MWCNT have multiple carbon sheets,it seems reasonable to have a higher value of perpendicular susceptibility forMWCNT’s than for SWCNT’s and to obtain a higher anisotropy.

4 CONCLUSIONS

A new method for determining MWCNT’s magnetic anisotropy was proposed.This method has the advantage of using low magnetic fields (less than 1 T)and very small amounts of substance with no special preparation as long asthe nanotubes easily disperse themselves by sonication in NLC. Using homo-geneous aligned LC cells is another advantage of the method by providing analigned group of MWCNT. Thus the random orientation considerably reducedand the measurements are more accurate.

5 ACKNOWLEDGMENT

The work has been funded by sectorial Operational Program for Human Re-sources Development 2007–2013 of the Ministry of European Funds throughthe Financial Agreement POSDRU/159/1.5/S/132397.

9

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