2012 AC]'IA UNIVERSI'IXTIS C]AROI,INAE MAI'HEMATICA IJ1' PIIYSICA vol. -53, NO. I

SEEKING INITRINSIC MAGNETISMIN CARBON NANOTUBES

B. BlTTovÁ. J. PoLTIERoVÁ_VEJPTRAVovÁ, s. suRteNovÁ. na. KALBAc], S. D^NIS

Praha

ReceivedJune 14,2011

Revi.sed September I 5, 20 I I

We have investigated magnetic rcsponse of rcsidual metal catalyst in thc raw and supcrpurified HiPco singlc wall carbon nanotubes (HiPco raw and HiPco-SP SWCNTs). Alsoseveral techniques leading to removal oí metal catalyst, such as oxidation in mild acid and

high temperaturc annealing have been pcrlormed. It has been shown in case of comrnercial

and commercially purified (Hipco-raw and SP) SWCNTs that the residual metal catalyst

is in the Íirrm of nanopartic|cs even in the HiPco SP SWCNTs that should contain mini-mal amount of the mctal. Mtissbaucr spectroscopy of the HiPco-raw SWCNTs provetl

the catalyst nanoparticles arc in the form of FeTC. Analysis of the synchrotron X ray

cliffraction measurcment togcthcr with magnetic studies by means of temperature depen

dence of magnetization, magnetization isotherms and susceptibility suggested a core shell

structure of thc nanoparticlcs in the HiPco-raw SWCNTs, with a magnctically orientcd

core and a paramagnetic shell, which is almost removed in case of the HiPco*SP cata-

lyst nanoparticles. Analysis oí'purified samplcs showed that in most cascs, the residrral

metal also rernains in lbrrn of sintercd nanoparticlcs with reduced shcll part. Only thc high

tempcratuÍe annealcd SWCNTs cxhibited diamagnetic responsc, pointing at thc high pu-

rity of SWCNTs, even much better than is the purity of commercially puriÍied HlPco'SPSWCNTS.

Instilute of Physics of the ASCR, v.v.i.' Na Slovance 2, I8221 Prague 8' Czeoh Rcpublic (B. Bittová.

J. Polticrová-VejptravoVá' S. Burianová)J. Heyrovsky Institute ol'Physical Chcmistry of the ASCR, v.v.i., Dolejskova 3' l8223 Praguc Íl,

Czech Republic (M. Kalbac)Charles University in Praguc, Faculty ol Mathematics and Physics, Departmcnt ol'Condensed Mattcr

Physics, Ke Karlovu -5, l2l l9 Prague 2, Czech Rcpublic (S. Ilanis)

This work was supported by thc Grant Agency of the Czech Rcpublic under project no . P2041 l0l 1611 .

Wc also thank to synchrotron radiation sourcc ANKA in Karlsruhc fbr providing thc bcarntime.

Key words and phra,se,s. Carbon nanotubes, intrinsic rnagnetism

E-ma il ad dre ss : biltova@fzu.cz

JJ

l. Introduction

Since the magnetism and superconductivity of the pure carbon materials has beentheoretically predicted and already observed in special cases (magnetic ordering inthe proton-irradiated graphite lEsquinazi et al.,2OO3l, pressure induced magnetismin fullerenes [Makarova et al., 20011), the possibility to study and utilize magneticresponse of carbon nanotubes (CNTs) for further applications in spintronics has ap-peared recently.

The CNTs could posses not even the semiconducting and metallic properties, de-pending on their chirality, but it has been also proved theoretically that the metallicCNTs could exhibit feromagnetic ground state IDresselhaus et al.,2OOl, Montiouxet al., 20011. In spite of these studies discussing the defect-induced magnetismin cNTs, this phenomenon has not been experimentally observed yet. It is mainlybecause of presence of the residual metal catalyst in the nanotubes and its untrivialremoval.

Because of mentioned reasons, purification of the CNTs started to be the crucialpoint. Many repofiS about the chemical and physical methods of puriÍication havebeen published since the year 2006, but only the few ones gave the evidence of theremoval of residual catalyst supporled by the comprehensive experimental analysis.

Because of that, we have tried several approaches of purification of nanotubesand investigated the properties of purified nanotubes by methods that provided usthe comprehensive information about the amount and nature of residual catalyst. Notonly the proportional amount of the metal in the sample is important, but also the formin which this metal is presented, because the magnetic response is different whetherthere are the nanoparticles or the single atoms.

Because the magnetic properties of the catalyst in the non-purified commerciallyavailable nanotubes were not studied yet, we have started with the deep investigationof HiPco raw swcNTs fBittova et al.,2o7t]. Also the HiPco_Sp SWCNTs werestudied to have the comparison of commercial and laboratory methods of purifica-tion. Discussion on magnetic properties of nanoparticles is based on the superpara-magnetism and related phenomena considering interparlicle interactions lNeel et al.,19491.

2. Exp erimental section

At first, the commercially available HiPco_raw and Hipco_sP nanotubes were in-vestigated. Then the several purification processes were performed on the HiPco_rawnanotubes, such as 1. low temperature annealing (400 "c) followed by the reflux inmixture of HCI and H2o2 (sample labelled as HiPco_400), 2. annealing at 1200'c instatic vacuum (HiPco-1200) and 3. high temperature vacuum annealing at22oo"C(HiPco_2200).

34

The samples have been characte

amount of data Ío analyze properly

ThermogravimetrY (TG) has bet

precursor in the SWCNTs' The sam

rate of 10 lýmin in atmosphere con

We have used comPlementary I

determination, respectively. The sy

for determination of catalyst phase I

alyst particles in the HlPco-raw ar

tion data has been taken at PDIFF I

with wavelength of 1'24 i\. The di

of 3-63' with the steP of 0.02".

software lWilles and Young,1982}

The MÓssbauer Spectra were en

mine the iron Phase in theHiPco-

transmission mode with 57Co diffu

constant acceleration. The spectn

foil and the isomer shift was exPt

HiPco-raw samPle was measured

to 4.2K. The litting of the sPectr

program. The samPles seem not

undetectable amount of metal cata

Magnetic measurements on all

SQUID device (Quantum Design)

24OOK. The zero-field-cooled (2

in low external magnetic fields (frt

measured at 10 and 300K uP to fpendence of the a.c. susceptibility

measured in non-zero magnetic fit

3. Resu

3.1 AnalYs

TG provided the mass contenl

values of ]5 wtŤo for the HiPcc

HiPco-1200 and O wt% for the

treated sample (HiPco-400) was t

not sufficient.

de-

alliciou.x

.ism

inlyvial

cial

ave

the

is.

bes

ust{ot

)rm

her

been

rg in

tism

retic

; ap-

'llyion

la-

ra-

tl. ,

The samples have been characterized by several methods to gain comprehensiveamount of data to analyze properly propertics of the rnetal catalyst.

Thermogravimetry (TG) has been used fbr setting the mass content of the metalprecursor in the SWCNTs. The samples were heated up to the 800'C with the heatingrate of l0 K/min in atmospherc containing 80a/o of He and 20a/o of Oz.

We have used complementary methods Íbr the phase analysis and particle sizedetermination, respective|y. The synchrotron radiation diÍŤiactiorr (S-XRD) was used

Íbr determination of catalyst phase and for estimation of the mean diameter of the cat-

alyst particles in the HIPco raw and HiPco-SP SWCNTs, respectively. The diÍŤiaction data has been taken at PDIFF bearnline in ANKA Karlsruhe, using the radiationwith wavelength of 1.24Á'. The diÍIraction patterns were collected within the rangeof 3-63' with the step oi 0.02". Further analyses have been done using FullProfsoftware IWilles and ktttng, 19821.

The MÓssbatler Spectra were employed as tr cornplementary experiment to deter-

mine the iron phase in theHiPco_raw sample. The measurement was done in the

transmission mode with 57Co difiused into the Rh matrix as the sourcc moving withconstant acceleration. The spectrometer was calibrated by means of a standard Fetbil and the isomer shift was expressed with respect to this standard at293 K. TheHiPco_raw sample was measured in cryostat at the temperatures varying from 293to 4.2K. The litting of the spectra was perfbrmed with the help of the NORMOSprogram. The samples seem not to be suitable for the experiment because of theundetectable amount of metal catalyst.

Magnetic measurements on all HiPco SWCNTs were perÍbrmed using MPMS7 -SQUID device (Quantum Design) up to magnetic Íield of 7 T in the temperature range2 400K. The zero-Íield coo|ed (ZFC) and Íield-cooled (FC) curves were measuredin low external rnagnetic Íjelds (Íiom 5 to _50 mT). The mtrgnetization isotherms weremeasured at l0 and 300K up to íield of 7T in both polarities. The temperatr'rre de-pendence of the a.c. susceptibility (with the alternating field arnplitude of 3 mT) wasmeasured in non-zero magnetic field (l-l00mT) in frequency range of 0. I l00Hz.

3. Results and discussion

3.1 Analysis of compound and structure

TG provided the mass content of metal precursor in the samples leading to thevalues of J5 wta/r, for the HiPco_raw, 5 wta/o for the HiPco_SP, 25 wtc/o lbr thcHiPco_1200 and 0 wtolo l'or the HiPco_2200 SWCNTs (Figure l). The mild acidtreated sample (HiPco_400) was not analysed because the amount of the sample wasnot suÍiicierrt.

n-

IW

in

in

C

35

saIc&c

oE

104

80

60

40

20

0

-20

:- -::;-,i i\--.\ \r"\ 'r \

1 r\l '\.\ it,\ \'r

\\\r,io-" -"i \'i .

-

HiPco sPHiPco l20CHiPco 22()0

2o0 4ÚÚ 600 800 1 000

TiK)

Frcunp l. The thermogravimetry data of all samples.

The S-XRD pattern of the HiPco_raw SWCNTs reveals the peak positions cor-responding to those of the cementite, Fe3C (Figure 2), which crystallizes in the or-thorombic Pnma space group with the four units in the unit cell (Z=4) [Shein et aL.,

20011. The eight of the iron atoms are in 8d positions (Fes), four are placed in 4cpositions (Fe") and the four carbon atoms sit in the interstitials. Because the qualityof the diftiaction pattern has not been suitable for the full profile fitting procedureby the Rietveld method, the mean size of the Fe3C parlicles was calculated from the( I 02) and (201 ) reflections, leading to the value of 1 .9 nm, considering the resolutionfunction.

The PXRD pattern of the HiPco*400 and the HIPco_l200 samples provided pres-ence both of Fe3C and Fe2O3 phases, confirming the partial removal of carbonousshell encapsulating nanoparlicles and subsequent oxidation of metal particles (data

are not presented).The MÓssbauer Spectroscopy conÍirmed the presence of Fe:C-cementite phase in

the HiPco_raw sample. No metal iron (zero izomer shift) has been detected. Theroom temperature spectrum consists of doublet indicating the superparamagnetic state

of the sample that can be attributed to the small size of Fe3C particles in nanotubes.

The spectrum was fitted with two doublets representing the two types of sites foriron atoms-the general (Fer) and special (Fe") sites (Figure 2). The intensities oflines were fixed up to 2:7. The obtained parameters are in good agreement with thosepresented by other authors lRon and Mathalone, 19711.

3.2 Magnetization studies and hysteresis

The zero-Íield-cooled (ZFC) and Íield-cooled (FC) curves (Figures 3-6) exhibitthe main attributes of the superparamagnetic (SPM) systems. The ZFC curves ex-hibit sharp maximum at the temperature ?nyay representing blocking temperature 7s

36

Frcuxs 2. Left: S-XRD 1

SWCNTs. The vertical mt

Bragg rcflections, the cross

of thc SWCNTs reflectionr

sured at room temperature

special Positions of iron in

of major fraction of Particles, ar

temperatures-the temPerature ol

as Tppp. The discrePancY betwee

case of a SPM system, signalizes

In case of commercial SWCI10 mT in case of the HiPco-rawtively and Tplpp are 202Kfot tbe

spectively. Also the reduction of

such a system, has been observed

temperature in case of the HiPcoparticle size or inter-particle inter

Inspecting the low temperatur(

the small saturation of the magnr

weak inter-particle interactions. I

is negligible, which is not surprisi

six times lower than in case of tl

particles within the sample leadir

In an ideal case of a SPM sYsten

Curie-Weiss law. Thus Plotting tl(result for the HiPco-SP samPle i

'qt*aonmw

1.001

0.ss8

I SS6

ri.s94

50

v { mm.s-11

5

Frcunn 2. Left: S-XRI) pattems lbr thc HiPco raw and HiPco-SPSWCNTs. Thc verl,ical marks correspond to the positions of the FerCBragg reflcctions, the cross-hatched arca illustrates expectcd positit.rns

ol the SWCNTs re1]cctiilns. Right': Fit oí'the Mijssbauer Spcctra mea-

surecl at foom {empcraturc by the two subspectra, reprcsenting the twcr

special positions of iron in F'erC.

of major fiaction of particles, and both the ZFC and FC curves coincide at high

temperatures-the temperature of deviation (l'e of the largest particles) is labelled

as Zpypp. The discrepancy between Tyaa and 7p1pp, that should be equal in the ideal

case of a SPM system, signalizes the particle size distribution in the sample.

In case of commercial SWCNTs, the blocking temperatures ?tp44x are 35 K at

l0mT in case of the HiPco_raw and 26K at l0mT for HiPco-SP, samples, respec-

tively and 7p1pp. i1Í€ 2o2K for the HiPco-raw and 278 K Íbr HiPco-SP samples, re-

Spectively. Also the reduction of the Zn,rex in increasing magnetic Íield, typical for

such a systrlm, has been observed (inset in Figure 3). Shift of the 71aa1 to the lower

temperature in case of the HiPco-SP sample could be attributed to the reduction ofparticle size or inter-particle interactions.

Inspecting the low temperature part of the FC curve of the HiPco-raw SWCNTs,

the small saturation of the magnetization was observed, signalizing the presence of

weak inter-particle interactions. Saturation of the FC curve of the HiPco-SP sample

is negligible, which is not surprising because the amount of magnetic metal is at least

six times lower than in case of the HiPco-raw sample, suggesting better dilution ofparticles within the sample leading to the minimization of inter-particle interactions.

ln an ideal case of a SPM system without interaction, the FC curve should obey the

Curie-Weiss law. Thus plotting the temperature dependence of inverse magnetization

(result for the HiPco_SP sarnple is illustrated in the inset of Figure 3), resulting curve

Fe3C l

l

.9

!E

':!ť

31

t,-

should bc linear. The non-linearity of such curve was observed íor both samples. as aconsequencc either of inter-particle interactions (more significant for the HiPco_rawsarnple), particle size distribr-rtion (the HiPco-SP sample) or combination of both ofthese eÍŤ'ects'

The measurement of rnagnetization isotherms provided the additional inÍbnnationabout structure of magnetic nar.roparticles in both samples. The hysteresis (typicalt'eature of the block state below the 7s) was observed atzK with the symmetricvalues ol'coercivity, H1; for opposite polarities of rnagnetic Íjeld, reachirrg values ofl50 mT for the HiPco-raw and l02 mT Íbr the HiPco-SP samples, respectively (Fig_ure 3). The dccrease ol-the coercivity points atthe reduction of the nanoparticlc sizeor inter-particle interactions in thc HiPco-SP sample. The magnetization isothermsirbove the I1j were analyzed by using the Íit of generalized Langevin function andthe average n-ragnetic moments per particle has been calculated. Knowing both themagnetic moment of the particle and that of the unit cell (r. equal to 2l .6ps[Sheinet a\.,2001 l), it is possible to calcr-rlate the volume and subsequently the "magnetic"size of the particle (Table l). It is obvious that the "magnetic size" of the particlein the HiPco-raw sample is larger than the size of the particle calculate<] Íiorn the<liÍŤiaction pattern. The discrepancy could be explained by the so-called core-shellmodel of the particle with the well crystalline ar.rd rnagnetically ordercd core (whichcontributes to the difŤiaction) and an amclrphous shell, which only increases rnagneticmoment of the particle by a linear, paramagnetic-like tcrm. Increase of magneticsize of the nanoparticles of the HiPco-SP sample in comparison with the HiPco_rawsarnple could be either the resr-rlt of the real increase of particle size in the HiPco-SPsarnple or more probably it ntcans that the shell parl of the particles in the HiPco_rawsample which decreases the resulting magnetic moment has been removed and thiscxplanation is valid whetl-rer the part oí the shell of the HiPco-raw nanoparticles isnot only amorphous, but also pararnagnetic. This assumption is confirmed also by re-duction of linear paramagnetic contribution to the HiPco-SP magnetization isothermmeasured at 300 K with respect to the HiPco_raw sample.

Regarc1ing discussion on nlagnetic properties of commercial SWCNTs. Íbllowingidea can be cleduced Íiom the results obtained on purificd SWCNTs. ln case of theHiPco-400 sample, the annealing irr air lead to the sintering of particles (as could bededuced fiom thc saturation of the low temperature part of the FC curve and shiÍi of7'ya1 to the much higher values. with the diameters of particles ranging Íbr 4.2 to6 nm). Mild acid treatment probably leads to the removal of the most of the particles(little saturation at the beginning of the FC curve is the consequencc of dilution ofparticles in the sample, thus of their partial removal).

Annealing ol SWCNTs at I 200 'C (the HiPco_ 1200 sarnple) lead to ( l) reducrionof number of particles (proved by only little saturation of the FC curve), (2) highlyprobably lead to partial removal of paramagnetic shell (as it could be deduced fromalmost similar course ol'magnetization isotherms measured at 2 and 300 K, Figure 6),and (3) further sintcring of remaining particles, as could be viewed from increase of

3u

3. tr

2.5

2.4

i FC ,.,6.2s- 6.1EJ: U,VSo

,S r.sE$ r.oř

0.5

Ů.0

6š 0'sES o.+ž

0.2

ll.0

-Ů ''t

1T

020T1

Frcuns 3. Lelt: The tcmp

nctization mcasured at 1(

plcs. Thc curves measurc(

ol- magnctization are in thr

surcd at <]iÍŤ-erent tcÍnpera

ples, respectivcly. Thc d

inset.

Trsr.p 1. Median, pre ant

rclation Lto = Ftr"^p(-ldo and d,.. compared witl

tcntperaturcs, d1111pp and

po x tttr(irrl d1 (nm)

t.l fZl 2.6 t 0.1

0.8

HiPco rawHiPco_SP

HiPco 12002.0 (2) 3.0 + 0.

4.8 (2) 4.0 + 0.,

magnetic size calculated from Íi

(Figure 6. Tablc l).Magnetic measurements Perf

magnetic response was purely dl

i,asa)_raw

rth of

ration,picai

ietricLes of(Fie-

: size

LCTMS

r and

h rhe

Shein

retic"

rliclen the-shell

vhich

;netic

;neticr_Iaw

o_SPr_faw

I this

les is

)y re-

herm

rwing

rf the

Lld be

rift of1.2 to

ticles

on of

.ction

ighlyfrom

re 6),

rse of

3.0

z_3

2.4

0. í]

'] 0

o.fi

6.2

6.1

6.0

ZFCFC

o)

E

'16

oS tsE$ r.oE

oš 06E$ o.+ž

0.2

0.0

-$.2

.:

20 40 60

T íK!t04E

-8

0

?_

4

6

' 300 l( -r**'"2K

'r,ť

H iPao raw $ Ť_ slu ý zF", 'fu,t' -J'.ru > ''

lÁ

"*@""'d_ď ].'

*...-*,-"*-.-*'#f -o.s B.o 0.5

- 2K" 3C|0 K

HipcÉ sF

tt)ml

-' T (Kl

-166

4

2

10a 200 300

p

E

=

!r- J

€.t-g

,o.u o.o o.

PoH {T)H iPao_sp

Frcur<s 3. Lel't: The tempcrature dcpcndencc of the 7tsC and FC rnag-

notization mcasured at 10mT Íor thc HiPoo_raw an<l HiPco SP sam-

ples. The curves measured at l 0 mT and I T and thc inverse dcpendencc

of magnetization are in thc insets. Right: Magnctization isothcrms mea-

suretl at dift'erent tcmperatufcs Íbr the HiPco raw ancl HiPcil-SP sam-

plcs, respectivcly. The dctail of thc loops measured at 2 K are in the

insct.

TeeI'e 1. Median, prs and mean, pm magnetic lloment oonnccted by

relation L!0 - Fnt*p ( i), with thc appropriate magnetic diameters,

do and d,,,, compared with particle diameters oalculated Íiom blockingtemperatures, dropr- and d11aa1.

10{:} 200 300

T (K)

3.0 t 0.74.0 + 0.6

/n^ .6 .4 '2 B 2 4

poH (T)

HiPco_rawHiPco SP

HiPco 1200

',,1 au tt -) tr p'1, i to-tp"i aI(nm) drrr,i (tt*) a.11*t' (nt")

0.9 (2) 2.4 x 0.3 2.4 x 0.4 4.3 + 0.5

1.5 (2) 2.1 + 0.3 2.2 x 0.5 4.1 + 0.1

4.3 (2) 3.6 + 0.3 3.7 + 0.5 10.0 + 0.90.-su

o.22

magnetic size calculated from fitting the unhysteretic data by the Langevin function(Figure 6, Table 1).

Magnetic measurements performed on the HiPco-2200 sample showed that the

magnetic response was purely diamagnetic (Figure 6). Together with the result from

I

F

T

C

HaPco 4U04.0

1.0

0.5

0.0

0.002

0.000. 10 mT

64

Es20

-2

r nÁŤ 0.3

< v.z

š o',0.0

o

E

=

-ooo'j'-0.004.]cogosc

-o ooa lI

-oooul y

iFu*ň-0 010 1

I

-0.0. , l- -z

100

t!qq 200

200

T (K)

r50

,;' ;; ;;T (K)

Frcunn 4. The temperat"ure dependence of thc ZFC and FC magnetiza-tion mcasured at 10 mT tor thc HiPco_400 sample alier annealing stepwith the insert depcndenoe o1'magnetization in the inset (leti) and aÍterthe mild acid reflux (right).

2.0

1.8

'1 .6

1.4

1.2

1.n

0.8

0.6

ťJ '4 -1.5100 200 300 400 -0.02 0.00 0.02 0.04

r ( K) uoH/I (T/K)

Frcur<s -5. The temperature dependencc of ZFC and FC magnetizationmeasurcd at 10mT for thc HiPco_1200 sample with the magnetizationisotherms in the inset (leÍt)' Thc example o1 the Íit of the wcight sumol the Langevin function to the data at 300 K in Langevin scaling themoment distribution lunction in the insct.

TG measurement, we should state that there is the undetectable amount of metal.As was claimed in the introduction, to study magnetism on SWCNTs, sample shouldcontain no metal, thus further investigation of atomic traces of iron within the samplesare required.

40

L5

Frcunp, 6. The temperatul

tion Íor the HiPco-2200 s

We have investigated structurt

in the commercial HiPco-raw an

The S-XRD and MÓssbauer Spec

SWCNTs. most in the form ofHiPco-raw samPle was determi

ter value equal to 1.9 nm. Resultr

structure of the particles, with tt

core. Even if the HiPco-SP saml

been demonstrated, this metal is

ticles with the blocking temperat

size with respect to the HiPco-rrThe increase ol mean magnetic n

with the decrease of coercivitY i

tization isotherms measured at 3

due to the removal of Paramagthat the HiPco-SP SWCNTs are

because further removal of meta

lnspecting magnetic ProPertisible sintering and removal of I

acid treated HiPco-400 samPle

quent sintering of nanoparticles.

HiPco-2200 sample together wi

suggested that this method lead t

1.0

0.5

EE

0q l

i-0.5 i

I

,.0 I

r3lrlr

Ú.002 r ' I

0"000

-0.002

-0. nil4

-0.0{}6

-0.008

-0.Ůl n

-Í} 012

T {K}

Frcunn 6. The tempcratllre <lepcndcnce of thc ZFC and f'C magnetiza-

tion Íor thc HiPco 2200 sample.

4. Conclusion

We have investigated structural and magnetic properties of the residual Fe catalystin the commercial HiPco-raw and HiPco-SP (super-puriÍied) SWCNTs, respectively.

The S-XRD and MÓssbauer Spectroscopy confirmed presence of Fe in the HiPco-rawSWCNTs, most in the form of cementite, Fe3C. Size of the nanoparticles in the

HiPco-raw sample was determined from the S-XRD, leading to the mean diame-

ter value equal to I .9 nm. Results of magnetic measurements pointed at the core-shellstructure of the particles, with the amorphous paramagnetic shell and the crystallinecore. Even if the HiPco_SP sample should contain less than 5 wto/o of metal, as it has

been demonstrated, this metal is also in the Íbrm of weakly-interacting SPM nanopar-

ticles with the blocking temperature aÍ26K, pointing either at the decrease of particlesize with respect to the HiPco_raw sample or reduction of inter parlicle interactions.

The increase of mean magnetic moment and "magnetic" diameter of particles together

with the decrease of coercivity and reduction of linear paramagnetic part in magne-

tization isotherms measured at 300 K finally confirmed the decrease of particles sizedr-re to the removal of paramagnetic shell. Besicles that, it has been demonstrated

that the HiPco-SP SWCNTs are not suitable Íbr reliable studies of CNTs magnetism

because l-urther removal of metal catalyst particles is required.lnspecting magnetic properties of purified HiPco-raw SWClÝTs resulted in pos-

sible sintering and removal of nanoparticles in low temperature annealed and mildacid treated HiPco 400 sample, partial reduction of paramagnetic shell and subse-

quent sintering of nanopafiicles. Diamagnetic response of high temperature annealed

HiPco_2200 sample together with the undetectability of rnetal via therrnogravimetry

suggested that this method lead to complete removal of metal particles and gave much

m*E

:ol* g*o3o519*$tx g$ryqo&oae'G**&ÚtssI

i

I

I

' * r 011: '1 í^]m!

tt'

40c

I tJt_rOU

10

)4

etal.

ruld

ples

4l

l

better purity than commercially treated SWCNTs (HiPco_SP). Further investigationof purity on atomic scalc and structure of treated nanotubes are required.

References

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A('IA L]NIVEItSIT,

AVERAGING PROBL]RE,LATTVITY AND C(

PETR KAŠPAR

Praha

Rece ived .Jtue I I , 201 I

Revised September I 8, 20 I l

It is tradition tn cosn

Robcrtson-Walker) sPi

tropic on small scalcs s

somc averaging Procccwill in gencral obtain I

ergy condition and so I

d iÍŤ-erent approachcs tt

ln General relativitY (GR) I

stein field equations. As emPl

tion do not commute, i... (f,the metric tcnsor and () is son

in cosmology one usuallY uses

Walker (FRW) metric and the

want to use a simple model al

scale function o(/) (not to use

should Put a new correlation 1

Charles UniversitY, FacultY of It

šovičkách 2, l 80 00 Praguo, Czech J

I would like to thank to Otakar I

supported by GAUK 39891I' GACI

Kev tvttruls and Phrases. Cr.neral

E - m.a il a d d re's s : Petrkaspar@ atl

42