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DOI: http://dx.doi.org/10.15688/)volsu10.2014.3.5
УДК 621.3.049.77 ББК 22.379
STRUCTURE, INTERACTIONS AND KINETICS OF RING-LIKE FORMATIONS OF CARBON NANOTUBES (NANOFIBERS) IN POLYMER NANOCOMPOSITES
Mikitaev Abdulah Kasbulatovich
Doctor of Chemical Sciences, Professor,
Kabardino-Balkarian State University named after H.M. Berbekov I_dolbin@mail.ru
Chernyshevskogo St., 175, 360004 Nalchik, Russian Federation
Kozlov Georgiy Vladimirovich
Senior Researcher,
Kabardino-Balkarian State University named after H.M. Berbekov I_dolbin@mail.ru
Chernyshevskogo St., 175, 360004 Nalchik, Russian Federation
Zaikov Gennadiy Efremovich
Doctor of Chemical Sciences, Professor,
Head of the Department of Biological and Chemical Physics of Polymers, Institute of Biochemical Physics named after N.M. Emanuel, RAS chembio@sky. chph. ras.ru
Kosygina St., 4, 119334 Moscow, Russian Federation
Abstract. It has been shown that the parameters of formation of carbon nanotubes ^ (nanofibers) ring-like structures can be described in the scope of fractal kinetics. In this case the main feature is represented by interactions in polymer matrix at the level of nanofiller. w The indicated model explained relatively high degree of bonds between the nanocomposites
rh
of polymer/carbon nanotubes at ultra small nanofiller contents.
Key words: nanocomposite, carbon nanotubes (nanofibers), interactions, ring-like
N structure, fractal kinetics.
>
d
"n Aims and Background degree), typical for the indicated nanofillers,
* result in formation by them of ring-like structures,
As it is well-known [12], carbon nanotubes outwardly resembling macromolecular coils [13;
¡> (nanofibers) possess very high longitudinal 17]. This circumstance has already been noted
.•S elasticity modulus (1000-2000 GPa) and low in literature. So, the authors [13] assumed, that
^ transverse stiffness. These factors together with carbon nanotubes ring-like structures can be
© a large ration length/diameter (high anisotropy considered as macromolecular coils in
semidiluted solutions. The authors [8] used Flory formula for rod-like macromolecules in case of carbon nanotubes percolation threshold in polymer nanocomposites determination. Nevertheless, such examples are rare enough and do not have systematic character.
It is obvious, that formation process of carbon nanotubes (nanofibers) ring-like structures can not be instantaneous for example in virtue of the polymer melt high enough viscosity, in which these structures are formed. Hence, the indicated process has definite duration, that makes necessary its kinetics study. Therefore purpose of the present work is the study of intercommunication of interactions, formation kinetics and structure of ringlike formations of carbon nanotubes (nanofibers) in polymer nanocomposites.
Experimental
Polypropylene (PP) "Kaplen" of mark 01030 was used as matrix polymer for the studied nanocomposites. This PP mark has a melt flow index of 2.3-3.6 g/10 min, molecular weight of ~ (2-3) x 105 and polydispersity index of 4.5.
Carbon nanotubes (CNT) of mark "Taunite", having an external diameter of20-70 nm, an internal diameter of 5-10 nm and length of 2 mcm and more, were used as a nanofiller. In the studied nanocomposites PP/CNT taunite content was varied within the limits of 0.25-3.0 mass %. Besides, the multiwalled nanofibers (CNF) were used, having a layers number of 20-30, diameter of 20-30 nm and length of the order of 2 mcm. In the nanocomposites PP/CNF CNF content Wn was varied within the limits of 0.15-3.0 mass %.
Nanocomposites PP/CNT and PP/CNF were prepared by the components mixing in melt on twin screw extruder Thermo Haake, model Reomex RTW 25/42, production of German Federal Republic. Mixing was performed at temperature 463-503 K and screw speed of 50 rpm during 5 min. Testing samples were prepared by casting under pressure method on a casting machine Test Samples Molding Apparate RR/TS MP of firm Ray-Ran (Taiwan) at temperature 503 K and pressure 43 MPa.
Uniaxial tension mechanical tests have been performed on the samples in the shape of two-sided spade with the sizes according to GOST 112 62-80. The tests have been conducted on the universal
testing machine Gotech Testing Machine CT-TCS 2000, production of German Federal Republic, at temperature 293 K and strain rate of ~ 2 x 10-3 s-1.
Results and Discussion
CNT (CNF) ring-like structures radius RCNT can be determined with the aid of the following percolation relationship [6] :
Ф« =
nLn
(2rcnt )
(1)
where jn is nanofiller volume contents, LCNT and rCNT are length and radius of carbon nanotube (nanofiber), respectively.
The value jn was calculated according to the well-known formula [11]:
W
Ф « =—, Pn '
(2)
where Wn is nanofiller mass contents, pn is its density, estimating for nanoparticles as follows [ibid.]:
Pn = 1
r)1/3, kg/m3
(3)
where DCNT is a carbon nanotube (nanofiller) diameter, which is given in nm.
A CNT (CNF) ring-like formations structure can be characterized most exactly with the aid of its fractal dimension D, which is true structural characteristic, since it describes the distribution of CNT (CNF) ring-like formations elements in space [ibid.]. The value RCNT calculation according to the equation (1) has shown its reduction at jn growth. At the largest from the used jn values, corresponding to Wn =3.0 mass %, the indicated dependences have the tendency of asymptotic branch achievement, that supposes achievement by CNT or CNF ring-like structures of their RCNT minimum values. By the analogy with macromolecular coils this means the achievement of maximally dense ring-like structure with the greatest limiting value of its fractal dimension Df ( Df™ ), which is determined according to the equation [7] :
D\
4{d +1)
7
(4)
where d is the dimension of Euclidean space, in which a fractal is considered (it is obvious, in our case d =3). For d =3 the value Df* =2.286.
r
Further for the value D ^ estimation the irreversible aggregation model can be used, which describes polymerization processes (macromolecular coil formation) and gives the following relationship for particles aggregates radius Ragr determination [16]:
agr
R.
-1/(d -Df )
(5)
where c0 is aggregating particles initial concentration.
Coefficient in the relationship (5) can be determined at the following conditions: Ragr = RCNT, c0= jn and Df=f The values RCNT and jn were accepted for Wn =3.0 mass %. As the estimations according to the indicated relationship have shown, the value Df grows at jn increasing (RCNT reduction) from 1.91 up to 2.29 for nanocomposites PP/CNT and from 1.76 up to 2.21 for nanocomposites PP/CNF.
As it is known [9], the process rate in fractallike medium is described by the following equation: 0 ~ r", (6)
where t is process duration, h is medium heterogeneity exponent (0 < h < 1), which is transformed into zero for homoheneous samples only [ibid.].
The value h was calculated according to the equation [10]:
Df -1 h = -f—
(7)
In Fig. 1 the dependences of RCNT on CNT (CNF) ring-like structures formation process rate J are adduced for the considered nanocomposites. As it was to be expected, the process rate J increasing results in RCNT growth, i.e. the value J characterizes not CNT (CNF) rolling up in ringlike structures, but their unrolling. The dependence RCNT(J) can be expressed analytically by the following empirical equations:
Rcnt = 90 + 5.0x103 û
for carbon nanotubes and
Rcnt = 45 + 2.70x103 û
(8)
(9)
for carbon nanofibers. The parameters t in the equation (6) and RCNT in the equations (8) and (9) are expressed in s and nm, respectively.
Let us note, that the smallest RCNT value according to the equations (8) and (9) is equal
approximately to 2DCNT at J=0, since for the obvious reasons the condition RCNT = 0 is impossible. The greatest value RCNT in case of homogeneous mediums ( h = 0) is equal to 5090 nm for CNT and 2745 nm for CNF.
Rcnt, nm
500
250
0
5
10 Sx102
Fig. 1. The dependences of CNT (CNF) ring-like formations radius RCNT on their unrolling rate J for nanocomposites PP/CNT (1) and PP/CNF (2)
Let us consider the intercommunication of CNT (CNF) ring-like structures formation rate J and interaction between them. At the indicated structure modeling as macromolecular coils the interaction between their elements and polymer matrix can be characterized by the parameter e, determined as follows [10]:
2 - D
e =
f
D
(10)
For macromolecular coils the value e is varied within the limits of -1/3 + 1.0. In the point D^ =2.0 parameter e changes its sign, that corresponds to the interactions type change from repulsion forces (positive e) up to attraction forces (negative e). In Fig. 2 the dependence of CNT (CNF) ring-like structures formation rate J on interaction parameter e is adduced for the considered nanocomposites. As one can see, the linear dependence of CNT (CNF) ring-like structures unrolling rate J at e increasing is obtained, i.e. the repulsion interaction intensification, which is described analytically by the following empirical equation:
û = 0.275 (e+0.215).
(11)
From the equation (11) it follows, that the value J = 0 is achieved at e = -0.215, i.e. at D f =2.548. The greatest value J = 0.334 is
c
0
2
realized at e = 1.0, that corresponds to h = 0.192 or D, = 1.384.
Fig. 2. The dependence of CNT (CNF) ring-like structures unrolling rate J on interaction parameter e for nanocomposites PP/CNT (1) and PP/CNF (2)
g
Fig. 3. The dependences of interaction parameter e on nanofiller volume contents j for nanocomposites PP/CNT (1) and PP/CNF (2)
As it is noted above, nanofiller contents j increasing results in dimension D^ enhancement and, according to the equation (10), in the exponent h increasing, i.e. in medium heterogeneity degree enhancement. In Fig. 3 the dependences of parameter e on the value 4(such form of the indicated dependences was chosen for their linearization) are adduced for the considered nanocomposites. As one can see, e linear reduction is observed, i.e. the attraction interactions intensification, at nanofiller contents
growth. This dependence can be expressed analytically by the following empirical equations:
e = 0.25 - 0.85<4 (12)
for carbon nanotubes and
e = 0.25 - 0.85<4 (13)
for carbon nanofibers.
The equations (11)-(13) combination demonstrates, that for the considered nanocomposites e variation is realized within the range, which is smaller than theoretical one for macromolecular coils (e = -1/3 + 1.0), namely, within the limits of e = -0.215 0.30. The condition of full balance of attraction and repulsion forces for CNT (CNF) ring-like structures e = 0 is realized at j = 0.0075 for nanocomposites PP/CNT and jn= 0.0155 for nanocomposites PP/CNF.
-Kcnt, nm
Fig. 4. The dependences of CNT (CNF) ring-like formations radius RCNT on nanofiller volume contents for nanocomposites PP/CNT (1) n and PP/CNF (2)
In Fig. 4 the dependences RCNT(jn) are adduced for the indicated nanocomposites, each one from which can be approximated by two straight lines with enough precision degree. The transition between these two parts of the dependences RCNT( jn) corresponds to jn» 0.0088 for nanocomposites PP/CNT and jn» 0.0120 for nanocomposites PP/CNF, that agrees well enough with the indicated above jn values, at which the condition e = 0 is achieved or, in other words, with values j , at which the
transition from attraction interaction up to repulsion interactions of CNT (CNF) ring-like structures is realized. The linear dependences RCNT(jn) slope is in about 15 times larger in case of the repulsion interactions in comparison with the attraction interactions. In other words, in case of interactions first type much more fast RCNT growth at jn reduction is observed, that influences positively on the characteristics of nanocomposites polymer/ carbon nanotubes [17]. This effect explains the indicated nanocomposites relatively high reinforcement degree at ultrasmall concentrations (jn< 0.0015) of carbon nanotubes [5; 8].
Conclusions
Thus, in the present work the results have shown that the formation (unrolling) rate of carbon nanotubes (nanofibers) ring-like structures in polymer nanocomposites can be described within the framework of fractal kinetics, where the indicated rate is defined by interactions level in these structures. A medium heterogeneity level or interactions degree and sign is controlled by nanofiller contents. The transition from attraction interactions up to repulsion interactions defines carbon nanotubes (nanofibers) ring-like structures radius fast growth, that results in nanocomposites relatively large reinforcement degree at ultrasmall contents of the indicated nanofillers.
REFERENCES
1. Bakhracheva Yu.S. Fracture Toughness Prediction by Means of Indentation Test. International Journal for Computational Civil and Structural Engineering, 2013, vol. 9, iss. 3, pp. 21-24.
2. Baron A.A, Bakhracheva Yu.S. A method for Impact Strength Estimation. Mechanika (Kaunas), 2007, vol. 66, no. 4, pp. 31-35.
3. Baron A.A, Bakhracheva Yu.S, Osipenko A.P. Fracture Toughness Estimation by Means of Indentation Test. Mechanika (Kaunas), 2007, vol. 67, no. 5, pp. 33-36.
4. Baron A.A., Gevlich D.S., Bakhracheva Yu.S. Specific Plastic Strain Energy as a Measure of the Cracking Resistance of Structural Materials. Russian metallurgy, 2002, no. 6, pp. 587-592.
5. Blond D., Barron V., Ruether M. et al. Enhancement of Modulus, Strength and Toughness in Poly(methyl methacrylate)-Based Composites by the Incorporation of Poly(methyl methacrylate)-
Functionalized Nanotubes. Advanced Functional Materials, 2006, vol. 16 (6), pp. 1608-1614.
6. Bridge B. Theoretical Modelling of the Critical Volume Fraction for Percolation Conductivity of Fibre-Loaded Conductive Polymer Composites. Journal of Materials Science Letters, 1989, vol. 8 (2), pp. 102-103.
7. Family F. Fractal Dimension and Grand Universality of Critical Phenomena. Journal of Statistical Physics, 1984, vol. 36, iss. 5-6, pp. 881-896.
8. Komarov B.A., Dzhavadyan E.A., Irzhak VI., Ryabenko A.G., Lesnichaya V.A., Zvereva G.I., Krestinin A.V. Epoxy-Amine Composites With Ultralow Concentrations of Single-Layer Carbon Nanotubes. Polymer Science Series A, 2011, vol. 53, iss. 6, pp. 502-509.
9. Kopelman R. Excitons Dynamics Resembling Fractal One: Geometrical and Energetical Disorder. Pietronero L., Tosatti E., eds. Fractals in Physics. Amsterdam, Oxford, New York, Tokyo, North-Holland, 1986, pp. 524-527.
10. Kozlov G.V, Dolbin I.V., Zaikov G.E., eds. The Fractal Physical Chemistry of Polymer Solutions and Melts. Toronto, New Jersey, Apple Academic Press, 2014. 316 p.
11. Mikitaev A.K., Kozlov G.V., Zaikov G.E. Polymer Nanocomposites: Variety of Structural Forms and Applications. New York, Nova Science Publishers Inc., 2009. 319 p.
12. Moniruzzaman M., Winey K.I. Polymer Nanocomposites Containing Carbon Nanotubes. Macromolecules, 2006, iss. 39 (16), pp. 5194-5205.
13. Schaefer D.W., Justice R.S. How Nano are Nanocomposites? Macromolecules, 2007, iss. 40 (24), pp. 8501-8517.
14. Semenova L.M., Bakhracheva Yu.S., Semenov S.V. Laws of Formation of Diffusion Layers and Solution of the Diffusion Problem in Temperature-Cycle Carbonitriding of Steel. Metal Science and Heat Treatment, 2013, vol. 55, no. 1-2, pp. 34-37.
15. Shapochkin V.I., Semenova L.M., Bakhracheva Yu.S., Gyulikhandanov E.L., Semenov S.V Effect of Nitrogen Content on the Structure and Properties of Nitrocarburized Steel. Metal Science and Heat Treatment, 2011, vol. 52, no. 9-10, pp. 413-419.
16. Shogenov VN., Kozlov G.V. Fractal Clusters in Physics-Chemistry of Polymers. Chapter 2. Multicomponent Polymeric Materials. Apple Academic Press, 2013, pp. 13-47.
17. Yanovsky Yu.G., Kozlov G.V., Zhirikova Z.M., Aloev V.Z., Karnet Yu.N. Special Features of the Structure of Carbon Nanotubes in Polymer Composite Media. International Journal of Nanomechanics Science and Technology, 2012, vol. 3, iss. 2, pp. 99-124.
СТРУКТУРА, ВЗАИМОДЕЙСТВИЯ И КИНЕТИКА КОЛЬЦЕОБРАЗНЫХ ОБРАЗОВАНИЙ УГЛЕРОДНЫХ НАНОТРУБОК (НАНОВОЛОКОН) В ПОЛИМЕРНЫХ НАНОКОМПОЗИТАХ
Микитаев Абдулах Касбулатович
Доктор химических наук, профессор,
Кабардино-Балкарский государственный университет имени Х.М. Бербекова I_dolbin@mail.ru
ул. Чернышевского, 175, 360004 г. Нальчик, Российская Федерация
Козлов Георгий Владимирович
Старший научный сотрудник,
Кабардино-Балкарский государственный университет имени Х.М. Бербекова I_dolbin@mail.ru
ул. Чернышевского, 175, 360004 г. Нальчик, Российская Федерация
Заиков Геннадий Ефремович
Доктор химических наук, профессор,
заведующий отделом биологической и химической физики полимеров, Институт биохимической физики им. Н.М. Эмануэля РАН chembio@sky. ЛрЬ ras.ru
ул. Косыгина, 4, 119334 г. Москва, Российская Федерация
Аннотация. В статье показано, что параметры формирования кольцеобразных образований углеродных нанотрубок (нановолокон) могут быть описаны в рамках фрактальной кинетики. В данном случае основной характеристикой указанного процесса являются взаимодействия в полимерной матрице на уровне нанонаполнителя. Описанная модель позволила объяснить относительно высокую степень связанности нано-композитов полимерных/углеродных нанотрубок при очень низком содержании нанона-полнителя.
Ключевые слова: нанокомпозит, углеродные нанотрубки (нановолокна), взаимодействия, кольцеобразная структура, фрактальная кинетика.
