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УДК 538.913 ББК 22.379
THE FRACTAL MODEL OF NANOCOMPOSITES POLYPROPYLENE/CARBON NANOTUBES MELT VISCOSITY
Kozlov Georgy Vladimirovich
Senior research associate
Kabardino-Balkarian state university of H.M. Berbekov I_dolbin@mail.ru
Chernyshevskogo St., 175, 360004 Nal'chik, Russian Federation
Pearce Eli M.
Doctor of Science, Professor of Brooklyn Branch of New York University EPearce@poly. edu
Jay St., 333, 12001 Brooklyn, United States of America
Zaikov Gennady Efremovich
Doctor of chemical sciences, Professor, Head of Division of biological and chemical physics of Polymer The Federal State Budget Institution of Science N. M. Emanuel Institute of Biochemical Physics Chembio@sky.chph.ras.ru
Kosygina St. 4, 119334 Moscow, Russian Federation
Abstract. The nanocomposites polypropylene/carbon nanotubes melt viscosity change at nanofiller contents variation was studied. It has been shown that continuous models, developed for polymer composites melt viscosity description, cannot describe this parameter in the nanocomposites case. The correct description of the last rheological properties can be obtained within the frameworks of the fractal model of viscous liquid flow.
Key words: nanocomposite, carbon nanotubes, melt, viscosity, fractal model.
Introduction
m o
^ The inorganic nanofiller of various types ^ usage for polymer nanocomposites production g obtains widespreading at present [6]. However, the indicated nanomaterials melt properties are not studied fully enough. As a rule, when nanofillers ^ application is considered, than compromise S3 between improvement of mechanical properties in § solid-phase state, melt viscosity enhancement at ^ processing, nanofillers dispersion problem and O process economic characteristics is achieved. § Proceeding from this, the relation between
n
^ nanofiller concentration and geometry and © nanocomposites melt properties is an important
aspect of polymer nanocomposites study. Therefore the purpose of the present paper is the study and theoretical description of the dependence of nanocomposites polypropylene/carbon nanotubes melt viscosity on nanofiller contents.
Experimental
Polypropylene (PP) "Kaplen" of mark 01 030 was used as matrix polymer. This PP mark has a melt flow index of 2.3-3.6 g/10 min, molecular weight of ~ (2-3)x105 and a polydispersity index of 4.5.
Carbon nanotubes (CNT) of mark "Taunite", having an external diameter of 2070 nm, an internal diameter of 5-10 nm and length
of 2 mcm and more, were used as nanofiller. They were prepared by chemical deposition (catalytic pyrolysis) of carbonhydrogens (CnHm) on catalysts (Ni/Mg) at atmospheric pressure and temperature of 853-923 K. CNT preparation process duration made up 10-80 min. In the studied nanocomposites taunite contents was changed within limits of 0.25-3.0 mass %.
Nanocomposites PP/taunite were prepared by 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 obtained 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.
The nanocomposites PP/CNT melt viscosity was characterized by a melt flow index (MFI). MFI measurements were performed on extrusion-type plastometer Noselab ATS A-MeP (Italy) with capillary diameter of2.095 ± 0.005 mm at temperature 513 K and load 2.16 kg. The sample was maintained at the indicated temperature during 4.5 ± 0.5 min.
Uniaxial tension mechanical tests have been performed on the samples in the shape of two-sided spade with sizes according to GOST 112 62-80. The tests have been conducted on universal testing apparatus Gotech Testing Machine CT-TCS 2000, production of German Federal Republic, at temperature 293 K and strain rate ~ 2 x 10-3 s-1.
Results and Discussion
For polymer microcomposites, i.e. composites with filler of micron sizes, two simple relationships between melt viscosity n, shear modulus G in solid-phase state filling volume degree 9 n were obtained [7]. The relationship between n and G has the following form:
Л
По
G
G:
(i)
where n0 and G0 are melt viscosity and shear modulus of matrix polymer, accordingly.
Besides, microcomposite melt viscosity increase can be estimated as follows (for 9 „ <0.40) [7]:
П ,
— = i + Ф„ По
(2)
In fig. 1 the dependences of ratios qj nm and G /G (where G and n are shear modulus
n m v n ' n
and melt viscosity of nanocomposite, G and n
mm
are the same characteristics for the initial matrix polymer, accordingly) on CNT mass contents Wn for nanocomposites PP/CNT are adduced. The shear modulus G was calculated according to the following general relationship [1]:
G = —
(3)
Fig. 1. The dependences of ratios of shear moduli GJGm (1) and melt viscosities nj nm (2) of nanocomposite G, n and matrix polymer G , n on nanofiller mass contents W for nanocomposites PP/CNT.
' n A J m7 ' m n A
where E is Young's modulus, d^ is nanocomposite structure fractal dimension, determined according to the equation [1]:
d f = {d -1)(1 + v)
(4)
where d is dimension of Euclidean space, in which a fractal is considered (it is obvious, in our case d = 3), v is Poisson's ratio, estimated according to the mechanical tests results with the aid of the relationship [5]:
ay 1 - 2v
E 6(1 + v)'
(5)
where sY is yield stress, E is elasticity modulus.
MFI reciprocal value was accepted as melt viscosity n measure. The data of Fig. 1 have demonstrated clearly, that in the studied nanocomposites case the relationship (1) is not fulfilled both qualitatively and quantitatively: GJ Gm increase corresponds to ratio nn/ nm decay at W enhancement and absolute values n / n are
n 1 n 1 m
lower essentially than the corresponding magnitudes GJGm.
In Fig. 2 the comparison of parameters nj nm and (1+9 n) for nanocomposites PP/CNT is adduced. Discrepancy of experimental data and relationship (2) is obtained again: discrepancy of absolute values n / n and (1+9 ) is observed
n m n
and melt relative viscosity reduction corresponds to (1+9n) enhancement. At the plot of Fig. 2
drawing the value 9 n was determined according to the formula [8]:
Фп
W„
(6)
where p n is carbon nanotubes density, which was determined as follows [6]:
:0.188(dC
-D"
V
г/
(7)
where D^T and D^T are the mean magnitudes of external and internal diameters of nanotube, accordingly.
Hence, the data of Figs. 1 and 2 have shown that the fulfilled in polymer microcomposites case the relationships (1) and (2) are not correct for nanocomposites PP/CNT. In case of the relationship (1) correctness and Kerner's equation application for shear modulus G calculation viscosity nn lower boundary can be obtained according to the equation [7] :
= 1 + 25Ф"
Пт
1 - Фп'
(8)
Since value n is inversely proportional to MFI, then in such treatment the equation (8) can be rewritten as follows:
П MFIm
Пт MFIn
= 1 +
2.5фи 1-Ф„
(9)
n
n
Fig. 2. The dependences of melt viscosities ratio of nanocomposite and matrix polymer nj nm on nanofiller volume contents (1+9n) (1) for nanocomposites PP/CNT. The straight line shows the relation 1:1
where nrei is nanocomposite melt relative viscosity, MFIm and MFIn are MFI values for matrix polymer and nanocomposite, accordingly.
In Fig. 3 the dependence of MFIn on CNT mass contents Wn for nanocom-posites PP/CNT, calculated according to the equation (9), is adduced. As one can see, the quantitative discrepancy of theoretical calculation (curve 1) and experimental data (points) is observed. If the equation (9) assumes melt viscosity increase (MFIn reduction) at Wn growth, then the experimental data find out opposite tendency (MFI > MFI ).
v n m>
The indicated discrepancy requires principally distinguished approach application at polymer nanocomposites melt viscosity description. Such approach can be fractal analysis, within the frameworks of which the authors [4] proposed the following relationship for fractal liquid viscosity n estimation:
n{l ) ~щ12
(10)
По is
where I is a flow characteristic linear scale, constant, df is fractal dimension.
As it is known [9], CNT in virtue of their strong anisotropy (in the taunite case the mean ratio of length to the diameter is more than 45) and low transverse stiffness form ring-like structures with radius RCNT, which can be determined with the aid of the equation [3]:
Фп
nlcnt rcnt (2 rcnt )
(11)
where LCNT and rCNT are length and radius of carbon nanotubes, accordingly.
Further the radius RCNT is accepted as l. Since CNT surface gets into contact with polymer then makes contact, then its fractal dimension d ,
' surf
was chosen as df. The value dsurf can be estimated as follows [6]. The value of CNT specific surface Su was estimated according to the equation [2]:
S =-
6
P DC
r n c
(12)
and then the dimension dsurf was calculated with the aid of the equation [6]:
S, = 410
De
is n
2
(13)
Calculation according to the equation (13) gives the value dsurf = 2.79. As it is known [1], polymer matrix macromolecular chain is not capable to "reproduce" CNT surface high roughness and therefore it "perceives" the indicated surface as much smoother. In this case one should use the effective value d , (def),
surf v surj''
which is equal to [10]:
dIurf = 5 dsurf.
(14)
And as earlier, the value n in the equation (10) was considered as reci-procal value of MFIn, and the constant n0 was accepted equal to 1.1 (MFIm)-1. At these conditions and replacement proportionality
MFIn, g/10 min
Fig. 3. The dependences of melt flow index MFIn on nanofiller mass contents Wn for nanocomposites PP/CNT. 1 - calculation according to the equation (9); 2 - calculation according to the equation (10); 3 - the experimental data
sign in the relationship (10) by equality sign the theoretical MFI values can be calculated, if the value
n '
Rcnt is given in microns. In Fig. 3 the comparison of the obtained by the indicated mode MFIn values and the experimental dependence MFIn(^n) is adduced, from which a good correspondence of theory and experiment follows.
The relationship (10) allows to make a number of conclusions. So, at the mentioned above conditions preservation RCNT increase results to nanocomposite melt viscosity reduction. Enhancement duur, i.e. CNT surface roughness degree increase in virtue of the equation (14) usage, influences similarly. The indicated factors, critical ones for CNT, are not taken into consideration in the continuous treatment of melt viscosity for polymer microcomposites (the equation (8)).
Conclusions
Obtained in the present paper results have shown that the developed for microcomposites rheology description models do not give adequate treatment of melt viscosity for polymer nanocomposites filled with carbon nanotubes. The correct description the indicated nanocomposites rheological properties can be obtained within the frameworks of fractal model of viscous liquid flow. It is significant that such approach distinguishes principally from the used ones at microcomposites description. So, for nanocomposites filled with
nanotubes the last rolling up degree in ring-like structures and their surface effective fractal dimension is necessary to take into consideration.
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ФРАКТАЛЬНАЯ МОДЕЛЬ НАНОТРУБОК НАНОКОМПОЗИТОВ ПОЛИПРОПИЛЕНА/УГЛЕРОДА
Козлов Георгий Владимирович
Старший научный сотрудник
Кабардино-Балкарского государственного университета им. Х.М. Бербекова I_dolbin@mail.ru
ул. Чернышевского, 175, 360004 г. Нальчик, Российская Федерация
Пирс Элай М.
Доктор наук, профессор
Бруклинского филиала Нью-Йоркского университета ЕРеагсе@ро1у. edu
Джей, 333, 12001 Бруклин, Соединенные Штаты Америки
Заиков Геннадий Ефремович
Доктор химических наук, профессор,
заведующий отделом биологической и химической физики полимеров Федерального государственного бюджетного учреждения науки Институт биохимической физики им. Н.М. Эмануэля РАН chembio@sky. ЛрЬ ras.ru
ул. Косыгина, 4, 119334 г. Москва, Российская Федерация
Аннотация. Было изучено изменение вязкости нанокомпозитов полипропилена/ углерода с нанотрубками при плавлении с разным содержанием нанонаполнителя. Было показано, что постоянные модели, принятые для соединений полимера, расплавляются до определенной вязкости, и нельзя использовать эти параметры в случае нанокомпозитов. Корректное описание последних реологических свойств может быть получено в пределах структур фрактальной модели вязкого жидкого потока.
Ключевые слова: нанокомпозит, углеродные нанотрубки, плавление, вязкость, фрактальная модель.
