CC BY
20
UDC 678.7-1
M. A. Mikitaev, G. V. Kozlov, A. K. Mikitaev, G. E. Zaikov
THE COMPOSITE MODELS APPLICATION FOR ELASTIC MODULUS OF BLENDS POLY(ETHYLENE TEREPHTHALATE)/POLY(BUTYLENE TEREPHTHALATE) DESCRIPTION
Keywords: blend, micromechanical model, percolation, fractal analysis, elastic modulus, interfacial adhesion.
The quantitative interpretation of the extreme dependence of elastic modulus on composition for blends poly(ethylene terephthalate)/poly(butylene terephthalate) has been offered, which uses the percolation theory and fractal analysis. It has been shown that elastic modulus extreme increasing is due to the corresponding growth of shear strength of blends components autohesional bonding. The micromechanical models do not give the indicated effect adequate description.
Ключевые слова: смесь, микромеханическая модель, перколяция, фрактальный анализ, модуль упругости, межфазная адгезия.
С использованием теории перколяции и фрактального анализа предложена количественная интерпретация экстремальной зависимости модуля упругости от состава для смесей поли(этилентерефталат)/поли(бутилентерефталат). Показано, что экстремальное повышение модуля упругости связано с соответствующим ростом предела прочности при сдвиге когезионной связи компонентов смеси. Микромеханические модели не дают указанному эффекту адекватное описание.
Introduction
The maximum of elastic modulus at equal contents of components in blends is one from outstanding features of the blends poly(ethylene terephthalate)/poly(butylene terephthalate) (PET/PBT) [1, 2]. In addition it is important to note, the elastic moduli of initial PET and PBT are practically equal -the discrepancy between them makes up ~ 1 % by absolute value, that is smaller than their determination experimental error. The authors [1, 2] supposed that variation of elastic modulus of blends PET/PBT at composition change was due to blends components miscibility variation. It is significant that PET and PBT are miscible partly, namely, amorphous phase miscibility (single glass transition temperature) can be realized, but crystalline phase's nonmiscibility (two crystallization temperatures) is observed [2]. In work [3] it has been proposed to consider semicrystalline polymers as composites, in which amorphous phase is played by matrix role and filler role - by crystallites. However, in such treatment the extreme change of crystalline phase characteristics is necessary, whereas regardless of blends PET/PBT production mode these characteristics are changed monotonously and not very significantly [4]. Nevertheless, the blends PET/PBT can be considered as polymer/polymeric composites [5], particularly at the condition, that one polymeric phase is dispersed in another as disperse particles with the size of 0.2-1.5 mcm [6]. With appreciation of the stated above considerations the purpose of the present work is the treatment of blends PET/PBT as polymer/polymeric composites within the frameworks of micromechanical [7] and percolation [8] models for quantitative description of the extreme dependence of their elastic modulus on composition.
Experimental
The industrial production polymers were used: PET PELPET, grade G5801 (intrinsic viscosity [|]=0.8 dL/g), procured from firm Reliance Industries Ltd (India), and PBT LUPOX, grade GP-1000 ([r|]=1.0 dL/g), supplied by firm LG Polymers India Pvt Ltd
(India). PET and PBT pellets were manually mixed and dried at temperature 393 K for 8 hours in a hot air circulating oven [2].
The blends with PET:PBT ratio of 80:20, 70:30, 60:40, 50:50, 40:60 and 20:80 by weight were prepared by components mixing in melt using twin-screw extruder Haake Rheocord 9000 of mark TW100 at the screw rate rotation of 40 rpm in the range of temperatures of 423-533 K. Then the extrudate was water cooled and granulated. The extruded pellets were molded into standard mechanical tests specimens by injection molding mode on molding machine Boolani Industries Ltd., production of India, within the range of temperatures 493-553 K [2].
The mechanical tests of blends PET/PBT on three-pointed bending were carried out on universal testing machine LR-50K, Lloyds Instrument according to ASTM 790M-90 at temperature 293 K and cross-head speed of 2.8 mm/min [2].
Results and Discussion
Let us consider the micromechanical models application of the description of blends PET/PBT elastic modulus. In the simplest from the possible cases two models were proposed [7]. For the case of parallel arrangement the uniform strain in both phases is assumed and upper boundary of elastic modulus of blends is given as follows [7]:
EU =En(Pn+Em(Pm, (1)
where En and Em are elastic moduli of filler and matrix, respectively, <n and <m are volume contents of filler and matrix, accordingly (<m=1-9„).
In case of series arrangement the stress is assumed to be uniform in them and the lower boundary
of elastic modulus of blends Elbl is determined according to the equation [7]:
E'=-
EрПm
* = (2)
EnVm +EmVn
At the condition En=Em, which is true for the considered blends, the equations (1) and (2) give the
trivial result:
pup = FI =p =p
i.e.
the indicated describing the
equations are not capable of experimentally observed maximum on the dependence of elastic modulus on composition for blends PET/PBT [1, 2]. This is explained by the fact, that all micromechanical models require fulfillment of the condition En>Em for their correct application. One more obvious deficiency of micromechanical models is apriori used in them assumption of perfect adhesion between phases of composite, that is far from always being fulfilled for real composites [9].
The percolation model gives the following relationship for Ebi determination [8]:
E=i+пы1-'
^ m
(3)
The relationship (3) does not also take into consideration interfacial adhesion level between composite phases and therefore the authors [5] modified it as follows:
E=i+ii&
E m
ы
■J1"7
(4)
where ba is a dimensionless parameter, characterizing the interfacial adhesion level (in case of perfect adhesion ba=1.0 [5]).
By its physical essence interfacial adhesion between PET and PBT represents the formation of autohesional bonding, shear strength of which %c can be determined as follows [10]:
rc= 6.28 x10-5/Vc383, MPa, (5)
where Nc is the number of intersections (contacts) of macromolecular coils in boundary layer of two polymers (in the considered case - PET and PBT).
Within the frameworks of fractal analysis the value Nc can be determined according to the relationship [11]:
Nc ~ Rg-d , (6)
where Rg is gyration radius of macromolecular coil, Df is its fractal dimension, d is the dimension of Euclidean space, in which a fractal is considered (it is obvious, that in our case d=3).
The value Df is calculated according to the following technique. First Poisson's ratio value v was estimated with the aid of the formula [12]:
uY _ 1 -2v " 6(1 + v) '
where ct7 is blend yield stress.
Then the structure fractal blends PET/PBT was determined equation [13]: df = (d-1) (1 +v) .
And at last for linear polymers the value Df is determined as follows [14]:
(9)
(7)
dimension df for according to the
(8)
Df =
2df
In Fig. 1 the relation between parameter ba, determined with the aid of the equation (4), and shear strength %c of autohesional contact PET-PBT is adduced. As it was to be expected from the most general considerations, between parameters ba and %c the linear correlation is observed, which passing through
coordinates origin, described by the following empirical equation:
ba= 4.6tc . (10)
Fig. 1 - The relation between parameter ba, characterizing interfacial adhesion level, and shear strength xc of autohesional bonding for blends PET/PBT
The equations (4) and (10) combination allows to obtain the following relationship for determination of blends PET/PBT elastic modulus: Eu=Em\ + 11(4.6rc^ )17 ]. (11)
It is obvious, that PBT relative fraction at its content smaller than 50 mass % and PET relative fraction at its very same content is accepted as <p„. In Fig. 2 the comparison of theoretically calculated according to the equation (11) Ey and experimentally
obtained Ebi elastic modulus values for blends PET/PBT is adduced, which has show their good correspondence
(the average discrepancy between Ey and Ebl makes
up smaller than 5 %).
Вы, GPa
Fig. 2 - The comparison of theoretically calculated according to the equation (11) Ey and experimentally measured Ebi values of elastic modulus for blends PET/PBT
Conclusions
Thus, the present work results have demonstrated, that micromechanical models cannot describe correctly the dependence of elastic modulus on composition for blends PET/PBT. This is due to non-fulfilment of the conditions, obligatory for the indicated models: essentially larger value of filler elastic modulus in comparison with corresponding characteristic for polymer matrix and assumption of perfect interfacial adhesion (as far as we know, the Sato-Furukawa model [15] is sole micromechanical model, taking into consideration real level of interfacial adhesion in composites). The considered blends elastic modulus enhancement is due to the growth of contacts number of macromolecular coils of PET and PBT in boundary layer and corresponding enhancement of interfacial adhesion level. The offered model, using percolation theory and fractal analysis notions, allows enough precise quantitative description of the experimental data.
Work is performed within the complex project on creation of hi-tech production with the participation of the Russian higher educational institution, the Contract of JSC "Tanneta" with the Ministry of Education and Science of the Russian Federation of February 12, 2013 No. 02.G25.31.0008 (Resolution of the Government of the Russian Federation No. 218).
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© M. A. Mikitaev - Ph.D., Kh.M. Berbekov Kabardino-Balkarian State University, Nal'chik, Russia, G. V. Kozlov - Senior Researcher, Kh.M. Berbekov Kabardino-Balkarian State University, Nal'chik, Russia, A. K. Mikitaev - Doctor of Chemistry, Full Professor of Organic Chemistry and Macromolecular Compounds Department, Kh.M. Berbekov Kabardino-Balkarian State University, Nal'chik, Russia, G. E. Zaikov - Doctor of Chemistry, Full Professor, Plastics Technology Department, Kazan National Research Technological University, Kazan, Russia, [email protected].
© М. А. Микитаев - кандидат химических наук, Кабардино-Балкарский государственный университет им. Х.М. Бербекова, Нальчик, Россия, Г. В. Козлов - старший научный сотрудник, Кабардино-Балкарский государственный университет им. Х.М. Бербекова, Нальчик, Россия, А. К. Микитаев - доктор химических наук, профессор кафедры Органической химии и высокомолекулярных соединений, Кабардино-Балкарский государственный университет им. Х.М. Бербекова, Нальчик, Россия, Г. Е. Заиков - доктор химических наук, профессор кафедры Технологии пластических масс, Казанский национальный исследовательский технологический университет, Казань, Россия, [email protected].
