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© Mikitaev M.A., Kozlov G.V, Mikitaev A.K., Artsis M.I., Zaikov G.E., 2015
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ТЕХНИКО-ТЕХНОЛОГИЧЕСКИЕ ИННОВАЦИИ
DOI: http://dx.doi.org/10.15688/jvolsu10.2015.3.4
УДК 669.017 ББК 24.4
THE COMPOSITE MODELS APPLICATION FOR ELASTIC MODULUS OF POLY (ETHYLENE TEREPHTHALATE)/ POLY(BUTYLENE TEREPHTHALATE) BLENDS DESCRIPTION
Muslim Abdulakhovich Mikitaev
Candidate of Chemical Sciences, Senior Researcher,
Department of Organic Chemistry and Macromolecular Compounds, Kabardino-Balkarian State University named after H. M. Berbekov [email protected]
Chernyshevskogo St., 175, 360004 Nalchik, Russian Federation
Georgiy Vladimirovich Kozlov
Senior Researcher, Department of Organic Chemistry and Macromolecular Compounds, Kabardino-Balkarian State University named after H. M. Berbekov [email protected]
Chernyshevskogo St., 175, 360004 Nalchik, Russian Federation
Abdulakh Kasbulatovich Mikitaev
Doctor of Chemical Sciences, Professor,
Department of Organic Chemistry and Macromolecular Compounds, Kabardino-Balkarian State University named after H. M. Berbekov [email protected]
Chernyshevskogo St., 175, 360004 Nalchik, Russian Federation
Marina Izraylevna Artsis
Candidate of Chemical Sciences, Researcher,
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
Gennadiy Efremovich Zaikov
Doctor of Chemical Sciences, Professor,
Head of 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
ISSN 2305-7815. Вестн. Волгогр. гос. ун-та. Сер. 10, Иннов. деят. 2015. № 3 (18) 4 5
ТЕХНИКО-ТЕХНОЛОГИЧЕСКИЕ ИННОВАЦИИ ----
Abstract. The quantitative interpretation of the extreme dependence of elastic modulus on the composition of poly(ethylene terephthalate)/poly(butylene terephthalate) blends has been proposed. At this, the authors apply the basics of the percolation theory and fractal analysis. It has been shown that the extreme increase in elastic modulus is due to the corresponding growth of shear strength of blends components during the autohesional bonding. It is noted that the micromechanical models do not give the adequate description of the indicated effect.
Key words: blend, micromechanical model, percolation, fractal analysis, elastic modulus, interfacial adhesion.
Introduction
The maximum of elastic modulus at equal contents of components in blends is one of the outstanding features of the blends of poly(ethylene terephthalate)/poly(butylene terephthalate) (PET/PBT) [2; 3]. 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 [2; 3] 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 phases nonmiscibility (two crystallization temperatures) is observed [2]. In the work [6] 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 [13]. Nevertheless, the blends PET/PBT can be considered as polymer/ polymeric composites [11], particularly at the condition, that one polymeric phase is dispersed in another as disperse particles with the size of 0.2-1.5 mcm [10]. 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 [1] and percolation [5] 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 ([^]=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
9 000 of mark TW100 at the screw rate rotation of 40 rpm in the range of temperatures of 423533 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 [1]. For the case of parallel arrangement the uniform strain in both phases is assumed and upper boundary of elastic modulus of blends EJ is given as follows [1]:
4 6 The Composite Models Application for Elastic Modulus of PET/PBT Blends Description
ТЕХНИКО-ТЕХНОЛОГИЧЕСКИЕ ИННОВАЦИИ
Ebp = E rn + Em (1)
bl птп ттт v '
where E and E are elastic moduli of filler and matrix, respectively, mn and mm are volume contents of filler and matrix, accordingly (mm =1 - mn).
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 [1]:
E1 =-
J-^L1
EE
E m + E m
n>m m^n
(2)
At the condition E = E , which is true for the considered blends, the equations (1) and (2) give the trivial result: E’Up = Elbl = En = Em, i. e. the indicated equations are not capable of describing the experimentally observed maximum on the dependence of elastic modulus on composition for blends PET/PBT [2; 3]. 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 Ebl determination [5]:
El = 1+и(Фп )L7. (3)
m
The relationship (3) does not also take into consideration interfacial adhesion level between composite phases and therefore the authors [11] modified it as follows:
El = 1+11( ba Фп )17 (4)
m
where ba is a dimensionless parameter, characterizing the interfacial adhesion level (in case of perfect adhesion ba = 1.0 [11]).
By its physical essence interfacial adhesion between PET and PBT represents the formation of autohesional bonding, shear strength of which xc can be determined as follows [15]:
rc = 6. 28 x 105 N3; 83 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 [14]:
N ~ R2Df -d (6)
c g v '
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 [8]:
or 1 - 2 v
Ebl = 6 (1+v)
where ar is blend yield stress.
(7)
Then the structure of fractal dimension df for blends PET/PBT was determined according to the equation [4]:
df =(d -1)(1 + v). (8)
And at last for linear polymers the value Df is determined as follows [7]:
2df
Df =-f. (9)
In Fig. 1 the relations between parameter ba, determined with the aid of the equation (4), and shear strength xc of autohesional contact PET-PBT is adduced. As it was expected from the most general considerations, between parameters ba and xc the linear correlation is observed, which passes through coordinates origin described by the following empirical equation:
ba = 46V (10)
The combination of equations (4) and (10) allows to obtain the following relationship for determination of blends PET/PBT elastic modulus:
Eh, = E
bl m
1 + 11( 4.6^ )L
(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
ISSN 2305-7815. Вестн. Волгогр. гос. ун-та. Сер. 10, Иннов. деят. 2015. № 3 (18) 4 7
ТЕХНИКО-ТЕХНОЛОГИЧЕСКИЕ ИННОВАЦИИ
accepted as фп. In Fig. 2 the comparison of theoretically calculated according to the equation (11) ETbl and experimentally obtained Ebl elastic modulus values for blends PET/PBT is adduced, which show their good correspondence (the average discrepancy between Еты and Ebl makes up less than 5 %).
b
a
Fig. 1. The relation between parameter ba, characterizing interfacial adhesion level, and shear strength xc of autohesional bonding for blends PET/PBT
Ebi, GPa
Fig. 2. The comparison of theoretically calculated according to the equation (11) Еты and experimentally measured Ebl values of elastic modulus for PET/PBT blends
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 [12] is a sole micromechanical model taking into consideration the 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 proposed model in which the percolation theory and fractal analysis notions are used, allows precise quantitative description of the experimental data.
Acknowledgements
The present research has been performed within the complex project on creation of hi-tech production with the participation ofthe Russian higher educational institution, Tanneta JSC, 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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The Composite Models Application for Elastic Modulus of PET/PBT Blends Description
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7. Kozlov G.V, Mikitaev A.K., Zaikov G.E. The Fractal Physics of Polymer Synthesis. Toronto, New Jersey, Apple Academic Press, 2014. 359 p.
8. Kozlov G.V., Sanditov D.S. Anharmonic Effects, and Physical and Mechanical Properties of Polymers. Novosibirsk, Nauka Publ., 1994. 261 p. (in Russian).
9. Kozlov G.V., Yanovskiy Yu.G., Zaikov G.E.
Structure and Properties of Particulate-Filled Polymer Composites: The Fractal Analysis. New York, Nova Science Publishers Inc., 2010. 282 p.
10. Maruhashi Y., Tida S. Transparency of Polymer Blends. Polymer Engineering Science, 2001, vol. 41, pp. 1987-1995.
11. Mikitaev A.K., Kozlov G.V., Zaikov G.E.
Polymer Nanocomposites: Variety of Structural
Forms and Applications. New York, Nova Science Publishers, Inc., 2008. 319 p.
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13. Szostak M. Calculation of the Formation and Migration Energies for a Vacancy in the Naphthalene Crystal. Mol Cryst. Liq. Cryst., 2004, vol. 416, pp. 209-215.
14. Vilgis T.A. Flory Theory of Polymeric Fractals - Intersection, Saturation and Condensation. Physica A, 1988, iss. 153, pp. 341-354.
15. Yakhyaeva Kh.Sh., Kozlov G.V, Magomedov G.M. The Dependence of Interfacial Adhesion Level on Carbon Nanotubes. Fundamental Problems of Modern Engineering Science, 2014, iss. 11, pp. 206-209.
ЗАВИСИМОСТЬ МОДУЛЯ УПРУГОСТИ ОТ СОСТАВА СМЕСИ В КОМПОЗИЦИОННЫХ МОДЕЛЯХ ПОЛИ(ЭТИЛЕН ТЕРЕФТАЛАТА)/ПОЛИ(БУТИЛЕН ТЕРЕФТАЛАТ)
Муслим Абдулахович Микитаев
Кандидат химических наук,
старший научный сотрудник кафедры органической химии и высокомолекулярных соединений,
Кабардино-Балкарский государственный университет им. Х. М. Бербекова
ул. Чернышевского, 175, 360004 г. Нальчик, Российская Федерация
Георгий Владимирович Козлов
Старший научный сотрудник кафедры органической химии и высокомолекулярных соединений,
Кабардино-Балкарский государственный университет им. Х. М. Бербекова
ул. Чернышевского, 175, 360004 г. Нальчик, Российская Федерация
Абдулах Касбулатович Микитаев
Доктор химических наук,
профессор кафедры органической химии и высокомолекулярных соединений, Кабардино-Балкарский государственный университет им. Х. М. Бербекова [email protected]
ул. Чернышевского, 175, 360004 г. Нальчик, Российская Федерация
Марина Израйлевна Арцис
Кандидат химических наук,
научный сотрудник отдела биологической и химической физики полимеров, Институт биохимической физики им. Н. М. Эмануэля РАН chembio@sky. chph. ras.ru
ул. Косыгина, 4, 119334 г. Москва, Российская Федерация
ISSN 2305-7815. Вестн. Волгогр. гос. ун-та. Сер. 10, Иннов. деят. 2015. № 3 (18) 4 9
ТЕХНИКО-ТЕХНОЛОГИЧЕСКИЕ ИННОВАЦИИ
Геннадий Ефремович Заиков
Доктор химических наук, профессор,
заведующий отделом биологической и химической физики полимеров, Институт биохимической физики им. Н. М. Эмануэля РАН chembio@sky. chph. ras.ru
ул. Косыгина, 4, 119334 г. Москва, Российская Федерация
Аннотация. Была показана прямая зависимость модуля упругости от состава смесей поли(этилен терефталата)/поли(бутилен терефталат), которая может быть использована для перколяции и фрактального анализа. Показано, что модуль упругости показывает экстремальный рост, что обусловлено соответствующим ростом сдвиговой прочности смеси компонентов системы. Микромеханические модели не дают адекватного описания указанного эффекта.
Ключевые слова: смесь, микромеханические модели перколяции, фрактальный анализ, модуль упругости, межфазная адгезия.
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The Composite Models Application for Elastic Modulus of PET/PBT Blends Description
