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УДК 539.3
Простые модели расчета межфазных характеристик для нанокомпозита полипропилен/монтмориллонит/СаС03
Y. Zare1, K.Y. Rhee1, S.-J. Park2
1 Университет Кёнхи, Йонъин, 446-701, Республика Корея 2 Университет Инха, Инчхон, 22212, Республика Корея
В работе предложен метод моделирования на основе микромеханических моделей (типа модели Pukanszky) для определения межфазных свойств в трехкомпонентных полимерных нанокомпозитах с двумя различными нанонаполнителями. Предлагаемые модели позволяют рассчитать объемную долю, толщину и прочность межфазных границ между наночастицами и полимерной матрицей с использованием экспериментальных значений модуля Юнга и предела текучести. Проведен расчет свойств межфазных границ для нанокомпозита полипропилен/монтмориллонит (Mt)/CaCO3 с различным содержанием нанонаполнителя (2, 4, 6 мас. % Mt и 2, 8, 14, 20 мас. % CaCO3). Расчеты показали разную зависимость толщины межфазного слоя от размера на-нонаполнителя, а также объемных долей нанонаполнителя и межфазного слоя. Прочность межфазного слоя прямо зависит от межфазного взаимодействия и адгезии между наночастицами и полимерной матрицей.
Ключевые слова: тройные полимерные нанокомпозиты, межфазные свойства, модуль Юнга, предел текучести
DOI 10.24411/1683-805X-2019-14011
Simple models for interphase characteristics in polypropylene/ montmorillonite/CaC03 nanocomposites
Y. Zare1, K.Y. Rhee1, and S.-J. Park2
1 Department of Mechanical Engineering, College of Engineering, Kyung Hee University, Yongin, 446-701, Republic of Korea 2 Department of Chemistry, Inha University, Incheon, 22212, Republic of Korea
This work suggests a modeling method based on micromechanical models such as Pukanszky one to determine the interphase properties in ternary polymer nanocomposites containing two nanofillers. The developed models can calculate the volume fraction, thickness and strength of interphases between nanoparticles and polymer matrix using the experimental data of Young's modulus and yield strength. The properties of interphases are calculated and discussed for polypropylene/montmorillonite (Mt)/CaCO3 ternary polymer nanocomposites at different nanofiller contents (2, 4 and 6 wt % of Mt and 2, 8, 14 and 20 wt % of CaCO3). The developed models demonstrate that the thickness of interphase differently depends on nanofiller size and volume fractions of nanofiller and interphase. In addition, it is shown that the strength of interphase directly correlates to the interfacial interaction/adhesion between nanoparticles and polymer matrix.
Keywords: ternary polymer nanocomposites, interphase properties, Young's modulus, yield strength
1. Introduction
The fine dispersion of the nanoparticles such as mont-morillonite (Mt) in polymer matrices has encouraged much international research on polymer nanocomposites in recent years [1-3]. This motivation is attributed to the remarkable improvement of mechanical, physical, thermal and flame retardation properties of nanocomposites by a low mass fraction of nanofiller (less than 5 wt %) [4-10]. The high specific surface area and the stiffening effect of nanoparticles as well as the strong interfacial interaction
between polymer matrix and nanoparticles provide the significant properties in polymer nanocomposites [11-14]. The nanofiller structure and morphology play the important roles in overall behavior of nanocomposites [15-20]. Accordingly, the shape, aggregation/agglomeration and dispersion/ distribution of nanoparticles significantly affect the properties. Additionally, a strong interphase produced by strong interfacial interaction/adhesion between polymer matrix and nanoparticles is required to create the desired mechanical properties in polymer nanocomposites [21-23]. The inter-
© Zare Y., Rhee K.Y., Park S.-J., 2019
phase is defined as a zone of polymer matrix neighboring nanoparticles with different chemical and mechanical properties from both matrix and nanoparticles.
Many researchers have tried to predict the properties of polymer nanocomposites in recent studies. The Young's modulus of polymer nanocomposites has been calculated using conventional models such as Halpin-Tsai and Takaya-nagi [24]. However, they cannot exactly predict the modulus, due to the absence of some important terms such as interfacial interaction or interphase properties. Therefore, the development of classical models can be carried out to give a simple and valuable method for describing the interphase properties. All these models can easily calculate the properties of interphase in polymer nanocomposite. However, the detailed properties of two interphases between polymer and nanofillers in ternary polymer nanocomposites containing two nanofillers have not been investigated in previous studies. Since the ternary polymer nanocomposites has received much attention in recent years, an accurate model for interphases properties in ternary polymer nano-composites will help the researchers in this area.
Some theoretical studies have been performed on the interphase properties in polypropylene (PP)/Mt/CaCO3 ternary polymer nanocomposites, such as the expansion of Hashin-Shtrikman [25] and Ji [26] models for tensile modulus of ternary polymer nanocomposites assuming interphase regions. These studies generally characterized the interphase zones in ternary polymer nanocomposites, but they have not expressed the interphase properties as a function of effective parameters. The main objective of the present work is to determine the detailed interphases properties in ternary polymer nanocomposites containing two nanofillers by simple and suitable models. Some models are developed to calculate the volume fraction, thickness and strength of interphases between two nanoparticles and polymer matrix by Young's modulus and yield strength results. The models are compared to the experimental results of prepared PP/Mt/CaCO3 ternary polymer nanocomposites and the interphases properties are determined. Also, the effects of important parameters on the interphase characteristics are evaluated.
2. Models and equations
Assuming the formation of interphase, the Young's modulus of polymer nanocomposites can be expressed [27] as
E = Em[1 + 11(<Pf +<pi)1'7], (1)
where Em is the Young's modulus of matrix, pf and pi are the total volume fractions of nanofillers and interphases, respectively. In the current ternary polymer nanocomposites, pf is stated as
Pf = Pf1 +Pf2> (2)
where pf1 and pf2 are the volume fractions of Mt and CaCO3, respectively. Similarly, pi1 and pi2 are defined as the volume fractions of polymer-Mt and polymer-CaCO3 interphases, respectively:
PiX = Pi
Pi2 = Pi
Pfi Pf Pf2 Pf
Also, PiX and Pi2 can be calculated by PiX =Pfi-f '
Pi2 = Pf 2
r + r
- X
(3)
(4)
(5)
(6)
where t and r are the thickness of Mt and radius of CaCO3, respectively, t{ and ri are the thicknesses of polymer-Mt and polymer-CaCO3 interphases. By rearranging of above equations, the interphase thicknesses between polymer and two nanofillers are given by
ft = t-P-
2Pf
r = r3+ X -X.
Pf2
(7)
(8)
Pukanszky [28] developed a simple model to describe the composition dependence of yield strength in composites as
X-Pf
-exp (Bpf),
(9)
1 + 2.5pf
where ar is the relative yield strength as ac/ am, where ac and am are the yield strength of composite and matrix, respectively. Interfacial parameter B displays the quantitative extent of polymer-filler adhesion as
B = (1 + ^cpfti)ln|-i- |,
(10)
where Ac and pf are the specific surface area (the surface area per gram) and density of filler, respectively, ai is the strength of interphase. The Pukanszky model can be restructured to
lnla,.^! | = BPf X-Pf
(11)
which can offer B from a linear connection between ln[ar(X + 2.5pf)/(X-Pf)] and Pf.
In the present study on ternary polymer nanocomposites, the B interphase parameter can be defined for each interphase. According to Eq. (10), B is related to properties of interface/interphase such as interfacial area and thickness and strength of interphase. The interfacial area and interphase thickness can be correlated to piX/p, and Pi2/p, terms (see Eqs. (5) and (6)). The strength of polymer-filler interphase mostly depends to the nanofiller strength. As a result, interphase parameter B is separately expressed for polymer-Mt and polymer-CaCO3 interphases as
Bj = 0.5
= 0.5
9,2
+ -
B,
Jf2
(12) (13)
L+.CTf
where af1 and af2 are the tensile strength of Mt and CaCO3, respectively; at is defined as the total strength of nanofillers as
CTt = CTfj + CTf2. (14)
Also, B = B1 + B2 at different filler fractions by combination of Eqs. (12) and (13). The strength of interphases can be calculated by B1 and B2 parameters (Eq. (9)) as
°i2 =°mexp
B
1 + 4Pf1*i
(15)
(16)
1 + ^Pf2ri.
where subscripts 1 and 2 indicate Mt and CaCO3, respectively. However, for CaCO3 nanoparticles is calculated as
^2 — = -
4nr2
3
Pf r
(17)
m pfv pf 4/3rtr3 where A, m and v are surface area, mass and volume of CaCO3 nanoparticles, respectively. As a result, ai2 is calculated by the latter equations as
°i2 =°rneXP
1 + 3rJ r
(18)
3. Experimental
Polypropylene (PP) ZH500 with melt flow index (MFI) of 10 g/10 min (230°C and 2.16 kg) was bought from Navid Zar Shimi Company, Iran. Montmorillonite Cloisite 20A modified with a quaternary ammonium salt was provided from Southern Clay Products. The maleic anhydride grafted PP (PPgMA), polybond PB3150 with 0.5 wt % of maleic anhydride was used as compatibilizer. CaCO3 (Socal312) with average size of 70 nm and a coated layer of stearic acid was received from Solvay. Similar contents of PPgMA and Mt were used in all prepared samples.
The melt mixing of samples was performed by a co-rotating twin screw extruder, Brabender TSE 20/40D with D = 20 mm and L/D = 40. The screw speed and the feeding rate were kept at 250 rpm and 3 kg/h and the temperature profile was set at 210 to 230°C from hopper to die. The injection molding of the extruded samples was carried out using MonoMat 80 injection molding machine at melt and mold temperatures of 245 and 80°C, respectively.
4. Results and discussion
The experimental results of yield strength and Young's modulus of PP/Mt/CaCO3 ternary polymer nanocomposites are shown in Table 1. The experimental data show that the
addition of nanoparticles slightly affects the tensile strength and most nanocomposites have less strength than neat PP. The incorporation of a high amount of nanoparticles certainly leads to sever filler agglomeration and hence the reduction of strength is mainly related to stress concentration within the agglomerated fillers.
The highest yield strength is attained in sample including 6 wt % of Mt and 14 wt % of CaCO3. However, the lowest yield strength is found in nanocomposite containing 6 wt % of Mt and 20 wt % of CaCO3, due to the reduced dispersion of nanoparticles and thus, poor interfacial properties (interfacial area and adhesion) between PP matrix and both nanofillers. In addition, the Young's modulus of prepared samples increases by adding both nanofillers. The increment of CaCO3 content in Mt contents of 2 and 4 wt% commonly raises the Young's modulus, but a diverse trend is observed at 6 wt % of Mt. These phenomena strongly express that the mechanical properties of polymer nanocomposites such as yield strength and Young's modulus not only associate with the reinforcement effects of nanofillers, but also depend on other parameters such as the interphase properties or interfacial interaction [29-31]. The experimental results are applied into the suggested models to determine the properties of interphases in ternary polymer nano-composites. The comparison between experimental modulus and predicted results by Eq. (1) calculates the in ternary polymer nanocomposites. Volume fraction 9 is obtained as 0.03, 0.035 and 0.035 at 2, 4 and 6 wt % of Mt. Clearly, disregarding of results in unsuitable prediction of Young's modulus indicating the important role of interphase in nanocomposites.
Table 1
The experimentally measured yield strength and Young's modulus for PP/Mt/CaCO3 ternary polymer nanocomposites
No. Mt, wt % CaCO3, wt % Yield strength, MPa Young's modulus, GPa
1 0 0 40.0 ±1.28 2.17±0.07
2 2 2 38.4± 1.15 2.41 ±0.15
3 2 8 39.2± 1.18 2.49 ±0.08
4 2 14 39.5± 1.13 2.57±0.13
5 2 20 36.8± 1.15 2.70±0.05
6 4 2 38.0± 1.16 2.48±0.16
7 4 8 38.2± 1.12 2.57±0.12
8 4 14 38.8± 1.15 2.65 ±0.05
9 4 20 38.3± 1.13 2.95±0.13
10 6 2 38.2± 1.17 2.60±0.17
11 6 8 38.4± 1.21 2.71 ±0.11
12 6 14 43.2± 1.13 2.92±0.13
13 6 20 34.4± 1.28 2.52 ±0.08
Table 2 Table 3
The volume fraction and thickness of interphases The interfacial parameters and interphases strength
in ternary polymer nanocomposites samples in ternary polymer nanocomposites samples
No. Mt, wt % (Pfl) CaCO3, wt % (Pf2) Pi1 Pi2 ti, nm ri, nm No. Mt, wt % CaCO3, wt % Bx B2 MPa MPa
1 2 (0.0105) 2 (0.0069) 0.0181 0.0119 0.04 34.20 1 2 2 2.16 0.58 326.1 46.3
2 2 (0.0110) 8 (0.0287) 0.0083 0.0217 0.02 34.10 2 2 8 1.71 1.03 215.0 52.1
3 2 (0.0115) 14 (0.0524) 0.0054 0.0246 0.01 34.05 3 2 14 1.60 1.14 193.0 53.8
4 2 (0.0120) 20 (0.0783) 0.0040 0.0260 0.01 34.03 4 2 20 1.30 1.04 145.1 52.2
5 4 (0.0213) 2 (0.0069) 0.0264 0.0086 0.03 34.14 5 4 2 2.03 0.31 289.4 43.3
6 4 (0.0222) 8 (0.0290) 0.0152 0.0198 0.02 34.08 6 4 8 1.65 0.69 202.6 47.7
7 4 (0.0232) 14 (0.0530) 0.0107 0.0243 0.01 34.05 7 4 14 1.51 0.83 179.8 49.4
8 4 (0.0243) 20 (0.0792) 0.0082 0.0268 0.01 34.04 8 4 20 1.41 0.93 162.0 50.1
9 6 (0.0322) 2 (0.0070) 0.0287 0.0063 0.02 34.10 9 6 2 3.05 0.32 803.7 43.4
10 6 (0.0336) 8 (0.0293) 0.0187 0.0163 0.01 34.06 10 6 8 2.57 0.80 510.4 49.1
11 6 (0.0351) 14 (0.0536) 0.0139 0.0211 0.01 34.05 11 6 14 2.33 1.04 399.0 52.3
12 6 (0.0368) 20 (0.0801) 0.0110 0.0240 0.01 34.03 12 6 20 2.18 1.19 348.3 54.3
The pi findings are applied into Eqs. (3) and (4) to calculate the values of pi1 and pi2 at all nanofiller contents. The calculated values of pi1 and pi2 are exhibited in Table 2. The pi1 decreases upon increasing in CaCO3 content at the same Mt contents, while pi2 grows by increasing CaCO3 contents in all samples. At the same CaCO3 concentration, pi1 increases with increasing in Mtconcen-tration, whereas pi2 shows an opposite trend in this condition. These evidences demonstrate that the higher volume fraction of well-dispersed nanoparticles in ternary polymer nanocomposites causes the higher volume of polymer-nanoparticle interphase, due to the high surface area of nanoparticles, which are well dispersed in polymer matrix.
Substituting of pi1 and pi2 values into Eqs. (7) and (8) calculates the interphases thicknesses (ti and ri) assuming the average t and r as 5 and 35 nm, respectively. As observed in Table 2, ti and ri vary in the ranges of 0.01 to 0.04 nm and 34.03 to 34.2 nm, respectively. Moreover, ti and ri decrease by increasing in volume fraction of CaCO3 at a constant Mt content. Possibly, some agglomerations of nanofillers at high nanofiller contents reduce the dispersion of nanofillers, which diminish the interfacial area and the thickness of interphase [15, 32-35].
As revealed in Eqs. (7) and (8), the interphase thickness directly relates to nanofiller thickness and a greater nanoparticle causes a thicker interphase in ternary polymer
0.03 Pi2
0.01 20
r2, nm
Fig. 1. The effects of r2 and pi2 on the interphase thickness ri2 at an average pf2 = 0.04 (Eq. (7)): 3D (a) and contour plots (b) (color online)
Fig. 2. 3D (a) and contour plots (b) of B1 parameter (Eq. (11)) as a function of and Gfl at ^ = 0.04, cf2 = 100 MPa and B = 3 (color online)
nanocomposites. The effects of r and 9i2 on the interphase thickness ri are shown in Fig. 1 at average %2 = 0.04 according to Eq. (8). The 3D and contour plots illustrate that the highest level of ri is achieved by the highest values of r and %2 in present samples. In addition, small nanopar-ticles show a thin interphase at different volume fractions of polymer-filler interphase demonstrating the important effect of nanoparticle size on the interphase thickness.
Pukanszky model (Eq. (9)) is also applied to the yield strength data of ternary polymer nanocomposites. The experimental data well fit to this model by B values of 2.74, 2.34 and 3.37 at 2, 4 and 6 wt % of Mt, respectively. Equations (12) and (13) calculate B1 and B2 parameters and the results are exhibited in Table 3 at all nanofiller contents. The tensile strength of Mt and CaCO3 are assumed as 2500 and 60 MPa, respectively.
The B1 data change from 1.3 for sample 4 containing 2 wt % of Mt and 20 wt % of CaCO3 to 3.05 for sample 9 with 6 wt % of Mt and 2 wt % of CaCO3, which show the higher interfacial adhesion between PP and Mt at smaller Mt content. However, B2 varies from 0.31 for sample 5 containing 4 wt % of Mt and 2 wt % of CaCO3 to 1.19 for sample 12 with 6 wt % of Mt and 20 wt % of CaCO3, indicating that the highest values of PP-CaCO3 interfacial adhesion is found at the highest Mt and CaCO3 contents. However, B2 data are lower than B1 in all samples, which reveal the poorer interfacial adhesion between PP matrix and CaCO3 nanoparticles compared to PP-Mt one. As explained, the higher levels of af and interface area in Mt lead to a greater B1 in ternary polymer nanocomposites.
Figure 2 depicts the B1 parameter as a function of 9i1 and CTf1 (Eq. (12)) at ^ = 0.04, af2 = 100 MPa and B = 3. The high levels of B1 are achieved by the high values of 9i1 and af1 in ternary polymer nanocomposites, while decreasing in 9i1 and af1 reduces B1. It demonstrates that the content of interphase and the strength of nanoparticles
determine the level of B1 in ternary polymer nanocomposites. In other words, and af1 parameters have positive influences on the B1 interfacial parameter.
Table 3 shows the calculations of ai1 and ai2 (Eqs. (15) and (18)). The values of A1 were reported in our previous work [36]. The densities of PP, Mt and CaCO3 are assumed as 0.91, 1.77 and 2.71 g/cm3, respectively. The calculations demonstrate the stronger interphases than polymer matrix in ternary polymer nanocomposites. The ai1 changes from 145.1 to 803.7 MPa for samples 4 and 9, respectively. In addition, ai1 decreases by increasing in CaCO3 content. These values show that the highest level of ai1 is obtained at the highest Mt concentration (6 wt %) and the least CaCO3 content (2 wt %). In addition, the weakest interphase between PP and Mt is found at low Mt (2 wt %) and high CaCO3 (20 wt %) concentrations, due to the stiffening effect of Mt as well as the poor dispersion of CaCO3 at high nanofiller contents. As a result, a good dispersion of nanoparticles is necessary to achieve the high interphase properties. Furthermore, the least ai2 is calculated as 43.3 MPa for sample 5, while the highest level of ai2 as 54.3 MPa is achieved in sample 12. Accordingly, the smallest interphase strength is reported at medium Mt and low CaCO3 contents, while the highest concentrations of Mt and CaCO3 produce the best ai2. These observations reveal the important effect of CaCO3 content on ai2. In addition, the larger interfacial area between PP and Mt and the higher strength of Mt provide the higher levels of ai1 compared to ai2 in present samples.
5. Conclusions
A modeling technique was developed to characterize the interphase properties in PP/Mt/CaCO3 ternary polymer nanocomposites, which can predict the volume fraction, thickness and strength of polymer-Mt and polymer-CaCO3 interphases. The findings show that the volume fraction of
polymer-Mt interphase decreases upon increasing in CaCO3 content at all Mt concentrations, while pi2 grows in this condition. Increasing in Mt content enhances pi1 and decreases pi2 at a same CaCO3 concentration. The small nanoparticles demonstrate a thin interphase at different volume fractions of interphases indicating the important effect of large nanoparticles on the interphase thickness. The reported results also represent that B2 is lower than B1 in all samples, which reveal the poorer interfacial adhesion between PP matrix and CaCO3 nanoparticles compared to that of PP-Mt, due to the high level of af and Ac in Mt compared to CaCO3 nanoparticles. The highest level of CTi1 is obtained by the highest Mt (6 wt %) and the least CaCO3 (2 wt %) contents. In addition, the weakest PP-Mt interphase is found at low Mt (2 wt %) and high CaCO3 (20 wt %) concentrations, due to the stiffening effect of Mt as well as the poor dispersion of CaCO3 at high nanofiller contents. Accordingly, good dispersion and high stiffening effect of nanoparticles lead to the significant properties of polymer-filler interphase in ternary polymer nanocompo-sites.
References
1. MiyagawaH., RichM.J., DrzalL.T. Amine-cured epoxy/clay nanocom-
posites. II. The effect of the nanoclay aspect ratio // J. Polymer Sci. B. Polymer Phys. - 2004. - V. 42. - P. 4391-4400.
2. Zare Y., Rhee K.Y. Evaluation and development of expanded equations based on Takayanagi model for tensile modulus of polymer nanocom-posites assuming the formation of percolating networks // Phys. Meso-mech. - 2018. - V. 21. - No. 4. - P. 351-357.
3. Badamshina E.R., Goldstein R.V., Ustinov K.B., Estrin Ya.l. Strength and fracture toughness of polyurethane elastomers modified with carbon nanotubes // Phys. Mesomech. - 2018. - V. 21. - No. 3. - P. 187192.
4. Zare Y., Rhee K.Y. Multistep modeling of Young's modulus in polymer/clay nanocomposites assuming the intercalation/exfoliation of clay layers and the interphase between polymer matrix and nanoparticles // Composites. A. Appl. Sci. Manufactur. - 2017. - V. 102. - P. 137144.
5. Zare Y., Rhee K.Y. A power model to predict the electrical conductivity of CNT reinforced nanocomposites by considering interphase, networks and tunneling condition // Composites. B. Eng. - 2018. -V. 155.- P. 11-18.
6. Zare Y., Rhee K.Y. Simplification and development of McLachlan model
for electrical conductivity of polymer carbon nanotubes nanocom-posites assuming the networking of interphase regions // Composites. B. Eng. - 2019. - V. 156. - P. 64-71.
7. Rostami A., Vahdati M, Nazockdast H. Unraveling the localization behavior of MWCNTs in binary polymer blends using thermodynamics and viscoelastic approaches // Polymer Compos. - 2018. -V. 39. - P. 2356-2367.
8. Javidi Z., Tarashi Z., Rostami A., Nazockdast H. Role of nanosilica localization on morphology development of HDPE/PS/PMMA immiscible ternary blends // eXPRESS Polymer Lett. - 2017. - V. 11. -P. 362.
9. Farahi A., Najafpour G.D., Ghoreyshi A. Enhanced ethanol separation by corona-modified surface MWCNT composite PDMS/PES. PVP Membrane // JOM. - 2019. - V. 71. - P. 285-293.
10. Golovnev I.F., Golovneva E.I., Utkin A.V. A study into the temperature and size effects in nanostructures on their fracture under external
mechanical loads // Phys. Mesomech. - 2018. - V. 21. - No. 6. -P. 523-528. - doi 10.1134/S1029959918060073.
11. Chehrazi E., Sharif A., Omidkhah M, Karimi M. Modeling the effects of interfacial characteristics on gas permeation behavior of nanotube-mixed matrix membranes // ACS Appl. Mater. Interfaces. -
2017. - V. 9. - P. 37321-37331.
12. Razavi R., Zare Y., Rhee K.Y. A two-step model for the tunneling conductivity of polymer carbon nanotube nanocomposites assuming the conduction ofinterphase regions // RSC Advances. - 2017. - V. 7. -P. 50225-50233.
13. Liu Z., Peng W., Zare Y., Hui D., Rhee K.Y. Predicting the electrical conductivity in polymer carbon nanotube nanocomposites based on the volume fractions and resistances of the nanoparticle, interphase, and tunneling regions in conductive networks // RSC Advances. -
2018. - V. 8. - P. 19001-19010.
14. Chehrazi E., Raef M., Noroozi M., Panahi-Sarmad M. A theoretical model for the gas permeation prediction of nanotube-mixed matrix membranes: Unveiling the effect of interfacial layer // J. Membrane Sci. - 2019. - V. 570. - P. 168-175.
15. Shokri-Oojghaz R., Moradi-Dastjerdi R., Mohammadi H., Behdi-nan K. Stress distributions in nanocomposite sandwich cylinders reinforced by aggregated carbon nanotube // Polymer Compos. - 2019. -V. 40. - No. 52. - P. E1918-E1927.
16. Khoramishad H., Khakzad M, Fasihi M. The effect of outer diameter of multi-walled carbon nanotubes on fracture behavior of epoxy adhesives // Sci. Iran. Trans. B. Mech. Eng. - 2017. - V. 24. -P. 2952-2962.
17. KhoramishadH., EbrahimijamalM., Fasihi M. The effect of graphene oxide nano-platelets on fracture behavior of adhesively bonded joints // Fatigue Fract. Eng. Mater. Struct. - 2017. - V. 40. - P. 1905-1916.
18. Zare Y Shear, bulk, and Young's moduli of clay/polymer nanocompo-sites containing the stacks of intercalated layers as pseudoparticles // Nanoscale Res. Lett. - 2016. - V. 11. - P. 479.
19. Zare Y., Rhee K.Y. Expression of normal stress difference and relaxation modulus for ternary nanocomposites containing biodegradable polymers and carbon nanotubes by storage and loss modulus data // Composites. B. Eng. - 2019. - V. 158. - P. 162-168.
20. Bakhtiari S.S.E., Karbasi S., Tabrizi S.A.H., Ebrahimi-Kahrizsangi R. Chitosan/MWCNTs composite as bone substitute: Physical, mechanical, bioactivity, and biodegradation evaluation // Polymer Compos. -
2019. - V. 40. - P. E1622.
21. Zare Y., Garmabi H., Rhee K.Y. Prediction of complex modulus in phase-separated poly (lactic acid)/poly (ethylene oxide)/carbon nanotubes nanocomposites // Polymer Testing. - 2018. - V. 66. - P. 189194.
22. Zare Y., Rhee K.Y. A two-step technique for tensile strength ofmontmo-rillonite/polymer nanocomposites assuming filler morphology and interphase properties // Appl. Clay Sci. - 2017. - V. 150. - P. 42-46.
23. Zare Y., Rhim S., Garmabi H., Rhee K.Y. A simple model for constant storage modulus of poly (lactic acid)/poly (ethylene oxide)/carbon nanotube nanocomposites at low frequencies assuming the properties of interphase regions and networks // J. Mech. Behavior Biomed. Mater. - 2018. - V. 80. - P. 164-170.
24. Fornes T., Paul D. Modeling properties of nylon 6/clay nanocomposites using composite theories // Polymer. - 2003. - V. 44. - P. 49935013.
25. Zare Y., Rhee K.Y. Development of Hashin-Shtrikman model to determine the roles and properties of interphases in clay/CaCO3/PP ternary nanocomposite // Appl. Clay Sci. - 2017. - V. 137. - P. 176182.
26. Zare Y., Garmabi H. A developed model to assume the interphase properties in a ternary polymer nanocomposite reinforced with two nanofillers // Composites. B. Eng. - 2015. - V. 75. - P. 29-35.
27. Yanovsky Yu.G., Kozlov G.V., Karnet Yu.N. Fractal description of significant nanoeffects in polymer composites with nanosized fillers. Aggregation, phase interaction, reinforcement // Phys. Mesomech. -2013. - V. 16. - No. 1. - P. 9-22.
28. Pukanszky B. Influence of interface interaction on the ultimate tensile properties of polymer composites // Composites. - 1990. - V. 21.-P. 255-262.
29. Zare Y., Rhee K.Y. Expansion of Kolarik model for tensile strength of polymer particulate nanocomposites as a function of matrix, nanopar-ticles and interphase properties // J. Colloid Interface Sci. - 2017. -V. 506. - P. 582-588.
30. Zare Y., Rhee K.Y. Modeling of viscosity and complex modulus for poly (lactic acid)/poly (ethylene oxide)/carbon nanotubes nanocomposites assuming yield stress and network breaking time // Composites. B. Eng. - 2019. - V. 156. - P. 100-107.
31. Zare Y., Rhee K.Y. Tensile modulus of polymer/CNT nanocomposites containing networked and dispersed nanoparticles // AIChE J. - 2018.-V. 64. - P. 220-225.
32. Hassanzadeh-Aghdam M., Ansari R., Mahmoodi M., Darvizeh A. Effect of nanoparticle aggregation on the creep behavior of polymer nanocomposites // Compos. Sci. Technol. - 2018. - V. 162. - P. 93100.
33. Ma X., Zare Y., Rhee K.Y. A two-step methodology to study the influence of aggregation/agglomeration of nanoparticles on Young's modulus of polymer nanocomposites // Nanoscale Res. Lett. - 2017. -V. 12.- P. 621.
34. Zare Y., Rhee K.Y., Park S.-J. A modeling methodology to investigate the effect of interfacial adhesion on the yield strength of MMT reinforced nanocomposites // J. Indust. Eng. Chem. - 2018. - V. 69. -P. 331-337.
35. Zare Y., Rhee K.Y. Evaluation of the tensile strength in carbon nano-tube-reinforced nanocomposites using the expanded Takayanagi model // JOM. - 2019. - P. 1-9.
36. Zare Y., Garmabi H. Modeling of interfacial bonding between two nanofillers (montmorillonite and CaCO3) and a polymer matrix (PP) in a ternary polymer nanocomposite // Appl. Surf. Sci. - 2014. -V. 321.- P. 219-225.
Received May 13, 2019, revised July 08, 2019, accepted July 12, 2019
Сведения об авторах
Yasser Zare, PhD, Dr., Kyung Hee University, Republic of Korea, [email protected] Kyong Yop Rhee, PhD, Prof., Kyung Hee University, Republic of Korea, [email protected] Soo-Jin Park, Inha University, Republic of Korea, [email protected]
