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polymer nanocomposites by yield strength data
Applied Clay Science 115 (2015) 61–66
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Research paper
Estimation of material and interfacial/interphase properties in clay/polymer nanocomposites by yield strength data Yasser Zare Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 6 April 2015 Received in revised form 9 July 2015 Accepted 10 July 2015 Available online xxxx Keywords: Clay/polymer nanocomposites (CPN) Material characteristics Interfacial/interphase properties Yield strength
a b s t r a c t In this article, a new and simple approach is presented for calculation of material and interfacial/interphase properties in clay/polymer nanocomposites (CPN) by the experimental results of yield strength. The “B” interaction parameter from Pukanszky model is correlated with several material and interfacial/interphase characteristics such as yield strength of polymer matrix (σm), the aspect ratio of clay (α), the stress transfer parameter (s), thickness (ti) and strength (σi) of interphase. The suggested equations are applied to calculate and examine the material and interfacial/interphase properties for several samples of CPN. Also, the effects of all parameters on “σi” and “ti” are determined to predict the relations between material and interfacial/interphase properties. According to the suggested equations, low “B” and high “ti” produced insignificant “σi” in CPN. Furthermore, a thick interphase caused a large stress transfer from polymer matrix to clay at interphase region. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The interest in clay/polymer nanocomposites (CPN) has been grown in both industry and academy, due to the high potentials that they show by improved physical, chemical, thermal and mechanical properties (Adame and Beall, 2009; Zare et al., 2011; Zare and Garmabi, 2012b; Zare, 2015d; Fernández et al., 2013; Huskić et al., 2013; Zare, 2013; Norouzi et al., 2015). The well exfoliated clay in polymer matrix establishes significant improvement in modulus, stiffness, thermal stability, barrier properties and flame retardation (Kalbasi et al., 2012; Mallakpour and Dinari, 2013; Hajibeygi et al., 2015). As a result, the polymer nanocomposites can be assumed as low-cost substitutes for high-performance materials for many commercial applications such as automotive, household goods, packaging, etc. (Monfared and Jalali-Arani, 2015; Shabanian et al., 2015). In the recent years, many attempts have been made to realize and characterize the parameters which governor the structure–property relationship in the polymer nanocomposites (Fasihi and Abolghasemi, 2012; Nazari et al., 2012; Zare and Garmabi, 2012a, 2015a; Zare, 2015a, 2015b). It is well known that many factors related to nanofiller including volume fraction, aspect ratio, strength and dispersion quality as well as the properties of interfacial/interphase region between polymer matrix and dispersed particles such as thickness and strength significantly change the mechanical properties of CPN (Zare, 2015e; Zhu et al., 2011; Li et al., 2012; Zare and Garmabi, 2014a, 2014b; Zare, 2015c). The region around the clay is much important, because the
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http://dx.doi.org/10.1016/j.clay.2015.07.021 0169-1317/© 2015 Elsevier B.V. All rights reserved.
chemical and physical properties of polymer matrix are largely changed in this area and the molecular interactions determine the efficiency of stress transfer through polymer to nanofiller. An efficient stress transfer from matrix to nanoparticles is essential to take the advantages of clay in the nanocomposites such as high modulus and strength. Therefore, the polymer–nanofiller interface/interphase in nanocomposites is a challengeable matter and many researchers have tried to characterize the interface/interphase characteristics by experimental and theoretical methods (Zare, 2014, 2015a; Zare and Garmabi, 2015a, 2015b). The mechanism of stress transfer in matrix/fiber composites was explained by various models such as Cox (Zare and Garmabi, 2014a) or Kelly–Tyson (Zare, 2015a) and several techniques such as microRaman spectroscopy (Daniel Wagner, 2002). However, the experimental methods for measurement of size and strength of interphase in nanocomposites are challenging, due to the technical difficulties in manipulation of nanoparticles at nano-scales. From a modeling view, many approaches have been suggested in this area. Pukanszky (1990) proposed a semi-empirical equation to determine the effects of filler volume fraction and interfacial interactions on the yield strength of filled polymer composites. The Pukanszky model has been successfully applied for polymer nanocomposites containing various nanofillers such as clay, carbon nanotubes, CaCO3, etc. (Lazzeri and Phuong, 2014). The Pukanszky model presents an interaction parameter (B) which assumes the capacity of stress transfer between polymer matrix and nanofiller. The “B” parameter can be straightforwardly calculated from the yield strength of nanocomposites. In this paper, many attempts have been made to show the correlations between the “B” interaction parameter from Pukanszky model and the material and interphase properties which have strong effects
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Y. Zare / Applied Clay Science 115 (2015) 61–66
on the mechanical properties of nanocomposites. The new suggested approach is applied to calculate and evaluate many characteristics in several CPN from valid literature.
When ϕ → 0, the first logarithmic term is approximated to: αs αs ϕ ≅− 1− ϕ: ln 1− 1− σm σm
ð8Þ
2. Theoretical analysis The dependence of yield strength of polymer composites on the interfacial interactions and the material properties (Callister and Rethwisch, 2007) can be shown as: σR ¼ 1 þ
αs −1 ϕ σm
ð1Þ
where “σR” is relative yield strength as σR = σc/σm; σc and σm are the yield strengths of the composite and the polymer matrix, respectively. “α” is the aspect ratio of the filler defined as α = l/t; “l” and “t” are length and thickness of the dispersed particles, respectively. Also, “s” is an interfacial stress transfer parameter, which shows the quality of interfacial adhesion at the interface and “ϕ” is the volume fraction of the filler. Although this model was firstly proposed for short fiber reinforced polymer composites, it has been used for different polymer nanocomposites containing clay in the literature (Durmus et al., 2008; Zare et al., 2014). Eq. (1) can be rearranged for CPN as: αs ϕ σ R ¼ 1− 1− σm
ð2Þ
In this condition (ϕ → 0), the second logarithmic term in Eq. (7) is approximately correlated to “ϕ” as: ln
1 þ 2:5ϕ ≅3:4ϕ: 1−ϕ
ð9Þ
As a result, Eq. (7) can be rearranged to: αs ϕ þ 3:4ϕ ¼ Bϕ: − 1− σm
ð10Þ
Accordingly, the “B” parameter as the slope of Pukanszky plot (Eq. (5)) is obtained as: B¼
αs þ 2:4 σm
ð11Þ
which provides a direct link between “B” and different material and interfacial characteristics such as “α”, “σm” and “s”. “Ac” can be defined for nanocomposites containing plate-like clay with “t” thickness and both length and width of “l” (l ≫ t) as: 2
which links the yield strength of nanocomposites with various materials and interfacial properties. The Pukanszky model (Pukanszky, 1990) is expressed as:
σR ¼
1−ϕ expðBϕÞ 1 þ 2:5ϕ
where
1−ϕ ” “ 1þ2:5ϕ
ð3Þ
term indicates the decrease of effective load-bearing
cross section, due to the filler introduction. “B”, as an interfacial parameter considers the capacity of stress transfer between the constituent components. “B” depends on the thickness and strength of interphase as: B ¼ ð1 þ Ac ρ f ti Þ ln
σi σm
ð4Þ
where “Ac” is the specific surface area of the filler and “ρf” is the filler density. Also, “ti” and “σi” are the thickness and strength of interphase, respectively. The Pukanszky model can be rewritten as: 1 þ 2:5ϕ ln ðσ Reduced Þ ¼ ln σ R ¼ Bϕ 1−ϕ
ð5Þ
where the plot of ln (σReduced) against “ϕ” results in a linear correlation with a slope equal to “B” parameter. Now, Eq. (2) is connected with Eq. (5) to find the dependency of “B” to various material and interfacial characteristics. Eq. (5) can be extended to: 1 þ 2:5ϕ 1 þ 2:5ϕ ¼ ln ðσ R Þ þ ln ¼ Bϕ: ln σ R 1−ϕ 1−ϕ
A A 2l þ 4lt 2 4 2α 4 2ðα þ 2Þ 2α ¼ ¼ þ ¼ þ ¼ ≅ : ð12Þ ¼ 2 l ρf v ρfl ρfl ρf l ρf l ρf l ρf l ρf l l
where “A”, “m” and “v” are surface area, mass and volume of clay, respectively. Therefore, by replacing of “Ac” from above equation into Eq. (4): σ 2α σi i ¼ 1þ B ¼ 1 þ Ac ρ f t i ln t i ln σm σm l
ð13Þ
Connecting “B” from Eq. (11) with the obtained “B” by Eq. (13) gives:
B¼
2α σi αs 1þ ¼ þ 2:4: ti ln σm l σm
ð14Þ
From the latter equation, “σi” can be obtained as: 0 αs
1 þ 2:4 σ B C σ i ¼ σ m exp@ m A 2αti 1þ l
ð15Þ
which correlates “σi” with different material and interfacial parameters. Correspondingly, replacing “s” from Eq. (11) into above equation leads to a relation between “σi” and “B” as: 0
1
B B C σ i ¼ σ m exp@ A 2αti 1þ l
ð16Þ
ð6Þ From Eq. (14), “ti” can be also correlated to different parameters as:
Substituting “σR” from Eq. (2) into Eq. (6) gives: αs 1 þ 2:5ϕ ϕ þ ln ln 1− 1− ¼ Bϕ: σm 1−ϕ
Ac ¼
ð7Þ
αs þ 2:4 σm −1: ti ¼ 2α σi ln σm l
ð17Þ
Y. Zare / Applied Clay Science 115 (2015) 61–66
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Table 1 The calculations of various properties by suggested equations for different CPN samples. No.
Samples
B (Eq. (3))
σm MPa
s (Eq. (11)) MPa
σi (Eq. (15)) MPa
Ref.
1 2 3 4 5 6
OMt1/PPgMA2/HDPE3 OMt4/PEgMA5/PE6 OMt7/PP OMt8/PS9 OMt10/PA611 OMt12/PA12
7.53 19.4 14.62 2.76 −2.28 1.77
18 7.5 34.5 32.8 74 31.5
0.92 1.28 4.22 0.12 b0 b0
81.16 363.18 642.24 56.96 – –
Lee et al. (2005) Kato et al. (2003) Baniasadi et al. (2010) Su et al. (2004) Swain and Isayev (2009) Aït Hocine et al. (2008)
1
Modified clay with octadecylamine, partially intercalated/exfoliated layers. Maleic anhydride grafted polypropylene. 3 High density polyethylene. 4 Octadecylamine modified clay, fully exfoliated and dispersed layers. 5 Maleic anhydride grafted polyethylene. 6 Polyethylene. 7 Organically modified with hexadecyl trimethylammonium bromide, fully exfoliated clay. 8 Butadiene-modified clay, partially intercalated/exfoliated clay. 9 Polystyrene. 10 Organically modified clay with quaternary ammonium salts, poor dispersion of clay. 11 Polyamide 6. 12 Methyl, tallow, bis-2-hydroxyethyl ammonium exchanged clay, partially intercalated/exfoliated clay. 2
Also, “ti” can be correlated with “B” by rearranging of Eq. (14) as: σi l B− ln σm ti ¼ σi 2α ln σm
ð18Þ
in which “ti” is simply predicted by various material and interphase properties. 3. Results and discussion 3.1. Calculation and evaluation of interfacial/interphase properties In the previous section, different correlations between material and interphase properties were established for CPN. Now, the suggested equations are applied for many samples from valid literature (Kato et al., 2003; Su et al., 2004; Lee et al., 2005; Aït Hocine et al., 2008; Swain and Isayev, 2009; Baniasadi et al., 2010) and the calculations are discussed. Various examples of CPN from valid literature are presented in Table 1. The yield strength of reported samples is fitted to “ϕ” to calculate “B” values by the Pukanszky model (Eq. (3)). As observed in Table 1, “B” changed from a negative value of −2.28 for polyamide 6 (PA6)/organically modified montmorillonite (OMt) sample (No. 5) to a large value of 19.4 for polyethylene (PE)/maleic anhydride grafted polyethylene (PPgMA)/OMt nanocomposite (No. 2).
The “B” parameter obtained by the experimental data of yield strength depends to various material and interfacial properties such as composition, the component properties, the compatibility between polymer and clay (the interfacial interactions), the dispersion quality of clay, etc. (Zare, 2014; Zare and Garmabi, 2014b). As a result, the properties of neat components and also, the characteristics of interface/ interphase create different “B” values in CPN. In PE/PEgMA/OMt sample (No. 2), clay was fully exfoliated and dispersed in PE matrix at nanometer scale using PEgMA and appropriate condition of processing (Kato et al., 2003). Also, the high level of mechanical properties indicated the large level of interfacial interactions/adhesion in this sample. So, a high “B” of 19.4 was obtained for this sample (Table 1). On the other hand, the samples No. 5 and 6 display a poor dispersion of clay. Likewise, the less improved level of mechanical properties expressed the less interfacial properties. Accordingly, these samples demonstrate low “B” values (Table 1). In addition, it is realized from Eq. (11) that B b 2.4 creates undesirable values for “s” parameter. The negative values of “s” for the reported samples display a smaller “B” than 2.4. As a result, B N 2.4 is necessary to calculate a meaningful value for “s” and gain the strengthening effect of nanoparticles in polymer matrix (see Eq. (1)). It means that B N 2.4 is required to obtain higher nanocomposite strength than the matrix strength. Starting from “B” and “σm” data and average “α” of 100 for clay, the values of “s” were calculated by the suggested equation (Eq. (11)) for the reported samples. As shown in Table 1, different “s” values were calculated for the reported samples based on the dissimilar values of “B” and “σm”. The highest “s” of 4.22 MPa was obtained for polypropylene (PP)/OMt sample (No. 3) with B = 14.62 and σm = 34.5 MPa. The
Fig. 1. The dependence of “σi” to “s” and “α” parameters according to Eq. (15) at average σm = 30 MPa, l = 500 nm and ti = 10 nm: a) 3D and b) contour plots.
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Fig. 2. a) 3D and b) contour plots of “σi” as a function of “B” and “ti” (Eq. (16)) at σm = 30 MPa, l = 500 nm and α = 100.
high level of “s” parameter was confirmed by the completely intercalated/exfoliated clay in the prepared nanocomposite by in situ polymerization as well as the strong interfacial adhesion between polymer and the exfoliated clay layers, which produce the high mechanical properties (Baniasadi et al., 2010). Similarly, the poor dispersion of clay beside the low mechanical properties of samples No. 5 and No. 6 showed the low level of interfacial properties, which is expressed by negative “s” in Table 1. Additionally, the values of “σi” for the present samples (Table 1) were calculated by Eq. (15) at average α = 100, l = 500 nm and ti = 10 nm (Zare and Garmabi, 2015b). The “σi” calculations exhibited in Table 1 changed from 56.96 to 642.24 MPa for samples. The different values of “σi” were expected, because “σi” is a function of “s” and “σm” (Eq. (15)). It should be noted that “σi” is not defined for the samples which show B b 2.4. As a result, a minimum “B” that gives an expressive value for interface/interphase was determined as 2.4. Lazzeri and Phuong (2014) also determined the minimum value of “B” parameter, which is necessary for the composite strength to be better than the strength of the neat matrix. A minimum “B” value of about 3 was obtained for composites reinforced with short fibers. They stated that this condition is also suitable for nanocomposites containing clay and carbon nanotubes. Their estimation is close to our expression for a minimum “B” value that produces a better strength in the nanocomposite sample compared to the strength of neat matrix. As mentioned, the clay concentration, aspect ratio, stiffness and dispersion play main roles in the final behavior of nanocomposites. A clay layer has a thickness of about 1 nm, while its width and length commonly reach to few microns. As a result, the high aspect ratio and
specific surface area of clay create a high level of interface area, which can cause strong mechanical involvements between polymer and clay. However, these advantages significantly depend upon the level of intercalation/exfoliation of the clay. Undoubtedly, the less intercalation/exfoliation of clay or aggregation of nanoparticles reduce the aspect ratio and specific surface area of clay and limit the achievement of desirable properties. Accordingly, beside the intrinsic properties of clay, the morphology of clay in the polymer matrix is very important. Moreover, since an efficient stress transfer from matrix to nanoparticles is required to obtain the best advantages of clay, the interfacial interactions and interphase characteristics meaningfully affect the mechanical properties of CPN. The nonbonded interactions between polymer matrix and clay are totally in the form of van der Waals forces (Zare and Garmabi, 2014b). Although the hydrogen atoms of polymer chains have relatively low partial charges, their large numbers make the highest level of interaction with the clay layers. Additionally, a hydrogen bonding can be formed between the polar groups in the polymer chains and the nanoparticles. The suggested equations are very appropriate for CPN, due to the low volume fraction and high aspect ratio of clay layers in the polymer matrix. Therefore, they can be used to determine and analyze the interfacial/interphase properties in CPN. The suggested models (Eqs. (1) and (3)) express the physical interactions at the interface. The strong chemical bonds are rarely formed in polymer nanocomposites, so the proposed models are very suitable for CPN. Also, the calculated parameters are well supported by the experimental observations. As explained, the high levels of “s” and “B” parameters
Fig. 3. The effects of “s” and “α” parameters on “ti” values (Eq. (17)) at σm = 30 MPa, l = 500 nm and σi = 100 MPa: a) 3D and b) contour plots.
Y. Zare / Applied Clay Science 115 (2015) 61–66
65
Fig. 4. a) 3D and b) contour plots for dependence of “ti” on “B” and “σi” parameters (Eq. (18)) at σm = 30 MPa, l = 500 nm and α = 100.
were confirmed by the fully intercalated/exfoliated clay as well as the strong interfacial adhesion between polymer and clay, which produce the high mechanical properties. Likewise, the poor dispersion of clay and the low mechanical properties in some samples (Nos. 5 and 6) show the low level of interfacial properties expressed by small “s” and “B” parameters. 3.2. Relations among the parameters The dependence of “σi” to “s” and “α” parameters (Eq. (15)) is illustrated in Fig. 1 at average values of σm = 30 MPa, l = 500 nm and ti = 10 nm. “σi” rises with increment of “s” and “α”. The reported results in Table 1 demonstrate the direct connection between “σi” and “s” in which the high levels of “σi” and “s” showed a strong interphase between polymer and clay. However, it was observed that the effect of “s” level on “σi” was more important than the influence of “α”, because “σi” was constant in a large range of “α”, i.e. α N 40 approximately produced a constant “σi” at each “s”. To obtain high “σi” and “s”, the interfacial properties may be improved by compatibilization of polymer and particles phases, treatment of nanofiller and functionalization of components. Also, “σi” as a function of “B” and “ti” parameters (Eq. (16)) is illustrated in Fig. 2 at σm = 30 MPa, l = 500 nm and α = 100. “σi” was negligible at little “B” and large “ti” as well as the medium values of these parameters. However, with increase in “B”, “σi” improved at slighter “ti” and reached to the most extent at the largest “B” and the smallest “ti”. These plots illustrated the positive influence of “B” on “σi”, but a dissimilar trend was found between “σi” and “ti”. Based on Eqs. (15) and (16), a high level of “σi” was obtained with large “σm”, “l”, “s”, “α” and “B” as material and interfacial parameters. Additionally, the effects of “s” and “α” parameters on “ti” values (Eq. (17)) are depicted in Fig. 3 at σm = 30 MPa, l = 500 nm and σi = 100 MPa. The smallest “ti” was obtained with small “s” at α N 70, while the highest “ti” was achieved by high “s” and small “α”. Conclusively, “α” as a material parameter plays a negative role in the interphase thickness. The illustration indicates the positive effect of “s” parameter on “ti”, which expresses that a thick interphase displays a large stress transfer from polymer matrix to clay at the interphase region in CPN. Also, α b 60 can significantly change the “ti” at various “s”, but α N 60 commonly produces ti b 20 nm at all “s” levels. In other words, “s” has a largely positive effect on “ti” at α b 60 and a high level of “ti” is obtained at α b 40 and s N 2 MPa. The dependence of “ti” to “B” and “σi” parameters (Eq. (18)) at σm = 30 MPa, l = 500 nm and α = 100 is shown in Fig. 4. “ti” increased by increment in “B” especially at low level of “σi” (σi b 100 MPa). However, a large “σi” caused a small “ti” at different “B” values, which demonstrated the inverse relation between “σi” and “ti” in polymer nanocomposites. Also, it was revealed that σi N 100 MPa at different “B” extents causes ti b 40 nm. To obtain a larger “ti”, a high “B” as well as a low “σi” is
necessary. As expected by Eqs. (17) and (18), a higher “ti” is created by larger material properties such as “σm” and “l”. In addition, some interfacial parameters such as “B” and “s” have positive influences on “ti”. However, the high levels of “α” and “σi” introduce a small “ti”, i.e. a thin interphase. 4. Conclusions In this paper, a simple methodology was suggested for characterizing of various material and interaction/interphase properties in CPN using the yield strength data. The “B” interfacial parameter could easily be determined by the Pukanszky model for CPN. “B” was correlated with various material factors such as “α” and “σm”, as well as interfacial/ interphase properties including “σi”, “ti” and “s”. Afterwards, these parameters were calculated and evaluated for some samples reported in valid literature. The calculations showed different values for “s” and “σi” attributed to dissimilar levels of “B” and “σm” in CPN. Also, it was established that “s” and “σi” are not defined for the samples which show B b 2.4 and so, B = 2.4 is a minimum level which will give the expressive data for interface/interphase properties. Furthermore, it was possible to predict the correlations among the material and interaction properties in CPN. This analysis expressed the direct relations of “σi” and “ti” with “σm”, “s”, “B” and “l”. Similarly, the findings revealed that “ti” extent has a negative influence on “σi” result in CPN. References Adame, D., Beall, G.W., 2009. Direct measurement of the constrained polymer region in polyamide/clay nanocomposites and the implications for gas diffusion. Appl. Clay Sci. 42, 545–552. Aït Hocine, N., Médéric, P., Aubry, T., 2008. Mechanical properties of polyamide-12 layered silicate nanocomposites and their relations with structure. Polym. Test. 27, 330–339. Baniasadi, H., Ramazani, S.A., Javan Nikkhah, S., 2010. Investigation of in situ prepared polypropylene/clay nanocomposites properties and comparing to melt blending method. Mater. Des. 31, 76–84. Callister, W.D., Rethwisch, D.G., 2007. Materials science and engineering: an introduction. Wiley, New York. Daniel Wagner, H., 2002. Nanotube–polymer adhesion: a mechanics approach. Chem. Phys. Lett. 361, 57–61. Durmus, A., Kaşgöz, A., Macosko, C.W., 2008. Mechanical properties of Linear Low-density Polyethylene (LLDPE)/clay nanocomposites: estimation of aspect ratio and interfacial strength by composite models. J. Macromol. Sci., Part B: Phys. 47, 608–619. Fasihi, M., Abolghasemi, M.R., 2012. Oxygen barrier and mechanical properties of masterbatch-based PA6/clay composite films. J. Appl. Polym. Sci. 125, E2–E8. Fernández, M.J., Fernández, M.D., Aranburu, I., 2013. Effect of clay surface modification and organoclay purity on microstructure and thermal properties of poly (L-lactic acid)/vermiculite nanocomposites. Appl. Clay Sci. 80, 372–381. Hajibeygi, M., Shabanian, M., Khonakdar, H.A., 2015. Zn–AL LDH reinforced nanocomposites based on new polyamide containing imide group: from synthesis to properties. Appl. Clay Sci. 114, 256–264. Huskić, M., Žigon, M., Ivanković, M., 2013. Comparison of the properties of clay polymer nanocomposites prepared by montmorillonite modified by silane and by quaternary ammonium salts. Appl. Clay Sci. 85, 109–115.
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Applied Clay Science journal homepage: www.elsevier.com/locate/clay
Research paper
Estimation of material and interfacial/interphase properties in clay/polymer nanocomposites by yield strength data Yasser Zare Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 6 April 2015 Received in revised form 9 July 2015 Accepted 10 July 2015 Available online xxxx Keywords: Clay/polymer nanocomposites (CPN) Material characteristics Interfacial/interphase properties Yield strength
a b s t r a c t In this article, a new and simple approach is presented for calculation of material and interfacial/interphase properties in clay/polymer nanocomposites (CPN) by the experimental results of yield strength. The “B” interaction parameter from Pukanszky model is correlated with several material and interfacial/interphase characteristics such as yield strength of polymer matrix (σm), the aspect ratio of clay (α), the stress transfer parameter (s), thickness (ti) and strength (σi) of interphase. The suggested equations are applied to calculate and examine the material and interfacial/interphase properties for several samples of CPN. Also, the effects of all parameters on “σi” and “ti” are determined to predict the relations between material and interfacial/interphase properties. According to the suggested equations, low “B” and high “ti” produced insignificant “σi” in CPN. Furthermore, a thick interphase caused a large stress transfer from polymer matrix to clay at interphase region. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The interest in clay/polymer nanocomposites (CPN) has been grown in both industry and academy, due to the high potentials that they show by improved physical, chemical, thermal and mechanical properties (Adame and Beall, 2009; Zare et al., 2011; Zare and Garmabi, 2012b; Zare, 2015d; Fernández et al., 2013; Huskić et al., 2013; Zare, 2013; Norouzi et al., 2015). The well exfoliated clay in polymer matrix establishes significant improvement in modulus, stiffness, thermal stability, barrier properties and flame retardation (Kalbasi et al., 2012; Mallakpour and Dinari, 2013; Hajibeygi et al., 2015). As a result, the polymer nanocomposites can be assumed as low-cost substitutes for high-performance materials for many commercial applications such as automotive, household goods, packaging, etc. (Monfared and Jalali-Arani, 2015; Shabanian et al., 2015). In the recent years, many attempts have been made to realize and characterize the parameters which governor the structure–property relationship in the polymer nanocomposites (Fasihi and Abolghasemi, 2012; Nazari et al., 2012; Zare and Garmabi, 2012a, 2015a; Zare, 2015a, 2015b). It is well known that many factors related to nanofiller including volume fraction, aspect ratio, strength and dispersion quality as well as the properties of interfacial/interphase region between polymer matrix and dispersed particles such as thickness and strength significantly change the mechanical properties of CPN (Zare, 2015e; Zhu et al., 2011; Li et al., 2012; Zare and Garmabi, 2014a, 2014b; Zare, 2015c). The region around the clay is much important, because the
E-mail address: [email protected].
http://dx.doi.org/10.1016/j.clay.2015.07.021 0169-1317/© 2015 Elsevier B.V. All rights reserved.
chemical and physical properties of polymer matrix are largely changed in this area and the molecular interactions determine the efficiency of stress transfer through polymer to nanofiller. An efficient stress transfer from matrix to nanoparticles is essential to take the advantages of clay in the nanocomposites such as high modulus and strength. Therefore, the polymer–nanofiller interface/interphase in nanocomposites is a challengeable matter and many researchers have tried to characterize the interface/interphase characteristics by experimental and theoretical methods (Zare, 2014, 2015a; Zare and Garmabi, 2015a, 2015b). The mechanism of stress transfer in matrix/fiber composites was explained by various models such as Cox (Zare and Garmabi, 2014a) or Kelly–Tyson (Zare, 2015a) and several techniques such as microRaman spectroscopy (Daniel Wagner, 2002). However, the experimental methods for measurement of size and strength of interphase in nanocomposites are challenging, due to the technical difficulties in manipulation of nanoparticles at nano-scales. From a modeling view, many approaches have been suggested in this area. Pukanszky (1990) proposed a semi-empirical equation to determine the effects of filler volume fraction and interfacial interactions on the yield strength of filled polymer composites. The Pukanszky model has been successfully applied for polymer nanocomposites containing various nanofillers such as clay, carbon nanotubes, CaCO3, etc. (Lazzeri and Phuong, 2014). The Pukanszky model presents an interaction parameter (B) which assumes the capacity of stress transfer between polymer matrix and nanofiller. The “B” parameter can be straightforwardly calculated from the yield strength of nanocomposites. In this paper, many attempts have been made to show the correlations between the “B” interaction parameter from Pukanszky model and the material and interphase properties which have strong effects
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Y. Zare / Applied Clay Science 115 (2015) 61–66
on the mechanical properties of nanocomposites. The new suggested approach is applied to calculate and evaluate many characteristics in several CPN from valid literature.
When ϕ → 0, the first logarithmic term is approximated to: αs αs ϕ ≅− 1− ϕ: ln 1− 1− σm σm
ð8Þ
2. Theoretical analysis The dependence of yield strength of polymer composites on the interfacial interactions and the material properties (Callister and Rethwisch, 2007) can be shown as: σR ¼ 1 þ
αs −1 ϕ σm
ð1Þ
where “σR” is relative yield strength as σR = σc/σm; σc and σm are the yield strengths of the composite and the polymer matrix, respectively. “α” is the aspect ratio of the filler defined as α = l/t; “l” and “t” are length and thickness of the dispersed particles, respectively. Also, “s” is an interfacial stress transfer parameter, which shows the quality of interfacial adhesion at the interface and “ϕ” is the volume fraction of the filler. Although this model was firstly proposed for short fiber reinforced polymer composites, it has been used for different polymer nanocomposites containing clay in the literature (Durmus et al., 2008; Zare et al., 2014). Eq. (1) can be rearranged for CPN as: αs ϕ σ R ¼ 1− 1− σm
ð2Þ
In this condition (ϕ → 0), the second logarithmic term in Eq. (7) is approximately correlated to “ϕ” as: ln
1 þ 2:5ϕ ≅3:4ϕ: 1−ϕ
ð9Þ
As a result, Eq. (7) can be rearranged to: αs ϕ þ 3:4ϕ ¼ Bϕ: − 1− σm
ð10Þ
Accordingly, the “B” parameter as the slope of Pukanszky plot (Eq. (5)) is obtained as: B¼
αs þ 2:4 σm
ð11Þ
which provides a direct link between “B” and different material and interfacial characteristics such as “α”, “σm” and “s”. “Ac” can be defined for nanocomposites containing plate-like clay with “t” thickness and both length and width of “l” (l ≫ t) as: 2
which links the yield strength of nanocomposites with various materials and interfacial properties. The Pukanszky model (Pukanszky, 1990) is expressed as:
σR ¼
1−ϕ expðBϕÞ 1 þ 2:5ϕ
where
1−ϕ ” “ 1þ2:5ϕ
ð3Þ
term indicates the decrease of effective load-bearing
cross section, due to the filler introduction. “B”, as an interfacial parameter considers the capacity of stress transfer between the constituent components. “B” depends on the thickness and strength of interphase as: B ¼ ð1 þ Ac ρ f ti Þ ln
σi σm
ð4Þ
where “Ac” is the specific surface area of the filler and “ρf” is the filler density. Also, “ti” and “σi” are the thickness and strength of interphase, respectively. The Pukanszky model can be rewritten as: 1 þ 2:5ϕ ln ðσ Reduced Þ ¼ ln σ R ¼ Bϕ 1−ϕ
ð5Þ
where the plot of ln (σReduced) against “ϕ” results in a linear correlation with a slope equal to “B” parameter. Now, Eq. (2) is connected with Eq. (5) to find the dependency of “B” to various material and interfacial characteristics. Eq. (5) can be extended to: 1 þ 2:5ϕ 1 þ 2:5ϕ ¼ ln ðσ R Þ þ ln ¼ Bϕ: ln σ R 1−ϕ 1−ϕ
A A 2l þ 4lt 2 4 2α 4 2ðα þ 2Þ 2α ¼ ¼ þ ¼ þ ¼ ≅ : ð12Þ ¼ 2 l ρf v ρfl ρfl ρf l ρf l ρf l ρf l ρf l l
where “A”, “m” and “v” are surface area, mass and volume of clay, respectively. Therefore, by replacing of “Ac” from above equation into Eq. (4): σ 2α σi i ¼ 1þ B ¼ 1 þ Ac ρ f t i ln t i ln σm σm l
ð13Þ
Connecting “B” from Eq. (11) with the obtained “B” by Eq. (13) gives:
B¼
2α σi αs 1þ ¼ þ 2:4: ti ln σm l σm
ð14Þ
From the latter equation, “σi” can be obtained as: 0 αs
1 þ 2:4 σ B C σ i ¼ σ m exp@ m A 2αti 1þ l
ð15Þ
which correlates “σi” with different material and interfacial parameters. Correspondingly, replacing “s” from Eq. (11) into above equation leads to a relation between “σi” and “B” as: 0
1
B B C σ i ¼ σ m exp@ A 2αti 1þ l
ð16Þ
ð6Þ From Eq. (14), “ti” can be also correlated to different parameters as:
Substituting “σR” from Eq. (2) into Eq. (6) gives: αs 1 þ 2:5ϕ ϕ þ ln ln 1− 1− ¼ Bϕ: σm 1−ϕ
Ac ¼
ð7Þ
αs þ 2:4 σm −1: ti ¼ 2α σi ln σm l
ð17Þ
Y. Zare / Applied Clay Science 115 (2015) 61–66
63
Table 1 The calculations of various properties by suggested equations for different CPN samples. No.
Samples
B (Eq. (3))
σm MPa
s (Eq. (11)) MPa
σi (Eq. (15)) MPa
Ref.
1 2 3 4 5 6
OMt1/PPgMA2/HDPE3 OMt4/PEgMA5/PE6 OMt7/PP OMt8/PS9 OMt10/PA611 OMt12/PA12
7.53 19.4 14.62 2.76 −2.28 1.77
18 7.5 34.5 32.8 74 31.5
0.92 1.28 4.22 0.12 b0 b0
81.16 363.18 642.24 56.96 – –
Lee et al. (2005) Kato et al. (2003) Baniasadi et al. (2010) Su et al. (2004) Swain and Isayev (2009) Aït Hocine et al. (2008)
1
Modified clay with octadecylamine, partially intercalated/exfoliated layers. Maleic anhydride grafted polypropylene. 3 High density polyethylene. 4 Octadecylamine modified clay, fully exfoliated and dispersed layers. 5 Maleic anhydride grafted polyethylene. 6 Polyethylene. 7 Organically modified with hexadecyl trimethylammonium bromide, fully exfoliated clay. 8 Butadiene-modified clay, partially intercalated/exfoliated clay. 9 Polystyrene. 10 Organically modified clay with quaternary ammonium salts, poor dispersion of clay. 11 Polyamide 6. 12 Methyl, tallow, bis-2-hydroxyethyl ammonium exchanged clay, partially intercalated/exfoliated clay. 2
Also, “ti” can be correlated with “B” by rearranging of Eq. (14) as: σi l B− ln σm ti ¼ σi 2α ln σm
ð18Þ
in which “ti” is simply predicted by various material and interphase properties. 3. Results and discussion 3.1. Calculation and evaluation of interfacial/interphase properties In the previous section, different correlations between material and interphase properties were established for CPN. Now, the suggested equations are applied for many samples from valid literature (Kato et al., 2003; Su et al., 2004; Lee et al., 2005; Aït Hocine et al., 2008; Swain and Isayev, 2009; Baniasadi et al., 2010) and the calculations are discussed. Various examples of CPN from valid literature are presented in Table 1. The yield strength of reported samples is fitted to “ϕ” to calculate “B” values by the Pukanszky model (Eq. (3)). As observed in Table 1, “B” changed from a negative value of −2.28 for polyamide 6 (PA6)/organically modified montmorillonite (OMt) sample (No. 5) to a large value of 19.4 for polyethylene (PE)/maleic anhydride grafted polyethylene (PPgMA)/OMt nanocomposite (No. 2).
The “B” parameter obtained by the experimental data of yield strength depends to various material and interfacial properties such as composition, the component properties, the compatibility between polymer and clay (the interfacial interactions), the dispersion quality of clay, etc. (Zare, 2014; Zare and Garmabi, 2014b). As a result, the properties of neat components and also, the characteristics of interface/ interphase create different “B” values in CPN. In PE/PEgMA/OMt sample (No. 2), clay was fully exfoliated and dispersed in PE matrix at nanometer scale using PEgMA and appropriate condition of processing (Kato et al., 2003). Also, the high level of mechanical properties indicated the large level of interfacial interactions/adhesion in this sample. So, a high “B” of 19.4 was obtained for this sample (Table 1). On the other hand, the samples No. 5 and 6 display a poor dispersion of clay. Likewise, the less improved level of mechanical properties expressed the less interfacial properties. Accordingly, these samples demonstrate low “B” values (Table 1). In addition, it is realized from Eq. (11) that B b 2.4 creates undesirable values for “s” parameter. The negative values of “s” for the reported samples display a smaller “B” than 2.4. As a result, B N 2.4 is necessary to calculate a meaningful value for “s” and gain the strengthening effect of nanoparticles in polymer matrix (see Eq. (1)). It means that B N 2.4 is required to obtain higher nanocomposite strength than the matrix strength. Starting from “B” and “σm” data and average “α” of 100 for clay, the values of “s” were calculated by the suggested equation (Eq. (11)) for the reported samples. As shown in Table 1, different “s” values were calculated for the reported samples based on the dissimilar values of “B” and “σm”. The highest “s” of 4.22 MPa was obtained for polypropylene (PP)/OMt sample (No. 3) with B = 14.62 and σm = 34.5 MPa. The
Fig. 1. The dependence of “σi” to “s” and “α” parameters according to Eq. (15) at average σm = 30 MPa, l = 500 nm and ti = 10 nm: a) 3D and b) contour plots.
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Y. Zare / Applied Clay Science 115 (2015) 61–66
Fig. 2. a) 3D and b) contour plots of “σi” as a function of “B” and “ti” (Eq. (16)) at σm = 30 MPa, l = 500 nm and α = 100.
high level of “s” parameter was confirmed by the completely intercalated/exfoliated clay in the prepared nanocomposite by in situ polymerization as well as the strong interfacial adhesion between polymer and the exfoliated clay layers, which produce the high mechanical properties (Baniasadi et al., 2010). Similarly, the poor dispersion of clay beside the low mechanical properties of samples No. 5 and No. 6 showed the low level of interfacial properties, which is expressed by negative “s” in Table 1. Additionally, the values of “σi” for the present samples (Table 1) were calculated by Eq. (15) at average α = 100, l = 500 nm and ti = 10 nm (Zare and Garmabi, 2015b). The “σi” calculations exhibited in Table 1 changed from 56.96 to 642.24 MPa for samples. The different values of “σi” were expected, because “σi” is a function of “s” and “σm” (Eq. (15)). It should be noted that “σi” is not defined for the samples which show B b 2.4. As a result, a minimum “B” that gives an expressive value for interface/interphase was determined as 2.4. Lazzeri and Phuong (2014) also determined the minimum value of “B” parameter, which is necessary for the composite strength to be better than the strength of the neat matrix. A minimum “B” value of about 3 was obtained for composites reinforced with short fibers. They stated that this condition is also suitable for nanocomposites containing clay and carbon nanotubes. Their estimation is close to our expression for a minimum “B” value that produces a better strength in the nanocomposite sample compared to the strength of neat matrix. As mentioned, the clay concentration, aspect ratio, stiffness and dispersion play main roles in the final behavior of nanocomposites. A clay layer has a thickness of about 1 nm, while its width and length commonly reach to few microns. As a result, the high aspect ratio and
specific surface area of clay create a high level of interface area, which can cause strong mechanical involvements between polymer and clay. However, these advantages significantly depend upon the level of intercalation/exfoliation of the clay. Undoubtedly, the less intercalation/exfoliation of clay or aggregation of nanoparticles reduce the aspect ratio and specific surface area of clay and limit the achievement of desirable properties. Accordingly, beside the intrinsic properties of clay, the morphology of clay in the polymer matrix is very important. Moreover, since an efficient stress transfer from matrix to nanoparticles is required to obtain the best advantages of clay, the interfacial interactions and interphase characteristics meaningfully affect the mechanical properties of CPN. The nonbonded interactions between polymer matrix and clay are totally in the form of van der Waals forces (Zare and Garmabi, 2014b). Although the hydrogen atoms of polymer chains have relatively low partial charges, their large numbers make the highest level of interaction with the clay layers. Additionally, a hydrogen bonding can be formed between the polar groups in the polymer chains and the nanoparticles. The suggested equations are very appropriate for CPN, due to the low volume fraction and high aspect ratio of clay layers in the polymer matrix. Therefore, they can be used to determine and analyze the interfacial/interphase properties in CPN. The suggested models (Eqs. (1) and (3)) express the physical interactions at the interface. The strong chemical bonds are rarely formed in polymer nanocomposites, so the proposed models are very suitable for CPN. Also, the calculated parameters are well supported by the experimental observations. As explained, the high levels of “s” and “B” parameters
Fig. 3. The effects of “s” and “α” parameters on “ti” values (Eq. (17)) at σm = 30 MPa, l = 500 nm and σi = 100 MPa: a) 3D and b) contour plots.
Y. Zare / Applied Clay Science 115 (2015) 61–66
65
Fig. 4. a) 3D and b) contour plots for dependence of “ti” on “B” and “σi” parameters (Eq. (18)) at σm = 30 MPa, l = 500 nm and α = 100.
were confirmed by the fully intercalated/exfoliated clay as well as the strong interfacial adhesion between polymer and clay, which produce the high mechanical properties. Likewise, the poor dispersion of clay and the low mechanical properties in some samples (Nos. 5 and 6) show the low level of interfacial properties expressed by small “s” and “B” parameters. 3.2. Relations among the parameters The dependence of “σi” to “s” and “α” parameters (Eq. (15)) is illustrated in Fig. 1 at average values of σm = 30 MPa, l = 500 nm and ti = 10 nm. “σi” rises with increment of “s” and “α”. The reported results in Table 1 demonstrate the direct connection between “σi” and “s” in which the high levels of “σi” and “s” showed a strong interphase between polymer and clay. However, it was observed that the effect of “s” level on “σi” was more important than the influence of “α”, because “σi” was constant in a large range of “α”, i.e. α N 40 approximately produced a constant “σi” at each “s”. To obtain high “σi” and “s”, the interfacial properties may be improved by compatibilization of polymer and particles phases, treatment of nanofiller and functionalization of components. Also, “σi” as a function of “B” and “ti” parameters (Eq. (16)) is illustrated in Fig. 2 at σm = 30 MPa, l = 500 nm and α = 100. “σi” was negligible at little “B” and large “ti” as well as the medium values of these parameters. However, with increase in “B”, “σi” improved at slighter “ti” and reached to the most extent at the largest “B” and the smallest “ti”. These plots illustrated the positive influence of “B” on “σi”, but a dissimilar trend was found between “σi” and “ti”. Based on Eqs. (15) and (16), a high level of “σi” was obtained with large “σm”, “l”, “s”, “α” and “B” as material and interfacial parameters. Additionally, the effects of “s” and “α” parameters on “ti” values (Eq. (17)) are depicted in Fig. 3 at σm = 30 MPa, l = 500 nm and σi = 100 MPa. The smallest “ti” was obtained with small “s” at α N 70, while the highest “ti” was achieved by high “s” and small “α”. Conclusively, “α” as a material parameter plays a negative role in the interphase thickness. The illustration indicates the positive effect of “s” parameter on “ti”, which expresses that a thick interphase displays a large stress transfer from polymer matrix to clay at the interphase region in CPN. Also, α b 60 can significantly change the “ti” at various “s”, but α N 60 commonly produces ti b 20 nm at all “s” levels. In other words, “s” has a largely positive effect on “ti” at α b 60 and a high level of “ti” is obtained at α b 40 and s N 2 MPa. The dependence of “ti” to “B” and “σi” parameters (Eq. (18)) at σm = 30 MPa, l = 500 nm and α = 100 is shown in Fig. 4. “ti” increased by increment in “B” especially at low level of “σi” (σi b 100 MPa). However, a large “σi” caused a small “ti” at different “B” values, which demonstrated the inverse relation between “σi” and “ti” in polymer nanocomposites. Also, it was revealed that σi N 100 MPa at different “B” extents causes ti b 40 nm. To obtain a larger “ti”, a high “B” as well as a low “σi” is
necessary. As expected by Eqs. (17) and (18), a higher “ti” is created by larger material properties such as “σm” and “l”. In addition, some interfacial parameters such as “B” and “s” have positive influences on “ti”. However, the high levels of “α” and “σi” introduce a small “ti”, i.e. a thin interphase. 4. Conclusions In this paper, a simple methodology was suggested for characterizing of various material and interaction/interphase properties in CPN using the yield strength data. The “B” interfacial parameter could easily be determined by the Pukanszky model for CPN. “B” was correlated with various material factors such as “α” and “σm”, as well as interfacial/ interphase properties including “σi”, “ti” and “s”. Afterwards, these parameters were calculated and evaluated for some samples reported in valid literature. The calculations showed different values for “s” and “σi” attributed to dissimilar levels of “B” and “σm” in CPN. Also, it was established that “s” and “σi” are not defined for the samples which show B b 2.4 and so, B = 2.4 is a minimum level which will give the expressive data for interface/interphase properties. Furthermore, it was possible to predict the correlations among the material and interaction properties in CPN. This analysis expressed the direct relations of “σi” and “ti” with “σm”, “s”, “B” and “l”. Similarly, the findings revealed that “ti” extent has a negative influence on “σi” result in CPN. References Adame, D., Beall, G.W., 2009. Direct measurement of the constrained polymer region in polyamide/clay nanocomposites and the implications for gas diffusion. Appl. Clay Sci. 42, 545–552. Aït Hocine, N., Médéric, P., Aubry, T., 2008. Mechanical properties of polyamide-12 layered silicate nanocomposites and their relations with structure. Polym. Test. 27, 330–339. Baniasadi, H., Ramazani, S.A., Javan Nikkhah, S., 2010. Investigation of in situ prepared polypropylene/clay nanocomposites properties and comparing to melt blending method. Mater. Des. 31, 76–84. Callister, W.D., Rethwisch, D.G., 2007. Materials science and engineering: an introduction. Wiley, New York. Daniel Wagner, H., 2002. Nanotube–polymer adhesion: a mechanics approach. Chem. Phys. Lett. 361, 57–61. Durmus, A., Kaşgöz, A., Macosko, C.W., 2008. Mechanical properties of Linear Low-density Polyethylene (LLDPE)/clay nanocomposites: estimation of aspect ratio and interfacial strength by composite models. J. Macromol. Sci., Part B: Phys. 47, 608–619. Fasihi, M., Abolghasemi, M.R., 2012. Oxygen barrier and mechanical properties of masterbatch-based PA6/clay composite films. J. Appl. Polym. Sci. 125, E2–E8. Fernández, M.J., Fernández, M.D., Aranburu, I., 2013. Effect of clay surface modification and organoclay purity on microstructure and thermal properties of poly (L-lactic acid)/vermiculite nanocomposites. Appl. Clay Sci. 80, 372–381. Hajibeygi, M., Shabanian, M., Khonakdar, H.A., 2015. Zn–AL LDH reinforced nanocomposites based on new polyamide containing imide group: from synthesis to properties. Appl. Clay Sci. 114, 256–264. Huskić, M., Žigon, M., Ivanković, M., 2013. Comparison of the properties of clay polymer nanocomposites prepared by montmorillonite modified by silane and by quaternary ammonium salts. Appl. Clay Sci. 85, 109–115.
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