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Mechanical characterization of interfaces in epoxy-clay nanocomposites by molecular simulations
Polymer 54 (2013) 766e773
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Polymer journal homepage: www.elsevier.com/locate/polymer
Mechanical characterization of interfaces in epoxy-clay nanocomposites by molecular simulations Y. Chen a, J.Y.H. Chia a, b, Z.C. Su a, T.E. Tay a, V.B.C. Tan a, * a b
Department of Mechanical Engineering, National University of Singapore, Singapore 117576, Singapore Institute of Materials Research and Engineering, A*STAR, Singapore 117602, Singapore
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 July 2012 Received in revised form 8 November 2012 Accepted 15 November 2012 Available online 21 November 2012
Ultra high interface/volume ratio is an important feature of polymer-clay nanocomposites resulting from the nanometer scale dimensions of the clay particle. An understanding of the behavior of these interfaces on the molecular level is essential as they are largely responsible for the material propertiesof nanocomposites. In polymer-clay nanocomposites the concept of a binding energy is too simplified to be able to account for the presence of multi-phase interfaces. The gallery interface within intercalated clay particles and the interphase region with the polymer matrix are investigated. They are subjected to Mode I splitting deformation through molecular dynamics simulations and characterized by their tractione separation relationships. Several key parameters including peak strength, fracture energy and final splitting separation distances are qualified from the tractioneseparation curves which can be integrated into continuum models. The simulations reveal that the alkyl chain length of surfactants plays an essential role in the mechanical performance of these interfaces. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Polymer-clay nanocomposites Gallery interfaces Matrix interphase
1. Introduction Polymer-clay nanocomposites are a subject of growing interest as they often exhibit markedly improved material properties compared to pure polymer matrix and traditional micro/macro composites [1e5]. These improved material properties are usually attributed to the ultra high interface/volume ratio in nanocomposites resulting from the nanometer scale dimensions of clay particles. However, these interfaces are not well understood and have not been characterized because of the breakdown of traditional micromechanical models and theories. Continuum methods are unable to uncover the effects of chemical compositions and molecular details and thus cannot be used to characterize the mechanical behaviors of interfaces. Experimental tools are also not fully developed for studying structures and phenomena on the nanometer scale. Advanced techniques such as nano-indentation [6,7] and AFM [8] are still unable to test isolated clay particle and related interfaces. The breakdown of continuum methods and lack of experimental techniques have made it difficult to investigate nanometer interfaces such as those that strongly affect the structureeproperty relationships of polymer-clay nanocomposites.
* Corresponding author. Tel.: þ65 6516 8088. E-mail address: [email protected] (V.B.C. Tan). 0032-3861/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.polymer.2012.11.040
Molecular simulations are now routinely employed to study phenomena on the molecular level and quantitatively predict physical properties of nanometer sized constituents. They are increasingly accepted as an effective tool for studying nanostructures. Due to intensive computational requirement, the models in molecular simulations are usually limited to nanometer scale and cannot be used to simulate nanocomposites at the macroscale. Thus, molecular simulations are selectively employed to focus only on certain critical regions of the nanocomposites, such as single silicate sheets [9,10] or interfaces [11e14]. Molecular simulations are performed on polymer-clay interfaces to characterize their interfacial behaviors. Tanaka [11] and Fermeglia [12] calculated the binding energies between surfactants, silicate sheets and Nylon chains and they tried to build a connection between the binding energies and interfacial strength using the Griffith criterion based on the assumption that the binding energy between the silicate sheet and other molecules equals to the fracture energy needed to split the clayepolymer interface. Toth et al. [13] followed an analogous approach and concluded that organic surfactants would enhance the binding energy between clay particles and organic polymers. Zhang and co-authors [14] also calculated the binding energies between the clay particle and surrounding polymers and proposed that high interfacial binding energy is responsible for high mechanical performance of nanocomposites. These previous works aim to establish a correlation
Y. Chen et al. / Polymer 54 (2013) 766e773
between the binding energy profiles and the overall mechanical performance of nanocomposites. However, there are no direct evidences or theories to support the hypothesis. Whether high binding energy between clay particles and surrounding polymers necessarily means high mechanical strength of the interface is important yet not well addressed. Fig. 1(a) shows a typical two-phase interface. The binding energy [11e14] between phase A and phase B is calculated as following:
EBinding ¼ EA
isolated
þ EB
isolated
EAB
interface
(1)
The binding energy represents the energy that is required to separate the interfaces. This is true only if the fracture surface exactly passes along the phase boundary as illustrated in Fig. 1(a). For an interface consisting of multiple phases as an example in Fig. 1(b), the binding energy between any two phases can still be easily calculated using the above formula. However, it is difficult to correlate the binding energies with the overall performance of the interface as the fracture surface may not exactly follow the phase boundary and may even pass through these phases. Binding energy actually represents the energy difference between two individual phases and the combined interface under equilibrium condition. It is a term that indicates how tough the interface is rather than how strong it is, whereas the mechanical strength of an interface might be governed by the evolution of molecular configuration during the failure process. The concept of binding energy may not be suitable to characterize the complex interfaces in nanocomposites as they mostly possess complex phases with various molecules. A different approach should be proposed for the mechanical characterization of these interfaces, providing a basis for their material parameterization in continuum modeling of nanocomposites. We present an alternative to characterize the interfaces in epoxy-clay nanocomposites via the manner of fracture mechanics. The fracture surface may propagate in three ways: (i) Mode I crack e opening mode, (ii) Mode II crack e sliding mode and (iii) Mode III crack e tearing mode. In this study, full atomistic models of these interfaces are constructed and they are subjected to Mode I separation to obtain the traction stress versus separation distances relations. Mode II and III separation not considered. The tractione separation relations obtained in this manner makes no prior assumption of the crack evolution. Even for interfaces with multiple phases, the fracture surface would correspond to the least energetic one. Key parameters such as peak strength (for damage initiation criterion), fracture energy and final failure separation distance (for post damage evolution) can be quantified from the tractioneseparation curves which can then be used to parameterize the interfaces in continuum models. 2. Models and simulation details 2.1. Epoxy-clay nanocomposites Epoxy-clay nanocomposites are a typical family of polymeric nanocomposites comprising an epoxy matrix and nanosized clay particles. In this work, the epoxy matrix is Diglycidyl ether of bisphenol-A þ Diethylmethylbenzenediamine (DGEBA þ DETDA),
Fig. 1. Schematic illustration of two-phase interface and multi-phases interfaces.
767
a widely used thermosetting polymer in industry. Their molecular structures are presented in Fig. 2. The clay is usually referred to as natural minerals and in this work it is specified as montmorillonite (MMT). It has a multi-layer structure consisting of stacked silicate sheets with interlayer galleries in between. Epoxy-clay nanocomposites have complex micro-structure resulting from the sensitivity of the morphology of clay particles to the dispersion condition. The morphological state is influenced by many factors such as clay content, particle size, cation exchange capacity (CEC), organic surfactant, moisture content and synthesizing condition. Broadly, MMT exist in three typical forms e immiscible, intercalated and exfoliated. For organically treated montmorillonite (OMMT), the co-existence of intercalated and exfoliated ones is frequently observed in samples. Fig. 3 shows a schematic illustration of the micro-structure of epoxy-clay nanocomposites. It is regarded as a multi-phase system consisting of bulk matrix, silicate sheets, gallery interfaces and matrix interphase surrounding the silicate sheets as labeled. The focus is on related interfaces including gallery interface and matrix interphase. The following sections will give a detailed introduction to the two typical interfaces. 2.2. Gallery interface The gallery interface is defined as the interlayer region between two stacked silicate sheets. A gallery interface exists in OMMTs that are not exfoliated. The gallery may or may not have epoxy molecules within. In this work, we focus on these particles with certain amount of epoxy molecules intercalated. The gallery interface is characterized by the d-spacing (also known as basal plane spacing) defined as the distance from a certain plane of one silicate sheet to the corresponding plane of another parallel one. The value of the dspacing is the sum of the thicknesses of one silicate sheet and one organic gallery. Experimental techniques such as the wide angle Xray scattering (WAXS) are used to measure the d-spacing and many studies show that the d-spacing is in the range of 1e4 nm [15e17] depending on the extent of intercalation. A typical gallery interface consists of two adjacent silicate sheets, surfactants and intercalated epoxy molecules. For the silicate sheet, the crystal lattice structure is adopted from Heinz’ works [17e19]. They constructed the MMT model according to the X-ray crystal structure [17]. The spatial distribution of 10 Al3þ>Mg2þ defects was modeled following solid-state NMR data [18]. The corresponding CEC resulting from these cation defects equals to 91 mequiv/100 g. The chemical composition of this model is Na [Si4O8]3Al5MgO6(OH)6 e a close representation of the product from Southern Clay Products, Inc, US [20]. Heinz and his co-workers also developed a force field based on CFF91 specially for modeling layered silicate structures, such as Mica and MMT. They derived the atomic charges based on atomization enthalpies, ionization potential and comparison with reported electron deformation densities [21]. They integrated these parameters into the CVFF force field and to obtain the Phyllosilicate Force Field embedded in the Consistent Valence Force Field (PFF_CVFF) [22] which was employed in this work. All the molecular models in this work are constructed and modified in Material Studio 4.3 [23] and then imported into a parallel MD simulator LAMMPS [24] for equilibration and Mode I deformation. The second component is the surfactant, which is selected from a group of small organic molecules with particular functional groups of one positive charged ammonium head group (NHþ 3 ) and at least one alkyl chain (Cn). The function of the ammonium head group is to replace the cations (such as Naþ, Kþ) in the gallery of pristine MMT and help the surfactants adhere to silicate sheet surfaces. The function of the alkyl chain is to improve the
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Fig. 2. Molecular structures of epoxy resin (DGEBA) and curing agent (DETDA). Atoms: Gray (C), White (H), Red (O), Blue (N). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
compatibility between silicate sheet and matrix polymers and hence achieve better dispersion with higher exfoliation degree. Simulations using a series of surfactants with a single ammonium head group and one alkyl chain of various lengths were carried out. The surfactant, NHþ 3 C18 H37 , is used throughout this work except for the Section 3.4, where the effects of alkyl chain length on interfacial behaviors are investigated. The intercalated epoxy molecules are DGEBA resins and DETDA hardeners. They are crosslinked together using an iterative algorithm [25,26]. Fig. 4 shows the molecular model of the gallery interface. Periodic boundary conditions (PBC) are applied in the in-plane (X and Y) directions to replicate the large aspect ratio of clay particles whose in-plane dimensions are from several hundred nanometers to several millimeters. PBC is also employed in the Z direction in order to mimic the stacking situation in the normal direction. A single periodic cell includes a silicate sheet, 10 surfactants, 10 resins and 5 hardeners molecules. The silicate sheet is characterized by 10 negative charges resulting from cation substitutions. The negative charges are compensated by the 10 surfactants, each with an ammonium head groups possessing a positive charge. It should be pointed out that the surfactant molecules are placed close to the silicate surface because they have been strongly adsorbed on the surface during organic treatment before dispersing clay particles into epoxy matrix. The corresponding d-spacing of this model after stress relaxation is 2.95 nm, which falls in the range of experimental observations [17e19]. Initially the model is subjected to NPT ensemble for 5 ns to release the internal stress before applying tension. This gallery model is subjected to Model I splitting loading to obtain the tractioneseparation relation. Within each tensile step, the cell length in Z direction is elongated by a value of s ¼ 0.05 nm and the coordinates of all atoms within the cell are rescaled to fit the new geometry followed by a equilibration of the NLiPjPkT ensemble, in which the cell length in the deformed direction i is fixed while the two lateral sides j and k are kept at atmospheric pressure (negligible compared to the traction stress). The equilibration time for each step is 250 ps corresponding to a stretching velocity of 0.2 m/s. The normal traction stress s is calculated using the Virial theorem [27] throughout the whole periodic cell and is time-averaged over
the latter half of the equilibrium interval. It is recorded versus the separation distance d to derive the tractioneseparation curve. 2.3. Matrix interphase For both intercalated and exfoliated clay particles, the outer surfaces of silicates sheets are in contact with matrix phase and these regions are defined as the matrix interphase. Due to its proximity to the silicate, interphase properties will be different from the bulk matrix properties. Fig. 5 shows the molecular model of a typical matrix interphase containing 5 surfactants, a silicate sheet, 5 surfactants and a thick epoxy matrix layer stacked in sequence. It should be emphasized that two vacuum layers of 20 nm are padded on two sides of the periodic cell to eliminate the effect of self-images and mimic the non-stacking situation. In order to apply mode I loading on this matrix interphase model, the bottom surfactants plus the silicate sheet and far away epoxy matrix are defined as two rigid blocks while leaving middle part unconstrained. Mode I loading is also applied in a stepwise fashion. For each step, an opposite displacement (0.05 nm, 0.05 nm) is applied to the bottom and top rigid blocks respectively and the middle mobile zone is then equilibrated for 500 ps. This loading is continued until the complete separation of the top and bottom halves occurs. The traction stress is calculated using Virial theorem throughout the middle mobile zone only. 3. Results and discussions 3.1. Tractioneseparation curve of gallery interface Fig. 6 shows the tractioneseparation curve of the gallery interface. The traction stress s initially increases rapidly and reaches the maximum value of 99.87 MPa when d is 0.25 nm in Fig. 7(b). The maximum traction stress is defined as peak strength T and this value is usually used to parameterize the damage initiation criterion in continuum modeling. At the early stage, the increase in traction stress mainly results from the adjustment of the
Fig. 3. Polymer-clay nanocomposites at different scales.
Y. Chen et al. / Polymer 54 (2013) 766e773
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Fig. 4. Molecular model of gallery interface. The in-plane dimensions are 2.7 nm 2.6 nm. The epoxy molecules are displayed using stick model and the surfactants are displayed using ball-stick model. The surfactant is NHþ 3 C18 H37 .
equilibration positions of atoms by the van der Waals and electrostatic interaction. The slippage and repetition of backbones as well as side chains are not expected. Beyond the peak stress, the traction stress begins to decrease gradually due to the debonding between surfactants and epoxy molecules as observed in Fig. 7(c) and (d). It should be noted that during the debonding process the ammonium head groups of surfactants remain adhered to the silicate surface and the alkyl chains are stretched by the epoxy molecules. The strong adhesion between ammonium groups and silicate sheets is due to the opposite charges that they possess. The interaction between alkyl chains and epoxy molecules is relative weak as this interaction is mainly governed by van der Waals force. Such phenomenon indicates that surfactants-epoxy boundary is
the weakest region. Consequently, the fracture surface passes through this region. With further debonding between surfactants and epoxy molecules, the traction stress decreases and finally drops to zero when d reaches about 2.3 nm. At that displacement, the alkyl chains are totally pulled away from the epoxy molecules. The area under the tractioneseparation curve is defined as fracture energy G and this value is often used for parameterization of post damage evolution in continuum modeling. The fracture energy for gallery interface is calculated to be 0.084 J/m2, several orders lower than those in bulk material [28] and macroscale interface testing [29]. The difference is because the separation distance of the gallery failure of this work is only 2e3 nm while the separation distances in macroscale samples are usually on the order
Fig. 5. Molecular model of matrix interphase. The in-plane dimensions are 2.7 nm 2.6 nm. The epoxy molecules are displayed using stick model and the surfactants are displayed using ball-stick model. The surfactant is NHþ 3 C18 H37 .
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This failure mechanism is similar to that observed in the gallery interface. 3.3. Density profiles
Fig. 6. Tractioneseparation curve of gallery interface during Mode I splitting deformation.
of millimeters. Thus, the ultra low fracture energy in this work is only for nanosized interfaces.
The increase in the traction stress in the early stage mainly results from the van der Waals and electrostatic forces. A measure of the contribution of these non-bond interactions is the local molecular density. This density distribution is investigated to understand why the matrix interphase exhibit higher peak strength and fracture energy than the gallery interface as reported in previous sections. Fig. 10 shows the density profiles of both interfaces. It is seen that the density of the organic gallery is about 0.76 g/cm3, which is much lower than that of the matrix interphase. The low density of the gallery interfaces is likely responsible for its lower peak strength as well as fracture energy. The low density is attributed to nano-confinement effects of the gallery sandwiched between stacked silicates. As the gallery thickness is only several nanometers, polymer chains can’t relax and extend sufficiently. This especially affects the epoxy because the crosslinked networks are not flexible. The proposal of nano-confinement effects is further supported by the comparison in Fig. 10(b). It shows that the density of the polymer near the silicate sheets is also slightly lower than that far away from the interphase. In addition, no obvious layering configuration is observed in the polymers near the silicate sheet.
3.2. Tractioneseparation curve of matrix interphase 3.4. The effects of the surfactant on interfacial behaviors Fig. 8 shows the curve of traction stress versus separation distance for the matrix interphase surrounding the clay particle. The traction stress initially increases and reaches a peak value of about 131 MPa. This is higher than the gallery interface peak stress and could be a reflection of the difference between confined and unconfined systems. After that, the traction stress begins to drop because of the debonding between surfactants and epoxy molecules and finally approaches zero when the separation distance d is about 2.25 nm. The fracture energy is calculated to be 0.1266 J/m2 and is also higher than that of the gallery interface. Fig. 9 shows the molecular configuration of the matrix interphase as it is breaking up. It is found that the fracture occurs between the surfactants and epoxy layer. The ammonium groups remain adhered to the silicate surface as the alkyl chains are being stretched and then released after the peak stress value is attained.
For both the gallery interface and matrix interphase around the clay particles, the fracture surfaces are found to be between surfactants and epoxy molecules and the failure process is characterized by the stretching of the alkyl chains and continuous debonding. It is evident that the alkyl chain plays an essential role in the interfacial failure. Several surfactants with alkyl chains of different lengths are examined. Table 1 summarizes the key features of these tractione separation curves in both gallery interfaces and matrix interphase. For the gallery interface, the peak strength generally falls in the range of 80e100 MPa and it is highest when the number of carbon atoms of the alkyl chains is 18. The fracture energy is dominated by the final separation distance which increases with the alkyl chain length. Since failure is an energy adsorbing process,
Fig. 7. Molecular configuration evolution of gallery interface during splitting deformation. The surfactant is NHþ 3 C18 H37 .
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Fig. 8. Tractioneseparation curve of matrix interphase during Mode I splitting deformation.
this suggests that alkyl chain length plays an important role in determining the amount of energy adsorbed. For the matrix interphase model, the highest peak strength appears in the C_12 model and reaches higher than 140 MPa. The fracture energy and separation distance again increase with the alkyl chain length, similar to the gallery interface model. Overall, the dependence of the feature parameters on the alkyl chain length suggests that that modifying the molecular structure of surfactants might be an effective way to control the interfacial behaviors and consequently influence the material properties of nanocomposites at the macroscale.
Fig. 10. Density profiles of gallery interface and matrix interphase in the normal direction.
Table 1 Features of tractioneseparation curves with different alkyl chain lengths. Alkyl chain of surfactants
C_6 C_12 C_18 C_24 C_30
Gallery interface T (MPa)
G
93.45 96.53 99.87 88.2 83.06
0.0495 0.0748 0.0840 0.1217 0.1324
(J/m2)
Matrix interphase
dFailure
T (MPa)
G
dFailure
(nm) 1.25 1.70 2.30 2.70 3.50
137.34 144.59 131.07 137.41 122.76
0.0767 0.0902 0.1266 0.1508 0.1764
1.30 1.80 2.40 2.90 3.70
(J/m2)
(nm)
PS: C_N, where N is the number of carbon atoms in the alkyl chain of surfactants.
Toth et al. [13] calculated the binding energies of many systems and concluded that shorter alkyl chains were more effective in producing higher binding energies between clay particles and the surrounding polymers, resulting in high mechanical properties [14]. The binding energies reported by Toth et al. were calculated based simply on the final equilibrated state of the systems. No information on the evolution of the configuration of the systems is used in the determination of the binding energies. In our work, however, it is shown that shorter alkyl chains actually lead to lower peak strength and fracture energy. The peak strength and fracture energy are measured during the splitting deformation and their values are determined by how these molecules evolve during this process. The difference between Toth’s work and this study arises Table 2 Comparison between binding energies and fracture energies for the matrix interphase model. Alkyl chain of surfactants
Fig. 9. Molecular configuration evolution of matrix interphase in splitting deformation. The surfactant is NHþ 3 C18 H37 .
C_6 C_12 C_18 C_24 C_30
Binding energy EBinding (J/m2) Case I
Case II
0.2382 0.2124 0.2459 0.2338 0.2776
0.1561 0.1375 0.1389 0.1987 0.1942
Fracture energy G (J/m2) 0.0767 0.0902 0.1266 0.1508 0.1764
PS: the binding energy is normalized by the cross section area of the periodic cell.
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Fig. 11. Strength comparison of gallery interface, matrix interphase and bulk matrix.
from how the interfaces are characterized, statically or dynamically. Static calculation of binding energies may not be suitable for characterizing the mechanical properties of multi-phase interfaces. Investigating the entire splitting process in a dynamic manner may be a more effective way to estimate the overall strength and toughness of such complex interfaces. 3.5. Binding energy and fracture energy For the gallery interface model, the binding energy can’t be appropriately calculated due to the presence of self-imaging. For the matrix interphase model, the self-imaging effect is eliminated by padding two vacuum layers on two sides. Following the idea of binding energy as a static calculation, the fracture path that separate the system into part A and part B is not determined. Here, two cases that the fracture surface may pass through silicate/surfactants boundary (case I) and surfactants/epoxy boundary (case II) are considered. The corresponding binding energies of the two cases in five models are calculated and compared with the fracture energy obtained by Mode I loading in Table 2. It is seen that the binding energy for the case II is always higher than that of the case I, which means that the adhesion between surfactants and epoxy molecules are weaker than that between silicate and surfactants. This agrees well with the observed phenomenon in Mode I loading that the surfactants remain adhered to the silicate surface and the tails are stretched by the epoxy and finally separated from the epoxy molecules. It is clear that the binding energy depends on the fracture surface defined in the calculation. However, for complex interfaces with multi-phases, it is difficult or even impossible to define the specific fracture surface that corresponds to the lowest binding energy. Besides, it is found that the binding energies are insensitive to the alkyl chain length as their values are largely dependent on the local molecular density near the fracture surface, which is not strongly affected by the alkyl chain length. However, the fracture energy is obviously sensitive to the alkyl chain length as it is dominated by the final separation distance that are controlled by the alkyl chain. The longer the alkyl chain it is, the higher fracture energy that the interface possess. This again indicates that binding energy is not suitable for mechanical characterization as its value do not reflect the influence of local molecular structure on the mechanical behaviors of complex interfaces.
subjected to loading, the silicate sheet is unlikely to fail due to its perfect crystal structure with ultra high stiffness and strength. The possible failure regions would be within the other three. Fig. 11 compares the tractioneseparation curves of gallery interface and matrix interphase as well as the stressestrain curve of bulk epoxy. The peak strengths of gallery interface and matrix interphase regions are both lower than that of bulk epoxy, suggesting that that damage is more likely to initiate in gallery interface or matrix interphase rather than the bulk matrix domain if stress concentration is not considered. In actual composites, the stiffness mismatch between rigid silicate sheets and surrounding polymers leads to higher localized stress, which would advance the damage in gallery interfaces or matrix interphases. This comparison provides a simple yet effective reference for predicting the weak zones in polymer-clay nanocomposites. For accurate identification of damage initiation, continuum model of polymer-clay nanocomposites with micro-structural details should be developed and it is under our work progress currently. 4. Conclusion Binding energy, a common measure to characterize interfacial properties, may not be applicable to interfaces with complex multiphase features. In this work, molecular dynamics simulations of Mode I loading of interfaces are proposed to study such interfaces resulting in tractioneseparation relations that have been used to characterize the failure process of the interfaces in terms of quantifiable parameters including peak strength, fracture energy and final separation distance. These parameters are useful for progressive damage techniques in continuum modeling, e.g., the cohesive zone model (CZM) [30,31]. The gallery interface and matrix interphase e two typical types of interfaces in polymer-clay nanocomposites e are investigated. It is found that the peak strength and fracture energy of the matrix interphase are generally higher than those of the gallery interface. This is explained by comparing their density profiles near the silicate sheet. It is further found that the energy absorbed during the interfacial failure process highly depends on the alkyl chain length of surfactants. This suggests a mean for tailoring macroscale properties of nanocomposites via modifying the structures of surfactants on the molecular scale. Acknowledgment
3.6. Strength of gallery interface, matrix interphase and bulk matrix As introduced in Fig. 3, the polymer-clay nanocomposite consists of four basic constituents. When a macroscale sample is
The authors acknowledge the financial support given to this study by the Agency for Science, Technology and Research (A*STAR, Project Number-1123004033), Singapore.
Y. Chen et al. / Polymer 54 (2013) 766e773
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
Komarneni S. Journal of Materials Chemistry 1992;2:1219. Giannelis EP. Advanced Materials 1996;8:29. Bharadwaj RK. Macromolecules 2001;34:9189. Alexander M, Dubois P. Materials Science and Engineering: R: Reports 2000;28:1. Podsiadlo P, Kaushik AK, Arruda EM, Waas AM, Shim BS, Xu J, et al. Science 2007;318:80. Dhakal HN, Zhang ZY, Richardson MOW. Polymer Testing 2006;25:846. Hu Y, Shen L, Yang H, Wang N, Liu T, Liang T, et al. Polymer Testing 2006;25:492. Mojumdar SC, Raki L, Mathis N, Schimdt K, Lang S. Journal of Thermal Analysis and Calorimetry 2006;85:119. Manevitch OL, Rutledge GC. Journal of Physical Chemistry B 2004;108:1428. Suter JL, Coveney PV, Greenwell HC, Thyveetil M. Journal of Physical Chemistry C 2007;111:8248. Tanaka G, Goettler LA. Polymer 2002;43:541. Fermeglia M, Ferrone M, Pricl S. Fluid Phase Equilibria 2003;212:315. Toth R, Coslanich A, Ferrone M, Fermeglia M, Pricl S, Miertus S, et al. Polymer 2004;45:8075. Zhang Q, Ma X, Wang Y, Kou K. Journal of Physical Chemistry B 2009;113: 11898.
773
[15] Ray SS, Okamoto MM. Progress in Polymer Science 2003;28:1539. [16] Chen B. British Ceramic Transactions 2004;103:241. [17] Heinz H, Castelijns HJ, Suter UW. Journal of the American Chemical Society 2003;125:9500. [18] Heinz H, Suter UW. Journal of Physical Chemistry B 2004;108:18341. [19] Heinz H, Vaia R, Farmer BL. Journal of Chemical Physics 2006;124:224713. [20] http://www.scprod.com/. [21] Cygan RT, Greathouse JA, Heinz H, Kalinichev AG. Journal of Materials Chemistry 2009;19:2470. [22] http://www.poly-eng.uakron.edu/heinz-interface-force-field.php. [23] Material Studio 4.3, Accelrys Inc., San Diego, http://accelrys.com/. [24] Plimption S. Journal of Computational Physics 1995;117:1. [25] Wu CF, Wu WJ. Polymer 2006;47:6004. [26] Li C, Strachan A. Polymer 2011;52:2920. [27] Tsai DH. Journal of Chemical Physics 1979;70:1375. [28] Johnsen BB, Kinloch AJ, Mohammed RD, Taylor AC, Sprenger S. Polymer 2007; 48:530. [29] Ridha M, Tan VBC, Tay TE. Composite Structures 2011;93:1239. [30] Borst R, Gutiérrez MA, Wells GN, Remmers JJC, Askes H. International Journal for Numerical Methods in Engineering 2004;60:289. [31] Zhang B, Yang Z, Sun X, Tang Z. Computational Materials Science 2010;49:645.
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Polymer journal homepage: www.elsevier.com/locate/polymer
Mechanical characterization of interfaces in epoxy-clay nanocomposites by molecular simulations Y. Chen a, J.Y.H. Chia a, b, Z.C. Su a, T.E. Tay a, V.B.C. Tan a, * a b
Department of Mechanical Engineering, National University of Singapore, Singapore 117576, Singapore Institute of Materials Research and Engineering, A*STAR, Singapore 117602, Singapore
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 July 2012 Received in revised form 8 November 2012 Accepted 15 November 2012 Available online 21 November 2012
Ultra high interface/volume ratio is an important feature of polymer-clay nanocomposites resulting from the nanometer scale dimensions of the clay particle. An understanding of the behavior of these interfaces on the molecular level is essential as they are largely responsible for the material propertiesof nanocomposites. In polymer-clay nanocomposites the concept of a binding energy is too simplified to be able to account for the presence of multi-phase interfaces. The gallery interface within intercalated clay particles and the interphase region with the polymer matrix are investigated. They are subjected to Mode I splitting deformation through molecular dynamics simulations and characterized by their tractione separation relationships. Several key parameters including peak strength, fracture energy and final splitting separation distances are qualified from the tractioneseparation curves which can be integrated into continuum models. The simulations reveal that the alkyl chain length of surfactants plays an essential role in the mechanical performance of these interfaces. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Polymer-clay nanocomposites Gallery interfaces Matrix interphase
1. Introduction Polymer-clay nanocomposites are a subject of growing interest as they often exhibit markedly improved material properties compared to pure polymer matrix and traditional micro/macro composites [1e5]. These improved material properties are usually attributed to the ultra high interface/volume ratio in nanocomposites resulting from the nanometer scale dimensions of clay particles. However, these interfaces are not well understood and have not been characterized because of the breakdown of traditional micromechanical models and theories. Continuum methods are unable to uncover the effects of chemical compositions and molecular details and thus cannot be used to characterize the mechanical behaviors of interfaces. Experimental tools are also not fully developed for studying structures and phenomena on the nanometer scale. Advanced techniques such as nano-indentation [6,7] and AFM [8] are still unable to test isolated clay particle and related interfaces. The breakdown of continuum methods and lack of experimental techniques have made it difficult to investigate nanometer interfaces such as those that strongly affect the structureeproperty relationships of polymer-clay nanocomposites.
* Corresponding author. Tel.: þ65 6516 8088. E-mail address: [email protected] (V.B.C. Tan). 0032-3861/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.polymer.2012.11.040
Molecular simulations are now routinely employed to study phenomena on the molecular level and quantitatively predict physical properties of nanometer sized constituents. They are increasingly accepted as an effective tool for studying nanostructures. Due to intensive computational requirement, the models in molecular simulations are usually limited to nanometer scale and cannot be used to simulate nanocomposites at the macroscale. Thus, molecular simulations are selectively employed to focus only on certain critical regions of the nanocomposites, such as single silicate sheets [9,10] or interfaces [11e14]. Molecular simulations are performed on polymer-clay interfaces to characterize their interfacial behaviors. Tanaka [11] and Fermeglia [12] calculated the binding energies between surfactants, silicate sheets and Nylon chains and they tried to build a connection between the binding energies and interfacial strength using the Griffith criterion based on the assumption that the binding energy between the silicate sheet and other molecules equals to the fracture energy needed to split the clayepolymer interface. Toth et al. [13] followed an analogous approach and concluded that organic surfactants would enhance the binding energy between clay particles and organic polymers. Zhang and co-authors [14] also calculated the binding energies between the clay particle and surrounding polymers and proposed that high interfacial binding energy is responsible for high mechanical performance of nanocomposites. These previous works aim to establish a correlation
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between the binding energy profiles and the overall mechanical performance of nanocomposites. However, there are no direct evidences or theories to support the hypothesis. Whether high binding energy between clay particles and surrounding polymers necessarily means high mechanical strength of the interface is important yet not well addressed. Fig. 1(a) shows a typical two-phase interface. The binding energy [11e14] between phase A and phase B is calculated as following:
EBinding ¼ EA
isolated
þ EB
isolated
EAB
interface
(1)
The binding energy represents the energy that is required to separate the interfaces. This is true only if the fracture surface exactly passes along the phase boundary as illustrated in Fig. 1(a). For an interface consisting of multiple phases as an example in Fig. 1(b), the binding energy between any two phases can still be easily calculated using the above formula. However, it is difficult to correlate the binding energies with the overall performance of the interface as the fracture surface may not exactly follow the phase boundary and may even pass through these phases. Binding energy actually represents the energy difference between two individual phases and the combined interface under equilibrium condition. It is a term that indicates how tough the interface is rather than how strong it is, whereas the mechanical strength of an interface might be governed by the evolution of molecular configuration during the failure process. The concept of binding energy may not be suitable to characterize the complex interfaces in nanocomposites as they mostly possess complex phases with various molecules. A different approach should be proposed for the mechanical characterization of these interfaces, providing a basis for their material parameterization in continuum modeling of nanocomposites. We present an alternative to characterize the interfaces in epoxy-clay nanocomposites via the manner of fracture mechanics. The fracture surface may propagate in three ways: (i) Mode I crack e opening mode, (ii) Mode II crack e sliding mode and (iii) Mode III crack e tearing mode. In this study, full atomistic models of these interfaces are constructed and they are subjected to Mode I separation to obtain the traction stress versus separation distances relations. Mode II and III separation not considered. The tractione separation relations obtained in this manner makes no prior assumption of the crack evolution. Even for interfaces with multiple phases, the fracture surface would correspond to the least energetic one. Key parameters such as peak strength (for damage initiation criterion), fracture energy and final failure separation distance (for post damage evolution) can be quantified from the tractioneseparation curves which can then be used to parameterize the interfaces in continuum models. 2. Models and simulation details 2.1. Epoxy-clay nanocomposites Epoxy-clay nanocomposites are a typical family of polymeric nanocomposites comprising an epoxy matrix and nanosized clay particles. In this work, the epoxy matrix is Diglycidyl ether of bisphenol-A þ Diethylmethylbenzenediamine (DGEBA þ DETDA),
Fig. 1. Schematic illustration of two-phase interface and multi-phases interfaces.
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a widely used thermosetting polymer in industry. Their molecular structures are presented in Fig. 2. The clay is usually referred to as natural minerals and in this work it is specified as montmorillonite (MMT). It has a multi-layer structure consisting of stacked silicate sheets with interlayer galleries in between. Epoxy-clay nanocomposites have complex micro-structure resulting from the sensitivity of the morphology of clay particles to the dispersion condition. The morphological state is influenced by many factors such as clay content, particle size, cation exchange capacity (CEC), organic surfactant, moisture content and synthesizing condition. Broadly, MMT exist in three typical forms e immiscible, intercalated and exfoliated. For organically treated montmorillonite (OMMT), the co-existence of intercalated and exfoliated ones is frequently observed in samples. Fig. 3 shows a schematic illustration of the micro-structure of epoxy-clay nanocomposites. It is regarded as a multi-phase system consisting of bulk matrix, silicate sheets, gallery interfaces and matrix interphase surrounding the silicate sheets as labeled. The focus is on related interfaces including gallery interface and matrix interphase. The following sections will give a detailed introduction to the two typical interfaces. 2.2. Gallery interface The gallery interface is defined as the interlayer region between two stacked silicate sheets. A gallery interface exists in OMMTs that are not exfoliated. The gallery may or may not have epoxy molecules within. In this work, we focus on these particles with certain amount of epoxy molecules intercalated. The gallery interface is characterized by the d-spacing (also known as basal plane spacing) defined as the distance from a certain plane of one silicate sheet to the corresponding plane of another parallel one. The value of the dspacing is the sum of the thicknesses of one silicate sheet and one organic gallery. Experimental techniques such as the wide angle Xray scattering (WAXS) are used to measure the d-spacing and many studies show that the d-spacing is in the range of 1e4 nm [15e17] depending on the extent of intercalation. A typical gallery interface consists of two adjacent silicate sheets, surfactants and intercalated epoxy molecules. For the silicate sheet, the crystal lattice structure is adopted from Heinz’ works [17e19]. They constructed the MMT model according to the X-ray crystal structure [17]. The spatial distribution of 10 Al3þ>Mg2þ defects was modeled following solid-state NMR data [18]. The corresponding CEC resulting from these cation defects equals to 91 mequiv/100 g. The chemical composition of this model is Na [Si4O8]3Al5MgO6(OH)6 e a close representation of the product from Southern Clay Products, Inc, US [20]. Heinz and his co-workers also developed a force field based on CFF91 specially for modeling layered silicate structures, such as Mica and MMT. They derived the atomic charges based on atomization enthalpies, ionization potential and comparison with reported electron deformation densities [21]. They integrated these parameters into the CVFF force field and to obtain the Phyllosilicate Force Field embedded in the Consistent Valence Force Field (PFF_CVFF) [22] which was employed in this work. All the molecular models in this work are constructed and modified in Material Studio 4.3 [23] and then imported into a parallel MD simulator LAMMPS [24] for equilibration and Mode I deformation. The second component is the surfactant, which is selected from a group of small organic molecules with particular functional groups of one positive charged ammonium head group (NHþ 3 ) and at least one alkyl chain (Cn). The function of the ammonium head group is to replace the cations (such as Naþ, Kþ) in the gallery of pristine MMT and help the surfactants adhere to silicate sheet surfaces. The function of the alkyl chain is to improve the
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Fig. 2. Molecular structures of epoxy resin (DGEBA) and curing agent (DETDA). Atoms: Gray (C), White (H), Red (O), Blue (N). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
compatibility between silicate sheet and matrix polymers and hence achieve better dispersion with higher exfoliation degree. Simulations using a series of surfactants with a single ammonium head group and one alkyl chain of various lengths were carried out. The surfactant, NHþ 3 C18 H37 , is used throughout this work except for the Section 3.4, where the effects of alkyl chain length on interfacial behaviors are investigated. The intercalated epoxy molecules are DGEBA resins and DETDA hardeners. They are crosslinked together using an iterative algorithm [25,26]. Fig. 4 shows the molecular model of the gallery interface. Periodic boundary conditions (PBC) are applied in the in-plane (X and Y) directions to replicate the large aspect ratio of clay particles whose in-plane dimensions are from several hundred nanometers to several millimeters. PBC is also employed in the Z direction in order to mimic the stacking situation in the normal direction. A single periodic cell includes a silicate sheet, 10 surfactants, 10 resins and 5 hardeners molecules. The silicate sheet is characterized by 10 negative charges resulting from cation substitutions. The negative charges are compensated by the 10 surfactants, each with an ammonium head groups possessing a positive charge. It should be pointed out that the surfactant molecules are placed close to the silicate surface because they have been strongly adsorbed on the surface during organic treatment before dispersing clay particles into epoxy matrix. The corresponding d-spacing of this model after stress relaxation is 2.95 nm, which falls in the range of experimental observations [17e19]. Initially the model is subjected to NPT ensemble for 5 ns to release the internal stress before applying tension. This gallery model is subjected to Model I splitting loading to obtain the tractioneseparation relation. Within each tensile step, the cell length in Z direction is elongated by a value of s ¼ 0.05 nm and the coordinates of all atoms within the cell are rescaled to fit the new geometry followed by a equilibration of the NLiPjPkT ensemble, in which the cell length in the deformed direction i is fixed while the two lateral sides j and k are kept at atmospheric pressure (negligible compared to the traction stress). The equilibration time for each step is 250 ps corresponding to a stretching velocity of 0.2 m/s. The normal traction stress s is calculated using the Virial theorem [27] throughout the whole periodic cell and is time-averaged over
the latter half of the equilibrium interval. It is recorded versus the separation distance d to derive the tractioneseparation curve. 2.3. Matrix interphase For both intercalated and exfoliated clay particles, the outer surfaces of silicates sheets are in contact with matrix phase and these regions are defined as the matrix interphase. Due to its proximity to the silicate, interphase properties will be different from the bulk matrix properties. Fig. 5 shows the molecular model of a typical matrix interphase containing 5 surfactants, a silicate sheet, 5 surfactants and a thick epoxy matrix layer stacked in sequence. It should be emphasized that two vacuum layers of 20 nm are padded on two sides of the periodic cell to eliminate the effect of self-images and mimic the non-stacking situation. In order to apply mode I loading on this matrix interphase model, the bottom surfactants plus the silicate sheet and far away epoxy matrix are defined as two rigid blocks while leaving middle part unconstrained. Mode I loading is also applied in a stepwise fashion. For each step, an opposite displacement (0.05 nm, 0.05 nm) is applied to the bottom and top rigid blocks respectively and the middle mobile zone is then equilibrated for 500 ps. This loading is continued until the complete separation of the top and bottom halves occurs. The traction stress is calculated using Virial theorem throughout the middle mobile zone only. 3. Results and discussions 3.1. Tractioneseparation curve of gallery interface Fig. 6 shows the tractioneseparation curve of the gallery interface. The traction stress s initially increases rapidly and reaches the maximum value of 99.87 MPa when d is 0.25 nm in Fig. 7(b). The maximum traction stress is defined as peak strength T and this value is usually used to parameterize the damage initiation criterion in continuum modeling. At the early stage, the increase in traction stress mainly results from the adjustment of the
Fig. 3. Polymer-clay nanocomposites at different scales.
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Fig. 4. Molecular model of gallery interface. The in-plane dimensions are 2.7 nm 2.6 nm. The epoxy molecules are displayed using stick model and the surfactants are displayed using ball-stick model. The surfactant is NHþ 3 C18 H37 .
equilibration positions of atoms by the van der Waals and electrostatic interaction. The slippage and repetition of backbones as well as side chains are not expected. Beyond the peak stress, the traction stress begins to decrease gradually due to the debonding between surfactants and epoxy molecules as observed in Fig. 7(c) and (d). It should be noted that during the debonding process the ammonium head groups of surfactants remain adhered to the silicate surface and the alkyl chains are stretched by the epoxy molecules. The strong adhesion between ammonium groups and silicate sheets is due to the opposite charges that they possess. The interaction between alkyl chains and epoxy molecules is relative weak as this interaction is mainly governed by van der Waals force. Such phenomenon indicates that surfactants-epoxy boundary is
the weakest region. Consequently, the fracture surface passes through this region. With further debonding between surfactants and epoxy molecules, the traction stress decreases and finally drops to zero when d reaches about 2.3 nm. At that displacement, the alkyl chains are totally pulled away from the epoxy molecules. The area under the tractioneseparation curve is defined as fracture energy G and this value is often used for parameterization of post damage evolution in continuum modeling. The fracture energy for gallery interface is calculated to be 0.084 J/m2, several orders lower than those in bulk material [28] and macroscale interface testing [29]. The difference is because the separation distance of the gallery failure of this work is only 2e3 nm while the separation distances in macroscale samples are usually on the order
Fig. 5. Molecular model of matrix interphase. The in-plane dimensions are 2.7 nm 2.6 nm. The epoxy molecules are displayed using stick model and the surfactants are displayed using ball-stick model. The surfactant is NHþ 3 C18 H37 .
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This failure mechanism is similar to that observed in the gallery interface. 3.3. Density profiles
Fig. 6. Tractioneseparation curve of gallery interface during Mode I splitting deformation.
of millimeters. Thus, the ultra low fracture energy in this work is only for nanosized interfaces.
The increase in the traction stress in the early stage mainly results from the van der Waals and electrostatic forces. A measure of the contribution of these non-bond interactions is the local molecular density. This density distribution is investigated to understand why the matrix interphase exhibit higher peak strength and fracture energy than the gallery interface as reported in previous sections. Fig. 10 shows the density profiles of both interfaces. It is seen that the density of the organic gallery is about 0.76 g/cm3, which is much lower than that of the matrix interphase. The low density of the gallery interfaces is likely responsible for its lower peak strength as well as fracture energy. The low density is attributed to nano-confinement effects of the gallery sandwiched between stacked silicates. As the gallery thickness is only several nanometers, polymer chains can’t relax and extend sufficiently. This especially affects the epoxy because the crosslinked networks are not flexible. The proposal of nano-confinement effects is further supported by the comparison in Fig. 10(b). It shows that the density of the polymer near the silicate sheets is also slightly lower than that far away from the interphase. In addition, no obvious layering configuration is observed in the polymers near the silicate sheet.
3.2. Tractioneseparation curve of matrix interphase 3.4. The effects of the surfactant on interfacial behaviors Fig. 8 shows the curve of traction stress versus separation distance for the matrix interphase surrounding the clay particle. The traction stress initially increases and reaches a peak value of about 131 MPa. This is higher than the gallery interface peak stress and could be a reflection of the difference between confined and unconfined systems. After that, the traction stress begins to drop because of the debonding between surfactants and epoxy molecules and finally approaches zero when the separation distance d is about 2.25 nm. The fracture energy is calculated to be 0.1266 J/m2 and is also higher than that of the gallery interface. Fig. 9 shows the molecular configuration of the matrix interphase as it is breaking up. It is found that the fracture occurs between the surfactants and epoxy layer. The ammonium groups remain adhered to the silicate surface as the alkyl chains are being stretched and then released after the peak stress value is attained.
For both the gallery interface and matrix interphase around the clay particles, the fracture surfaces are found to be between surfactants and epoxy molecules and the failure process is characterized by the stretching of the alkyl chains and continuous debonding. It is evident that the alkyl chain plays an essential role in the interfacial failure. Several surfactants with alkyl chains of different lengths are examined. Table 1 summarizes the key features of these tractione separation curves in both gallery interfaces and matrix interphase. For the gallery interface, the peak strength generally falls in the range of 80e100 MPa and it is highest when the number of carbon atoms of the alkyl chains is 18. The fracture energy is dominated by the final separation distance which increases with the alkyl chain length. Since failure is an energy adsorbing process,
Fig. 7. Molecular configuration evolution of gallery interface during splitting deformation. The surfactant is NHþ 3 C18 H37 .
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Fig. 8. Tractioneseparation curve of matrix interphase during Mode I splitting deformation.
this suggests that alkyl chain length plays an important role in determining the amount of energy adsorbed. For the matrix interphase model, the highest peak strength appears in the C_12 model and reaches higher than 140 MPa. The fracture energy and separation distance again increase with the alkyl chain length, similar to the gallery interface model. Overall, the dependence of the feature parameters on the alkyl chain length suggests that that modifying the molecular structure of surfactants might be an effective way to control the interfacial behaviors and consequently influence the material properties of nanocomposites at the macroscale.
Fig. 10. Density profiles of gallery interface and matrix interphase in the normal direction.
Table 1 Features of tractioneseparation curves with different alkyl chain lengths. Alkyl chain of surfactants
C_6 C_12 C_18 C_24 C_30
Gallery interface T (MPa)
G
93.45 96.53 99.87 88.2 83.06
0.0495 0.0748 0.0840 0.1217 0.1324
(J/m2)
Matrix interphase
dFailure
T (MPa)
G
dFailure
(nm) 1.25 1.70 2.30 2.70 3.50
137.34 144.59 131.07 137.41 122.76
0.0767 0.0902 0.1266 0.1508 0.1764
1.30 1.80 2.40 2.90 3.70
(J/m2)
(nm)
PS: C_N, where N is the number of carbon atoms in the alkyl chain of surfactants.
Toth et al. [13] calculated the binding energies of many systems and concluded that shorter alkyl chains were more effective in producing higher binding energies between clay particles and the surrounding polymers, resulting in high mechanical properties [14]. The binding energies reported by Toth et al. were calculated based simply on the final equilibrated state of the systems. No information on the evolution of the configuration of the systems is used in the determination of the binding energies. In our work, however, it is shown that shorter alkyl chains actually lead to lower peak strength and fracture energy. The peak strength and fracture energy are measured during the splitting deformation and their values are determined by how these molecules evolve during this process. The difference between Toth’s work and this study arises Table 2 Comparison between binding energies and fracture energies for the matrix interphase model. Alkyl chain of surfactants
Fig. 9. Molecular configuration evolution of matrix interphase in splitting deformation. The surfactant is NHþ 3 C18 H37 .
C_6 C_12 C_18 C_24 C_30
Binding energy EBinding (J/m2) Case I
Case II
0.2382 0.2124 0.2459 0.2338 0.2776
0.1561 0.1375 0.1389 0.1987 0.1942
Fracture energy G (J/m2) 0.0767 0.0902 0.1266 0.1508 0.1764
PS: the binding energy is normalized by the cross section area of the periodic cell.
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Fig. 11. Strength comparison of gallery interface, matrix interphase and bulk matrix.
from how the interfaces are characterized, statically or dynamically. Static calculation of binding energies may not be suitable for characterizing the mechanical properties of multi-phase interfaces. Investigating the entire splitting process in a dynamic manner may be a more effective way to estimate the overall strength and toughness of such complex interfaces. 3.5. Binding energy and fracture energy For the gallery interface model, the binding energy can’t be appropriately calculated due to the presence of self-imaging. For the matrix interphase model, the self-imaging effect is eliminated by padding two vacuum layers on two sides. Following the idea of binding energy as a static calculation, the fracture path that separate the system into part A and part B is not determined. Here, two cases that the fracture surface may pass through silicate/surfactants boundary (case I) and surfactants/epoxy boundary (case II) are considered. The corresponding binding energies of the two cases in five models are calculated and compared with the fracture energy obtained by Mode I loading in Table 2. It is seen that the binding energy for the case II is always higher than that of the case I, which means that the adhesion between surfactants and epoxy molecules are weaker than that between silicate and surfactants. This agrees well with the observed phenomenon in Mode I loading that the surfactants remain adhered to the silicate surface and the tails are stretched by the epoxy and finally separated from the epoxy molecules. It is clear that the binding energy depends on the fracture surface defined in the calculation. However, for complex interfaces with multi-phases, it is difficult or even impossible to define the specific fracture surface that corresponds to the lowest binding energy. Besides, it is found that the binding energies are insensitive to the alkyl chain length as their values are largely dependent on the local molecular density near the fracture surface, which is not strongly affected by the alkyl chain length. However, the fracture energy is obviously sensitive to the alkyl chain length as it is dominated by the final separation distance that are controlled by the alkyl chain. The longer the alkyl chain it is, the higher fracture energy that the interface possess. This again indicates that binding energy is not suitable for mechanical characterization as its value do not reflect the influence of local molecular structure on the mechanical behaviors of complex interfaces.
subjected to loading, the silicate sheet is unlikely to fail due to its perfect crystal structure with ultra high stiffness and strength. The possible failure regions would be within the other three. Fig. 11 compares the tractioneseparation curves of gallery interface and matrix interphase as well as the stressestrain curve of bulk epoxy. The peak strengths of gallery interface and matrix interphase regions are both lower than that of bulk epoxy, suggesting that that damage is more likely to initiate in gallery interface or matrix interphase rather than the bulk matrix domain if stress concentration is not considered. In actual composites, the stiffness mismatch between rigid silicate sheets and surrounding polymers leads to higher localized stress, which would advance the damage in gallery interfaces or matrix interphases. This comparison provides a simple yet effective reference for predicting the weak zones in polymer-clay nanocomposites. For accurate identification of damage initiation, continuum model of polymer-clay nanocomposites with micro-structural details should be developed and it is under our work progress currently. 4. Conclusion Binding energy, a common measure to characterize interfacial properties, may not be applicable to interfaces with complex multiphase features. In this work, molecular dynamics simulations of Mode I loading of interfaces are proposed to study such interfaces resulting in tractioneseparation relations that have been used to characterize the failure process of the interfaces in terms of quantifiable parameters including peak strength, fracture energy and final separation distance. These parameters are useful for progressive damage techniques in continuum modeling, e.g., the cohesive zone model (CZM) [30,31]. The gallery interface and matrix interphase e two typical types of interfaces in polymer-clay nanocomposites e are investigated. It is found that the peak strength and fracture energy of the matrix interphase are generally higher than those of the gallery interface. This is explained by comparing their density profiles near the silicate sheet. It is further found that the energy absorbed during the interfacial failure process highly depends on the alkyl chain length of surfactants. This suggests a mean for tailoring macroscale properties of nanocomposites via modifying the structures of surfactants on the molecular scale. Acknowledgment
3.6. Strength of gallery interface, matrix interphase and bulk matrix As introduced in Fig. 3, the polymer-clay nanocomposite consists of four basic constituents. When a macroscale sample is
The authors acknowledge the financial support given to this study by the Agency for Science, Technology and Research (A*STAR, Project Number-1123004033), Singapore.
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References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
Komarneni S. Journal of Materials Chemistry 1992;2:1219. Giannelis EP. Advanced Materials 1996;8:29. Bharadwaj RK. Macromolecules 2001;34:9189. Alexander M, Dubois P. Materials Science and Engineering: R: Reports 2000;28:1. Podsiadlo P, Kaushik AK, Arruda EM, Waas AM, Shim BS, Xu J, et al. Science 2007;318:80. Dhakal HN, Zhang ZY, Richardson MOW. Polymer Testing 2006;25:846. Hu Y, Shen L, Yang H, Wang N, Liu T, Liang T, et al. Polymer Testing 2006;25:492. Mojumdar SC, Raki L, Mathis N, Schimdt K, Lang S. Journal of Thermal Analysis and Calorimetry 2006;85:119. Manevitch OL, Rutledge GC. Journal of Physical Chemistry B 2004;108:1428. Suter JL, Coveney PV, Greenwell HC, Thyveetil M. Journal of Physical Chemistry C 2007;111:8248. Tanaka G, Goettler LA. Polymer 2002;43:541. Fermeglia M, Ferrone M, Pricl S. Fluid Phase Equilibria 2003;212:315. Toth R, Coslanich A, Ferrone M, Fermeglia M, Pricl S, Miertus S, et al. Polymer 2004;45:8075. Zhang Q, Ma X, Wang Y, Kou K. Journal of Physical Chemistry B 2009;113: 11898.
773
[15] Ray SS, Okamoto MM. Progress in Polymer Science 2003;28:1539. [16] Chen B. British Ceramic Transactions 2004;103:241. [17] Heinz H, Castelijns HJ, Suter UW. Journal of the American Chemical Society 2003;125:9500. [18] Heinz H, Suter UW. Journal of Physical Chemistry B 2004;108:18341. [19] Heinz H, Vaia R, Farmer BL. Journal of Chemical Physics 2006;124:224713. [20] http://www.scprod.com/. [21] Cygan RT, Greathouse JA, Heinz H, Kalinichev AG. Journal of Materials Chemistry 2009;19:2470. [22] http://www.poly-eng.uakron.edu/heinz-interface-force-field.php. [23] Material Studio 4.3, Accelrys Inc., San Diego, http://accelrys.com/. [24] Plimption S. Journal of Computational Physics 1995;117:1. [25] Wu CF, Wu WJ. Polymer 2006;47:6004. [26] Li C, Strachan A. Polymer 2011;52:2920. [27] Tsai DH. Journal of Chemical Physics 1979;70:1375. [28] Johnsen BB, Kinloch AJ, Mohammed RD, Taylor AC, Sprenger S. Polymer 2007; 48:530. [29] Ridha M, Tan VBC, Tay TE. Composite Structures 2011;93:1239. [30] Borst R, Gutiérrez MA, Wells GN, Remmers JJC, Askes H. International Journal for Numerical Methods in Engineering 2004;60:289. [31] Zhang B, Yang Z, Sun X, Tang Z. Computational Materials Science 2010;49:645.