Young's modulus of effective clay clusters in polymer nanocomposites

Polymer 53 (2012) 3735e3740

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Young’s modulus of effective clay clusters in polymer nanocomposites Wen Xu a, Qinghua Zeng a, b, Aibing Yu a, * a b

School of Materials Science and Engineering, The University of New South Wales, Sydney, NSW 2052, Australia School of Computing, Engineering and Mathematics, Penrith, NSW 2751, Australia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 May 2012 Accepted 25 June 2012 Available online 2 July 2012

In polymer nanocomposites, the interfacial region plays a key role in the reinforcement of materials properties. Traditional two-phase micromechanical models usually ignore the contribution of such interfacial region to the overall materials properties. In this study, we use molecular dynamics simulation to determine the effective size and the Young’s modulus of effective clay clusters which are regarded as basic building blocks in clay-based polymer nanocomposites. Two types of clay clusters are considered: one is fully exfoliated clay and another is partially exfoliated clay. The calculated Young’s modulus of effective clay clusters can be used to predict the overall mechanical properties of clay-based polymer nanocomposites. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Exfoliated nanocomposites Molecular dynamics simulation Young’s modulus

1. Introduction Polymers reinforced with nanoparticles (e.g., nanospheres, nanotubes, nanorods, or nanoplates) have received extensive attention in the academia and industry in the past two decades [1,2]. The great advantages of polymer nanocomposites lie in their multifunctionality and the possibility of realizing unique combinations of properties (e.g., mechanical, electrical, thermal, gas barrier, and biodegradable) unachievable with conventional polymer composites [3,4]. The enhanced mechanical properties of polymer nanocomposites are often achieved by reinforcing polymer with stiff fillers [5]. For instance, polymer nanocomposites reinforced with clay clusters (i.e., single clay platelet, or stack of a few clay platelets) have been extensively studied [6]. In such a system, clay clusters have been regarded as the ideal reinforcing agent due to their extremely high aspect ratio and the equivalent length scale of filler thickness and polymer chain structure [7,8]. Additionally, the unique layered structure and perfect cationic exchangeability of clays makes it easy to insert polymer chains into the interlayer space of clays, and even split them into single clay platelets, which can significantly enhance the interactions between clay and polymer matrix and hence the overall mechanical properties of polymer nanocomposites. The excellent reinforcement of montmorillonite (MMT), a typical smectite clay, in nylon 6 was firstly reported by Toyota research groups in 1987 [9]. Such smectite clay has become the major nanofillers used in polymer nanocomposites. However, the key to the reinforcement is dependent on the degree of clay

* Corresponding author. Tel.: þ61 2 93854429; fax: þ61 2 93856565. E-mail address: [email protected] (A. Yu). 0032-3861/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.polymer.2012.06.039

exfoliation and dispersion within the polymer matrix [10]. In the past decade, many experimental efforts have been made to achieve the fully exfoliated structures of clay in a variety of polymers [11], including polystyrene [12e14], nylon 6 [15e17] and epoxy [18e20]. It is well known that there is a close relationship between material structure and properties, which is particularly true to clayepolymer mixtures and polymer nanocomposites [21]. It is generally believed when the clays are mixed with the continuous polymer matrix, the ideal situation of fully exfoliated nanocomposites is not usually accomplished, rather, partially exfoliated nanocomposites are often formed [15,22e25]. That is, some polymers penetrate into the interlayer space of clay and cause the interlayer space (d001) to expand to some degree. Most previous numerical models assumed fully exfoliated nanocomposites, which leads to inconsistent results with experimental data [26,27]. In this work, we assume the existence of both fully and partially exfoliated clay clusters in polymer matrix and expect to provide a better prediction of the mechanical properties of polymer nanocomposites. In addition, we will also consider the contribution of claypolymer interface in predicting the properties of polymer nanocomposites. The concept of constrained region or interface in MMT/ nylon 6 nanocomposites was first introduced by Kojima et al. [28]. The interface is defined as a region near the clay surface where the polymer mobility is reduced and the surfactant concentration is increased [29]. When the particle size is in microscale and the interface is in nanometer scale, the influence of interface on overall properties is negligible. However, if the particle size is in the nanometer scale comparable to that of interface, the effect of interface is significant. Some studies have taken into account the effect of the interface on the reinforcement of mechanical properties of polymer nanocomposites [7,29e35]. For instance, Ji et al. [33] predicted the

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tensile modulus of polymer nanocomposites based on the modulus of interfacial region. However, in their approach, the interface thickness was approximate without accurate justification. Experimentally, different techniques have been used or developed to determine the characteristics of the interface, such as nanoindentation and nanoscratch [36] and tensioned-fibre method [37]. Because of the unclear boundaries and the nanoscale nature of the interface, it is extremely challenging to quantify the thickness of interface and its effects on the mechanical properties of the polymer nanocomposites. In this work, molecular dynamics (MD) simulation will be applied to determine the interface thickness of the interface and thus the effective size of both fully and partially exfoliated clay clusters, and finally the Young’s moduli of effective clay clusters.

Fig. 2. Molecular models of (a) nylon 6 polymer and (b) surfactant of octadecyltrimethyl ammonium (ODTMA). Colour: hydrogen atom in white; carbon atom in grey; nitrogen atom in blue; and oxygen atom in red. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

chosen for partially exfoliated polymer nanocomposites with clay clusters of two and three clay platelets, respectively. 2.2. Simulation conditions

2. Simulation method 2.1. Model construction The models in Fig. 1 represent the fully exfoliated nanocomposites and partially exfoliated nanocomposites with clay clusters of either two or three clay platelets respectively. The clay model (i.e., montmorillonite) is based on experimental structure and has a formula of Na0.333 [Si4O8][Al1.667Mg0.333O2(OH)2] and cationic exchangeable capacity (CEC) of 90 mmol/100 g. Each clay layer model is made up of an octahedral sheet of aluminium or magnesia sandwiched by two silica tetrahedral sheets [38,39]. The polymer used is nylon 6, and the surfactant is octadecyltrimethyl ammonium (ODTMA). Their molecular models are shown in Fig. 2. The overall dimension of the MD cell for fully exfoliated nanocomposites is a ¼ 25.959 Å, b ¼ 27.0459 Å, c ¼ 175 Å, and a ¼ b ¼ g ¼ 90 , in which there are ten ODTMAs and ninety nylon 6 chains. For the partially exfoliated nanocomposites, the basal spacing (d001) of ODTMA modified montmorillonite is 22.3 Å [40]. The a and b dimensions in the MD cells are the same as those in fully exfoliated nanocomposites, while c ¼ 130 Å and 150 Å are

Fig. 1. MD models of (a) fully exfoliated nanocomposites in which clay platelet is surrounded by surfactants and polymer chains; (b) partially exfoliated nanocomposites in which two clay platelets are stacked and surrounded by surfactants and polymer chains; (c) partially exfoliated nanocomposites in which three clay platelets are stacked and surrounded by surfactants and polymer chains.

Molecular dynamics simulations were carried out using the Discover module and Forcite module in MATERIALS STUDIO 4.3, a commercial software (Accelrys Co.). To achieve a maximum mixing of the different components, a canonical (constant atom number, volume and temperature (NVT)) MD simulation was initially performed at elevated temperature of 513 K for 10 ps, and then 50 ps at 298 K. The equilibrium state has been achieved at 298 K in the first 5 ps, judged from the stable potential energy. The data collection has been made to the last 45 ps. The concentration profiles of different molecules (i.e., polymer and surfactant) and MSD (mean squared displacement) profiles of different layers were obtained from Forcite analysis module. Both types of profiles will be used to determine the interface thickness and effective size of clay clusters. Then, the MD models of effective clay clusters were built and subjected to a relaxation process, followed by an isothermal-isobaric (constant atom number, pressure and temperature (NPT)) MD simulation of 100 ps to obtain the Young’s modulus. During MD simulation, the structure was subjected to an external tensile stress applied along one axis direction, and the data was collected at the last 50 ps to analyse the Young’s modulus under such particular stress. The final structure was subjected to further MD simulations under larger external tensile stresses to obtain their corresponding Young’s moduli. In total, five different external stresses were applied and an average Young’s modulus was obtained. The force field employed was the modified CVFF (Consistent Valence Force Field) reported by Heinz et al. [41]. The equations of motion were solved with the Verlet velocity algorithm [42]. The time step of integration was set to 1 fs. The van der Waals and Coulomb forces were calculated by the Ewald summation method. Initial velocities were randomly assigned according to the Boltzmann distribution. Temperature was controlled by the Anderson method, while the controlling method of pressure is set to the Parrinello method, the cell mass is 20.00 a.m.u. The MD trajectory files were obtained by saving the coordinates of all atoms at every 100 fs. In the present work, we have treated the clay sheet as both rigid structure and flexible structure depending on what issues concerned. In particular, a rigid structure is used during the NVT MD simulation to determine the interaction energies between the different components (i.e., clay, surfactant, and polymer). This treatment has widely been employed in the previous studies on inorganic nanoparticleepolymer nanocomposites [38,43,44], because it is believed that the strength of inorganic particles (e.g., single clay sheet) is much higher than that of polymers. Indeed, as will be shown later, a single clay sheet has a very high Young’s modulus. On the other hand, a flexible structure (i.e., all atoms in clay sheet are allowed to move) is used during the NPT MD

W. Xu et al. / Polymer 53 (2012) 3735e3740

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simulation to determine the Young’s modulus of single clay sheet and effective clay clusters. This is because a high loading or pressure may cause a certain degree of deformation on clay sheet. 2.3. Model and method validation Young’s modulus of single clay platelet was calculated to validate the simulation model and methods. First, the Young’s modulus of single clay platelet was calculated by given tensile stress as described above. Secondly, the Young’s modulus of single clay platelet along both longitudinal and lateral directions was calculated. Finally, the results were compared with the theoretical data in the literature. 3. Results and discussion 3.1. Molecular interactions at the interface The molecular movement at the interface was observed during MD simulation. Especially, the head groups of ODTMA (i.e., nitrogen atoms in large blue ball) moved toward clay surface at the beginning and finally attached to the surface. This phenomenon can be explained by the strong electrostatic interaction between negative clay surface and positive head group of surfactants [45,46]. At the same time, the polymer molecules were found to mix up with the surfactant molecules at the interface, which can be seen in Fig. 3a. Such mixing may be attributed to the exposed clay surface available to polymer chains as suggested by Fornes et al. [47], and possible strong van der Waals interaction between alkyl groups, e(CH2)e, of nylon 6 and long alkyl chains of surfactants. To quantify the interface interactions between different components (e.g., clay, surfactant, and nylon 6), each complex consisting of two components was extracted from the final snapshot (at 0.1 ns) as shown in Fig. 4. Taking the interaction energies

Fig. 4. Extracted complexes of the final snapshot: (a) clay þ polymer, (b) clay þ surfactant, (c) polymer þ surfactant.

between polymer and surfactant for example, the polymeresurfactant complex, isolated polymer, and isolated surfactant were extracted from the final simulation snapshot as shown in Fig. 3. The total interaction energies between polymer (a) and surfactant (b) as well as the individual contributions of different interactions (i.e., electrostatic, van der Waals, and Born repulsion) were calculated by using the following equation [44].

Eab ¼ Eab  Ea  Eb

(1)

where Eab is the interaction energy (in Kcal) between the two components, Eab is the potential energy of the twoecomponent complex, Ea is the potential energy for isolated component a, and Eb is the potential energy for isolated component b. The calculated results (Table 1) showed that the overall interactions of clay-surfactant and clay-nylon 6 are strongly attractive, while the overall interaction of surfactant-nylon 6 is strongly repulsive. Moreover, the interactions of clay-surfactant and claynylon 6 are dominated by electrostatic interaction, while the interaction energy of surfactant-nylon 6 is almost equally attributed to the vdW attraction and Born repulsion. This result further confirmed the assumption that the strong adhesion strength between polymer matrix and the nanoparticle is a main factor in determining the effectiveness of the interface in transferring the applied load from the polymer matrix to the nanofiller. The result also indicates that the interaction between the hydrocarbon tail of

Table 1 Interaction energies (Kcal) among different components of a system with 1 mol clay, 0.333 mol surfactant and 3 mol nylon 6.

Fig. 3. Extracted configurations from the final snapshot: (a) complex of polymer and surfactant, (b) isolated polymer, (c) isolated surfactant.

Interaction

Electrostatic

vdW

Born

Total

Eclayesurfactant Eclayenylon 6 Esurfactantenylon

7580.3 59520.7 7088.8

678.0 35995.8 18990.8

918.2 33368.6 17493.5

7340.0 62148.0 5591.5

6

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5-6 nm 4-5 nm 3-4 nm 2-3 nm 1-2 nm 0-1 nm clay 0-1 nm 1-2 nm 2-3 nm 3-4 nm 4-5 nm 5-6 nm

z

y x

Fig. 7. Schematic presentation of different layer zones of a clay cluster. Fig. 5. MD model of an effective clay cluster in fully exfoliated nylon 6 nanocomposite.

surfactant and polar nylon 6 chain is endothermic. The quantitative interaction result agrees well with the conclusion of endothermic heat of mixing between polar polyamide and hydrocarbon chain of surfactant proposed by Fornes et al. [47]. 3.2. Effective thickness of the interface One of the major characteristics of the interface indicated in Fig. 5 is its thickness which is defined here as the distance from which the atomic properties (e.g., atomic density profile, atomic mobility) are different from those in bulk systems. The atomic concentration profiles of surfactant, polymer and all molecules (Fig. 6) display that the surfactants locate within 3 nm from clay surface. Meanwhile, the polymer matrix reaches its uniform bulk density beyond 3 nm from clay surface. This phenomenon illustrates that within 3 nm, the major molecules are surfactants. As the polymer concentration is decreased in this interface region, the material properties should be quite different from the bulk material which contains mainly nylon 6. In this particular system, we can estimate the interface thickness to be 3 nm. For a molecular system at equilibrium state, all atoms still move around their equilibrium locations. The MSD (mean squared displacement) of the atoms or groups is used to represent such

12.0

3.0

10.0

2.5

8.0

2.0

6.0

1.5

movement. Based on the Brownian motion, the MSD is proportional to the time elapsed, depicted as follows:

D E r 2 ¼ 6Dt þ C;

(2)

where D is the most critical parameter in this equation which represents the self-diffusion of atoms. D value is equal to the initial slope in a MSDetime curve. The MSD curves are obtained along the direction perpendicular to clay surface (i.e., z direction) at 300 K. The exfoliated clay system is divided into 6 layer zones along the z direction from clay surface to the top with the thickness of each layer of 1 nm (Fig. 7). It was observed (Fig. 8) that the dynamic motion of the atoms increases with their distance from clay surface, indicated from the steeper slopes. Moreover, there is a significant change (Fig. 9) of atomic mobility occurring at a distance beyond 3 nm away from clay surface, which means that the atoms start to move faster beyond this distance. Because of the less constraint from the clay surface, the atoms beyond this area can move much more freely compared with the ones in the interface region. The thickness of 3 nm obtained is identical with that from the above atomic concentration profiles. Similar studies have been made on the partially exfoliated nylon 6 nanocomposites, i.e. the two and three clay platelet clusters. Fig. 10 are the representative results showing the atomic arrangements. They are similar to that in Fig. 5. The effective thickness of clay clusters in such a partially exfoliated nylon 6 nanocomposite

2.0 0.0 0.0

1.0 0.5

1.0

2.0

3.0

4.0

5.0

0.0 6.0

Distance from clay surface (nm) Fig. 6. Atomic concentration profiles of surfactant, polymer and both of them at the interface.

0-1 nm MSD ( Angstrom^2)

Surfactant Polymer Total

4.0

Relative concentration(%)

Relative concentration(%)

3.0

1-2 nm 2-3 nm

2.0

3-4 nm 4-5 nm 5-6 nm

1.0

0.0

0

5

10

15

20

25

30

Time (ps) Fig. 8. MSD plots of atoms within each of the six layers (in Fig. 7) of thickness 1 nm from clay surface.

0.08

5

0.07

4

0.06

3

Relative Concentration (%)

Atomic mobility

W. Xu et al. / Polymer 53 (2012) 3735e3740

0.05 0.04 0.03 0.02 0.01 0.00 0.0

1.0

2.0

3.0

4.0

5.0

6.0

Distance from clay surface (nm) Fig. 9. Dependence of atomic mobility on the distance from clay surface.

was obtained from atom density profiles (Fig. 11). The effective thickness of two clay platelet clusters and three clay platelet clusters are 3 nm, the same as that of fully exfoliated single clay layer. This result is identical with the prediction reported by Wang et al. [31]. The thickness of interface region is unlikely to change with the size and shape of the nanofiller. 3.3. Calculation of Young’s modulus 3.3.1. Single clay platelet To validate our MD method, we calculated the moduli of single clay platelet along both longitudinal (z axis) and lateral (x or y axis) directions which are listed in Table 2. During the simulation, tensile stresses of 0.1, 0.2, 0.3, 0.4, and 0.5 MPa are consecutively applied to the single clay platelet along either longitudinal or lateral directions. Then an average modulus is obtained from the data under five different stress conditions. The average Young’s moduli along the three directions are similar, i.e., C11 ¼ 277.0 GPa, C22 ¼ 277.8 GPa, and C33 ¼ 271.4 GPa (C11and C22 are the Young’s

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Surfactant Polymer Total

2 1 0 4 3 2 1 0

0

1 2 3 4 5 Distance from Clay Surface (nm)

6

Fig. 11. Atomic concentration profiles of nylon 6 nanocomposites with clay clusters of two clay platelets (top) and three clay platelets (bottom).

moduli of single clay platelet in the direction perpendicular to the z axis, C33 is the Young’s modulus along z axis). Our results are close to those in the literature, i.e., C11 ¼ 255 GPa, C22 ¼ 265 GPa, C33 ¼ 244 GPa for single clay platelet [48,49]. 3.3.2. Effective clay clusters Further simulations have been done to determine the Young’s moduli of effective clay clusters along the longitudinal direction in a similar way to that of single clay platelet. In this work, we assumed the Young’s moduli of effective clay clusters along the lateral directions are the same as that of single clay platelet. Different applied pressures ranging from 0.6 to 1.4 MPa were used. The calculated Young’s moduli along the longitudinal direction C33 are 36.8  3.22 GPa, 51.7  2.26 GPa, and 60  0.98 GPa for the effective clay clusters with single, two, and three clay platelets, respectively. They are not sensitive to the applied pressure in the range considered. 3.3.3. Polymer nanocomposites The Young’s moduli of the effective clay clusters obtained above could be used to predict the overall Young’s modulus of clay-based polymer nanocomposites by traditional micromechanical models. Our calculated results and experimental data in literature [15] are shown in Fig. 12. Anoukou et al. [15] have studied experimentally the relationship between Young’s modulus and volume fraction of silicate or clay. They demonstrated that fully exfoliated clay platelet predominates in the nanocomposites if the clay volume fraction is as low as 0.5%. With the increase of clay volume fraction, the number of individual clay platelets is decreased and partially exfoliated structures start to occur. In the present calculation, we assumed that three types of clay clusters may respectively exist in polymer nanocomposites. They are the fully exfoliated single-layer clay nanocomposites (N ¼ 1), partially exfoliated two-layer clay Table 2 The calculated Young’s modulus (GPa) of single clay platelet.

Fig. 10. MD models of effective clay clusters in partially exfoliated nylon 6 nanocomposite: (a) two clay platelet clusters and (b) three clay platelet clusters.

Applied stress (MPa)

0.1

0.2

0.3

0.4

0.5

Average

Longitudinal, C33 Lateral, C11 Lateral, C22

267 280 278

279 264 275

271 281 270

270 288 278

270 272 288

271.4 277.0 277.8

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12 10

E (GPa)

program. The authors would like to thank Professor Donald Paul for his encouragement and helpful suggestion.

N=1 N=2 N=3 Experimental data (Anoukou et al. 2011)

14

References

8 6 4 2 0 0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

fs(Volume fraction of silicate) Fig. 12. Calculated and measured overall Young’s moduli of nylon 6/MMT nanocomposites. N ¼ 1: fully exfoliated single-layer clay nanocomposites; N ¼ 2: partially exfoliated two-layer clay nanocomposites; N ¼ 3: partially exfoliated three-layer clay nanocomposites.

nanocomposites (N ¼ 2), and partially exfoliated three-layer clay nanocomposites (N ¼ 3). As shown in Fig. 12, qualitatively there is a good agreement between the calculated and measured results: all indicate increasing the volume fraction of silicate can increase Young’s modulus. Quantitatively, calculations based on partially exfoliated structures agree with the measurements better. Considering the complexity of clay clusters in polymer nanocomposites, which should be studied in the future, the results in Fig. 12 indicate that the information about effective clay clusters as basic building blocks can be used to approximate the overall Young’s modulus, and other mechanical properties, of clay-based polymer nanocomposites. This approach should be explored further in the future. 4. Conclusions We have reported herein the use of molecular dynamics simulation to determine the effective size of some representative clay clusters in polymer nanocomposites and their corresponding Young’s moduli, and the resulting information is further used to calculate the overall Young’s moduli of clay-based polymer nanocomposites. The effective thickness of the interface between clay platelet and polymer matrix in nylon 6 nanocomposites is calculated to be 3 nm based on the relative atomic concentration profiles and mean squared displacement curves. The thickness of the effective clay clusters is then obtained as the sum of their physical thickness and the interface thickness. The calculated Young’s moduli of the single clay platelet along lateral directions are 277.0 GPa and 277.8 GPa. The Young’s moduli along the longitudinal direction are 271.4 GPa, 36.8 GPa, 51.7 GPa, and 60.0 GPa for the single clay platelet, fully exfoliated effective clay cluster, partially exfoliated effective clay clusters with two and three clay platelets, respectively. Such Young’s moduli are useful in estimating the overall Young’s modulus of clay-based polymer nanocomposites. Acknowledgements The authors are grateful to the ARC and the DIISR for the financial support through the Australia-India collaborative research

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