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Altered Phase Model for Polymer Clay Nanocomposites Debashis Sikdar, Shashindra M. Pradhan, Dinesh R. Katti,* Kalpana S. Katti, and Bedabibhas Mohanty Department of CiVil Engineering, North Dakota State UniVersity, Fargo, North Dakota 58105 ReceiVed February 22, 2008 This paper describes a multiscale approach used to model polymer clay nanocomposites (PCNs) based on a new altered phase concept. Constant-force steered molecular dynamics (SMD) is used to evaluate nanomechanical properties of the constituents of intercalated clay units in PCNs, which were used in the finite element model. Atomic force microscopy and nanoindentation techniques provided additional input to the finite element method (FEM) model. FEM is used to construct a representative PCN model that simulates the composite response of intercalated clay units and the surrounding polymer matrix. From our simulations we conclude that, in order to accurately predict mechanical response of PCNs, it is necessary to take into account the molecular-level interactions between constituents of PCN, which are responsible for the enhanced nanomechanical properties of PCNs. This conclusion is supported by our previous finding that there is a change in crystallinity of polymeric phase due to the influence of intercalated clay units. The extent of altered polymeric phase is obtained from observations of a zone of the altered polymeric phase surrounding intercalated clay units in the “phase image” of PCN surface, obtained using an atomic force microscope (AFM). An accurate FEM model of PCN is constructed that incorporates the zone of the altered polymer. This model is used to estimate elastic modulus of the altered polymer. The estimated elastic modulus for the altered polymer is 4 to 5 times greater than that of pure polymer. This study indicates that it is necessary to take into account molecular interactions between constituents in nanocomposites due to the presence of altered phases, and furthermore provides us with a new direction for the modeling and design of nanocomposites.
1. Introduction Polymer clay nanocomposite (PCN) is a novel nanocomposite material synthesized by addition of a small proportion of expansive clay minerals (about 1–9% of the weight of polymer) to polymeric materials. The clay is usually modified with an organic modifier to improve its miscibility with a hydrophobic polymer such as polyamide 6 (PA6). Often the polymer phase comprises more than 90% of the weight of the PCN. The presence of nanoclay particles dispersed in the polymer results in a nanocomposite with significantly enhanced mechanical properties,1–12 thermal properties,7,13–20 and liquid and gas barrier properties in com* Author to whom all correspondences should be addressed. Tel.:+701 231 7245; fax: +701 231 6185. E-mail address:
[email protected]. (1) Okada, A.; Kawasumi, M.; Usuki, A.; Kojima, Y.; Kurauchi, T.; Kamigaito, O. Mater. Res. Soc. Symp. Proc. 1990, 171, 45–50. (2) Pinnavaia, T. J.; Lan, T. Proc. Am. Soc. Compos., Tech. Conf. 1996, 11, 558–565. (3) Giannelis, E. P. AdV. Mater. 1996, 8(1), 29–35. (4) Maity, P.; Yamada, K.; Okamoto, M.; Ueda, K.; Okamoto, K. Chem. Mater. 2002, 14(11), 4656–4661. (5) Pramanik, M.; Srivastava, S. K.; Biswas, K. S.; Bhowmick, A. K. J. Appl. Polym. Sci. 2003, 87(14), 2216–2220. (6) Zhang, G.; Jiang, C.; Su, C.; Zhang, H. J. Appl. Polym. Sci. 2003, 89(12), 3155–3159. (7) Wang, D.; Wilkie, C. A. Polym. Degrad. Stab. 2003, 80(1), 171–182. (8) Lim, S. T.; Lee, C. H.; Choi, H. J.; Jhon, M. S. J. Polym. Sci., Part B: Polym. Phys. 2003, 41(17), 2052–2061. (9) Park, H. M.; Lee, W. K.; Park, C. Y.; Cho, W. J.; Ha, C. S. J. Mater. Sci. 2003, 38(5), 909–915. (10) Chen, G. X.; Hao, G. J.; Guo, T. Y.; Song, M. D.; Zhang, B. H. J. Mater. Sci. 2002, 21, 1587–1589. (11) Ma, C. C. M.; Kuo, C. T.; Kuan, H. C.; Chiang, C. L. J. Appl. Polym. Sci. 2003, 88(7), 1686–1693. (12) Pramoda, K. P.; Liu, T.; Liu, Z.; He, C.; Sue, H. J. Polym. Degrad. Stab. 2003, 81(1), 47–56. (13) Wang, S.; Hu, Y.; Wang, Z.; Yong, T.; Chen, Z.; Fan, W. Polym. Degrad. Stab. 2003, 80(1), 157–161. (14) Zhang, J.; Wilkie, C. A. Polym. Degrad. Stab. 2003, 80(1), 163–169. (15) Liu, T.; Lim, K. P.; Tjiu, W. C.; Pramoda, K. P.; Chen, Z. K. Polymer 2003, 44(12), 3529–3535. (16) Kim, T. H.; Lim, S. T.; Lee, C. H.; Choi, H. J.; Jhon, M. S. J. Appl. Polym. Sci. 2003, 87(13), 2106–2112.
parison to the pristine polymer. Most notably, PCN displays good improvement in elastic modulus,4–6 increased tensile strength,7,9 enhancement of thermal resistance, and decreased flammability.7–12 This renders PCN as a material of interest for potential applications in geotextile, automobile, structural, and other polymer industries where enhancement of these material properties is extensively sought after. The microstructure, physical properties of individual constituents, and the molecular interactions between constituents are important contributors to the physical properties of nanocomposites.21 The microstructure of the composite is influenced by its structural orientation and the morphology of the constituents. Also, material properties of the constituent materials at the nanoscale are greatly influenced by molecular interactions among themselves. Thus the nanoscopic material properties of the constituents of nanocomposites such as PCN may be quite different from the properties of these constituents in their native state. The enhancement of material properties of the constituents of a composite system PCN (clay, organic modifier, and polymer) have been qualitatively shown in a number of previous studies.1–20 These studies include methods such as X-ray diffraction (XRD), differential scanning calorimetry (DSC),22 Fourier transform infrared spectroscopy (FTIR),23–25 and molecular dynamics (17) Priya, L.; Jog, J. P. J. Polym. Sci., Part B: Polym. Phys. 2003, 41(1), 31–38. (18) Krikorian, V.; Kurian, M.; Galvin, M. E.; Nowak, A. P.; Deming, T. J.; Pochan, D. J. J. Polym. Sci., Part B: Polym. Phys. 2002, 40(22), 2579–2586. (19) Xu, M.; Choi, Y. S.; Kim, Y. K.; Wang, K. H.; Chung, I. J. Polymer 2003, 44(20), 6387–6395. (20) Tang, Y.; Hu, Y.; Song, L.; Zong, R.; Gui, Z.; Chen, Z.; Fan, W. Polym. Degrad. Stab. 2003, 82(1), 127–131. (21) Katti, K. S. Colloids Surf., B: Biointerfaces 2004, 39(3), 133. (22) Sikdar, D.; Katti, D.; Katti, K.; Mohanty, B. J. Appl. Poly Sci. 2007, 105, 790–802. (23) Zhang, G.; Li, Y.; Yan, D. J. Polym. Sci., Part B: Polym. Phys. 2004, 42, 253. (24) Katti, K. S.; Sikdar, D.; Katti, D. R.; Ghosh, P.; Verma, D. Polymer 2006, 47, 403–414.
10.1021/la800583h CCC: $40.75 2008 American Chemical Society Published on Web 04/18/2008
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Figure 3. Stress–strain plot of clay obtained from constant-force SMD simulation. Figure 1. Intercalated model of PCNs showing the thickness of the clay sheet, the organic layer, and the interaction zone.
Figure 4. Modulus mapping image of PCN showing the elastic modulus of surface-exposed clay as 352.9 GPa.
Figure 2. Compressive stress is applied on the oxygen atoms lying on the top surface of theclay sheet of PCN, keeping the base of the bottom clay sheet fixed.
(MD).26,27 The understanding of mechanisms responsible for the enhanced properties of PCN would lead to the ability to design PCNs with adequate control over desired properties. The goal of this study is to develop a multiscale method for evaluating the nanomechanical properties of the constituents of PCN to obtain a mechanical response of PCN and also to elucidate a new approach for modeling nanocomposite systems similar to PCN. Our previous MD studies28,29 indicate that there are strong nonbonded interactions between clay and organic modifier. Additionally, from DSC and XRD results22 it is observed that the nonbonded interactions between the constituents (clay, polymer, and modifier) have a significant influence on the crystallinity of a polymer. The crystallinity of a polymer decreases by different amounts, depending on the type of organic modifier used. With a reduction in the crystallinity of a polymer, due to the presence of different organic modifiers, there is an increase in the elastic modulus of PCN, and an increase in the loss modulus and loss factor of PCN obtained using nano dynamic mechanical analysis (nanoDMA).22 In nanoDMA experiments, a sinusoidal load is applied to a viscoelastic material. A portion of the applied energy is stored in the material (represented by storage modulus (25) Wan, C.; Zhang, Y.; Zhang, Y. Polym. Test. 2004, 23, 299. (26) Gardebien, F.; Gaudel-Siri, A.; Bredas, J. L.; Lazzaroni, R. J. Phys. Chem. B 2004, 108, 10678. (27) Vaia, R. A.; Giannelis, E. P. Macromolecules 1997, 30, 8000. (28) Sikdar, D.; Katti, D. R.; Katti, K. S. Langmuir 2006, 22, 7738–7747. (29) Sikdar, D.; Katti, D.; Katti, K. J. Appl. Polym. Sci. 2008, 107, 3137–3148.
and results in elastic recovery of the material), and the other portion of the energy is dissipated (represented by loss modulus and is due to viscous loss) within the material. Loss factor is the ratio of loss modulus to storage modulus. Hence, to understand the mechanism behind this enhanced mechanical response of PCN, it is necessary to incorporate the effect of the change in crystallinity of a polymer on the stiffness of a polymer resulting from molecular interactions between the constituents. However, evaluation of the influence of intercalated clay blocks on the stiffness of a polymer at a molecular scale is beyond the means of present-day computational resources owing to the large length scale involved. To overcome this problem, we have adopted the hierarchical multiscale modeling approach to bridge nanoscopic and mesoscopic scales using MD and finite element method (FEM), supplemented by experiments carried out at both of these length scales. 2. Evaluation of Material Parameters of PCN Constituents. The mechanical properties of constituents of PCN used in this work are obtained from constant-force steered molecular dynamics (SMD) simulations, nanoindentation experiments, and literature. The nanomechanical properties of clay, intercalated polymer, and organic modifier in PCNs are greatly influenced by the molecular-scale interactions between them. The mechanical response of these constituents at the nanoscale was simulated using constant-force SMD, and their elastic modulus and Poisson’s ratio were evaluated. In the constant-force SMD, constant force is applied to individual atoms in the molecular model in specified directions for the duration of the simulation. The representative molecular model of intercalated PCN is shown in Figure 1. The PCN model is composed of PA6 as the polymer, 12-aminolauric acid as the organic modifier, and montmorillonite (MMT) as clay. For the purpose of evaluating nanomechanical properties of constituents, the representative PCN model is divided into
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Table 1. Summary of Elastic Properties of Different Phases of PCN Obtained from Constant-Force SMD Simulations and Nanoindentation phase
elastic modulus (GPa)
Poisson’s ratio
clay sheet organics interaction zone pure polymer
696.55 7.03 55.88 3.35
0.47 0.037 0.096 0.01
three parts as shown in Figure 1: (1) clay sheet, (2) intercalated polymer and organic modifier referred to as “organics” in this work, and (3) the zone of interaction between the clay sheet and the “organics”. For finding the elastic modulus and Poisson’s ratio, the bottom layer of the clay sheet is fixed, and a compressive load is applied on the top surface of the clay sheet as shown in Figure 2. As seen in Figure 2, the oxygen atoms are projected over the clay surface. A uniform compressive point load is applied on each of the oxygen atoms lying on the top surface of the clay to simulate a uniformly distributed compressive load on the clay sheet. This procedure was used to study clay-water and clay-amino acid interlayer response.30–33 There are a total of 108 oxygen atoms on the top surface of the clay sheet, which has a projected load bearing area of 778.1093 Å2 in the x-y plane. During the application of load, the displacements of all the atoms on the top surface of clay sheet are unrestrained in the z direction and restricted in the x and y directions. In case of the bottom clay sheet, the atoms on its base are fixed by restricting their displacement in all x, y, and z directions. The constant-force SMD simulation of this representative PCN model is carried out using MD software NAMD 2.5.34 Visualization and image analysis software VMD 1.835 is used for analysis and visualization. The forcefield used for simulation is CHARMm.36 The CHARMm force field parameters used for clay were previously found.30–32 For evaluating the elastic properties (elastic modulus and Poisson’s ratio) of clay, 12 different constant-force SMD simulations varied the constant force per atom on the surface oxygen of clay sheets lying in intercalated PCN. The different constant forces used in the simulation are 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, and 160 pN/atom. Each constant-force SMD simulation is run for 200 ps with a time step of 0.5 fs. The simulation parameters including periodic boundary conditions, cut-off distance, switch distance, and so forth are similar to those of our previous MD work.28,33 The evaluations of the desired mechanical properties are based on the average change in dimension of the components of the PCN model upon the application of load with respect to the original state. The average thicknesses of the clay sheet, organic layer, and interaction zone are 6.66, 3.93, and, 1.93 Å, respectively. Using the trajectory file obtained from each constant-force SMD simulation, the average thickness and width of the clay sheet, organic layer, and interaction zone are calculated for the last 80 frames of application of the specified force on the atoms. The (30) Katti, D. R.; Schmidt, S.; Ghosh, P.; Katti, K. S. Clays Clay Miner. 2005, 52(2), 171–178. (31) Schmidt, S.; Katti, D.; Ghosh, P.; Katti, K. Langmuir 2005, 21, 8069– 8076. (32) Katti, Dinesh, R.; Schmidt, S.; Ghosh, P.; Katti, K. S. Can. Geotech. J. 2007, 44, 425–435. (33) Katti, D. R.; Ghosh, P.; Schmidt, S.; Katti, K. S. Biomacromolecules 2005, 6, 3276–3282. (34) Kalé, L.; Skeel, R.; Bhandarkar, M.; Brunner, R.; Gursoy, A.; Krawetz, N.; Phillips, J.; Shinozaki, A.; Varadarajan, K.; and Schulten, K. J. Comput. Phys. 1999, 151, 283–312. (http://www.ks.uiuc.edu/Research/namd/). (35) Humphrey, W.; Dalke, A.; Schulten, K. J. Molecular Graphics 1996, 14(1), 33–38. (http://www.ks.uiuc.edu/Research/vmd/). (36) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4, 187–217.
Figure 5. Schematic representation of a PCN model showing the dispersion of intercalated clay blocks in the polymer matrix.
Figure 6. Phase image of PCN showing the dispersion of submicron clay blocks in the polymer matrix. Clay is in lighter shades, and polymer is in darker shades.
stress and strain in the z direction, and Poisson’s ratio of the phases of PCNs, are calculated from the displacement response obtained from constant-force SMD simulations. The stress–strain response of the clay sheet obtained from the entire range of constant-force SMD simulations containing different values of constant forces per atom is presented in Figure 3. By using the least-squares method, the average elastic modulus of the clay sheets is estimated to be about 696.55 GPa. This value is larger compared to the elastic modulus of about 352.9 GPa obtained from a “modulus mapping” experiment performed on the exposed surface of the clay sheet as shown in Figure 4. However, the values obtained computationally and experimentally have the same order of magnitude. The lower value of elastic modulus from the experiment can be explained in terms of the composite deformation response of the thin clay sheet and the thick layer of relatively soft polymeric phase below the clay sheet. The thick and soft polymeric phase undergoes deformation when the overlaying nanoclay block is indented during the “modulus mapping” experiment, which causes the experimental elastic modulus to be underestimated. Hence, it is evident that the elastic modulus of clay estimated from constant-force SMD simulations is reasonable. The average values of elastic moduli of the organic layer and interaction zone are found to be 7.03 and 55.88 GPa, respectively, using a method similar to the one used for clay platelets. The elastic modulus of pure polymer subjected to the same conditions in the synthesis process of PCN is directly obtained from the nanoindentation experiment to be 3.35 GPa.22
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Figure 7. Schematic representation of intercalated clay blocks showing clay sheets, organic layers, and interaction zone. The figure is not dawn in scale.
Figure 8. Orthogonal view of the 7_7_12 PCN model showing mesh on the clay blocks and polymer matrix.
By measuring the average deformation of phases (clay sheet, organic layer, and interaction zone) in the x, y, and z directions upon application of load during constant-force SMD simulation, the average Poisson’s ratio is calculated. The estimated values of Poisson’s ratio for the clay sheet, organic layer, and interaction zone are 0.47, 0.037, and 0.096, respectively. In the case of clay, volumetric incompressibility is assumed, and Poisson’s ratio is considered to be 0.5. For the polymer (PA6), we have used an average Poisson’s ratio of 0.01 as reported in the literature.37 The summary of elastic properties of different phases is given in Table 1. 3.1. Description of PCN Model. For construction of finite element model of the PCN, the intercalated clay units are assumed to be dispersed in the polymer matrix, as shown in Figure 5. To determine the average spatial dimension of the intercalated clay sheets, we conducted “phase imaging” of a PCN sample using an atomic force microscope (AFM), which is shown in Figure 6. The phase image displays different shades (37) Zhang, F.; Wan, Z.; Du, X., J. Elastomers Plast. 2002, 34, 265–278.
of color that represent various phases present on the scanned surface of the PCN. The lighter shades represent the intercalated clay sheets, and the darker shades represent the polymer. From the phase image it is seen that the submicron size clay sheets are uniformly dispersed in the polymer matrix. The average size of the clay sheets is found to be 0.32 µm. The spatial dimension of the clay sheets considered for constructing an intercalated clay block is 0.50 µm or 5000 Å. From the literature we have found that the “average number of clay platelets per stack is 5 with a 95% confidence interval of 0.4”. This number was determined from a total of 20 stacks using transmission electron microscopy (TEM) images.38 Other researchers have also reported that the number of clay sheets in the intercalated clay blocks in PCNs vary from 4 to 18 clay sheets per clay block.6–8,13–15,39 In our work, we used six stacks of clay sheets in the intercalated clay block. The magnified view of intercalated clay block used in our PCN model is shown in Figure 7. The thicknesses of the clay sheet, organic layer, and interaction zone of the intercalated clay are taken from the molecular model of PCNs as shown in Figure 1. The thicknesses of the clay, organics, and interaction zone are 6.66, 3.93, and 1.93 Å, respectively. These intercalated clay blocks are placed uniformly in the polymer matrix, maintaining the actual ratio of weight percentage used in the synthesis of the PCN sample. As shown in Figure 7, the dimensions of the intercalated clay block in the x, y, and z directions are 5000 Å × 5000 Å × 90.704 Å with a volume of 2.27 × 109 Å3. In this study, the PCN-9% model is considered, which contains 9 wt % of intercalated clay blocks mixed with polymer. The densities of the polymer, clay, and PCN obtained for our samples are 1.134, 2.65, and 1.184 g/cc, respectively. The density of intercalated organics is assumed to be the same as the density of the organic modifier, which is 1.85 g/cc. Available computational resources allowed us to build a maximum PCN model size of 4.2 µm × 4.2 µm × 1.4308 µm, which is shown schematically in Figure 5. Spacing between the clay blocks corresponding to 9 wt % of intercalated organically modified (38) Chen, B.; Evans, J. R. G. Macromolecules 2006, 39, 747–754. (39) Lan, T.; Pinnavaia, T. J. Chem. Mater. 1994, 6, 2216–2219.
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Table 2. Cauchy Stress and Strain of PCN Calculated from the 7_7_12 Model load increment
displacement (A)
strain
stress (pN/Å2)
stress (GPa)
elastic modulus (GPa)
0 1 2 3 4 5 6 7 8 9 10
0.00E+00 -2.40E+00 -4.80E+00 -7.20E+00 -9.60E+00 -1.20E+01 -1.44E+01 -1.68E+01 -1.92E+01 -2.16E+01 -2.40E+01
0.00E+00 -1.68E-04 -3.35E-04 -5.03E-04 -6.71E-04 -8.39E-04 -1.01E-03 -1.17E-03 -1.34E-03 -1.51E-03 -1.68E-03
0 0.006 0.012 0.018 0.024 0.03 0.036 0.042 0.048 0.054 0.06
0 0.0006 0.0012 0.0018 0.0024 0.003 0.0036 0.0042 0.0048 0.0054 0.006
0 -3.58E+00 -3.577660045 -3.577660293 -3.577660417 -3.57766079 -3.577661287 -3.577659512 -3.577660045 -3.577660459 -3.57766079
clay loading is found to be 875 Å in the x and y directions and 1016.946 Å in the z direction. The space between the intercalated clay blocks in PCN is filled with polymer matrix. 3.2. Construction of Finite Element Model and Simulation Details. Construction of the model is carried out using MSC.MENTAT 2005 of the MSC Software Corporation. Our PCN model contains 7 clay blocks in the x and y directions and 12 clay blocks in the z direction. Such a 3-D model in this work is named the7_7_12 model as shown in Figure 8. After mesh generation, the total number of elements present in this model is 0.53 million. The finite element simulation for the PCN model is conducted using the finite element software, MSC.MARC of the MSC Software Corporation, Santa Ana, CA. Simulations were run on an SGI Altix 3300 shared-memory server at the center for high performance computing at North Dakota State University. It is equipped with 12 1.6 GHz Itanium-II processors containing 48 GB RAM. MSC.MENTAT is used for visualization and analysis of results. The finite element software MSC.MARC used in our simulations has a powerful geometric domain decomposition tool to
Figure 9. Schematic representation showing the influence zone of nano clay blocks in PCNs.
Figure 10. Phase image of PCN showing the extent of influence of nano clay blocks on the crystallinity of a polymer matrix.
effectively utilize the parallel processing abilities of computer hardware and speed up computations without compromising accuracy. A domain decomposition algorithm subdivides the model (domain) into a predetermined number of subdomains, taking into consideration aspects such as boundary between domains, balancing the processor load, and optimizing solution time within each domain. An algorithm monitors communication between processors to ensure the passing of appropriate boundary information between processors. Our PCN model uses domain decomposition with eight subdomains and utilizes eight Altix Itanium-II 64 bit processors. A compressive stress of 0.006 GPa is applied on the top surface of the model, which is about 0.01% of the tensile strength of the PCN, which is about 57.1 MPa.11 Considering a lower compressive load allows us to assume the resulting deformations to be within the elastic regime. The load is applied in 10 equal increments. The computational resource required for running one simulation is about 20 h of clock time with 30-35 GB RAM and eight processors. The size of the output file is about 4 GB. All the phases present in the PCN model are assumed to be linearly elastic for this stress range. Using FEM simulation results, the stress and strain of the PCN model is calculated, and the elastic modulus of the PCN is found to be 3.58 GPa, which is shown in Table 2. However, the elastic modulus of the PCNs obtained from the nanoindentation experiment is 5.46 GPa,22 which is larger than that obtained from simulation. The lack of good match is a result of a fact that, in this finite element model, we have not taken into account molecular interactions occurring between intercalated clay blocks and the surrounding polymer. It appears that, to predict correct mechanical properties of PCNs, the change in crystallinity of the polymeric phase due to nonbonded interactions with intercalated clay blocks reported in our previous work should be incorporated in the model.22,29,40,41 4.1. “Altered Phase Model”: A New Approach for Modeling a Nanocomposite-PCN Using Two Phases of Polymer. From the DSC experiments, it is evident that the crystallinity of a polymer is altered due to localized interactions of the polymer with intercalated nanoclay blocks, as shown in Figure 9.22 The crystallinity of PCNs containing 9 wt % of clay loading decreases to 23.05% from the value of 27.61% for pure PA6.22 From the MD study of our previous work, it is estimated that the major portion of polymer lies outside the clay gallery in intercalated PCNs.28,29 From the magnitude of change of crystallinity it appears that, because of the localized interaction of intercalated (40) Sikdar, D.; Katti, K. S.; Katti, D. R. J. Nanosci. Nanotechnol. 2008, 8, 1–20. (41) Sikdar, D.; Katti, D. R.; Katti, K. S.; Bhowmik, R. Polymer 2006, 47, 5196–5205. (42) Katti, D. R.; Katti, K. S.; Sopp, J.; Sarikaya, M. Comput. Theor. Polym. Sci. 2001, 11, 397–404. (43) Katti, D. R.; Katti, K. S. J. Mater. Sci. 2001, 36, 1411–1417. (44) Katti, K.; Katti, D. R.; Tang, J.; Pradhan, S.; Sarikaya, M. J. Mater. Sci. 2005, 40, 1749–1755. (45) Katti, K. S.; Katti, D. R. Mater. Sci. Eng. 2006, 26(8), 1317–1324.
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Figure 11. Schematic representation showing the existence of singlephased polymer outside clay blocks in the 7_7_12 PCN model.
clay blocks, not only does the polymer inside the clay interlayer gallery change, but the polymer outside the clay blocks also changes considerably. This phenomena is presented in Figure 9 where we see that polymer outside the clay gallery is altered up to a certain distance from the surface of clay blocks. For the first time, we propose a finite element model with altered polymeric phase to represent particulate-based nanocomposites. The spatial extent of the influence of intercalated clay blocks on polymer crystallinity is estimated from “phase images” of PCNs, as shown in Figure 6. The “phase image” is obtained from a phase imaging experiment carried out using an AFM. The magnified view of Figure 6 is shown in Figure 10. From Figure 10, the different phases present in PCNs are observed. The pink colored spots in the phase image represent the clay particles exposed to the surface, and those in light green shades represent the clay sheets overlain by a thin layer of polymer. The dark brown spots represent the uninfluenced polymer outside the clay gallery. Between intercalated clay blocks and dark shaded polymer there are zones of lighter brown shades. These light brown shades represent altered polymeric zones formed as a rseult of the influence of nanoclay blocks. This zone, named in this work as “altered polymer”, is a consequence of nonbonded interactions between polymer and clay blocks. The altered polymer has different crystallinity as well as different mechanical properties compared to the unaltered polymer. The average thickness of this altered polymer obtained from AFM phase images is about 250 Å. If the properties of unaltered polymer are assumed to be similar to those of altered polymer, significant error is introduced in the prediction of the structure and mechanical behavior of aa polymer, which is the reason for the lower elastic modulus obtained from the 7_7_12 PCN model, where polymer outside the clay gallery is assumed to be single phase. Incorporating both of the phases of polymer (i.e., altered and unaltered polymer) into a model is a new approach for modeling nanocomposites in which the change in material properties due to molecular interactions between constituents is taken into consideration. 4.2. Construction of a Finite Element Model Incorporating an Altered Polymeric Zone. To incorporate the altered polymer or two-phase polymer in the new FEM model, the polymer outside the clay gallery is divided into two phases: (i) altered polymer and (ii) unaltered polymer. The difference between the previous (7_7_12 PCN) and new (7_7_7 PCN) model is schematically represented in Figures 11 and 12, respectively. As seen from Figure 11, the polymer outside the clay gallery is assumed to be the same throughout, whereas, in Figure 12, the polymer outside the clay gallery has two different phases. However the physical dimensions of altered polymer as well as its mechanical properties are not known. Using atomic force microscopy, the dimension of altered polymer is measured from a phase image of PCNs, as
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Figure 12. Schematic representation showing the existence of twophased polymer present outside clay blocks in the new PCN model in the x and y directions. Table 3. Spatial Dimension of Altered Polymer in PCN Measured from a Phase Image Using Atomic Force Microscopy data points
spatial dimension of altered polymer (Å)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
29.509 34.215 29.411 19.608 29.411 24.509 19.61 29.41 14.706 14.71 19.61 14.71 24.51 29.41 29.41 14.71 14.71 29.41 34.313 19.608 29.41 24.51 29.41 29.41 34.31 24.51 29.41
shown in Figure 13. The results from the observation are tabulated in Table 3, indicating that the average dimension of altered polymer outside the clay gallery is 261.44 Å. In this model, we have used a thickness of altered polymer surrounding the intercalated clay blocks of 250 Å, as shown in Figure 12. The spacing between clay blocks in the x and y directions is 875 Å, and in the z direction it is 1016.946 Å, corresponding to 9 wt % clay loading in PCNs. Hence, in the new PCN model, the dimension of unaltered polymer is 375 Å in the x and y directions, as shown in Figure 12. The height of altered and unaltered polymer in the z direction surrounding each clay block is 250 and 516.946 Å, respectively. We are aware that the change in crystallinity and mechanical properties within the altered “influence zone” will likely not be uniform. In our model, we have assumed uniform property distribution within the 250 Å influence zone surrounding the clay blocks. 4.3. Simulation Details of the “Two-Phase Polymer” Finite Element Model of PCNs. This model contains two phases of polymer: altered and unaltered polymer. The available compu-
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Figure 13. Using atomic force microscopy, the extent of altered polymer is measured from a phase image of PCNs.
Figure 14. Orthogonal view of the 7_7_7 PCN model showing the placement of clay blocks in a polymer matrix and application of compressive stress at the top surface of the PCN model.
tational resources allowed the incorporation of seven intercalated clay units each in the x, y, and z directions. This new PCN model shown in Figure 14 is referred to in this work as the 7_7_7 PCN model. The dimension of the 7_7_7 PCN model in the x, y, and z directions are 42 000, 42 000, and 8770.4966 Å, respectively, and has a total of 0.63 million elements. It is observed that seven organic layers are dispersed in the polymer matrix of the PCN model in the x and y directions. Magnified view of the PCN model in the x-y plane is shown in Figure 15, where we can see the meshing of the FEM model of PCNs through altered and unaltered polymer and the organic layers present in the PCN model. The snapshot of the PCN model in the y-z plane is shown in Figure 16. It shows seven layers of clay blocks stacked in the z direction in the PCN model surrounded by altered polymer and embedded in uninfluenced polymer.
Figure 15. Magnified view of the 7_7_7 PCN model in the x-y plane, showing influenced (light blue color) and uninfluenced polymer (green color) and organic layer (pink color) in the PCN model, as well as meshing of different phases of the PCN model.
The material properties of the clay sheet, polymer, organics, and interaction zone are taken from Table 1 as in the previous model (7_7_12 PCN), in which altered polymer was not present. The model 7_7_7 is simulated with various values of the elastic modulus of influenced/altered polymer, and the composite elastic response of the PCN model is evaluated for each of the cases. The values of elastic moduli of altered polymer used in simulation are 300, 200, 50, 25, 15, 10, and 3.35 GPa (same as polymer). The elastic responses obtained from simulation of the PCN model are compared with those obtained from nanoindentation tests in order to estimate a reasonable value of the elastic modulus of altered polymer. The Poisson ratio for influenced/altered polymer is taken to be 0.30, a value intermediate between that of polymer (0.001) and clay (0.47). During simulation, all the constituents of the PCN model are assumed to be linearly elastic in nature. For simulating the elastic response of the PCN model, a maximum compressive stress of
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Figure 16. Snapshot of the 7_7_7 PCN model in the y-z plane showing influenced (light blue color) and uninfluenced polymer (green color) and clay layer (white color) in the PCN model, as well as meshing through the PCN model. Table 4. Elastic Modulus Computed from Finite Element Analysis of the 7_7_7 PCN Model Containing Different Trial Values of Elastic Modulus at the Layers of Altered Polymer stress (GPa)
strain
elastic modulus of PCNs (GPa)
300 200 50 25 20 15 10 3.35
8.69E-04 9.69E-04 1.01E-04 0.0002 0.0011 0.0011 0.0002 0.0017
6.22 6.19 5.96 5.71 5.45 5.24 5.14 3.54
0.006 GPa is applied on the top surface of the 7_7_7 PCNs model, and the bottom surface is fixed in position, as shown in Figure 14. The load is applied in 10 equal increments, and the resulting strain is evaluated for each of the load increments to evaluate the elastic modulus of PCN model.
5. Results and Discussion Finite element simulation of the PCN model (7_7_12 PCN model) with a single phase of polymer (only unaltered polymer) resulted in a lower elastic modulus of 3.58 GPa compared to the experimentally obtained value of 5.46 GPa as described in section 3.2. This model does not incorporate the altered nanomechanical property of polymer arising from nonbonded interactions with intercalated clay blocks, which is a major source of difference between the simulated and experimental response. The polymer in PCN is in fact a two-phase system consisting of the altered/ influenced polymer near intercalated clay blocks and the polymer that is not affected. The existence of an altered phase of polymer is described in section 4.2, the spatial extent of which is estimated by phase imaging of a PCN sample. The finite element analysis of a PCN model (7_7_7 PCN model) consisting of two phases of polymer is carried out at various values of elastic modulus of altered polymer. This allows us to see variation of the composite elastic response of the model with respect to the elastic modulus of the altered polymer and predict an appropriate elastic modulus of the altered polymer corresponding to the experimental elastic modulus of PCNs (5.46 GPa).22 The 7_7_7 PCN model is shorter in the z direction compared to the 7_7_12 PCN model. Therefore, for the purpose of comparison, the 7_7_7 PCN model is simulated by considering the elastic modulus of altered polymer to be the same as that of unaltered polymer. This resulted in a composite elastic modulus of 3.54 GPa, which
Figure 17. Elastic modulus computed from finite element analysis of the 7_7_7 PCN model containing different trial values of elastic modulus at the layers of altered polymer.
is very close to the value of 3.58 GPa for the 7_7_12 PCN model. This establishes consistency of the results obtained from the FEM simulations of these two models. The elastic response of a model corresponding to various elastic moduli of altered polymer is presented in Table 4 and plotted in Figure 17. It is seen that the elastic response of the 7_7_7 PCN model compares with the experimental results for PCN (elastic modulus of PCN is 5.46 GPa) when the elastic modulus of altered polymer is about 15 GPa. This prediction of elastic modulus implies that there is a significant enhancement in the stiffness of altered polymer compared to pure polymer, which has an elastic modulus of 3.35 GPa. A similar result was observed for biopolymers by the Katti research group, in which the protein of nacre shows an elastic modulus of 20 GPa, whereas regular protein has an elastic modulus on the order of 5-50 MPa.42–47 The altered crystallinity of polymer in PCNs is responsible for the large improvement in the elastic modulus of polymer, which has a major role in enhancing the mechanical property of PCNs. The variation of elastic modulus of PCN with respect to elastic modulus of the altered polymer shown in Figure 19 indicates that there is a large improvement in the elastic modulus of PCN between a 10 and 40 GPa elastic modulus of altered polymer. At larger values of elastic modulus of altered polymer, beyond about 40 GPa, there is only a small improvement of elastic modulus of PCN. It is interesting to note that the experimental elastic modulus of PCN (5.46 GPa) lies in a zone of transition between the initial steeper region and the latter flatter region of the curve. Hence, the predicted elastic modulus of altered polymer (15 GPa) corresponds to the value that results in the most optimum improvement in the elastic modulus of PCN. The z-displacement contour of the PCN model corresponding to the elastic modulus of 15 GPa for altered polymer is shown in Figure 18. It is observed that elements on the edge of the model have slightly higher displacements in comparison to the displacements of elements at the inner side of model. However, the difference in displacements is not appreciable, and the relative extent over which the edge effect is seen is small compared to the region unaffected. This indicates that, in our PCNs model, the effect of edge on deformations could be considered negligible. (46) Katti, D. R.; Pradhan, S.; Katti, K. ReV. AdV. Mater. Sci. 2004, 6, 162– 168. (47) Katti, K.; Katti, D. R.; Pradhan, S.; Bhosle, A. J. Mater. Res. 2005, 20(5), 1097–1100.
Altered Phase Model for PCNs
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Figure 18. Displacement contour in the z direction of the whole 7_7_7 PCN model under a compressive stress of 0.006 GPa applied in the z direction on the top surface of the PCN model when the trial value of the elastic modulus is 15 GPa for altered polymer.
6. Conclusions
Figure 19. Magnified view of the strain contour of the 7_7_7 PCN model in the x-z plane under a compressive stress of 0.006 GPa applied to the top surface of the PCN model in the z direction when the trial value of elastic modulus is 15 GPa for altered polymer.
The magnified view of strain contour of the whole PCN model in the x-z plane is shown in Figure 19 when the of elastic modulus of altered polymer is 15 GPa. It is observed that strain is maximum in the unaltered polymer followed by altered polymer. The strain gradually reduces in the elements as they get closer to the clay sheet and attains the minimum values in the elements forming clay layers. From the strain distribution it is evident that maximum stress occurs at the clay layers followed by altered polymer and unaltered polymer. Hence, it is evident that clay blocks together with the zone of altered polymer impart PCN with an added stiffness that is responsible for the enhanced mechanical property of PCNs.
Multiscale modeling of PCNs is carried out using SMD, experimental techniques using atomic force microscopy and nanoindentation, and finite element analysis to study mechanisms responsible for the enhancement of properties of PCNs over pristine polymers. This study indicates that, for correctly modeling the mechanical behavior of PCNs, the altered properties of polymer resulting from nonbonded interactions (van der Waals, electrostatic interactions) with nanoclay particles must to be taken into account. The extent of altered polymer influenced by clay blocks, measured using an AFM, is found to be about 250 Å. This indicates that, in PCN, where nanosized clay is uniformly dispersed, the significant volume of polymer is influenced by clay compared to conventional microcomposites. The predicted elastic modulus of altered polymer, obtained from FEM simulation of a representative PCN model, is on the order of 15 GPa, which is a multiple-fold improvement compared to the elastic modulus of unaltered polymer (3.35 GPa). The enhanced mechanical property of polymer, resulting from molecular interactions with clay blocks, and molecular interaction between different constituents are key to modeling mechanical behavior of PCN. This study provides a new direction for modeling and design of nanocomposites systems similar to PCNs, where there are significant molecular interactions between the constituents. We believe that a similar phenomenon for property enhancement may occur for other particulate nanocomposite systems. Acknowledgment. The authors acknowledge the use of computational resources at the Center for High Performance Computing (CHPC), NDSU, and Biomedical Research Infrastructure Network (BRIN). The atomic force microscopy equipment used in this work was purchased through NSF Grant IMR# 0315513. The authors thank Dr. Gregory H. Wettstein for his assistance with hardware and software support at CHPC. LA800583H
