Article pubs.acs.org/JPCC
Computational Investigation on the Effect of Graphene Oxide Sheets as Nanofillers in Poly(vinyl alcohol)/Graphene Oxide Composites Ning Ding,† Xiangfeng Chen,‡ Chi-Man Lawrence Wu,*,†,‡ and Xiaoqing Lu†,§ †
Department of Physics and Materials Science, City University of Hong Kong, Hong Kong SAR, People's Republic of China Key Laboratory for Applied Technology of Sophisticated Analytical Instruments, Shandong Academy of Sciences, Jinan, Shandong, People's Republic of China § College of Science, China University of Petroleum, Qingdao, Shandong, People's Republic of China ‡
ABSTRACT: Poly(vinyl alcohol)/graphene oxide (PVA/ GO) composites were studied by molecular mechanics and molecular dynamics methods to analyze the effect of GO sheet addition on PVA material. The properties of polymer/GO composites with different oxidation degrees and dispersion states of GO sheets in a PVA matrix were compared. The interfacial binding characteristics, mechanical properties, and glass transition temperature of PVA/GO composites were obtained. It was found that the oxidation degree of the GO sheet would influence the strength of interfacial binding characteristics between the polymer and GO sheet. A high oxidation degree of GO would enhance the interaction between the GO sheet and PVA matrix, thus improving the properties of PVA/GO composites. By reinforcing pure PVA with GO to give PVA/GO composites, its Young’s modulus, bulk modulus, and shear modulus, as well as the glass transition temperature of the PVA/GO composites, were obviously enhanced. For GO paper, the interaction between GO sheets inside the GO paper was stronger than the interaction between the GO paper and PVA matrix.
1. INTRODUCTION Graphene and graphene-based materials have attracted much attention in the past several years because of their unique properties.1−8 Among numerous graphene-based materials, graphene oxide (GO), which possesses many advantages such as low cost, extraordinary structure, and convenient fabrication, has great potential to be used as the reinforcing phase in composite materials.9−19 GO is the oxidation product of graphene. After oxidation, many oxygen-containing functional groups such as the hydroxyl group, epoxide group, and carbonyl group are attached on the surface of GO sheets, making them easy to combine with a wide range of organic and inorganic materials.18 Such a combination can be used as a sensor for detection of protein, nucleic acids, and some other small molecules.20−24 For example, GO was reported as an ideal substrate for hydrogen storage23 and a possible DNA-based optical sensor.24 To obtain a fundamental understanding of the unique behavior of GO, many theoretical works were also carried out.25−27 Boukhvalov obtained the optimized structures of GO corresponding to the minimum total energy based on density functional calculations.25 Shenoy and co-workers investigated the hydrogen bond network in GO composite paper by the molecular dynamics method.26 It was found that the large-scale properties of GO paper were controlled by the hydrogen bond networks. Polymer materials are widely used in industry, e.g., for transparent film and paper coating.28−30 It is of practical importance to improve the mechanical and thermal properties of some polymers by physical or chemical methods. For © 2012 American Chemical Society
example, the addition of GO sheets in a polymer matrix to form polymer/GO composites can be an effective method to improve the mechanical, thermal, and electrical properties of polymers.31−37 Many kinds of polymer/GO composites were prepared and analyzed. Zhong and co-workers prepared a type of polystyrene (PS)/GO composites by the solution blending method and found that the PS/GO composites exhibited a better storage modulus and thermal stability than pure PS material.31 Yang et al. carried out the preparation of layerstructured poly(vinyl alcohol) (PVA)/GO composites and significantly improved the thermal and mechanical properties of the nanocomposites.32 Shi et al. employed a solvent exchange method to obtain polybenzimidazole/GO composites which enabled a full exfoliation and high concentration of GO in organic solvent in the preparation process.34 All these experimental results indicated that if GO sheets were dispersed well on the molecular scale in a polymer matrix, the properties of the polymer would be improved significantly. Therefore, it is necessary to obtain a uniform dispersion state of GO sheets in the polymer matrix and to have insight into the prerequisite of the interfacial binding information. In the past few years, the interfacial binding characteristics of polymer/graphene composites38 and polymer/carbon nanotube (CNT) composites39,40 have been studied by molecular mechanics (MM) and molecular dynamics (MD) methods. For example, for a PS/ Received: June 9, 2012 Revised: August 31, 2012 Published: September 27, 2012 22532
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with different chemical compositions and oxidation degrees were constructed according to the experimental data in ref 25, that is, C8H2O2 (GO1) and C8H2.4O3 (GO2). The dimensions of the GO sheet were set as 60.0 Å × 32.0 Å. Figure 1 shows the molecular structures of the PVA molecules and GO1 sheet.
CNT system, it was found that electrostatic and van der Waals interactions play dominant roles between the CNT and PS matrix. The interfacial shear stress of the PS/CNT system was significantly higher than that of most carbon fiber reinforced polymer composite systems.40 However, there are few computational works focusing on the interfacial information and properties of polymer/GO composites. Actually, several methods were used to synthesize GO sheets with different chemical compositions and oxidation degrees (usually from C8H2O2 to C8H4O5),25 such as the Hummers method and the Staudenmaier method.41 It was reported that GO sheets have a collective behavior to form GO papers, which are “paperlike” composites composed of stacked GO sheets, in solution. There are three general states of GO sheet dispersion in a polymer matrix: stacked state, intercalated state, and exfoliated state.42 An interesting question is whether the oxidation degree and dispersion states of GO sheets in a polymer matrix will influence the properties of polymer/GO composites. Inspired by this question, we focus on the interaction between the polymer matrix and GO sheets with different degrees of oxidation and dispersion states. Since PVA is a widely used industrial material, it has been chosen to illustrate the characteristics of the polymer/GO composites. In this paper, PVA/GO composites were analyzed by MM and MD methods to study the effect of GO sheet addition in PVA material. The properties of PVA/GO composites with different oxidation degrees and dispersion states of GO sheets in a PVA matrix were compared. The interfacial binding characteristics, mechanical properties, and glass transition temperature of PVA/GO composites were obtained.
Figure 1. Structures of the (a) PVA molecule and (b) GO1 sheet.
Two types of composites, namely, the single-GO system and the triple-GO system were constructed, as shown in Figure 2.
2. COMPUTATIONAL DETAILS 2.1. Computational Method. In this work, the MM and MD methods were employed to study the PVA/GO composites by using the Discover module of Material Studio (Accelrys Inc.). The condensed-phase optimization molecular potentials for atomistic simulation studies (COMPASS) force field was chosen to describe the whole system. Although COMPASS cannot cover all elements in the periodic table, it has been reported and verified as an appropriate force field to predict the properties of polymers in condensed states.43 In the COMPASS force field, the potential energy of a molecule system can be expressed as Etotal = Evalence + Ecross‐term + Enonbond (1)
Figure 2. Molecular models of single-GO1 and triple-GO1 systems: (a) cross-sectional view of the single-GO1 system before optimization; (b) cross-sectional view of the single-GO1 system after optimization; (inset of (b)) side view of the single-GO1 system; (c) cross-sectional view of the triple-GO1 system before optimization; (d) cross-sectional view of the triple-GO1 system after optimization; (inset of (d)) a possible configuration of a PVA molecule adsorbing on a GO sheet.
Figure 2a shows the single-GO1 system with dimensions of 60.6 Å × 60.6 Å × 50.0 Å. This calculation unit contained one GO1 sheet that was randomly surrounded by 215 PVA molecules. The periodic boundary condition was added to the unit cell. An energy minimization was carried out, and then a series of MD simulations were performed on the composite system. It contained a 10 ps NPT simulation (T = 298 K, P = 105 Pa) with a time step of 1 fs when the coordinates of the GO1 sheet were constrained, a 20 ps NVT simulation (T = 298K) with a time step of 1 fs when the coordinates of the GO1 sheet were constrained, and a 50 ps NVT simulation (T = 298 K) with a time step of 1 fs when the coordinates of the GO1 sheet were not constrained. After these simulations the GO1 sheet was dispersed inside the PVA matrix well, as shown in Figure 2b. A similar operation was implemented on the single-GO2 system. At equilibrium, both the single-GO1 and single-GO2 systems contained approximately 3 vol % GO sheets. As mentioned above, the GO sheets have a collective behavior to form GO papers in the preparation process of
where Evalence is the valence energy which contains the energy of bond stretching, valence angle bending, and dihedral angle torsion and inversion. The energy of cross-terms, Ecross‑term, denotes the energy between different bonded items, for example, the bond−bond cross-term energy, bond−angle cross-term energy, and angle−torsion cross-term energy. Enonbond reflects the interactions between nonbond atoms which are mainly caused by the van der Waals effect. In the MM process the steepest descent (SD) and conjugate gradient (CG) methods were conducted to perform the simulation. For the nonbond interaction, the atom-based method was chosen to calculate the van der Waals energy with a cutoff of 9.5 Å, while the Ewald method44 was used to calculate the electrostatic energy. 2.2. Molecular Models. In this section, a PVA monomer with 10 repeat units was selected as the polymer material to make up the polymer/GO composites. To study the effect of GO filling on PVA/GO composites, two types of GO sheets 22533
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composites. In view of this, we constructed the triple-GO systems. Figure 2c shows a triple-GO1 system with dimensions of 63.0 Å × 63.0 Å × 69.5 Å. This calculation unit contained three GO1 sheets (that is a GO1 paper) and 300 PVA monomers randomly surrounding the GO1 paper. The initial average distance between the adjacent GO1 sheets was set as 6 Å according to recent calculations and experimental results.25,45,46 After the MM and MD processes, the resulting configuration of the triple-GO1 system is shown in Figure 2d. The triple-GO2 system has a similar configuration. Besides, both triple-GO1 and triple-GO2 systems contained approximately 8 vol % GO paper. As each of the PVA/GO composite systems contains about 20 000 atoms, it needs about two weeks to obtain an equilibrium PVA/GO composite system with respect to our computing resource.
Table 1. Interaction Energy and Interfacial Binding Energy of PVA/GO Composite Systems system single-GO1 system single-GO2 system triple-GO1 system (middle) triple-GO1 system (top) triple-GO1 system (whole) triple-GO2 system (middle) triple-GO2 system (top) triple-GO2 system (whole)
3. RESULTS AND DISCUSSION 3.1. Interaction in PVA/GO Composites. For the four PVA/GO composite systems, the energy information was collected to reflect the interaction between GO sheets and the PVA matrix. The interaction energy, ΔE, is defined as ΔE = Etotal − (EGO + E PVA + rGO)
contact area, A (Å2)
interaction energy, ΔE (kcal/mol)
interfacial binding energy, γ (kcal/mol·Å2)
3840
−1159
−0.151
3840
−1370
−0.178
3840
−1314
−0.171
3840
−1185
−0.154
5280
−1403
−0.133
3840
−1789
−0.233
3840
−1497
−0.195
5280
−1462
−0.138
(2)
Taking the triple-GO1 system as an example, the interfacial binding energy for the middle GO1 sheet was 11% higher than that of the top one and 28.5% higher than that of the whole GO1 paper. That is, the interaction inside the GO paper is much higher than that between the GO paper and PVA matrix. 3.2. Pullout Simulation of GO Sheets from PVA/GO Composites. Interfacial shear stress is a key parameter to reflect the interfacial characteristics of PVA/GO composites. To obtain the interfacial shear stress of the four systems, a pullout simulation39 was performed on GO sheets in a PVA matrix. The energy information was collected during the simulation. Figure 4 shows the snapshots along the pullout
where Etotal is the potential energy of the whole composite system and EGO is the potential energy of the GO sheets. For a triple-GO system, there are three chosen manners of GO sheets (shown in Figure 3): the middle one, the top one, and the
Figure 3. Targets of GO sheets: (a) the middle one; (b) the top one; (c) the whole GO paper.
whole GO paper. EPVA+eGO is the potential energy of the PVA matrix and the GO sheets that is not involved in EGO. What we follow with interest is the interaction between the selected GO sheets and the remaining system. On the basis of the interaction energy, the interfacial binding energy, γ, can be defined as47 ΔE (3) 2A where A is contact area of the selected GO sheets with the remaining system. The interaction energy and interfacial binding energy of the four types of PVA/GO composite systems were obtained and are shown in Table 1. When comparing the single-GO systems, it was found that the interaction energy of the single-GO2 system was 211 kcal/mol higher than that of the single-GO1 system. The interfacial binding energy of the single-GO2 system was 0.027 kcal/mol·Å2 higher than that of the singleGO1 system. These indicated that the interaction strength between the GO2 sheet and the PVA matrix was about 18% stronger than that between the GO1 sheet and the PVA matrix. For both triple-GO1 and triple-GO2 systems, it was found that the interfacial binding energy for the middle GO sheet was higher than that of the top one and the whole GO paper. γ=
Figure 4. Snapshots of the pullout process of the GO1 sheet in the single-GO1 system.
process for the single-GO1 system. In this process, the single GO1 sheet was pulled out from the PVA matrix along the tangential direction of the GO surface with a displacement step of 10 Å. For the triple-GO systems, we considered three types of pullout manners (as shown in Figure 3): pulling out the middle GO sheet (case M), pulling out the top GO sheet (case T), and pulling out the whole GO paper (case W). 22534
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Figure 5. Interaction energy (a) and interfacial binding energy (b) between the GO sheet and PVA matrix of single-GO systems along the pullout process.
For single-GO systems as well as the case M and case T pullout processes of triple-GO systems, the interfacial shear stress, τ, is calculated by the following equations:38 x=l
Epullout =
∫x=0
x=l
Aτ dx =
∫x=0
Table 2. Pullout Energy and Interfacial Shear Stress of PVA/ GO Composite Systems system
2
2d(l − x)τ dx = l τd
single-GO1 system single-GO2 system triple-GO1 system (middle) triple-GO1 system (top) triple-GO1 system (whole) triple-GO2 system (middle) triple-GO2 system (top) triple-GO2 system (whole)
(4)
and τ=
Epullout l 2d
(5)
where Epullout is the pullout energy of the GO sheet, which is defined as the potential energy difference between the initial and final configurations in the pullout process. d and l are the width and length of the GO sheet, respectively. For the case W pullout process of triple-GO systems, the interfacial shear stress, τ, can be calculated by the follow relations: x=l
Epullout =
∫x=0
=
∫x=0
x=l
2(d + h)(l − x)τ dx (6)
and τ=
Epullout 2
l (d + h)
pullout energy (kcal/mol)
interfacial shear stress, τ (MPa)
16525 16655 24735
733 817 843
44.2 49.3 50.8
24735
763
46.0
24735
839
36.8
25125
1168
70.4
25125
950
57.3
25125
1116
48.9
GO1 system. Considering the comparison mentioned above, it is obvious that the oxidation degree of GO influences the interfacial binding characteristics between the GO sheet and PVA matrix. A high oxidation degree of GO would enhance the interaction between the GO sheet and PVA matrix. As mentioned in some previous works,19,36 the interlink of PVA molecules and the GO sheet mainly depended on hydrogen bonds. It is interesting whether the number of hydrogen bonds would affect the interaction between the PVA matrix and GO sheet. To give insight into the mechanism behind the observed trends, a series of quantum calculations based on the density functional theory (DFT) were performed using a truncated model of the system (see the inset of Figure 2d). The simplified model contained a GO sheet only with epoxy groups and a PVA molecule with two repeat units. The PVA molecule was located on the surface of the GO sheet with one of the hydroxyl groups close to an epoxy group on the GO sheet. After a geometry optimization simulation, a typical hydrogen bond was observed between the two functional groups. The distance between the hydrogen atom in the hydroxyl group and the oxide atom in the epoxy group was 2.505 Å, which agreed with a past theoretical result for a typical O···H bond.19 The calculated interaction energy between the PVA molecule and GO sheet was −0.14 eV. Furthermore, we added one more epoxy group on the GO surface to construct another hydrogen bond between the PVA molecule and GO sheet. According to
Aτ dx
= l 2τ(d + h)
no. of atoms
(7)
where h is the height of GO paper in the triple-GO systems. First, on the basis of eqs 2 and 3, the interaction energies and interfacial binding energies of the single-GO1 system and single-GO2 system during the pullout process were compared. As shown in Figure 5a, the interaction energies for both singleGO1 and single-GO2 systems decrease from the range of 1200−1400 kcal/mol to around zero when the GO sheets are pulled out of the PVA matrix. Figure 5b shows interfacial binding energies of the two systems during the pullout process. The interfacial binding energy ranged from −0.13 to −0.15 kcal/mol·Å2 for the single-GO1 system and from −0.15 to −0.22 kcal/mol·Å2 for the single-GO2 system. The pullout energy and interfacial shear stress of the two single-GO systems are presented in Table 2. The interfacial shear stress of the single-GO2 system was 5.1 MPa higher than that of the single22535
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Figure 6. Interaction energy (a) and interfacial binding energy (b) between the GO sheet and PVA matrix of triple-GO systems along the pullout process.
of the triple-GO1 system, while for pullout case T, the interfacial shear stress of the triple-GO2 system was 11.3 MPa higher than that of the triple-GO1 system. These further supported the point that a high oxidation degree of GO will enhance the interaction between GO sheets or between the GO sheet and PVA matrix. The interfacial shear stress of case W pullout simulation for both the triple-GO1 system and triple-GO2 system can be found in Table 2. For the triple-GO1 system, the shear stress along the case W pullout process was 14.0 MPa lower than that of case M and 9.2 MPa lower than that of case T, while for the triple-GO2 system, the interfacial shear stress of the case W pullout process was 21.5 MPa lower than that of case M and 8.4 MPa lower than that of case T. By comparing the values of shear stresses among case W, case M, and case T, it is clear that the bonding between GO sheets is stronger than that between the GO sheet and PVA. In other words, it is easier to pull out the whole GO paper from the PVA matrix than pulling out the middle GO sheet inside the GO paper. A possible reason for the relatively strong interaction inside the GO paper may be the hydrogen bond networks between GO sheets. It was mentioned in a previous theoretical work26 that the interlayer hydrogen bond networks would influence the large-scale properties of GO paper. Although there are hydrogen bonds distributed both inside the GO paper and between the GO paper and PVA matrix, it is believed that the hydrogen bonds between the GO paper and PVA matrix are easier to break than the interlayer hydrogen bonds inside the GO paper. That is because the PVA molecules can reorient themselves easily due to the shear load from the pullout action. Besides, a relatively weak interfacial shear stress between the GO paper and PVA matrix indicates that an individual GO sheet would provide better load transfer than the whole GO paper. This phenomenon can also be found in the polymer/carbon nanotube rope composite system.39 3.3. Mechanical Properties. GO possesses outstanding mechanical properties. For instance, our calculations showed that Young’s moduli of single GO1 and GO2 sheets were 63 and 50 GPa, respectively. When compared with our calculated value of about 3.3 GPa for Young’s modulus of PVA, GO is clearly a prospective reinforcing phase. In this section, a pure PVA matrix (PVA system) with a density of 1.2 g/cm3 is constructed to compare the changes of mechanical properties
the calculation results, the interaction energy between the PVA molecule and GO sheet increased by 200 meV due to the increase of the hydrogen bond. This value was close to the hydrogen bond strength (320 meV) between two water molecules.19 The difference between these two values may be caused by the energy loss during the deformation process of the PVA molecule. In view of the above discussion, the energy release during the formation of the hydrogen bond between PVA and GO is higher than the energy loss caused by the deformation of the PVA molecule. Thus, a high oxidation degree of GO, which could increase the probability of hydrogen bonds, would enhance the interaction between the GO sheet and PVA matrix. On the other hand, the theoretical work in ref 39 had pointed out that stronger interaction between nanofillers and a polymer matrix would provide better load transfer between them. Therefore, the load transfer would be better between the GO2 sheet and PVA matrix than between the GO1 sheet and PVA matrix. Now, we turn to the triple-GO systems. Figure 6 shows the interaction energies and interfacial binding energies of the triple-GO1 system and the triple-GO2 system along the pullout process with case M and case T. The pullout energies and interfacial shear stresses of the two systems during different pullout processes can also be found in Table 2. For the tripleGO1 system, the interaction energy for both case M and case T decreased and finally became nearly zero when the GO sheet was pulled out of the PVA/GO paper matrix. The interfacial binding energy was in the range from −0.15 to −0.20 kcal/ mol·Å2 for case M and from −0.11 to −0.15 kcal/mol·Å2 for case T. In addition, during the pullout process, the interfacial shear stress of case M was 4.8 MPa higher than that of case T. Similarly, for the triple-GO2 system, the interfacial binding energy at each point of case M was higher than the corresponding point of case T along the z axis. The interfacial shear stress of case M was 13.1 MPa higher than that of case T. All of the above discussions indicated that the interaction between GO sheets inside the GO paper is about 10−20% stronger than the interaction between the GO sheet and PVA matrix. A similar result was also found in the theoretical simulation of an epoxy resin/carbon nanotube rope composite system.39 On the other hand, for pullout case M, the interfacial shear stress of the triple-GO2 system was 19.6 MPa higher than that 22536
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etry possesses a better Young’s modulus than a composite containing GO sheets with C10O1(OH)1 stoichiometry under the same weight conditions. With reference to the results in this work and according to the above discussion on energy, we believe that the improvement in mechanical properties of the single-GO2 system was caused by the higher oxidation degree of the GO2 sheet and led to a stronger interaction and better load transfer between the GO2 sheet and PVA matrix. However, further investigations are needed to explore the variation of mechanical properties of the GO composite under different orientations of the GO system and weight percentages of GO. 3.4. Glass Transition Temperature. A series of NPT simulations was carried out to obtain the glass transition temperature (Tg) of PVA, single-GO1, and single-GO2 systems. For each system, the NPT simulation (P = 105 Pa) begins with a temperature of 600 K. Then, with temperature decreasing from 600 to 50 K with a step of 50 K, a 10 ps NPT simulation (P = 105 Pa) was carried out at each temperature point to obtain the relationship between the temperature and density of the system. As shown in Figure 7, the Tg of the PVA system is 343 K, while the Tg values of the single-GO1 and single-GO2 systems are 345 and 352 K, respectively. It is obvious that the incorporation of GO sheets can increase the Tg of the PVA material. In addition, the incorporation of GO2 sheets provides a better effect on PVA/GO composites than incorporating GO1 sheets. This indicates that GO sheets as the nanofiller in a PVA matrix would enhance the thermal property of the PVA material and is in agreement with recent experimental results.32 A higher oxidation degree of GO sheets would lead to better improvements in the thermal properties of the PVA material.
with the PVA/GO composite systems. The single-GO1 system and single-GO2 system are chosen as examples to compare with the PVA system. The static method, which has been verified to be an effective method for elastic property study, was used to predict the mechanical properties of the chosen systems. Young’s modulus, Poisson’s ratio, the bulk modulus, and the shear modulus of the three systems are shown in Table 3. Table 3. Mechanical Properties of PVA and PVA/GO Composite Systems system PVA system single-GO1 system single-GO2 system
Young’s modulus (GPa)
Poisson’s ratio
bulk modulus (GPa)
shear modulus (GPa)
3.312 4.772
0.2779 0.2387
2.486 3.044
1.296 1.926
6.379
0.2170
3.759
2.621
When comparing with the pure PVA system, Young’s modulus, the bulk modulus, and the shear modulus of the PVA/GO system were enhanced obviously. For the single-GO1 system, Young’s modulus, the bulk modulus, and the shear modulus were improved by 44.1%, 22.4%, and 48.6%, respectively, while for the single-GO2 system, these parameters were improved by 92.6%, 51.2%, and 102.2%, respectively. These results indicated that the incorporation of GO sheets could enhance the mechanical properties of PVA and were in agreement with the results of previous experimental works.32 It is important to note that the incorporation of GO2 sheets can give a better property than incorporating GO1 sheets, as shown in Table 3. It is noted that the oxidation process may decrease the in-plane mechanical properties of a GO sheet compared with those of graphene.13 To verify this phenomenon, we obtained by calculations that Young’s moduli of a single graphene sheet, a single GO1 sheet, and a single GO2 sheet were 200, 63, and 50 GPa, respectively. This shows that the GO1 sheet exhibits a higher Young’s modulus than the GO2 sheet. On the other hand, previous theoretical and experimental results19,26 have pointed out that, in GO composites, the density of hydrogen bonds around GO sheets would dramatically affect the mechanical properties of GO composites. A higher density of oxygen-containing functional groups on the GO surface can form more hydrogen bonds between the GO sheet and surrounding molecules and thus gives the composite better mechanical properties. For example, in ref 26, a water/GO composite containing GO sheets with C10O2(OH)2 stoichiom-
4. CONCLUSIONS In this paper, PVA/GO composites were studied by MM and MD methods. Two types of GO sheets with different oxidation degrees were chosen to fabricate PVA/GO composites. It was found that a higher oxidation degree of GO would enhance the interaction between the GO sheet and PVA matrix and thus improve the properties of PVA/GO composites obviously. Also, two different GO dispersion manners in the PVA matrix were considered. The calculation results showed that the interaction between GO sheets inside the GO paper is stronger than the interaction between the GO paper and PVA matrix.
Figure 7. Tg of the (a) PVA system, (b) single-GO1 system, and (c) single-GO2 system. 22537
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by a grant from the City University of Hong Kong (Grant 7008184) and the Shandong Province Special Grant for High-Level Overseas Talents (Grant tshw20120745).
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