Mechanical Properties of a Polymer at the Interface Structurally

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Mechanical Properties of a Polymer at the Interface Structurally Ordered by Graphene Stanislav G. Falkovich, Victor M. Nazarychev, Sergey V. Larin, Josè M. Kenny, and Sergey V. Lyulin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11028 • Publication Date (Web): 04 Mar 2016 Downloaded from http://pubs.acs.org on March 7, 2016

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The Journal of Physical Chemistry

Mechanical properties of a polymer at the interface structurally ordered by graphene Stanislav G. Falkovich,a Victor M. Nazarychev,a Sergey V. Larin,a José M. Kenny,a,b Sergey V. Lyulin a,c,* a

Institute of Macromolecular Compounds, Russian Academy of Sciences, Bol’shoi pr. 31 (V.O.), St. Petersburg, 199004 Russia.

b

Materials Science and Technology Centre, University of Perugia, Loc. Pentima, 4, Terni, 05100 Italy.

c

Department of Physics, St. Petersburg State University, Ul’yanovskaya str. 1, Petrodvorets, St. Petersburg, 198504 Russia.

*Corresponding author. Sergey Lyulin Fax: +7 (812) 328686; Tel: +7 (812) 3285601; E-mail: [email protected]

ACS Paragon Plus Environment

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KEYWORDS Nanocomposite, Graphene, Molecular dynamics, Computer Simulation, Mechanical properties, Polyimides

ABSTRACT

In this study, for the first time, molecular-dynamics simulations helped identifying the substantial mechanical properties changes of a crystallizable polyimide related to the ordering of the polymer chains along the graphene surface. It is demonstrated that graphene-induced polymer ordering at the nanofiller-polymer interface leads to mechanical properties exceeding those of the unfilled amorphous polymer. Moreover, simulation results confirm that the mechanical properties anisotropy is related to the polymer ordering anisotropy induced by graphene-polymer interactions.

INTRODUCTION Polymer composites are widely used in many industrial applications. Recently, researchers have increased the focus on nanocomposites since the addition of low contents of nano-scale filler particles may significantly improve the thermal and mechanical properties of the polymer matrix.1-5 Due to the high specific area of dispersed nanoparticles, nanocomposites feature a higher volume fraction of the polymer at the interface than conventional composites. The properties of the nanoparticle-polymer interface, including the mechanical ones, depend both on


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the properties of the nanoparticles themselves and of the polymeric matrix in the near-surface area (so-called interface). It is almost impossible to experimentally distinguish contributions between nanoparticles themselves and that of the polymer at interface to the change of the nanocomposite mechanical properties. The question that arises is how important is the contribution of the structurally ordered polymer at the interface? This question can be worded differently: do the properties of the polymer at interface differ significantly from the properties of the polymer without filler? If yes, how big is this difference and how thick is the interface? Answers to these questions are relevant for the development of new polymer nanocomposites with controlled properties. They are also important for solving engineering tasks during the simulation using the finite elements approach, which may account for specific properties of the polymer at interface.6 The investigation reported here deals with structural and mechanical properties of the polymer at the interface using the atomistic molecular-dynamics simulation which considers the polymer chemical structure in detail. In order to answer these questions the heat-resistant crystallizable polyimide R-BAPB (based on 1,3-bis-(3’,4-dicarboxyphenoxy)benzene (dianhydride R) and diamine 4,4’-bis-(4’’-aminophenoxy)-diphenyl (diamine BAPB)) has been taken in consideration (Fig. 1). The objective of this study is to clear up the influence of polymer precrystallization ordering induced by the interaction with the graphene nanoparticle on the mechanical properties of nanocomposites. There is a number of studies devoted to semi-crystalline polymer nanocomposites with carbon nanofillers and their mechanical properties, both experimental and simulation. Most of the atomistic modeling of such systems is devoted to nanocomposites based on polymers with relatively simple chemical structure, such as alkanes. It was shown in the study by Wang et al.7, by atomistic molecular dynamics simulations, that the crystallization of a polyethylene single


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chain on the surface of graphene occurs into two steps: the adsorption of the chains and further crystallization. A similar result was obtained in the Monte Carlo simulation in Nie et al. 8 and in Anwar et al.9,10 The ordering of one or several alkane chains on the surface of nanotubes or graphene was studied by Yang et al.11and Anwar et al.9,10by atomistic molecular dynamics method. It was shown that the chain of alkanes immediately pulled along a surface of the CNT (which is a kind of director for their ordering), while in the interaction with graphene alkane chains first adsorb on graphene flat surface and only after that ordering starts. Therefore, crystallization induced by nanotubes is faster than the crystallization induced by graphene. A similar result was obtained by Xu et al.12 in the experimental study of the crystallization of polylactic acid, which occurs in the presence of CNTs faster than in the presence of graphene. It should also be noted that there are experimental data for semi-crystalline polyimide R-BAPB,13 showing that this polymer crystallizes faster in the presence of graphitic carbon than in the presence of CNTs possibly due to an orientating effect of the graphene like surface. A potential orienting effect of graphene has been indirectly confirmed by the results of Wei, who showed by atomistic molecular dynamics that, depending on the chirality of CNT, alkanes crystallization occurs with varying degrees of effectiveness. Furthermore, it was shown in works of Rissanou et al.14and Bacova et al.15 by atomistic molecular dynamics simulations that a mobility of polyethylene near the surface of the graphene is slowed down. The authors also showed anisotropy of molecular diffusion, which was lower along the direction perpendicular to the nanotube axis than along a direction parallel to it. This observation contradicts the results obtained by atomistic molecular dynamics simulations for polyimides16,17 where a stretching of the polymer chains along the axis of the nanotube or graphene surface when ordering was shown.


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The crystallization of polymers in the presence of carbon nanofillers has been reported in several papers: in addition to the above-mentioned work by Yudin et al.,13 we would like to refer to the experimental papers of Jia et al. and of the group of Dingemans,18 where the crystallization of a non-crystallizable polyimide was shown in the presence of CNTs. Furthermore, they reported that a crystallization resulted in a significant increase in the Young's modulus. In particular, the results reported by Hegde et al.18 emphasize the fundamental role of the CNTpolymer interface in providing higher values of the nanocomposites Young's modulus. An increase in the modulus due to crystallization caused by nanotubes and graphene (see Sharma et al., 201419and Sharma et al., 201520, respectively) was also observed for nanocomposites of poly vinyl alcohol. Changes in the properties of the polymer interacting with the carbon nanofillers were studied in Liu et al. using molecular dynamics simulations. A more significant increase in stiffness of the polymer was shown in the case of graphene, than in the case of the nanotube or fullerene, which is attributed to the formation of long fibrils of oriented polymer, in agreement with our previous study of an effect of carbon nanofiller curvature on crystallization of polyimides.16 The mechanical properties of graphene-epoxy nanocomposites were studied in the paper of Rahman by atomistic molecular dynamics simulations. A substantial increase in the Young's modulus upon addition of graphene to an epoxy matrix was shown. It was also demonstrated that a well-dispersed graphene possesses enhanced elastic modulus compared to the agglomerated graphene-epoxy system. The anisotropy of the polymer caused by crystallization and influencing its mechanical properties was studied in a number of experimental researches. The appearance of ordered structures of stacked parallel polymer chains oriented along CNTs (shish kebab) was shown for a number of polymers such as polyethylene21 and polylactic acid.22 Such ordering in polymer


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systems can appear not only related to the presence of a carbon nanofiller but as a consequence of the tension applied as it was shown for polyethylene,23 PET24 and other polymers. A similar effect is strain (strain-induced crystallization) as it was shown for poly(keto-ether-imide) films, which is similar in chemical structure to polyimides.25 After a careful revision of the scientific literature, it is evident that the process of crystallization of polymers initiated by carbon nanofillers, as well as the study of the mechanical properties of nanocomposites with carbon fillers have been widely investigated both experimentally and theoretically using atomistic simulations. However, it should be noted that in all the above-mentioned papers on atomistic simulation in which the mechanical properties of polymer nanocomposites were investigated, the load was applied to the sample, which included both the polymer matrix and the nanoparticles. In our atomistic simulation we have separated the components after the interaction and we have calculated the mechanical properties of the ordered polymer without the nanofiller. In fact, we are convinced that the computation of the intrinsic mechanical properties of the polymer, ordered by the filler nanoparticles has a relevant interest. In particular, modeling such systems is important for a correct parameterization of calculations by finite elements. Obviously, such a study of the mechanical properties of nanocomposites separating the mechanical properties of the polymer matrix from those of a nanofiller is not possible experimentally but we demonstrate here that this problem can be solved via atomistic simulation.


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Figure 1. Chemical structure of the repeated unit of R-BAPB polyimide (upper part) and part of the infinite graphene sheet16 (lower part). The red and blue arrows indicate the vectors corresponding to the rigid fragment of the R-BAPB repeated unit chosen for structural analysis.

The choice of the R-BAPB-based graphene-filled nanocomposite as research target is determined by the following reasons: R-BAPB is a semi-crystalline thermoplastic polyimide and the incorporation of nanoparticles into crystallizable polymers further improves their mechanical properties26 increasing the material rigidity and preventing microscopic crack formation at the interface between crystalline and amorphous areas taking advantage of the formation of multiple randomly oriented nanoscale crystallites.18,27-29 The excellent thermal and mechanical properties of semi-crystalline thermoplastic polymers determine that these polymers and their nanocomposites are highly promising materials to be used in aerospace, automotive and other industries.4,18,28 For R-BAPB, it was shown experimentally that the addition of carbon nanofillers may significantly accelerate its crystallization rate compared to the rate of the non-filled polymer.13 To explain this phenomenon, in our previous studies16,17 we simulated the interaction of carbon nanofillers (graphene and nanotubes) and the R-BAPB matrix using atomisticallydetailed molecular dynamics. Notably, such simulations allow to study the initial steps of the crystallization of polymers such as polyolefines;9-11 obtaining results in line with experimental


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data.30 In the case of less flexible and more complex heterocyclic polymers with a higher viscosity, the simulation of a crystallization process is hindered even when high-performance computational packages such as Gromacs,31,32 and modern supercomputers are used. However, during the microsecond-scale simulation we have observed a substantial number of linear fragments of repeated units of this polyimide oriented parallel to the nanofiller surface,16,17 which can be interpreted as a precursor stage of the crystallization.9,10 Graphene causes stronger ordering of R-BAPB than CNT; a greater number of chain segments are oriented parallel to the graphene plane than those which are oriented parallel to the CNT surface, which correlates well with experimental data.13 The presence of graphene affected the R-BAPB in all the volume of the sample considered. In fact, ordering involved not only the first sub-surface layer of R-BAPB but the whole volume of the polymer. This paper deals with the investigation of the influence of the structural ordering of the polymer at the interface with graphene on the mechanical properties of R-BAPB.

THEORETICAL METHODS A repeat unit of R-BAPB consists of dianhydride R (1,3-bis-(3',4-dicarboxyphenoxy)-benzene) and diamine BAPB (4,4'-bis-(4''-aminophenoxy)-diphenyl. Our study is based on our experience in atomistic simulation of polyimides,16,17,33-38 including R-BAPB. For the simulation, we used R-BAPB chains with a polymerization degree of Np = 8 in the samples of graphene-filled and non-filled R-BAPB samples containing 27 chains each. The atomistic simulation using the molecular-dynamics method was performed in the force field Gromos53a539 using the Gromacs package.31,32 The samples were obtained from the rarefied chain gas; the procedure is described in detail in our previous papers.16,17,33,37 The compaction was followed by a microsecond-long


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simulation. During the simulation, the average chain size reached constant values close to those calculated analytically.16,17,33 The simulations were carried out in the NpT ensemble. Constant temperature T = 600 K, that is 5K higher than the experimentally-determined value of the R-BAPB melting temperature,13,40 and pressure P = 1 bar were maintained using a Berendsen thermostat and barostat,41,42 with time constants of τT = 0.1 ps and τP = 0.5 ps, respectively. All bond lengths were kept constant with the LINCS algorithm.43 Atomistic partial charges were taken equal to zero since their negligence has a weak impact on the structural properties of the relatively weakly polarized R-BAPB, accelerating the polymer structural transformations by many times.16,17 During the simulation of the system with graphene, the mobility of its atoms was restricted by introducing additional potentials (position restraints) and a change of the periodic cell size in XY plane of graphene was prohibited in order to maintain the graphene sheet area.7 Nine configurations of the graphene-filled R-BAPB samples were chosen during productive run after each 50 ns and 11 configurations of the non-filled amorphous R-BAPB were chosen after each 100 ns. Starting from these configurations, the systems were cooled from 600 to 290 К which is much lower than the glass-transition point of R-BAPB.13 The research procedure was as follows: the polymer nanocomposite was equilibrated for 1 microsecond at T = 600 K and P = 1 bar and waited for the polymer matrix structural ordering near the graphene to occur.16,17 Then the system was cooled down to T = 290 K well below the glass transition temperature and hence all polymer degrees of freedom were arrested. Nine configurations of the system were selected each 100 ns from the final part of the MD trajectory to be cooled and then pulled. As it was shown in our previous papers,17,33,37 100 ns in enough to consider configurations of a nanoscale R-BAPB system as independent. Thus, a set of


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independent quenched samples was obtained for further study of their mechanical properties. The cooling procedure consisted in gradual decrease of the temperature, with the temperature being reduced by 10 K at each step, followed by a 4 ns relaxation of the system.17,33,37 The size of the simulation cell was 6×6×6 nm. Then graphene atoms were removed simultaneously and the gap produced was eliminated by a short NpT run (1.5 ns at 50 bar along Z direction perpendicular to the plane where graphene laids, and 20 ns of equilibration at 1 bar), i.e. the two ordered surfaces were basically "glue" or pressed against each other to create a "bulk"-like environment, yet preserving the chain ordering created by the graphene. This was followed by the simulation of the uniaxial deforming of the structurally ordered polymer at the interface in various directions. For reference, mechanical properties of the non-filled amorphous R-BAPB sample were studied as well. Periodic boundary conditions were used at all simulation stages. The uniaxial deformation changes the periodic cell size at a constant rate, along the positive direction of one – X, Y or Z - of the reference axes, so that the isotropic Berendsen barostat with a time constant =0.5 ps was replaced with the anisotropic Berendsen barostat with =1 ps. The samples remained incompressible in the direction of the applied deformation, i.e. the compressibility of the system in this direction was set to zero. In the transverse direction the system compressibility was set to 4.5×10-10 Pa-1. Therefore, upon stretching, a simulation cell elongates in the direction of deformation and compresses in the directions transversal to deformation in response to the external pressure (1 bar). During deformation the values , = , , of the pressure tensor and the simulation cell size in the stretching direction were saved each 1 ps. The characteristics obtained were converted to the dependence of the stress σ on the relative strain as


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= − = ( − )/

(1)

where is the simulation cell size prior to the deformation (t=0). The initial part of the () dependence shows a linear regime up to ~2% of the deformation , and the elastic modulus E is defined as =

(2)

The value of E was determined as a slope of the linearly approximated dependence σ(ε) in the linear viscoelasticity regime. The error bars in elasticity modulus calculations were computed as mean-square deviations from the average value of the elastic modulus, obtained by averaging over all samples and the three deformation directions. To study the mechanical properties of the amorphous and graphene-ordered R-BAPB samples, we carried out a uniaxial deformation of each of them with a rate of 1 m/s along the axes X, Y and Z, with the LINCS algorithm that maintains the covalent bond length constant switched off. The stress-strain curves obtained for each sample served as the basis for the calculation of the elasticity modulus and yield stress values. To determine the elasticity modulus, the initial linear section of the stress-strain curve with the relative strain of 0-2% was approximated by a linear function, and the elasticity modulus value was calculated as a tangent of the approximating straight line. The yield point was determined from the stress-strain curve as the offset yield peak, i.e. from the intersection height of the axis of ordinates and the straight line approximating the plateau of stress-strain curves.44The elasticity modulus and yield point values obtained for individual samples of the graphene-ordered and amorphous R-BAPB samples were approximated, with errors being evaluated as mean square deviations from the average value.


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The presence of trustworthy distinctions between the average values was assessed using the Mann-Whitney criterion.45 In order to check out whether the removal of the graphene influences the properties of an ordered polymer matrix we have tested the MD-trajectory and found that the “glued” gap at the place where graphene was located does not become wider under pulling, see figure 2, where the gap is located at the left and right sides of density profiles. It is seen that polymer density at the gap increases under pulling. Thus we can conclude that the gap is not the “weak site” of the system and a comparably low resistance of the ordered polymer matrix to pulling in the Z direction is really due to its structural peculiarities, not due to the gap.

Figure 2. Density profiles along Z axis for R-BAPB with removed graphene before pulling (black curve) and at 10% strain (red curve).

RESULTS AND DISCUSSION Figure 3 shows the stress-strain curves for graphene-ordered and for amorphous R-BAPB polyimide samples averaged upon deforming along the axes X, Y and Z. According to Figure 3 results, the stress-strain curves for both the oriented and amorphous samples have a similar shape: initial growth until a the plateau is reached without any recognizable yield point. At the


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same time, the stress-strain curve for the oriented sample is located above the one for the amorphous sample along the entire strain length. Table 1 reports the results of the comparison of the elasticity modulus 〈〉 and the yield stress 〈 〉 values for amorphous and graphene-ordered R-BAPB samples, with errors bars being evaluated as mean square deviations from the average values obtained during the processing of individual stress-strain curves.

Figure 3. Stress-strain curves averaged over three directions (along the axes X, Y and Z) both for R-BAPB samples ordered by graphene and for amorphous R-BAPB samples.

Table 1. Comparison of mechanical properties (average values of elasticity modulus 〈〉 and yield stress values 〈 〉) of amorphous and graphene-ordered R-BAPB samples. 〈〉, GPa

〈 〉, MPa

amorphous

2.7±0.3

169±4

ordered by graphene

3.8±0.9

191±4

As shown in Table 1, the elasticity modulus and yield stress values for the graphene-ordered R-BAPB samples are higher than those for the amorphous one. Experiments also demonstrate3,4


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that the addition of graphene can improve mechanical properties of the material. However, these experiments addressed the mechanical properties of nanocomposites filled with graphene whereas we simulate mechanical properties of the ordered polymer at the polymer-nanofiller interface showing that the polymer at the interface can significantly contribute to the mechanical properties of the nanocomposite. Therefore, such properties are clearly influenced by factors other than mechanical properties of the filler nanoparticles. Consequently, the specific behavior of the polymer at the interface should be taken into account when solving engineering tasks, for example, while using the finite elements simulations for nanocomposites.

Figure 4. Averaged stress-strain curves of (a) non-filled amorphous R-BAPB samples and (b) graphene-ordered R-BAPB samples, obtained after deforming along axes X (black curves), Y (red curves), and Z (blue curves)

In order to take a closer look at the influence of the R-BAPB structural ordering caused by graphene on its mechanical properties, we considered separately the stress-strain curves obtained as a result of deforming along the axes X, Y and Z (the graphene sheet was located in the XY plane). Figure 4 shows the curves averaged over all individual stress-strain curves, and


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demonstrates that all three stress-strain curves have the same shape as the averaged curve in Figure 3. Moreover, the stress-strain curve obtained upon deforming along the X axis is located higher than the curve obtained upon deforming along the Y axis which, in turn, is located above the curve obtained upon deforming along the Z axis. At the same time, in the case of the nonordered (amorphous) R-BAPB sample, the stress-strain curves obtained after deforming in various directions coincide. This fact confirms the significant anisotropy of mechanical properties of the polymer at the interface. Such shape of the stress-strain curves is an argument supporting the fact that the low resistance of the ordered polymer matrix to pulling in the Z direction is not caused by the gap produced by the graphene removal. In fact, in the case of a gap growth under pulling the stress should decrease, but this is not observed, see figure 4b. It is seen from Fig. 4 that the stress-strain curve for the amorphous polymer lays between the curves for Y and Z directions for the ordered polymer. This may be attributed to the amorphous polymer “avoiding” deformation paths where the already stretched segments should be additionally stretched as in the case of pulling along X direction. Table 2 features the elasticity modulus and yield stress values obtained during deforming along various axes averaged for 9 samples. The comparison of these results also confirms the anisotropy of the polymer mechanical properties at the interface: elasticity modulus values obtained by deforming along various axes differ (Mann-Whitney significance level45 p < 0.05), as well as the yield stress values (p < 0.01) show a similar behavior. On the contrary, the amorphous R-BAPB sample displays no anisotropy of mechanical properties.


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Table 2. Comparison of mechanical properties of the graphene-ordered R-BAPB sample – average values of elasticity modulus 〈〉 and yield stress 〈 〉 obtained at deforming in various directions. amorphous R-BAPB

ordered R-BAPB

deforming

!"

〈〉, GPa

〈 〉, MPa

〈〉, GPa

〈 〉, MPa

X

2.8±0.3

165±3

4.8±0.8

244±11

0.27±0.09

0.22±0.09

Y

2.7±0.2

169±4

3.8±0.9

190±6

0.17±0.08

0.20±0.10

Z

2.8±0.4

171±3

2.9±0.4

140±6

0.02±0.01

0.03±0.03

direction

To answer the question why the structural ordering causes the anisotropy of mechanical properties of R-BAPB, we investigated the relation between the computed mechanical properties and the orientation degree of rigid segments of R-BAPB chains (Fig. 1) along the coordinate axes. The segments are regarded as oriented along one of the axis if the angle between them and a given axis is less than a critical angle assumed as equal to 30 degrees (results for other critical angle values were qualitatively similar). We calculated the average proportion of segments , oriented along each of the axes X, Y and Z, for two representative polymer segments and the results are given in Table 2. We can see that the fraction of segments oriented along the axis X is always higher than that of segments oriented along the axis Y, and that the fraction of segments oriented along the axis Y is much higher than that of segments oriented along the axis Z (p < # % & 0.01); that is > > . Therefore, it is possible to establish a qualitative correlation

where most molecules are parallel to the XY plane and a stronger orientation of rigid fragments leads to a much stronger resistance of the sample in the same direction. Theses finding confirm


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that the structural ordering of R-BAPB fragments is responsible for the anisotropy of the mechanical properties of the polymer ordered at the matrix-graphene interface. Moreover, we can confirm that the origin of the polymer anisotropy at the matrix-nanoparticle interface is provided by the nanostructuration driven by the graphene structure. It is very well known that π-π interactions promote strong interactions among aromatic structures46 like those present in R-BAPB chains and in the graphene structure. Moreover, the π-π interactions of graphene with aromatic molecules have been well reported.47 A difference in tensile properties in X and Y is seen from Table 2 and Figure 4. It is unexpected because R-BAPB is ordered perpendicular to Z direction and thus a mechanical isotropy in X and Y is expected. One of the possible causes of this difference is an orientation effect of graphene which leads to an orientation of R-BAPB segments along X axis. Another possible cause is that an appearance of 3D ordering characteristic to crystals may occur even at the pre-crystallization stage leading to an anisotropy of mechanical properties along all three axis. This effect will be studied in our future simulations.

CONCLUSIONS The mechanical properties of a thermoplastic semi-crystalline polyimide R-BAPB, ordered by graphene were studied by atomistic molecular dynamics simulations. A novel method of modeling was developed, which consists in removing the graphene sheet before deformation, allowing the study of the intrinsic properties of the ordered polymer. The obtained results confirm that a pre-crystallization, also showed for polyolefins,9,10 affects the mechanical properties of the polyimide. This is crucial for the correct parameterization of the interface properties, which is necessary for simulation of the microscopic characteristics of


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nanocomposites by finite elements methods48. A comparison of the results of the simulation of polymer nanocomposites by atomistic molecular dynamics with experimental data is always a non-trivial task. One of the few ways to compare is to study the dielectric relaxation by means of both simulation and experiments (see, eg, Wu et al.49 and Klonos et al.50); however, this study is devoted to a research of another kind. The results obtained in the study reported here can be compared with experimental studies of the mechanical properties of nanocomposites based on crystallizing polyimides filled with ordered graphene sheets. Such ordering can be achieved with the help of the application of a strong electric field.46 The method of studying the nanocomposite films using bugle test seems to be promising for this kind of comparison.51,52 The results can also be compared with those obtained in computer simulations of polymer nanocomposites filled with small graphene sheets.52 Therefore, the anisotropy of mechanical properties is relevant for practical applications of nanocomposites based on crystallizable polymers and graphene for micro- and nanoscale devices.53

ACKNOWLEDGMENT The study was carried out with the financial support from the Ministry of Education and Science of the Russian Federation under the Contract No. 14.Z50.31.0002 (megagrant of the Government of the Russian Federation according to the Resolution No. 220 of April 9, 2010). The simulations were carried out with the use of the computational resources of the Institute of Macromolecular Compounds, Russian Academy of Sciences, and the Lomonosov supercomputer at Moscow State University.


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TOC GRAPHICS

(left) a snapshot of the first layer of R-BAPB polyimide near graphene (right) stress strain curves of R-BAPB, structurally ordered by the graphene


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Figure 1. Chemical structure of the repeated unit of R-BAPB polyimide (upper part) and part of the infinite graphene sheet7 (lower part). The red and blue arrows indicate the vectors corresponding to the rigid fragment of the R-BAPB repeated unit chosen for structural analysis. 81x40mm (300 x 300 DPI)


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Figure 2. Density profiles along Z axis for R-BAPB with removed graphene before pulling (black curve) and at 10% strain (red curve) 82x57mm (300 x 300 DPI)



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Figure 3. Stress-strain curves averaged over three directions (along the axes X, Y and Z) both for R-BAPB samples ordered by graphene and for amorphous R-BAPB samples 59x42mm (300 x 300 DPI)


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Figure 4. Averaged stress-strain curves of (a) non-filled amorphous R-BAPB samples and (b) grapheneordered R-BAPB samples, obtained after deforming along axes X (black curves), Y (red curves), and Z (blue curves) 61x22mm (300 x 300 DPI)



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TOC graphics 39x19mm (300 x 300 DPI)


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Mechanical Properties of a Polymer at the Interface Structurally

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